\\£ IC/80/72
INTERNATIONAL CENTRE FOR •2t i / -Tr/ THEORETICAL PHYSICS
QUARK-LEPTON UNIFICATION AND PROTON DECAY
Jogesh C. Pati
and
Abdus Salam
INTERNATIONAL ATOMIC ENERGY AGENCY
UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1980 MIRAMARE-TRIESTE
IC/60/72
QUABK-LEFTON UNIFICATION AND PROTON DECAY
I. INTRODUCTION
Jogesh C. Pati The hypothesis of prnncS unification servinR to unify all basic particles - quarks and leptons - and their force:; - weak, International Centre for Theoretical Physics, Trieste, Italy, electromagnetic as well as strong - stands at present primarily and on its aesthetic merits. It gives the flavour of synthesis in that it provides a rationale for the existence of quarks and Department of Physics, University of Maryland, College Park, leptons by assigning the two sets of particles to one multiplet + Maryland, USA, of a gauge symmetry G. It derives their forces through one principle-gauge unification.
and With quarks and leptons in one multiplet of a local sponta- neously broken gauge symmetry G, baryon and lepton number conserv- ation cannot be absolute. This line of reasoning had led us to Abdiis Salam suggest in 1973 that the lightest baryon - the proton - must ultimately decay into leptons 2. Theoretical considerations International Centre for Theoretical Physics, Trieste, Italy, suggest a lifetime for the proton in the ran^e of 102° to 1033 a and years "5. Its decay modes and corresponding branching ratios depend In general upon the details of the structure of the symmetry Imperial College, London, England. Kroup and its breaking Dattern. What is worth noticing »t this Junction Is that studies of (i) proton decay modes, (il) n-n oscillation (iii) neutrinoless double 6-deeay and (iv) the weak angle T sin26y are perhaps the only effective tools we would have for sometiae to probe into the underlying design of grand unification. ABSTRACT Experiments are now underway to test proton stability to an accuracy one thousand times higher than before . In view of this, we shall concentrate primarily on the question of expected proton decay modes within the general hypothesis of quark-lepton unifi- cation and on the question of intermediate mass scales filling the Complexions for proton decay arising within a maximal symmetry £ 1 for quark-lepton unification, which leads to spontaneous rather grand plateau between 10 and lO- ^ GeV, which influence proton than intrinsic violations of B, L and F are considered. Four decay. At the end we shall indicate some new features, which may major modes satisfying AB = -1 and flF « 0, -2, -U and -6 are arise if quarks and leptons are viewed - perhaps more legitimately - noted. It is stressed that some of these modes ran coexist In as composites of more elementary objects - the "preons". accord with allowed solutions for renormalization group equations for coupling constants for a class of unifying symmetries. None Much of what we say arises in the context of maximal of these remarks Is dependent on the nature of quark charges. quark-lepton unifying symmetries of the type proposed earlier " . It is noted that if quarks and leptons are made of constituent wespecify such symmetries in detail later. One characteristic preons, the preon binding is likely to be magnetic. feature worth noticing from the beginning is that within such symmetries & linear combination of baryon and lepton numbers as well as fermion number F are locally gauged and are therefore conserved in the gauge Lagrangian. They are violated spontaneously and unavoidably as the associated gauge particles acquire masses. MIRAMARE - TRIESTE The purpose of the talk would be many-fold:
May I960
The presentation here follows the talks given by J.C. Pati at the Grand Unification Workshops held at Erice, March 1979 and at Durham, New Hampshire, April 1930. Address until 1 December 1980. -2- Permanent address (after 1 December 1980). l) First to repress in the light of recent developments that with- is the sum of B^ and L: F = B + L. Since for proton in maximal symmetry framework' the proton may in general decay via decayiquark number must change t>y a fixed amount AB = -3, there is four major modes ^l^, which ^j^ characterized by a change in baryon number by -1 and that in fermion number'defined below) by 0, -2, a one-one relationship between change of fermion number F and that -U and -6 units ™ of any other linear combination of Bq and L for example of [(Bg/3) - L] = B - L for the proton decay modes as exhibited in (D-d).
p •* 3« + » AF = 0 2) Our main emphasis here is that these four alternative decay = -li modes can in general coexist. 2\J IT p •+ + e~ + ir etc % = -3, Ve wish: (1) 3) To streBB that observation of any three of the decay modes satisfying AF e 0, -2 and -6 would unquestionably signal the + + p + e~* » , V* , e~K n AF « -2 existence of one or several intermediate mass scales filling the 2 1 + + _-. + _' .A(B-L) ' -2 plateau between 10 and lO ^ GeV. [Existence of such intermediate AB = -3, AL = +1 mass scales is a feature which naturally rhymes with (a) maximal p -* e v-v^e e e ir i etc 1 ) (2) symmetries and the consequent spontaneous rather than intrinsic + 0 — + +0 nature of B, L, F violations and (h) partial quark-lepton AF — -k 1 6 2 10 p •+ e ii , V^T , M K unification at moderate energies • 10 * - 10 GeV.] . Lfl(B-L) = 0 ,vn,eee etc ABq = -3, AL = -1| U) To point out that the complexions of proton-decay f (3) selection rules alter if one introduces intrinsic left-right pj,i + +- - + +- - 1 AF -f symmetry in the basic Lagrangian thereby permitting the existence + TT , e « v ,e e VTT etc) _\ A(B-L) = +2 AB = -3, AL of Vj,' s parallel to v^' s and (M 5) To stress that none of the remarks (l)-(U) is tied to the (Here Bo denotes quark number which is +1 for all quarks, -1 for nature of quart charges. These remarks hold for Integer as well antiquarks and 0 for leptons. The familiar baryon number F^ as fractional quark charges. fin the later case ffractional charges), 5U(3) colour symmetry is exact.] which is +1 for the proton, is one third of quark number (B Bq/3). L denotes lepton number which is +1 for (v ,e ,u~,v,,,...)^ -1 for their antipartioles and 0 for quarts. Fermion number ' F To motivate these remarks let us first specify what we mean by "maximal" symmetry. Maximal symmetry 9 corresponds to gauging all fermionic degrees of freedom with fermions consisting of quarks FlJThat the proton may decay via all these four modes {AF - 0, .-2, and leptons. Thus vith n two component left-handed fermions Fj -h and -6) was to our knowledge fir3t observed in Hef.9. The modes' plus n two component right-handed fermions F^, the symmetry G AP = 0 and -1* occur vithin specific models of Ftefs.2 and 3, is SU(n)jj * SU(n)p. One may extend the symmetry G by putting respectively, while the questioning of baryon number conservation fermions FT and antifermions FV (as a substitute for Fp) in the (Bef.2) is based on more general considerations and is tied simply, to the same multipiet. In this case the symmetry G is RU(2n), which is idea of quark-lepton gauge unification^ together with spontaneous symmetry breaking. truly the maximal symmetry of 2n two component fermions. As an F2)we are not listing decay modes satisfying AB = -1 and AF = +2,k example, for a single family of two flavours and four colours in- etc. corresponding to p •+ (5 or 7 leptons) + IT'S. These appear cluding leptonic colour, n = 8 and thus G = SU(l6). One word of to he suppressed compared to those listed • qualification! Such symmetries generate triangle anomalies, which are avoided however by postulating that there exist a conjugate mirror set of fermions F™ p supplementing the basic fermions FTj R F3)The reader may note that in our previous papers we had by with the helicity flip coupling represented by the discrete symmetry convention chosen to call quark number B as baryon number B. Therefore the 15th generator of SU(>0 q(f?ef.2) which was written C as (B-3L) stood for (Bq - 3L). With the more conventional that in this case one must assume that Vp and v^ combine definition of baryon number, as adopted in the present note, to form a light k component Dirac particle and that ny >> m^ R B - 3L is Just 3(B-L). (To conform with astrophysical limit one may need i\, > 50 ^ see G. Steigman, Erice Workshop Proceedings, March -H 1980,) The alternative of vR acquiring a heavy Majorana mass-is of course permissible; but such heavy \>R will not be a decay product in proton decay.
-3- -k- ). Thus by "maximal" symmetries we shall mean L K,L for reasons stated above -Or the gauging of subgroup ff leads to a "squeezing" of gauges of the maximal symmetry G such that one and symmetries which are maximal upto the discrete mirror symmetry. the same gauge particle couples for example to the diquark (qcq) as Though old, it is now useful to recall the argument leading to well as to the quark-lepton (
Bef.ll). But all simple models end up with an unstable proton (Refs.1-3). SU(2)L x su(2)n * (6)
F8) For example [SOU)]** and [SU(6) l"4 contain (B-L) as a local j)R operates on the flavour indices (u,d)j p and symmetry, but not F (though F is a global symmetry in the basic k+p operates on the four colour indices (r,y,h,t).J* It is the Lagrangian of these models). S!.'(l6) operating on 16 folds of e, SU(lt) colour symmetry which intimately links quarks and leptons. u and T family fermions (see Table I) is a subgroup of [SU(l6)]3 The symmetry •& has three features: i) First it is one of the B and likc- and SU(I*8). It contains B-L and F with B = Be + T simplest subunificatlon models containing the low energy symmetry wise for L and F. SU(2)L x U(l) * SU(3)£+R on the one hand and realizing quark-lepton
F9)Examples of this type are S"(5) (Ref.3) and r,o(lO) (Ref.12). SU(5) does not contain B-L or F as local symmetries. "0(10) contains (B-L) but not F. Both Sll(5) and 30(10} violate B, L and F explicitly in the basic gauge Lagrangian.
-5-
-6- unification on the other. It gauges through the SU(I») colour ayiranetry (linking quarkB and leptons) the combination All the unifying symmetries listed In Table I are left-right (Bq-31.) = 3(B-L) as a local symmetry, ii) Second, it is non- symmetric. By contrast one may consider the left-right asymmetric abelian end thus provides a simple raison for the quantization model 3 SU(5), which is the smallest grand unifying symmetry of of charges, iii) Its gauge structure is left-right symmetric . all vith the multlplet structure (indeed the idea of lepton number ' as the fourth colour requires that neutrinos must tie introduced with left and right helicities F and thereby the basic matter multiplet must be left-right symmetric (5 (5 + 10). given that quarks enter into the basic Lagrangian with both helicities.) In which the right-hancted neutrinos (v , ) are missing. Note that A* contrast to the models listed e'v'x in Table I the The symmetry ^ , because of its simplicity, might be the MUltlplet structure for SU(5) is reducible-(5 + 10) within one right stepping stone tovards grand unification. It should of course family. ' be viewed as a subunification symmetry as it contains at least two Even if Nature Is intrinsically left-right asymmetric, froa gauge coupling constants - one ^ for SU(2)L p and the other for n other the point of view of maximal gauging, the underlying family symmetry SU(M^n. * words, it Bhould be regarded as part of a bigger would be SU(15), for which the (5 + 10) form a single 15-fold. It unifying symmetry G possessing a Bingle gauge coupling constant. Is worth remarking that SU(l5) , S0(l0} and SU(5) may There are a number of candidates for G, which do contain the sub- all be viewed as subgroups of SU(l6). The symmetry SU(l6) gauges unification symmetry ^ . Table I provides a list of some of bo^h fermion number F as well as B-L as local symmetries and these symmetries. thereby conserves both in the gauge Lagrangian before their Table I f spontaneous violation.SO(lO), however, gauges B-L (since it contains SU(2V x su(2) x " ' - gg D ^ SO(lt) « SO(6)) but not the (1) tsuCOl flavours x U colours) R fermion number F. In fact F is violated so far as the S0(10) gouge + (U flavours x It colours) , Lagrangian is concerned due to squeezing of SU(l6) gauges in the (Ref.2) T>T sense mentioned earlier. By contrast Su(5) gsjigse-neUber F- nor B-L as local symmetries. For SU(5) like S0(l0), F is explicitly (2) [Su<6)] flavours x 6 colours) violated In the gauge Lagrangian. Depending upon the choice (Ref.15) of~~the Higgs structure'and the fermion-Higgs Yukawa interactions, B-B may or may not be a good global quantum number for SU(5). (3) Maximal symmetry for a family (For exampleithe simplest SU(5) model with a SU. and % of Higgs SU(16) & + l6u+ 16 conserves (B-L)j but this is not a general property of SU(5)-) •I.C C . C Ci In general, since SU(16) OSO(lO) and SU(5), it may descend l6 id, e e = [u,«e u ,v J, spontaneotwiy to 3U(2) x U(l) " SU(3) via S0(10) or SU(5) as (Refs.9,16) Intermediate steps. Alternatively, it may descend via SUfS)- * U(l)-,, where U(l)_ gauges fermion number and B r r ft of a given (h) S0(10) L6e + 16 + l6T SU(8), and SU(8)B operate on the octets of FL and (Bef.12) family. By Introducing Higgs corresponding to both typeB of descent, one may descend directly to SUC(2) x 3UR(2) x SU(U) (5) Eg .. ... >:ne + 27 + 2TT or even to SUL(2) x SUR(£) * SU1+H(3) u(l). Low energy (Bef.17) phenomena Including complexions for proton decay would depend t The symmetries [SU(n)] and Sll(l6) require the presence of mirror upon which of these alternative routes is chosen. Some of these tensions for cancellation of anomalies (see discussion, in Sec.I). possibilities are exhibited in Fig.l.
being distinct from v Fll)¥ith V F12)SO(1O) 1B the simplest extension of SUL(2) * SUR(2) x SDL+RC»)' because the latter is isomorphle with PO(U)
-6- Maximal symmetry and spontaneous violations of B, L and F
A maximal symmetry SU(2n), which puts n left-handed quarks and leptons as veil as their charge conjugate fields within the same multiplet F = [q,*|qc,ltc], generates the sets of gauge fields shovn in Fig.2. We note that within maximal gauging each of the gauge particles of the Lagrangian before spontaneous breaking carries definite baryon, lepton and fermion numbers and thus these quantum numbers are conserved. The violations of these quantum nunbers arise however as the gauge particles (barring the photon and the octet of gluona for the fractional charge quark case) acquire masses through spontaneous breakdown of the local symmetry G. The violations come about in two distinct ways. Q (a) Gauge mixing: Spontaneous symmetry breaking induces mixings of gauge particles carrying different seta of values of B, L and F and this leads to violations of these quantum numbers. In particular, the A(B-L) = 0, AF = -U and A(B+L) = 0, AF = -2 proton decays arise through the gauge mixings noted below:
Symmetry violation Decay mode
AB «= -3, AL - -1, AF* -A p •+ I + mesons
AB = -3, AL = «•!, AF = -£ p •+ £+ mesons
These two kinds of spontaneously induced mixings are exhibited in Figs.3a and 3b, respectively. For SU(l6) the Y *—* Y' mixing leads to AF = -k decays. Such mixings can be induced for Fn] {CD} example by Higgs of the type ' n{AB} ' where A> B* C, D range over 1-16. These violate B, L, ? but respect (B-L). If in addition we also introduce Higgs of the adjoint {255) type Fig.1: Same alternative routes for spontaneous descent of SU(l6). £B , SU(l6) breaks down to SU (8) x SU (8) x U(l). The^iescent to lev energy symmetry. The subscripts ±1 for (&.1) and (1,8) denote the respective fermion numbers. to SUL(2) x 3UR(2) x SU(lt), through both these types of Higgs and the fact that X-gauge bosons belong to SU(*O must ensure that 2 2,22 ""x •£ IY1* 1BY' "Y1 where fiYY' is the mixin8 parameter in the Y-Y' mass matrix. F13)The detailed patterns of symmetry breaking as correlated with the helicities of particles involved in the decay will be presented in a paper with J. Strathdee.
-10- -9- 9 S partlele-qcuntum numbers \f 1 > Cb) (4F • - -2) p •* 1 + mesons
Figa.3e,b: Spontaneous violntions of B,L and F in a maximal symmetry W,gluons = 0, B = L • 0 leading to Rauge mixings', These induce, for example, AF = -It and -2 proton decays. £J , and f. „ are Hipgs fields (see text).
F»0, B = - L = -1 1
~/-*«'\^\/>yv>£~^ F = 2, B = 2, L=0 ct; : Spontaneous violations ooff B,B,LL ((and in general F) leading to Effective Yukawa transitions: q1 •+ I + f1 These transitions in third order induce iF = 0 proton decaysy ? p 3*- + mesons (and analogously 4F = -6 decays: p + 31 + mesons), nee text. lepto-antiquark/ F = +2, B = L - +1
F = 2, B =0, L = +2
Fig.5: AF = 0 proton decays through spontaneous violations of B and L. These utilize the effective Yukawa transitions of Fig.lt Fig.3'. Gauge particles vithin a maximal symmetry. Here Bq, L and thrice. Note that the mechanism of Figs, 3, k and 5 apply to F = B_ + L denote quark, lepton and fermion numbers, respectively, integer as well as fractionally charged quarks. as defined in Sec.I.
-11- -12- The amplitude for AF = -h transition (generated via Fig.3a) is: (b) The violations of B,L and F may also arise through spontaneously induced three point Yukawa transitions of the type 2 ]/ A(3a + I)flF _ _3 «(s 4Y' 4 "r • q •* 1 + $ {see Figs.Ua and lib)
This is bounded below by g my/my and above by g Any . The lover and
upper bounds correspond to the minimal and maximal values of AYvt 2 2 2 mentioned above.{Note that the maximal value Av«, =• nu, - ffiy, is the case for example for iSo(lO) which contains Y = (Y + V)lj2 type gauge particles only.) This is recoverable from SU(l6) vhen (Y - Y')//2 gauge mesons are of infinite mass.
The Y + X mixing leads to AF = -2 transitions (Fig.3b). This could arise for example from VKV's of a "iggs of the type ff015] L AB J Writing as ^V^ *
the same quantum numbers vithin a l6 fold as V , and \i&. u A(3q - respectively, while A possesses I„ = - = -1/2. The VEV or g 2 2 and are of order (HL. /g), vhile must be L Vr of order (BL, /g) or (uL,/g), whichever is lower. The effective R It is worth noting from the above that if has its maximal valu. _ e Yukava transitions (7), used thrice, induce AF = 0 proton decays 2 •" •VIL , then AF * -It amplitude would always dominate over AF = -2 {see Tig.5) of the type amplitude by a factor %• (m ) » 1. The two amplitudes would be 2 is much smaller than m^ {see next comparable however if Ayy' section). FlU) We face here, as elsewhere, the problem of gauge hierarchies; i.e. the question, are all VEV's of Higgs fields always of the same order of magnitude? If this is the case <¥ > la also of order (in /g). 2 L
-13- where UT p denotes either the charged or the neutral lepton. These transitions are made possible through quartic scalar Interactions unambiguous evidence for one quark charge pattern versus the which permit for example (C][ + c| + B3) to make a transition Into other.'^Jve therefore still keep our options open regarding the BJ and thereby disappear into vacuum through ^"il^ ^ " (see nature of quark charges and " await experiment to settle this question*3^?) Ve stress however that the twin discussion? later). Fermi statistics together with the colour 1]2 singlet nature of the proton inhibits both neutrlfios in the suggestions of quark-lepton unification and consequent baryon 1 number violation are not tied in any way to the nature of quark final state from having the seme helicity 8 (see (3)). charges. They are more general.] An analogous mechaninra induces the Yukawa transitions t + llj which in third order induce proton decays satisfying Spontaneous versus explicit violations of B, L and F -6 It is now instructive to compare violations of E, L and F, vhich are spontaneous in origin (as outlined above) to those which p + 3q = (3l •I'S) + 3x •* (31 + IT'S) +
-16- -15- III. CONDITIONS FOR HELEVAHCE OF ALTERNATIVE PROTON DECAY MODES an Infinite mass-) The exchange of the Ys particle thus leads to a violation of B, L and F in the second order of the basic gauge II n interactions (see Fig.g) and induces the AF = -It decays We now proceed to obtain the necessary and sufficient conditions for alternative proton decay modes satisfying AF * o, -?, -h and -6 to be relevant for either the forthcoming or the second (10) generation proton decay searches. For this purposewe shall consider only those mechanisms for proton decay which arise within a maximal symmetry, outlined in the previous section. Depending upon the We see that explicit violations of B, L and F arising through decay modesF1°'tbe experimental searches are expected to be sensitive squeezed gauging can in general lead to similar consequences for to proton lifetimes varying between 1030 to 1033 years. proton decay as the case of spontaneous violation arising for a maximal symmetry (compare Fig.g vith Fig.3a}. To state it differently, Wow let us first observe the restrictions which arise from the If arid arc given masses In BU(l6) spontaneously,!!! the"' effective low energy symmetry being 8V{2)-^ x u(l) x SU(3)coiour. Weinberg and Wilczek and.Zee ^9 have shown that the effective Infinite limit for the mass of Y , ye recover the predictions of proton decay interactions based on operators of lowest dimension, 30(10). In this sense such predictions axe contained in those which is ai*"''tautomatically conserve B-L, if they are con- obtained from SU(l6). strained to satisfy the low energy symmetry SU(2)L*U(l)xSU(3) 1 Based on this observation theyhave concluded that proton decay °Ur The two cases - spontaneous versus explicit violations of should be dominated by the AF « -b modes (e.g. p •+ e+*0, v»* etc.) B, L and F - appear to possess an absolute distinction from each which conserve B-L. In drawing this conclusion they were motivated other at high temperatures within the range of temperatures by the assumption that the theory possesses essentially only two mass scales my,, — 100 CeV and F1°)MY —101* - 101* CeV, in which between m and m and 'beyond m where mg and case the alternative decay modes AF » 0, -2, -6 - requiring the masses of the combinations of the fields Y and higher dimensional operators and/or violation of SU(2)L "11(1) - would be damped at least by a factor ""(my /My) compared to the "allowed" (B-L) conserving decay modes in the amplitudes.
There are however good reasons why one may consider departures from this assumption.
+ F±>3)for the two-body modes such up* e*n° and n •* e n~ satisfying 4F s -k aa well as n-» ^~v* satisfying AF = -2, the forthcoming experiments may be sensitive to proton lifetimes -S 1033 years. For the multiparticle modes such as p + e~ + 2v + ir*ir+ and n •+ e~ + 2v + ir+ satisfying if ™ 0, the sensitivity might be two or three orders of magnitude lower, while for AF = *-6 modes such Fig. 6; Explicit . violations of B,L and F through gauge squeezing. is p * e* * 5. + v2, the sensitivity may lie inbetween (see Ref.T for details). Here for example, YB = (Y + ?')"/ Vsf is a gauge particle of the basic Lagrangian but the orthogonal combination (Y-Y')/-^ is 717) Thus these can include in general only operators of the form absent or effectively has Infinite mass. Fueh gauge squeezings q -18- -17- With these to serve as motivations for the existence of The most important is that there do exist grand unification intermediate mass scales let us first present a scenario for the models such as [BirCO] . [SU(6)r and their extended maximal hierarchy of gauge masses. This is depicted in Fig*f. We discuss versions Involving fermlon number gauging (such as SU(32), SU(*48) later hoy. 3uch a scenario can be realized within maximal or the smaller tribal group [SU(l6)]3), which do permit intermediate symmetries in accord with renormalization group equations for the mass scales filling the gap between 10* and lO1? GeV with the gauge coupling constants. The characteristic feature of this lightest leptoquark gauge particle X as light as scenario Is that the leptoquark gauge particles (X) are rather '10H-10J CeV. "'•"•" It is precisely because of the existence of light characterising the fact that they belong to the lover sub- The femion these Intermediate mass scales why models of Fefs.2 ajjd 9 have unification symmetry SU(2), * SU(2)R x'SlK^L+F • permitted all along alternative proton decay modes '.Thi-f s we number ±2 gauge particles T, Y' and Y" defined already range elaborate below. in masses between 1010 and 1015 GeV with all possible mutual orderlngs including the possibility that they may all be nearly The second reason why such Intermediate mass scales degenerate. are worthy of consideration Is purely experimental-. They provide the scope for discovery of new physics through tangible evidence for quark-lepton unification In the conceivable future, especially if there axlst leptoquark (x) gauge particles In the 10-100 TeV region. F = ±2 1010 - 1015 GeV The third reason is that if these intermediate mass scales do exist they would permit AF • 0, -2 and -6 modes, whose F = 0 V+A rates may in general even exceed the rate of the iF = -k mode (p + w° + e+). Experiments mUBt therefore be designed to look for 6 such modes. F = 0 10** - 10 OeV One other reason for the existence of intermediate mass scales F = 0 V-A 100 GeV (with successive steps perhaps differing by powers of a or -20- -19- Using these amplitudes for q + I + (Higgs) transitions, taking (Later we show that these requirements are met within a class of maximal symmetries.) BL. (3 to 10) x 10 GeV, and allowing a reasonable range for the Higgs parameters (which are constrained by the gauge masses, see AF ° 0 modes (p •* 3t + T'S) Eef.lB for details) the proton decay rate (ignoring all but AT = 0 These decays occur for either integer or fractionally charged odes) is found to be 18 quarks as follows. Each quark makes a virtual transition to a lepton + a Hlggs field • *; the three Higg6 fields generated there- by combine to annihilate into vacuum through a VEV ^*i'>t 0 28 3lt (see rigs. Jl and ^ and discussion in the previous section). The 10 - 10 years (13) preferred configuration corresponds to one quark being right handed, which emits a, B* field, and the other two 'being left handed, which emit appropriate components of C* field3^"J .Further- more it turns o«t, owing to selection rules, that one of the quarks The main point worth noting is that the AF 0 modes become Important must proceed via a tree (Figa.^a) and the other two via loops 5 F23J if the leptoquark gauge 'boson X has - IP GeV). A (Fig.t)b). .The corresponding amplitudes(suppressing spinors) are given by similar mass range is also obtained iu Eef.21. AF = -2 modes (p •* e~ir ir etc) These decays arise through X -~» l~ ADVmixing .see Flg.3& and also Sec.il). Since such a mixing violates SU(2)T x U{l), the 2 2 corresponding mixing (mass) denoted by & must be proportional to a VBVJ^ m^ . Taking A^j • m^ m^ (or conservatively m^ ), and nt_ 5*10 GeV (as before), we see that AF • -2 proton decay wh^j* '>,p superscripts,!, and R and the sets of parameters < '•', >. my ) and ( < BJ > , m^ ) go with the transitions of left and right-handed quarks, respectively. ffiJ Recall B and C transform as (1,2,1!) and (2,l,Ii) respectively under SU(2)L x SU(2)H x SU(U). Together C and B* make a 16 fold of SU(l6). C and B fields have the same quantum numbers as the fermlon fields FL and FR. Thus only Cjl and B^- possess non-aero VEV, which give masses to HJ and W| respectively (see Sec.II), With integer charges for quarks, additional components of C and/or B multiplets can acquire non-zero VEV (see Ref.2); but these do not materially alter the complexions of proton decay. F23) This is under the assumption that leptoquark gauge particles (X1) coupling to cross currents of the form (eu) and (vd) are much heavier than those coupling to (Cu)and (ed), which are denoted by X. This situation emerges automatically if the unifying symmetry G descends to low energy symmetries via 5U(2)L * 3U(2)R * (U)^ See Hef.l8 for a more general discussion. -21- -22- would permit the possibility that AF = 0, -2 and -It modes can co- exist and be relevant to present searches. The possible co- existence of the AF = -6 mode dependB upon some further considerations vhich we shall not pursue here. Our task now is to Bhow that such mass pattern* as outlined interaction viewed as an effective four feralon interaction would have in (15) can be realized within unifying symmetries in accord with a strength (A™)/{m^ m^). This would exceed the canonical value renormalization gfoup equations as well as observed values of ;slO~29 GeV~2 for m^ «1013 GeV (or 3 " 10 GeV), leading to proton ^ and ag. 31 32 lifetime in the range of 10 - 10 years. We thus see that for HL, «10 - 105 GeV and IL a 3 < 10 IV. SOLUTIONS TO HIERARCHY EQUATIONS FOH A CLASS OF UNIFYING 10 GeV (the precise number depending upon k_ ). AF = 0 as veil as SYMMETRIES &F~ = -2 eoald coexist with comparable rates and be relevant to forth- Perturbative renormaliiation group equations for the running coupling constants of a spontaneously broken unifying symmetry coming proton decay searches. permit in general solutions for the gauge masses ", which exhibit a hierarchy. We refer to, these equations as hierarchy equations and aak: Do there exist solutions to these equations within some AF - -k modes (p •* e ff etc) class of unifying symmetries which permit Y1 mass mixing (see Fig.3a). These arise through Y li 5 Denoting the mixing (mass) by y " the corresponding amplitude (a) «L«-10 - l(r CeV 2 2 2 2 AB explained in Sec.II, A^2y (b) My^] - 1015 GeV is Ay^/tm^ ^m^,). AB explained in Sec.II, A^yi can be as large as >• m? ~m?,. This is the case for example if SU(l6) dtscends to (c) sin2fl. .23 and low energy symmetries without passing throi«* SU(8) * SU(8) * U(l). If 4 ^ 2 2 V its maximum value my » m^, (ae in the case for example for B0(l0l^. Cd) (16) then the AF = -k amplitude would have a strength «l/rav an (IT) flavour Vx (15) Here SU(l») acts on (u,d,c,s)L R flavours. 5U{2)^ and r r D act u,d)T and (c,s), ' doublets respectively; on (u.u^k The gauge particles of SU{2)£+11 is their diagonal sum -23- -2U- symmetric liait.F This is best illustrated by the three family symmetry 22 [SU(6)] , which operators on six flavours (u,d,c,s,t,b) and six colours. There are three leptonic colours rhyming with 11 are related to those of SU(2)*' by V^* • ^ +. u]})}f2..L ,,Tt . Thus, three quark colours (r,y and b). There are the six observed leptons if g is the symmetric gauge coupling constant of each SUfO plus twelve unobserved heavy leptons in the model. 'Here the factor, the coupling constant g2 of the low energy symmetry SU(2). low energy flavour SU(2)T is obtained by diagonal summing of three would approach g/ V2 in the symmetry limit. Likewise the L coupling constant g^ for vector colour S1)(3)L+R would also SU{2)'s, which respectively act on (u,d), (c,s) and (t,b) - doublets. approach g/ V2 , since it is obtained by diagonal summing of SU(3)' Thus g2 = g//T in the symmetric limit. In this case, even if the s and yL$)R • By contrast the coupling constant g£ for chiral low energy colour symmetry is vectorial SU(3)J+R • g- ™ g/-J 3' colour "^SUO^ x SU(3)R (relevant to the lower Chain) would < iX * "]8* ln the symmetric limit. This, together with the fact that approach g in the symmetric limit. Thus * o 2 2 the; bare value of the veak angle ' ain &Q = 9/28 (rather than 3/8), leads again to a low unification mass for the descent vector colour gi •= -*• (symmetric limit) 5 L «S10 GeV, i.e. i^elO GeV. (SO) flavour versus colour coupling constants, translates into a factor 5:2.5, which multiplies the logarithm of t^/ii . It alters In this case one furthermorree obtains aa desirable value for the weak drastically the determination of the unification mass VL and one angle 23 obtains 10 T 15 (21) For vector colour < * 10 GeV We thus see that quark-lepton unification could take place through leptoquark gauge Interactions at an energy scale 105 GeV. For * » 0.20 the chiral descent [SU(6)] * SU(2)PfII+I11 * U(l) * SUj(3) Mi = 10* IJ For chiral colour the unification mass could be lower still ( « KT GeV). What about the masses of the fermion number F » ±2 gauge particles Y, Y' and Y" arising within a maximal symmetry? To obtain (19) a scenario in which the masses of these gauge particles lie in the range of 1010 - 1015 OeV, while tteZ's are as light as a lCT-lO? The mass of X is about a factor of 10 lover than M^ Thus we - proceed as follows Assume (following the C1 GeV> la 10 GeV> M deslrea famijy f " T^ii1 r "x * - However the case of the two (SU(U)J * descending via chiral colour is2 now excluded experimentally, Bince it yields too high a value for sin Bw (= 0.30} compared to ?25)This ingredient hastens the "meeting" of the colour and the the experimental value of sr0.23. SU(2) flavour coupling constants. There is a second ingredient which cam speed up the "meeting" of SU(2) and U(l) coupling Severtheless the above example provides the clue for low mass constants. This is realized through a lowering of the bare value 2 unification. The idea is to create through spontaneous descent of the weak angle sin BQ from the canonical value 3/8. This: iv the a dichotomy between low energy flavour versus colour coupling on constants such that the former is lower than the latter in the case for [SU(6)] where sin eQ = ^ account of the presence of the extra leptons. However for 5U(l6) or [SU(l6)] , sin BQ has the chiral colour symmetry must break to vectorial colour eventually. But if this breaking takes place by a mass scale <. "canonical" value g- . m^ , one can ignore the effect of such a breaking for studies of is without counting the mirror fermions . renor'malization group eauations at momenta ' m . F27)The discussions to follow are based on a forthcoming paper by \ B. Deo, J.C. Pati, S. Rajpoot and Abdus Salaa (Ref.2U). -25- -26- illustration for [SUCt)] and [(SU(6)] ) that each individual In short the scenario which we are led to consider for the family defines a distinct SU{2) within the parent symmetry C; these sake of obtaining Intermediate mass Bcales and thereby signals for distinct SU(2)'s combine (or following a terminology used before, grand unification at moderate energies is this: The families thev are "squeezed") through spontaneous symmetry breaking by a rela- a define distinct SU(2)'s and possibly even distinct SU(3) or SU(lt) tively heav^aass seaie-Ji£ J M^to yield the diagonally summed SU(2),which is colour symmetries at the level of the parent symmetry. The the SU(2) of low energy electroweak symmetry. Thus allowing for distinction 13 lost and thereby universality of families defined q left-handed families we envisage the descent by discrete symmetries e *•» w <-» T emerges at low energies due to spontaneous symmetry breaking. F3l) '"*.;; -i-; — (22) Such family distinctions are not realized within smaller SSB symmetries such as SU[5), S0(l0) and SU(l6). But they do exist 3 Recall that for [SU(fc)]\ q - 2, while for [SU(6)] , q = 3. If the within symmetries such as [su(l*)]\ [SU(6)]\ [su{5)] = SU{5^e theory is left-right symmetric, there would be the corresponding 3 3 ( SU(5) * SU(5) C 3U(15) and likewise [SO{10)] and [SU(l6}] "squeezing of [EU(2)R] 1 into a single SU(2)R or even U(1)R through a heavy mass scale Mj, We are aware that the symmetries of the latter kind are gigantic. But then Nature appears io be proliferated anyway q [SU<2)R] SU(2)R or U(l)R (23) beyond one's imagination at the quark-lepton level. Why are there families at all? If families proliferate, why not the gauge mesons? In general the parent symmetry G may contain distinct SU(lt) colour At the present stage of our ignorance there is no basic reason symmetries *29'as vell» which are distinguished fron each other why the family universality should be an exact principle for all either through helicity of fermions on which they operate, or energies. The gigantic symmetries are the price one Is paying for through the family attribute, or both. For generality assume that believing quarks and leptons are fundamental entitles. We return there are p SU(tO colour symmetries within C. To be specific we to this problem towards the end. shall furthermore assume that these are vectorial L+R symmetries. With these remarks to serve as motivations, we consider the (The generalization to chiral SUCO colour is straightforward.) F3j>) possibility that the parent symmetry G breaks spontaneously to These p SUCOL+P symmetries are "squeezed" through SSB to a single low energy components as follows: 24 SUCOJ^JJ by a heavy mass scale H^. The single SUCOj^p subsequently descends also spontaneously to SU(3)L+R *"" x ^K^L+R v*a a heavT mass scale M^. The leptoquark gauge particles X^s receive their __>r instance, taking only two families e and y , there are mass through M3 with MJJ•* H3/IO. Thus the colour sector may break tvo distinct W's (W and W ) in the basic Lagrangian. Due to as follows: hierarchical SSB {V - W )/ Jz acquires a heavy mass £1CT GeV, but (W + W )///2 acquires a mass only of order 100 GeV. Hence the low energy e f—> u universality. Such a picture Is logically feasible, since tests of e *—*. v universality In weak Interactions extend at best upto 10 to 30 GeV of centre-of-mass energies. Do reaiije the known universality of different families in there exist additional W's and Z's which couple to differences of eleetroveak interactions and to preserve the GIM mechanism upto its e and'piicurrents? Tests of such family universality should provide knoim accuracy M^ should exceed about 10^ GeY. F29)The fo\p"th colour is lepton number. an important motivation for building high energy accelerators in F30)Alternatively (SU(U)]P may descend first to [SU(3)IP * ["(l)]P, the 1-100 TeV region. which subsequently descends to [SU(3)] * U(l). This is considered in Ref.2b. -28- -27- We now ask, are there solutions to these equations for some p and q which correspond to the constraints on gauge masses as veil as sin 6 and a as listed in the relation 0-6)7 (Note that chiral 2k colour corresponds to p * 2.) We find that there is no solution satisfying constraint CL6 ) for p = q = 1; such values of p and q , Csut2)L tS0(4)L+lll xUti) correspond to SU(5) and S0(10). There is also no solution for p = 2, q = 1 which correspond to SU(l6). But there do exist solutions for p = q. =» 2; for p = 2, q = 3 and for p = q = 3. Such values of p and 3 3 SUC4) q. can be obtained for example within tSO(lO)] , [SU(l6}] . These solutions and the corresponding coexistence of alternative proton decay modes are listed below: M ~ OeV, M^- M ~ tL — 1012 GeV 5 5 5 M, — 1O ' GeV ^ YT~ 10 GeV ^ (25) TJtus- flF * 0 ana AF -!fc can coexist, but Such a hierarchy leads to the following two equations via the AF •= -2 Is suppressed renormalizatlon group equations for the coupling constants: M ar ar 1012 OeV, ss 1010 GeV 5 1 1 VL -a 10' GeV, M ( 10 CeV - 10 * GeV ol C.s Qo 3 tl /*• 2, 1 AF • 0, -2 and -It can coexist * 10 W v _{3V2|»\ 11 M« 1>L ~10 GeV, 10 . GeV, M ^s U — q - 3 105 GeV^M 10 "* GeV AF 0, -2 and -It can coexist (27) We thus see that within maximal symmetries permitting Intrinsic family distinctions proton can decay through alternative decay F modes as claimed in the introduction. 32)it ie aiao vorth noting that for three families vith p • q - 3, the family universality of weak interactions can disappear at an energy scale of order 100 TeV corresponding to M_ ss 10° GeV. P32) Recently, Weinberg (Ref.21) has noted that in addition to the + (26) A(B-L) * 0, 4F - -Umode (p + e ir0) there can be only one other proton decay mode satisfying either AF - 0, AF - -2, or AF - -6. He vu led to this observation by arguing that the AF = 0, -2 or -6 processes, which, are mediated by intermediate mass scales Mi « M ~1011* GeV would have rates -vaT or a2T In the early Universe at temperatures ihe reductions shown on the right sidea of the tvo top equations in the range M >> T >> Mr. 3uch processes vith rates exceeding the rate of expansion of the Universe vould be in thermal equilibrium correspond to a single stage descent G -^->SU(2)L x u(l) and therefore wipe out any baryon excess generated In earlier epochs - M » (due to AF = - (3) Proton decay modes can provide an important clue to the underlying design of grand unification. For example, observation For thia reason, the preon idea appears to be attractive. But of AP - 0, -2 or -6 mode at any level vithin the conceivable can it be sustained dynamically? The single most important future will signal the existence of intermediate mass scales, which problem which confronts the preon-hypothesis is this: What is the in turn will reflect upon the nature of the parent symmetry G. In nature and what is the origin of the force which binds the preons particular, the observation of the A? •» 0 node will strongly suggest to make quacks and leptons? the existence of new interactions in the 10 to 100 TeV region. Thus, a search for such decay modes, if need be through second Our first observation , following tJurircrk. of one" of UB , is that ; and third generation experiments,would be extremely important in «di»« yv"electrie" type forces F3c) _ abelian or non-abellan -l that such searches would have implications for building of high within the «rr«nil energy accelerators. F33) {!*) Observation of proton decay will strongly support the This section follows a recent paper by J.C. Pati idea that quark and leptonlc matters are ultimately of the same (Ref.SSj. See also remarks by Abdua Salam,Concluding talk, EPS kind, though thia has no bearing on the question of whether quarks Conference, Geneva, 1979- and leptons represent the ultimate constituents of matter. __^For simplicity let us proceed with the notion that lepton number is the fourth colour {Bef.2.). In this case the composite structure Is as follows: (a ) - u + (r,y or b) + C, while This leads to the second part of dtfir'ieawtdeTrstione where we in- \) " u + I * ; etc. Withiniii r'y>D the preon-idea leptons may dicate the di-Kectionjr-**. which-»«fe of th«f dK*ng<« might eftfeur for the however differ from quarks by more than one attribute. For unification hypothesis, if quarks and leptons are viewed as r composites of more elementary objects - the preons, and also how example, we may have v » u + I + i, where (; 4 t)• Such variants the preons may bind. will be considered elsewhere. ?35) with the spinon preBent the flavons and chromons can carry integer spin 0 or 1. F39J By "electric" type forces we mean forces whose effective coupling strength Is of order a » 1/137 at the unification point M. -31- -32- unification hypothesis are inadequate to bind preona to make quarks FBS) and leptons unless we proliferate preons much beyond the level above is unity) that n is much larger than SU(3). Using re- depicted above. normalization group eauations for variations of the coupling constants ab and ac, one may verify that r^, minimally is S')(5} The argument goes as follows: Since quarks and leptons are and correspondingly the dimension of the space on which point-like - their sizes are smaller than 10"1 cm as evidenced operates is minimally 5- (especially for leptons} by the (g-S) experiments - it follows that the preon binding force Ft must be strong or superstrong at short How the preons (P^,) which bind to make quarks and leptons must distances r 4 10""^ - 10"1 cm corresponding to running momenta be non-trivial with respect to both, C^ and 6^. Since each of G Q %1 to 10 TeV. (Recall for comparison the* the ehromodynamic k and Gjj requires for their operations a space, which is minimally s mBietr a ive dimensional, it follows that the n forces generated by the SU(3) 0iour" y y * strong (a •£. 1) five dimensional, it follows that the number of preons W_ needed (under the hypothesis above) la mainly N,. only at distances of order 1 Fermi, which correspond to the Bizes of the known hadrons.) This says that the symmetry generating the preon binding force must lie outside of the familiar * 5 - 25 (29) s V SU(2) x uCl) * U(3)col symmetry. We may consider relaxing the'assumption that the emebedding How consistent with our desire to adhere to thf> grand factor is unity. This wouldpermit the ratio [jLdjJ/g iv)} -M to unification hypothesis, we shall assume that the preon binding be a number like yfz or /3 for example. In turn cthisw can force F. derives its origin either intrinsically or through the result in a reduction In the size of G^. But siraultaneosuly such spontaneous breakdown of a grand unifying symmetry G, Thus either a step necessitates an increase in the slue of 0^ or effectively the basic symmetry G is of the form 0j[ x G^ vith G^ generating the of the number N. with the result that the minimal number of preona known electroweak'-strong forces and (3^ generating the preon-binding needed Hp >. Hk x ]ffe is not reduced below 21. forces, (in this case Gy. and G. are related to each other by a discrete symmetry so as to permit a single gauge coupling constant); This number 2? (or 21) representing the minimal number of or the unifying symmetry 0 breaks spontaneously as follows: preons needed already exceeds or Is close to the number of quarks and leptons which we need at present, which is 2k. And if we in- SSB (28) clude, more desirably, the leptonic ehromon I and the spinon C ir U(l)-f*=tors] the preonlc degrees of freedom, the number of preons needed would Increase to 35 (or 27). In the second case Gjj need not be related to Gp by discrete symmetry. But in either case G^ contains the familiar Such a proliferation of preons defeats from the start the very SU(2) x U(l)_., x SU{3) , -symmetry and therefore the number of TL Ei* colour purpose for which they were introduced - economy. In turn, this attributes (Mjj) on which Gjj operates needs to be at least 5. This poses a serious dilemma. On the one hand giving up the preon Idea corresponds to having 2 flavons (u,d) plus three chromons (r,y,b). altogether and living with the quark-lepton system as elementary To Incorporate leKonic ehromon 1 and possibly also the spinon ?, runs counter to one's notion of elementarily and is thus unpalatable. Hjj may need to be at least 7j but for the present we shall take On the other hand, giving up the grand-unification hypothesis Is conservatively H^ 4> 5- not aesthetically appealing. 25 How consider the size VT G^.On the one hand the effective Because of this impasse, it has recently been suggested that coupling constant £ of the binding symmetry G, is equal to the the preons carry not only electric but also magnetic charges and that their effective coupling constant g,, of the familiar SU(3)-colour bidding force is magnetic in nature. The two types of charges are symmetry (up to embedding factors 10 like 1/^F or I//!" etc.) at related to each other by the familiar Dirac-like quantization the unification mass scale M » 10" GeV. On the other hand, conditions 28,29 for charge-monopole or dyon systems, which imply to 2 5b = SvV *•» needs to exceed unity at a momentum Bcale ub *• 1 that the magnetic coupling strength a £ s /*** is 0(l/ae) * 0(137) 10 TeV, where the ehromodynamic coupling constant ac << 1. It and thus is superstrong. In other words, the magnetic force can therefore follows (assuming that the embedding factor mentioned This incidentally excludes the possibility that Oj, is abelian. these considerations we assume all along that the conventional perturbative renormaliiation group approach applies to the variations of «ti running coupling constants down to such momenta, where they are small (gj/'nr £ 0-3) (see Ref.6). -33- -3".- arise through an abelian U(l)-component within the unification There ie a second alternative, which is the simplest of all in hypothesis (as remarked further at the end) and yet it can be respect of its gauge structure. Assume that the basic Lagrangian superstrong. This is what gives it the power to bind preons into of the preonB is generated simply by the abelian symmetry systems of small Bize without requiring a proliferation. Quarks U(l)EX U(DH- ^e U(1)E generates "electric" and U(I)M the and leptons do not exhibit this superstrong force because they are "magnetic" interactions of preons. Subject to subsidiary conditions. magnetically neutral (see remarks below). the theory generates only one photon coupled to electric as well as magnetic charges 32. The charges are constrained by the Dirac We first discuss the consistency of this idea with presently quantization condition. In this model the baBlc fields are only known phenomena from a qualitative point of view and later indicate the apin 1 preons and the' spin-1 pnotou. The strong magnetic the possible origin of this magnetic force. force binds preons to make spin j quarks and leptons as discussed earlier. Simultaneously it makes spin-1 and spin-0 composites (1) Since; the electric fine structure coastant a » e /Uw of even number of preons (including antipreons), which alBO have varying with running momentum remains small •*• 10" almost every- very small sizes like the quarks and leptons. The spin-0 and spin-1., where (at least up to momenta /— 101* GeV anci therefore up to fields carry charges and, Interact with luarks and leptons as well distances <^10~2° cm), the magnetic "fine structure" constant 5 aa among themselves. The use of a recently suggested "theorem" <*m s A* related to ae by the reciprocity relations is super- would then suggest that their effective interactions must be strong even at distances as short as 10-28 cm (if not at r •+ 0). generated from a local non-ab«lian symmetry of the Yang-Mills type, It is this strong short distance-component of the magnetic force, which is broken spontaneouslyf in order that they may be re- which makes quarks, and leptons so point-like with sizes r << 10""eni- normaliz&ble. The spin-0 composites will now play the role of Their precise size would depend upon the dynamics if the super- Hlggs-fields.3^It i« amusing that if this picture can be sustained, strong force which we are not yet equipped to handle. For our _„ the proliferated non-abelian quark-lepton gauge structure 0^ jj purposes we shall take r to he as short as perhBps i./M ] ~lCI •>•* purposes we shall take r0 to be nas short as perhaps n planc t with the associated spin J, spin-1 as well as spin-0 quanta may 1 cm but as large as perhaps 10"- -" cm (i.e. rQ < 10~^ have its origin in the simplest interaction of all: electro- magnetism defined by the abelian symmetry 0p • U(1>E * U(1'M • (2) Quarks and leptons do not exhibit even .a trace of the superstrong interactions of their constituents because they are The idea of the magnetic binding of preons and its origin magnetically neutral composites of preons and their sizes are needs to be further developed. What !*!>• . argued here is that small compared to the distances R >. 10 cms which are probed by within the unification context a magnetic binding of preons present high energy experiments. appears to be called for if we are not to proliferate preons unduly. (3) We mention in passing that had we assumed, following Schwinger =9, that quarks (rather than preons) carry magnetic charges, we vould not understand why they interact so weakly at short distances as revealed by deep inelastic ep-scattering. CO Due to their extraordinarly small sizes, it can also be argued =5 that low energy parameters such as (g-2) of leptons We wish to thank Bibhuti Deo, Victor Ellas, Subhas Rajpoot and would not show any noticeable departures from the normal expectat- especially John Strathdee for several stimulating discussions. The ions. Similar remark applies to the P and T violations for quarks research of J.C.P. was supported in part by the U.S. National Science and leptons, which would be severely damped in spite of large P and Foundation, and in part by the John Simon Guggenheim Memorial Foundation T violations for preons carrying electric and magnetic charges. Fellowship. What can be the possible origin of magnetic charges of preons? 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Ellis, M.K. Oaillard, 16. J.C. Pati, AMsa Salaa «JU.J.-Strathd**, forthcoming m$xi*t, ICTP, h. Malanl and B. Zumlno, preprint LAPP-TH-15.CEF1H Th 26Ul. . ***•***, prajriB* IC/8C/72. 3*7 Ih such a picture there vould be a natural reason why electric 17. F. Gursey, P. Famond and P. SiXivie, Phys. Letters 60B^, 177 charge may be absolutely conserved and correspondingly th« (1976). For other references see talks of B. Stech, photon may remain truely massless, despite spontaneous symmetry R. Barblerl and D. Nanopoulos at this Conference. breaking, since the photon is distinguished by the fact that it 18. B. Deo, J.C. Pati, S. Rajpoot and Abdus Salam, preprint In is responsible for the very existence of the coopoaite Higgs preparation; Abdus Balam, Proceedings of the EPS Conference particles which trigger spontaneous symmetry breaking. Geneva (1979). 19- S. Weinberg, PhyB. Rev. Letters U3_, 1566 (1979); - 38 - - 37 - jr.'.-j.....--.L. 4 4* i# -