Alexey A. Petrov Wayne State University

Alexey Petrov (WSU) ITEP Meeting, July 24-25, Moscow

Alexey A. Petrov

Wayne State University

Table of Contents:

• Introduction• Mixing: theoretical expectations

• Standard Model• New Physics

• Mixing: current/future experimental constraints• Conclusions and outlook

Physics of charm: mixing and CP-violation

27


Charm transitions serve as excellent probes of New Physics

1. Processes forbidden in the Standard Model to all orders

Examples:

2. Processes forbidden in the Standard Model at tree level

Examples:

3. Processes allowed in the Standard Model

Examples: relations, valid in the SM, but not necessarily in general

0D p

XDXDDD ,,mixing00

1. Introduction: charm and New Physics

26

CKM triangle relations


D-mixing is our last chance to see New Physics in meson oscillations!!!

25

With the recent measurement of ms in Bs-mixing…


Introduction: mixing

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

00 )()()(

)()( DtbDta

tb

tatD

)()(2

)(2

2

tDAq

pAtD

iMtD

ti

Time-dependence: coupled Schrödinger equations

002,1 DqDpD

Diagonalize: mass eigenstates flavor eigenstates

2

, 1212 yMM

xMass and lifetime differences of mass eigenstates:

24


Introduction: mixing

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

00 )()()(

)()( DtbDta

tb

tatD

)()(2

)(2

2

tDAq

pAtD

iMtD

ti

Time-dependence: coupled Schrödinger equations

Diagonalize: mass eigenstates flavor eigenstates

2

, 1212 yMM

xMass and lifetime differences of mass eigenstates:

1 0 0No CPV:1,2 2

D D D DCP

24


Introduction: why do we care?

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!

00 DD 00 BB

)()( ds mfmfrate 2tmrate

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

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

2nd order effect!!!

23


2. Mixing: theoretical estimates

Theoretical predictions are all over the board… so:

Can x,y ~ 0.5% be a SM signal?

What is the relationship between x and y (x ~ y, x > y, x < y?) in the Standard Model? • x from new physics

� y from Standard Model Δ x from Standard Model(papers from SPIRES )

Standard Model mixing predictions

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1 4 7 10 13 16 19 22 25 28 31 34 37 40

Reference Index

|x|

or

|y|

New Physics mixing predictions

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

Reference Index

|x|

Updated predictionsA.A.P. hep-ph/0311371

22

Is mc large???


Theoretical estimates I

A. Short distance gives a tiny contribution

… as can be seen form a “straightforward computation”…

with .,2

41 2200 etcB

m

mF

N

NDcucuD D

D

DD

C

C

mc IS large !!!

21

Notice, however, that at NLO in QCD (xNLO,yNLO) >> (xLO, yLO) :

Similar for x (trust me!)Example of NLO contribution E. Golowich and A.A.P.Phys. Lett. B625 (2005) 53

6 6

4 4

s

s

m

m

2

2s

c

mz

m

… xLO >> yLO !!!

xNLO ~ yNLO!


Theoretical estimates I

A. Short distance + “subleading corrections” (in {ms, 1/mc } expansion):

4422

222)6(

6622

22

2

222)6(

shadc

dssd

shadc

ds

c

dssd

mm

mmx

mm

mm

m

mmy

…subleading effects?

2 unknown matrix elements

33)9(

33)9(

ssd

ssd

mx

my15 unknown matrix elements

22)12(

2220

)12(

sSsd

ssd

mx

myS

Twenty-something unknown matrix elements

Guestimate: x ~ y ~ 10-3 ?Leading contribution!!!

H. Georgi, …I. Bigi, N. Uraltsev

20


Resume: model-independent computation with model-dependent

result

19


Theoretical estimates II

B. Long distance physics dominates the dynamics…

KDBrKDBr

DBrKKDBry

00

002

cos2

If every Br is known up to O(1%) the result is expected to be O(1%)!

mc is NOT large !!!

… with n being all states to which D0 and D0 can decay. Consider K, KK intermediate states as an example…

01100110

2

1DHnnHDDHnnHDy C

WC

WC

WC

Wn

n

cancellation expected!

The result here is a series of large numbers with alternating signs, SU(3) forces 0

x = ? Extremely hard…

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

Need to “repackage” the analysis: look at the complete multiplet contribution

18


Results

• No (symmetry-enforced) cancellations• Disp relation: compute x (model-dependence)

naturally implies that x,y ~ 1% is not excluded in the Standard Model

17

E.Golowich and A.A.P.Phys.Lett. B427, 172, 1998

A.F., Y.G., Z.L., Y.N. and A.A.P.Phys.Rev. D69, 114021, 2004

Lifetime difference for a multiplet

Fraction for a multiplet


Resume: model-dependent computation with model-dependent result

16


How would New Physics affect x and y?

I ID

jC

WC

Wi

Dj

CWi

DijD

ij imm

DHIIHD

mDHD

mm

iM

22

0110

020)0(

2

1

2

1

2

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

15

Double insertion of C=1 affects x and y:

0 1 1C C SM NPn SM NP n nA D H H n A A

Example: 1 1 1

2 2 2

SM NP SM SM NPSM NP SM NP SMn n n n nn n n n n n n n

n n n

y A A A A A A A A A A

exp. uncertainty 10%NP SMn nA A O Suppose

1TeV 1GeV

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


14

New Physics in mixing

1TeV

1GeV

Multitude of various models of New Physics can affect x

1TeV


Global Analysis of New Physics in x

13

Let’s write the most general C=2 Hamiltonian

… with the following set of 9 independent operators…

1GeV

1TeV

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

E.Golowich, J. Hewett, S. Pakvasa and A.A.P.

Each model of New Physics provides unique matching condition for Ci(NP)


New Physics in x and y: lots of extras

Extra gauge bosons

12

Extra scalars

Extra fermions

Extra dimensions

Extra global symmetries

Left-right models, horizontal symmetries, etc.

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

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

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

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

Example: two-Higgs doublet model:

2 2

22 4,2

tan ,2

C F WR Rub cb HH b H c L L

G mH V V A x x x u c u c

1LL

NPC 1LL

NPQ

E.Golowich, J. Hewett, S. Pakvasa and A.A.P.


Summary of theoretical estimates

• x from new physics

� y from Standard Model Δ x from Standard Model(papers from SPIRES )

Standard Model mixing predictions

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1 4 7 10 13 16 19 22 25 28 31 34 37 40

Reference Index

|x|

or

|y|

New Physics mixing predictions

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

Reference Index

|x|

Updated predictionsA.A.P. hep-ph/0311371

11


3. Experimental constraints on mixing

2

1sincos1 m

CP

Rxy

KKD

KDy

1. Time-dependent or time-integrated semileptonic analysis

2. Time-dependent analysis (lifetime difference)

3. Time-dependent analysis KtD )(0

22 yxrate Quadratic in x,y: not so sensitive

KKtD )(0

Sensitive to DCS/CF strong phase

Idea: look for a wrong-sign final state

sincos',sincos' xyyyxx

2222

20

4sin'cos')( txy

RtxyRRRAeKtD m

mK

t

2

2 ,m

qR

p

10


What if time-dependent studies are not possible I?

f3

f1

f2

1 2D f f

0 0 00 0 01 2 2 1

1

1( ) ( ) ( ) ( )

2LD D D k D k D k D k

-charm factory (BES/CLEO-c)

3 4D f f

f4

Time-integrated analysis: DCSD contribution cancels out for double-tagged

decays!

KD0

))((00 KKDD

0000200

2

1

2

1DDΗKKDDΗKKKDDA effeff

CF DCS

2

2

222

2 q

pr

q

pyx

KK

KKR D

Quadratic in x,y: not so sensitive wanted: linear in x or y

H. Yamamoto; I. Bigi, A. Sanda

9


What if time-dependent studies are not possible II?

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

KS

0

CP Eigenstate (-)

f1

f2

21)( ffDCP

)()()1()()(

2

11

0

20

2

0

1000 kDkDkDkDDD L

L

-charm factories have good CP-tagging capabilities CP anti-correlated (3770): CP(tag) (-1)L = [CP(KS) CP(0)] (-1) = +1 CP correlated (4140)

(-)

-charm factory (BES/CLEO-c)

Can still measure y: tot

CPl XlDB

l

l

l

l

B

B

B

By

4

1cos

D. Atwood, A.A.P., hep-ph/0207165D. Asner, W. Sun, hep-ph/0507238

8


CP violation in charm

7


4. How would CP violation manifest itself in charm?

Possible sources of NP in CP violation in charm transitions:

CPV in decay amplitudes (“direct” CPV)

CPV in mixing matrix

CPV in the interference of decays with and without mixing

f

fim

f

ff A

AeR

A

A

p

q

fDAfDA

00 DD

12

2

1212

1212

2

2

iM

iM

q

pRm

6

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

At this point CP-violating signal is a “smoking gun” signature of New Physics


CP violation: experimental constraints

2

2

1

1

CP

f f

f f

D f D fA f

D f D f

A A

A A

1. Standard analysis: rate asymmetries

Mode E791, % FOCUS, % CLEO, %

D0 → K+K- -1.0±4.9±1.2-

0.1±2.2±1.5

0.0±2.2±0.8

D0 → +- -4.9±7.8±3.04.8±3.9±2.

51.9±3.2±0.

8

D0 → KS0 0.1±1.3

D0 → 0+K- -3.1±8.6… which is of the first order in CPV parameters, but requires tagging

2. Recall that CP of the states in are anti-correlated at (3770):

a simple signal of CP violation:

2222222 2121

21

2112

2 FFFFm

FFFF yxyx

R

))((3770 00 CPCPDD))(( 21

00 FFDD

f

ff A

A

p

q … which is of the second order in CPV parameters, i.e. tiny

5


CP violation: new experimental possibilities

Look for CPV signals that are 1. first order in CPV2. do not require flavor

tagging

Consider the final states that can be reached by both D0 and

D0, but are not CP eigenstates (, KK*, K, K, …)

where

,f fU

CPf f

A f t

0 0f D f t D f t

A.A.P., PRD69, 111901(R), 2004hep-ph/0403030

4


CP violation: untagged asymmetries

Expect time-dependent asymmetry…

0

0

iA D f

ReA D f

2 22 22 sin sin cos cos ,f ff f

B y R A A A A

21,U t

CPA f t e A B t C tD t

… whose coefficients are computed to be

22 22 21 1 ,f ff f f

A A A A R A A

This is true for any final state f

2

.2

xC A

… and time-integrated asymmetry 1

, 2UCPA f t A B C

D

3


CP violation: untagged asymmetries (K+)

For a particular final state K, the time-integrated asymmetry is simple

This asymmetry is1. non-zero due to large SU(3) breaking2. contains no model-dependent hadronic parameters (R and are experimental

observables)3. could be as large as 0.04% for NP

sin sinUCPA K y R

Note: larger by O(100) for SCS decays (, …) where R ~ 1

A.A.P., PRD69, 111901(R), 2004hep-ph/0403030

2


Conclusions

Charm provides great opportunities for New Physics studies– large available statistics – mixing: x, y = 0 in the SU(3) limit (as V*

cbVub is very small)– mixing is a second order effect in SU(3) breaking– it is conceivable that y ~ x ~ 1% in the Standard Model– it is possible for y to be dominated by New Physics

Quantum coherence will allow CLEO-c/BES to perform new measurements of strong phases in charm mixing studies– important inputs to time-dependent studies of mixing and 1/

Quantum coherence will allow BES/CLEO-c to perform new studies of mixing – no DCSD contamination in double-tag K studies– new mixing measurements unique to tau-charm factories

Observation of CP-violation or FCNC transitions in the current round of experiments provide “smoking gun” signals for New Physics - untagged asymmetries are more sensitive to CPV

1


Additional slides

0


Questions:

1. Can any model-independent statements be made for x or y ?

2. Can one claim that y ~ 1% is natural?

What is the order of SU(3) breaking? i.e. if what is n?

nsmyx ,

-1


Theoretical expectations

At which order in SU(3)F breaking does the effect occur? Group theory?

))(())(())(())((

))(())(())(())((

))(())(())(())((

))(())(())(())((

21

2111

116

21

2111

1115

sdcussucdssscussucss

ddcusducdsdscududsO

sdcussucdssscussucss

ddcusducdsdscududsO

0000 DHHDDHHD WWWW

is a singlet with that belongs to 3 of SU(3)F (one light quark)

Introduce SU(3) breaking via the quark mass operator

ijkkji Heiqqcq 33615333..,

All nonzero matrix elements built of must be SU(3) singlets

iDD

The C=1 part of HW is

),,( sduij mmmdiagM

ij

ijki MHD ,,

-2



0000 DHHDDHHD WWWW

note that DiDj is symmetric belongs to 6 of SU(3)F

36152486

D mixing is prohibited by SU(3) symmetry

Explicitly,

WW HH6

'154260

6

OOOHH

DDD

WW

1. No in the decomposition of no SU(3) singlet can be formed

2. Consider a single insertion of transforms as still no SU(3) singlet can be formed

MDM ij 6

NO D mixing at first order in SU(3) breaking

3. Consider double insertion of

6)361524(

)61515244260()88(6:

SDMMM

D mixing occurs only at the second order in SU(3) breaking

A.F., Y.G., Z.L., and A.A.P.Phys.Rev. D65, 054034, 2002

-3


Quantum coherence: supporting measurements

2222

20

4sin'cos')( txy

RtxyRRRAeKtD m

mK

t

Time-dependent analysis KtD )(0

2

K

K

A

AR

sincos'

sincos'

xyy

yxx

A. Falk, Y. Nir and A.A.P., JHEP 12 (1999) 019

Strong phase can be measured at CLEO-c!

where and

Strong phase is zero in the SU(3) limit and strongly model-dependent

KDAKDAKDA CP

002

KDBrR

KDBrKDBr CPCP02

cos With 3 fb-1 of data cos can be

determined to | cos | < 0.05!Silva, Soffer;Gronau, Grossman, Rosner

-4



iSUi AA )3(

KDandD 44 00

Most probably don’t exists…

• If SU(3) breaking enters perturbatively, it is a second order effect…

• Known counter-example:

1. Very narrow light quark resonance with mR~mD

RD

DR

RD

DR

mmm

g

mm

gyx

020

2

2

22

2

2~~,

• What happens if part of the multiplet is kinematically forbidden?

see E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998

Example: both are from the same multiplet, but the latter is kinematically forbidden

see A.F., Y.G., Z.L., and A.A.P.Phys.Rev. D65, 054034, 2002

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

-5


CP violation: new experimental possibilities 1

1. Time dependent (lifetime difference analysis):

separate datasets for D0 and D0

This analysis requires 1. time-dependent studies2. initial flavor tagging (“the D* trick”)

0 0

0 0cos sin

2m

CP

D K K D K K AA f y x

D K K D K K

KKtD )(0

Cuts statistics/sensitivity

-6


SU(3) and phase space

RRR FnF

RFRF

RF nDyFDBryy 0,

0,

1~

• “Repackage” the analysis: look at the complete multiplet contribution

• Does it help? If only phase space is taken into account: no (mild) model dependence

Each is 0 in SU(3)y for each SU(3) multiplet

R

R

R

R

Fn

FnWnW

FnWnW

FnWnW

RF

nD

DHnnHD

DHnnHD

DHnnHD

y

)( 0

00

00

00

,

if CP is conserved

Can consistently compute

-7


Example: PP intermediate states

,,,6

1,

6

1,

,,,3

1,

2

1,

2

1

00

0000021

2

8, 0

KKKKKK

KsAAN

• n=PP transforms as , take 8 as an example:

• This gives a calculable effect!

Numerator:

1. Repeat for other states2. Multiply by BrFr to get y

182788 S

Denominator:

)(,2

1,,

6

1 21

0002

8, 0sOKKKAAD

421

8,

8,8,2 108.1038.0 s

A

Ay

D

N

phase space function

-8

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Alexey A. Petrov Wayne State University