Topics in B-physics

Nuclear Physics B (Proc.*Suppl.) 11 (1989) 325-341 North-Holland, Amsterdam

325

TOPICS IN B-PHYSICS

James D . Bjorken Fermi National Accelerator Laboratory Batavia, Illinois, USA

We discuss a few issues in quark . These includes

the

burgeoning

field

of

physics of hadrons containing the b-

1) A simple parametrization of the Kobayashi-Maskawa matrix featuring a triangle in the complex plane, 2) a review of Bs and Bd mixing with special attention given to width-mixing and the CPviolating same-sign dilepton asymmetry, 3) a discussion of the CP-violating decay Bd --~ -® and 4) a discussion of CP-violating rate asymetries in the two-body decays Ab pK- . The concluding discussion concerns generalizations beyond these specific topics .

INTRODUCTION Of the

fundamental parameters

twenty-odd

of the standard model, four of them reside in the Kobayashi-Maskawa mixing obviously

high

of

priority

of

measurements

overdetermine them .

to

It is

not

only

to provide a redundant

measure them well but set

matrix .

sufficient

Only

to

such a way can

in

the standard-model description

one test that

is indeed valid . hadrons containing b-quarks

The decays of appear to

a

be

doing this .

most

promising

avenue for

Even CP-violating effects can be

anticipated to be large in various rare decay and

mixing

phenomena .

And

although

the

experiments are extremely difficult, there is growing

optimism

that

eventually

the

measurements will be done .1 The subject of

b-physics is quite large .2

In this talk, we discuss in detail only a specialized

items

as

enumerated

in

few the

0920-5632/89/$03 .50 © Elsevier Science Publishers B .V . (North-Holland Physics Publishing Division)

abstract, and

more general remarks

reserve

for the concluding section . 1 . THE KOBAYASHI-MASKAWA MATRIX The amplitude for Qi and antiquark qj where g is the

to decay into quark

is proportional to gVij, weak

characterizing

pure

factor Vij is,

by

coupling

leptonic

constant

decays .

The

definition, an element of

n Kobayashi-Maskawa "mixing-matrix",

the n x where

W+

n

number

the

generations .

It

strengths

non-leptonic

of

accounts

which depend sensitively

standard-model

of

is

for

the varying

decay processes,

upon

the amount of

flavor-violation which is present . It is a requirement of the standard-model

that the matrix Vij be unitary, in order that electroweak to corrections radiative processes

be

finite

and

not

lead

to

unacceptably large amounts of flavor-changing

J. D. Bjorken/Topics in B-physics

326 neutral

currents .

addition

In

unitarity constraint, there of

freedom of choice

to

the

is an additional

phases of the elements

of Vii because physics does not change if the phases of the quark fields in the theory are redefined .

does

ei (i - aj) Vii ,

c

not

change,

even

though the This

trization invariance is somewhat like gauges

lagrangian : (and spaces!),

but

implies physics

remains

gauge-

invariant . Traditionally, descriptions of Vii

two

or

have

three-generation used a generalized

Euler-angle representation .

This works fine,

but rapidly becomes quite cumbersome for more

than three generations . simple description

which

.23

.23- .05Vi

.97

V

- .05- .23V&

.0

.01

1 .00

Here we advocate4 a introduces no such

angles, but simply fixes the 2n - 1 phases of the diagonal and upper-right next-to-diagonal

the first Neglecting 5% corrections,

Unitarity implies orthogonality and third rows . this simplifies to

of

Vûb + Vtd 'g .011 * .002

different

sometimes different Hilbert the

.97

Vtd

gauge-invariance in field theories : choice of different

I

(1 .1)

lagrangian of the theory does change .3 repay

V

That is, if Vii

physics

u

This is a triangle

relations

to e and

the

(1 .4)

in the complex

plane, as shown in Fig. 1 . Note that the height of the triangle is proportional to the strength of CP-violation, i .e . proportional el/e

The square of

of

Vtd is

amplitude for Bd -

Bd

"surprisingly" large .

neutral kaon system .

proportional to the mixing, observed to be

Allowed region(Harari and NO

YAt

elements of Vij such that they are all real and positive . That is,

V

where the elements marked R are not only real but also positive . Independent parameters may be chosen to be the magnitudes and residual independent phases of all elements above and to the right of the diagonal . For the 3-generation case, one finds, using unitarity plus reliable data :

FIGURE 1 Unitarity triangles, with allowed regions for the vertex for various assumed values of top quark mass mt . The base is normalized to sin 8c (We thank H . Harari for this suggestion), and the bounds are transcribed from Ref . 6) .

327

J .D . Biorken/Topic s in B-physics The squared magnitude

of Vûb is proportional

to rlB -o- nonleptonic

"surprisingly

the

of 66 --® ppff+ and have not

been

uncharmed states) .

large"

Bd ---+ Prow- hold up (they

confirmed

implies a relatively triangle into

If

ARGUS measurements

the

by

Cornell), this

large

Vub, forcing the

obtuse

in Fig . 1 .

shape

One way of keeping the mass of

exists even in freedom

this

triangle we can express

features of b-physics :

some interesting

1) Determination of the Via,

in

particular

evidently whether

magnitudes of the Vub

sufficient or

not

nondegenerate,

to

the

i .e .

there real'

are

This

piece

simple

and

Vtd, is determine

triangle

whether

or

is not

CP-violating phases .

recently inspired

of

geometry

lengthy

has

and learned

CP-violating

phase

simply

angles of

related the

to

the

interior

triangle ; examples will

to

an

important experimental issu®

determine

whether

triangle closes, i .e . is satisfied .

If

of CP-violation all, then

there

indeed

the

is possible at

sufficient richness and

should be possible . comparable

determination

The situation is in some to

the

of

validation

the

Cabibbo-angle

Before concluding this overview of Vij, it emphasized

the

spin

longitudinal . in

associated

with

breaking in the Higgs gaugeless couplings

limit, of

that

degree of This

third

fact nothing other

Nambu-Goldstone

spinless,

ssless

spontaneous symmetry sector .

Vij

Thus in this

measures

ambu-Goldstone

the

Yuka a

bosons

to

quarks . To go deeper into the physical origin of these couplings goes beyond questions of known gauge interactions .

It is

likely however that there is linkage between

the origin of quark mixings and the origin of

2 . B-B NIXING

neutral B K-K mixing

The mixing phenomenology for the system

is

similar

to

frame of the neutral

B,

the

In the rest

the Schrridinger

equation reads

the

Kobayashi-Naskawa parameters

origin of the is

at

B 2

B

where the common mass and width, i .e. the factor exp - i(m - it/2)t, has been reproved. Unlike the situation for kaons, one has

and

description of strange-particle decays . must be

the

am - i

variety within it that such overdetermination ways

. This decay qj + limit of vanishing gauge

it does, the angles

b-decays

is

doing this, the

whether Eqn . 1 .4

the program of observation in

el

-

provided is

than the

and sides should be overdetermined . I believe that if

Upon

phenomenology, but sim ler .9

be seen later . 3) It is

w, as to zero, so standard

angles

associated with varioas decay processes are

, or

polarization state is boson

is to set the

quark mass .

theoretical treatises .' 2) The

16

Qig3 go into Qi

theorists, is quite shaky . In terms of

this

goes to zero, so that processes

But this inference, presently favored by most acute triangle is far from being ruled out .6

other

parameters fixed .$

couplings

A right or even

appPeciating

gauge coupling constants

quite deep .

IArI «

®

m

(2.2)

This is based on the empirical measurement of Am and strict upper bounds on df (more to come later) . If one neglects for now , then

J.D. Bjorken/Topics in B-physics

323

®m

and the

le

is

like

uniform magnetic field .

spin-rotation in a

favors

relatively

a

quark mass .

I B> -

2

sin

Amt 2

I~

om)

V ts

Bs

The favored value between 5

t (t)> = cos Am I-B>

sin

2

2

IB>

and

of

this

"box-diagram" (virtual

Bs

This very

vioiation in double B-B pair .

(2 .5)

r The origin

60 .

makes "complete"

likely, i .e . several

mixing oscillations per mean life. The width difference Ar/r, while small, is

a = ^. 0 .7

the ratio is somewhere

of

important for the possible observation of CP-

Experimentally for the Bd one has

m

(2 .7)

V td

mixing of the Amt

and/or top

Vtd

that

The solution is

ie i

large

immediate inference is also

An

(Am) IB(t)> = cos A mt

experimental value

large"

The "surprisingly (2 .3)

(2 .6)

Box . mt Vtd

semileptonic

decay of a

One looks at the asymmetry

N(++)

- N(--)

=

N(++) + N(--)

Im Ar

,

(2 .8)

AM

described pictorially in Fig . 3, which can be is

believed annihilation

pairs) as shown 16 Fig . 2 .

FIGURE 2 "Box-diagram" believed to Bd - d mixing .

to be the into W-

readily shown to equal Im

/®m, as indicated

above .

Roughly

e responsible for

FIGURE 3 Mechanism for same sign dilepton asymmetry .

J.D. Bjorken/Topics in The width difference, according to the Golden Rule,

is

fed

which

couple

intermediate property,

by to

intermediate states

real both

states

because

at

decay products of Bd

Bd

and

Bd .

do

not

have

the

quark

Most this

level the

mainly consist of cd(ud

B-physics

Now

these three classes o contributions probably destructively interfere . The reason is that were the charm quark degenerate in

mass with the up quark, there ~.rauld be no CPviolation effect . (This is a general principle ; the

extra

+ c°s) which is not identical to the principal

an SU(2) rotation

td products cd(id +

our

j6f/TI -

1 .4

which do feed

I

Zs) .

/®ml

This alone implies

<<

1.

The channels

are of three categories (cf .

phase

in

c-u

conventions,

chosen real) .

To

that in

limit

for

Fig . 4)®

flavor symmetry allows

that

categories

space which, with allows

Vb u

to

be

see this directly, we note the phase-space factors

1,

II,

and

III

become

identical, and

Ar a

(Vcb V cd+ VubV ud ,2

®(

- V t V td)

2

-

-

(2 .9) Here

unitarily of the mixing-matrix has been

invoked, along with

the observation that the

phase of (VtbVt ) 2 is the same as the phase of AN as calculated from the "box diagram" . In the presence of unequal c and u masses, one can

still use the unitarity constraint to

eliminate category III in terms of categories

FIGURE 4 A redrawing of the "box-diagram", Fig . 2, illustrating the presence of "real" intermediate states (shown here only at the quark level) .

I and II .

Structurally one has

a = Im

.Sp .)1-(Ph .SP .)III loc(VcbVcd)2 (Ph

f

.Sp .)II-(Ph .Sp .)III + ( V ubVud) 2 (P' (2 .10)

Intermediate State

Phase K-M Factor

I.

ccdd

(VcbVcd) 2

II .

uûdd

(VubVûd) 2

Space limited vast

I 1I . 1 cûdd ucdd)

(VcbVcd)(Vubyûd)

intermediate

At the quark

level,

looked

at

this

order-of-magnitude the quark

and

for a is no

argued

vancellatïons

leve111

need

hadron level, so

that

imprudently low .

But

to work the

value

Altomari, Wolfenstein, and

larger than 10-3 . 110

the

value

up

the

not

that the present at

exist at the

10 - 3 estimate is

it is near impossible to

1% .

A reasonable

J.D. Bjorken/Topics in B-physics

330 statement is certainly

that

below

asymmetry

the 10-2,

but

is almost

the theoretical

uncertainties are much too large to support a claimed upper bound of 10-3 .

where the factor 1/2 allows

Po _'

i )

d ->

Ks -,>

'i)

and

CP-violating

decays into final III .

But

decays,

states

these

"allowed" ;

their

suppressed

by

in

final

such

as

categories I states

are

ratios

branching K-

factors

not are

lVbu/Vbcl 2 ,

An "allowed" CP-invariant IVcd/Vcsl 2 , etc . which has a very favorable final state Ks . It i s ;ouch di scussed12

signature i s Bd -~ as a

CP-violation measurement .

prototypical

variant

Here we choose a

from category I of

suppressed decays, namely Bd --I' Wl- . It is actually the same final state as #K s ; the only difference being that the dipion emerges from

the

downstream . advantage .

decay

B

This

vertex

should

rather

than

be are experimental

And while one has paid a price of

a factor 20 in

IVcd/Vcsl 2 ,

be compensated .

r (B. -

=

1

f

We guess that

much of this may

In particular

Ks )

r (Bd --"

K°)

(3 .1)

20%

40 (3 .4)

can

There

also

be

dipions (not

to

spins

which

2

2)

Ks

the

can

add

more

to

the

We furthermore expect that kaon vertex may be that the "V2" 2-prong

secondary

occasionally lost, and vertex

be s-wave

contributions from

mention

branching ratio . for

to

expected

is

somewhat

difficult

more

vertex

suspect the overall

detection efficiency for

-

exceeds

that

of

for

#Ks,

i-.

to

resolve than the V4

So I

although this

assertion needs checking . But the erode

main

here

present

is

in

reason to

the

for discussing this

point

out

final-state

CP-violation

can

distributions

and

be

the

we

in

have

tagged

Bd,

course

mixes)

was

produced

with a

Bu

Ab .

Then

or

phenomenology . angular

To examine this, we

simplicity i .e .

richness

Dalitz-plot distributions

in a variety of ways .13 assume for

the

seen

neutral

eigenstate F it is easy

3 vector

3 ® 3

in the B system

exploit the interference between CP-violating mixing

po, we find

r (Bd -®

3 . THE DECAY any CP-violating effects

-o

well as Bd

as

for Bd -+

a sample of B

(which of

in association for

a

given CP

to work out the time

distribution for the decays final

states are more

prevalent than pseudoscalarss

r (Bd

ro 1 3

r (B d --~

~)

(3 .2)

r (Bd

F(0)

e-rt[i+(Im

A F )sin

2

po) OK.

s 2

/w w ( 3 .3)

emt (3 .5)

Here

Then using

r (Bd --®

dr F (t ) _

Im A F = e2ia T(Bd T

-->

F)

(d --6, F)

(3 .6)

J.D. Bjorken/Topics in B-physics Again a is AN .

The

the

of

ratio

depends o and is of

phase of the mass-difference

upon

the

decay amplitudes T

the mixing-matrix elements

modulus

unity ;

therefore this is

331

T(Bd) _ [s(®p)+ip(

T ~d)

;

)®k+ip(

_ [s ®p) -i p ( (

) ®k-i P (f

)] ® VcbVcd

Q] -

also true for AFs

(3 .9) (3 .7)

Note that while neither the phase of

[AN]

the ratio of T's nor

is rephase-invariant, the

observable XF is ; indeed

Here the amplitudes s

and

state phase-shift

p-wave

of

the

p system i s zero,

it is unity .

AF

(VtdVtb)(VcdVcb) ® (CP) (3 .8) F (complex-conjugate)

=

The factor (CP)F eigenvalue of the

ti

accounts

state

F

for the CP

in question .

In

very

interior angle of

the

If that angle is ) 150, For dipion masses

£

vertex

on the right .

lIm AFB

is > 0 .5!

1

GeV we expect the

final state is a combination waves .

If

s-wave

eigenvalue of the one is assured

of only s and p

dominates, final

of

state

then

the CP

is fixed and

a big integral asymmetry .

If this is not the case, then Dalitz-plat and angular-distribution the CP-violation . amplitudes is

asymmetries

will

show

The structure of the decay

must be in a p-wave

The phase of P is that of This, as well as

regarding the phases

amplitudes, is true under the

reasonable

the

i .e . twice the

which .

assertion

of the s and p

is twice the

Vtd,

while for the p to

I=0 s-wave ir-ir scattering . the previous

negligible

of

-w scattering,

The third amplitude P describes

relative to the

terms of the triangle, Fig . 1, the phase of A phase

p have the final-

dominated by the P resonance . Evidently for the s term, the orbital angular moment of

a J=O, I=0 dipion =

VcbVcd

assumption

final-state

that

interaction

there

is

between

and the dipion . Note that the CP

eigenvalue of the s-wave

i¢p configuration is

opposite

two p-wave

terms .

p and

extra structure in

to that of the This provides an

the time distribution for

the decay of Bd(t) and a suitable normalization

bd(t) .

e have, with

J.D. Bjorken / Topics in B-physics

332

-a dN fe l dt

--) = T

7

e I°t

+

s"®

cos

2

®mt ®mt + IX si n 2 2 cos Amt 2

-

is

sin Amt 2 (3 .10)

To obtain the corresponding distribution for

gd,

one simply replaces A by A * and p,P by -p,-P : 2

e shall not

explicitly

the general

case .

i nteresting

information

expand this out for

However

there

is very

these

angular

distributions, in particular for the

decay .

in

For example, suppose for 0, s

ip

violation .

and

X

simplicity that P

= 1, signifying maximal CP

Now introduce the anglo

the decay planes of

between

and p® dN

cos

sin

n

n

2

(3.12)

x p ®k

'We see that,

as

a

of p .

(3.13)

The rate

4

rotates relative to that

of rotation is ®m/2f radians

per mean lifetime .

The direction of rotation

(right-handed versus Od(t) and Bd(t) .

(3 .14)

function of proper time,

the decay plane of

Then

On the other hand,

+ Amt +

a sin 2

One

left) can

is

opposite for

hardly ask for a

more graphic demonstration of CP violation .

J.D. Bjorken /Topics in B-physics The general case looks rather complicated . However

number

the

of

parameters

characterize all distributions

Is/PI

probably two numbers that are needed .

This

dipion mass

p, and P on

calculable

in

a resonance

are

may be required as

input . Thus

data

principle

(3 .18) The energy of the

ïtted in the

a

global fit for all be

a

practical

Bd

actually be possible to

this

To estimate the branching

do experimentally? -I'

~-,

we

start with the

observed branching ratio

(3 .19)

The

energy

(better,

spectator d is GeV .

Because the

momentum

r d

-" total

1

= 1 .1%

(3 .l5)

1

evidently this

leads,

distribut at

the

will

be

a

dominated

contributions, probably shown in Fig . third

Xnonstrange) â ®2 x 1 % c

of

5. the

a f

a - 3

ion,

<

maximum of

In real life the low-mass

GeV2,

the

orientation of the d quark

is

isotropically,

GeV2 .

of

of the take it to be - 0 .5

e

level , to a uniform distribution in

We therefore expect

r ( Bd -'>

momentum)

characteristic

minimum of zero to B

eak decay

is

state wave function .

Will any of

1 - cos



In addition there

procedure .

ratio for

2Ed

which is the goal of

the measurement . in

N

only the normalizations

is the parameter arg X, should

Ip/PI are all

and

follows because the s,

approximation ; hence

2pd®pd

is not large ;

functions

dependence of the

2 .

which

,

ir,

Duality total

by

resonance

p, and Al, as would imply one

distribution

is

concentrated in the mass region below 1 GeV . 5 x 10-4

N

rtot (3 .16) estimated is the fraction

What remains to be of non-strange final charged dipions .

states

We

end up as

that

guess, consistent with

the general ideas of duality, that

dr

N

dr

(3 .17)

dM2 dM2 Parton level where M2 is

the

squared

system Xnonstrange At

the

parton

recoiling

level

produced in the weak

mass of the hadron

this

against the is

decay b--P-

a

ccd

d

quark

together

with the spectator d in the initial Bd meson . The squared mass of the dd system is

FIGURE 5 Sketch of the expected mass distribution of X. hadrons X produced in the decay of B

J.D . Bjorken /Topics in B-physics

334 Taki n low

put - 70% of this

1/2/3 would

ss contribution into two charged pions . branching ratio would then be

The net

x !_ x 20

r tot To

this

be

must

included

ilepton

+- or e+e- .

branching ratio of 7% for

modes

presuming both dile ton

the

Even

can be found,

this implies a net branching ratio of 1 .7 x 10-5 . Assuming 1000 or Bd are needed to

1

(3 .20)

x 0 .7 - 1 .2 x 10 -4

3

4.

-°o

-

AND

Ab

pK- AS EXAMPLES OF

-p-

"PENGUIN" PROCESSES As

we

have

seen,

distinct mechanisms

there

for

are

b-decays

by

measure well the distributions, this requires

hamiltonians .

For example, we may write, for

500 x (1 .7)-1 x 105 -

decays with initial and

the course of the

experiment, or roughly 108

quark pairs . many

final states of zero

net strangeness

this does not include

But

experimental

effective

weak

characterized

3 x 107 Bd produced in

different

several to occur,

inefficiencies .

For

Hwk =

these include, but

hadron-ha ron collisions, are not limited to

uHu + fCHc + ftHt + h .c .

with (i = u, c, t)

Isolating the decay vertex (factor 2?) Geometrical acceptance (factor 5?)

CI = dib Vtd

Detection efficiency (factor 3?) Finding

and

tagging

(which ideally

the

should

be

spectator a

Bu or

(factor -~ 3?) This leads to

an

103, or a number the apparatus sources of

extra of

in

b)

factor in excess of

bb quarks produced into

excess

hadron

only the SSC

B

of

collisions,

holds

1011 .

Amongst

the

SSC and

out promise of providing

such a large nurWzr of produced b-quarks . If one uses

e+e-

the loss factors may even if they

are

a

103, this implies 109 sample of 1000

colliders, in principle e greatly reduced . But factor 10 instead of bb produced to get the decays .

and Hi = b~yp(1-75)gi il 7ià (1 -,y5)d Note that the CP violation

Hi are CP-invariant operators ; is

due

to

the

phases of the

mixing amplitudes Ci . Normally, it only consider

is one

calculating a given

a of

good approximation to these

three terms in

decay process .

there are circumstances

when,

However,

due to strong

J .D. Bjorken /Topics in B-physics final-state

interactions,

contributes

significantly .

coefficients

Ci

this can lead

to

(CP-invariant) multiply

have

than

one

Because

the

distinct complex phases

CP violation, provided the

decay

Ci

the

more

amplitudes

are

out

of

Ti

which

phase .

The

observable CP-violating effect is a particleantiparticle branching

ratio

asymmetry, and

its generic structure is

är _ r (B r

- f)

-

r (B -+ f)

rtot

= 2 (Im

r tot

ei g

jC i T j

(IM T i Tjjl

+

CjT112

Here i and j label the two contributing terms in Hwk . Let us now specialize to decays containing no charm in

the

final

state .

interested in particular

in

We will be

the decay Ab -I'

pr- , although what we do is applicable to Bu -> per- , Bd --I' w+r- , as wel l as quite a few other processes . Hu, the source estimating

Normally one considers only of

these

the

"tree amplitude" . in

processes .

The

two

remaining contributors may

be expected to be

dealt with perturbatively,

since the strong-

interaction contribution annihilation .

We

may

AT

=f t

includes

cc

or ti

write, for the strong

corrections ~flTln>
n containing top

-N

+

c

.,/, fITIn>

n containing charm ,/, f l T l n>

n where use of

the

perturbation theory in the

last term is more dubious .

But, as we shall

En -N+le

En

- N + CC (4 .2)

J.D. Bjorken/Topics in B-physics

336 diately

see,

contribution

level

the relevant diagrams

important features to this

There are several contribution,

s crucial .

At the quark a

short-distance

its

(in

the

Jargon, the "electric

penguin") : 1) The logarithmic divergence is cancelled

shown in Fig . 6 .

via unitarity of the mixing matrix : (u+ c+ t)log 2 '-0 2) This implies states

provided

in the

off at a

top contribution can

the

be eliminated,

the sum-over-

remaining terms is cut of order the top-

mass-scale

quark mass . 3) The short-distance dis, tance

contribution of the

remaining

charmless

large ; it

provides

to

the

part

is

not too

a small correction

leading

tree

diagram

contribution . 4) The

tb?

charm

contribution

because of the intermediate

possibility states

Nevertheless it is

The loop, has

the

after

Fierz

structure

larization

loop

factors of t

it

rearrangement, still

of a

a la

will,

good QED .

old

vacuum

Aside from

in momentum space,

take the fo

1

®

2 ®

q2

In

®..2

2~

( .3)

of real c'c the

decay . still a

arguably14

contribution,

short-distance FIGURE 6 Tree (a) an penguin () contributions to the decays , -. The subprocess enclos y the dashed box is, to good approximation, local .

in

complex

is

being

a

coarse-grained superposition of Feynman propagators with

mass

parameter ~ 3-4

GeV . Thus the net result'

is that the effective

short-distance interaction to

be

dominated

contribution,

by

the

can be considered (cut-off)

It has the structure

charm

J.D . Bjorken/ Topics in B-physics

"H

Here the Ai

J2

QCD

of

(which

Mc

matrices .

color

as _t c bX7 _i 2 Il,,

Note

the final-state interaction does

conjugation

1

1n Mt +i Penuln-GF 9 _ [ 2

are

that because phase

2

OI

not

when

undergo

complex

particles

external

are

replaced by antiparticles) "H" penguin is not hermitian . With 40 GeV < Mt < 200 GeV, this /(In m?/mg) is

phase-factor

a

/(8 .2 t 1 .6),

or about 150 .

suspect

"tree" it

contribution?

to

also

We

suffer

small "electric-penguin" contribution already However,

good approximation

basically a defense, for the

of

nonleptonic B-decays of charm decays .

u

singlet

ûd

pair

of

a u

collinear

+ (ûd) - .

The color

recoils

the direction

in

In order that it has good

relative

order 2 .5 GeV .

decay

nearly

pion it has low

overlap with the final-state virtual mass

the

level the decay b -

as

opposite to the u .

to

its

momentum, of

It follows that the formation

time of the pion will

be lop

relativistic time-dilation .

because of the By the time the

pion is formed it is several fermas away from the color fields existing in the neighborhood of the original time the (ûd)

Bd

or

system

and

long

growing

Ab . is

dipole,

arguable

will

significantly

not

that

spectator system . here

to

time .

this

check

is

It is

small dipole

interact

There

let

only slowly

formation

therefore

with

the

a calculation

this,

but

to

knowledge it has not been done . In

the

absence

interactions, the

of

such

decay

product of two factors,

final-state

amplitude becomes a one

of which is the

usual pion decay amplitude, and the other one same

(real)

form

factor

decays .

therefore, is

a

What

appearing in is

i

direct relationship between

the nonleptonic pionic decay and semileptonic

decays . An easy calculation gives15

1 .0 GeV 2

argument is based on

configuration of b --P,

color

less justifiably,

evolution

begins

11

"factorization"

and,

At the quark

+ W-

s

in calculations of

The

space-time

final-state

semileptonic decays .

as

is

process,

products .

because of the

semileptonic

of

a

interaction,

the

hypothesis widely used16

the

weak

amplitude

is real ,

+h .c .

is

shall argue that to

free

phases

This argument15 this

we this

as

essentially interaction

it

u

originating from the pointlike, color-si

might

final-state

beyond the arguably

interaction phase-shifts discussed .

fields,

iaX -i 2

possible

Now what about the phase of the presumably dominant

(1y5)d l ,

7

And during the

within those color

dM2

~b -~ pe-v ) e

2 - 0

(4 .5)

This is indeed a general test of factorization ; the p can be replaced by any low-mass hadron system, and meson B .

It

is

quite

the

important

by any b

to test

this factorization hypothesis sharply wherever possible . There may already be a and way to do this in decays such as B B - Or. Returning to the b decay, we may estimate the branching ratio as before . We take

338

J. D.

Bjorken /Topics in B-physics

(4.6)

e Implies a sum over all uncha d e have (nonstran e) aryonic final states . not studied the ilepton mass distribution but guess an average ( ss)2 of - 5 GeV2 . The To in accordance with Eqn . 4.5, we take Xe,,)

m2 =0

1

(0.2 GeV-

r (Ab --'>

Xezv)

Evidently ,2 Vub

(Phase Space) - 2 .5

Vcb

V ub

2 (4 .8)

Vcb

it a 15% s ile tonic (eao) branching ratio, e can put all these numbers together to get 2

,_ (1 .0 GeV) Z" (0.2)" (0.2 GeV-

9"2.5I Vub f " (0.15) Vch

_ (1 .5 x 10-1

it lVub/Vc l2 - (1-2) x 10-2, this implies, very roughly, a branching ratio of (1 .5-3) x 10-5 . This is actually surprisingly large for a "first-forbidden" weak transition into a two-body final state . This fact provides additional support for the factorization thesis . It is ha to see how c licated strong-interaction mechanisms can lead o an effective "squared form factor" of

1

Vubl2

(4 .9)

Vch 10-3 (after taking out the IVub/Vcbl 2 factor) at a parent mass scale of 5 GeV (Compare e+e° Hence it is -' pp, or -~ pp, e c.) . credible that the factorized contribution in fact dominates . Less certain is the relative magnitude of the "penguin" and "tree" contributions. We here do not try to estimate the ratio.

However, for a

large

range of magnitudes of

339

B-physics

J.D. Bjorken /Topics in

It changes sign

upon replacing the particles

penguin amplitudes, the issue can be finessed when comparing the Ab -I' px- and Ab - pKprocesses . For the latter process, the tree

by antiparticles .

amplitude

assumed

is

suppressed -

Cabibbo-angle ®c

by

0 .23,

a

factor

of

while the Penguin

contribution (Fig . 6) is enhanced by a factor ®cl .

Thus it is very likely that the process

--I'

Ab

pK-

is

dominated

contribution .

by

the

Penguin

e write

=

Table

p o ll +

BclV

I

I

we

Penguin-amplitude

JP/TI = 0 .3,

0 .1,

for the px - mode,

®

a

ubl [T' l

apK

=

Il Vub

In both

I TI

o

I

1

equations

+

Vub

l LT

oc .

I FxI

lVubl

® IT

I V cbl

parameter

_ Im Vub ® Im P ? t 0 .2

I PI

a

(4 .13)

asymmetry

uncertain

does

elements

not

depend on the

(other

strong-interaction

than

the

phases

) a (PK_)

) a(

+ [Vc!j

il

is the

strength possible :

IVubl

® ®c -

IVub/dcbI JP/TI r(PK°)/I'(

ratio of CP-violating strength to the maximum

n

This

(4 .10)

F

The mean

2

211 IFKl

the

or both .

Eqns .

TABLE I

FIr

zr

mode,

FK

(4 .10)

(4.11) i

strengths (namely

0 .03) and values for

from

2VI

Consequently, we estimate

Vcb

pK°

because,

question of entering V) .

I-

and

Vub (we take Vub/Vcb = .14 and .07) . s that the asymmetry tends to be large either

most

o ec (FKl

decay

(4 .11),

r l

r

the

2

Nfi+2 o

l

tabulate

asymmetries and decey widths for a variety of

follows

( r (Ab --+ Pe)

In

(4 .l2)

.07

0 .3

17

8%

3%

.07

0 .1

2

13%

9%

.07

0 .03

.17

4%

22%

.14

0 .3

4

18%

5%

.14

0 .1

0 .5

6%

15%

.14

0 .03

0 .04

2%

20%

J.D. Bjorken /Topics in B-physics

340 . C

CL

R

I

RS

and The specific examples of B --o':road only special cases of a a class of similar decay modes which can exhibit CP violation and other interesting effects in similar ways . One can find these emu rations in many places .17 But it y interesting case well end u that the most experimentally is not on the theorists' long lists or at least not one which has received adequate scrutiny . o emphasis has been to scrutinize low-multiplicity, all-charged decay modes of b-ha rons, where the multiplicity count includes the cascade decays of intermediate charm or strange systems. Restriction to total ch S 4 still leaves - 60 channels, essentially all of which are in principle quite interesting for one reason or another .18 The decay branching ratios are in some cases utable at the level of accuracy discussed and , pK . Others (e.g. etc .) are re uncertain. All can benefit from re theoretical effort expended upon them. I find the duality techniques described above

re

trustworthy

than

direct

wave-functions, but that is a matter of taste. I would prefer most of all results based upon current-algebra or QCD sum rules ; here the prototypical analogue is the set of estimates for strange-particle decays, e.g . K -® ly, calculation using bound state

using the

Ade

To my knowledge

llo-Gatto-theorem approach .19 not

much

has

been done in

this direction . As for experimental

prospects of reaching

the sensitivities required, there is still a long the

CP-violation

requires at

way level

it is clear that to go . of

To get to sensitivity

least 10 1 bb pairs produced into the detection apparatus per experiment .20

Once that level is reached, many experimental opportunities open up .

This

implies to me

that if this is possible at all, the study of CP-violation

in

the

B-system

discovery .

program, not only a important because,

as

becomes

a

This will be

we already mentioned,

it is overdetermination of the K-N parameters that both tests

the

estimate

and provides some of

the

validity of the picture of the reliability and

measurements

calculations . What

facilities

might

theoretical this?

provide

electron-positron

Present-generation

colliders should provide between 106 and 107 bb/experiments New ideas promise another order of

magnitude .

The

choices appear to be ZO .

Hadron-hadron

109 bb

triggering

to

but

over

can yield from 1011

(SSC) per

background,

problems

achievable

cms energy

either the T(4S) or the col l i dens

(Tevatron)

experiment,

best

rate,

make

detection

uncertain at present .

the

and

overall

efficiency

very

And in every minute of

fixed-target operation at Fermilab, about 107 bb pairs are produced in

made . the

While,

beam

alas, they are

dumps,

there is hope

that very high-luminosity experiments looking at

the

simplest

decays2l or

decay

decays

modes

with

a

(eg two-body 1n the final

state22 ) will be possible . No

matter

what

experiments

are

20110 years

as

the

very the

reach the CP level physics will not

approach

is, these

difficult .

I guess

relevant

time scale to

of sensitivity . go

given spectacular

out

of

successes

But this

fashion .

Even

with physics up

to the TeV mass scale via SLC/LEP, Tevatron,

and SSC, I cannot find a scenario which would diminish the

importance

It deserves a great

of

this b-physics .

deal of effort, not only

by experimentalists and accelerator builders, but also by theorists .

J.D . Bjorken / Topics in B-physics ACKNOWLEDGMENTS Much of this material because of many

stimulation

Fermilab

also would like

has been worked out and interaction with

experimental

colleagues .

I

to especially acknowledge I .

Dunietz and J . Rosner and my collaborators T . Altomari and L . Wolfenstein . to

E.

Floratos,

P.

Thanks also go

Dittus,

and

A.

Verganelakis for their excellent organization of the Crete Workshop .

REFERENCES 1.

Prospects for future experiments can be found in the Proceedings of the Workshop on High Sensitivity Beauty Physics at Fermilab, Nov . 1987, ed . A . J . Slaughter, N . Lockyer, and M . Schmidt (Fermilab, 1988), and references therein .

reviews; see for example N . Uraltsev, and A . I . Bigi, V . Khose, also J . Rosner, Sanda, SLAC-PUB-4476 ; preprint EFI-88/37 .

2 . There are many

3. An extensive discussion is given by C. Jarlskog,

1039(1985) .

Phys .

Rev .

Lett .

55,

4 . J .D. Bjorken and I . Dunietz, Phys. Rev. 136 ,7(1987), and references therein . 5.

10 . T . Altomari, L. olfenstein, Bjorken, Phys . Rev . D37, 1860(1988) . 11 . J . Hagelin, Nucl . Phys . B 193 , 123(1981) . 12 . See for example B . Cox and D . a r, Physics of the Su erco ucti Su erco er, . R. na son a J. Marx Sno ss, Colo, 1986), . 83 . 13 . The general idea goes back to S . Phys . Letts . and J. Geris, 319(1979) .

rshay

14 . The line of argument requires a coarseat is grained energy average similar to used in comparing R(e+e- ) to perturbative . Quinn a QCO calculations ; see e .g . 115 .S . Weinberg, Phys . Rev . D13 , 1958(1986) Phys . Rev . alsoR . Shankar, . Barnett, . Dine, a 755(1977) and R . L . cLerran, Phys . Rev . D22 , 594(1980) . 15 . I am told this is in the folklore but do not know a good reference .

16 . M. Wirbel, B. Stech and . Bauer, Zeit. Phys . C29, 637(1985) ; . Bauer, B. Stech, . Wirbel, and 103(1987) .

Zeit .

Phys .

C34,

17. For example, ref . 16. ; I . Dunietz and J . Rosner, Phys. Rev . D34, 1404(1986) . 18. My own compilation is unpublished, but available upon request . 19. M. Ademollo and R. Gatto, Phys. Rev. Lett 13, 264(1964) .

Y . Keung, Phys . Rev . L . L . Chau and W . Lett . 53, 1802(1984) ; C . Hamzaoui, J . Rosner, and A . Sanda ; also reference 3 .

20 . There are many such estimates extant, A sampling can e none very reliable .

6.

The input data used in Fig . 1 come ., from the analysis of H . Harari and Y . Nir, Phys . Lett . 8 195 , 586(1987) ; Y . Nir, SLAC preprint SLAC-PUB-4368(1981) .

7.

(Talk ITP preprint 8/87 C . Jarlskog, 4th LEAR Workshop, presented at the Switzerland,(Sept . Villars-sur-Ollons, 1987) .

the Areas for Experimental and Supercollider; Berkeley, Ca ., ed ., R . Gilchriese, (World Donaldson and Scientific, 1987), p . 759 ; also the talks of N . Lockyer and D . acfarlane in ref . 1.

8.

For a discussion of this gaugeless limit, Proceedings of the 7th see J . Bjorken, Exotic "New and Moriond Workshop, Fackler and J . Tran Phenomena", ed ., 0 . Editions Frontieres (Gif-surThanh Van, Yvette, France, 1987), p . 1 .

9.

A useful discourse on this is provided by H . Lipkin, preprint ANL-HEP-PR- ?/88 ; to be written .

found in K. Foley et . al, Proceedings of the Workshop on Experiments, Detectors,

Fe slab proposal P21 . D . Kaplan et . al ., 789 ; see the discussions by P . Garbincius and by D . Kaplan et . al . i n ref . 1 . 22 . B . Cox et . al ., Fev,erla experiment Eby P. discussions the 771 ; see d by .. a oner, an by D . Garbincius, Selove in Ref . 1 .