Weak Interactions. Introduction to Elementary Particle Physics. Diego Bettoni Anno Accademico

Transcription

1 Wak Intractions Introduction to Elmntary Particl Physics Digo Bttoni Anno Accadmico -

2 Introduction Wak intractions wr first obsrvd in th slow rocss of nuclar dcay. Thy tak lac in circumstancs whr th much fastr strong or lctromagntic dcays ar forbiddn by th consrvation laws, or rocsss involving nutrinos, which can only hav wak intraction. Examls: n n 3 s 43 cm s 8 s B, Q, L S= Enrgy Wak rocsss ar charactrizd by smallr cross sctions and longr liftims than for strong and lctromagntic rocsss. N N N N 38 6 cm cm at GV

3 Th wak intractions can b classifid as to whthr thy involv ltons only, ltons and hadrons or hadrons only: D n n D Ltonic Smiltonic Nonltonic S = S = S = ; C =

4 Natural Radioactivity Discovrd in 896 by H. Bcqurl (on yar bfor th lctron was discovrd and svral yars bfor nucli wr known to xist!!!) Thr tys of radiation, classifid by Ruthrford: -rays. Easy to absorb. Bnt slightly in th rsnc of magntic filds (ositiv charg, "havy"). -rays mittd by a wll dfind isoto ar mononrgtic. -rays. Hardr to absorb than -rays. Bnt significantly in th rsnc of magntic filds (ngativ charg, "light"). -rays. Not bnt in th rsnc of magntic filds (no charg), vry hard to absorb. Each ty of radiation is du to a diffrnt intraction: strong, wak, lctromagntic.

5 Nuclar dcay Early studis of -rays rvald two fundamntal rortis of this ty of radiation: Thy wr idntical to cathod rays (lctrons). Thir nrgy sctrum was discrt (lik th sctrum of -rays) studis of th absortion of -rays smd to indicatd that ths wr mononrgtic. th sctrum of a -ray bam incidnt on a hotograhic lat in th rsnc of a constant magntic fild smd to b discrt. -ray mission was a quantum hnomnon, to b associatd to a discrt sctrum. A Z A (Z+) + - nrgy consrvation imlis E( - ) = M( A Z) M( A (Z+)) Only in 94 did Chadwick show that th obsrvd -ray sctrum is continuous and only 5 yars latr it was shown that th nuclar -ray sctrum is continuous.

6 A Wrong Modl for th Nuclus In th 9 s it was ostulatd that nucli wr mad u of rotons and lctrons, such that A Z containd A rotons and A-Z lctrons (.g. 4 H = 4; 4 N = ). In addition to nrgy consrvation in -ray mission thr wr svral othr roblms: Magntic momnt of nucli:, nuclo. Imossibl if th nuclus is mad of rotons and lctrons. Sin-statistics: according to this modl 4 N consists of an odd numbr of frmions (4+7 - ), imlying a half-intgr sin, whras xrimntally it was found to b a boson. Solution: lctrons bound in nucli bhav diffrntly from fr lctrons!!! (Bohr) Gamow: This would man that th ida of nrgy and its consrvation fails in daling with rocsss involving th mission or catur of nuclar lctrons. This dos not sound imrobabl if w rmmbr all that has bn said about culiar rortis of lctrons in th nuclus.

7 Pauli and th nutron In 93 W. Pauli mad th hyothsis that thr was a third constitunt insid th nuclus: th nutron : a frmion with no lctric charg, which intractd vry wakly with mattr and with a mass of lss than % of th roton mass: 4 N= In this way: Th sin-statistics roblms was solvd, sinc th numbr of frmions in th nuclus was now corrct. Th aarnt violation of nrgy consrvation in -dcay was xlaind assuming that th corrct hysical rocss was: A Z A (Z-) i.. a thr-body dcay, with a continuous nrgy sctrum for th lctron.

8 Pauli (93) Dar Radioactiv Ladis and Gntlmn, I hav com uon a dsrat way out rgarding th wrong statistics of th 4 N and 6 Li nucli, as wll as th continuous sctrum, in ordr to sav th altrnation law of statistics and th nrgy law. Namly, th ossibility that thr could xist in th nuclus lctrically nutral articls, which I shall call nutrons, which hav sin ½ and satisfy th xclusion rincil and which furthr diffr from light quanta in that thy do not travl with th sd of light. Th mass of th nutrons should b of th sam ordr of magnitud as th lctron mass and in any cas not largr than. tims th roton mass. Th countinuous sctrum would thn bcom undrstandabl from th assumtion that in dcay a nutron is mittd along with th lctron, in such a way that th sum of th nrgis of th nutron and th lctron is constant. For th tim bing I dar not ublish anything about this ida and addrss myslf to you, dar radioactiv ons, with th qustion how it would b with xrimntal roof of such a nutron, if it wr to hav th ntrating owr qual to about tn tims largr than a ray.

9 I admit that my way out may not sm vry robabl a riori sinc on would robably hav sn th nutrons a long tim ago if thy xist. But only th on who dars wins, and th sriousnss of th situation concrning th continuous sctrum is illuminatd by my honord rdcssor, Mr Dby, who rcntly said to m in Brussls: Oh, it is bst not to think about this at all, as with nw taxs. On must thrfor discuss sriously vry road to salvation. Thus, dar radioactiv ons, xamin and judg. Unfortunatly I cannot aar rsonally in Tübingn sinc a ball in Zürich maks my rsnc hr indisnsibl. Your most humbl srvant, W. Pauli From a lttr writtn by W. Pauli, datd 4 dcmbr 93, to th hysicists attnding a Nuclar Physics confrnc in Tübingn.

10 Th Discovry of th Nutron In 93 Chadwick discovrd a nutral nuclar constitunt. By studying th rortis of th nutral radiation n mittd in th rocss 9 B + C + n h found out that th articl n, th nutron, was a dly ntrating nutral articl slightly havir than th roton, quit distinct from -rays, i.. a diffrnt articl from th nutron ostulatd by Pauli. Givn th fact that Chadwick s nutron was much havir than Pauli s, Frmi rnamd Pauli s nutron th nutrino.

11 Frmi Thory of Dcay n d u s u - g W - g d M W = GV/c q << M W u - G d Th intraction is ractically ointlik, dscribd by a 4 frmion couling G g M W

12 In Frmi thory th transition robability r unit tim is givn by: W G if J(ltons) = M = Frmi transition if J(ltons) = M = 3 Gamow-Tllr transition de E dn stats M dn de P,T -, E T, E, E kintic nrgis of roton, lctron, antinutrino Enrgy and momntum consrvation P q T E E E E mn m m. 8 MV q, E

13 T P.8 MV 3 MV T M MV In th hyothsis m = E qc E E For th lctron th numbr of stats with momntum btwn and +d is givn by: dn dd 4 dn intgrating ovr d 3 d h h h 4q dq dn Similarly for th nutrino: 3 Hnc considring and q as uncorrlatd: 6 d N 6 h q ddq h E E de q dq c c d d N 6 E 6 3 de h c Hnc if M is constant th lctron sctrum is givn by: N( ) d E E d E d

14 uri Plot ) ( ) ( m E E E vs N ) ( ) ( m E E m c E E N

15 From uri lot on can masur th mass of th nutrino. Som masurmnts from tritium dcay H 3 H 3 Langr, Moffatt 95 m < kv Brgkvist 97 m < 65 V Trtyakov 976 m < 35 V Lyubimov 98 m < 3 V Fritschi 986 m < 8 V Robrtson 99 m < 9.3 V Stoffl 995 m < 7 V Winhimr 999 m <.8 V Lobashv 999 m <.5 V rsnt limit M ( ) 3 V

16 Sargnt Rul Th total dcay rat is obtaind intgrating ovr th lctron nrgy sctrum. For xtrm rlativistic lctrons E c and w obtain: N E E ( ) N d E E E de ( ) 5 E 3 Sargnt rul From Frmi s rul, th valu of G can b obtaind from th obsrvd dcay rat. For xaml: O 4 N 4* From = 3 s w obtain. G M Frmi transition J P = + J P = + c GV

17 Projct Poltrgist and th Discovry of th Nutrino Th goal of th rojct was th dtction of (anti)nutrinos from th invrs dcay n. Original ida: dtct antinutrinos from a nuclar xlosion: Th antinutrinos from th nuclar xlosion would hav rachd a liquid scintillator susndd in an undrground cav at a distanc of 4 m from th 3m high towr. In th original schm of Rins and Cowan antinutrinos would hav givn ris to invrs dcay, whras th dtctor would hav rgistrd th ositrons roducd in th rocss.

18 Th Savannah Rivr Exrimnt (956-96) A,B watr tanks, whos rotons actd as targts for th antinutrinos, whras th function of th Cadmium Chlorid was to catur th nutrons. I, II, III scintillator dtctors.

19 It is rlvant to not that a diffrnt tchniqu for obsrving antinutrinos was trid, without succss, in aralll with rojct Poltrgist. In 955 a radiochmical xrimnt ld by Ray Davis locatd nxt to a nuclar ractor sit faild to obsrv invrs chlorin dcay, i.. th raction: + 37 Cl Ar dos not han with a masurabl rat. This null rsult can b intrrtd as vidnc that nutrinos and antinutrinos ar distinct articls. W currntly intrrt this null rsult as du to a consrvation law, i.. lton numbr consrvation. A similar stu was vntually usd to study solar nutrinos.

20 Parity Violation in Dcay Parity violation in wak intractions had bn ostulatd in 956 by L Yang to xlain th xistnc of th two dcay mods: (- aradox) To tst arity consrvation an xrimnt was carrid out by Wu t al (957) who mloyd a saml of 6 Co at T=. insid a solnoid. 6 J Co 5 6 J Ni * 4 Gamow-Tllr Transition At a tmratur of. a high roortion of 6 Co nucli ar alignd. Th rlativ lctron intnsitis along and against th magntic fild dirction wr masurd. - θ H J (Co)

21 Th rsults for lctron intnsitis wr consistnt with a distribution of th form: I( ) E v cos c J J,E lctron momntum and nrgy This form for I() imlis a for-aft asymmtry which in turn imlis that th intraction violats arity consrvation. π θ J θ J scchio Undr arity: I( ) v c cos

22 Lt us now considr th hlicity of th lctrons mittd in 6 Co dcay. Th consrvation of J z imlis that also th sin of th lctron oint in th dirction J. L:t s b a unit vctor ointing in th lctron sin dirction: s I ( ) E Th avrag longitudinal olarization (or nt hlicity) can b dfind as: It turns out that: H H v c I I I I I I I( ) I( ) Exrimntally: H v c v c ( ) ( ) z (H) J=5 J=4 J z= ν - Co Ni * ( ) + ν L R

23 Hlicity of th Nutrino From th rvious discussion it follows that for a masslss nutrino (v=c) hlicity can assum th valus H=+ o H=-. This articl is thrfr fully olarizd. Goldhabr xrimnt (Phys Rv 9(5)958) orbital lctron of Euroium 5 Sm Eu Sm 5 5 * * Z 63, J Z 6, J 5 Sm J J (96V In this rocss th 5 Sm * has th sam olarization as th nutrino. - Sm * ν s J s ν ν RH ν ) s J s ν ν ν LH

24 Th 5 Sm * is xcitd (bcaus it lacks on intrnal lctron) dcays to its fundamntal stat mitting a 96 kv ( 3-4 s). In this rocss th travlling in th dirction of 5 Sm * hav th sam olarization as th. J J LH 5 Sm * LH (forward) LH 5 Sm * 5 Sm * RH 5 Sm * RH (forward) RH To dtrmin th olarization of th foward rays (and thus of th nutrino) th rsonant scattring rocss was usd: 5 5 * Sm Sm 5 For which th forward mittd -rays carry th right nrgy. Sm

25 To dtrmin th olarization of th thy wr mad to ass through magntizd iron. S S B B LH RH Th transmission in th iron is biggr for th LH than for RH ; th olarization can b dtrmind comaring th counts with B u and B down. I risultati danno licità ngativa r i nutrini. Particl - + Hlicity -v/c +v/c - +

26 Parity Violation in Dcay n (35.8%) B. R. ( (8.3 ).5)% In th roduction rocss th sin of th must b orthogonal to th roduction lan, in ordr to consrv arity. A olarization in th roduction lan gnrally changs sign undr P and is not allowd. Exrimntally th man transvrs olarization is found to b 7 % N P N N Numbr of counts with sin u N N N Numbr of counts with sin down

27 Dcay rocss: z y x Th angular distribution is of th I( ) P cos This u-down asymmtry is a manifstation of arity violation in dcay.

28 Th Discovry of A nutrino bam coming from th dcay of chargd ions + (/) was snt on a sark chambr: only muons wr roducd, but no lctrons dmonstrating th xistnc of two tys of nutrino: X Y X Y

29 Th Third Lton Family and th In 975 an xrimnt ld by M. Prl unvild th xistnc of th third lton, th. This imlid th xistnc of a third nutrino flavour. A first indirct vidnc for th xistnc of a third nutrino cam from th LEP xrimnts, whr th masurmnt of th invisibl width of th Z was consistnt with th rdictions of th Standard Modl with thr nutrinos. Cosmological calculations basd on th quantity of 4 H in th univrs indicat th xistnc of thr nutrino scis at th tim of th Big Bang. Th dirct obsrvation of th was mad in thanks to th DONUT xrimnt (Dirct Obsrvation of NU Tau) at Frmilab, which dtctd four vnts du to intractions ovr a background of.34 vnts, consistnt consistnt with th rdictions of th Standard Modl.

30 Th DONUT Exrimnt Th xrimnt was dsignd to dtct th CC intractions of th, idntifying th as th only chargd lton in th vnt. At th nrgis of DONUT th dcays within mm into a final stat with a singl chargd articl (BR 86 %), thrfor th signatur is a rong with a kink. Th dtctor consists in an mulsion targt followd by a magntic sctromtr. Th nutrino bam is mad starting from th 8 GV rotons from th Frmilab Tvatron hitting a bam dum mad of tungstn, m in lngth and locatd 36 m ustram of th mulsions. Th rimary sourc of is th dcay D S and th subsqunt dcay of th into.

31 h X h X

32 Th V-A Intraction Frmi dvlod his thory of dcay in analogy with lctromagntic intractions. q () j ( ) j n (N ) j () j n n ) ( ) ( j j m q M ) ( ) ( j j q M ) ( ) ( J N J n W G M G is th wak couling constant Th wak currnt J changs th sign of th lctric charg: chargd wak currnt. In th matrix lmnt thr is no roagator: th intraction is ointlik.

33 Th matrix lmnt writtn in this way is a scalar quantity and it imlis arity consrvation. Th violation of arity in th wak intraction rquirs rquirs th inclusion of a arity-violationg trm 5. Th wak currnt turns out to b a combination of a Lorntz vctor ( ) and of a sudovctor (or axial vctor, 5 ). Hnc th nam V-A. Th matrix lmnt is writtn as: M A similar xrssion can b writtn for muon dcay. Th chargd wak currnt G couls an incoming LH lctron to an outgoing LH nutrino. Th amlituds for wak intraction ar of th form: ( ) ( ) ( n ) n 5 5 J M 4G ) ( 5 J J

34 Intrrtation of G If w comar lctromagntic and wak amlituds w s that G rlacs /q. Hnc G is not dimnsionlss: [G] = [GV] -. W can try to xtnd th btwn m and wak intraction by ostulating that th lattr ar also mdiatd by vctor boson, for instanc: - W - - M g ( 5) g ( 5) M q If q << M W (as is th cas for and dcays) G W g 8MW and th wak intraction bcoms ointlik. W s that th intraction is wak not bcaus g <<, but bcaus th W mass is big. If g than for nrgis >> M W lctromagntic and wak intractions ar of comarabl strngth. g unification of lctromagntic and wak intractions.

35 and Dcay In th + rst systm + + Th has sin, th is LH, thus also th must b LH. In th subsqunt muon dcay th ositron nrgy sctrum is akd in th rgion of th maximum nrgy, so th most likly configuration is th following: Th angular distribution is of th form + + is RH dn cos d 3 in agrmnt with V-A. Th muon liftim is givn by: G m 9 Using th valus m = MV/c and =.979 s w obtain: 5 G.6637 GV 5 3

36 Th Dcay of th Angular momntum consrvation rquirs that th ltons hav th sam hlicity. Th ltons ar mittd with hlicitis v c v c,μ,μ L L + + Th robability that an + or a + ar mittd with vlocity v and hlicity v/c is roortional to (-v/c) v c In ordr to obtain th transition robability w must tak into account th has sac: dn d de de

37 L L + + c m,, v m,, m In th rst systm Th total nrgy is thus m m E m m de d 4 8 ) )( ( m m m m m de d m m m m c v 4 m m m c v de d M 4.75 m m m m Exrimntally:

38 Positron nrgy sctrum for th dcays:

39 Som commnts on th rsult: Th dcay would b nourmously favord by has sac with rsct to. Howvr angular momntum consrvation forcs th chargd lton to hav th wrong hlicity. This is mor asily ralizd for th, whos mass is aroximatly tims biggr than th lctron s. In th calculations w usd th sam valu of G for both rocsss. Univrsality in th couling of ltons to to wak intraction. Following th sam schm th V-A thory rdicts for th msons:.5 to b comard with th masurd valu:

40 Dcay S\I 3 +½ -½ Production mchanisms: E. 9 GV n n E. 5 GV E 6. GV Thrfor with a bam of suitabl nrgy it is ossibl to roduc a ur bam of. ar th kaon ignstats as far as th strong intraction is concrnd. Th kaons can dcay by th wak intraction (S=) into or 3. 3 ( t) ( t) ( t)

41 CP CP W can form two CP ignstats: and ar distinguishd by thir mod of dcay CP CP, + - Bos Symmtry CP=+ + - L=; CP( + - )=+, CP( )=- CP= - (CP= if L>) P=-, C=+ CP= - 3 CP CP s s

42 Strangnss Oscillations and, ar not articl and antiarticl, thrfor thy hav diffrnt mass, bcaus of thir diffrnt wak coulings. Lt us writ th amlitud for th as a function of tim: a I( t) ( t) a a () t ie t * ( t) a ( t) I() t / E =/ In th rst systm E =m (rst mass), = ror liftim a ( t) a() t im a ( t) a() t im nrgy liftim If w start from a ur bam: a( ) a()

43 Aftr a tim t: I( ) a 4 ( t) a ( t) a * ( t) a ( t) t t t cos( m t * ) m =.5 m = m -m m MV Intnsity m m 7 5 t/

44 Starting from a ur bam aftr a high numbr of only th surviv. In th targt th strong intraction rgnrats th comonnts of S=+, S=-. ar absorbd diffrntly, sinc th only undrgos lastic scattring and charg xchang, whras th can also giv ris to hyrons. Thus aftr th rgnrator w hav comonnts f > and f >, with f<f<. Thrfor aftr th rgnrator: f f f f f f f f f f Sinc f f th comonnt has bn rgnratd.

45 CP Violation in Dcay In 964 it was discovrd that th ignstat of CP=- ( ) can also dcay to with a branching ratio of th ordr of -3. L L S S whr is a aramtr which quantifis CP violation. Indirct CP violation S L S L Thr xists also a dirct CP violation, which originats in th dcay.

46 Slction rul: S Examl: Wak Dcays of Strang Particls I s d S S S n I I I Th nuclon and th ion in th final stat must b in an I=/ isosin stat 3 ' ' n ' 3 ' ( ( n ) n ) ( ) Exrimntal valu: isosin has sac

47 Smiltonic Dcays Th smiltonic dcays oby th slction rul Q = S. Q and S ar th changs in charg and strangnss of th hadrons. Q=S= follows from Q=I 3 +(B+S)/ if I 3 =/. Examls: dds S Q Q Dviations from th I = ½ rul S Q n udd S BR.8 S Q 3 uus S Q Q S Q n udd S BR 5 6 S Q whras th slction rul rdicts a ratio of.. Thus th amlitud I=3/ is also rsnt, although havily surssd.

48 Cabibbo Thory Ltons and quarks intract wakly through V-A currnts which ar built starting from th following ltonic doublts (LH): In addition w also hav u-s coulings, for xaml: Furthrmor dcays with S= ar surssd by a factor of about with rsct to thos with S=. Cabibbo(963): th d and s quark stats articiating in th wak intraction ar rotatd by a mixing angl C (Cabibbo angl) For ithr of ths sts of doublts th wak couling constant rmains G. s c d u? u s C C s d u sin cos

49 For S= (d u) transitions th couling will thus b roortional to cos C, whras for S= (s u) it will b roortional to sin C. Thus for xaml: which yilds C 5 o. ( ( ) ) W thrfor hav favord ( cos C ) and surssd ( sin C ) transitions. Examls: sin C W + u W + u cos C d sin C s Cabibbo favord Cabibbo surssd

50 Wak Nutral Currnts In 973 th xistnc of muon nutrino intractions without a chargd lton in th final stat was first dmonstratd in a bubbl chambr xrimnt at CERN. N N Wak Nutral Currnts, with rats comarabl to chargd currnts N N X X X X N X.5.45 N X - W + Z X X N N Chargd currnt Nutral currnt

51 Th GIM Modl and Charm All nutral currnt rocsss obsrvd ar charactrizd by th slction rul S =. Indd th ida of wak nutral currnts had bn discardd bcaus thy had nvr bn obsrvd in dcay rocsss: 5 S Wak nutral currnts ar givn by th diagrams: u u Z Z dcos C + ssin C + uu dd cos C ss sin C S dcos C + ssin C sd sd sin C cosc S Thrfor nutral currnts with S = should b ossibl (Strangnss Changing Nutral Currnts, SCNC)

52 In ordr to xlain th absnc of SCNC Glashow, Iliooulos Maiani roosd in 97 th introduction of a fourth quark, th charm (c), with charg /3, which allowd to introduc a scond quark doublt for wak intractions: u d cos s sin C C d c sin s cos W hav thrfor two nw diagrams contributing to th wak nutral currnt: c c Z Z -dsin C + scos C + Thrfor th wak nutral currnt bcoms: dd ss cos ss dd C C -dsin C + scos C uu cc C sin C S sd sd sd sd sin C cosc S Th introduction of th fourth flavor cancls xactly th SCNC. Th charm quark was discovrd xrimntally in 974.

53 Wak Mixing with 6 Quarks and th CM Matrix With four flavors th wak currnt has th form: s d U c u J ) ( 5 C C C C U cos sin sin cos With th introduction of two mor flavors (b, charg -/3 and t, charg /3): b s d M t c u J ) ( 5 i i i i c c s s c s c c s c s s c s s c c s s c c c s c s s s c c M CM matrix (Cabibbo-obayashi Maskawa) i i i i s c sin cos,, 3 mixing angls, has

54 CM Matrix V ud = n V cd =.4. V us =..6 V cs = l V ub =( ) -3 B l V cb =(4.3.5) -3 D l D l B l D B d V td =.48.4 B d B s V ts = B s V tb = W t b