b d d t,c,u d t,c,u w- t,c,ub t,c,u - nikhef · pdf fileseminar, nikhef, amsterdam a. lenz,...

Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 1

B-mixingWhat did we learn from LHCb in 2011?

b

d

t,c,u

t,c,u

W-

b

db

dt,c,u t,c,uW

-b

d

Alexander LenzCERN, Theory Division


Content

■ Introduction

■ CKM+: The CKM paradigm is great■ CKM0: The CKM paradigm might be better■ CKM−: The CKM paradigm is violated by New Physics!

■ Status of B-mixing after Moriond 2012

■ Wish-list for Experiments


Introduction I


Introduction II - Baryon Asymmetry

symmetric initial conditions(Inflation: initial asymmetry is wiped out)

⇒ Nmatter = Nantimatter

But we exist and stars and...

Search for annihilation lines, nucleosynthesis, CMB,...




ηB =nB − nB̄

nγ≈ 6 · 10−10

How can this be created from symmetric initial conditions?




ηB =nB − nB̄

nγ≈ 6 · 10−10

How can this be created from symmetric initial conditions?

1967 Sakharov: The fundamental laws of nature must have several properties,in particular

CP-violation: 1964 K-Mesons (NP 1980) 2000 B-Mesons

Can our fundamental theory cope with these requirements?


Success of the SM I

Elegant description of nature at per mille precision


Success of the SM II

Elegant description of nature at per mille precision

• Electroweak precision tests

measσ) / meas - Ofit

(O

-3 -2 -1 0 1 2 3

tmbm

cm

WΓWM

)2

Z(M

(5)

hadα∆

b0R

c0R

bA

cA

0,bFBA

0,cFBA

)FB

(Qlepteff

Θ2sin

(SLD)lA

(LEP)lA

0,lFBA

lep0R

0had

σZΓZM

0.3

-0.0

-0.0

0.2

-1.3

-0.1

-0.8

0.1

0.6

-0.1

2.5

0.9

-0.7

-2.0

0.2

-0.9

-1.0

-1.7

0.1

0.1G fitter SM

AU

G 11

[GeV]tm140 150 160 170 180 190 200

[GeV

]W

M

80.15

80.2

80.25

80.3

80.35

80.4

80.45

80.5

80.55

=114 GeV

HM

=300 GeV

HM =1000 GeV

HM

WAtop band for mσ1

WAW

band for Mσ1

68%, 95%, 99% CL fit

top, mWcontours excl. M

68%, 95%, 99% CL fit contours , incl. Higgs searches

t, mWexcl. M

=114 GeV

HM

=300 GeV

HM =1000 GeV

HM

G fitter SM

AU

G 11


Success of the SM IIIElegant description of nature at per mille precision

• CKM-mechanism NP 2008How can CP-violation be incorporated in the SM?

1972 only u,d and s-quarks were known, Kobayashi and Maskawa postulatedsix quarks!


CKM+: Status of CKM in early 2012

Good overall consistency

VCKM =

0.97426± 0.00030 0.22545± 0.00095 0.00356± 0.00020

0.22529± 0.00077 0.97341± 0.00021 0.04508+0.00075−0.00528

0.00861+0.00021−0.00037 0.04068± 0.00138 0.999135+0.000057

−0.000018

Fit from A.L, Nierste, CKMfitter 1008.1593see also UTfit 1010.5089, Lunghi/Soni 1010.6069, Laiho/Lunghi/Van de Water

1102.3917, PDG, HFAG ...

NP 2008


CKM+: The status of CKM in early 2012

γ

γ

αα

dm∆Kε

Kε

sm∆ & dm∆

ubV

βsin 2

(excl. at CL > 0.95) < 0βsol. w/ cos 2

excluded at CL > 0.95

α

βγ

ρ-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

η

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5excluded area has CL > 0.95

Summer 11

CKMf i t t e r

Picture from A.L, Nierste, CKMfitter 1008.1593, see also UTfit, Lunghi/Soni, Laiho et al...

A = 0.815+0.011

−0.029

λ = 0.22543(77)

ρ̄ = 0.1444+0.029

−0.018

η̄ = 0.342(16)


CKM+: b → sγ- Another success of CKM

Br(b→ sγ)Exp = (3.55± 0.26) · 10−4

Br(b→ sγ)Theo = (3.15± 0.23) · 10−4

Exp: HFAG, BaBar, BELLE, CLEOTheory in NNLO Misiak et al. 2007,...List of References in Misiak, PoS(FPCP 2010)025

8 8


CKM0: The first row: Vud

■ Nuclear β-decay■ Neutron β-decay■ Pion β-decay

|Vud| = 0.97425± 0.00022

PDG 2010, Hardy, Towner 2009


CKM0: The first row: Vus

■ Kl3-decays■ Hadronic τ decays■ Semi leptonic Hyperon decays

|Vus| = 0.2254± 0.0013

Antonelli et al. 1005.2323; Boyle et al. 1004.0886


CKM0: The first row: Vub

Exclusive |Vub| = 0.00351± 0.00047

Inclusive |Vub| = 0.00432± 0.00027

B → τν |Vub| = 0.00504± 0.00064

Fit |Vub| = 0.00356± 0.00020

HFAG; HPQCD 2007; MILC Fermilab 2008;Ball/Zwicky 2005; Lange/Neubert/Paz 2005;Andersen/Gardi 2006,2008; Gambino/Giordano/Ossola/Uraltsev 2007; Aglietti/Di

Lodovico/Ferrera/Ricciardi 2009; Aglietti/Ferrera/Ricciardi 2007; Bauer/Ligeti/Luke2001,...

■ Vub is actually of order λ4 and not λ3: 0.00356 = (0.2254)3.79

■ Hadronic uncertainties (lattice, LCSR) underestimated?■ Soni and Lunghi: do not to use Vub in the global fit■ Crivellin0907.2461; Buras/Gemmler/Isidori 1007.1993: RH currents ⇒ incl. 6= excl.

■ New Physics in B → τν vs. Bd-mixing


CKM0: The first row: Vub′

Test the accuracy of the CKM elements of the first row:

δ(Vud) = 0.00022

δ(Vus) = 0.00130

δ(Vub) = 0.00020√1− V 2

ud − V 2us = 0.00564+0.02669

−0.00564

Investigate a hypothetical 4th generation of fermionsAssume VCKM4 is unitary

⇒ Vub′ can still be much larger than Vub: Vub′ < 0.04 ≈ λ2

Bobrowski, A.L., Rohrwild, Riedl, 0902.4883; Buras et al. 2010; Eberhardt, A.L.,Rohrwild 1005.3505; Das, London, Sinha, Soffer 1008.4925; Alok, Dighe, London1011.2634; Soni and Nandi 1011.6091;...


CKM0: The second row: Vcd

■ Semi leptonic Charm decays D → πlν

■ Charm Production in Neutrino Interactions

|Vcd| = 0.230± 0.011

PDG 2010


CKM0: The second row: Vcs

■ Neutrino Scattering■ On-shell W decays■ Semi leptonic Charm decays

|Vcs| = 1.023± 0.036

PDG 2010


CKM0: The second row: Vcb

■ B → Xclν

■ B → D(∗) transitions

Inclusive |Vcb| = (41.85± 0.43± 0.59) · 10−3

Exclusive |Vcb| = (38.85± 0.77± 0.84) · 10−3

HFAG 2010; Gambino/Uraltsev (2004); Benson/Bigi/Uraltsev (2005);Benson/Bigi/Mannel/Uraltsev (2003);...■ Inclusive is again larger■ Try to make some combinations

|Vcb| =

{(40.6± 1.3) · 10−3 PDG 2010(40.89± 0.38± 0.59) · 10−3 1008.1593


CKM0: The second row: Vcb′

Test the accuracy of the CKM elements of the second row:

δ(Vcd) = 0.011

δ(Vcs) = 0.036

δ(Vcb) = 0.013

Investigate a hypothetical 4th generation of fermionsAssume VCKM4 is unitary

⇒ Vcb′ can still be much larger than Vcb: Vcb′ < 0.15 ≈ λ

Bobrowski, A.L., Rohrwild, Riedl, 0902.4883; Buras et al. 2010; Eberhardt, A.L.,Rohrwild 1005.3505; Das, London, Sinha, Soffer 1008.4925; Alok, Dighe, London1011.2634; Soni and Nandi 1011.6091;


CKM0: The third row: Vtd

Im Vtd vs. Re Vtd

Eberhardt,

A.L.,Rohrwild

1005.3505


CKM0: The third row: Vts

Vts vs. Re Vts

Eberhardt,

A.L.,Rohrwild

1005.3505


CKM0: The third row: Vtb

Im Vtb vs. Re Vtb

Eberhardt,A.L., Rohrwild

1005.3505

Single Top production Wagner 1101.4235; CDF 0903.0885,1004.1181; D0 0903.0850

Vtb = 0.88± 0.07


CKM0: The CKM values should be known better!

■ Overall picture looks very good: CKM+

■ But looking in more detail: CKM0

◆ more precise value of Vus desireable◆ Vub problem◆ more precise values of Vcx needed◆ (almost) no direct information on Vtx

There is still a lot of room for deviations ⇒ Look for it — LHCb, SuperB-factories

■ It becomes worse (or more interesting?): CKM−

There are several hints for deviations from the CKM picture!


CKM−: Flavor Physics in the news

■ 17.5.2010 New York TimesA new Clue to explain existence

■ 19.5.2010 BBC NewsNew Clue to anti-matter mystery

■ 20.5.2010 Scientific AmericanFermilab finds new mechanism for matter’s dominance over antimatter

■ 20.5.2010 The TimesAtom-smasher takes man closer to heart of matter

■ 25.5.2010 SpiegelNeue Asymmetrie zwischen Materie und Antimaterie entdeckt

■ 28.5.2010 ScienceHints of greater matter-antimatter asymmetry challenge theorists

■ 28.5.2010 Die ZeitRätselhafte Asymmetrie

■ 29.5.2010 Chicago TribuneFermilab test throws off more matter than antimatter - and this matters

■ ...


The dimuon asymmetry■ 1005.2757 Dzero (submitted sunday, 16.5.2010) 178 citations

Evidence for an anomalous like-sign dimuon charge asymmetry

V.M. Abazov,36 B. Abbott,74 M. Abolins,63 B. S. Acharya,29 M. Adams,49 T. Adams,47 E. Aguilo,6 G.D. Alexeev,36

Selected for a Viewpoint in PhysicsPHYSICAL REVIEW D 82, 032001 (2010)

We measure the charge asymmetry A of like-sign dimuon events in 6:1 fb 1 of p $p collisions recorded

with the D0 detector at a center-of-mass energyffiffiffi

sp ¼ 1:96 TeV at the Fermilab Tevatron collider. From

A, we extract the like-sign dimuon charge asymmetry in semileptonic b-hadron decays: Absl ¼ 0:00957# 0:00251 ðstatÞ # 0:00146 ðsystÞ. This result differs by 3.2 standard deviations from the

standard model prediction AbslðSMÞ ¼ ð 2:3þ0:5 0:6Þ ' 10 4 and provides first evidence of anomalous

CP violation in the mixing of neutral B mesons.

DOI: 10.1103/PhysRevD.82.032001 PACS numbers: 13.25.Hw, 11.30.Er, 14.40.Nd

[1] A. Lenz and U. Nierste, J. High Energy Phys. 06 (2007)

072.

[2] C. Amsler et al., Phys. Lett. B 667, 1 (2008), and 2009

partial update for the 2010 edition.

[3] A. D. Sakharov, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967)

[15] V.M. Abazov et al. (D0 Collaboration), Nucl. Instrum.

Methods Phys. Res., Sect. A 565, 463 (2006).

[16] S. N. Ahmed et al., arXiv:1005.0801 [Nucl. Instrum.

Methods Phys. Res. Sect. A (to be published)]; R.

Angstadt et al., arXiv:0911.2522.

17.5.’10 NYT: “A new clue to explain existence” (26.5 · 106 google entries)

■ 1106.6308: 9 fb−1, Absl = (−0.787± 0.172(stat)± 0.093(syst))% ⇒ 3.9σ


TeVatron gave us many presents, and then ...


Mixing I

Time evolution of a decaying particle: B(t) = exp [−imBt− ΓB/2t]can be written as

id

dt

(|B(t)〉

|B̄(t)〉

)=

(M̂ −

i

2Γ̂

)(|B(t)〉

|B̄(t)〉

)

BUT: In the neutral B-system transitions like Bd,s → B̄d,s are possible due toweak interaction: Box diagrams

b

d

t,c,u

t,c,u

W-

b

db

dt,c,u t,c,uW

-b

d


Mixing II

Mixing is a macroscopic quantum effect!

It was observed in

■ K0-system: 1950s (see text books, regeneration...)■ Bd-system: 1986■ Bs-system: 2006■ D0-system: 2007

Strongly suppressed in the SM (due to virtual top-quarks)New physics effects might be of comparable size

?Is QCD under control?


Mixing III

Time evolution of a decaying particle: B(t) = exp [−imBt− ΓB/2t]can be written as

id

dt

(|B(t)〉

|B̄(t)〉

)=

(M̂ −

i

2Γ̂

)(|B(t)〉

|B̄(t)〉

)

BUT: In the neutral B-system transitions like Bd,s → B̄d,s are possible due toweak interaction: Box diagrams

b

d

t,c,u

t,c,u

W-

b

db

dt,c,u t,c,uW

-b

d

⇒ off-diagonal elements in M̂, Γ̂: M12, Γ12 (complex)Diagonalization of M̂, Γ̂ gives the physical eigenstates BH and BL with themasses MH , ML and the decay rates ΓH , ΓL

CP-odd: BH := p B + q B̄ , CP-even: BL := p B − q B̄ with |p|2 + |q|2 = 1


Mixing IV

|M12|, |Γ12| and φ = arg(−M12/Γ12) can be related to three observables:

■ Mass difference: ∆M :=MH −ML = 2|M12|(1− 1

8|Γ12|

2

|M12|2sin2 φ+ ...

)

|M12| : heavy internal particles: t, SUSY, ...

■ Decay rate difference: ∆Γ := ΓL − ΓH = 2|Γ12| cosφ(1 + 1

8|Γ12|

2

|M12|2sin2 φ+ ...

)

|Γ12| : light internal particles: u, c, ... (almost) no NP!!!

■ Flavor specific/semileptonic CP asymmetries:

B̄q → f and Bq → f̄ forbiddenNo direct CP violation: |〈f |Bq〉| = |〈f̄ |B̄q〉|e.g. Bs → D−

s π+ or Bq → Xlν (semileptonic)

asl ≡ afs =Γ(Bq(t) → f)− Γ(Bq(t) → f)

Γ(Bq(t) → f) + Γ(Bq(t) → f)= −2

(∣∣∣∣q

p

∣∣∣∣− 1

)= Im

Γ12

M12=

∆Γ

∆Mtanφ


The Mass Difference ∆M

Calculating the box diagram with an internal top-quark yields

M12,q =G2F

12π2(V ∗tqVtb)

2M2WSo(xt)BBq

f2BqMBq

η̂B (Inami, Lim ’81)

■ Hadronic matrix element: 83BBq

f2BqMBq

= 〈B̄q|(b̄q)V−A(b̄q)V−A|Bq〉

■ Perturbative QCD corrections η̂B (Buras, Jamin, Weisz, ’90)

Theory 1102.4274 vs. Experiment : HFAG 11

∆Md = 0.543± 0.091 ps−1 ∆Md = 0.507± 0.004 ps−1

ALEPH, CDF, D0, DELPHI, L3,

OPAL, BABAR, BELLE, ARGUS, CLEO

∆Ms = 17.30± 2.6 ps−1 ∆Ms = 17.70± 0.12 ps−1

CDF, D0, LHCb

Important bounds on the unitarity triangle and new physics


Determination of Γ12

Sensitive to real intermediate states ⇒ much more complicated than M12

1. OPE I: Integrate out W: like M12 ∝ f2BB

2. OPE II: Heavy quark expansion ⇒ Γ(j)i ∝ f2B

∑CkBK

Γ12 =

(Λ

mb

)3(Γ(0)3 +

αs4π

Γ(1)3 + ...

)+

(Λ

mb

)4(Γ(0)4 + ...

)+

(Λ

mb

)5(Γ(0)5 + ...

)+ ...

1996: Beneke, Buchalla, Dunietz1998: Beneke, Buchalla, Greub, A.L., Nierste

2003: Ciuchini, Franco, Lubicz, Mescia, Tarantino; Beneke, Buchalla, A.L., Nierste2006: A.L., Nierste

2007: Badin, Gabbiani, Petrov

∆Γs = ∆Γ0s

(1 + δLattice + δQCD + δHQE

)

= 0.142 ps−1 (1− 0.14− 0.06− 0.19)


HQE under attack!

OPE II might be questionable - relies on quark hadron duality

■ Mid 90’s: Missing Charm puzzle nExp.c < nSMc , semi leptonic branching ratio

■ Mid 90’s: Λb lifetime is too short■ before 2003: τBs

/τBd≈ 0.94 6= 1

■ 2010/2011: Di-muon asymmetry too large

Theory arguments for HQE

⇒ calculate corrections in all possible “directions”, to test convergence⇒ Γ12 seems to be ok!

⇒ test reliability of OPE II via lifetimes (no NP effects expected) “directions”, totest convergence⇒ τ(B+)/τ(Bd) Experiment and theory agree within hadronic uncertainties


HQE under attack!


■ 2012: n2011PDGc = 1.20± 0.06 vs. nSMc = 1.20± 0.04

Eberhardt, Krinner, A.L., Rauh in prep.

■ Mid 90’s: Λb lifetime is too short■ before 2003: τBs

/τBd≈ 0.94 6= 1






HQE under attack!


■ 2012: n2011PDGc = 1.20± 0.06 vs. nSMc = 1.20± 0.04


■ HFAG ’03 τΛb= 1.212± 0.052 ps−1 −→ HFAG ’11 τΛb

= 1.425± 0.032 ps−1

Shift by 4σ ⇒Eagerly waiting for new LHCb results!!!■ before 2003: τBs

/τBd≈ 0.94 6= 1






HQE under attack!


■ 2012: n2011PDGc = 1.20± 0.06 vs. nSMc = 1.20± 0.04



= 1.425± 0.032 ps−1

Shift by 4σ ⇒Eagerly waiting for new LHCb results!!!■ Moriond 2012 LHCb: τBs

/τBd= 1.001± 0.014 LHCb-CONF-2012-002






The Bs lifetime

Moriond 2012 LHCb vs SM A.L., Nierste 2011

τBs

τBd

Exp= 1.001± 0.014

τBs

τBd

SM= 0.996...1.000

■ 0.940± 0.014 would have been a desaster for SM = may be NP :-)■ Update of effective lifetimes

Fleischer et al used 1011.1096, 1109.1112, 1109.5115: τBs= 1.477 ps

Exp. SM-old SM-new

τEff(K+K−) 1.468± 0.046 1.390± 0.032 1.43± 0.03

τEff(ψf0) 1.70± 0.12 1.582± 0.036 1.63± 0.03

τFS 1.417± 0.042 −−− 1.54± 0.03


HQE under attack!


■ 2012: n2011PDGc = 1.20± 0.06 vs. nSMc = 1.20± 0.04



= 1.425± 0.032 ps−1

Shift by 4σ ⇒Eagerly waiting for new LHCb results!!!■ Moriond 2012 LHCb: τBs

/τBd= 1.001± 0.014 LHCb-CONF-2012-002

■ 2010/2011: Di-muon asymmetry too large — Test Γ12 with ∆Γs!





∆Γs in NLO-QCD I

A brief history of theory predictions

′81... Hagelin; Buras et al.;... ∆Γ ∝ O(0.15 ps−1

)

′93 Aleksan et al.; ... ∆Γ ∝ O(0.10 ps−1

)

′96 Beneke, Buchalla, Dunietz ∆Γs =(0.11+0.07

−0.06

)ps−1

′00 Beneke, A.L. ∆Γs = (0.06± 0.03) ps−1

′03 Ciuchini, et al ∆Γs = (0.050± 0.016)ps−1

′06 A.L., Nierste ∆Γs = (0.096± 0.036)ps−1

′11 A.L., Nierste ∆Γs = (0.087± 0.021)ps−1

Crucial dependence on non-perturbative parameters!2011 fBs

= 231± 15 MeV used.Newer Results:■ 1110.4510 - HPQCD:fBs

= 225± 4 MeV ⇒ ∆Γs = (0.083± 0.017) ps−1

■ 1112.3051 - Fermilab:fBs= 242± 9.5 MeV ⇒ ∆Γs = (0.095± 0.021) ps−1

■ 1201.3956 - chiral QM:fBs= 262±? MeV ⇒ ∆Γs = (0.112±?) ps−1


∆Γs in NLO-QCD II

Improvement in theoretical accuracy

∆ΓSMs 2011 2006

Central Value 0.087 ps−1 0.096 ps−1

δ(BR̃2

) 17.2% 15.7%

δ(fBs) 13.2% 33.4%

δ(µ) 7.8% 13.7%

δ(B̃S,Bs) 4.8% 3.1%

δ(BR0) 3.4% 3.0%

δ(Vcb) 3.4% 4.9%

δ(BBs) 2.7% 6.6%

... .... ...∑δ 24.5% 40.5%


Finally ∆Γs is measured! (naive: 6.1σ)

∆ΓSMs = (0.087± 0.021) ps−1

LHCb from Bs → J/ψφ Dunietz, Fleischer, Nierste

LP 2011 ∆Γs = (0.123± 0.031) ps−1 ⇒∆ΓExp

s

∆ΓSMs

= 1.41± 0.50

Moriond 2012 ∆Γs = (0.116± 0.019) ps−1 ⇒∆ΓExp

s

∆ΓSMs

= 1.33± 0.39

■ D0 8fb−1 1109.3166: ∆Γs = (0.163± 0.065) ps−1

■ CDF 9.6fb−1 Public Note 10778: ∆Γs = (0.068± 0.027) ps−1


Finally ∆Γs is measured! (naive: 6.1σ)

Get rid off the dependence on fBs(No NP in ∆M )

∆Γs∆Ms

= 10−4 ·

[46.2 + 10.6

B̃′S

B−

(13.2

BR̃2

B− 2.5

BR0

B+ 1.2

BRB

)]

= 0.0050± 0.0010

HQE vs. Experiment

(∆Γs∆Ms

)Exp

/

(∆Γs∆Ms

)SM

= 1.30± 0.34

HQE works also for Γ12!How precise does it work? 30%? 10%?

Still more accurate data needed! TeVatron, LHCb, Super-B(elle)


∆ΓCPs /Γs = 2Br(Bs → D

(∗)+s +D

(∗)−s )?

■ 1993 Aleksan; Le Yaouanc, Olivre, Pene, Raynal:The above equation holds in the limit: mc → ∞;mb − 2mc → 0;Nc → ∞Corresponds to negligible 3-body final state contributions to Γs12

∆ΓsΓs

∝ O(0.15)

■ 1107.4325 Chua, Hou, Shen Reanalysis of the exclusive approach◆ 2-body final states contribute 0.100± 0.030 to ∆Γ/Γ

Aleksan et al were lucky...◆ 3-body final states contribute about 0.06...0.08

This is comparable to 2-body final states! ⇒ bad approximation ⇒ test exp.

We strongly discourage from the inclusion of Br(Bs→ D(∗)+ +D(∗)−) in averages with∆Γs determined from clean methods.

A.L., Nierste; hep-ph/0612167


Semi leptonic CP-asymmetries afs and ∆Γd

SM predictions: A.L., U. Nierste, 1102.4274; A.L. 1108.1218

asfs = (1.9± 0.3) · 10−5 φs = 0.22◦ ± 0.06◦

adfs = − (4.1± 0.6) · 10−4 φd = −4.3◦ ± 1.4◦

Absl = 0.406assl + 0.594adsl = (−2.3± 0.4) · 10−4

Experimental bounds

asfs = (−1150± 610) · 10−5 (HFAG 11)

φs = −51.6◦ ± 12◦ (A.L., Nierste, CKMfitter, 1008.1593)

= −0.1◦ ± 5.0◦ LHCb Moriond 2012

adfs = − (49± 38) · 10−4 (HFAG 11)

∆ΓdΓd

= (−17± 21) · 10−3 (Belle EPS 2011 )

Absl = −(7.87± 1.72± 0.93) · 10−3(D0,1106.6308)

Absl(Exp.)/Absl(Theory) = 34 3.9− σ-effect


New Physics in B-Mixing I

Γ12,s = ΓSM12,s , M12,s =MSM

12,s ·∆s ; ∆s = |∆s|eiφ∆

s

∆s = r2se2iθs = CBs

e2iφBs = 1 + hse2iσs

∆Ms = 2|MSM12,s| · |∆s|

∆Γs = 2|Γ12,s| · cos(φSMs + φ∆s

)

∆Γs∆Ms

=|Γ12,s|

|MSM12,s|

·cos(φSMs + φ∆s

)

|∆s|

asfs =|Γ12,s|

|MSM12,s|

·sin(φSMs + φ∆s

)

|∆s|

sin(φSMs ) ≈ 1/240

For |∆s| = 0.9 and φ∆s = −π/4 onegets the following bounds in thecomplex ∆-plane :


New Physics in B-Mixing II

Combine all data till end of 2011 and neglect penguinsfit of ∆d and ∆s 1203.0238 (update of 1008.1593) soon v2!

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

End of 2011

CKMf i t t e r mixing dB -

d New Physics in B

)s

(BSL

) & ad

(BSL & aSLA

FSsτ & sΓ ∆

sm∆ & dm∆s

β-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

End of 2011

CKMf i t t e r mixing sB -

s New Physics in B

■ Fits not so good anymore (LHCb vs. Dzero)■ B → τν vs. sin 2β solved with φ∆d — No tension for ǫK


The dimuon asymmetry

The central value of the di µasymmetry is larger than theoretically possible!

AMax.sl ≈ (0.594± 0.022)(5.4± 1.0) · 10−3 sin(φ

SMd + φ∆d )

|∆d|

+(0.406± 0.022)(5.0± 1.1) · 10−3 sin(φSMs + φ∆s )

|∆s|

≈ (−3.1;−4.8[1σ];−9.0[3σ]) · 10−3

AD0sl = (−7.8± 2.0) · 10−3 A.L. 1108.1218

Possible solutions:

■ HQE violated by O(200%− 3300%) now excluded!■ Huge new physics in Γ12? - No! Bobeth, Haisch 1109.1826■ Contradiction to Bs → J/ψφ from LHCb? - Be aware of Penguins!■ Stat. fluctuation (1.5 σ) of the D0 result? (Actual value is below -4.8 per mille?)

Independent measurements of semi leptonic asymmetries needed!


?New physics in Γ12?

■ Large (O(200− 3400%) NP effects in Γ12? Why not seen somewhere else?

A new operator bs→ X with Mx < MB contributes not only to assl but also tomany more observables, e.g.:◆

b b

q q

Γ3 ⇒

{τ(Bs)/τ(Bd)

∆Γs

◆

b b

Γ0 ⇒

τ(Bx)

Bsl

Br(b→ s no charm)

◆ M12, operator mixing with e.g. b→ sγ, ...

◆ A promising candidate for X seems to be τ+ + τ− -> Bobeth, Haisch ’11.Current best bound Br(Bs → ττ < 5%) - LHCb should do better :-)



■ Missing charm puzzle , e.g.Bigi et al ’94; Bagan et al. ’94; Falk, Wise, Dunietz ’95, Neubert ’97... A.L.

,hep-ph/0011258Look at inclusive b-decay into 0, 1, 2 c-quarksDefine r(x charm) := Γ(b→x charm)

Γsl: m5

bV2cb cancels; Γsl seems safe

The average number of charm quarks per b-decay reads

nc = 0 + [r(1c) + 2r(2c)]BExp.sl

= 1 + [r(2c)− r(0c)]BExp.sl

= 2− [r(1c) + 2r(0c)]BExp.sl

Buchalla, Dunietz, Yamamoto ’95◆ nExp.

c < nTheoryc = missing charm puzzle

May be enhanced b→ s g... Kagan ...◆ latest Data from BaBar and CLEO agree within large uncertainties

Recent and future experiments can do better!◆ Any unknown, even invisible decay mode has an effect on r(0, 1, 2 charm)

!!! ⇒ Need new experimental values for r(0c, 1c, 2c) = Γ0c,1c,2c/Γsl and Bsl!!!



Step I: Forget about all the bounds and fit ∆Γ, asl and ∆M :

SM

)dδIm(-10 -5 0 5 10

) sδIm

(

-10

-5

0

5

10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0p-value

End of 2011

CKMf i t t e r New Physics Scenario IV

A.L, Nierste, CKMfitter 1203.0238Step II: Take your favourite model which gives new contributions to Γ12

■ Determine contributions to δd, δs■ Determine contributions to τBs

, nc, ....■ Exclude the model :-)


How large are Penguins?

Angular analysis of Bs → J/ψφ at CDF, D0 and LHCb:

SSMψφ = 0.0036± 0.002 → sin

(2βs−φ

∆s − δPeng,SMs − δPeng,NP

s

)= 0.002± 0.087

LHCb Moriond 2012Is this a contraction to the dimuon asymmetry?

Depends on the possible size of penguin contributions

■ SM penguin are expected to be very smallbut see also Faller, Fleischer; Mannel 2008

■ NP penguins might be larger

But: even small penguin contributions have a sizeable effect! A.L. 1106.3200


Wish-list for Experiments

a) Congratulations to LHCb for the first measurement of ∆Γs!◆ Still more precision needed: LHCb, TeVatron, Super-B Bs → J/ψη(

′)

◆ Do not use Br(Bs → D(∗)+s D

(∗)−s ) = ∆ΓCP

2Γ - check size of 3-body FS!

b) τBs= (1.001± 0.014)τBd

: strong constraint on NP and duality violation◆ Combine with other determinations of τBs

: LHCb, ATLAS?, CMS?◆ Bs: Effective lifetimes, flavor specific lifetimes (2.x sigma deviation)◆ τΛb

, ...

c) Di muon asymmetry Absl◆ HQE fails? No! At most 30− 40% — more precise test via τ(Bs),∆Γs, ...◆ NP acts in Γ12? No! At most 40%! — More precise tests viaτ(Bs),∆Γs,∆Γd, nc, Bsl, r(0, 1, 2 charm), Bs → ττ, B → Kττ, ...

◆ ???◆ Experimental cross-check via adsl and assl!

d) φLHCbs ≪ φAb

sls How large is the penguin pollution?

◆ Even small penguins can be important!◆ Values for many penguin modes e.g. Bs → J/ψKs, K

0K̄0, φφ, η(′)η(

′)...


What to do list - Theory

Test of HQE with lifetimes

• τB+/τBdand τBs/τBd

fits well ⇒ currently no hints for deviations from HQE

• Precise non-perturbative matrix elements for 4-quark oper ators urgently needed

• Beautiful Mesons and Baryons on the Lattice ECT* Trento, 2-6 April 2012• Perturbative improvements of lifetime predictions

Theoretical predictions for mixing observables

• Precise decay constants and Bag parameter for ∆M

• Additional Bag parameters at dimension 6 and 7 for Γ12

• αs/mb corrections for Γ12

• α2s corrections for Γ12

Theoretical predictions for charm mixing observables

• Push HQE to its limits

• Try to imrove the exclusive approach

Update of theoretical predictions for inclusive rates - con trol penguins!!!


Moriond 2012: Conclusion from B-Mixing

It is actually not bad, what the Grinch left for us

Expansion in 1/mb works so well,What does this tell about charm? 1/mc ≈ 3 · 1/mb


CKM−: How large are Penguins? II

Many observables in the Bs mixing system:

Elimination of ΓTheo12 via ( No hint for incorrectness of ΓTheo

12 except: Absl is 1.5σabove bound)

assl = −∆Γ

∆M

Sψφ√1− Sψφ2

·δ

not possible at that simple level, because δ 6= 1

δ =tan

(φSMs + φ∆s

)

tan(−2βSM

s + φ∆s + δpeng,SMs + δpeng,NPs

)

A.L. 1106.3200


CKM−: How large are Penguins? III

0.5 1.0 1.5 2.0 2.5 3.0Φ

- 1.0

- 0.5

0.5

1.0

1.5

2.0∆

■ Above relation can be used to determine δpeng,SMs + δpeng,NPs

■ To extract φ∆s one needs Γs,SM12

δpeng,SMs + δpeng,NPs = 10◦




φSMs = 0.22◦ ± 0.06◦

−2βs = (2.1± 0.1)◦

A.L. 1106.3200


Lifetimes: τB+/τBd in NLO-QCD I

τ1τ2

= 1 +

(Λ

mb

)3 (Γ(0)3 +

αs4π

Γ(1)3 + ...

)+

(Λ

mb

)4 (Γ(0)4 + ...

)+ ...

2002: Beneke, Buchalla, Greub, A.L., Nierste; Franco, Lubicz, Mescia, Tarantino

2004: Greub, A.L., Nierste; 2008 A.L.

E1

d

b

d

b

E2

d

b

d

b

E3

d

b

d

b

E4

d

b

d

b

d

b

d

b

u

c D1

d

b

d

b

u

c D2

d

b

d

b

u

c D3

d

b

d

b

u

c D4

d

b

d

b

u

c

D5

d

b

d

b

u

c D6

d

b

d

b

u

c D7

d

b

d

b

u

c D8

d

b

d

b

u

c D9

d

b

d

b

u

c D10

d

b

d

b

u

c D11

[τ(B+)

τ(B0d)

]

LO,NLO,HFAG10

= 1.047± 0.049 ↔ 1.063± 0.027 ↔ 1.071± 0.009


Lifetimes: τB+/τBd in NLO-QCD II

τ1τ2

= 1 +

(Λ

mb

)3 (Γ(0)3 +

αs4π

Γ(1)3 + ...

)+

(Λ

mb

)4 (Γ(0)4 + ...

)+ ...

2002: Beneke, Buchalla, Greub, A.L., Nierste; Franco, Lubicz, Mescia, Tarantino

2004: Greub, A.L., Nierste; 2008 A.L.

E1

d

b

d

b

E2

d

b

d

b

E3

d

b

d

b

E4

d

b

d

b

d

b

d

b

u

c D1

d

b

d

b

u

c D2

d

b

d

b

u

c D3

d

b

d

b

u

c D4

d

b

d

b

u

c

D5

d

b

d

b

u

c D6

d

b

d

b

u

c D7

d

b

d

b

u

c D8

d

b

d

b

u

c D9

d

b

d

b

u

c D10

d

b

d

b

u

c D11

[τ(B+)

τ(B0d)

]

LO,NLO,HFAG11

= 1.047± 0.049 ↔ 1.044± 0.024 ↔ 1.079± 0.007


Lifetimes: τB+/τBd in NLO-QCD III

τB+

τBd

− 1 = 0.0324

(fB

200MeV

)2

[(1.0± 0.2)B1 + (0.1± 0.1)B2

− (17.8± 0.9)ǫ1 + (3.9± 0.2)ǫ2 − 0.26]

with non-perturbative input from Becirevic hep-ph/0110124

B1 = 1.10± 0.20

B2 = 0.79± 0.10

ǫ1 = −0.02± 0.02

ǫ2 = 0.03± 0.01

Update urgently needed!


Lifetimes: Lifetimes of heavy hadrons

■ τ(B+)/τ(Bd): HQE seems to fit, but we need urgently more precise hadronicmatrix elements

■

τ(Bs)

τ(Bd)= 0.996...1.000 ↔ 0.969± 0.017 HFAG 2011

A.L. 1102.4274 ↔ 1.004± 0.018 LHCb-Conf2011-049

More data as well as non-perturbative matrix elements needed

■ τ(Λb), τ(Ξb) and τ(Bc): more data and further theory work (perturbative andnon-perturbative) neccessary

■ τ(D), D-mixing: work in progressBigi, Uraltsev 2001; Bobrowski, A.L., Riedl, Rohrwild 1002.4794; 1011.5608;Bobrowski, A.L. Nierste, Prill, to appearIt is not unplausible that HQE might give reasonable estimates


Theory statements about CPV in D before LHCb

b d d t,c,u d t,c,u w- t,c,ub t,c,u - nikhef · pdf fileseminar, nikhef, amsterdam a. lenz,...

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