Nuclear Physics B (Proc . Suppl .) 16 (1990) 635-637 North-Holland
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
symmetry ^ould be broken dynamically ,
the use of Higgs scalars, while maintaining the successful gauge boson mass relation p=M2W /M2 Z cos 2 9w 1 .
GTC which confines at Arc N 1TeV is introduced together
(T+ ' *,
By analogy with QCD dynamics,
T -l )
global chiral symmetry SU(2) L xSU(2) R in the TC A
is broken to SU(2)L+R " massless composite technipions v+ TC " 'ff TC , 'OTC result from Goldstone's theorem, but they do not
they are eaten by W+ , W- , longitudinal masses are 1 :
F,s t ,F.o
Zo and become their
MW t = gF, 1t /2, MZ o =gFT /2cos8w are
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
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
(i .e .quarks
0920-5632/90/$3 .50 © Elsevier Science Publishers B .V . North-Holland
momentum dependent technifermion self-mass E(p) to be
which acquire a mass mf_(1/M2ETC) . where ti (1/2v2 )
is determiLd by a gap equation (see
and E(p) later) .
Unfortunately the ETC bosons also generate fermion-fermion
flavour-changing neutral currents2 (FCNC's) .The most severe constraint arises from AS=2 operators
sdsd which mediate
id - ds
The KL-KS mass difference leads to the
constraint METC leads to
a bound mf 61-4 MeV,
But this value is
estimate of the condensate . too small to
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
B& TC Bp
where *TC=gTC2/4s, and b is given by b=(
C 2 (G) -
S.F. King/ Technicolor today
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
"iCC TC where 0
operator TLTR .
TR >= A2TC MEN . fermion mass becomes
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
(up to logarithms) . In practice the logarithmic
fall-off of aTC is usually sufficiently fast to ensure that the asymptotic solution sets in
ered by a number of authors 4 . The above enhancement of rests on the assumption of a fixed-point in order to achieve pTC=O . However, similar but less spectacular enhancements of the condensate are possible for free
The solutions E(p) can be simply described .
The new bound on
fixed-point approach has recently been consid-
where a = a(max (k2 ,p 2 )) .
leading to a value of the
almost immediately, condensate
rough agreement with the
estimate -A3TC . In fixed-point theories fC (p)x ac over the whole on the other hand and hence E(p)N1/p over the whole
range of p, range,
Walking technicolor theories rely
~A2TC HETC° In walking TC the coupling falls off more slowly than a logarithm, and
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-
or o f=2
rep R>>Ro of
technifermions in a very large GTC
(type A theories),
resulting condensate enhancement has been studied numerically 7 .
The gap equation
other combination (type B theories),
tions from various other sources 8-11 . The next
Care must be
order technigluon corrections beyond the ladder
(to maintain ASF),
and cac 3
ensure that b>0
ac-a,/3C 2 (R) is the critical coupling at
which chiral symmetry breaking takes place . In
theories, and by about 20% for type C theories . for techniquarks
is QCD gluon exchange9 . Technileptons, which by definition
receive no such corrections .
This can result
tion l0 ,
renormalisation group improved gap equation is in ladder approximation 2 I(p )=
3C 2 (R) 4v
ing to Eulidean space, performing the angular a
Landau gauge (for which Z(p)=0), after continuintroducing
/-10 . Fi10,11 nally, ETC boson exchange corrections have
Another important correction
important coupling strong .
k 2 dk 2a max(k2
ï(k2 ) 2)
k2+ 12 k2
four-fermion full to
theory ll ,
approximaand F,, if
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 .
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
TeV, although the technirho could be as as 300 GeV in some models l5 .
It should be clear that ETC can no longer be ruled
theories of flavour at mass scales METC-1-1000 TeV which will someday be accessible to experimentation .
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
sor, QED . I'
D .Ross .
like am also
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) .
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 .
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 .