Lecture 11: Weak Interactions Cross-Section and the W Coupling The Cabibbo Angle and the CKM Matrix Parity Violation Kaons and Mixing CP Violation Sections 4.51, 8.1, Chapter 10 Useful Sections in Martin & Shaw:

(from ''Telephone Poles and Other Poems," 1963) Neutrinos, they are very small. They have no charge, they have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids down a drafty hall Or photons through a sheet of glass... John Updyke in fact, point-like in the Standard Model and little (< 2eV) hardly true should not be taken to indicate a sensitive detection technique interaction cross-section much higher than for typical neutrino energies obvious foreshadowing of electroweak theory Cosmic Gall

++ e (Pauli) Beta Decay Beta Decay n  p + e 

Reversed Beta-Decay

(Pauli) Inverse Beta-Decay ''Inverse" Beta Decay e + p  n + e +

 ~ 2  /c  ''cross-sectional area" of wave packet time spent by wave packet in presence of the proton typical timescale for weak interaction to occur e + p  n + e + Inverse  -decay: (Pontecorvo) From standard  -decay, the lifetime of the free neutron is  ~ 1000 s and the energies of the e  and e are ~ 1 MeV  = h/p ≃ 1200fm = 1.2x10  10 cm thus,  ~ (1.2x cm) 3 /[(3x10 10 cm/s)(1000s)] ~ 10  43 cm 2 Note  E  3 t  1 and, from previous discussion, t  1  E 5   ~ 10  43 (E MeV ) 2 cm 2 Almost exactly right! (and very, very small!!!) Pontecorvo Estimate

Interaction Length for a 1 MeV Neutrino in Lead   ~ cm 2 (per proton)  = (11.4 g/cm 3 ) x [ 1/(207 g/mole) ] x (6.02x10 23 atoms/mole) x (82 protons/atom) = 2.7x10 24 protons/cm 3 = 1/(2.7x ) cm = 3.7 x cm = 4 light-years !! Interaction Length in Lead

n  p + e - + e e  p  n + e + Reines and Cowan, 1956 First Neutrino Detection (Nobel Prize – 1995 !!)

Parity Violation in Weak Interactions First suggested in 1956 by Lee & Yang based on review of kaon decay modes 60 Co ee ee P nuclear spins aligned by cooling to 0.01 o K in a magnetic field Should be the same under parity transformation, but fewer electrons are actually seen going forward ! Directly observed by Wu et al. in 1957 from the decay 60 Co  60 Ni* + e  + e Parity Violation  (1.173 MeV) +  (1.332 MeV) (degree of polarisation determined from the anisotropy of  -rays)

Garwin, Lederman & Weinrich (1957) e+  e  ++ ++ precess polarised muons (polarised)

Also, in 1958, Goldhaber et al. measured the helicity of the neutrino: e  Eu (J=0)  152 Sm* (J=1) + e 152 Sm (J=0) +  events were chosen with the final states collinear   and e travel in opposite directions, so helicity of the neutrino is found from that of the gamma  all neutrinos are left-handed ! Neutrino Helicity

Leon Lederman, Melvin Schwartz and Jack Steinberger, 1962 Neutrinos of the ''Second Kind" (not as popular as the Spielberg sequel) Neutrinos of the 2nd Kind

Assume some Yukawa-like exchange process is at work. Weak interactions obey a simple symmetry : So, for example, for the process      +  (pion decay): but, unfortunately, it is found experimentally that the couplings are not the same!  W ud ≃ 0.95  W dudu WW     ''Near Symmetry" and the W  W  It can change u  d (like  -decay) s  c t  b and, for leptons, e  e      -decay (n  p+e  + e ) tells us the exchange particle must be charged

susu WW     Another hitch: shouldn’t occur, but does ! (albeit infrequently) We can explain all this (or, at least, parameterize our ignorance) by adopting the somewhat bizarre notion that the weak interaction actually couples to mixtures of quarks. So, initially just considering the first two generations, the relevant quark doublets are: udud cscs ( ) and ( ) where d  d cos  C + s sin  C s   d sin  C + s cos  C  C  ''Cabibbo angle" or, alternatively d   s sin  C + d cos  C s   s cos  C + d sin  C  W ud =  W cos 2  C  W us =  W sin 2  C The Cabibbo Angle

~ 1/20  C = degrees )                = tan 2  C (The factor of 1/20 delineates ''Cabibbo-suppressed" and ''Cabibbo-allowed" processes) Generalizing to 3 generations and all possible mixings between quarks: dsbdsb V ud V us V ub dsbdsb ( ) [ ]( ) = (Cabibbo, Kobayashi and Maskawa) CKM matrix The CKM Matrix  W us  W ud =

Kaons : K o = ds K o = sd (S = +1) (S =  1) But S is not conserved in weak interactions so K o -K o mixing can occur: u u dsds sdsd W + W  KoKo KoKo We can thus define two orthogonal mixtures:  K 1 o  = 1/  2 (  K o  +  K o  )  K 2 o  = 1/  2 (  K o    K o  ) Note: C P  K 1 o  K 1 o  and C P  K 2 o  K 2 o  K 1 o   +   ;  o  o K 2 o   +    o ;  o  o  o Allowed Neutral Kaons K 1 o   +    o ;  o  o  o K 2 o   +   ;  o  o Forbidden

Experimentally, 2 kaon states are observed with different lifetimes: K S o       ;  o  o  ≃ 9x10  11 s So we associate K S o  K 1 o and K L o  K 2 o However, in 1964, Christenson, Cronin, Fitch & Turlay discovered KLo  + KLo  +  (branching ratio ~ 2x10  3 ) CP Violation K L o        ;  o  o  o ;   l epton ( )  ≃ 5x10  s 

30 GeV protons steel target beam collimator magnets sweeps out charged particles l ead-glass cuts out photons K S +K L K L 18 m K L beam direction CM of  +   pair  CP Experiment

 K S o  = 1/      (  K 1 o    K 2 o  )  K L o  = 1/      (  K 1 o  +  K 2 o  ) where   small complex number parameterizing the size of the CP violation (experimentally,  ≃ 2.3x10  3 ) What does this mean?? Reason for antimatter assymmetry ?? Perhaps we can learn more from studying CP violation in other particle systems... CP Violating Term

Basically compare the rates for B 0 =  + K S 0 (  +   mode) B 0 =  + K S 0 versus (  +   mode) BaBaR

dsbdsb V ud V us V ub dsbdsb ( ) [ ] ( ) = ?? CP violation could be parameterized as part of the mixing angles in the CKM matrix Unitarity of the matrix is needed to allow for local gauge symmetry Which imposes constraints on the angles:      ''Unitarity Triangle" Unitarity Triangle

Matter-Antimatter Asymmetry Revisited: Sakarov Conditions (1967) 1) Baryon Number Violation allows baryons and anti-baryons to appear and disappear independently of each other 2) CP Violation so the rate of appearance/disappearance of baryons is different from anti-baryons Establishes Asymmetry 3) Non-Equilibrium Conditions since equilibrium would then tend to ''average-out" any asymmetry Locks In Asymmetry !!! (GUTs) Sakarov Conditions