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635

TECHNICOLOR TODAY Stephen F . KING Physics Department, The University, Southampton, S09 5NH, England The present status of technicolor theories is reviewed, with emphasis on the recent idea of walking technicolor .

1 . A BRIEF HISTORY OF TECHNICOLOR The idea of technicolor (TO is due to Weinberg and

Susskind l

who

showed

electroweak

that

symmetry ^ould be broken dynamically ,

without

the use of Higgs scalars, while maintaining the successful gauge boson mass relation p=M2W /M2 Z cos 2 9w 1 .

A

gauge group

technicolor

GTC which confines at Arc N 1TeV is introduced together

with

an

doublet

anomaly-free

of

half-integer charge

technifermions

(T+ ' *,

which

rep

butare

QCD

By analogy with QCD dynamics,

the

are

singlets .

in

some

R

of

GTC

T -l )

global chiral symmetry SU(2) L xSU(2) R in the TC A

sector

triplet

of

is broken to SU(2)L+R " massless composite technipions v+ TC " 'ff TC , 'OTC result from Goldstone's theorem, but they do not

occur

in

the

physical

they are eaten by W+ , W- , longitudinal masses are 1 :

(L)

F,s t ,F.o

the

spectrum .

Instead

Zo and become their

components .

The

resulting

MW t = gF, 1t /2, MZ o =gFT /2cos8w are

technipion

decay

constants

which are equal due to techni-isospin symmetry SU( 2 )L+R "

Soon afterwards Dimopoulos and Susskind 2 and showed how quark and lepton

Eichten and Lane

masses could arise within a dynamcal framework called

extended

technicolor

(ETC) .

The

basic

idea is to embed G TC in a larger gauge group broken at a scale METC to GETC which is where G TCx . . . ., METC >ATC - 1 TeV . The heavy mass METC generate ETC gauge bosons of couplings

between

fermions

technifermions .

leptons)and

(i .e .quarks

and

0920-5632/90/$3 .50 © Elsevier Science Publishers B .V . North-Holland

This

allows

the

momentum dependent technifermion self-mass E(p) to be

fed

down

radiatively

to

the

fermions,

which acquire a mass mf_(1/M2ETC)

METC

pdp E(p)

is determiLd by a gap equation (see

and E(p) later) .

Unfortunately the ETC bosons also generate fermion-fermion

couplings

hence

and

flavour-changing neutral currents2 (FCNC's) .The most severe constraint arises from AS=2 operators

sdsd which mediate

-(1/M2 ETC)

mixing .

id - ds

The KL-KS mass difference leads to the

constraint METC leads to

h500-1000

TeV .

a bound mf 61-4 MeV,

in

turn

But this value is

estimate of the condensate . too small to

This

using the naive

account for most fermion masses

-hence the FCNC problem . 2 . WALKING TECHNICOLOR

Back in 1981 Holdom suggested a way around

the FCNC problem3 .

Holdom proposed that the TC

theory was born at a fixed point gTCoO, PTC=O " where 9TC is the TC coupling constant and pTC is the beta function describing the evolution of this coupling : p

ßTC

B& TC Bp

-ba

2 TC

COLTC

3

..

where *TC=gTC2/4s, and b is given by b=(

31

C 2 (G) -

3 T(R)nfJ

S.F. King/ Technicolor today

636

where C2(G) is the Casimir of the adjoint rep G, T(R) is the index of the technifermion rep R and of is the number of Dirac technifermions . For a fixed-point the condensate is given by3 [ HETC )v

NC

"iCC TC where 0

operator TLTR .

TR >= A2TC MEN . fermion mass becomes

For p

8(p)=ï(0)

scale,

(flat) .

For

pap,

where perturbation theory is more trustworthy, depends upon the value *TC(p)x of aTC(p)6 . In the region where ac, 1 ac,l(p)_1/p . However, for c, ;(p) < E(p)N1/p the

behaviour of

i(p)

the

(up to logarithms) . In practice the logarithmic

mf

The

fall-off of aTC is usually sufficiently fast to ensure that the asymptotic solution sets in

4

1-2

GeV .

ered by a number of authors 4 . The above enhancement of

The solutions E(p) can be simply described .

The new bound on

fixed-point approach has recently been consid-

asymptotically

where a = a(max (k2 ,p 2 )) .

theories

(ASF)

in

which

leading to a value of the

almost immediately, condensate

rough agreement with the

in

naive

estimate

range of p, range,

leading

to

an

condensate

enhanced

Walking technicolor theories rely

on either a large number o f>>2 technifermions

hence the solution 1(p) -1/p, persists over a

in the fundamental rep Ro of GTC (type C theo-

larger

p TCeO

and

the

(walking) .

ries)

or o f=2

rep R>>Ro of

coupling

is

slowly

running

technifermions in a very large GTC

(type A theories),

resulting condensate enhancement has been studied numerically 7 .

or some

range of

p.

The

The gap equation

receive correc-

may also

other combination (type B theories),

in order

tions from various other sources 8-11 . The next

to arrange

Care must be

taken to

order technigluon corrections beyond the ladder

(to maintain ASF),

and cac 3

approximiation8

that

. b%0

ensure that b>0

convergence

of

the

series),

ac-a,/3C 2 (R) is the critical coupling at

which chiral symmetry breaking takes place . In

order

to

enhancements

estimate

which

technicolor

theories

haviour

ï(p)

of

the

arise we

using

must

study

gap

walking the

decrease

to few

be-

for

type

A

theories, and by about 20% for type C theories . for techniquarks

is QCD gluon exchange9 . Technileptons, which by definition

carry technicolor

receive no such corrections .

not

colour,

This can result

been

integrations

tion l0 ,

cut-off,

the

renormalisation group improved gap equation is in ladder approximation 2 I(p )=

3C 2 (R) 4v

2 HETC

JO

in

condensate

but

ing to Eulidean space, performing the angular a

In

the critical

per cent

Landau gauge (for which Z(p)=0), after continuintroducing

equation .

by a

and

the

tend

ac

Another important correction

condensate

for

coupling

studied

important coupling strong .

k 2 dk 2a max(k2

ï(k2 ) 2)

k2+ 12 k2

and

splitting

in in

the the

corrections to

four-fermion full to

theory ll ,

technifermions

and is

approximaand F,, if

give the

sufficiently

S.F. King/ Technicolor today 3 . CONCLUDING REMARKS There are so many TC models in the literature it is impossible to review them all . The best model

I have been able to write down is

called chirally extended technicolorl 2 (XETC) . The phenomenology of TC theories is very model dependent .

For example,

models with a single

family of technifermions (such as XETC) produce a very rich spectrum of pseudo-Goldstone bosons (PGB's) which have been well studiedl 3 . But the most model independent prediction of TC is that W±L=v±TC , ZoL=40TC so there should be some kind of resonance corresponding to pTC visible in the production at W LW L e +e-supercolliders l4 , in the

SSC13 mass

and

at

range

1-2

TeV, although the technirho could be as as 300 GeV in some models l5 .

light

It should be clear that ETC can no longer be ruled

out

feature

on

about

the

basis

ETC

models

of

FCNC's .

are

that

The they

nice are

theories of flavour at mass scales METC-1-1000 TeV which will someday be accessible to experimentation .

True,

ETC

theories

appear

rather

Phys .Rev .Lett . 56 (l986)1335 ; Phys .Lett . B178 (1986) 308 ; M .Bando, T .Morozumi, H .So, K .Yamawaki, Phys .Rev .Lett . 59 (1987) 389 ; V .A .Miransky, Nuovo Cimento 90A (l985)149 and S .T .Love, W .A .Bardeen, C .N .Leung Phys .Rev .Lett .56 (l986)1230 ; Nucl .Phys . B273 (1986) 649 ; 5 . B .Holdom, Phys .Lett . B150 (1985) 301 . T .Appelquist, D .Karabali and L .C .R . Wijewardhana, Phys .Rev .Lett .57 (1986) 157 ; T .Appelquist, and L .C .R .Wijewardhana Phys .Rev .D35 (1987) 774 ; Phys .Re'v .D36 (1987) 568 . 6 . K .Lane, Phys .Rev .D10 (1974) 2605 ; H .D .Politzer, Nucl .Phys .B117 (1976) 397 . M .E .Peskin, in : Recent advances in field mechanics,Les and statistical theory eds .J .B .Zuber Houches Lectures (1982), Amsterdam, (North-Holland) and R .Stora 1984) 7 . T .Appelquist,D .Carrier,L .C .R .Wijewardhana and W .Zheng, Phys .Rev .Lett . 60 (1988) 1114 ; S .King and D .Ross, Phys .Lett .B228 (1989) 363 . 8 . T .Appelquist, K .Lane and U .Mahanta, Phys .Rev .Lett .61 (1988) 1553 B .Holdom, Phys .Lett .B213, (1988) 365 .

baroque compared to the standard model . But it

9 . B .Holdom, Phys .Rev .Lett .60 (1988) 1233

is also true that the standard model itself is

10 .T .Appelquist, T .Takeuchi, M .Einhorn and L .C .R .Wijewardhana, Phys .Lett .B220 (1989) 223 ; B . Holdom, Phys .Lett . B2" : (l989)137

rather baroque when compared to

its

predeces-

sor, QED . I'

would

D .Ross .

I

like am also

to

thank

grateful

my to

collaborator the

SERC

for

the support of an Advanced Fellowship .

11 .S .King and D .Ross, Technicolor in the presence of extended technicolor interactions,Southampton preprint SHEP 88/89-17 (submitted to Phys .Lett .B) .

REFERENCES

12 .S .King, Phys .Lett . B229 (1989) 253

1 . S . Weinberg, Phys .Rev . D19 (l979)1277 ; L .Susskind, Phys .Rev .D20 (1979) 2619

13 .E .Eichten, I .Hinchliffe, K .Lane and C .Quigg, Phys .Rev .D34 (1986) 1547 ; Rev .Mod .Phys . 56 (1984)579 .

2 . S .Dimopoulos and L .Susskind, Nucl .Phys .B155 (1979) 237 E .Eichten and K .Lane, Phys .Lett .B90 (1980) 125 3 . B .Holdom Phys .Rev . D24 (1981) 1441 4 . K .Yamawaki, M .Bando, K .Matumoto .

637

14 .S .King and M .Machacek, Proc . of the summer study on High Energy physics in the 1990's, June 27-July 15, 1988, Snowmass, Colarado, Ed .S .Jenson . 15 .K .Lane and E .Eichten, Phys .Lett . B222 (1989) 274 .