Section VIII. The Weak Interaction

Transcription

1 Sction VIII Th ak Intraction

2 Th ak Intraction Th AK intraction accont for many cay in particl phyic xampl: Charactriz by long liftim an mall cro-ction - - p n π ; ; 69

3 Two typ of AK intraction: CHARGD CURRNT (CC): ± Boon NUTRAL CURRNT (NC): Z Boon Th AK forc i miat by MASSIV VCTOR BOSONS: M ~ 8 GV xampl: M Z ~ 9 GV ak intraction of lctron an ntrino: Z Z 7

4 Boon Slf-Intraction In QCD th glon carry COLOUR charg. In th AK intraction th ± an Z boon carry th AK CHARG ± alo carry M charg BOSON SLF-INTRACTIONS γ Z Z Z Z γ γ γ 7

5 Frmi Thory ak intraction takn to b a 4-frmion contact intraction No propagator Copling trngth givn by th FRMI CONSTANT, G F G F.66 x -5 GV - β Dcay in Frmi Thory p n p - n G F U Frmi Goln Rl to gt th tranition rat Γ π M fi ( ) whr M if i th matrix lmnt an ρ( f ) i th nity of final tat. ρ f ( ) ρ f N f 7

6 Dnity of Final Stat: -boy v. -boy (pag 46) TO BODY FINAL STAT: N π ( ) Ω Rlativitic ( ~ p) i.. nglct ma of final tat particl. Only conir on of th particl inc th othr fix by (,p) conrvation. THR BODY FINAL STAT (.g. β cay): N Ω ( π) ( π) Now ncary to conir two particl th thir i givn by (,p) conrvation. Ω 7

7 In nclar β cay, th nrgy rla in th nclar tranition,, i har btwn th lctron, ntrino an th rcoil kintic nrgy of th ncl: Trcoil Sinc th ncl i mch mor maiv than th lctron /ntrino: an th nclar rcoil nr momntm conrvation. For a GIVN lctron nrgy : N N Ω ( π) ( π) Ω 74

8 Aming iotropic cay itribtion an intgrating ovr Ω Ω giv: N ( ) ( ) 4π ( ) ( ) π Γ Γ π π M fi M fi 4π 4 ( ) ( ) π 4 4π 4π 4 Matrix lmnt In Frmi thory, M G an trat, a fr particl fi M fi F G F ψ n ψ ψ ψ p p ψ v v ip ψ v r ( p p ) v v r ψ n r v ψ 4-point intraction v r v ip v r 75

9 p v r v Typically, an hav nrgi ~ MV, o << iz of ncl an ψ,ψ Corrpon to zro anglar momntm (l ) tat for th an. ALLOD TRANSITIONS - Th matrix lmnt i thn givn by M fi GF ψ p ψn r v G F M nclar whr th nclar matrix lmnt accont for th ovrlap of th nclar wav-fnction. If th n an p wav-fnction ar vry imilar, th nclar matrix lmnt M nclar M nclar M fi larg an β cay i favor: SUPRALLOD TRANSITIONS 76

10 M nclar Hr, am (prallow tranition): Γ Γ Γ G π F GF π GF 6π ( ) 5 ( ) G π F M fi G F SARGNT RUL: 5.g. - an - cay ( latr) By tying liftim for nclar bta cay, w can trmin th trngth of th wak intraction in Frmi thory: β G F -5 (. 6 ±.) GV 77

11 Bta-Dcay Spctrm Γ G F ( ) Γ Plot of vr i linar ( ) π Γ ( ) KURI PLOT Γ H H ( kv ) 78

12 Ma m (nglct ma of final tat particl) n point of lctron pctrm m (allow for ma of final tat particl) p Dnity of tat N Ω N Ω (pag 46) π ( π) p ( ) Γ G π F ( ) m ( ) m m known, m mall only ignificant ffct i whr 79

13 KURI PLOT Γ Γ ( ) m Γ 4 m ( ) 4 xprimntal roltion Mot rcnt rlt (999) Tritim β cay: m < V If ntrino hav ma, m << m hy o mall? 8

14 Ntrino Scattring in Frmi Thory (Invr β Dcay). σ σ π M GF π n p fi N π whr i th nrgy of th in th cntr-of-ma ytm an i th nrgy in th cntr-of-ma ytm. In th laboratory fram: ( pag 6) σ G F ( π) only intract AKLY hav vry mall intraction cro-ction Hr AK impli that yo n approximatly 5 light-yar of watr to top a MV ntrino! Howvr, a th cro-ction can bcom vry larg. Violat maximm allow val by conrvation of probability at (UNITARITY LIMIT). Ω Frmi thory brak own at high nrgi. m n -4 ( in MV) cm ~ Appnix F n G F p 74 GV 8

15 ak Charg Crrnt: ± Boon Frmi thory brak own at high nrgy Tr intraction crib by xchang of CHARGD ± BOSONS Frmi thory i th low nrgy q << m FFCTIV thory of th AK intraction. β Dcay: n Scattring: p ( ) G F n G F g g q M p 8

16 Compar AK an QD intraction: α AK g 4π g g q M QD γ g m gm q g m α 4 π CHARGD CURRNT AK INTRACTION At low nrgi, q << M, propagator q M M i.. appar a POINT-LIK intraction of Frmi thory. Maiv propagator hort rang M 8.4 GV Rang ~. fm M xchang boon carri lctromagntic charg. FLAVOUR CHANGING ONLY AK intraction chang flavor PARITY VIOLATING ONLY AK intraction can violat parity conrvation. 8

17 Compar Frmi thory c.f. maiv propagator - q << M G F For compar matrix lmnt: G F i mall bca m i larg. Th prci rlationhip i: g - Th nmrical factor ar partly of hitorical origin ( Prkin 4 th., pag ). M 8.4 GV an GF g an α 5 GV Th intrinic trngth of th AK intraction i GRATR than that of th lctromagntic intraction. At low nrgi (low q ), it appar wak to th maiv propagator. 84 g 4π g M g 8M G g F G F α ( latr to why β iffrnt to ) 4π 7 G F

18 Ntrino Scattring with a Maiv Boon Rplac contact intraction by maiv boon xchang iagram: q Intgrat to giv: g g σ σ M GF π GF M π σ q π ( q M ) with q inϑ whr θ i th cattring angl. g 4 (imilar to pag 48) << >> M M Appnix G Total cro-ction now wll bhav at high nrgi. 85

19 Parity Violation in Bta Dcay Parity violation wa firt obrv in th β cay of 6 Co ncli (C.S. t. al. Phy. Rv. 5 (957) 4) Align 6 Co ncli with fil an look at irction of miion of lctron Unr parity: B Co Ni B v v v r v r; v v L r p J5 J4 Pˆ v v p v p v L; If PARITY i CONSRVD, xpct qal nmbr of lctron paralll an antiparalll to B v B v - 86

20 Polariz T. K Unpolariz A 6 Co hat p, thrmal xcitation ranomi th pin Mot lctron mitt oppoit to irction of fil PARITY VIOLATION in β DCAY 87

21 Origin of Parity Violation SPIN an HLICITY Conir a fr particl of contant momntm, p v. v v v Total anglar momntm, J L S, i ALAYS conrv. v v v Th orbital anglar momntm, L r p, i prpniclar to p v Th pin anglar momntm,, can b in any irction rlativ to p v Th val of pin S v along p v S v i alway CONSTANT. Dfin th ign of th componnt of pin along th irction of motion a th HLICITY v p v h v p v h v p v h RIGHT-HANDD LFT-HANDD p v 88

22 Th AK intraction itingih btwn LFT an RIGHT-HANDD tat. Th wak intraction copl prfrntially to LFT-HANDD PARTICLS an RIGHT-HANDD ANTIPARTICLS v v p v p v In th ltra-rlativitic (mal) limit, th copling to RIGHT-HANDD particl vanih. i.. vn if RIGHT-HANDD xit thy ar nobrvabl! 6 Co xprimnt: p v B 6 Co 6 Ni J5 J4 p v 89

23 Parity Violation Th AK intraction trat LH an RH tat iffrntly an thrfor can violat PARITY (i.. th intraction Hamiltonian o not commt with Pˆ ). xampl J P P PARITY i ALAYS conrv in th STRONG/M intraction η η π π P π π PARITY CONSRVD π π π ( ) ( ) ( L L P π P π )( ) ( ) P ; L L! PARITY VIOLATD Branching fraction % Branching fraction <.% η J P P η π π P π π π ( ) ( P π )( ) L P ; L 9

24 PARITY i USUALLY violat in th AK intraction bt NOT ALAYS! xampl J P K P K P ; L PARITY VIOLATD π π π π P π P π ( ) ( )( ) L ( ) ( ) ( )( ) L ( ) L Branching fraction ~ % Branching fraction ~ 6% J P P π K π π K π π π - P π P π P π P ; L L PARITY CONSRVD! 9

25 Th ak CC Lpton Vrtx All wak charg crrnt lpton intraction can b crib by th boon propagator an th wak vrtx:,,,, α g 4π g STANDARD MODL AK CC LPTON VRTX antiparticl Boon only copl to th lpton an ntrino within th SAM gnration.g. no copling Univral copling contant g 9

26 xampl: - -,, -, -, -,, n p - - n Bc J ψ p Bc b c c c J ψ 9

27 Dcay Mon ar fnamntal lpton (m ~ 6 m ). lctromagntic cay i NOT obrv; th M intraction o not chang flavor. Only th AK CC intraction chang flavor. Mon cay wakly: γ g - g - G F m << M A can FRMI thory to calclat cay with (analogo to β cay). 94

28 FRMI thory giv cay with proportional to (Sargnt rl). 5 m Howvr, mor complicat pha pac intgration (prvioly nglct kintic nrgy of rcoiling ncl) giv Γ G F 5 m 9π Mon ma an liftim known with high prciion. 6 (.97±.4) U mon cay to fix trngth of AK intraction G F G F (.66.) 5 ± GV G F i on of th bt trmin fnamntal qantiti in particl phyic. 95

29 Univrality of ak Copling Can compar G F mar from cay with that from β cay. g - From mon cay mar: From β cay mar: Ratio G F β G F G G β F F g Concl that th trngth of th wak intraction i ALMOST th am for lpton a for qark. will com back to th origin of thi iffrnc ( coϑ C ) n (.66.) 5 ± GV -5 (. 6 ±.) GV.974 ±. p 96

30 Th ma i rlativly larg an a m m > Dcay (.777 ±.) GV { m, m, m,k} thr ar a nmbr of poibl cay mo. π ρ xampl Ta branching fraction: haron (7.8 ±.%) (7. ±.%) (64.7 ±.%) 97

31 Lpton Univrality Tt whthr all lpton hav th am AK copling from marmnt of th cay rat an branching fraction. Compar g - Γ g GF 9π If nivral trngth of AK intraction, xpct m 5 5 m MV m, m, ar all mar prcily m ( 777. ±.) MV.97±.4 Prict (.9± Mar (.9±.) m 5.78 m B( ) g Γ g GF.78 9π B( ) m 5 ( 7.8 ±.% ) 6 ( ) SAM AK CC COUPLING FOR AND 98

32 Alo compar g g g g IF am copling xpct: B B ( - ) ( - ).976 (th mall iffrnc i to th light rction in pha pac to th non-ngligibl mon ma). ( ) - B Th obrv ratio ( ).974 ±.5 i conitnt with - th priction. B SAM AK CC COUPLING FOR, AND LPTON UNIVRSALITY 99

33 ak Intraction of Qark In th Stanar Mol, th lptonic wak copling tak plac within a particlar gnration: - Natral to xpct am pattrn for QUARKS, i.. b Unfortnatly, not that impl!! xampl: Th cay K ggt a copling c t K

34 For-Flavor Qark Mixing Cabibbo Mixing Angl Th tat which tak part in th AK intraction ar ORTHOGONAL combination of th tat of finit flavor (, ) For 4 flavor, {,, an c}, th mixing can b crib by a ingl paramtr o CABIBBO ANGL (from xprimnt) ak igntat Copling bcom: co ϑ co ϑ C C in ϑ in ϑ C C co ϑ in ϑ c g C g C ϑc in ϑ co ϑ co ϑ C co ϑ C C C c Flavor igntat g g in ϑc in ϑc c

35 xampl: Nclar β cay Rcall β G F G F n -5 (. 6 ±.) GV (.66.) 5 ± GV p trngth of copling β M co ϑ ( ) C G F Hnc, xpct It work, g co G β F GF coϑ C.6.66 ϑ C o co ϑc o Cabibbo Favor M co ϑc Cabibbo Sppr g g co ϑ C in ϑ C M in ϑc g g co ϑ C in ϑ C c c

36 xampl: K copling Cabibbo ppr M in ϑc K g in ϑ C g xampl: D xpct c D g Γ Γ K coϑ C g π, D K K π coϑ C π 4 K π in ϑ 4 K π co ϑ.8 ( D ) ( D ) C C D c - g in ϑ C g in ϑ C π K Mar.8 ±.8 D K π i DOUBLY Cabibbo ppr

37 CKM Matrix Cabibbo-Kobayahi-Makawa Matrix xtn to gnration b V ak igntat CKM Giving copling V V V c t g V V V V c t V V V b cb tb V b coϑc in ϑ. C CKM g V b in ϑ coϑ C c C.5 Flavor igntat..5 λ λ λ g V b λ λ λ t λ λ λ in ϑ C b 4

38 Th ak CC Qark Vrtx All wak charg crrnt qark intraction can b crib by th boon propagator an th wak vrtx: q {,c,t} α g V qq g 4π q {,,b} STANDARD MODL AK CC QUARK VRTX antiparticl boon CHANG qark flavor lik to copl to qark in th SAM gnration, bt qark tat mixing man that CROSS-GNRATION copling can occr. -Lpton copling contant -Qark copling contant g g V CKM 5

39 B xampl: b M g V cb g Ma (Log cal) 4 B g D 4 in ϑc t c - ϕ π K D c D Charg / Charg -/ K c M g V c g g 4 V b 4 co ϑc ϕ π g w V, V c, V tb O() g w V c, V O(λ) g w V cb, V t O(λ ) t, b O(λ ) vry mall ϕ - M g V g 4 λ in ϑ C K g V 4 in ϑc 6 K

40 Smmary AK INTRACTION (CHARGD CURRNT) ak forc miat by maiv boon ak forc intrinically trongr than M intraction α cf αm 7 Univral copling to qark an lpton Qark tak part in th intraction a mixtr of th flavor igntat Parity can b VIOLATD to th HLICITY trctr of th intraction Strngth of th wak intraction givn by G F M ( 8.4 ±.8) GV (.66.) 5 ± GV from mon cay. 7