On models of weak interaction symmetry breaking by colour forces

Volume 132B, number 4,5,6

PHYSICS LETTERS

l December 1983

ON MODELS OF WEAK INTERACTION SYMMETRY BREAKING BY COLOUR FORCES K. KONISH1 INFN, Sezione di Pisa, Istituto di Fisica, Universit~ di Pisa, Pisa, Italy

and R. TRIPICCIONE Scuola Normale Superiore, Pisa, Italy and INFN, Sezione di Pt'sa, Pisa, Italy

Received 8 July 1983

Comments are made on models in which the Weinberg-Salam symmetry is broken by colour forces. In particular, we discuss the relevance of compositeness of quarks, leptons and new fc,rmions (including a family of colour sextets).

In a recent paper [1 ], models [2] based on the standard SU(3) X SU(2) X U(1) gauge interactions,

(ilL) = (6;2 ;-1/3),

qL = aL

£ = £0 (no Higgs scalars) + 2 ' , (tR = aR = ( 6 , 2 ; 2/3)/ £' =

~ i~7#Duff , new fermions

(1)

have been discussed, with main emphasis on their phenomenological implications. In eq. (1), £0 is the standard QCD-Weinberg-Salam lagrangian [3] with quarks and gluons but w i t h o u t terms involving Higgs scalars. The set of new fermions { if} contains precisely one family of colour sextet fermions plus, possibly, a number of new colour singlet fermions. The coloursextet fermions play the role of "techniquarks" [4] : the electroweak SU(2) X U(1) symmetry is spontaneously broken down to Uem (1) by the condensate of colour sextet fermions at the mass scale g ~ 250 GeV. Assuming the dynamical possibility of such a scenario, models of this type are simple and elegant. We wish to add a few observations regarding these models. 1. The first concerns the quantum number assignments of the new fermions in eq. (1). A particularly interesting possibility, which was not mentioned in refs. [1,2], is the following anomaly-free set: { ~} = {qL,R, QiL,R i = 1,2},

=.2;1) \ eiL

[eiR

(i= 1 , 2 ) .

(1

; 1 ; 2)

(2)

Namely, the U y ( 1 ) charges of Cl and J~are opposite to those of the quarks (q) and leptons (2) respectively. As pointed out in ref. [1], the model predicts a set of new species of hadrons involving el's, the lightest among which are of the type qq~t or qctg (q = quark; g = gluon). Because of the ~t-number conservation, some of these states (with mass ~0.25 TeV?) are expected to be absolutely stable. The assignments of eq. (2) are such that all the states qq~ and q/lg - in fact all colour singlet states - are integer-charged. (This is in contrast to the cases mentioned in ref. [1 ].) This avoids potential problems with the abundance o f fractionally charged particles on the earth, produced by high-energy cosmic rays ,1. ,1 One of us (K.K.) is grateful to Chart Hong-Mo for pointing this out and for discussion.

0.031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland

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2. The idea that all fermions - quarks, leptons and those of eq. (2) - are composite seems to fit well and complement the model. There are several points: (i) Existence itself of the light colour-sextet fermions along with colour-singlets (leptons) and colourtriplets (quarks) looks natural in a composite model in which some of the preons (fundamental particles) carry colour. (ii) It might happen that 't Hooft's consistency conditions [5] which have been found rather difficult to satisfy in a realistic model force the presence of the new set of fermions, eq. (2), besides the three families of quarks and leptons. (This is indeed what happens in the model discussed below.) (iii) Since fermions are all composite, the full lagrangian contains effective non-renormalizable interaction terms, among which are terms of the form (see eq. (8) of ref. [1]), £" = const. (~l~t)(~q).

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of flavour changing neutral currents persists. See also the comment at 3. (iv).] (iv) The quantum number assignments of eq. (2) for the colour-sextet fermions which is preferred phenomenologically is precisely the one expected in a composite model. If one (or more) preons carry the fundamental charge of colour, the composite fermions get the SU(3) quantum number according to, e.g., 3X3Xl=3*+6. It is thus natural to expect that the colour 3* (antiquarks) and 6 fermions share the same quantum numbers with respect to the orthogonal SU(2) × U(1) group, as in eq. (2). Indeed, this occurs in the model discussed below. 3. A model. The points made in 2 (and others) are well illustrated in the following model. The fundamental fermions (preons) and their quantum numbers are shown in table 1. We take the SU(3)QCD X SU(2) × U(1) gauge symmetry to be exact betore and after confinement, and the strong confining (hypercolour) interactions to be of QCD-type, SU(3)H C. The global symmetry group is a product of three U(1)'s, as indicated in table 1. In the limit where all coupling constants related to SU(3) X SU(2) X U(1) are set to zero, the model possesses a larger global symmetry,

(3)

At energies/a <~ 250 GeV, these terms play the role of Yukawa interaction terms in the original WeinbergSalam model. The smallness of the (effective) Yukawa coupling constants is the consequence of the fact that the scale of compositeness is larger than 250 GeV - the scale of weak interaction symmetry breaking. [The actual magnitude ofgyukawa'S is however not understood this way: the well-known problem of the suppression

C~0) = SU(8)L × SU(8)R × UV(I ) .

(4)

Table 1 Elementary fermions (preons). UA(1) is generated by the anomaly free linear combination, QA = Q(A Q) - 3Q~ ), of Q and L axial charges. Preons

QL =

(uL)

Gauge group

Global sym.

SU(3)H C SU(3)QCD × (SU(2) × U(I))GWS

UQ(1)

UL(1)

UA(1)

3

3

2

1/3

1

0

1

DL UR

3

3

1

4/3

1

0

-1

~DR

3

3

1

-2/3

1

0

-1

LL = ~ - }

3

1

2

-1

0

1

-3

NR

3

1

1

0

0

1

3

~ER

3

1

1

-2

0

1

3

QR =

~12,Lt

LR=

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Volume 132B, number 4,5,6

PHYSICS LETTERS

As the hypercolour forces become strong at/~ ~ AHC , preons are confined and the global symmetry is dynamically broken to some subgroup G F C G (0). Since (by assumption) the weak gauge symmetries are un-

1 December 1983

broken at # < AHC, G F should contain at least SU(3) × SU(2) × U(1). Hence, G F cannot be a subgroup such as diagonal SUv(8), as might be expected from the simplest set of preon condensates. We assume that

Table 2 Composite fermions, qL,R and ~L,R carry the standard quantum numbers under SU(3) × SU(2) X U(1), while those of ftL,R and ~L,R are as in eq. (2).

qL

UQ(1)

UL(I)

mult.

-2

-1

2

,

2

1

-2

-1

2

1

2

1

DRDRQL

3

0

2

(vrI

NRNRLL

0

3 1

(/

DRDR

3

0

2

0

3

1

2

1

1

"1

1

-3

2

(u) (c) d L SL

[QLQLILL, URDRLL°rQLURI~R

ttt

\ b !L qR

[UR (CR

[QLQL]

(dR [SR tR

~NR NRNR

bR

~L

(Ve) (v~)

( _ER , URDR/E_R or (DRDRNR ~NR ~URURER

/UR [DR

\e-/L \~t-/L \ fT--L QR

v~ v~ ~eR~R uR rR

gtR

(DR NRNR

NR [ER

~1

[QLQL] LL, URDRLL or QLURER

'fiR ~1R

[QLQL1

~ER ER or , URDR , NR (NR (URURER

2

~L \ ~1L / \ ~2 / L

~R

(b,R(b2R ~elRte2R

~R(N-R

0

(ER

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Volume 132B, number 4,5,6

PHYSICS LETTERS

G F is given by G v = (SU(3) X SU(2) X U(1)) X UQ(1) X UL(1 ) . (5) The set of composite fermions, satisfying 't Hooft's anomaly-matching conditions with respect to this group, are shown in table 2. There are nine nontrivial consistency equations, apart from those involving only vector like vertices (SU(3)QCD , UQ(1) and UL(1)) which are satisfied by construction. Explicit check shows that all these conditions are indeed satisfied. Several remarks are in order. (i) 't Hooft's conditions are satisfied by the presence of precisely those fermions of eq. (2), together with three families of quarks and leptons. No solutions are found if colour-sextet composites are excluded from the beginning. It should be remarked however that the set o f table 2 is not the minimal one required by 't Hooft equations. In fact, the third family of left handed leptons and two new families of right handed (~L))'s produce the total index - 1 . (Analogously for the third ~R and (~R) "~'S.) (ii) The quantum number assignments of the new fermions is as expected [2.(iv)] : ct and ~ have opposite quantum numbers with respect to SU(2) X U(1) as compared to q and !~. (iii) Fermions can get Dirac masses, upon condensation of colour-sextet fermions (at # "~ 250 GeV), e.g. through effective four fermion interactions*2. (iv) The strong P and C P problem is solved in this model b y the presence of an axion of the type of Kim [6], related to the UA(1 ) o f table 1. The mechanism has been discussed in ref. [7] in a general context of

,2 In this model there is a possibility for neutrinos to be much lighter than other fermions. Besides the Dirac mass of ordinary size, a large (~ AHC) nondiagonal Majorana mass term Mu_ Re v Re, + h.c connecting uR to uit" ~ [QLQL] DR or _ _ URURD R is allowed by G R. Diagonalization of the mass term leads to one massless state. Although interesting, in this case'one of 't Hooft's conditions (with three UQ(1) vertices) would no longer be satisfied.

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1 December 1983

composite models, and there is an astrophysical argument [8] leading to a constraint, AI4c ~> 1 0 8 - 1 0 9 G e V , on the scale of hypercolour interactions. Such a high scale is also welcome in view of the strong suppression of flavour changing neutral currents. Naive estimates of the masses o f light fermions would then come out to be too small, however. Clearly there is much to be understood on the origin o f the quark and lepton masses. (v) Although there is no lepton number or baryon number conservation as such, the UQ(1) and UL(1 ) symmetries forbid the proton to decay in this model. Indeed, table 2 shows that processes of the type qq + ct~ or @ are not allowed for the first two families. Baryon number violating processes involving the third family are however not forbidden in general. The model presented here is certainly not a realistic one. One difficulty, for instance, is that there is no mixing o f the third family of quarks with the first two. A more fundamental problem is the lack of dynamical understanding of the model (pattern of symmetry breaking, etc.). Nonetheless, this discussion was present ed to illustrate how a composite model of quarks, leptons and new fermions can complement and give an improved picture of the scheme of eqs. (1) and (2). References

[1] K. Konishi and R. Tripiccione, Phys. Lett. 121B (1983) 403. [2] W.J. Marciano, Phys. Rev. D21 (1980) 2425. [3] S. Weinberg, Phys. Rev. Lett. 19 (1967) 1267; A. Salam, Proc. 8th Nobel Syrup. (1968), ed. N. Svartholm: S. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D2 (1970) 1285. [41 For a review, see: E. Fahri and L. Susskind, Phys. Rep. 74C (1981) 277. [5] G.'t Hooft, Carg~se Lectures, III (1979). [6] J.E. Kim, Phys. Rev. Lett. 43 (1979) 103; M.A. Shifman et al., Nucl. Phys. B166 (1980) 493. [7] M. Konishi, Nucl. Phys. B207 (1982) 313. [8] D.A. Dicus et al., Phys. Rev. D18 (1978) 1829; M. Fukugita, Phys. Rev. Lett. 48 (1982) 1522.