ific.uv.esific.uv.es/~nebot/idpasc/material/flavourtheory/flavourtheory-slides.pdf · basics c,p,t...
TRANSCRIPT
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Theory of Flavour physics and CP violation
Ulrich Nierste
Karlsruhe Institute of Technology
IDPASC School on Flavour Physics, May 2013
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
14 November 2012Rare particle decay delivers blow tosupersymmetryBy Lucie Bradley
Cosmos Online
The popular physics theory of supersymmetry has been called into question by new results from CERN.
SYDNEY: The popular physics theory of supersymmetry has been called into question by new
results from CERN.
Physicists working at CERN’s Large Hadron Collider (LHC) near Geneva, Switzerland, have
announced the discovery of an extremely rare type of particle decay.
While discoveries are usually accompanied by excitement there is also a tinge of uncertainty
surrounding this latest finding from CERN. It has dealt a hefty blow to the popular physics theory
of supersymmetry.
The results were presented at the Hadron Collider Physics Symposium in Kyoto, Japan, and will
also be submitted to the journal Physical Review Papers.
A three in one billion chance
Scientists have been searching for this type of particle decay for the last decade and so the results
from CERN have ”generated a lot of excitement now that it has been found,” according to physicist
Mark Kruse, from Duke University, North Carolina, USA. “And it hasn’t ruled out supersymmetry –
just some of the more favoured variants of it.”
The traditional theory of subatomic physics is known as the Standard Model, but it is unable to
explain everything observed in the world around us, including gravity and dark matter.
Supplementary theories exist to help explain these inconsistencies. Of these theories,
supersymmetry, which proposes that ‘superparticles’ exist – massive versions of those particles
that are already known – is arguably the most popular.
Researchers at the LHCb experiment at CERN measured the decay time of a particle known as a Bs
A typical decay of the Bs (B sub s) meson into two muons.
The two muons traversed the whole LHCb detector, which
originated from the B0s decay point 14 mm from the
proton-proton collision. Credit: LHCb
COSMOS Magazine
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Contents
Basics
Discrete symmetries
CKM metrology
New physics
Global analysis of Bs−Bs mixing and Bd−Bd mixing
Supersymmetry
The rare decays Bd ,s → µ+µ− and Bs → φπ0, φρ0
Summary
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Basics
Flavour physics
studies transitions between fermions of different generations.
flavour = fermion species
(uL,uL,uL
dL,dL,dL
) (cL, cL, cL
sL, sL, sL
) (tL, tL, tL
bL,bL,bL
)
uR ,uR ,uR cR , cR , cR tR , tR , tRdR ,dR ,dR sR , sR , sR bR ,bR ,bR(νe,L
eL
) (νµ,LµL
) (ντ,LτL
)
eR µR τR
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour quantum numbers:
quantum number d u s c b t e,νe µ,νµ τ ,ντD -1 0 0 0 0 0 0 0 0U 0 1 0 0 0 0 0 0 0
strangeness S 0 0 -1 0 0 0 0 0 0charm C 0 0 0 1 0 0 0 0 0beauty B 0 0 0 0 -1 0 0 0 0
T 0 0 0 0 0 1 0 0 0electron number Le 0 0 0 0 0 0 1 0 0
muon number Lµ 0 0 0 0 0 0 0 1 0tau number Lτ 0 0 0 0 0 0 0 0 1
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour quantum numbers:
quantum number d u s c b t e,νe µ,νµ τ ,ντD -1 0 0 0 0 0 0 0 0U 0 1 0 0 0 0 0 0 0
strangeness S 0 0 -1 0 0 0 0 0 0charm C 0 0 0 1 0 0 0 0 0beauty B 0 0 0 0 -1 0 0 0 0
T 0 0 0 0 0 1 0 0 0electron number Le 0 0 0 0 0 0 1 0 0
muon number Lµ 0 0 0 0 0 0 0 1 0tau number Lτ 0 0 0 0 0 0 0 0 1
baryon number Bbaryon =−D + U − S + C − B + T
3lepton number L = Le + Lµ + Lτ
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour quantum numbers:
quantum number d u s c b t e,νe µ,νµ τ ,ντD -1 0 0 0 0 0 0 0 0U 0 1 0 0 0 0 0 0 0
strangeness S 0 0 -1 0 0 0 0 0 0charm C 0 0 0 1 0 0 0 0 0beauty B 0 0 0 0 -1 0 0 0 0
T 0 0 0 0 0 1 0 0 0electron number Le 0 0 0 0 0 0 1 0 0
muon number Lµ 0 0 0 0 0 0 0 1 0tau number Lτ 0 0 0 0 0 0 0 0 1
baryon number Bbaryon =−D + U − S + C − B + T
3lepton number L = Le + Lµ + Lτ
antifermions have opposite quantum numbers
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour quantum numbers are respected by the stronginteraction, so we can use them to categorise hadrons.E.g. a B+ meson has B = U = 1, shorthand notation:
B+ ∼ bu
For a Bd ≡ B0 (with B = −D = 1) we write
Bd ∼ bd
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Some flavoured mesons
charged:
K+ ∼ su, D+ ∼ cd , D+s ∼ cs, B+ ∼ bu, B+
c ∼ bc,
K− ∼ su, D− ∼ cd , D−s ∼ cs, B− ∼ bu, B−
c ∼ bc,
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Some flavoured mesons
charged:
K+ ∼ su, D+ ∼ cd , D+s ∼ cs, B+ ∼ bu, B+
c ∼ bc,
K− ∼ su, D− ∼ cd , D−s ∼ cs, B− ∼ bu, B−
c ∼ bc,
neutral:
K ∼ sd , D ∼ cu, Bd ∼ bd , Bs ∼ bs,
K ∼ sd , D ∼ cu, Bd ∼ bd , Bs ∼ bs,
In flavour physics only the ground-state hadrons which decayweakly rather than strongly are interesting.Weakly decaying baryons are less interesting, because theyare produced in smaller rates and are theoretically harder tocope with.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Some flavoured mesons
charged:
K+ ∼ su, D+ ∼ cd , D+s ∼ cs, B+ ∼ bu, B+
c ∼ bc,
K− ∼ su, D− ∼ cd , D−s ∼ cs, B− ∼ bu, B−
c ∼ bc,
neutral:
K ∼ sd , D ∼ cu, Bd ∼ bd , Bs ∼ bs,
K ∼ sd , D ∼ cu, Bd ∼ bd , Bs ∼ bs,
The neutral K , D, Bd and Bs mesons mix with theirantiparticles, K , D, Bd and Bs thanks to the weak interaction(quantum-mechanical two-state systems).
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Some flavoured mesons
charged:
K+ ∼ su, D+ ∼ cd , D+s ∼ cs, B+ ∼ bu, B+
c ∼ bc,
K− ∼ su, D− ∼ cd , D−s ∼ cs, B− ∼ bu, B−
c ∼ bc,
neutral:
K ∼ sd , D ∼ cu, Bd ∼ bd , Bs ∼ bs,
K ∼ sd , D ∼ cu, Bd ∼ bd , Bs ∼ bs,
The neutral K , D, Bd and Bs mesons mix with theirantiparticles, K , D, Bd and Bs thanks to the weak interaction(quantum-mechanical two-state systems).
⇒ gold mine for fundamental parameters
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Strong isospin: Instead of U and D use (I, I3):
Fundamental doublets (I =12
):(
ud
)and
(d−u
).
For mu = md the QCD lagrangian is invariant under SU(2)
rotations of(
ud
)and
(d−u
).
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Strong isospin: Instead of U and D use (I, I3):
Fundamental doublets (I =12
):(
ud
)and
(d−u
).
For mu = md the QCD lagrangian is invariant under SU(2)
rotations of(
ud
)and
(d−u
).
“QCD cannot distinguish up and down”
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Strong isospin: Instead of U and D use (I, I3):
Fundamental doublets (I =12
):(
ud
)and
(d−u
).
For mu = md the QCD lagrangian is invariant under SU(2)
rotations of(
ud
)and
(d−u
).
“QCD cannot distinguish up and down”
Owing to md −mu ≪ Λhad ∼ 500 MeV, strong isospin holds to∼ 2% accuracy. E.g. MBd
−MB+ = (0.37± 0.24)MeV.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Isospin triplet:
π+ ∼ ud , π0 ∼ uu − dd√2
, π− ∼ du.
Compare with spin triplet
↑↑, ↑↑ + ↓↓√2
, ↓↓
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour–SU(3):Since ms −mu,d < Λhad we can try to enlarge isospin–SU(2) to
SU(3)F with fundamental triplet
uds
U-spin subgroup: SU(2) rotations of(
ds
)
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Pedestrian’s use of U-spin:(i) Draw all diagrams contributing to some process.(ii) Replace s ↔ d to connect the hadronic interaction in
different processes.
Example: One can relate the strong interaction effects inBs → K+K− and Bd → π+π−. Dunietz; Fleischer
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Pedestrian’s use of U-spin:(i) Draw all diagrams contributing to some process.(ii) Replace s ↔ d to connect the hadronic interaction in
different processes.
Example: One can relate the strong interaction effects inBs → K+K− and Bd → π+π−. Dunietz; Fleischer
Accuracy of SU(3)F: 30% per s ↔ d exchange.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Electroweak interactionGauge group:
SU(2)× U(1)Y
doublets: Q jL =
(u j
Ld j
L
)und L j =
(ν j
Lℓ j
L
)
j = 1, 2, 3 labels the generation.
Examples: Q3L =
(tLbL
), L1 =
(νeL
eL
)
singlets: u jR, d j
R and e jR.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Electroweak interactionGauge group:
SU(2)× U(1)Y
doublets: Q jL =
(u j
Ld j
L
)und L j =
(ν j
Lℓ j
L
)
j = 1, 2, 3 labels the generation.
Examples: Q3L =
(tLbL
), L1 =
(νeL
eL
)
singlets: u jR, d j
R and e jR.
Important: Only left-handed fields couple to the W boson.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
How many interactions does the Standard Model comprise?
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
How many interactions does the Standard Model comprise?
Five!
• three gauge interactions
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
How many interactions does the Standard Model comprise?
Five!
• three gauge interactions
• Yukawa interaction of Higgs with quarks and leptons
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
How many interactions does the Standard Model comprise?
Five!
• three gauge interactions
• Yukawa interaction of Higgs with quarks and leptons
• Higgs self-interaction
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Yukawa interaction
Higgs doublet H =
(G+
v + h0+iG0√
2
)with v = 174 GeV.
Charge-conjugate doublet: H =
(v + h0−iG0
√2
−G−
)
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Yukawa interaction
Higgs doublet H =
(G+
v + h0+iG0√
2
)with v = 174 GeV.
Charge-conjugate doublet: H =
(v + h0−iG0
√2
−G−
)
H
Yukawa lagrangian:
−LY = Y djk Q j
L H d kR + Y u
jk Q jL H u k
R + Y ljk L j
L H e kR + h.c.
Here neutrinos are (still) massless.The Yukawa matrices Y f are arbitrary complex 3× 3 matrices.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Yukawa interaction
Higgs doublet H =
(G+
v + h0+iG0√
2
)with v = 174 GeV.
Charge-conjugate doublet: H =
(v + h0−iG0
√2
−G−
)
H
Yukawa lagrangian:
−LY = Y djk Q j
L H d kR + Y u
jk Q jL H u k
R + Y ljk L j
L H e kR + h.c.
Here neutrinos are (still) massless.The Yukawa matrices Y f are arbitrary complex 3× 3 matrices.The mass matrices M f = Y f v are not diagonal!
⇒ ujL,R , d
jL,R do not describe physical quarks!
We must find a basis in which Y f is diagonal!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Any matrix can be diagonalised by a bi-unitary transformation.Start with
Y u = S†QY uSu with Y u =
yu 0 00 yc 00 0 yt
and yu,c,t ≥ 0
This can be achieved via
Q jL = SQ
jk Q k ′L , u j
R = Sujku k ′
R
with unitary 3× 3 matrices SQ, Su.This transformation leaves Lgauge invariant (“flavour-blindness ofthe gauge interactions”)!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Next diagonalise Y d :
Y d = V †S†QY dSd with Y d =
yd 0 00 ys 00 0 yb
and yd ,s,b ≥ 0
with unitary 3× 3 matrices V , Sd .Via d j
R = Sdjkd k ′
R we leave Lgauge unchanged, while
−LquarkY = QLVY d H dR + QLY u H uR + h.c.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Next diagonalise Y d :
Y d = V †S†QY dSd with Y d =
yd 0 00 ys 00 0 yb
and yd ,s,b ≥ 0
with unitary 3× 3 matrices V , Sd .Via d j
R = Sdjkd k ′
R we leave Lgauge unchanged, while
−LquarkY = QLVY d H dR + QLY u H uR + h.c.
To diagonalise Md = VY dv transform
d jL = Vjkd k ′
L
This breaks up the SU(2) doublet QL.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Next diagonalise Y d :
Y d = V †S†QY dSd with Y d =
yd 0 00 ys 00 0 yb
and yd ,s,b ≥ 0
with unitary 3× 3 matrices V , Sd .Via d j
R = Sdjkd k ′
R we leave Lgauge unchanged, while
−LquarkY = QLVY d H dR + QLY u H uR + h.c.
To diagonalise Md = VY dv transform
d jL = Vjkd k ′
L
This breaks up the SU(2) doublet QL. ⇒ Lgauge changes!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the new “physical” basis Mu = Y uv and Md = Y dv arediagonal.⇒ Also the neutral Higgs fields h0 and G0 have only
flavour-diagonal couplings!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the new “physical” basis Mu = Y uv and Md = Y dv arediagonal.⇒ Also the neutral Higgs fields h0 and G0 have only
flavour-diagonal couplings!
The Yukawa couplings of the charged pseudo-Goldstonebosons G± still involve V :
−LquarkY = uLVY d dR G+ − dLV †Y u uR G− + h.c.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the new “physical” basis Mu = Y uv and Md = Y dv arediagonal.⇒ Also the neutral Higgs fields h0 and G0 have only
flavour-diagonal couplings!
The Yukawa couplings of the charged pseudo-Goldstonebosons G± still involve V :
−LquarkY = uLVY d dR G+ − dLV †Y u uR G− + h.c.
The transformation d jL = Vjkd k ′
L changes the W-bosoncouplings in Lgauge:
LW =g2√
2
[uLVγµ dL W+
µ + dLV †γµ uL W−µ
]
The Z-boson couplings stay flavour-diagonal because ofV †V = 1.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
V is the Cabibbo-Kobayashi-Maskawa (CKM) matrix.
V =
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
V is the Cabibbo-Kobayashi-Maskawa (CKM) matrix.
V =
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
Leptons: Only one Yukawa matrix Y l ; the mass matrixM l = Y lv of the charged leptons is diagonalised with
L jL = SL
jkL k ′L , e k
R = Sejke k ′
R
No lepton-flavour violation!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
V is the Cabibbo-Kobayashi-Maskawa (CKM) matrix.
V =
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
Leptons: Only one Yukawa matrix Y l ; the mass matrixM l = Y lv of the charged leptons is diagonalised with
L jL = SL
jkL k ′L , e k
R = Sejke k ′
R
No lepton-flavour violation!
⇒ Add a νR to the SM to mimick the quark sector or
add a Majorana mass term Y M LHHT Lc
M.
The lepton mixing matrix is thePontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Discrete symmetries
Parity transformation P: ~x → −~xCharge conjugation C: Exchange particles and
antiparticles, e.g. e− ↔ e+
Time reversal T: t → −t
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
C and P
1954/1955: CPT is a symmetry of every Lorentz-invariantquantum field theory.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
C and P
1954/1955: CPT is a symmetry of every Lorentz-invariantquantum field theory.
1956/1957: P is not a symmetry of the microscopic lawsof nature!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
C and P
1954/1955: CPT is a symmetry of every Lorentz-invariantquantum field theory.
1956/1957: P is not a symmetry of the microscopic lawsof nature!
1964: CP is not a symmetry of the microscopic lawsof nature!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
C and P
1954/1955: CPT is a symmetry of every Lorentz-invariantquantum field theory.
1956/1957: P is not a symmetry of the microscopic lawsof nature!
1964: CP is not a symmetry of the microscopic lawsof nature!
⇒ Also the T symmetry must be violated,there is a microscopic arrow of time!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
K and M
1973: Explanation of CP violation by postu-lating a third fermion generation.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
K and M
1973: Explanation of CP violation by postu-lating a third fermion generation.
Makoto Kobayashi and Toshihide Maskawa:CP Violation in the Renormalizable Theoryof Weak Interaction,Prog.Theor.Phys.49:652-657,1973,
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
K and M
1973: Explanation of CP violation by postu-lating a third fermion generation.
Makoto Kobayashi and Toshihide Maskawa:CP Violation in the Renormalizable Theoryof Weak Interaction,Prog.Theor.Phys.49:652-657,1973,∼7300 citations (ranks 3rd in elementaryparticle physics).
Nobel Prize 2008.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
K and M
1973: Explanation of CP violation by postu-lating a third fermion generation.
Makoto Kobayashi and Toshihide Maskawa:CP Violation in the Renormalizable Theoryof Weak Interaction,Prog.Theor.Phys.49:652-657,1973,∼7300 citations (ranks 3rd in elementaryparticle physics).
Nobel Prize 2008.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Strong interaction
The QCD lagrangian permits a term which violates P, CP, andT , but experimentally the corresponding coefficient θ is found tobe smaller than 10−11.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Strong interaction
The QCD lagrangian permits a term which violates P, CP, andT , but experimentally the corresponding coefficient θ is found tobe smaller than 10−11.
⇒ The strong interaction essentially respectsC, P, and therefore T ,[Hstrong, P
]=[Hstrong,C
]=[Hstrong,T
]= 0
⇒ We can assign C and P quantum numbers, whichcan be +1 or −1, to hadrons.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Strong interaction
The QCD lagrangian permits a term which violates P, CP, andT , but experimentally the corresponding coefficient θ is found tobe smaller than 10−11.
⇒ The strong interaction essentially respectsC, P, and therefore T ,[Hstrong, P
]=[Hstrong,C
]=[Hstrong,T
]= 0
⇒ We can assign C and P quantum numbers, whichcan be +1 or −1, to hadrons.
Example: A π0 meson has P = −1 and C = +1. A π+ hasP = −1, but is no eigenstate of C, because C|π+〉 = |π−〉.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Strong interaction
The QCD lagrangian permits a term which violates P, CP, andT , but experimentally the corresponding coefficient θ is found tobe smaller than 10−11.
⇒ The strong interaction essentially respectsC, P, and therefore T ,[Hstrong, P
]=[Hstrong,C
]=[Hstrong,T
]= 0
⇒ We can assign C and P quantum numbers, whichcan be +1 or −1, to hadrons.
Example: A π0 meson has P = −1 and C = +1. A π+ hasP = −1, but is no eigenstate of C, because C|π+〉 = |π−〉.
Also QED respects C,P, and T .
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Parity violation
1956: θ − τ puzzle:A seemingly degenerate pair (θ, τ) of two mesons with P= +1and P= −1, weakly decaying as
“θ” → ππ P = +1
“τ ” → πππ P = −1
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Parity violation
1956: θ − τ puzzle:A seemingly degenerate pair (θ, τ) of two mesons with P= +1and P= −1, weakly decaying as
“θ” → ππ P = +1
“τ ” → πππ P = −1
Explanation by Lee and Yang:“θ” and “τ ” are the same particle, instead the weak interactionviolates parity.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Parity violation
1956: θ − τ puzzle:A seemingly degenerate pair (θ, τ) of two mesons with P= +1and P= −1, weakly decaying as
“θ” → ππ P = +1
“τ ” → πππ P = −1
Explanation by Lee and Yang:“θ” and “τ ” are the same particle, instead the weak interactionviolates parity.
K+ = “θ” = “τ ”.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Maximal P violation
In the SM only left-handed fields feel the charged weakinteraction, no couplings of the W-boson to u j
R, d jR, and e j
R.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Early monograph on parity violation:
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Early monograph on parity violation:
Lewis Carroll:Alice through the looking glass
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Maximal parity violation
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Maximal parity violation
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Charge conjugation C maps left-handed (particle) fields onright-handed (antiparticle) fields and vice versa:
ψLC←→ ψC
L , where ψCL ≡ (ψC)R is right-handed.
⇒ The weak interaction also violates C!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Charge conjugation C maps left-handed (particle) fields onright-handed (antiparticle) fields and vice versa:
ψLC←→ ψC
L , where ψCL ≡ (ψC)R is right-handed.
⇒ The weak interaction also violates C!
But: Nothing prevents CP and T from being goodsymmetries. . .
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Charge conjugation C maps left-handed (particle) fields onright-handed (antiparticle) fields and vice versa:
ψLC←→ ψC
L , where ψCL ≡ (ψC)R is right-handed.
⇒ The weak interaction also violates C!
But: Nothing prevents CP and T from being goodsymmetries. . .
. . . except experiment!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CP violation
Neutral K mesons:Klong and Kshort (linear combinations of K and K ).
Dominant decay channels:
Klong → πππ CP = −1
Kshort → ππ CP = +1
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CP violation
Neutral K mesons:Klong and Kshort (linear combinations of K and K ).
Dominant decay channels:
Klong → πππ CP = −1
Kshort → ππ CP = +1
1964: Christenson, Cronin, Fitch and Turlay observe
Klong → ππ
and therefore discover CP violation.
ǫK ≡〈(ππ)I=0|Hweak |Klong〉〈(ππ)I=0|Hweak |Kshort〉
= (2.229± 0.010) · 10−3ei0.97π/4.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CP violation in the SM
Example: W coupling to b and u:
LW =g2√
2
[VubuLγ
µ bL W+µ + V ∗
ubbLγµ uL W−
µ
]
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CP violation in the SM
Example: W coupling to b and u:
LW =g2√
2
[VubuLγ
µ bL W+µ + V ∗
ubbLγµ uL W−
µ
]
CP transformation uLγµ bL
CP−→ −bLγµ uL
W+µ
CP−→ −W−µ
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CP violation in the SM
Example: W coupling to b and u:
LW =g2√
2
[VubuLγ
µ bL W+µ + V ∗
ubbLγµ uL W−
µ
]
CP transformation uLγµ bL
CP−→ −bLγµ uL
W+µ
CP−→ −W−µ
HenceLW
CP−→ g2√2
[VubbLγ
µ uL W−µ + V ∗
ubuLγµ bL W+
µ
]
Is CP violated?
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CP violation in the SM
Example: W coupling to b and u:
LW =g2√
2
[VubuLγ
µ bL W+µ + V ∗
ubbLγµ uL W−
µ
]
CP transformation uLγµ bL
CP−→ −bLγµ uL
W+µ
CP−→ −W−µ
HenceLW
CP−→ g2√2
[VubbLγ
µ uL W−µ + V ∗
ubuLγµ bL W+
µ
]
Is CP violated? Not yet. . .Rephasing bL → eiφbL, uL → eiφ′uL amounts to
LWCP+reph.−→ g2√
2
[Vubei(φ′−φ)bLγ
µuLW−µ + V ∗
ubei(φ−φ′)uLγµbLW+
µ
],
so that we can achieve Vubei(φ′−φ) = V ∗ub.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Alternatively we could have used the rephasing to render Vub
real from the beginning.
Observation by Kobayashi and Maskawa:
A unitary n × n matrix hasn(n + 1)
2phases. In an n-generation
SM one can eliminate 2n − 1 phases from V by rephasing the
quark fields. The remaining(n − 1)(n − 2)
2phases are
physical, CP-violating parameters of the theory!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Alternatively we could have used the rephasing to render Vub
real from the beginning.
Observation by Kobayashi and Maskawa:
A unitary n × n matrix hasn(n + 1)
2phases. In an n-generation
SM one can eliminate 2n − 1 phases from V by rephasing the
quark fields. The remaining(n − 1)(n − 2)
2phases are
physical, CP-violating parameters of the theory!
n(n − 1)(n − 2)
21 02 03 1 Kobayashi-Maskawa phase δKM
4 3
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CKM metrology
The Cabibbo-Kobayashi-Maskawa (CKM) matrix
V =
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
involves 4 parameters: 3 angles and the KM phase δKM.Best way to parametrise V : Wolfenstein expansion
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Expand the CKM matrix V in Vus ≃ λ = 0.2246:
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
≃
1− λ2
2 λ Aλ3(1 + λ2
2
)(ρ− iη)
−λ− iA2λ5η 1− λ2
2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 − iAλ4η 1
with the Wolfenstein parameters λ, A, ρ , η
CP violation⇔ η 6= 0
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Expand the CKM matrix V in Vus ≃ λ = 0.2246:
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
≃
1− λ2
2 λ Aλ3(1 + λ2
2
)(ρ− iη)
−λ− iA2λ5η 1− λ2
2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 − iAλ4η 1
with the Wolfenstein parameters λ, A, ρ , η
CP violation⇔ η 6= 0
Unitarity triangle:Exact definition:
ρ+ iη = −V ∗ubVud
V ∗cbVcd
=
∣∣∣∣V ∗
ubVud
V ∗cbVcd
∣∣∣∣ eiγ
ρ+iη 1−ρ−iη
βγ
α
C=(0,0) B=(1,0)
A=(ρ,η)
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the SM the flavour violation only occurs in the couplings ofW±µ and G± to fermions.⇒ At tree-level flavour-changes only occur in charged-
current processes.
![Page 76: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/76.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the SM the flavour violation only occurs in the couplings ofW±µ and G± to fermions.⇒ At tree-level flavour-changes only occur in charged-
current processes.
Semileptonic decays:
�Wd �`u` �Ws �`u` �Wb �` ` �Wb �`u`determining |Vud | |Vus| |Vcb| |Vub|.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour-changing neutral current (FCNC) processes
Examples:
b
s
s
b
u,c,t
u,c,t
b s
t
W
Bs−Bs mixing penguin diagram
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour-changing neutral current (FCNC) processes
Examples:
b
s
s
b
u,c,t
u,c,t
b s
t
W
Bs−Bs mixing penguin diagram
FCNC processes are the only possibility to gain information onVtd and Vts. However: FCNC processes are highly sensitive tophysics beyond the SM.
![Page 79: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/79.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour-changing neutral current (FCNC) processes
Examples:
b
s
s
b
u,c,t
u,c,t
b s
t
W
Bs−Bs mixing penguin diagram
FCNC processes are the only possibility to gain information onVtd and Vts. However: FCNC processes are highly sensitive tophysics beyond the SM.
In principle can determine all parameters λ, A, ρ , η fromtree-level processes.
⇒ View FCNC processes as new physics analysersrather than ways to measure Vtd and Vts.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
B−B mixing basics
Consider Bq−Bq mixing with q = d orq = s:A meson identified (“tagged”) as a Bq attime t = 0 is described by |Bq(t)〉.
b
q
q
b
u,c,t
u,c,t
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
B−B mixing basics
Consider Bq−Bq mixing with q = d orq = s:A meson identified (“tagged”) as a Bq attime t = 0 is described by |Bq(t)〉.
b
q
q
b
u,c,t
u,c,t
For t > 0:
|Bq(t)〉 = 〈Bq|Bq(t)〉|Bq〉+ 〈Bq|Bq(t)〉|Bq〉+ . . . ,
with “. . . ” denoting the states into which Bq(t) can decay.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
B−B mixing basics
Consider Bq−Bq mixing with q = d orq = s:A meson identified (“tagged”) as a Bq attime t = 0 is described by |Bq(t)〉.
b
q
q
b
u,c,t
u,c,t
For t > 0:
|Bq(t)〉 = 〈Bq|Bq(t)〉|Bq〉+ 〈Bq|Bq(t)〉|Bq〉+ . . . ,
with “. . . ” denoting the states into which Bq(t) can decay.
Analogously: |Bq(t)〉 is the ket of a meson tagged as a Bq attime t = 0.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Schrodinger equation:
iddt
(〈Bq|Bq(t)〉〈Bq|Bq(t)〉
)=
(Mq − i
Γq
2
)( 〈Bq|Bq(t)〉〈Bq|Bq(t)〉
)
with the 2× 2 mass and decay matrices Mq = Mq† andΓq = Γq†.(〈Bq|Bq(t)〉〈Bq|Bq(t)〉
)obeys the same Schrodinger equation.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Schrodinger equation:
iddt
(〈Bq|Bq(t)〉〈Bq|Bq(t)〉
)=
(Mq − i
Γq
2
)( 〈Bq|Bq(t)〉〈Bq|Bq(t)〉
)
with the 2× 2 mass and decay matrices Mq = Mq† andΓq = Γq†.(〈Bq|Bq(t)〉〈Bq|Bq(t)〉
)obeys the same Schrodinger equation.
3 physical quantities in Bq−Bq mixing:
∣∣Mq12
∣∣ ,∣∣Γq
12
∣∣ , φq ≡ arg
(−Mq
12
Γq12
)
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Diagonalise Mq − i Γq
2 to find the two mass eigenstates:
Lighter eigenstate: |BL〉 = p|Bq〉+ q|Bq〉.Heavier eigenstate: |BH〉 = p|Bq〉 − q|Bq〉
with masses MqL,H and widths Γq
L,H .
Further |p|2 + |q|2 = 1.
![Page 86: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/86.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Diagonalise Mq − i Γq
2 to find the two mass eigenstates:
Lighter eigenstate: |BL〉 = p|Bq〉+ q|Bq〉.Heavier eigenstate: |BH〉 = p|Bq〉 − q|Bq〉
with masses MqL,H and widths Γq
L,H .
Further |p|2 + |q|2 = 1.
Relation of ∆mq and ∆Γq to |Mq12|, |Γ
q12| and φq:
∆mq = MH −ML ≃ 2|Mq12|,
∆Γq = ΓL − ΓH ≃ 2|Γq12| cosφq
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Mq12 stems from the dispersive (real)
part of the box diagram, internal t .Γq
12 stems from the absorpive (imag-inary) part of the box diagram, inter-nal c, u.
b
q
q
b
u,c,t
u,c,t
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Solve the Schrodinger equation to find the desired Bq−Bqoscillations:
|〈Bq |Bq(t)〉|2 = |〈Bq |Bq(t)〉|2 =e−Γq t
2
[cosh
∆Γq t2
+ cos (∆mq t)]
|〈Bq |Bq(t)〉|2 ≃ |〈Bq |Bq(t)〉|2 ≃ e−Γq t
2
[cosh
∆Γq t2− cos (∆mq t)
]
with Γq ≡Γq
L + ΓqH
2
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Time-dependent decay rate:
Γ(Bq(t)→ f ) =1
NB
d N(Bq(t)→ f )d t
,
where d N(Bq(t)→ f ) is the number of Bq(t)→ f decays withinthe time interval [t , t + d t ].NB is the number of Bq ’s present at time t = 0.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Time-dependent decay rate:
Γ(Bq(t)→ f ) =1
NB
d N(Bq(t)→ f )d t
,
where d N(Bq(t)→ f ) is the number of Bq(t)→ f decays withinthe time interval [t , t + d t ].NB is the number of Bq ’s present at time t = 0.
With |f 〉 ≡ CP|f 〉 define the time-dependent CP asymmetry:
af (t) =Γ(Bq(t)→ f )− Γ(Bq(t)→ f )
Γ(Bq(t)→ f ) + Γ(Bq(t)→ f )
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Example 1:Bd → J/ψKS ⇒ |f 〉 = −|f 〉 (CP-odd eigenstate)
�dc
s
b
c
Bd
J/ψ
KS
�b
cc
sd
Bd
J/ψ
KS
aJ/ψKS(t) ≃ − sin(2β) sin(∆md t),
where β = arg[−VcdV ∗
cb
VtdV ∗tb
]
![Page 92: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/92.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Example 2:Bs → (J/ψφ)L=0 ⇒ |f 〉 = |f 〉 (CP-even eigenstate)
�sc
s
b
c
Bs
J/ψ
φ�b
cc
ss
Bs
J/ψ
φ
a(J/ψφ)L=0(t) = − sin(2βs) sin(∆mst)
cosh(∆Γst/2)− cos(2βs) sinh(∆Γst/2),
where βs = arg[− VtsV ∗
tb
VcsV ∗cb
]≃ λ2η
![Page 93: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/93.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
The Wolfenstein parameters λ and A are well determined fromthe semileptonic decays K → πℓ+νℓ and B → Xcℓ
+νℓ, ℓ = e, µ.
![Page 94: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/94.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Metrology of the unitarity triangle:The apex (ρ,η) is currently constrained from the followingexperimental input:
• |Vub| ∝√ρ2 + η2 measured in B → πℓνℓ, B → Xuℓνℓ and
B+ → τ+ντ .
![Page 95: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/95.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Metrology of the unitarity triangle:The apex (ρ,η) is currently constrained from the followingexperimental input:
• |Vub| ∝√ρ2 + η2 measured in B → πℓνℓ, B → Xuℓνℓ and
B+ → τ+ντ .
• γ extracted from B± → ( )
DK±
![Page 96: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/96.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Metrology of the unitarity triangle:The apex (ρ,η) is currently constrained from the followingexperimental input:
• |Vub| ∝√ρ2 + η2 measured in B → πℓνℓ, B → Xuℓνℓ and
B+ → τ+ντ .
• γ extracted from B± → ( )
DK±
• ∆md ∝√(1− ρ)2 + η2
![Page 97: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/97.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Metrology of the unitarity triangle:The apex (ρ,η) is currently constrained from the followingexperimental input:
• |Vub| ∝√ρ2 + η2 measured in B → πℓνℓ, B → Xuℓνℓ and
B+ → τ+ντ .
• γ extracted from B± → ( )
DK±
• ∆md ∝√(1− ρ)2 + η2
• ∆md/∆ms ∝√(1− ρ)2 + η2
![Page 98: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/98.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Metrology of the unitarity triangle:The apex (ρ,η) is currently constrained from the followingexperimental input:
• |Vub| ∝√ρ2 + η2 measured in B → πℓνℓ, B → Xuℓνℓ and
B+ → τ+ντ .
• γ extracted from B± → ( )
DK±
• ∆md ∝√(1− ρ)2 + η2
• ∆md/∆ms ∝√(1− ρ)2 + η2
• sin(2β) from aJ/ψKS(t) and other b → ccs decays
![Page 99: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/99.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Metrology of the unitarity triangle:The apex (ρ,η) is currently constrained from the followingexperimental input:
• |Vub| ∝√ρ2 + η2 measured in B → πℓνℓ, B → Xuℓνℓ and
B+ → τ+ντ .
• γ extracted from B± → ( )
DK±
• ∆md ∝√(1− ρ)2 + η2
• ∆md/∆ms ∝√(1− ρ)2 + η2
• sin(2β) from aJ/ψKS(t) and other b → ccs decays
• α determined from CP asymmetries in B → ππ, B → ρρand B → ρπ decays.
![Page 100: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/100.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Metrology of the unitarity triangle:The apex (ρ,η) is currently constrained from the followingexperimental input:
• |Vub| ∝√ρ2 + η2 measured in B → πℓνℓ, B → Xuℓνℓ and
B+ → τ+ντ .
• γ extracted from B± → ( )
DK±
• ∆md ∝√(1− ρ)2 + η2
• ∆md/∆ms ∝√(1− ρ)2 + η2
• sin(2β) from aJ/ψKS(t) and other b → ccs decays
• α determined from CP asymmetries in B → ππ, B → ρρand B → ρπ decays.
• ǫK (the measure of CP violation in K−K mixing), whichdefines a hyperbola in the (ρ,η) plane.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Global fit in the SM from CKMfitter:
γ
α
α
dm∆
Kε
Kε
sm∆ & dm∆
ubV
βsin 2(excl. at CL > 0.95)
< 0βsol. w/ cos 2
α
βγ
ρ−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0
η
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
excl
uded
are
a ha
s C
L >
0.9
5Moriond 09
CKMf i t t e r
Statistical method: Rfit, a Frequentist approach.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Global fit in the SM from UTfit:
ρ-1 -0.5 0 0.5 1
η
-1
-0.5
0
0.5
1γ
β
α
)γ+βsin(2
sm∆dm∆ dm∆
KεcbVubV
ρ-1 -0.5 0 0.5 1
η
-1
-0.5
0
0.5
1
Statistical method: Bayesian.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour experiments
B,D,τ : BaBar, BELLE (upgrade: BELLE-II)CDF, DØLHCb, also ATLAS, CMS
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour experiments
B,D,τ : BaBar, BELLE (upgrade: BELLE-II)CDF, DØLHCb, also ATLAS, CMS
D,τ : BES-III
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour experiments
B,D,τ : BaBar, BELLE (upgrade: BELLE-II)CDF, DØLHCb, also ATLAS, CMS
D,τ : BES-III
K: CERN-NA62, J-PARC, KLOE-2,
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour experiments
B,D,τ : BaBar, BELLE (upgrade: BELLE-II)CDF, DØLHCb, also ATLAS, CMS
D,τ : BES-III
K: CERN-NA62, J-PARC, KLOE-2,
µ→ eγ search: MEG (at PSI)
µ→ e conversion search: COMET (at J-PARC)
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour experiments
B,D,τ : BaBar, BELLE (upgrade: BELLE-II)CDF, DØLHCb, also ATLAS, CMS
D,τ : BES-III
K: CERN-NA62, J-PARC, KLOE-2,
µ→ eγ search: MEG (at PSI)
µ→ e conversion search: COMET (at J-PARC)
. . . plus many neutrino experiments
Future: Project X at Fermilab for rare K and µ decays.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
New physics
In the LHC era CKM metrology is less important and constraintson physics beyond the SM is the main focus of flavour physics.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the flavour-changing neutral current (FCNC) processes ofthe Standard Model several suppression factors pile up:
• FCNCs proceed through electroweak loops, no FCNC treegraphs,
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the flavour-changing neutral current (FCNC) processes ofthe Standard Model several suppression factors pile up:
• FCNCs proceed through electroweak loops, no FCNC treegraphs,
• small CKM elements, e.g. |Vts| = 0.04, |Vtd | = 0.01,
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the flavour-changing neutral current (FCNC) processes ofthe Standard Model several suppression factors pile up:
• FCNCs proceed through electroweak loops, no FCNC treegraphs,
• small CKM elements, e.g. |Vts| = 0.04, |Vtd | = 0.01,
• GIM suppression in loops with charm or down-type quarks,∝ (m2
c −m2u)/M
2W , (m2
s −m2d)/M
2W .
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the flavour-changing neutral current (FCNC) processes ofthe Standard Model several suppression factors pile up:
• FCNCs proceed through electroweak loops, no FCNC treegraphs,
• small CKM elements, e.g. |Vts| = 0.04, |Vtd | = 0.01,
• GIM suppression in loops with charm or down-type quarks,∝ (m2
c −m2u)/M
2W , (m2
s −m2d)/M
2W .
• helicity suppression in radiative and leptonic decays,because FCNCs involve only left-handed fields, so helicityflips bring a factor of mb/MW or ms/MW .
![Page 113: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/113.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the flavour-changing neutral current (FCNC) processes ofthe Standard Model several suppression factors pile up:
• FCNCs proceed through electroweak loops, no FCNC treegraphs,
• small CKM elements, e.g. |Vts| = 0.04, |Vtd | = 0.01,
• GIM suppression in loops with charm or down-type quarks,∝ (m2
c −m2u)/M
2W , (m2
s −m2d)/M
2W .
• helicity suppression in radiative and leptonic decays,because FCNCs involve only left-handed fields, so helicityflips bring a factor of mb/MW or ms/MW .
![Page 114: ific.uv.esific.uv.es/~nebot/IDPASC/Material/FlavourTheory/FlavourTheory-Slides.pdf · Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary Rare particle decay delivers](https://reader033.vdocuments.mx/reader033/viewer/2022041612/5e38a2e1aa78b5659871818b/html5/thumbnails/114.jpg)
Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
In the flavour-changing neutral current (FCNC) processes ofthe Standard Model several suppression factors pile up:
• FCNCs proceed through electroweak loops, no FCNC treegraphs,
• small CKM elements, e.g. |Vts| = 0.04, |Vtd | = 0.01,
• GIM suppression in loops with charm or down-type quarks,∝ (m2
c −m2u)/M
2W , (m2
s −m2d)/M
2W .
• helicity suppression in radiative and leptonic decays,because FCNCs involve only left-handed fields, so helicityflips bring a factor of mb/MW or ms/MW .
Spectacular: In FCNC transitions of charged leptons the GIMsuppression factor is even m2
ν/M2W !
⇒ The SM predictions for charged-lepton FCNCs are es-sentially zero!
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
The suppression of FCNC processes in the Standard Model isnot a consequence of the SU(3)× SU(2)L × U(1)Y symmetry.It results from the particle content of the Standard Model andthe accidental smallness of most Yukawa couplings. It is absentin generic extensions of the Standard Model.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
The suppression of FCNC processes in the Standard Model isnot a consequence of the SU(3)× SU(2)L × U(1)Y symmetry.It results from the particle content of the Standard Model andthe accidental smallness of most Yukawa couplings. It is absentin generic extensions of the Standard Model.Examples:
extra Higgses ⇒ Higgs-mediated FCNC’s at tree-level ,helicity suppression possibly absent,
squarks/gluinos ⇒ FCNC quark-squark-gluino coupling,no CKM/GIM suppression,
vector-like quarks ⇒ FCNC couplings of an extra Z ′,SU(2)R gauge bosons ⇒ helicity suppression absent
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
The suppression of FCNC processes in the Standard Model isnot a consequence of the SU(3)× SU(2)L × U(1)Y symmetry.It results from the particle content of the Standard Model andthe accidental smallness of most Yukawa couplings. It is absentin generic extensions of the Standard Model.Examples:
extra Higgses ⇒ Higgs-mediated FCNC’s at tree-level ,helicity suppression possibly absent,
squarks/gluinos ⇒ FCNC quark-squark-gluino coupling,no CKM/GIM suppression,
vector-like quarks ⇒ FCNC couplings of an extra Z ′,SU(2)R gauge bosons ⇒ helicity suppression absent
Bd−Bd and Bs−Bs mixing and rare decays like Bs,d → µ+µ−
and K → πνν are sensitive to scales above Λ ∼ 100 TeV.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Win-win situation
If ATLAS and CMS find particles not included in the SM:
Flavour physics will explore their couplings to quarks.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Win-win situation
If ATLAS and CMS find particles not included in the SM:
Flavour physics will explore their couplings to quarks.
If ATLAS and CMS find no further new particles:
Flavour physics probes scales of new physicsexceeding 100 TeV.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
New-physics analysers:
• Global fit to UT: overconstrain (ρ, η),probes FCNC processes K−K , Bd−Bd and Bs−Bs mixing.
s
d
d
s
u,c,t
u,c,t
b
d
d
b
u,c,t
u,c,t
b
s
s
b
u,c,t
u,c,t
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
New-physics analysers:
• Global fit to UT: overconstrain (ρ, η),probes FCNC processes K−K , Bd−Bd and Bs−Bs mixing.
• Global fit to Bs−Bs mixing: mass difference ∆ms, widthdifference ∆Γs, CP asymmetries in Bs → J/ψφ and( )
Bs → Xℓνℓ.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
New-physics analysers:
• Global fit to UT: overconstrain (ρ, η),probes FCNC processes K−K , Bd−Bd and Bs−Bs mixing.
• Global fit to Bs−Bs mixing: mass difference ∆ms, widthdifference ∆Γs, CP asymmetries in Bs → J/ψφ and( )
Bs → Xℓνℓ.
• Penguin decays: B → Xsγ, B → Xsℓ+ℓ−, B → Kπ,
Bd → φKshort, Bs → µ+µ−, K → πνν.
b s
t
W
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
New-physics analysers:
• Global fit to UT: overconstrain (ρ, η),probes FCNC processes K−K , Bd−Bd and Bs−Bs mixing.
• Global fit to Bs−Bs mixing: mass difference ∆ms, widthdifference ∆Γs, CP asymmetries in Bs → J/ψφ and( )
Bs → Xℓνℓ.
• Penguin decays: B → Xsγ, B → Xsℓ+ℓ−, B → Kπ,
Bd → φKshort, Bs → µ+µ−, K → πνν.
• CKM-suppressed or helicity-suppressed tree-level decays:B+ → τ+ν, B → πℓν, B → Dτν, probe charged Higgsesand right-handed W-couplings.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
B−B mixing and new physics
Bq−Bq mixing with q = d or q = s:
New physics can barely affectΓq
12, which stems from tree-leveldecays.Mq
12 is very sensitive to virtualeffects of new heavy particles.
b
q
q
b
u,c,t
u,c,t
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Generic new physics
The phase φs = arg(−Ms12/Γ
s12) is negligibly small in the
Standard Model:φSM
s = 0.2◦.Define the complex parameter ∆s through
Ms12 ≡ MSM,s
12 ·∆s , ∆s ≡ |∆s|eiφ∆s .
In the Standard Model ∆s = 1. Use φs = φSMs + φ∆s ≃ φ∆s .
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Confront the LHCb-CDF average
∆ms = (17.719± 0.043) ps−1
with the SM prediction:
∆ms =(
18.8± 0.6Vcb± 0.3mt
± 0.1αs
)ps−1 f 2
BsBBs
(220 MeV)2
Largest source of uncertainty: f 2Bs
BBs from lattice QCD.
Here fBs is the Bs decay constant and f 2Bs
BBs parametrises ahadronic matrix element calculated with lattice QCD.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
With
fBs = (229± 2± 6)MeV, BBs = 0.85± 0.02± 0.02
find ∆mSMs = (17.3± 1.5) ps−1 entailing
|∆s| = 1.02+0.10−0.08.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
With
fBs = (229± 2± 6)MeV, BBs = 0.85± 0.02± 0.02
find ∆mSMs = (17.3± 1.5) ps−1 entailing
|∆s| = 1.02+0.10−0.08.
Too good to be true: prediction is based on many calculation offBs and the prejudice BBs = 0.85± 0.02± 0.02.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour-specific decay: Bs → f is allowed, whileBs → f is forbidden
CP asymmetry in flavour-specific decays (semileptonic CPasymmetry):
asfs =
Γ(Bs(t)→ f )− Γ(Bs(t)→ f )
Γ(Bs(t)→ f ) + Γ(Bs(t)→ f )
with e.g. f = Xℓ+νℓ and f = Xℓ−νℓ. Untagged rate:
asfs,unt ≡
∫∞0 dt
[Γ(
( )
Bs → µ+X )− Γ(( )
Bs → µ−X )]
∫∞0 dt
[Γ(
( )
Bs → µ+X ) + Γ(( )
Bs → µ−X )] ≃ as
fs
2
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Relation to Ms12:
asfs =
|Γs12||Ms
12|sinφs =
|Γs12|
|MSM,s12 |
· sinφs
|∆s|= (4.4± 1.2) · 10−3 · sinφs
|∆s|
A. Lenz, UN, 2006,2011,2012
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Dilepton events:
Compare the number N++ of decays (Bs(t),Bs(t))→ (f , f ) withthe number N−− of decays to (f , f ).
Then asfs =
N++ − N−−N++ + N−−
.
At the Tevatron all b-flavoured hadrons are produced. Still onlythose events contribute to (N++ −N−−)/(N++ +N−−), in whichone of the b hadronises as a Bd or Bs and undergoes mixing.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
New physics
Ms12 is highly sensitive to new physics, unlike the tree-level
decay b → ccs responsible for Bs → J/ψφ and Γs12.
It is plausible to consider a generic scenario, in which the M12
elements in Bs−Bs , Bd−Bd , and K−K mixing are affected bynew-physics, while all other quantities entering the global fit tothe UT are as in the Standard-Model.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Recall: In the Standard Modelφs = 0.22◦ ± 0.06◦ and φd = −4.3◦ ± 1.4◦.
A new-physics contribution to arg Mq12 may enhance
|aqfs| ∝ sinφq
to a level observable at current experiments.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Recall: In the Standard Modelφs = 0.22◦ ± 0.06◦ and φd = −4.3◦ ± 1.4◦.
A new-physics contribution to arg Mq12 may enhance
|aqfs| ∝ sinφq
to a level observable at current experiments.
But: Precise data on CP violation in Bd → J/ψKS andBs → J/ψφ preclude large NP contributions to argφd andargφs.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
New physics
Trouble maker:
ASL = (0.532± 0.039)adfs + (0.468± 0.039)as
fs
= (−7.87± 1.72± 0.93) · 10−3 DØ 2011
This is 3.9σ away from aSMfs = (−0.24± 0.03) · 10−3.
A. Lenz, UN 2006,2011
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Global analysis of Bs−Bs mixing and Bd−Bd mixing withA. Lenz and the CKMfitter Group (J. Charles,S. Descotes-Genon, A. Jantsch, C. Kaufhold, H. Lacker,S. Monteil, V. Niess) arXiv:1008.1593, 1203.0238
Rfit method: No statistical meaning is assigned to systematicerrors and theoretical uncertainties.
We have performed a simultaneous fit to the Wolfensteinparameters and to the new physics parameters ∆s and ∆d ,
∆q ≡ Mq12
Mq,SM12
, ∆q ≡ |∆q|eiφ∆q ,
and further permitted NP in K−K mixing as well.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CKMfitter September 2012 update of 1203.0238:
)s
(BSL
) & ad
(BSL & aSLA
)0
fψ(J/sτ) & -K+(Ksτ & FSsτ & sΓ ∆
sm∆ & dm∆
sβ-2s
∆φ
SM point
s∆Re -2 -1 0 1 2 3
s∆Im
-2
-1
0
1
2
excluded area has CL > 0.68
ICHEP 2012
CKMf i t t e r mixing sB -
s New Physics in B
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
CKMfitter September 2012 update of 1203.0238:
expα
)s
(BSL
) & ad
(BSL & aSLA
sm∆ & dm∆SM point
)d
β+2d ∆φsin(
)>0d
β+2d ∆φcos(
d∆Re -2 -1 0 1 2 3
d∆Im
-2
-1
0
1
2
excluded area has CL > 0.68
ICHEP 2012
CKMf i t t e r mixing dB -
d New Physics in B
ASL and WA forB(B → τν) prefersmall φ∆d < 0.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Pull value for ASL: 3.3σ⇒ Scenario with NP in Mq
12 only cannot accomodate theDØ measurement of ASL.
The Standard Model point ∆s = ∆d = 1 is disfavoured by 1σ,down from the 2010 value of 3.6σ.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Supersymmetry
The MSSM has many new sources of flavour violation, all in thesupersymmetry-breaking sector.
No problem to get big effects in Bs−Bs mixing, but rather tosuppress the big effects elsewhere.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Squark mass matrix
Diagonalise the Yukawa matrices Y ujk and Y d
jk⇒ quark mass matrices are diagonal, super-CKM basis
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Squark mass matrix
Diagonalise the Yukawa matrices Y ujk and Y d
jk⇒ quark mass matrices are diagonal, super-CKM basis
E.g. Down-squark mass matrix:
M2d=
(M d
1L
)2∆d LL
12 ∆d LL13 ∆d LR
11 ∆d LR12 ∆d LR
13
∆d LL12
∗(
M d2L
)2∆d LL
23 ∆d RL12
∗
∆d LR22 ∆d LR
23
∆d LL13
∗
∆d LL23
∗(
M d3L
)2∆dRL
13
∗
∆d RL∗23 ∆d LR
33
∆d LR11
∗
∆dRL12 ∆dRL
13
(M d
1R
)2∆d RR
12 ∆d RR13
∆d LR12
∗
∆d LR∗
22 ∆dRL23 ∆d RR
12
∗(
M d2R
)2∆d RR
23
∆d LR13
∗
∆d LR23
∗
∆d LR33
∗
∆d RR13
∗
∆d RR23
∗(
M d3R
)2
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Squark mass matrix
Diagonalise the Yukawa matrices Y ujk and Y d
jk⇒ quark mass matrices are diagonal, super-CKM basis
E.g. Down-squark mass matrix:
M2d=
(M d
1L
)2∆d LL
12 ∆d LL13 ∆d LR
11 ∆d LR12 ∆d LR
13
∆d LL12
∗(
M d2L
)2∆d LL
23 ∆d RL12
∗
∆d LR22 ∆d LR
23
∆d LL13
∗
∆d LL23
∗(
M d3L
)2∆dRL
13
∗
∆d RL∗23 ∆d LR
33
∆d LR11
∗
∆dRL12 ∆dRL
13
(M d
1R
)2∆d RR
12 ∆d RR13
∆d LR12
∗
∆d LR∗
22 ∆dRL23 ∆d RR
12
∗(
M d2R
)2∆d RR
23
∆d LR13
∗
∆d LR23
∗
∆d LR33
∗
∆d RR13
∗
∆d RR23
∗(
M d3R
)2
Not diagonal! ⇒ new FCNC transitions.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
b q
q b
g g
b
q
q
b
δdLLq3
δdLLq3
b q
q b
g g
b
q
q
b
δdLLq3
δdLLq3
b q
q b
χ− χ−
t
c
c
t
δu LL23
δu LL23
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Model-independent analyses constrain
δq XYij =
∆q XYij
16
∑s
[M2
q
]ss
with XY = LL, LR,RR and q = u, d
using data on FCNC (and also charged-current) processes.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Model-independent analyses constrain
δq XYij =
∆q XYij
16
∑s
[M2
q
]ss
with XY = LL, LR,RR and q = u, d
using data on FCNC (and also charged-current) processes.
Remarks:
• For Mg & 1.5Mq the gluino contribution is small forAB = LL,RR, so that chargino/neutralino contributions areimportant.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Model-independent analyses constrain
δq XYij =
∆q XYij
16
∑s
[M2
q
]ss
with XY = LL, LR,RR and q = u, d
using data on FCNC (and also charged-current) processes.
Remarks:
• For Mg & 1.5Mq the gluino contribution is small forAB = LL,RR, so that chargino/neutralino contributions areimportant.
• To derive meaningful bounds on δq LRij chirally enhanced
higher-order contributions must be taken into account.A. Crivellin, UN, 2009
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
0 500 1000 1500 2000���������������
mg�
GeV
0.1
0.2
0.3
0.4
0.5ÈDs
g�
È
msq = 500GeV
The gluino contribution vanishes for Mg ≈ 1.5Mq, independentlyof the size of ∆d LL
23 (curves correspond to 4 different values).
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
The flavour violation in the supersymmetry-breaking terms areviewed as trouble makers (supersymmetric flavour problem).
Could they instead be helpful to understand the SM flavourpuzzle?
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
The flavour violation in the supersymmetry-breaking terms areviewed as trouble makers (supersymmetric flavour problem).
Could they instead be helpful to understand the SM flavourpuzzle?
We observe: Flavour violation is small in the quark sector,because the Yukawa matrices possess an approximateSU(2)× SU(2)× SU(3) flavour symmetry. In the exactsymmetry limit only the top quark has mass and V = 1.
What causes the small deviations leading to V 6= 1?
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour violation from trilinear terms
Origin of the SUSY flavour problem: Misalignment of squarkmass matrices with Yukawa matrices.Unorthodox solution: Set Y u
ij and Y dij to zero, except for
(i , j) = (3, 3).⇒ No flavour violation from Y u,d
ij and VCKM = 1.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour violation from trilinear terms
Origin of the SUSY flavour problem: Misalignment of squarkmass matrices with Yukawa matrices.Unorthodox solution: Set Y u
ij and Y dij to zero, except for
(i , j) = (3, 3).⇒ No flavour violation from Y u,d
ij and VCKM = 1.
VCKM 6= 1 is then generated radiatively, through finitesquark-gluino loops. ⇒ SUSY-breaking is the origin of flavour.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Flavour violation from trilinear terms
Origin of the SUSY flavour problem: Misalignment of squarkmass matrices with Yukawa matrices.Unorthodox solution: Set Y u
ij and Y dij to zero, except for
(i , j) = (3, 3).⇒ No flavour violation from Y u,d
ij and VCKM = 1.
VCKM 6= 1 is then generated radiatively, through finitesquark-gluino loops. ⇒ SUSY-breaking is the origin of flavour.
Radiative flavour violation: S. Weinberg 1972
flavour from soft SUSY terms:W. Buchmuller, D. Wyler 1983,T. Banks 1988,F. Borzumati, G.R. Farrar,
N. Polonsky, S.D. Thomas 1998, 1999J. Ferrandis, N. Haba 2004
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Today: Strong constraints from FCNCs probed at B factories.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Today: Strong constraints from FCNCs probed at B factories.
But: Radiative flavour violation in the MSSM is still viable, albeitonly with Ad
ij and Auij entering
M d LRij = Ad
ij vd + δi3δj3ybµvu, M u LRij = Au
ij vu + δi3δj3ytµvd .
Andreas Crivellin, UN, PRD 79 (2009) 035018
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Today: Strong constraints from FCNCs probed at B factories.
But: Radiative flavour violation in the MSSM is still viable, albeitonly with Ad
ij and Auij entering
M d LRij = Ad
ij vd + δi3δj3ybµvu, M u LRij = Au
ij vu + δi3δj3ytµvd .
Andreas Crivellin, UN, PRD 79 (2009) 035018
dfL diR diRdfLYdfi
H0
d
H0
d
Adfi
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Electric dipole moments
Darkest corner of the MSSM: The phases of Aqii and µ generate
too large EDMs. If light quark masses are generated radiativelythrough soft SUSY-breaking terms, this “supersymmetric CPproblem” is substantially alleviated:
• The phases of Aqii and mq are aligned, i.e. zero.
• The phase of µ (essentially) does not enter the EDMs atthe one-loop level, because the Yukawa couplings of thefirst two generations are zero.
Borzumati, Farrar, Polonsky, Thomas 1998,1999
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Bd ,s → µ+µ−
LHCb 2013:
B(Bs → µ+µ−) =(
3.2+1.5−1.2
)· 10−9
B(Bd → µ+µ−) < 9.4 · 10−10 @95% CL
b s
t
W
Z
Theory:
B(Bs → µ+µ−
)= (3.52± 0.08) · 10−9 ×
τBs
1.519 ps
[ |Vts|0.040
]2 [ fBs
230 MeV
]2
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Lattice QCD results of ETMC, HPQCD and FNAL/MILC(1107.1441, 1112.3051, 1202.4914). Personal combination:
fBs = (230± 10) MeV.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Lattice QCD results of ETMC, HPQCD and FNAL/MILC(1107.1441, 1112.3051, 1202.4914). Personal combination:
fBs = (230± 10) MeV.
Bs → f decays involve two exponentials:
Γ(( )
Bs → f , t) = Af e−ΓLt + Bf e
−ΓH t ,
since Bs−Bs mixing leads to a sizable decay-width differenceΓL − ΓH = ∆Γs = (0.078± 0.022) ps−1.⇒ correct B(Bs → µ+µ−) for this De Bruyn et al, 1204.1737
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Supersymmetry
COSMOS Magazine 14 Nov 2012:Rare particle decay delivers blow to supersymmetry
The popular physics theory of supersymmetry has beencalled into question by new results from CERN. Physicistsworking at CERN’s Large Hadron Collider (LHC) nearGeneva, Switzerland, have announced the discovery ofan extremely rare type of particle decay.. . .
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Supersymmetry
COSMOS Magazine 14 Nov 2012:Rare particle decay delivers blow to supersymmetry
The popular physics theory of supersymmetry has beencalled into question by new results from CERN. Physicistsworking at CERN’s Large Hadron Collider (LHC) nearGeneva, Switzerland, have announced the discovery ofan extremely rare type of particle decay.. . .
MA: mass of the pseudoscalar Higgs boson A0
tanβ: ratio of the two Higgs-vevs of the MSSM:
B(Bs → µ+µ−) ∝ tan6 β
M4A
⇒ Bs → µ+µ− places lower bounds on MA for large valuesof tanβ, similarly to searches for A0 → τ+τ− at ATLASand CMS.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
MSSM
HaLHbLHdL
HcL
200 400 600 800 1000 1200
10
20
30
40
50
60
MA HGeVL
tanΒ
M3 = 3M2 = 6M1 = 1.5 TeVmf = 2 TeVAb = At = Aτ ,
so thatmh = 125 GeV.
a) µ = 1 TeV, At > 0,b) µ = 4 TeV, At > 0,c) µ = −1.5 TeV, At > 0,d) µ = 1 TeV, At < 0,
Excluded areas:Gray: A0
,H0→ τ
+τ−
Red: Bs → µ+µ−
Altmannshofer et al., 1211.1976
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Partial Compositeness
Models with non-elementaryHiggs und additional non-elementary fermions⇒ FCNC-Z-couplings
Red, brown, blue:Three models; the bluemodel has a U(2)3-flavoursymmetry.
Straub, 1302.4651
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Bs → φπ0, φρ0
QCD penguins do not contribute toBs → φπ0 and Bs → φρ0:Strong isospin: I(Bs) = I(φ) = 0
and I(π0) = I(ρ0) = 1b → s QCD penguin diagrams are ∆I = 0transitions.Tree diagrams are suppressed by Ruλ
2.
Bs → φπ0 and Bs → φρ0 therefore probeZ penguins.
b s
t
W
b s
t
W
Z
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Bs → φπ0, φρ0
New physics can enhance the branchingfractions by a factor of 5 over the SM val-ues:
B(Bs → φπ0) =(
1.6+1.1−0.3
)· 10−7,
B(Bs → φρ0) =(
4.4+2.7−0.7
)· 10−7
Hofer et al., 1011.6319, 1212.4785
b s
t
W
b s
t
W
Z
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Summary
• Flavour physics probes new physics associated with scalesabove 100 TeV. It complements collider physics.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Summary
• Flavour physics probes new physics associated with scalesabove 100 TeV. It complements collider physics.
• All measured non-zero CP-violating quantities involveFCNC amplitudes. CP asymmetries are excellent probesof new physics, because the SM is predictive (one CPphase only!) and many CP asymmetries are hadronicallyclean and are further sensitive to high scales throughFCNC loops.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Summary
• Flavour physics probes new physics associated with scalesabove 100 TeV. It complements collider physics.
• All measured non-zero CP-violating quantities involveFCNC amplitudes. CP asymmetries are excellent probesof new physics, because the SM is predictive (one CPphase only!) and many CP asymmetries are hadronicallyclean and are further sensitive to high scales throughFCNC loops.
• New physics of order 20% in the Bs−Bs and Bd−Bd mixingamplitudes is still allowed.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Summary
• Flavour physics probes new physics associated with scalesabove 100 TeV. It complements collider physics.
• All measured non-zero CP-violating quantities involveFCNC amplitudes. CP asymmetries are excellent probesof new physics, because the SM is predictive (one CPphase only!) and many CP asymmetries are hadronicallyclean and are further sensitive to high scales throughFCNC loops.
• New physics of order 20% in the Bs−Bs and Bd−Bd mixingamplitudes is still allowed.
• Supersymmetry with non-minimal flavour violation gainsattractivity as it comes with (multi-)TeV squark masses.The deviation of V from the unit matrix may come fromsupersymmetric loops (Radiative Flavour Violation).
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Summary
• In supersymmetry the rare decay Bs → µ+µ− constrainstan6 β/M4
A.
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Summary
• In supersymmetry the rare decay Bs → µ+µ− constrainstan6 β/M4
A.
• Suggestion for LHCb and Belle-II: Study Bs → φπ0, φρ0 tolook for isospin-violating new physics (electroweakpenguins).
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Basics C,P,T CKM new physics global analysis SUSY Rare decays Summary
Penguins: Wake-up call for new physics?