M. Cobal, PIF 2006/7. Leptoni

Transcription

1 Ltoni

2 Frmions: th lmntary layrs Th lmntary articl familis: frmions Why 3 familis? Ar thr mor? 1st gnration 2nd gnration 3rd gnration Imossibil visualizzar l'immagin. La mmoria dl comutr otrbb ssr insufficint r arir l'immagin our l'immagin otrbb ssr dannggiata. Riavviar il comutr arir di nuovo il fil. S vin visualizzata di nuovo la x rossa, otrbb ssr ncssario liminar l'immagin insrirla di nuovo. Imossibil visualizzar l'immagin. La mmoria dl comutr otrbb ssr insufficint r arir l'immagin our l'immagin otrbb ssr dannggiata. Riavviar il comutr arir di nuovo il fil. S vin visualizzata di nuovo la x rossa, otrbb ssr ncssario liminar l'immagin insrirla di nuovo. Imossibil visualizzar l'immagin. La mmoria dl comutr otrbb ssr insufficint r arir l'immagin our l'immagin otrbb ssr dannggiata. Riavviar il comutr arir di nuovo il fil. S vin visualizzata di nuovo la x rossa, otrbb ssr ncssario liminar l'immagin insrirla di nuovo. 2/3 2/3 Quarks Ltons -1/3 0-1 Ltons and quarks form doublts undr wak intractions -1/3 0-1

3 Muons Whr first obsrvd in 1936, in cosmic rays Cosmic rays hav two comonnts: 1) Primaris: high-nrgy articls coming from outr sac mostly H 2 nucli 2) Scondaris: articls roducd in collisions rimaris-nucli in th Earth atmoshr s ar 200 havir than and ar vry ntrating articls Elctromagntic rortis of s ar idntical to thos of lctron (uon th ror account of th mass diffrnc) Tauons Is th havist of th ltons, discovrd in - annihilation xrimnts in 1975

4 Ltons Ltons ar s = ½ frmions, not subjct to strong intractions ν ν ν m < m < m Elctron -, muon - and tauon - hav corrsonding nutrinos: ν, ν and ν Elctron, muon and tauon hav lctric charg of -. Nutrinos ar nutral Nutrinos hav vry small masss For nutrinos only wak intractions hav bn obsrvd so far

5 Anti-ltons ar ositron, ositiv muons and tauons and anti-nutrinos ν ν ν Nutrinos and anti-nutrinos diffr by th lton numbr. For ltons L α = 1 (α =, or ) For anti-ltons L α = -1 Lton numbrs ar consrvd in any raction Lton ν ν lton numbr lctron numbr muon numbr

6 No n Ys n No No n Ys n ν ν γ ν ν Consqunc of th lton nr consrvation: som rocsss ar not allowd... Ldrman, Schwarts, Stinbrgr Nutrinos Nutrinos cannot b rgistrd by dtctors, thr ar only indirct indications of thm First indication of nutrino xistnc cam from β-dcays of a nuclus N A Z N A Z N ν ) 1, ( ), (

7 Elctron is a stabl articl, whil muon and tauon hav a finit liftim: = 2.2 x 10-6 s and = 2.9 x s Muon dcay in a urly ltonic mod: ν ν Tauon has a mass sufficint to roduc vn hadrons, but has ltonic dcays as wll: ( a) ( b) ν ν ν ν Fraction of a articular dcay mod with rsct to all ossibl dcays is calld branching ratio (BR) BR of (a) is 17.84% and of (b) is 17.36%

8 Imortant assumtions: 1) Wak intractions of ltons ar idntical lik lctromagntic ons (intraction univrsality) 2) On can nglct final stat lton masss for many basic calculations Th dcay rat for a muon is givn by: Γ( Whr G F is th Frmi constant ν ν ) = G 2 F m 195π 5 3 Substituting m with m on obtains dcay rats of tauon ltonic dcays, qual for (a) and (b). It xlains why BR of (a) and (b) hav vry clos valus

9 Using th dcay rat, th liftim of a lton is: B( l ν ν l ) l = Γ( l ν ν ) Hr l stands for and. Sinc muons hav basically on dcay mod, B= 1 in thir cas. Using xrimntal valus of B and formula for Γ, on obtains th ratio of and liftims: l m m Again in vry good agrmnt with indndnt xrimntal masurmnts Univrsality of lton intraction rovd to big xtnt. Basically no diffrnc btwn lton gnrations, aart from th mass

10 Flavour Mass MV MV 1777 MV

11 Crisis around 1930 Mattr is mad of: Particls: γ, -, Atoms: Small nuclus of rotons surroundd by a cloud of lctrons bfor Pauli: Obsrvations: Nuclar β-dcay: 3 H 3 H- Uniqu lctron nrgy? vnts Exrimntal lctron nrgy lctron nrgy Enrgy consrvation violatd?

12 Pauli s hyothsis Pauli: Variabl lctron nrgy! Pauli's lttr of th 4th of D cmbr 1930 Dar Radioactiv Ladis and Gntlmn, As th barr of ths lins, to whom I graciously ask you to listn, will xlain to you in mor dtail, how bcaus of th "wrong" statistics of th N and Li 6 nucli and th continuous bta sctrum, I hav hit uon a dsrat rmdy to sav th "xchang thorm" of statistics and th law of consrvation of nrgy. N am ly, th ossibility that thr could xist in th nucli lctrically nutral articls, that I w ish to call nutrons, w hich hav sin 1/2 and oby th xclusion rincil and which furthr diffr from light quanta in that thy do not travl with th vlocity of light. Th mass of th nutrons should b of th sam ordr of magnitud as th lctron mass and in any vnt not largr than 0.01 roton masss. T h continuous bta sctrum w ould thn bcom undrstandabl by th assum tion that in bta dcay a nutron is m ittd in addition to th lctron such that th sum of th nrgis of th nutron and th lctron is constant... U nfortunatly, I cannot aar in T ubingn rsonally sinc I am indisnsabl hr in Z urich bcaus of a ball on th night of 6/7 D cm br. With my bst rgards to you, and also to Mr Back. Your humbl srvant. W. Pauli

13 What is a β-dcay? It is a nutron dcay: n ν Ncssity of nutrino xistnc coms from th aarnt nrgy and angular momntum non-consrvation in obsrvd ractions For th sak of lton numbr consrvation, lctron must b accomanid by an anti-nutrino and not a nutrino! Mass limit for of th β-dcay: ν can b stimatd from th rcis masurmnts m E ΔM N m ν Bst rsults ar obtaind from tritium dcay 3 H 3 H ν it givs mν 2 V / c 2 (~ zro mass)

14 Nutrino s dtctd (1956) Cowan & Rins Cowan nobl riz 1988 with Prl (for discovry of -lton) Intns nutrino flux from nuclar ractor ν n followd by γ γ Powr lant (Savannah rivr lant USA) Producing ν ν ν-catur n γ γ Scintillator countrs and targt tanks - annihilation

15 An invrs β-dcay also taks lac: Howvr th robability of ths rocsss is vry low. To rgistr it on nds a vry intns flux of nutrinos Rins and Cowan xrimnt (1956) ν o Using antinutrinos roducd in a nuclar ractor, ossibl to obtain around 2 vts/h o Acquous solution of CdCl 2 (200 l 40 kg) usd as targt (Cd usd to catur n) o To sarat th signal from background, dlayd coincidnc usd: signal from n aars latr than from or ν n n

16 Schm of th Rins and Cowan xrimnt 2m 2m (a) Antinutrino intracts with, roducing n and (b) Positron annihilats with an atomic lctron roducs fast hoton which giv ris to softr hoton through Comton ffct (c) Nutron caturd by a Cd nuclus, rlasing mor hotons

17 Hlicity stats For a masslss frmion of ositiv nrgy, E = hlicity H masurs th sign of th comonnt of th articl sin, in th dirction of motion: j z = ±1/ 2 H=1 right-handd (RH) H=-1 lft handd (LH) Eχ σ χ = χ is a LH articl or a RH anti-articl Hlicity is a Lorntz invariant for masslss articls If xtrmly rlativistic, also massiv frmions can b dscribd by Wyl quations σ χ = χ σ H = = 1

18 Anti-nutrino s Nobl riz 2002 (Davis, Koshiba and Giacconi) Davis & Harmr If th nutrino is sam articl as anti-nutrino thn clos to owr lant: ν ν n n 37 ν 17 Cl Ar -615 tons kitchn claning liquid -Tyically on 37 Cl 37 Ar r day -Chmically isolat 37 Ar -Count radio-activ 37 Ar dcay Raction not obsrvd: Nutrino-anti nutrino not th sam articl Littl bit of 37 Ar obsrvd: nutrino s from cosmic origin (sun?) Rumor srad in Dubna that raction did occur: Pontcorvo hyothsis of nutrino oscillation ν 37 Cl - 37 Ar

19 Flavour nutrino s Nutrino s from πν idntifid as ν Two nutrino hyothsis corrct: ν and ν Ldrman, Schwartz, Stinbrgr (nobl riz 1987) For th nutrino bam mthod and th dmonstration of th doublt structur of th ltons through th discovry of th muon nutrino

20 LEP ( ) Dtrmination of th Z 0 lin-sha: Rvals th numbr of light nutrinos Fantastic rcision on Z 0 aramtrs Corrctions for has of moon, watr lvl in Lac du Gnv, assing trains, N ν 2.984± M Z 0 Γ Z ± GV ± GV Existnc of only 3 nutrinos Unlss th undiscovrd nutrinos hav mass m ν >M Z /2

21 Discovry of -nutrino (2000) DONUT collaboration Production and dtction of -nutrino s c Δ s ν ν Τ ν