IV. Weak interaction 1. Phenomenology of weak decays 2. Parity violation and neutrino helicity 3. V-A theory 4. Neutral currents

Transcription

1 IV. Wak intraction. hnonology of wak dcays. arity violation and ntrino hlicity 3. V-A thory 4. Ntral crrnts Th wak intraction was and is a toic with a lot of srriss: ast: Flavor violation, and C violation. Today: Wak dcays sd as robs for nw hysics

2 . hnonology of wak dcays All articls (xct hotons and glons articiat in th wak intraction. At sall q wak intraction can b shadowd by strong and lctro-agntic ffcts. Obsrvation of wak ffcts only ossibl if strong/lctro-agntic rocsss ar forbiddn by consrvation laws:.6 6 s lctroagntic dcay forbiddn by lton nbr consrvation

3 . Wak intraction and nclar -Dcay: n Fri s xlanation (933/34 of th nclar -dcay: n J N Two frionic vctor crrnts cold by a wak coling const. at singl oint (4-frion intract. Aly Fynan Rls J M G F J N, J G F Fri coling constant, dinsion = (/M v n Coling of th crrnts dscribd by coling constant G F a vry sall nbr ~ -5 GV -. xlains th waknss of th forc. Fri s ansatz was insird by th strctr of th lctroagntic intraction and th fact that thr is ssntially no nrgy dndnc obsrvd. robl: Ansatz cannot xlain arity violation (was no a robl in 933 3

4 Today s ictr of th -dcay Nclons ar coosd of qarks, which ar th fndantal frions. Th qarks col to th fndantal forcs. Th wak intraction is diatd by a assiv vctor fild (gag boson, W. Coling constant g w. Using th th qark lvl dcay on can dscrib wak hadron dcays (trating th qarks which ar not wakly intracting as sctators n d d n I 3 W g w g w d M Transition atrix: Crrnts: V-A strctr g ( igw Jqark q Mw J lton Strong isosin I 3 not consrvd. waknss rslt of (/M w srssion 4

5 . Wak hadronic dcays a Doinant dcay ods d d s c c d s I I 3 W d,s V d,c,c d,s W W If q is larg nogh th W can also dcay to (,d or ( d qark airs Historically d c s M ~ cos c ~.95 Cabibbo angl: c. 5

6 6 d c s s c d b srssd dcay ods ~.5 ~ sin M c W c, d,s s d d d s d K + K S S s c d W W Wak intraction dos not consrv strong isosin, strangnss or othr qark flavor nbrs. Lton nbr is consrvd. V s Qark flavor transition dscribd by th CKM atrix.

7 .3 Ntrino intractions n n n W crossing dcay Ntrino-nclon scattring Vry sall cross sction for N scattring: (N [GV]x -38 c [GV]x fb intns ntrino bas larg instrntd targts 7

8 . arity violation arity transforations ( = sac invrsion transforation rortis: : r r t t r Axial/sdo vctor.g.: Hlicity orator H s (sdo- scalar s H=+/ H=-/ xrintally: irroring at lan + rotation arond axis rndiclar to lan To tst arity it is sfficint to stdy th rocss in th irrord syst : hysics invariant ndr rotation 8

9 9. Historical / zzl (956 Until 956 arity consrvation as wll as T and C sytry was a doga : vry littl xrintal tsts don In 956 L and Yang roosd arity violation in wak rocsss. Starting oint: Obsrvation of two articls + and + with xactly qal ass, charg and strangnss bt with diffrnt arity: 3, ( ( ( ( ( ( ( ( / J J w L + Yang: + and + sa articl, bt dcay violats arity articl is K + : is consrvd ( is violatd ( K K To sarch for ossibl violation, a nbr of xrintal tsts of arity consrvation in wak dcays has bn roosd: 957 Obsrvation of violation in nclar dcays by Chin-Shing W t al. Historical nas (=-

10 . Obsrvation of arity violation, C.S. W t al. 957 Ida: Masrnt of th anglar distribtion of th ittd - in th dcay of olarizd 6 Co ncli 6 Co 6 Ni 6 Co J J 6 Co J=5 J=4 Gaov-Tllr Transition J= Obsrvabl: J - J If is consrvd, th anglar distribtion st b sytric in (sytric to dashd lin: transition rats for J and ar idntical. xrint: Invrt Co olarization and coar th rats at th sa osition. - J

11 NaJ dtctor to asr rat J 6 Co - J 6 Co Rslt: lctron rat oosit to Co olarization is highr than along th 6 Co olarization: arity violation Qalitativ xlanation: J=5 J=4 Today w know: Consqnc of xistnc of only lft-handd (LH ntrinos (RH anti-ntrinos lctron olarization H in dcays v c

12 .3 Dtrination of th ntrino hlicity Goldhabr t al., 958 Indirct asrnt of th ntrino hlicity in a K catr raction: 5 5 S 95KV 5 5 S K catr (96 kv J J - Ida of th xrint: 5 S J. lctron catr and ission 5 J S - J S ndrgos a sall rcoil ( rcoil =95 KV. Bcas of anglar ont consrvation Sin J= of S * is oosit to ntrino sin. Iortant: ntrino hlicity is transfrrd to th S nclos. 5 RH LH ossibilitis

13 . ission: 5 5 S ( J S( J Configration RH 5 S 5 S RH or LH LH - J J LH or RH hotons along th S rcoil dirction carry th olarization of th S * ncls How to slct hotons along th rcoil dirction? 3 How to dtrin th olarization of ths hotons? 4 3

14 Rsonant hoton scattring: S S S Rsonant scattring: To consat th nclar rcoil, th hoton nrgy st b slightly largr than 96 kv. This is th cas for hotons which hav bn ittd in th dirction of th S rcoil (Dolr-ffct. Rsonant scattring only ossibl for forward ittd hotons, which carry th olarization of th S * and ths th olarization of th ntrinos. 5 S 5 S 5 5 S S 5 S 4

15 4. Dtrination of th hoton olarization xloit that th transission indx throgh agntizd iron is olarization dndnt: Coton scattring in agntizd iron LH B RH B olarization of lctrons in iron (to iniiz ot. nrgy olarization of lctrons in iron Absortion lads to sin fli LH hotons cannot b absorbd: Good transission RH hotons ndrgo Coton scattring: Bad transission hotons w/ olarization anti-aralll to agntization ndrgo lss absortion 5

16 xrint S * ittd hotons ass throgh th agntizd iron. Rsonant scattring allows th hoton dtction by a NaJ scintillation contr. Th conting rat diffrnc for th two ossibl agntizations asr th olarization of th hotons and ths th hlicity of th ntrinos. Rslts:.66.4 hotons fro S * ar lft-handd. Th asrd hoton olarization is coatibl with a ntrino hlicity of H=/. Fro a calclation with % hoton olarization on xcts a asrabl val ~.75. Rason is th finit anglar acctanc. Also not xactly forward-going s can lad to rsonant scattring. Sary: Lton olarization in dcays - + H= -v/c +v/c - + 6

17 3. V-A Thory for chargd crrnt wak intractions 3. Lorntz strctr of th wak crrnts Fri: M C V J N, J C V v n Cannot xlain th arity violation in bta dcays. Mor gnral ansatz (Gaov & Tllr M i C i v i n i i S,, V, A, T i n bilinar Lorntz covariants: ( 4 4 7

18 S : n scalar i n : V : 5 n n sdo-scalar vctor A : T : 5 n n sdo-vctor tnsor i 5 i 3 I I i i i 5 I I Rark: r or A colings do not lad to obsrvabl arity violation! Mixtrs lik ( 5 or ( 5 do violat arity. 8

19 3. Chirality Orators L R 5 ( 5 ( ar rojction orators:,, i i L (rortis of 5 R L R working on th frion sinors thy rslt in th lft / right handd chirality coonnts: L R 5 ( ( 5 Not obsrvabl! In contrary to hlicity, which is an obsrvabl: 9

20 i y x z ( i z y x ( sin soltion sin soltion ( ( ( ( z along z along hlicity i.. hlicity i.. Rindr: Dirac sinors 3 3 k k 3 3 k k ignvctors of hlicity orator

21 5 for 5 for for for In th rlativistic liit hlicity stats ar also ignstats of th chirality orators. Dirac sinors and chirality rojction orators: 5 I I ositiv hlicity: Ngativ hlicity:

22 olarization for articls with finit ass Lft handd sinor coonnt of nolarizd lctron:, L, R L 5 ( nolarizd Not noralizd Hlicity olarization of lft handd chirality stat L : ol ( ( ( ( ( ( v ( ( c L L L L i.. th LH sinor coonnt for a articl with finit ass is not flly in th hlicity stat sin down (=-½. For assiv articls of a givn chirality thr is a finit robability to obsrv th wrong hlicity stat: = - (/