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Frsoolm^ LAPP-IH-09 November 1979 fRSOOlM^ LAPP-IH-09 November 1979 NEW QUARKS AND LEPTONS *5 Mary K. Gaillard LAPP, Annecy-le-Vieux, France Luciano Maiani Univ. of Rone, Italy CONTENTS 1. Introduction: a glimpse of quark and lcpton history 2. Elementary properties of quarks and leptons 3. Weak interactions of b and t quarks 4. Grand unified theories 5. Conclusions and outlook ' Lectures given at the Cargeae Institute, July 1979. I. A. P. r. (HtviN ur nmfwE Boiri. rosrAtr iv> ?ion ANNTCY IE.VICL'X crorx rnirnoNl TABLE OF CONTENTS P»ge 1. Introduction: a glimpse of quark and lepton history 1 2. Elementary properties of quarks and leptons 1 2.1 What do He really know ? 1 2.2 Renormalizable gauge theories 11 2.3 The fermion mass matrix and the structure of the veak currents 18 3. Weak interactions of fa and t quarks 21 3.1 The veak mixing angles 21 3.2 Zounds on the veak mixing angles 23 3.3 Weak decays of b and t 29 3.4 Multilepton configurations in b and t decays 34 4. Grand unified theories 4.1 The unification of veak, electromagnetic and strong interactions 37 4.2 The minimal model: SD(5) 42 4.3 Feraion masses and constraints on the number of generations 45 4.4 Proton decay 49 4.5 Sounds on the t-quark mass 54 5. Conclusions and outlook t. IHTKOWJCTIQW; A CL IMPS E OT QUAME àM XMTtQK HISTOit nowadays M era eeeustaeved to think of partiel* intereeeioas 1B »m of alaeaotary eouplinfs of quarks and leptona. In Table 1 w* list major step* which bave contributed to our presa&t picture, totriaa ia MUM bracket* refer to theoretical speculations; round brack*tad entries ara obuntd pturaoawaa which daavnatrat* tha ejnaaical reality of quark*, coaPleatttiting thair aliabraic reality which emerged fro* aa analysis of Che haaron spactrun. la this court* we will ba mainly concerned with tha weak couplings of quark* and Upton*, The prevailing view among theorist* it that quarks and leptoos hare a doublet structure with rcsptct to walk interaction*: e ).(';•). (ï),(;u:uîi..r that thnaa doable» ara charge daganarata for laptona (0,-1) and for quarki («2/3, -1/3), that thair cbargad current couplings ara of uatvaraal straagth and *a»a a T-A atruccura, and that thara ara aa many lapton doublata aa (color-criplat) quark doublota. The aubacript c in Iq. <l.l) carrlaa tha information that tha alganatatas of vaak couplings ara linaar coahi- nationa of charga daganarata aaae eigaaatataa. lacauaa of thair uoivaraal couplings lapton airing ia unobsimnla if nautrinoe ara all aaaalaaa, and quarfc aixing can ba dafinad (aa it conrantionallT ia) to occur only in tha charga -1/3 «actor. In Saccian 2 va ahall akatch aoaa of tha phaaoaanological arguaaats vhich aatabliah tha abova pictura aa vail aa ita thsorstical fouodationa. In Saction 3 va ahall invaatigata in aora datail tha axpactad vaak interaction propartiaa of baavy hadrcnt carrying top and Wttia quarka. In faction « w «hall introduco "grand vaifiad" thaorica vhich attaapt to daacriba vaak, alactroaagnatic and •trong iataractioaa in taraa of a aingla (ataractic*, vith particular aaphasla on tha aiaaiait •uch aodal, Sl)(3). In Saction S va ahov hov radiativa corractiona aay ha axploitad to bound unknown aaaa paraaatars of tha thaory and va auBWariaa our discuaaion in Saccion 6. glbliotraphy C,S. vu and S.A. Hoakovski, "lata Da car" (Intancianca Inoliahara, X.T., 1966). "Waak lotaractiora", tin, ad. H.K. Gaillard and M. Nikolic IN2P3, Paria, 197?), M.K. Gaillard in "vaak and glactrpsagaatic Intaractiona at High Enargiaa, Carglaa IB!", ad. M. ISvy, 3-1 laadavaat, ». Spaiaar and «.. Gaataana (Planua traaa, 1.1-, 1976 ). 2. EiJuarnjtT ncrami or genu A» anow S.t What do va «aalty fcnovt Laptona. To tha autant that laptona aaasaa ara uniajportast, a V-A coupling iapliea that only laft-handal laptona and righc-handad anti-Uptons intaract vaakly. this raatricta al­ low* kinaaatical configuration»In a »«7 vhich allova aiapl* ca«ts of tha thaory. CaMidar .M^HMMVW •f Tabu 1: Quark and Upton History. 71 , iro 1M2-M M»-.t 1?H, If»-?' lMti4_ JSISL. t?7?-7* 1224z2t_ »7? Bacqvaral ffauU.Fa: taints and H* » I • t) Co***: rj v iataraetioa tutbarfortii aoclava aiaaaaargïj «<*> J" CkaaVickf i «troa Cocvarsl at al: M waafcly Utaractiaf Gall-Maaa, atraaax Caaiate» ate. /aw \ partidas 10(3). fniiki: i Fanllab _1 carramta . Sdnrinftr- Daaby at. al. HiabijiHt M* at: V„jf v v.. iittractioc "ïara, ate m. sue, laato*-a,uai DfST., TaraifOuxmBoxmSt ab , -WW a Cham aum j SUCf KST, CEBK farmlab: __jnsrJLv.sV Atéraction Kobayaatii- Barb •t al: OUI Kaikava: •(bo.)? CP T(bE) violation: 6 flavor* for KXaapïa g-deeay 2* — Z *e- \, (2.1) For a collinsar configuration, there is no orbital angular aesenttai «loci tha decay axis; angular awwsntuai conservation therefore reatrieta th« allowed configuration* vhish dapaad on th* Upton halicities, aa illustrâtad in Tabla 2. For a |ij| - 0 nuclear transition, only tha parallel (t~»v) configuration ia allowad; this Mans that tha electron and anti-neutrino helicitiea are opposite which in turn means that Upton helieity ia conservad in tha decay «ad the interaction ia necessarily vector and/or axial vector. Heaauraawot of a negative electron bclicity pin* it do*» to V-A. For m fAJJ - 1 transition, tha anti parallel config­ uration is alao allowed, and if the decay meats are eoliinaar with ûî (for «xaatpl* in the decay of polarized cobalt) th« configuration is necessarily antiparalUl» with the Uft-hand- ed electron aaitted in the direction opposite to A$. Table 2 Allowed collintar decay configurations for a univers*! V-A inter­ action: (avail arrow* denote spin direction). For decays into positive Uptons, all helicitie* are reversed. S«c»yj Aîlomà CoaCituzstiooi - M - 0 ": «» ** "•»'" z * z • • • v «-4J 4J - 1 V«f'\* «-""'* -3+v~ lT * •" + v, • Ï, ,'t >V' ^ *» r-~vr*Zv M V , " " 1% T" * i" • \ * vT " "'VT The structure of the vdecey awtrix element ia partially inferred frosi the electron apactnae which will be hard (aa observed) if the configuration of Tabu 2 ia allowed. Thia ewana chat the neutritu* and eaci-navtriooahav* apposite heUcit£aa, «nd tha fact that tha electron is eaitted preferentially opposite to tha spin of poUriaad suons laçlit* a left- handed electron. The neutrino haiicities cannot b* datanaiuad without the «ttasptios that the four f amfon interaction factorisa» into aauwicaod en electronic vertex, e.g. via «-«change aa in Fig. la. Then the observation* described above ia*>W that the coupling ia V-A st both vevticee. •- /r o) b) Fig. 2 Factorization hypothesis for leptonie decays of leptons. ODC reaction vhaxc neutrino halicitiaa caa be «ensured is in th* 2-body leptonlc dacay of a pgeudoscalar swson as fr -* *.- -*-3>» / -' (2.2) Thaaa presses ar« forbidden ia th» limit of vanishing laptoa sue because «oacntisg con­ servation raquitaa tha |j| - 1 parallel configuration, wheraa* the initial atata has |j| - 0. Tha dacay «nplitudas ara therefor* proportional to tha charged lepton suss, and ita polar­ isation will be in th* "wrong" direction in otd« to balanc» th* halitity of the (presuaed mastless) neutrino. Existing aeasureaeats are crude but indeed indicate that the (anti-) neutrino is (right) left-handed. With the V-A hypotheeis established for («\>t> end (pv ) couplings, the factorisation hypothesis. Fig. lb, can be used to extract the Cry_> coupling fro» the final atate lepton spectra* is the decay. (2.3) heiicitics» and therefore « V-A (rwt) coupling. Just as the abaence of the dacay If -* €*X B.4) and of th* infraction (2.5) where tha incident neutrinos originated fro» pion decay (2.2), estsblishsd that the nonobservation1) of decsys lib* •C -» Jit, 3jt,//iee. (2.6) •nd of tt» Miction*) V* U -* <• +X (2.7) for neutrino* originating fro* * end £ dece^e, iaply that »* * *,£ An alternative poaaibility would bt J4 «r Va, with laptone foraine ^^ iaotriplet* like (e~v T } instead of th* conventional doublet* (1.1). Than tha decay rate for alactrooic T-dacay (Fia;, 2) would be twice that for the ani­ onic Bod*, and in Addition the electron «pectrua would be «oft becauac identical neutrino* in the final atata forbid the configuration of Tabla 2. t_ v. Fig. 2 Zxaaple of an unconventional lepton coupling hypothesia. The decay datet as veil ai the abaence of reaction (2.7) i also iaply Jft +\,Vf. (2.9) Litht quart». Th* Miiurtd fi-d*c*y aaplitudai, including the relative sign, for Ferai tranaitioni AJ - 0: V or S, and Caaww-Teller transition* ÛJ - 1: A or T, together with the observed lapton dacay configuration* which alUinate the halicity violating aaplituda* S and T, tell u* that the weak (np) coupling i« approxiaately V-A. Whet ve are ifit*r*at«d In axa «uart coupling*. If the (ud) coupling i* V-A, then the <np) coupling* cal­ culated in * nonraletivistic quark aodel «re (1»V * (3',,", * 1 (2.10) whereas the «assured values are The nonrclativistic quark aodal is not expected to be very reliable. A better probe of quark couplings is deep inelastic electron-nucleon scattering» which can be described as a sua of incoherent neutrino-quark scatterings. Fig. 3: dx d where f ._(x)/x is tha probility of finding the quark q. in the nucléon with noawntuai fraction x. 7T-* rig. 3 Partem aodel for daap inelastic v - M scattering. Tha V ± A natura pf the quark coupling ia reflected in tha dependence of the cross section on tha energy transferred to the hadrons: <2.J3«) whert Gf it the fatal coupling constant and y it tha «nergy fraction transferred to tha hadrons and ia siaely related to tha neutrino-quark c.au scattering angle: £v *• The y-dapindanca In Eq.
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