alexey a. petrov - physics & astronomy - wayne state ...apetrov/vanderbilt2011.pdf · alexey a...

Alexey A Petrov (WSU & MCTP) Vanderbilt U Colloquium, 22 September 2011

Alexey A. PetrovWayne State University

Michigan Center for Theoretical Physics

1. Introductiona. Standard Model and why we love itb. Standard Model and why we hate it

2. Flavor-changing neutral currents and meson mixing3. Need for New Physics4. Conclusions

The physics of flavor

...with some help from S. Harris

Wednesday, September 21, 11

Flavour, also spelled flavor, in particle physics, property that distinguishes

different members in the two groups of basic building blocks of matter, the

quarks and the leptons. There are six flavours of subatomic particle within

each of these two groups: six leptons (the electron, the muon, the tau, the

electron-neutrino, the muon-neutrino, and the tau-neutrino), and six quarks

(designated up, down, charm, strange, top, and bottom).


What is “flavor”?

43

In this presentation I will mainly talk about quarks.

The secret of being a bore is to tell everything (Voltaire). Le secret d'ennuyer est celui de tout dire.

(consult Prof. T. Weiler about leptons)


http://www.britannica.com/EBchecked/topic/445074/particle-physics

http://www.britannica.com/EBchecked/topic/445074/particle-physics

http://www.britannica.com/EBchecked/topic/486323/quark

http://www.britannica.com/EBchecked/topic/486323/quark

http://www.britannica.com/EBchecked/topic/336940/lepton

http://www.britannica.com/EBchecked/topic/336940/lepton

http://www.britannica.com/EBchecked/topic/570533/subatomic-particle

http://www.britannica.com/EBchecked/topic/570533/subatomic-particle

http://www.britannica.com/EBchecked/topic/183374/electron

http://www.britannica.com/EBchecked/topic/183374/electron

http://www.britannica.com/EBchecked/topic/397734/muon

http://www.britannica.com/EBchecked/topic/397734/muon

http://www.britannica.com/EBchecked/topic/584302/tau

http://www.britannica.com/EBchecked/topic/584302/tau

http://www.britannica.com/EBchecked/topic/410889/neutrino

http://www.britannica.com/EBchecked/topic/410889/neutrino

Why flavor?

Alexey A Petrov (WSU & MCTP) Vanderbilt U Colloquium, 22 September 201142Wednesday, September 21, 11

NSF CAREER award PHY-0547794

DOE grant DE-FG02-96ER41005


Faculty Competition for Post-Doctoral Fellows

★ In case DOE reviewers of my grant are in the room, this work was really supported by...



1. Introduction

The Standard Model of particle physics is a remarkably simple and powerful construct

40Wednesday, September 21, 11


1. Introduction

The Standard Model of particle physics is a remarkably simple and powerful construct

40

Gauge symmetries: all particles are (initially) massless



The Ultimate Equation?

Something is needed to give masses to all particles



+





+ Standard Model



=


LSM =⇤

⇥

⇤�µ�i⌅µ �

g1

2YW Bµ �

g2

2⌦⇥L

⌦Wµ

⇥⇤ + LB, kin + LW, kin + LHiggs


+ Standard Model


★ Part of the Lagrangian related to matter interaction with Higgs: flavor


=


m�

mµ� 17 ,

mµ

me� 207 .

Vud � 1, Vus � 0.2, Vcb � 0.04, Vub � 0.004

md

mu⇥ 2 ,

ms

md⇥ 21 ,

mt

mc⇥ 267 ,

mc

mu⇥ 431 ,

mt

mu⇥ 1.2� 105 .


Matter sector: experimental data

38

★ Ratios of masses of quarks and leptons

- quarks

- leptons

★ Quark mixing (Cabibbo-Kobayashi-Maskawa) matrix parameters



A couple of questions...

Note that gauge forces in SM do not distinguish between fermions of different generations:

- e, µ, τ have same electrical charge- quarks have same color charge

★ Why generations? Why only 3? Are there only 3?★ Why hierarchies of masses and mixings?★ Can there be transitions between quarks/leptons

of the same charge but different generations?



A couple of questions...

Note that gauge forces in SM do not distinguish between fermions of different generations:

- e, µ, τ have same electrical charge- quarks have same color charge

★ Why generations? Why only 3? Are there only 3?★ Why hierarchies of masses and mixings?★ Can there be transitions between quarks/leptons

of the same charge but different generations?

The flavor puzzle



Standard Model “solution”

36

1. Why generations? Why only 3? Are there only 3?



Standard Model “solution”

35

1. Why generations? Why only 3? Are there only 3?‣ ???

2. Why hierarchies of masses and mixings?

3. Can there be transitions between quarks/leptons of the same charge but different generations?

L1 = �y�⇥̄L⇥R� + h.c.⇥ �y�v⇤2

�⇥̄L⇥R + ⇥̄R⇥L

⇥,

m� = y�v/�

2

No explanation of the hierarchy, but mass hierarchy is related to hierarchy of Yukawa couplings

No transitions at tree level (no interactions that change flavor w/out changing electric charge), but...

yu � 10�5, yc � 10�2, yt � 1,

yd � 10�5, ys � 10�3, yb � 10�2,

ye � 10�6, yµ � 10�3, y� � 10�2.



FCNC in the SM: GIM-mechanism

34

Let’s calculate them! For each internal quark type we get

There are no ΔQ=2 interactions in the Standard Model… … but we can make them via a “two-step process” (loop diagram):

(k2)



FCNC in the SM: GIM-mechanism

34

Let’s calculate them! For each internal quark type we get

There are no ΔQ=2 interactions in the Standard Model… … but we can make them via a “two-step process” (loop diagram):

(k2)

Divergent: not good...



GIM-mechanism

33

Thus, in the limit where k >> mi, mj, MW:

However, CKM matrix is unitary: contribution of different internal flavors comes with different signs!

top:

top-charm:

top:

top-charm:

… and similarly for other quarks

A ��

i

m2i (VisV

�ib)

2gk(m2i ) Glashow-Iliopulous-Maiani

(k2)

(k2)



Experimental consequences of FCNC

32

★ FCNC can be seen experimentally

- ΔF = 1 processes (b→sγ , c→uγ , etc)

- ΔF = 2 processes (BB-mixing, KK-mixing, DD-mixing)

M. Purohit



2. Basics of meson mixing

ΔQ=2: only at one loop in the Standard Model: possible new physics particles in the loop ΔQ=2 interaction couples dynamics of D0 and D0

Time-dependence: coupled Schrödinger equations

Diagonalize: mass eigenstates flavor eigenstates

Mass and lifetime differences of mass eigenstates:

31

|D(t)� =�

a(t)b(t)

⇥= a(t)|D0� + b(t)|D0�



Mixing: charm and beauty

mixing mixing

• intermediate down-type quarks• SM: b-quark contribution is negligible due to VcdVub

*

• (zero in the SU(3) limit)

• intermediate up-type quarks• SM: t-quark contribution is dominant

• (expected to be large)

1. Sensitive to long distance QCD2. Small in the SM: New Physics! (must know SM x and y)

1. Computable in QCD (*)2. Large in the SM: CKM!

(*) up to matrix elements of 4-quark operators

Falk, Grossman, Ligeti, and A.A.P.Phys.Rev. D65, 054034, 2002 2nd order effect!!!

30

(hard) (easy)



Lifetime differences in mesons

29

This is “theoretical data”



Lifetime differences in mesons

29

K

D

Bd

Bs

This is “theoretical data”



Mixing in mesons

28

This is “real data”



Mixing in mesons

28

K Bd

Bs

This is “real data”


⇥MBs = 2 |M12| , ⇥�Bs =4Re (M12��

12)⇥MBs


id

dt

�Bq(t)Bq(t)

⇥=

⇤M � i

2�⌅

ij

�Bq(t)Bq(t)

⇥

Easy case: Bs system

Mixing parameters are sensitive probes of flavor physics

➡ Theoretical predictions?C.Liu, FPCP 2008

★ Time development of Bs system

★ Mixing parameters (concentrate on Bs)


�21(Bs) =�

k

Ck(µ)mk

b

⇥Bs|O�B=2k (µ)|Bs⇤.

M12(Bs) =G2

F MBs

12⇥2M2

W (VtbV�ts)

2 �̂BS0(xt)f2Bs

B


Bs system: Standard Model contributions

Both ΔMBs and ΔΓBs can be computed in the limit mb→∞:

∆MBs:

∆ΓBs:

A.Buras, M.Jamin, P.Weisz

+


�21(Bs) = � G2F m2

b

12⇥(2MBs)(V �

cbVcs)2 [[F (z) + P (z)] ⇥Q⇤

+ [FS(z) + PS(z)] ⇥QS⇤ + �1/m + �1/m2�

Q = (b̄isi)V�A(b̄jsj)V�A, QS = (b̄isi)S�P (b̄jsj)S�P

Q̃ = (b̄isj)V�A(b̄jsi)V�A, Q̃S = (b̄isj)S�P (b̄jsi)S�P

⇥�Bs =�0.0005B + 0.1732Bs + 0.0024B1 � 0.0237B2 � 0.0024B3 � 0.0436B4

+ 2⇥ 10�5�1 + 4⇥ 10�5�2 + 4⇥ 10�5�3 + 0.0009�4 � 0.0007�5

+ 0.0002⇥1 � 0.0002⇥2 + 6⇥ 10�5⇥3 � 6⇥ 10�5⇥4 � 1⇥ 10�5⇥5

� 1⇥ 10�5⇥6 + 1⇥ 10�5⇥7 + 1⇥ 10�5⇥8

⇥(ps�1).

�Q⇥ = 21 + Nc

Ncf2

BsM2

BsB

⇥QS⇤ =1 � 2Nc

Nc

M4Bs

(mb + ms)2f2

BsBS


Not so easy: SM contributions to ΔΓBs

ΔΓBs: a calculation yields:

★ ... with operators

★ ... so the result (up to 1/mb2) is:

A.Badin, F. Gabbiani, A.A.P. Phys. Lett. B653, 230 (2007)

WC (incl. pQCD corr): Beneke et al, Ciuchini et al

25

}


⇥MexpBs

= (117.0± 0.8)� 10�13 GeV

or xBs = ⇥MBs/�Bs = 26.2± 0.5.�M th

Bs= (117.1+17.2

�16.4)� 10�13 GeV


SM contributions to ΔΓBs

★ Compare to experimental measurements

24

Lifetime difference:

Mass difference:

A.Badin, F. Gabbiani, A.A.P. Phys. Lett. B653, 230 (2007)



Why is ΔΓBs interesting?

★ Probes of NP phase in Bs mixing in Bs ➛ J/𝜓 𝜙

23

Standard Model: βs is tiny; NP: anything!

Standard Model wins again...R. Van Kooten, LP-2011

G. Raven, LP-2011



Difficult case: D-mixing

★ Predictions of x and y in the SM are complicated-second order in flavor SU(3) breaking-mc is not quite large enough for OPE

-x, y << 10-3 (“short-distance”)-x, y ~ 10-2 (“long-distance”)

★ Short distance:-assume mc is large

-combined ms, 1/mc, as expansions-leading order: ms2, 1/mc6!

★ Long distance:-assume mc is NOT large

-sum of large numbers with alternating signs, SU(3) forces zero!-multiparticle intermediate states dominate

H. Georgi; T. Ohl, …I. Bigi, N. Uraltsev;

J. Donoghue et. al.P. Colangelo et. al.

Falk, Grossman, Ligeti, Nir. A.A.P.Phys.Rev. D69, 114021, 2004

Resume: a contribution to x and y of the order of 1% is natural in the SM

22

A.A.P. hep-ph/0611361



Experimental consequences of FCNC: charm

21

★ D-mixing predicted in the Standard Model...

★ ... and observed in 2007!

- no-mixing is excluded at 10.1σ

x = 0.63+0.19-0.20% y = 0.75 ± 0.12 %

HFAG 2011

- observations consistent with no-CP-violation

- |x| ~ [0.1%, 1%]

- y ~ 1%

Falk, Grossman, Ligeti, Nir. A.A.P.Phys.Rev. D69, 114021, 2004

Falk, Grossman, Ligeti, and A.A.P.Phys.Rev. D65, 054034, 2002

➡ Consistent with Standard Model!!!

Johns, Sheldon, Webster



Since all FCNC cases are adequately described by the Standard Model contributions, do we need New Physics???



Do we need to search for New Physics?

19

★ Standard Model has intrinsic problem related to Higgs mechanism (stabilization of quantum effects)

- BSM stabilization (e.g. SUSY), other mechanisms of EWSB

★ Standard Model does not have enough CP-violation to describe generation of baryon asymmetry

- need for BSM sources of CP-violation

★ Standard Model adequately describes experimental FCNC data, but does not provide solution to the flavor puzzle

- BSM solution to the flavor problem?



Solutions to the flavor problem?



Need for New Physics…

★ New Physics is needed!!!

★ But of what kind?★ Multi-Higgs/LR models? ★ Supersummetry (SUSY)?★ Large extra dimensions?★ Technicolor?★ Compositeness?★ … other weird theory?

★ Ultimately: strings, M-theory?



3. Need for New Physics

★ New Physics is needed!!!

★ But of what kind?★ Multi-Higgs/LR models? ★ Supersummetry (SUSY)?★ Large extra dimensions?★ Technicolor?★ Compositeness?★ … other weird theory?

★ Ultimately: strings, M-theory?

BUT: flavor is mainly an INPUT, not OUTPUT of models




14



- study FCNC (ΔF=2 and ΔF=1 processes) to get a glimpse of NP

Standard Model Supersymmetric SM




14



- study FCNC (ΔF=2 and ΔF=1 processes) to get a glimpse of NP

or

Standard Model Supersymmetric SM

or ???



How does New Physics affect x and y in charm?

Local ΔC=2 piece of the mass matrix affects x:

13

Double insertion of ΔC=1 affects x and y:

Example:

Suppose

Amplitude

phase space

Golowich, Pakvasa, A.A.P.Phys. Rev. Lett.98:181801, 2007


µ � 1 TeV µ � 1 GeV




13


Example:

Suppose

Amplitude

phase space






13


Example:

Suppose

Amplitude

phase space






13


Example:

Suppose

Zero in the SU(3) limitFalk, Grossman, Ligeti, and A.A.P.Phys.Rev. D65, 054034, 2002 2nd order effect!!!

Amplitude

phase space






13


Example:

Suppose

Zero in the SU(3) limitFalk, Grossman, Ligeti, and A.A.P.Phys.Rev. D65, 054034, 2002 2nd order effect!!!

Can be significant!!!

Amplitude

phase space




Global Analysis of New Physics: ΔC=2

Multitude of various models of New Physics can affect x



If all of those models of New Physics affect FCNC processes, how come all of them are described by the Standard Model so well???



If all of those models of New Physics affect FCNC processes, how come all of them are described by the Standard Model so well???

The “New Physics” flavor puzzle



Global Analysis of New Physics: ΔC=2

10

Let’s write the most general ΔC=2 Hamiltonian

… with the following set of 8 independent operators…

RG-running relate Ci(m) at NP scale to the scale of m ~ 1 GeV, where ME are computed (on the lattice) Each model of New Physics

provides unique matching condition for Ci(LNP)

E.Golowich, J. Hewett, S. Pakvasa and A.A.P.Phys. Rev. D76:095009, 2007


+

�⇧

⇤

L�R

⇥⌃

⌅ +H�C=2NP =

1�2

NP

8�

i=1

zi(µ)Q�i


Example: generic restrictions on FCNC from DD-mixing

★ Comparing to experimental value of x, obtain constraints on FCNC in charm sector- assume x is dominated by New Physics - assume no accidental strong cancellations b/w SM and NP

9

★ ... which are

�NP ⇤ (4� 10)⇥ 103 TeV

�NP ⇤ (1� 3)⇥ 102 TeV

Gedalia, Grossman, Nir, PerezPhys.Rev.D80, 055024, 2009

New Physics is either at a very high scales

tree level:

loop level:

or have highly suppressed couplings to charm!

★ Constraints on particular NP models available E.Golowich, J. Hewett, S. Pakvasa and A.A.P.Phys. Rev. D76:095009, 2007


�NP ⇤ (4� 10)⇥ 103 TeV

�NP ⇤ (1� 3)⇥ 102 TeV


Imaginary parts (CP-violation)

8

★ Assume that direct CP-violation is absent ( )- experimental constraints on x, y, ϕ, |q/p| exist

- can obtain generic constraints on Im parts of Wilson coefficients

Gedalia, Grossman, Nir, PerezPhys.Rev.D80, 055024, 2009

★ In particular,

New Physics is either at a very high scales

tree level:

loop level:

or have highly suppressed couplings to charm!

★ Constraints on particular NP models possible as well

H�C=2NP =

1�2

NP

8�

i=1

zi(µ)Q�i

Bigi, Blanke, Buras, Recksiegel,JHEP 0907:097, 2009



New Physics in x: lots of extras

Extra gauge bosons

7

Extra scalars

Extra fermions

Extra dimensions

Extra symmetries

Left-right models, horizontal symmetries, etc.

Two-Higgs doublet models, leptoquarks, Higgsless, etc.

4th generation, vector-like quarks, little Higgs, etc.

Universal extra dimensions, split fermions, warped ED, etc.

SUSY: MSSM, alignment models, split SUSY, etc.


New Physics contributions do not suffer from QCD uncertainties as much as SM contributions since they are short-distance dominated.



New Physics in x: lots of extras

Extra gauge bosons

7

Extra scalars

Extra fermions

Extra dimensions

Extra symmetries

Left-right models, horizontal symmetries, etc.

Two-Higgs doublet models, leptoquarks, Higgsless, etc.

4th generation, vector-like quarks, little Higgs, etc.

Universal extra dimensions, split fermions, warped ED, etc.

SUSY: MSSM, alignment models, split SUSY, etc.

Total: 21 models considered


New Physics contributions do not suffer from QCD uncertainties as much as SM contributions since they are short-distance dominated.



Dealing with New Physics-I

6

Consider an example: FCNC Z0-boson

1. Integrate out Z: for µ < MZ get

appears in models with extra vector-like quarks little Higgs models

2. Perform RG running to µ ~ mc (in general: operator mixing)

3. Compute relevant matrix elements and xD

4. Assume no SM - get an upper bound on NP model parameters (coupling)


HRS =2�krc

3M21

g2s (C1(Mn)Q1 + C2(Mn)Q2 + C6(Mn)Q6)


Dealing with New Physics - II

5

Consider another example: warped extra dimensions

1. Integrate out KK excitations, drop all but the lightest

FCNC couplings via KK gluons

2. Perform RG running to µ ~ mc


x(RS)D =

g2s

3M21

f2DBDMD

�D

�23[C1(mc) + C6(mc)]�

16C2(mc)�

512

C3(mc)⇥

HRS =g2

s

3M21

(C1(mc)Q1 + C2(mc)Q2 + C3(mc)Q3 + C6(mc)Q6)

Constrains LHC parameter space!!!


HRS =2�krc

3M21

g2s (C1(Mn)Q1 + C2(Mn)Q2 + C6(Mn)Q6)


Dealing with New Physics - II

5

Consider another example: warped extra dimensions

1. Integrate out KK excitations, drop all but the lightest

FCNC couplings via KK gluons

2. Perform RG running to µ ~ mc


x(RS)D =

g2s

3M21

f2DBDMD

�D

�23[C1(mc) + C6(mc)]�

16C2(mc)�

512

C3(mc)⇥

HRS =g2

s

3M21

(C1(mc)Q1 + C2(mc)Q2 + C3(mc)Q3 + C6(mc)Q6)

Implies: M1KKg > 2.5 TeV!

Constrains LHC parameter space!!!



Summary: New Physics in mixing

Considered 21 well-established models

Only 4 models yielded no useful constraints


4

A.A.P. and G. YeghiyanPhys. Rev. D77:034018, 2008

★ Flavor physics provides good constraints on New Physics models!

★ ... especially if used in correlation with other measurements!

E.Golowich, J. Hewett, S. Pakvasa and A.A.P.Phys. Rev. D79: 114030, 2009

Golowich, Pakvasa, A.A.P.Phys. Rev. Lett. 98:181801, 2007



So, what about models of flavor?

3

★ Proposed BSM solutions to the flavor problem

- continuous flavor symmetries- discrete flavor symmetries- accidental flavor symmetries

★ Dynamical mechanisms

- two-Higgs doublet models: tanβ as a large parameter

SM Lagrangian is U(3)5-invariant in the limit yi → 0

- Yukawas arise as a result of spontaneous breaking of a subgroup of U(3)5?

A. Blechman, A.A.P., G. YeghiyanJHEP 1011:075, 2010

★ Work is still continuing! LHC?

(consult Prof. T. Kephart about flavor models)



Flavor as a probe of New Physics: anomalies?

2

Simplest decay of heavy-flavored meson: B ➛ τ𝜈

Only one non-perturbative parameter fBs = 250(12) MeV (~5%)

Harbinger of New Physics?

Two-Higgs doublet model:



Before we conclude:

1

★ Are there more than three generations of quarks?

H. Bachacou, LP-2011

Higgs production at LHC is via gg ➛ H - extremely sensitive to 4th

generation quarks

H

g

g



Before we conclude:

1

★ Are there more than three generations of quarks?

Sequential 4th generation is in trouble...

H. Bachacou, LP-2011

Higgs production at LHC is via gg ➛ H - extremely sensitive to 4th

generation quarks

H

g

g



4. Conclusions

Flavor puzzle is still a big problem for particle physics– The reason(s) for generations and mass hierarchy are not known– Standard Models simply parameterizes the solution– New Physics models use flavor as input, not output

Flavor-changing neutral current transitions provide great opportunities for studies of flavor in the SM and BSM– several anomalies in Bs physics might point to New Physics “around the corner”– studies of charmed transitions experience explosive growth

• unique access to up-type quark sector• large available statistics/in many cases small SM background • D-mixing is a second order effect in SU(3) breaking (x,y ~ 1% in the SM)• large contributions from New Physics are possible, but not seen

Maybe flavor physics will be the first to see glimpses of New Physics Maybe flavor physics will be the only game in town to see New Physics...



Thank you for your attention!



Thank you for your attention!

0

Hopefully, I did better than him...



Additional slides



Full Standard Model contains CP violation!



Conditions for the asymmetry

Baryon (and lepton) number - violating processes

to generate asymmetry

Universe that evolves out of thermal equilibrium

to keep asymmetry from being washed out “Microscopic CP-violation”

to keep asymmetry from being compensated in the “anti-world”

Matter-antimatter imbalance in the UniverseA.D. Sakharov



2. What is CP(T)?



2. What is CP(T)?

P: parity (inversion of space)



2. What is CP(T)?


C: charge conjugation



2. What is CP(T)?


C: charge conjugation

T: time reversal



Can Standard Model violate CP?

Strong and electromagnetic interactions conserve C, P and T

All interactions (local QFT) conserve combination CPT

Weak interactions violate P and C… what about CP?

But: if SM contains operators with complex phases then there just might be CP violation in the Standard Model!



How to observe CP-violation?

I. Intrinsic particle properties electric dipole moments:




I. Intrinsic particle properties electric dipole moments:

Low energy strong interaction effects might complicate predictions!



5. CP-violation (preliminary)

16

In any quantum field theory CP-symmetry can be broken1. Explicitly through dimension-4 operators (“hard”)

Example: Standard Model (CKM):

2. Explicitly through dimension <4 operators (“soft”)

Example: SUSY

3. Spontaneously (CP is a symmetry of the Lagrangian, but not of the ground state)

Example: multi-Higgs models, left-right models

These mechanisms can be probed in charm transitions



CP-violation in charmed mesons Possible sources of CP violation in charm transitions:

CPV in Δc = 1 decay amplitudes (“direct” CPV)

CPV in mixing matrix (Δc = 2)

CPV in the interference of decays with and without mixing

15

One can separate various sources of CPV by customizing observables



A comment

14

Generic expectation is that CP-violating observables in the SM are small

Δc = 1 amplitudes Δc = 2 amplitudes

The Unitarity Triangle for charm:

Penguin amplitude



A comment

14

With b-quark contribution neglected: only 2 generations contribute real 2x2 Cabibbo matrix

Any CP-violating signal in the SM will be small, at most O(VubVcb*/VusVcs

*) ~ 10-3

Thus, O(1%) CP-violating signal can provide a “smoking gun” signature of New Physics

Generic expectation is that CP-violating observables in the SM are small

Δc = 1 amplitudes Δc = 2 amplitudes

The Unitarity Triangle for charm:

Penguin amplitude




13

There exists a variety of CP-violating observables

1. “Static” observables, such as electric dipole moment

2. “Dynamical” observables:

a. Transitions that are forbidden in the absence of CP-violation

b. Mismatch of transition probabilities of CP-conjugated processes

c. Various asymmetries in decay distributions, etc.

Depending on the initial and final states, these observables can be affected by all three sources of CP-violation


D0D0 � (F1)(F2)�(3770)� D0D0 � (CP±)(CP±)

CP [F1] = CP [F2]

�F1F2 =�F1�F2

R2m

⇤�2 + x2 + y2

⇥|�F1 � �F2 |2 +

�x2 + y2

⇥|1� �F1�F2 |2

⌅


a. Transitions forbidden w/out CP-violation

★ Recall that CP of the states in are anti-correlated at ψ(3770):★ a simple signal of CP violation:

★ CP-violation in the rate → of the second order in CP-violating parameters.★ Cleanest measurement of CP-violation!

CP eigenstate F1

CP eigenstate F2

τ-charm factory

12

I. Bigi, A. Sanda; H. Yamamoto; Z.Z. Xing; D. Atwood, AAP


DCP (+) � f1f2

Bl± =

�(DCP± � Xl�)�tot

y cos � =14

�Bl

+

Bl��

Bl�

Bl+

⇥


★ If CP violation is neglected: mass eigenstates = CP eigenstates★ CP eigenstates do NOT evolve with time, so can be used for “tagging”

KS

π0

CP Eigenstate (-)

f1

f2

★ τ-charm factories have good CP-tagging capabilities CP anti-correlated ψ(3770): CP(tag) (-1)L = [CP(KS) CP(π0)] (-1) = +1 CP correlated ψ(4140)

(-)

τ-charm factory (BES/CLEO-c)

Can measure (y cos φ): D. Atwood, A.A.P., hep-ph/0207165D. Asner, W. Sun, hep-ph/0507238

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What if F1 or F2 is not a CP-eigenstate



b. Mismatch of transition probabilities

Look at charged D’s:

10

At least two components of the transition amplitude are required

Then, charge asymmetry will provide a CP-violating observable

…or, introducing rf=|A2/A1|:Prediction sensitive to details of hadronic model

Same formalism applies if one of the amplitudes is generated by New Physics

need rf ~ 1 % for O(1%) charge asymmetry



b. Mismatch of transition probabilities - II

Those observables are of the first order in CPV parameters, but require tagging

9

This can be generalized for neutral D-mesons too:

and

Each of those asymmetries can be expanded as

direct mixing interference

1. similar formulas available for f2. for CP-eigenstates: f=f and yf’ → y


alexey a. petrov - physics & astronomy - wayne state ...apetrov/vanderbilt2011.pdf · alexey a...

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