Mixing in Weak Decays

Transcription

1 Mixing in ak Dcay Chargd ak Currnt xchang of cau on mmbr of a wak doublt to chang into th othr Tau and muon thrfor dcay into th lightt mmbr of th doublt thir nutrino lctron ar tabl a th,nu doublt i th lightt doublt. Th virtual can t convrt to anything dcay P46 - particl III

2 Mixing in ak Dcay In th am contxt, th havir quark doublt dcay via a c,t ar havir c t c " "; t b " " b and b quark hould thn b tabl thir lightt baryon a th lightt mmbr of thir doublt But thy arn t du to mixing btwn th gnration for quark th ma igntat ar not th am a th dcay igntat b ma igntat: what ha m b b dcay igntat: what intract with -t P46 - particl III

3 Quark Mixing: Gnration If aum only gnration. Mixing matrix M coθc inθc inθ coθ V V whr θ C i th Cabibbo angl M thn rotat from th ma igntat d, to th dcay igntat d, uually dal with mixing of charg / quark but both mix look at wak vrtic idntical way d d M c u d C C ud cd u u M c c V V P46 - particl III u c V c V cd c d c

4 Charm Dcay Charmd mon can Bta dcay to lightr mon which hav ithr or d quark D D..7 cd V.4 V d or ρ dd cd c in co θc θ C BF.5.95 BF.7. Modulo lightly diffrnt pha pac, th ratio of th dcay dpnd only on th diffrnt mixing. Dirct maurmnt of th mixing angl. d d c P46 - particl III 4

5 aon Dcay Hitorically firt plac mixing obrvd dcay rat dpnd on am pha pac and pin factor a chargd pion dcay Obrvd rat only 5% of what thy hould b and Cabibbo propod a mixing angl who ourc wa unknown at th tim Thi partially lad to a prdiction that th c quark mut xit m 494MV u τ. or or BF BF BF 8 BF c 64% % 7% 8% P46 - particl III 5

6 Quark Gnration For gnration nd X matrix. It i unitary and ha om pha which don t mattr and can b dfind by angl and pha pha giv particl antiparticl diffrnc.antiparticl u M* Hrmitian adjoint calld Cabibbo-obyahi-Makawa CM matrix and wa prdictd by -M bfor th third gnration wa dicovrd V V V ud cd td V V V u c t V V V ub cb tb Each V ij tll what factor ndd for vrtx. Shown ar xprimntal valu. No thory prdict th amount of mixing, P46 - particl III 6

7 P46 - particl III 7 CM Matrix Numrology For N gnration nd NXN unitary matrix. Matrix ha N trm ral and complx and it ha N contraint row x column,. For N quark hav N- arbitrary pha N N 4 9 N- 4 paramtr ndd 4 gnration angl Eulr angl pha CM * act on antiquark. pha cau a mall particl-antiparticl diffrnc. Nd at lat gnration to hav CP violation/mattr-dominatd Univr c c c c c c CM i i φ φ

8 B mon B mon contain b quark D mon contain c quark B ub B ub τ.7 B B B c db cb b B B B c db cb b τ.6 τ.5 τ.5 B, D and τ liftim ar jut long nough o thir path lngth can b dtctd u to maur B proprti and idntify B,D,τ in,pp colliion. For B mon E p γ v βγcτ 7 GV 5 GV.4.7c. mm c. mm c mm H Z bb, ττ bb, ττ t b P46 - particl III 8

9 B Dcay B mon ar dominatd by th dcay of th b quark. A larg ma, pha pac diffrnc ar mall and can gt branching fraction by jut counting dc, du D, x τ u c τ d db B B X B all 9 b b c u V V cb ub.4.4 maurd in data Γ B D Γ V V cb u m m 5 B P46 - particl III 9

10 Particl-antiparticl mixing and CP violation Thr i anothr typ of mixing which i rlatd to quark mixing. Thi can lad to obrvation and tudi of CP violation conidr th mon which ar nutral and compod of diffrnt typ of quark d d uc uc db db b ak intraction can chang particl into antiparticl a charg and othr quantum numbr ar th am. Th trangn tc ar changing through CM mixing d D D u,c,t u, c, t B B d d P46 - particl III d B B b

11 Dpnd onv ij at ach vrtx a V and V* ar diffrnt du to pha, giv particl-antiparticl diffrnc and CP violation any trm with t-quark pcially th tat which dcay ar admixtur of th trong tat a rotation. Thy can hav diffrnt ma and diffrnt liftim α α β β #particl v #antiparticl will hav a tim dpndnc. Eg. If all particl at t, will b a mixtur at a latr tim th phnomnology of i lightly diffrnt than B/D and w ll jut do in dtail. aon rotat and giv long-livd and hort-livd dcay. B/D alo rotat but liftim ar ~am. P46 - particl III

12 Nutral aon Smi-lptonicDcay Proprti for long and hort livd τ S : ma Smi-lptonic Bta dcay. Poitiv or ngativ lpton tll if or anti- dcayd d d 498MV, m c τ 5 du du or or partial width i xactly th am a chargd dcay though mallr BF for Short and largr for ong. BF BF 7. 4 S Γ Γ β β BF τ m BF τ 8 S c c 7 c MV P46 - particl III

13 P46 - particl III Nutral aon Hadronic Dcay Alo dcay hadronically Both dcay to am final tat which man th mixd tat and alo dcay to th pi and pi mod. Man initial tat can mix and hav intrfrnc or d or d or d or d d u d d u d u d u d

14 Sidnot CP for Pion Parity oprator Pfx,y,zf-x,-y,-z. Intrinic parity for pudocalr mon lik,pi i - Charg conjugation oprator C. Chang particl to antiparticl. C λ C λ C λ C λ C C C λ λ λ ± Can work out ignvalu. A C chang charg, C- for photon C - givn it dcay, pion ha C γγ BF BF γγ γγγ 7 < 4 P46 - particl III 4

15 Nutral aon Hadronic Dcay pion and pion ar CP igntat with ignvalu for pi and - for pi CP CP and alo CP igntat β S CP CP CP CP τ τ τ diffrnt valu of matrix lmnt if initial and final tat ar th am CP igntat or if thy ar not CP igntat lik or bta dcay if CP i conrvd, / dcay to pion and / dcay to pion. Mor pha pac for pion and o fatr dcay, hortr liftim. P46 - particl III 5 S ±

16 P46 - particl III 6 Dcay and Intrfrnc From Schrodingr q. plan wav olution th two amplitud hav to b addd and thn quard. Giv intrfrnc. Exampl: tart with pur Intnity i thi amplitud quard mall ma diffrnc btwn th two wak dcay igntat S im im S S A t A Γ Γ ψ ψ S S A A τ τ ψ / /, Γ t E iet m h h ; : aum [ ][ ] [ ] V m m m mt I S t t t S S S S 5 / * * co 4 Γ Γ Γ Γ ψ ψ ψ ψ

17 Dcay and Intrfrnc Do th am for anti- I 4 [ ][ ] * * ψ ψ ψ ψ S [ mt] Γ t Γ t Γ Γ t / co S gt mixing. Particl<->antiparticl varying with tim. At larg tim gt qual mixtur % th rat at which anti- dpnd on / m. You nd to mix <->anti bfor thy dcay to hav S and mτ But If S.47 " m >> τ S S "," jut " S " dcay " dcay P46 - particl III 7

18 S Rgnration Aum pur bam trik a targt mad up of particl p,n diffrnt trong intraction cro ction for and anti- d n Λ ud n Λ ud mix of -anti no longr :. Exampl, aum lo.5 anti,.. giv ignoring pha and o not quit right a a bs b Firt obrvd by drman t al. maur particl/antiparticl diffrnc. Uful xprimntal tchniqu a 4, b 4 P46 - particl III 8

19 CP Violation C chang particl to antiparticl P oprator flip pac mirror imag T tim rvral t -t fundamntal axiom thory? of quantum mchanic CPT i conrvd ak intraction violat all. CP violation i th am a T violation. Thr obrvation o far of thi Univr i motly mattr Sakharov 96 dcay to pion Chritianon, Cronin, Fitch and Turlay, 964 nutral B dcay P46 - particl III 9

20 park chambr and o poor ma rolution. Idntify -> a in forward dirction motly 45 ± 9 : P46 - particl III

21 CP Violation in dcay and th particl which hav diffrnt liftim ar NOT igntat of CP. Intad and ar, S ε ε ± ε ε ε. S hn dcay, motly it i dcaying to a CP- tat pion but omtim to a CP tat pion P46 - particl III

22 P46 - particl III CP violation in dcay CP i thn xplaind by having a pha in th mixing btwn and anti- othr ourc of CP violation fifth forc ar ruld out a inconitnt with th variou way of obrving CP violation d d u,c,t t c u,, arg ± Γ Γ Γ Γ ± δ S amp amp or aymmtry ch BF BF BF

23 Indirct v Dirct CP Indirct CP i du to th mixing th box diagram Dirct i in th dcay and that th chargd and nutral mod ar lightly diffrnt diffrnt iopin g BF BF amp amp ±.8 d u,c,t u, c, t d P46 - particl III

24 Frmilab propoal 67 January 979 yar xprimnt at FNA and CERN wrong. mall ffct and vry larg hadronic factor P46 - particl III 4

25 B : Mixing and CP violation Nutral B and D alo mix and hav CP violating dcay. Th dpnd on CM matrix lmnt and ar bttr at dtrmining thm than dcay. B and both ocillat a fw tim bfor thy dcay diffrnt than ytm a many dcay channl mot of which ar not CP igntat. Alo no,s a th liftim of th, tat ar about th am B, B ± B τ m mτ/hbar B B S d c c c Mv,.5 Mv,.5 Mv,9 h / h / h /.5.8 P46 - particl III 5

26 P46 - particl III 6

27 Glahow-inbrg-Salam Modl EM and wak forc mix or jut E forc. Bfor mixing Boon ar mal: Group Boon Coupling Quantum No. SU,, g T wak iopin U B g Y lptonic hyprcharg T Y / Q lc. charg Intraction agrangian i r r YB int gt g convrt to phyical fild. Nutral mix B, Z, photon.,z acquir ma. Forc photon ma. Higg Boon introducd to brak ma ymmtry A i am fild a in EM.4 vctor A inθ coθ B Z θ coθ wak mixing inθ B angl tanθ P46 - particl III g 7 g

28 Higg Boon braking lctrowak ymmtry giv: maiv Z Boon ma photon or mor calar particl Higg minimal SUSY, chargd and nutral Higg coupl to ma and implitically dcay to th mot maiv availabl particl ay to produc in conjunction with havy objct hlp to dicovr?? σ HZ σ H σ H production % m H GV P46 - particl III 8

29 Standard Modl Higg Boon Branching fraction dpnd on ma U ZH,H for m<5 GV U for m> 5 GV Currnt limit u - fb - D: Higg dcay channl analy combind ± H l bb ZH l l bb ZH bb H ll DCDF imit.4-8 tim SM 7 P46 - particl III 9

30 ook at EM and wak currnt EM EM EM g inθ T Y g inθ T A g inθ AQ A g coθ λ λ chargd currnt. Compar to mu/bta dcay hav maurd wak forc, g. wak mixing only nw fr paramtr cc g [ T ] gt λ G λ λ J λ m YB T λ g coθ Y / Q F M 5/ 4 5/ 4 8M GF λ g g inθ / inθ G F 7.GV inθ wak nutral currnt g NC g coθ / co 8M Z θ Z G T F in M Z θ Q M coθ g coθ Z λ J λ NC P46 - particl III

31 E modl ha lft-handd doublt right handd inglt and Z coupling R T Q [ T Q ] coupling to lft-handd componnt and alway ntially th am g ± T ± g doublt; R T in ± glt Q, Z to lft-handd doublt Z to right-handd inglt g g R " g " g z z " T Q in " Qin θ θ Z inθ coθ [ T Q in θ ] rdfin a Vctor and Axial part of V-A c c V A g gr T Q in θ g g R T Z c V A c P46 - particl III

32 P46 - particl III Z dcay/vrtic bb cc dd uu Z τ τ τ τ Q T V A A V c c c c Color factor of for quark. in in R A R V T g g c Q T g g c θ θ

33 Z Branching Fraction Can u coupling to gt branching mod PDG maurd valu in Z.6 Z all *.6 *.5 **.9 ** Z *.5.. Z all 7. Z bb * Z all 7. Z qq **.7 ** Z all 7. P46 - particl III

34 Nutrino Phyic Thr activ nutrino flavor from Z width maurmnt. Ma limit from bta dcay m m m τ < < < V. 8 MV MV m x m V x τ or inactiv Probably hav non-zro ma a thy ocillat right-handd nutrino? m up lctrowak Only hav wak intraction and can b ithr chargd or nutral currnt x 4 V x orτ charg nutral Z p n n,p, n,p, n P46 - particl III 4 n p p p p

35 Nutrino Cro Sction U Frmi Goldn Rul M matrix lmnt ha wak intraction phyic, Z xchang ~ contant at modt nutrino nrgi. Sam G factor a bta dcay G g 8M cro ction dpnd on pha pac and pin trm. ook at pha pac firt for chargd currnt. Momntum conrvation intgrat out on particl p Rat cm p p CC phapac h M q phapac M p dp σ p 4G dp M cm P46 - particl III 5 p E < M

36 P46 - particl III 6 Nutrino Cro Sction II ook in cntr-of-momntum fram i an invariant and can alo dtrmin in th lab fram cro ction grow with pha pac ithr nutrino nrgy or targt ma σ G p G p p E E E p p p p E M tot tot tot tot 4 r r σ me G me p m me E m E E E p p tot tot p m m p σ σ

37 Nutral Currnt Th dtction of om raction provd that nutral currnt and th Z xit p p th cro ction dpnd on th diffrnt coupling at ach vrtx and maur th wak mixing angl σ σ G G me me 4in 4 in 6 4 θ in θ 6 4 θ in θ about 4% of th chargd currnt cro ction. du to Z-- coupling compard to --nu coupling P46 - particl III 7

38 Nutrino Ocillation Diffrnt igntat for wak and ma wak,,,, : ma : τ can mix with a CM-lik x matrix with probably diffrnt angl and pha thn quark. Th nutrino liftim i ~infinit and o mix du to having ma and ma diffrnc lik and S xampl. Aum jut gnration angl coθ inθ inθ coθ aum that at t % muon-typ t t t coθ t inθ P46 - particl III 8

39 Nutrino Ocillation II Can now look at th tim volution from th Scrod. Eq. And auming that th nrgy i much largr than th ma ie m, t i, t, Ei p h c p probability of /mu typ v tim or lngth th nutrino ha travld i thn t co θ iet in θ ie t in θ in m c 4Ehc whr w now put back in th miing contant and ud trig idntiti t c E p inθ coθ in θ co E E t in P46 - particl III 9 4 E E t

40 Nutrino Ocillation III Ocillation dpnd on mixing angl and ma diffrnc but nd non-zro ma or no tim propagation t t in t θ in m c 4Ehc 4 o om muon-typ nutrino ar convrtd to lctron typ. Rat dpnd on nutrino nrgy and ditanc nutrino travl /E go to nutrino typ and will hav trm with mor than on mixing angl. Plu nutrino can ocillat into ithr of th othr two or to a fourth tril typ of nutrino which ha diffrnt coupling to th /Z than th known typ P46 - particl III 4

41 Nutrino Ocillation IV P46 - particl III 4

42 Nutrino Ocillation V ith thr gnration of nutrino th chang of on nutrino typ into anothr dpnd on many trm You can undrtand th trm by mauring at diffrnt nrgi and lngth Thr i anothr ffct intraction in mattr which w will kip that com into play Ocillation can alo violat CP b diffrnt if nutrino or antinutrino bam P46 - particl III 4

43 Dtcting Nutrino Ocillation Diapparanc: flux rduction largr /E Solar Nutrino. Maur rat for both lctron nutrino and all nutrino uing nutral currnt. ow nrgi fw MV cau xprimntal thrhold for om tchniqu. Compar to olar modl. rat Rat n p p,, τ pn,, τ n Atmophric nutrino. Maur rat a a function of nrgy and lngth from angl # # production alo lctron or muon nutrino producd at ractor or acclrator. Compar flux nar production to far away /E >> P46 - particl III 4

44 Nutrino from Sum from Particl Data Group p p H 8 B 8 B 7 B 7 i P46 - particl III 44

45 Dtcting Nutrino Ocillation Apparanc: tart with on flavor dtct anothr Idal. Tag nu production by dtcting th lpton. Thn dtct nutrino intraction. Poor rat conidrd pi/ bam and muon torag ring Ral. Tau nutrino vry difficult to dtct ourc of pur lcton nutrino ractor ar blow muon/tau thrhold u motly muon nutrino bam. can maur nutrino nrgy in dtctor if abov GV. Blow hurt by Frmi ga ffct. Can uually parat lctron from muon vnt with a vry good ~% activ dtctor P46 - particl III 45

46 Nova dtctor will b motly liquid cintillator lik BN nutrino xprimnt of th 98. Gratr than 8$%activ. P46 - particl III 46

47 High Priority Itm in Particl Phyic Quark Mixing and CP violation Nutrino Mixing and mayb CP violation ar Quark and Nutrino mixing rlatd? Sourc of Elctro-ak ymmtry braking Higg? Prciion maurmnt of currnt paramtr top,,z mag- what i dark mattr? dark nrgy? Sarch for Nw Phnomna Suprymmtry, Extra Dimnion, ptoquark, nw quark/lpton/boon, compoitn, why pin ½ v pin om NP can xplain othr qution ourc of CP, dark mattr, tc P46 - particl III 47

48 Extra Dimnion Poibl olution to th Hirarchy Problm M H ~ GV M GUT/Planck ~ 6-9 GV modl of Arkani-Hamd, Dimopoulo and Dvali gravity propagat to n xtra patial dimnion giv maiv tabl aluza-lin graviton G ffctiv Plank cal M Pl rlatd to fundamntal Plank cal in n4 dim M D alo modl of Randall-Sundrum xtra dim but larg curvatur SIGNA ral graviton - high E T ingl photon miing E T M Pl ~R n M D n - monojt miing E T SIGNA virtual graviton - high ma pair:,,γγ P46 - particl III 48

49 Suprymmtry add uprpartnr to quark, lpton, and boon Solv th Hirarchy Problm lightt uprymmtric particl SP candidat for dark mattr Unification of th gaug coupling R-Parity: if conrvd: SP i tabl, SUSY particl producd in pair not conrvd: may gnrat ma/mixing P46 - particl III 49

50 SUSY: Trilpton numbr of poibl dcay chain Vry clan mod - iolatd lpton - MET from or χ low σ BF <.5 pb lpton can b oft and dpnd on m ~χ SP P46 - particl III 5