Seminar. Signals of new physics in top quark decays

Transcription

1 Univrsiy of Ljubljana: Faculy of Mahmaics and Physics Sminar Signals of nw physics in op quark dcays Auhor: Jur Drobnak, Mnor: prof. dr. S. Fajfr Novmbr 9, 007 Absrac This papr givs a shor dscripion of wo phnomna ha sm o b good candidas for finding signals of nw physics. Thy ar boh rlad o op quark dcay. Th firs on is h polarizaion of W boson in h main op quark dcay channl and h scond on is h rar op quark dcay c V, whr V is a nural gaug boson. A shor inroducion of h sandard modl is givn a h bginning of h papr as wll as h main rasons for h nd o look byond i.

2 Conns 1 Inroducion 1 Th Sandard Modl.1 QED - firs building block of h SM Th Lagrangian Frmion gnraions Problms of h Sandard Modl 5 4 Top quark in SM Main dcay channl Hliciy of W FCNC dcay c V Top quark dcay in R MSSM Minimal Suprsymmric xnsion of SM Paricls and hir suprsymmric parnrs Th Lagrangian R-pariy c V in L MSSM Top quark dcay in B MSSM Conclusions 13 7 Appndix 14

3 1 Inroducion Th sarch for a hory ha would succssfully prdic h xprimnal obsrvaions in h physics of lmnary paricls has ld o h formulaion of h sandard modl (SM). Along wih quanum hory of filds i is abl o prdic obsrvabl oucoms of xprimns. Wihin h rang of nrgis ha ar rachabl in oday s xprimns, h SM prdicions ar mosly in gra agrmn wih xprimnal oucoms. Thr ar howvr clar indicaions ha h SM canno b h final hory of lmnary paricls. Thus, in h las hiry yars, xnsiv horical work has bn focusd on xnding h SM. Wihin hs nw modls calculaions of diffrn inracion procsss ar mad and awai h corrsponding xprimnal rsuls. Sinc w ar no abl o achiv high nough nrgis o prob highr ordr prurbaion corrcions of any procss a hand, w choos o s h SM on rar phnomna. Ths ar h phnomna for which h SM prdics vry small occurrnc probabiliis. Th ida is o xprimnally masur such probabiliis and, if hy ar considrably highr han wha h SM prdics, his could b an indicaion of nw physics govrning h procss. Today rar dcays of msons, consising of a quark and aniquark, and baryons, consising of hr quarks, ar bs candidas for finding signals of nw physics. Baryon dcays ar mor difficul o considr, so h main focus is on msons. Th havis of which ar h B msons. Wih h nw gnraion collidrs, h op quark physics will also bcom xprimnally accssibl. Top quark is h havis quark in h SM. Is vry high mass maks i vry snsiiv o ffcs of physics byond h SM. Du o is larg mass, op quark dcays bfor i can hadroniz - form msons and baryons. Tha is why, o a vry good approximaion, op quark dcays as a fr paricl. This maks h analysis of h dcay rlaivly simpl. Th Larg Hadron Collidr (LHC), schduld o sar opraing in May 008, will produc abou igh million vns pr yar in is firs sag [1]. I is hrfor xpcd ha op quark propris can b xamind wih significan prcision. Enirly nw masurmns can b conmplad on h basis of h larg availabl saisics. This papr bgins wih a shor rviw of h SM and h main rasons why w nd o look byond i. Basic propris of h op quark ar prsnd, and wo phnomna concrning op quark dcay ar discussd. Ths ar h polarizaion of W boson in h main op quark dcay channl, and flavor changing nural currn dcays of op quark. I is dmonsrad why hs wo phnomna ar vry good candidas for finding signals of nw physics. Th lar on is also discussd in h framwork of minimal suprsymmric xnsion of h sandard modl (MSSM). For his rason a shor inroducion o MSSM is prsnd. This should provid som insigh ino how horical calculaions work hand in hand wih xprimnal obsrvaions, as mor and mor bounds ar pu on fr paramrs plaguing nw proposd modls. 1

4 Th Sandard Modl In h SM, h lmnary paricls ar firs dividd ino frmions and bosons. Frmions hav spin s = 1/, bosons hav ingr spin s = 1 or s = 0. Quarks Lpons u c d s b µ τ ν ν µ ν τ Frmions consis of quarks and lpons. Quarks hav non-ingr lcromagnic (EM) charg and ar h consiuns of msons and baryons. Uppr quarks (u, c, ) hav /3 0 EM charg and lowr quarks (d, s, b) 1/3 0. Lpons consis of lcron, muon and au, which all hav 0 EM charg, and hir nurinos, which hav no EM charg and hav zro mass. Th abl abov has hr columns. Each column rprsns a frmionic gnraion. Paricls of diffrn gnraions ar disinguishd by diffrn masss. Bosons: γ W W Z 0 g h phoon wak bosons gluons Higgs scalar Th firs yp of bosons ar h so-calld gaug bosons. Thy ar vcors according o h Lornz ransformaions. SM includs a phoon, hr wak gaug bosons and igh gluons. Th hr fundamnal forcs of h sandard modl: lcromagnic, wak and srong (color), ar dscribd by xchang of gaug bosons. Th Higgs boson is a scalar, which is inroducd in h SM o gnra h masss of paricls. W will discuss h so calld Higgs mchanism in h following scions. I rmains h only paricl of h SM y o b obsrvd xprimnally..1 QED - firs building block of h SM Wll sablishd classical lcrodynamics and quanum hory of filds mrgd in o quanum lcrodynamics (QED). This is on of h mos succssful horis of all im. [ ] L = ψ iγ µ ( µ i A µ Q ) m ψ }{{} F µν F µν }{{}. (1) inracion dynamics of A µ Equaion (1) rprsns h Lagrang funcion of QED. To xplain h noaion: ψ is h wav funcion of a chargd frmion. A µ is a masslss gaug fild - phoon. is h QED coupling consan. I is also known as h lmnary charg and is a fr paramr of QED. Is valu is obaind xprimnaly. Q is h lcromagnic charg opraor. Th main ool for calculaion of QED procsss is h prurbaion hory. I was Richard Fynman ha inroducd a way o graphically prsn an inracion procss in quanum fild hory wih a so calld Fynman diagram. On such diagram is prsnd in (Fig-1). Th picur on h lf alon is no nough for us o calcula anyhing. Wha is missing ar h Fynman ruls. Evry lin and vry vrx of h diagram is assignd a crain mahmaical srucur as shown in h righ picur of (Fig-1). Onc a diagram is so quippd, w can wri down h xprssion for h marix lmn. Th qusion of wha is assignd o crain pars of h diagram is answrd by h spcific modl. Th abov illusraion is rlvan o QED of h SM. Bu QED facs srious a problm. In addiion o h diagram (Fig-1) prurbaion hory also allows for

5 u (s,p ) iγ µ u (s,p ) γ i gµν q µ µ u µ (s µ,p µ ) iγ ν u µ (s µ,p µ) Figur 1: Fynman diagram of lcron muon scaring of h firs ordr. On phoon is xchangd bwn and µ. γ γ γ µ γ µ µ µ µ µ Figur : Highr ordr diagrams of µ scaring. scond ordr diagrams such as displayd in (Fig-). Th problm is ha calculaion of such diagrams ofn includ ingrals ha ar divrgn. Th soluion lays in h concp of rnormalizaion. Rnormalizaion is a procdur ha maks h consans of h modl (such as in QED) dpndn on h nrgy scal a which a procss is aking plac ( = (E)). By crain procdurs infiniis ar hn rmovd from obsrvabl quaniis. If for a spcific hory rnormalizaion procdur works, h hory is said o b rnormalizabl and hus fr of infiniis. QED is a rnormalizabl hory. In addiion o rnormalizabiliy anohr imporan concp is prsn in QED. This is h gaug invarianc. QED Lagrangian is invarian undr h U(1) Q gaug ransformaions: ψ(x) iα(x)q ψ(x). Hr α(x) is a spac-im dpndn paramr of h ransformaion. This is why w call such ransformaion local or gaug ransformaion. W can hrfor acquir QED Lagrangian of (1) by imposing U(1) Q gaug invarianc on h Lagrangian for fr frmions. This dmand dicas an inroducion of a vcor fild A µ and a coupling consan. This is how by dmanding gaug invarianc undr U(1) Q group, phoon and lcromagnic inracions can b brough in o a fr frmion hory, o rconsruc h wll known QED Lagrangian. Th concp of gaug invarianc can b gnralizd o any Li group, including SU() and SU(3). I urns ou ha gaug invarian horis ar rnormalizabil. Sinc QED was vry succssful, h concp of gaug invarianc was also applid ono wak and color dgrs of frdom, o inroduc nw gaug bosons and inracions and, a h sam im, kp h hory rnormalizabl.. Th Lagrangian Fynman ruls for h whol sandard modl hory can b obaind from is Lagrangian. Firs w nd o choos h righ gaug group and assign h righ quanum numbrs o frmions. SM uss SU() L 3

6 U(1) Y SU(3) c and h following gaug numbrs wr assignd o frmions: SU() L U(1) Y SU(3) c U(1) Q u L 1/ 1/6 ripl /3 d L 1/ 1/6 ripl 1/3 ν L 1/ 1/ singl 0 L 1/ 1/ singl 1 u R 0 /3 ripl /3 d R 0 1/3 ripl 1/3 ν R 0 0 singl 0 R 0 1 singl 1 () Subscrips L and R dno handnss of frmions. Noic ha in h SM only lf-handd frmions carry wak charg. This mans ha only lf-handd paricls can paricipa in wak inracions. Th righhandd nurino is considrd o b nonxisn in h SM sinc i has no charg whasovr and can no inrac wih anyhing. Th color charg is only assignd o quarks so only quarks paricipa in srong (color) inracions. Following h principl of gaug invarian Lagrangian, w can consruc h L SM from h simpl L fr f for fr masslss frmions. I can b wrin as a sum of four rms L SM = L mar L gaug L Higgs L Yukava. Following h sps displayd in (Fig-3) w giv h basic propris of ach rm. L fr f dmand of gaug invarianc L mar = L fr f L in L gaug gaug invarian gaug boson mass rms gaug invarian L Higgs gaug bosons, frmion mass rms scalar Higgs boson L Yukava Figur 3: Sragy for consrucing h Lagrangian of h SM. W sar wih h Lagrangian for fr frmions. L mar : By imposing invarianc undr h SU() L U(1) Y SU(3) c gaug group w inroduc masslss gaug bosons. This givs masslss gaug bosons. Inracion bwn hm and frmions is brough in o h hory along wih hr coupling consans. L gaug : To mak h gaug filds which ar brough ino h hory hrough L mar ral dynamical variabls, w nd o includ rms of hir drivaivs in o h L SM. L gaug consiss of h mos gnral gaug invarian rms of gaug filds and drivaivs. For xampl: his rm yilds h Maxwll quaions for fr lcromagnic fild. L Higgs : To g mass rms for hr of h gaug bosons and kp h gaug invarianc, w nd o inroduc a scalar Higgs fild φ, a doubl of SU(). This fild coupls wih gaug filds. L Higgs is posulad o hav such a ponial, ha Higgs fild gs nonzro vacuum xpcaion valu (VEV). This is a so-calld sponanous symmry braking procdur. By xpanding φ around h VEV, hr xplici mass rms for gaug bosons mrg. L Yukava : Bcaus lf-handd frmions ar SU() doubls and righ-handd frmions ar SU() singls, h mass of frmions nds o b inroducd hrough so calld Yukava couplings wih h Higgs fild. As Higgs gs nonzro VEV, xplici frmion mass rms mrg. 4

7 .3 Frmion gnraions In 1963 Cabibbo inroducd h Cabibbo mixing angl. I was obsrvd xprimnally ha wak dcays wih chang of srangnss ar srongly supprssd in naur. For insanc, h widh of nuron is much biggr han h Λ s Γ s=0 (n udd p uud ν) Γ s=1 (Λ uds p uud ν). Cabibbo proposd ha quarks ha paricipa in chargd wak inracions ar no h physical ignsas of h mass, bu ar in rlaion o hos road by som angl: ( ) ( ) ( ) d wk cos ϑc sin ϑ = c d. sin ϑ c cos ϑ c s s wk A similar approach is akn in h SM. Th diffrnc is ha all six known quarks nd o b includd. A h bginning of h papr w sad ha SM includs hr gnraions of frmions. Th roaing marix hus has 3 3 dimnsions and is calld Cabibbo, Kobayashi, Maskawa (CKM) marix. 3 Problms of h Sandard Modl Now ha w hav sn how h sandard modl is formulad, i should b clar ha his canno b h final hory. In spi of h imprssiv succss in corrlaing all obsrvd low-nrgy daa in rms of vry fw paramrs, i is sill vry unsaisfacory sinc i builds on many assumpions and lavs many fundamnal qusions unanswrd. Blow w giv h lis of h mos imporan puzzls of h SM. 1.) Graviaion: Graviaion is no includd in h SM. This is no such a major concrn sinc h planc scal a which h srngh of graviaional forc bcoms comparabl o ohr fundamnal forcs is of ordr Λ Planck GV..) Zro nurino mass: In SM nurinos hav zro mass. I has bn provn by nurino oscillaions ha nurinos blonging o diffrn gnraions hav diffrn mass. Thir mass is hrfor no zro. 3.) Higgs divrgnc problm: (Fig-4) shows h Fynman diagram of a highr ordr procss ha conribus o h mass of Higgs boson. Thr ar infinily many such diagrams, involving mor h f h b h h f Figur 4: Highr ordr corrcions o Higgs boson mass. han on such frmion or boson loop. If w calcula h corrcions o h Higgs mass du o such loops, divrgncs o infiniy ar obaind. Ths infiniis ar much wors han h ons obaind in highr ordr mass corrcions for frmions and gaug bosons, which ar only logarihmic [5] [ m = m α π log Λ ] m 0. Evn if w insr for h cuoff Λ o b Λ h mass of all obsrvabl univrs, only a mods shif of lcron mass is obaind: m 1.7 m 0. Th corrcions o h mass of Higgs scalar, howvr, lad o quadraic divrgnc m h = (m 0 h) 1 16π λ Λ. (3) 5

8 Λ is h ulraviol cuoff of h loop ingral. W know ha nw physics nds o b inroducd a som poin. If no bfor, a h Planck scal M GV. If w considr h SM o b h xac hory for nrgis up o Planck scal, rnormalizaion hory lls us ha h paramr µ(0) of h Higgs ponial a low nrgis can b xprssd wih µ(m) a high nrgy scal a which nw physics appars: µ (0) = µ (M) M ( c 1 λ(m) c g(m) ). (4) Th M is a dirc consqunc of h Λ in (3). For µ(0) w can say, from h low nrgy physics, ha i is of ordr 10 GV. This is rquird o giv appropria masss o known paricls. Now w divid (4) wih M. µ (0) M [ 10 ] GV = = µ (M) GV M ( c 1 λ(m) c g(m) ). (5) This is a vry unrasonabl siuaion. I rquirs h dimnsionlss paramr µ(m )/M o cancl h complicad sris (c 1 λ(m) ) o 34 dcimal placs in ordr ha h world of ordinary paricls b as ligh as i is. To obain h cancllaion of (5) would rquir a miraculous conspiracy among h paramrs of h SM a h nrgy whr nw physics appars. In ohr words, h xisnc of a scal 10 GV in h SM wih a scond mor fundamnal scal a GV is unnaural. This is calld h gaug hirarchy problm (GHP) [3]. 4 Top quark in SM Th op quark, whn i was discovrd a Frmilab in 1995 [13], compld h hr-gnraion srucur of SM and opnd up h nw fild of op quark physics. I was discovrd in proon, aniproon collision a cnr mass nrgy of 1.8 TV. Th mass was masurd o b 176 ± 18 GV. b p p suff W b W Figur 5: Producion and main dcay of pair. 4.1 Main dcay channl Th main dcay channl for op quark is b W, as illusrad in (Fig-5). Dcays ino s or d quarks ar highly supprssd du o h small off-diagonal CKM marix lmns V s and V d. Th dcay ra Γ( b W ) rads [5]: Γ( bw ) = G Fm 3 [ ] 8π V b λ(1, x b, x W ) (1 x b ) x W (1 x b ) x W W nd o no ha his is h ra for unpolarizd op quarks. All calculaions o follow will rgard unpolarizd op quarks. To xplain h noaion of (6): x i = m i m, λ(x, y, z) = x y z xy xz yz. (6) 6

9 Using h following xprimnal daa for masss and consans [6] Using h sam numrical valus as [7], w g Γ( bw ) 1.55 GV. Du o his larg dcay ra, hr is no sufficin im for op quark o form bound sa hadrons. Th lifim /Γ 10 5 s is on ordr of magniud shorr han h ypical srong inracion im-scal for binding of quarks ino hadrons. 4. Hliciy of W Hliciy is dfind as h projcion of spin o h paricl momnum: ĥ = ˆp ŝ. Sinc W has spin 1, i has hr possibl hliciy sas. Th firs is h cas whr spin is in h sam dircion as h momnum, h scond whr h spin is in h opposi dircion and las possibiliy is h spin o b prpndicular o h momnum. W dno hs hr sas wih h, h and h 0, as illusrad in (Fig-6). Wihin h SM w can calcula h probabiliy for h W boson, which originas s s s p p p h sa h sa h 0 sa Figur 6: Illusraion of hr W hliciy sas. from a op quark dcay, o b in a crain hliciy sa. W dno hs as f = Γ /Γ, f = Γ /Γ and f 0 = Γ 0 /Γ. Hr Γ is h whol dcay ra: Γ = Γ Γ Γ 0. I urns ou ha in h firs ordr and h limi m b 0 f 0 polarizaion is dominan and f is forbiddn: A nonzro valu of f could aris from: a) Nonzro mass m b, f , f = 1 f , f = 0. b) O(α s ) radiaiv corrcions du o gluon mission, b b b g g W g W W Figur 7: QCD corrcions o bw dcay. c) Non-SM physics in h b W dcay. Boh a) and b) possibiliis hav bn considrd in [7]. I urns ou ha m b 0 changs ar vry small: f 0 m b 0 = f 0 ( ), f m b 0 = f ( ), f m b 0 =

10 Th QCD corrcions ar also small. In hs rsuls h mass m b = 0, so only QCD corrcions ar considrd 1. f 0 QCD = f 0 ( ), f QCD = f ( ), f QCD = As w can s QCD corrcion also fail o giv subsanial valu o fracion f. Th m b 0 corrcions can also b prformd on h QCD corrcions, obaining combind corrcions. This incrass h f by % : f m b 0,QCD = f QCD ( ) = If h xprimnal masurmns of f ar found o b a las of h ordr 10, his would b an indicaion of non-sm physics in h, W, b vrx. As w know, W is no a sabl paricl. On of h dcay channls is h W l ν l. Th angular disribuion ω of h chargd lpon mrging from W b l ν l dcay can b xprssd in rms of f fracions [8] ω(θ ) = 3 4 (1 cos θ )f (1 cos θ ) f 3 8 (1 cos θ ) f. θ is h angl bwn h chargd lpon in h W boson rs fram and W in h op rs fram as displayd in (Fig-8). Thr ar svral procdurs for obaining h f 0, f, f from xprimnal daa of l b W θ ν l Figur 8: Dfiniion of θ angl. angular disribuion. Som masurmns hav bn don and ar prsnd in [8], [9]. Boh conclud h agrmn of f wih h SM prdicion. Th rror bars, howvr, ar oo big o xclud h possibiliy of ovrlookd nw physics. Similar xprimns a LHC ar blivd o giv br rsuls, as h numbr of op dcay vns will b much grar. Modls byond SM ha could prdic incrass in f 0 ar lf-righ symmric modls (lik SU() L SU() R U(1) Y ) or modls wih mirrow frmions [9]. 4.3 FCNC dcay c V L us now urn our anion o rar op quark dcays. W considr a dcay of op quark ino lighr up quark and an EM nural gaug boson. W dno h boson V = γ, Z, g. I rprsns ihr a phoon, a nural wak boson or a gluon. This final sa canno b obaind hrough a r-lvl procss. I ffcivly involvs a flavor changing nural currn (FCNC), maning ha h flavor of h op quark is in h dcay procss changd, bu his EM charg rmains h sam. In h SM such a procss is no possibl in h firs ordr and is, as will b dmonsrad, highly supprssd. W can, howvr, raliz his wih a on-loop procss, prsnd in (Fig-9). Compuaion of Γ( c V ) corrsponding o his Fynman diagram is mor complicad, bcaus i posssss a loop. This compuaion is don in [10]. Th rsul is bs prsnd wih branching raios dfind as h fracion of h dcay ra a qusion and h main channl dcay ra: Br( c V ) = Γ( c V ) Γ( b W ). Figur (Fig-10) shows h branching raios dpndnc on h op quark mass for all hr final sa 1 Hr normalizaion facor Γ is h on prsnd in (6), as was in h cas of f mb 0. This is why h sum of all hr f QCD is no 1. In [8] f = 0.00 ± 0.13(sa) ± 0.07(sys.) 8

11 V W d i c V FCNC c = Figur 9: Fynman diagrams rsponsibl for h c V dcay. Figur 10: Branching raios for c, V plod for diffrn op quark mass. gaug bosons. Dashd lins mark h prsn op quark mass sima. W can s ha h raios ar vry small. Boh dcays ino masslss gaug bosons fall rapidly wih incrasing op quark mass. Th rsul for Z channl appars a op quark mass qual o m Z, sinc a smallr mass his dcay is no possibl. I is h vry high mass of h op quark ha maks his raios so small. A LHC h producion of around 10 8 op quark pairs pr yar is xpcd. On purly saisical basis, on should b abl o dc a paricular dcay channl whnvr is branching raio is largr han abou In pracic, w will s ha background problms and sysmaic will lowr his ponial by a fw ordrs of magniud. This mans ha hr is no hop for h c V dcay o b obsrvd if hr is no physics byond SM. Th dcion of his dcay would b a clar signal of nw physics. Th sragy now is o ry and compu similar raios in xndd modls. If h ras can b simad o b of ordr 10 5 or highr, hy should b dcd in fuur xprimns a LHC. This dcion would provid much ndd nw bounds on paramrs of diffrn proposd xnsions of SM, lik h MSSM. Hr w prsn h calculaion in h MSSM wih brokn R-pariy. 9

12 5 Top quark dcay in R MSSM 5.1 Minimal Suprsymmric xnsion of SM On of h mos obvious ways o cop wih GHP is o xnd h SM in such a way ha all highr ordr conribuions o Higgs mass xacly cancl ou. This rquirs posulaing a symmry bwn frmions and bosons. I is calld suprsymmry. I coupls frmions and bosons in such a way ha hir conribuions o scalar mass xacly cancl ou in all highr ordrs of prurbaion. Suprsymmry dicas qual numbr of frmions as bosons. In h minimal suprsymmric xnsion of h SM (MSSM), vry paricl prsn in SM p, gs a suprsymmric parnr dnod p. If p is a frmion, han p is a scalar boson. If p is a vcor boson or a scalar boson, p is a frmion. p and p posss all h sam quanum numbrs, xcp for spin. Th divrgn conribuions of loops from p and p diffr only in sign, so hy cancl ou. No suprsymmric parnrs of known paricls hav bn obsrvd. This mans ha h suprsymmry nds o b brokn in such a way, ha suprsymmric parnrs bcom much havir Paricls and hir suprsymmric parnrs Gaug bosons g frmionic parnrs. On SU() ripl, a U(1) singl and SU(3) oc. Frmions g scalar parnrs calld slpons and squarks. In suprsymmry righ-handd paricls ar usually rfrrd o as aniparicls (charg conjugas) of lf-handd paricls: f R fl c. Unforunaly non of h nw scalar filds can b rlad o h Higgs fild. This im w nd wo Higgs filds, boh SU() doubls bu opposi in U(1) Y charg. Th scond fild is ndd o cancl gaug anomalis riggrd by frmionic parnrs of h Higgs scalars. An ovrviw of MSSM filds is givn in abl (Tab-1) in h appndix. Only on family is prsnd Th Lagrangian Th nx hing o xamin is h inracions in his nw modl. Th Lagrangian of MSSM nds o b gaug invarian. Sinc w hav qui a fw nw paricls, L has nw rms. Th ons rlvan for our discussion ar h so calld l pon and baryon numbr violaing rms: L λ = ] λ ijk [ ν il ē kr ν il ẽ jl ē kr ν il ẽ kr ν ir c jl (i j) i,j,k λ ijk [ ν il dkr d jl d jl dkr ν il d kr ν ird c jl ẽ il dkr u jl ũ jl dkr il d ] krē c iru jl λ ijk ɛ αβγ [ũ iαr d jβr d c kγl d jβrū iαr d c kγl d kγrū iαr d c jβl Indics i, j, k rprsn gnraions and run from 1 o 3. Th λ ijk and λ ijk rms ar rsponsibl for lpon numbr violaion and λ ijk for baryon numbr violaion. Grk indcs α, β, γ in λ rm ar h color indics of quarks and squarks and run from 1 o R-pariy As w hav sn, h mos gnral form of L in MSSM includs lpon numbr (L) violaion, and baryon numbr (B) violaion. No ha hr wr no such couplings in h sandard modl du o is paricl conn and Lornz invarianc; i.. absnc of ripl frmion coupling is simply nsurd by angular momnum consrvaion. In h prsnc of scalar quarks and lpons, howvr, hr is no basic principl of physics which would prohibi hs lpon and baryon numbr violaing couplings [4]. A dirc consqunc is prsnd by h Fynmann diagram in (Fig-11). I rprsns a procss of proon dcay via quark, squark, lpon vrx (λ coupling) and quark, quark, squark vrx (λ coupling). Proon sabiliy rquirs h λ or λ o b vanishingly small. Th radiional prscripion for ovrcoming h proon dcay problm ] 10

13 p u u d d d d π 0 Figur 11: Proon dcay p π 0 allowd by h MSSM. has bn o banish all h Yukawa couplings wih λs: L λ = 0. consrving SUSY modl. R-pariy quanum numbr is dfind as: This rsuls in h sandard R-pariy R = ( 1) 3BLS, B - Baryon numbr, L - Lpon numbr, S - Spin. All SM paricls p hav R quanum numbr R(p) = 1. Thir suprsymmric parnrs p all hav R( p) = 1. I is hus obvious ha rms in L RPV viola R-pariy sinc hy coupl wo paricls and on sparicl. If p 1 p R = 1 R = 1 R = 1 p Figur 1: R-pariy in h L RPV couplings. w considr on of h lins as h final sa, hr is no way for h final sa o hav h sam R-pariy as h iniial sa rprsnd by h rmaining wo lins sinc R-pariy is a muliplicaiv quanum numbr. Whil R consrvaion implis proon sabiliy, h convrs is no ru. Proon sabiliy implis baryon or lpon numbr consrvaion, bu no ncssarily boh. Consqunly on has wo yps of R-pariy violaion ( R) SUSY modls consisn wih proon sabiliy: λ or λ 0: Lpon numbr violaion modl ( L), λ 0: Baryon numbr violaing modl ( B) Sinc hr is no complling rason for R consrvaion in h firs plac, boh hs modls ar considrd in many horical calculaions. As w hav sn, L includs many nw rms as w xnd SM o MSSM. W will giv calculaions in boh L and B vrsions. 5. c V in L MSSM Similarly as in h SM, his dcay is no possibl a r lvl. Rlvan on loop diagrams ar prsnd in (Fig-13). W can hav a squark and chargd lpon or chargd slpon and quark loop. Loop paricls can blong o any of h hr gnraions dnod by i and k. Th calculaion of h dcay ra is don in 11

14 d k (ẽ i ) V λ i3k i (d k ) V c λ ik FCNC c = Figur 13: Fynman diagrams rsponsibl for h c V dcay in L MSSM. [11]. To obain h numrical rsul w would hav o insr valus of h rlvan λ ijk coupling consans and masss of squarks and chargd slpons. Non of hs paramrs ar known. Thr ar, howvr, bounds. Mosly from failur o obsrv conribuions of R MSSM physics in diffrn procsss (low nrgy), uppr bounds on λ paramrs ar s. Som lowr limis for sparicl masss may also b s [1]. Thr ar also crain horical bounds ha can b s wihou any phnomnological considraion. Sinc h dcay ras incras wih coupling consan and dcras wih h incras of sparicl mass, w ar abl o giv maximum valus for branching raios [11]: Br( c Z) 10 9, Br( c γ) 10 10, Br( c g) For h squark mass valu of 100 GV was usd. Any highr valu would only lowr h branching raios. Th conclusion is ha h conribuions of L couplings o cv ar oo small o b of inrs. 5.3 Top quark dcay in B MSSM W mov on now o h baryon numbr violaing couplings. Th c V dcay again appars in on loop procss displayd in (Fig-14). Th loop now consis of a quark squark pair. Th paramrs ar d k V FCNC c = d j c λ 3jk V λ jk Figur 14: Fynman diagrams rsponsibl for h c V dcay in B MSSM. now appropria λ couplings and squark mass. Considring all squark masss o b h sam, h rsuls obaind by [11] ar nicly prsnd in (Fig-15). Th Br valu is dividd by a consan Λ dfind in [11] as: Λ = 1 λ jkλ 3jk. j 1

15 10 Br( c g)/(0. Λ) 10 3 Br( c Z)/(0. Λ) 10 4 Br( c γ)/(0. Λ) Figur 15: Branching raios for c, V in B MSSM plod agains squark mass. Th problm is h lack of any xprimnal bounds on λ jk. In [11] h bound usd is a horical on3 basd on crain assumpions and lads o conclusion ha Λ o b as larg as 5. This mans h ordrs of Br in (Fig-15) do no chang upon muliplying wih (0.Λ). Th high uppr limis for Br do no xclud h dcion of hs procsss. If hy ar no obsrvd howvr, his will giv xprimnal uppr bound for Λ. 6 Conclusions In h nw ra of xprimnal high nrgy physics, op quark dcays could play a considrabl rol. Two phnomna wr dmonsrad o b vry supprssd in h SM prdicions and offr good grounds for sarching for physics byond SM and shaping h nw modls. Th polarizaion of W boson from W b dcay could svrly s h (V-A) srucur of h wak currns posulad in h SM. Som xprimnal daa has alrady bn analyzd bu has givn no ral conclusions as h daa s is no larg nough. Th sarch dcays c V will hlp o s nw bounds on paramrs of nw modls. In his papr a paricular cas for MSSM was prsnd. Th obsrvaion as wll as failur o obsrv such dcays will conribu o h dvlopmn of nw horis. 3 Th consrain of prurbaiv uniariy a h SUSY braking scal M SUSY would bound (λ jk ) /(4π) < 1. 13

16 7 Appndix Suprfild Componn filds SU() L U(1) Y SU(3) c Spin Lpons and ( slpons ) νl L L L = (, 1, 1) 1 ( L ) νl L L = (, 1, 1) 0 ẽ L E c 1 L (1, 1, 1) ẽ c L (1, 1, 1) 0 Quarks and squarks ) Q Q L = ( ul d L Q L = ( ũl d L ) (, 1 6, 3) 1 (, 1 6, 3) 0 U u c L (1, 3, 3 1 ) ũ c L (1, 3, 3 ) 0 D d c L (1, 1 3, 3 1 ) d c L (1, 1 3, 3 ) 0 Gaug bosons and parnrs W V W (3, 0, 1) 1 W 3 W W W 3 (3, 0, 1) 1 B B (1, 0, 1) 1 1 B (1, 0, 1) G G (1, 0, 8) 1 1 G (1, 0, 8) Higgs ( filds ) φ H U H u = u φ 0 (, 1, 1) 0 u ) H u = ( φ u φ 0 u H D H d = ( φ 0 d φ d H d = ( φ0 d φ d ) ) (, 1, 1) 1 (, 1, 1) 0 (, 1, 1) 1 Tabl 1: Tabl of SM paricls and hir suprsymmric parnrs in MSSM for on family. 14

17 Rfrncs [1] M. Bnk al., hp-ph/ [] Ta-Pi Chng, Ling-Fong Li: Gaug hory of lmnary paricl physics, Oxford Univrsiy Prss, [3] L. Suskind: Th GHP, Tchnicolor, Suprsymmry, and all ha, SLAC Pubs and Rpors SSI [4] D.P. Roy: R-Pariy violaing SUSY modl, hp-ph/ [5] J.F. Donoghu: Dynamics of h sandard modl,cambridg Univrsiy Prss, 199. [6] S. Eidlman: Rviw of Paricl Physics, Physics Lrs B 59, 1 (004). [7] M. Fischr al. Phys. Rv. D 63, , hp-ph/ , (000). [8] V. M. Abazov al. hp-x/ [9] S. Cabrra rprsning CDF collaboraion, arxiv: [hp-x] (007). [10] G. Eilam, J.L. Hw, A. Soni, Phys. Rv. D 44, 1473 (1991). [11] Jin Min Yang, Bing-Lin Young, X. Zhang, Phys. Rv. D58, , hp-ph/ [1] M. Chmob: Phnomnological consrains on brokn R-pariy symmry in suprsymmry modls, hp-ph/ [13] F. Ab al. [CDF], Phys. Rv. L (1995) hp-x/