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Quark-Lepton Unification and Proton Decay

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Quark-Lepton Unification and Proton Decay \\£ 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 (<L(C) currents.^) In this case, violations of B, L and F. If all quark-lepton degrees of freedom baryon, lepton and fermion numbers are violated explicitly are gauged locally as in a maximal symmetry G specified above, , through the gauge interaction itself.
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