beach 2004, iit, chicago alexey petrov (wayne state univ.) alexey a. petrov wayne state university...

Alexey Petrov (Wayne State Univ.)

BEACH 2004, IIT, Chicago

Alexey A. Petrov

Wayne State University

Table of Contents:

• Introduction• Mixing: current/future experimental constraints• Mixing: theoretical expectations• CP violation in charm• Conclusions and outlook

Mixing and CP violation in charm



Murphy’s law:

Modern charm physics experiments acquire ample statistics; many decay rates are quite large.

THUS:

It is very difficult to provide model-independent theoretical description of charmed quark

systems.

Introduction

27



Charm transitions serve as excellent probes of New Physics

1. Processes forbidden in the Standard Model to all orders (or very rare)

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

0 0,D p D e

XDXDDD ,,mixing00

1

0

0

D

D

Introduction: charm and New Physics

26



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:

25



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

25



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!!!

24



How would new physics affect mixing?

I ID

jC

WC

Wi

Dj

CWi

DijD

ij imm

DHIIHD

mDHD

mm

iM

22

0110

020)0(

2

1

2

1

2

Real intermediate states, affect both x and y Standard Model

1. : signal for New Physics? : Standard Model?

2. CP violation in mixing/decay

yx yx

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

)()(2

)(2

2

tDAq

pAtD

iMtD

ti

Look again at time development:

Expand mass matrix:

Local operator, affects x, possible new phsyics

00 DD

new CP-violating phase

23



How would CP violation manifest itself in charm?

Possible sources of 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

22



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

21



Example: experimental constraints on yCP

Several groups have measured yCP

Experiment Value, %

FOCUS (2000) 3.4 ± 1.4 ± 0.7

E791(2001) 0.8 ± 2.9 ± 1.0

CLEO (2002) -1.2 ± 2.5 ± 1.4

Belle (2002) -0.5 ± 1.0 ± 0.8

BaBar (2003) 0. 2± 0.5 .

Belle (2003) 1.2 ± 0.7 ± 0.4

BaBar (2003, K+K-)

1.2 ± 0.7 ± 0.4

BaBar (2003, +-) 1.7 ± 1.2 .

0.50.4

1.20.6

World average: yCP = (0.9 ± 0.4)%

a. What if time-dependent studies are not possible?b. What are the expectations for x and y?

B. Yabsley

20



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 (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

19



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

CLEO-c has good CP-tagging capabilities CP anti-correlated (3770): CP(tag) (-1)L = [CP(KS) CP(0)] (-1) = +1 CP correlated (4140)

(-)

-charm factory (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/0207165

18



Mixing: theoretical estimates

Theoretical predictions are all over the board… so:

Can x,y ~ 1% be convincingly accommodated?

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

17



Theoretical estimates I

A. Short distance gives a tiny contribution, consider y as an example

22 2 2 22 22 1 2 14 2

' 2 2 22 1 1

2 22 2

12

2

2 2 1 21 2

1 2 1

s dC s dsd D C

C c c

C CD DC

C D Cc u

m mN m my X C C C C N

N m m

N NB M C C CN

N B C C Nm m

001DΤD

my

D

… as can be seen form the straightforward computation…

with .,2

41 2200 etcB

m

mF

N

NDcucuD D

D

DD

C

C

4 unknown matrix elements

similar for x (trust me!)

mc IS large !!!

16



Theoretical estimates I

A. Short distance + “subleading corrections” (in 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?

4 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

15



Resume: model-independent computation with model-dependent

result

14



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

13



Resume: model-dependent computation with model-dependent result

12



Theoretical expectations

Let’s compute both x and y. Consider the correlator

4 0 D

D

i q p zp D w w Dq i d z D p T H z H D p e

1

2 2Dp DD

ip m

m

pD(q) is an analytic function of q. To write a disp. relation, go to to

HQET:

A. Falk., Y. Grossman, Z. Ligeti, Y. Nir and A.A.P., hep-ph/0402204

...D p mv m H v

1 2

( ) ( )4 ˆ ...2

c cim v z im v zc cFw cq uq i i w v v

i

GH V V C O H e h e h

Now we can interpret pD(q) for all q

11




…this implies for the correlator

4 ( ) ( )

4 ( ) ( )

ˆ ˆ, 0

ˆ ˆ, 0 ...

D c

D

D c

i q p m v z c cp w v w v

i q p m v z c cw v w v

q i d z H v Te H h z H h H v

i d z H v Te H h z H h H v

2v q m E i E

HQ mass dependence drops out for the second term, so for v(q) = p

D(q)/mD

2

1

2QCD

Dm

Em P dE O

E m E

mass and width difference of a heavy meson with mass E

Rapidly oscillates for large mc

Thus, a dispersion relation

Compute , then find m!

10



Results:

Product is naturally O(1%)No (symmetry-enforced) cancellations

Naturally implies that y ~ 1%! What about x?A.F., Y.G., Z.L., and A.A.P.Phys.Rev. D65, 054034, 2002

RRR FnF

RFRF

RF nDyFDBryy 0,

0,

1~From each

multiplet:

9



Results: m/=x/y:

Computation naturally implies that y ~ x ~ 1%!

2

1R R R

R

R R R

F F FF

F D F D F Dm

x y E EdEr

y E m y m m

Also:

1. Assume 2-parameter model for

2. Compute rF for 4-body and 2-body intermediate multiplets

3. Model dependence remains…

/ forD Dg E E m E m

A. Falk., Y. Grossman, Z. Ligeti, Y. Nir and A.A.P., hep-ph/0402204

8



A bit more about CP violation in charm

7



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

6



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

5



CP violation: new experimental possibilities 2

2. 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 quite possible that y~ x ~ 1% in the Standard Model

Expect new data from BaBar/Belle/CLEO-c/CDF 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

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

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




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



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

-4



: 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

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

-5



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

beach 2004, iit, chicago alexey petrov (wayne state univ.) alexey a. petrov wayne state university...

Documents

introduction mixing

mixing q

mixing matrix cpv

standard model examples

possible new phsyics

possible new physics

y standard model

mass matrix