A summary of the CP working group

Nuclear PhysicsB (Proc. Suppl.) 13 (1990)505-513 North-Ilolland

505

A SUMMARY OF T H E CP W O R K I N G G R O U P t A. I. SANDA* RockfeUer University New York, N.Y. 10021 USA

perimental study of C P violation during the past year.

I. I N T R O D U C T I O N

•

The C P working group of the workshop covered

•

I

First, non-vanmhing en/e has been reported:

wide range of topics which are under current investie~/e ----(3.3 4- 1.1) x 10 -3

gation. They consist of a new search for C P violation in K £ -~ 7r° + e+ + e-decay, attempts to clearify theoretical predictions for B meson decay asymmetries, as

Second, a new upper limit for the neutron electric

well as physics of 4th generation quarks.

dipole moment (edm) has been anounced 2

Here we sum.,r.~i~e .-,~rious contributions to the workshop with more emphasis on giving physical un-

edm = ( - 6 4- 4 4- 2) x 10 -2~

derstanding of the issues and results. Readers are refered to individual contributions for details.

The nonvanishing el/e will rule out the super ~veak model of CP violation. 3 If CP violating interaction is

2. OVERVYEW

due to an exchange of Higg's boson, it tends to generate

There have been considerable progress in the ex-

edm

e/,

a large edm. Since this type of models have several free

Br(K/; --* ~r° + e + + e - )

( - 6 4- 4 4- 2)x10 -26 (3.3 i 1.1) × 10 -3 ezpectedsensitivity :I0 -1]

EXP

B asymmetry ? ?

Spont. CP

> 10 -25

< .05

L-R

0(10-2~)

adjust parameter

?

small

KM

< I0 - s l

(8 - I) x I0 - s

O(10 -11)

.12 - . 6 0

0

0

0

0

Sup. Weak

"

Table 1. The current status of experiments and theoretical models concerning CP violation

t Members of the working group: G. Eilam, 3. Flynn, J. M. Gerard, M. GI/ick, M. Gronau, K. Kang, B. Kayser, H. Lipkin, L. Randal A. Sanda, A. Soni. , Supported in part by the DOE Contract number D~AC-0~-87ER-40325 TASKB,the NSF Grant number INT-8613131, and the Rockefeller Weizmann exchange program. 0920-5632/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

A.L Sanda / Conveaor's summary: A summary of the CP working group

506

parameters, it is difficult to mathematically exclude them. The simplest version of the model which gives a

There are two types of "penguin" diagrams which may contribute to K -+ ~r~r decay:

precise lower bound for the edm4

W-

W°

edm > 10-25

fgl

is excluded by the measurment. The Left-Right symmetric models also have several free parameters and

q

q

q

t

q

not much can be said about their fate at this time. The Kobayashi-Maakawa model (KM) is not without ambiguities.

The parameters associated with

Fig.

1 The QCD and EM penguin graphs con-

tributing to d.

strong interaction matrix elements of weak operators as well as the top quark mass rn~ give uncertainties

At first, one might suspect that the electromagnetic

and thus it is not possible to make precise predictions.

(EM) penguin contribution is small ¢ompazed to the

The nonvanishing d/e as well as the new upper limit

QCD penguin by the factor of a / a s . There are how-

of the edm are, however, very encouraging for the KM

ever, couple of enhancement factors ior the EM pen-

model. The present status of the various models are

guin over that of QCD. Let us start with the definition

s,,mmarized in table I together with their experimen-

ore'.

tal prospects. d =

How can we put these models to fur thel"experimen-

i ~ei($z_$0){ I m A o . I m A z , 20~/2 " ReAo t- R---~z J

tal test? It is likely that experimen~,~ can be sensitive to the branching ratio for the CP violating decay at

where AI is the amplitude for K --* 7rlr with the two

the level ofs

pious in the isospin I state. Since

B r ( g £ ~ ¢r° + e + + e-) ~ 10- n in the next few years. Note also that certain CP asymmetries in B meson decays are as large as ( 1 0 - 60) percent. If precise predictions for these asymmetries can be made, it will be crucial in eliminating some of these models.

[ ReA2 [~ ~0 [aeAo [, the second term is enhanced by a factor of 20 over the first term. Next, note that QCD penguin contributes only to the first term, while EM penguin contributes to both, since the electromagnetic current has both I=0 and I=1 componets. Thus the EM penguin contribution to IrnA2 gets the factor of 20 enhancement. Also,

In the CP working group, we have focused our investigation to several aspects of K~ --+ ~ra + • + + e-decay, d/e, and B meson decays.

it is well known that (V-A)(V+A) componet of the penguin operators give ~se to a matrix element of the type (Ir¢c [ (~7-u 4- dT_d)(gT+d) I K).

2. THE EM PENGUIN CONTRIBUTION TO d/e The vacuum saturation approximation in evaluating

A . L Sanda / Convenor's summary: A s u m m a r y o f the C P working group •

.

the matrix element gives terms proportional to

507

6

1.25

.25

f v 4- f , ~

KL

,,~

7/.0

KL

Thus the isovector component of the EM penguin gets

~

r

another factor of 5 boost compared to the isoscalar

7/.0

e,

component of the QCD and EM penguins. Above is a rough argument why the EM penguin

(o)

diagram must be included in the analysis of d/e to-

(b)

gether with the QCD penguins. The reader is refered to Flynn and Randal's contribution to this workshop for details. It can be seen there that the EM penguin contribution to el/e can be as much as 20 percent of the

Fig 2. The two-photon CP onserving, and the onephoton CP violating decayamplitudes.

QCD penguin contribution. It shuld be noted also that the relative sign between the QCD and EM penguins

At first it was thought that the contribution from Fig.

changes depending on the top quark mass.

2a is negligible:

It is clearly important to include EM penguin con-

B r ( K L --* Ir°'y7 --~ ~r°ec) ~ 10-is

tribution in computing d. It is, however, likely that its presence will be over shadowed by the theoretical

compared to that from Fig. 2b,

ambiguity in computing the matrix element.

Br(KL ~

7r°~ - ~ 7r°ee) ~ 1 0 - 1 1

3. KL --* 7r° + e+ + e-DECAY The nonvanishing d / e signals exisitence of AS = 1 CP violating interaction.

This is in contrast with

AS = 2 CP violating interaction which is confined to the matrix element (K I H I [~'). For all milli-weak models of CP violation, non-vanishlng c p s i l o n l / e p s i l o n is essential. A possible alternative way of checking the predictions of the miUi-weak theories is to look for I ( L ~ 7r° + e + + e-decay. One photon exchange con-

tribution to this decay is CP violating. Also one might suspect that the CP violating effect is not kinemvtically suppressed in this process, unlike the case for d/e where there is a factor of 1/20 suppression from the A I = 1/2 rule. TLe amplitude for K L -~

theory. A second evaluation of Fig. 2a based on the vector dominance model, however, showed that terms which are higher order in chiral perturbation theory gave non-negligible contribution,s At this stage, it is not very fruitful to attempt to reach any theoretical conclusion on this issue. We should wait for the experimental result for KL -* 7r°77 decay which will enable us to give a lower bound on the CP conserving KL ~ lr°

+

e +

-I- c-decay. Henceforth, we dis-

cuss only the CP violating contribution, hoping that I(L ~ 7r°77 decay measurement will enable us to conelude that K L ~ ~r° -I- e + + e-decay is dominated by Fig. 2b.

u ° + e+ +

e-decay has

both CP conserving (Fig. 2a) and violating (FiK. 2b) components.T

This conclusion was based on the chiral perturbation

The branching ration for CP violating 17, 1Z, WW contribution 9 to K L ~ 7r° + e + + e-have been studied by many authors.1° The amplitude for the one photon

A.L Sanda / Convenor's summary: A summary of th~ CP working group

508

decay consists of two parts as shown in Fig. 3. Fig. 3a

at all, since the long distance hadronic contribution is

is a contribution where CP is violated in the K --*/~"

very important here. For example, K s --* lr°p° --* ~r°ee

mass mixing amplitude - the part which is of little in-

gives an absrptive paxt to ReCT.

terest. Fig. 3b represents the direct CP violation. Our

naively state:

Thus we can not

aim is to establish the presence of this contribution. IV(K1 --* 7r°oee) ] 1/2 ReCT ,~ t p ( K + ~ lr ee) as it is done by Dib et. al. in ref.11. Note that the phase of ReC7 is crucial in estimating the size of the K/; --~ 7r° + e + + e-branching ratio. This issue of long

e"

e-

(o}

distance contribution to ReC~ requires further study.

(b) 4. PENGUINS AND B ASYMMETRIES

Fig. 3. Two diagrams contributing to CP violating KL --* ~r° -{-e + -}- e-decay.

Bander, Silverman, and Soni 12 have computed the asymmertry for quark decay: r(b -~ duo) - r(b ~ d,~)

In this section we confine ourselves to one comment about the recent work on this subject. The amplitude If we write:

for this decay is given by 1] A(KL

~

~r° + e + +

e - ) = - G-~F=slI+

A(-bb --* d u ~ = Ae.~i~1 + Be±i~2ei~ du~ ~

x [(~ - i~)ReC~ + ilmC~]

x (PK + P~-)#e7/~e where si = sinS~, tl~e sin of KM angles, f+ is defined

where hi is a phase generated by the KM matrix e]aments, and ~ is a relative phase generated by the strol. interaction decay dynamics. The decay rate is given by:

by du~ ~

( K I J~,(O) I ~) = f ÷ ( p r + p,)~, + f - ( p x - p,)~,;

and the asymmetry is given by: e - i~ is proportional to the strength of the K -/~" transition amplitude, and finally, C7 is the coefficient function for the operator

A~m

= A2 + B2 + 2ABco~(~2 - ~I)co~(~)"

As it is well known, both nonvanishing A] - )~z and

QT = ( ~do )(V_A)( ~e)V.

are necessary inorder to generate the asymmetry. Note also that A - B maximizes it. For the quark decay

It has been pointed out that the QCD computation of

ReC7 represents considerable ambiguity. Actually, we do not expect QCD computation of ReC7 to be valid

under the present discussion, there are two diagrams:

A.L Sanda / Convenor's summary: A summary of the CP working group

509

Thus the concept of naive local duality can be invoked to conclude that the integrand can be approxinmted

W

reasonably well by computing the amplitudes using the b

Vub

U

b

d

free quark model. The denominator is another story. It is not in the form of the finite energy sum rule and one may not naively use the free quark model approximation. Thexe may be some subtraction constants.

"d

The dominance of the ~b intermidiate state, which en-

(a)

(b]

hances the decay rate by a large factor, implies gross deviation from the quark model result. Further analy-

Fig. 4. Two quark diagrams interfere to generate an asymmetry mentioned above.

sis is needed inorder to see how the asymmetry can be realized at the hadronie level.

Fig. 4b pocesses a physical intermediate state b -+ c~ --+ uftd. The threshold for c~ appears as a singularity

5. THEORETICAL ERROR ON CP ASYM. PRE-

in

DICTIONS

log( m~q2)=l°g(I m~ 4mc2

_

4mc2

_

q2 l) 4- iTr

The KM factors in these two diagrams are relatively

For the decays of neutral B mesons to CP eigenstate f, the asymmetry is given by

complex and they are about the same order of magni-

r ( B -+ f ) - r ( B -~ f ) = si.(zxmt)Zm(pp)

tude. These points lead to considerable asymmetry in

r(B

the quark decays as shown by these authors.

?7

s)

where q = .M~2_ ~r121 i •

Before this interesting result can be checked by ex-

1

periments, however, it is important to examine how this result can he modified by strong interaction when

and A(B -+ f )

we consider hadronic decays. For example,

P = A(9 -, f)

b --+ c~d -.+ ~ d --+ uftd

In the three family model, it is knownla that Vtd, is a process which enhances the decay rate by about a

AVcb, and Vub form a triangle on the complex plane as

factor of 100. This intermediate state not only changes

shown in Fig. 5.

but increases the amplitude B, thus reducing the asymmetry. The working group G. Eilam, 3-M Gerard, M. G1/~ck, M. Gronau, and A. Sanda have examined the free quark approximation. We have concluded

,•"•Vt

d

that the numerator of the asymmetry can be estimated by the free quark model. Note that it is given by:

),Vcb

2sin(A1 - A2) f dq2 A[Abs( Bei¢~)].

If A can be approximated by a free quark model, the integral takes the form of the finite energy sum rule.

Fig. 5. The unitarity triangle representing the 6

A.L Sands/ Conveaor's summary: A summary of the CP working group

510

model amplitude which depends on the KM matrix el-

physical observables.

ements. T h e n the expression simplifies: Then for certain CP eigenstate f, we can write

z,~(~p)~i.(2~)

A(B ----*f) _ (qt¢ ] O ] db) A(B --, f ) (q'¢ I O I bd)

=

For B ---*a'w decay we see that p -- arg(2VubVu*d)

where a is one of the angles of the triangle shown in Fig. 5. Gronau has studied the theoretical uncertainties

If we take ~b = Vud =

1, we have:

Im(Rqp) =

associated with this predictrion for Im(~qp). It is con-

sin(2arg(VcdVub)) so that the ,asymmetry is related to

venient to start with a theorem.

one of the angle of the triangle shown in Fig. 5. Simi-

Theorem: Suppose there is only one operator 0 which has non-vanishing matrix dement ( f ] O ] B)

larly, one can show that the asymmetry for B --~ CKs decay is related to the argument to VcbVtd.

responsible for B --* f decay. Also, suppose it is a good ,

1

approximation to write 14 ~ = (M~2/Mlz)~. Then:

Note that the final state interaction as well as the initial wave function dependence cancel in the ratio p. If there are more than one operator contributing to the decay, the relative contributions of the operators become important. This will depend on the detail of

where a is determined purely from the KM matrix.

the strong interaction. Let us give a specific example. B --* CKs decay is

Proof: First note that ~ -- arg(2VtdVt*~). To obtain p, write the amplitude

caused by

w

A(B ~ f ) .~ ( f l e i B)

b

=

~_~

c

b

(.flq'¢)(q'qJlOlqq)(qqlB)

where we have incerted complete set of quark states

$

C

with appropriate energy denominatom. Simmilarly,

A(~-~ f) ~ (f I0 I~)

Fig. 6 Two competing amplitudes which may introduce some ambiguity in p for B .--* ¢K8.

The penguin operator can not compete with the tree graph, although the KM factors for both diagrams are If there is only one operator 0 giving nonvanishing con-

expected to be similar. The emision of c~ states from a

tributlon to (q'~J I 0 [ qq), it is qiven by the free quark

gluon interaction is exprected to suppress the penguin

A.L Sanda / Convenor's summary: A summary of the CP wor/dnggroup

511

graph by at least a factor of 100. We thus expect the

an investigation along this line.

four fermi operator to completely dominate, and the

Kayser has discussed our preliminary result. Here we

condition of the theorem is satisfied. Such argument

shall outline our method using an exampk.

In this workshop,

may not work as well for B --* lrtr decay. Consider

B - , CR*~ ( B -~ CK*" + e+e-Ks~°

W b

u

b ~

d

decay. It is not a CP eigeustate as the eigen value depends on the relative orbital angular momentum of ¢ and K* Before we begin our discussion, we point out that the chsdn decay rate can be computed by treating the various spin states of ¢ and K* incoherently. By Fig. 7 Two competing amplitudes which may in-

this we mean:

troduce some ambiguity in p for B --~ ~rcc.

r(B - . CK* ~ e+e-Ks~r °) = The KM factor for both diagrams are again expected to be comparable. But, it is relatively easy to emit a light

~ r ( B -, ¢(~l)K*(s2))

q# pair through a gluon interaction. The amplitude is

Sl,S2

x r(g*(82)

down by about as

- . g s ~ °)

x r(¢(s~) - ,

Gronau has concluded that the theoretical uncer-

e+e-)

tainty in predicting the asymmetry is less than a percent for the B ---, CKs and at most 20 percent for the

Here we have made a narrow resonance approximation

B --, 7rlr decay.

and ignored terms of O(I",~/M,~) which is a good approximation. In principle, Feynman graphs for differ-

6. POLARIZATION ASYM. IN B DECAYS

ent ~b and It'* spin states interfere. Here we have kept that contribution in which a on-shell ~bis produced and

The decay rate asymmetry between B ~ f and

decayed to c+e -.

--* f for CP eigen state f can be predicted without Next, note that (Ks~r°) (e+e - ) which originates

much ambiguity from the hadronic dynamics. Since these are small fraction of the total decay channels, it is natural to ask if predictions can be made for channels which are not CP eigenstates.

from I K*, ¢, 0, 0), where (0, 0) denotes the helicities of K* and ¢, is a CP eigenstate. Thus if there is any way to isolate this helicity channel from (4-, :1:) steres, the asymmety

It is possible that the observables involving polarizations of B meson decay products might be predicted

r ( B -~ (¢K*)(o,o)) - r ( $ -~ (¢~'*)(0,o)) r ( B -~ (¢K*)(o.o)) + r ( B -~ (¢R*)(o,o))

without much ambiguity. With this hope, group of us: B. Kayser, M. Kuroda, R. Peccei, and A. Sanda at Snowmass workshop for physics of 1990's, have started

can

be predicted without any hadronic ambiguity.

512

A.L Saada / Conveaor's summary: A summary of the CP wor/daggroup mixing, and that (ii) t' contribution does not disturb

Now,

a r ( / ( . ( 0 ) -+ K s ~ * ) ~ cos20 dr

the phenomenology of the K meson system, following

dF(K*(-I-) ~ K$~r*) ~ sin2 0 dfl

500 GeV. (b) t' contribution to rare B decays are neg-

where 0 is a.-xmaple Ks makes relative to the momen-

two results are obvious. The last conclusion implies

tum of K* in the rest frame of K*.

that the unitarity constraint

conclusion can be derived: (a) t' must be heavier than

liable. (e) I ~rd~'b I<<1V'q*~V.~I" Relevance of the first

The angular distribution of Ks and ~r* in the rest frame of K* will, in principle, separate the (0, 0) state.

Vt~b + V,;V,b + V**aV~b+ ~;,,~,b = o

7. The 4 TH FAMILY QUARKS AND THE B SYS-

for the four generation KM matrix reduces to

TEM The B - / ~ mixing is much larger than expected~ and it may be the first sign that the effect of physics beyond the standard model is in sight. One obvious candidate for such a new physics is the fourth generation of quarks. The contribution of (b',~') quarks to B - / ~ mixing and rare dee:~ysof B mesons have been

which is identical to that for the 3 generation KM matrix element. Thus the concept of the triangle mentioned above still applies inspite of the fouth family of quarks.

studied extensively in the literature. They take a view

The effect of t' on the CP asymmetry is also inter-

point that experimenta~ checks of unitarity of 3 x 3

esting. Note that t' ma~v ¢~ntribute to ~lr12 but not to

KM matrix allows cousiderable freedom in the cou-

decay amplitudes. From the form of asymmetry given

pilngs between (b'~t') to 3 generation of quarks. For

in Eq(O) one notes that the presence of t' will affect

special range of parameters, there will be additional

but not p. This implies that the effect of t' is univer-

contribution from loop diagrams involving (b',t') which

sal to all asymmetry associated with B decaying to CP

dominate over the predictions based on the 3 families.

eigen states. This property is not unique to the exis-

Soni discussed effects of the 4th family of quarks in the

tence of a new generation. One expects, new physics

B system once one allows for a mild restriction on the

beyond the standard model to affect M'12 but not p.

KM matrix elements. Assume:

Thus if new physics exists, deviations of the experi-

q

mental results from theoretical predictions based on

v,,,~ < O(X)

the standard model are quite well defined. 8. CONCLUSIONS

Vt'd < )~V~'s and finally,

It is clear from above that this workshop has brought out more questions than it managed to an-

sin(2~,~) where ff~i = arg~j"

~ 0(1)

With these very mild assump-

tions, together with conditions that: (~) the box diagrams with t' in the internal line contribute to B - / ~

swer. But, that is how a good workshop should be.

A.L Sanda/ Conveaor's summary: A summary or"the CP workinggroup

ACKNOWLEDGMENTS On behalf the CP working group, I wish to thank P. Singer and his staff for working so hard to provide

513

11. Here we follow Dib et. al.given in Ref. 7. 12. M. Bander, D. Silverman, and A. Soai, Phys. Rev. Lett. 43, 242 (1979).

a good atmosphere for the workshop. I wish to thank

13. C. Hamzaoui, J. RGsner, and A. I. Sanda Fermilab

G. Eilam and M. Gronau for making my stay in Israel very pleasant. Part of this work was done while I was

workshop edited by N. Lockyerd, and J. Slaughter (1988).

visiting Weizmann Institue. I wish to thank Y. l~ish-

14. It is a good approximation of a heavy quark system.

mann and H. Lipkin for their hospitality. Also, this manuscript was completed while I was visiting KEK. I wish to thank M. Kobayashi for his hospitality while I was visiting KEK.

REFERENCES 1. H. Burkhardt at. al, Phys. Lett. B 206, (1988) 169. 2. B. Heckel, Second Int. Symp. on the 4th Family, Santa Monica, Feb. 89, Edited by D. Cline and A. Soni. New York Academiy of Science (New York). 3. L. Wolfenstein, Phys. Rev. Lett. 13, (1964) 562. 4. I.I. Bigi, A. I. Sanda, Phys. Rev. Lett. 58, (1987) 1604. 5. See Konisberg's review in the proceedings. 6. A. I. Vainshtein, V. I. Zakharov, and M. A. Shifmann Soy. Phys. JETP45,(1977)670. 7. See contribution by J. Flynn, and L. Pmadal; also, for discussion of this decay, and for earlier references, see C. O. Dih, I. Dnnietz, and F. J. Gilman, Phys. Rev. D 39,(1989)2639. 8. H. Iwasaki, and T. Morozumi Prog. Theo. Phys. in press; L. M. Sehgal, Phys. Rev. D 38, (1988) 808; J. Flynn, and L. Randal Phys. Left. B 13,(1989)221. 9. The WW interaction can be approximated by a current-current interaction which is CP violating. 10. See for example T. Inami and C. S. Lim Prog. Theo. Phys. 65,(1981)297.