Weak Interactions & Neutral Currents

Transcription

1 Weak Interactions & Neutral Currents Until the the mid-970 s all known weak interaction processes could be described by the exchange of a charged, spin boson, the W boson. Weak interactions mediated by a W-boson are called charged current interactions. A key prediction of the Glashow-Weinberg-Salam model was the existence of weak interactions mediated by the Z 0, a neutral vector boson. M&S CH 9. The Z 0 did not change the flavor of the lepton or quark. The GIM mechanism was invented to eliminate (first order) neutral current reactions where the flavor of the quark or lepton changed. The measured branching fractions of K 0 µ + µ - and K + µ + v e provided evidence for the absence of flavor (strangeness) changing neutral currents: BR(K 0 µ + µ ) BR(K + µ + v µ ) = µ + ν µ µ + µ - Charged current W +? Strangeness changing neutral currents u s d s K.K. Gan L: Neutral Current

2 The GIM mechanism eliminated strangeness changing neutral currents by adding a fourth quark (charm): d = cosθ c sinθ c s sinθ c cosθ c d s d d s s Adding the two amplitudes together: d d = d cosθ c + s sinθ c [ ] s s = d d sin θ c + s s cos θ c [d s + s d]cosθ c sinθ c d d + s s = d d + s s The strangeness changing terms are gone but there are still neutral current terms! Weak Interactions & Neutral Currents [ ] d cosθ c + s sinθ c = d d cos θ c + s s sin θ c +[d s + s d]cosθ c sinθ c 973: found first experimental evidence for neutral currents: ν µ + e ν µ + e This reaction cannot occur by W exchange!? 0? 0 K.K. Gan L: Neutral Current

3 Where do the neutrinos come from? How to Produce a Neutrino Beam? Proton-nucleon collisions produce lots of π's and K's which decay into neutrinos. Neutrino Beam Anti - Neutrino Beam Branching Ratio π + µ + v µ π µ v µ π + e + v e π e v e 0 4 K + µ + v µ K µ v µ 0.63 K + e + v e K e v e 0 5 K + π 0 µ + v µ K π 0 µ v µ 0.03 K + π 0 e + v e K π 0 e v e 0.05 Also get neutrinos from muon decay with branching ratio of 00%: µ e v e v µ µ + e + v e v µ Rough calculation of v µ /v e ratio: neglect neutrinos from muon decay. assume we produce 0X as many pions as kaons in a proton-nucleus collision. #ν µ (π ν µ )+ (K ν µ ) #ν e (π ν e )+ (K ν e ) 0BR(π + µ + ν µ )+ BR(K µ + ν µ )+ BR(K π o µ + ν µ ) 0BR(π + e + ν e )+ BR(K e + ν e )+ BR(K π o e + ν e ) Relatively easy to make a beam of high energy v µ s, but hard to make a pure beam of high energy v e. To make a pure beam of v e s use nuclear β decay which is below the energy threshold to produce µ s. K.K. Gan L: Neutral Current 3

4 Neutrino Induced Neutral Current Interactions Many other examples of neutral current interactions were discovered in the 970 s W exchange (charged current): v µ + N µ - + X Z exchange (neutral current): v µ + N v µ + X Neutrino cross section for neutral currents predicted to be /3 of charged current cross section. Typical layout for a neutrino beam line. The name derives from the giantess Gargamelle in the works of François Rabelais; she was Gargantua's mother. Observation of Neutrino-Like Interactions Without Muon or Electrons in the Gargamelle Neutrino Experiment, PL, V45, 973. CC: charged current event (e or µ in final state) NC: neutral current event (no e or µ in final state) Gargamelle was the name of the bubble chamber (BC). Expect neutrino interactions to be uniformly distributed in BC. Background from neutrons and K 0 s expected mostly in front of BC. Data in good agreement with expectation of Standard Model. NC = CC v sin θ W sin4 θ W = 0.± 0.03 NC CC ν = sin θ W sin4 θ W = 0.45± 0.09 NC > NC CC ν CC v Distributions along beam axis K.K. Gan L: Neutral Current 4

5 983: CERN was able to produce real Z s and W s and measure their properties: mass, branching fractions, and decay distributions. 989: accelerators that could produce Z s via e + e - Z were online: SLAC and CERN 999: CERN could produce W s via e + e - W + W -. Neutral Current The model of Glashow, Weinberg and Salam becomes the Standard Model. Coupling of the Z to quarks and leptons is different than the coupling of the W to quarks and leptons. W has a V-A coupling to quarks and leptons: γ µ ( - γ 5 ) Z coupling to quarks and leptons is much more complicated: γ µ (c f V c f A )γ 5 = γ µ (I f 3 I f 3 γ 5 Q f sin θ W ) I 3 : third component of weak isospin M&S 9.. f: fermion type θ W : Weinberg angle a fundamental parameter of the standard model. θ W 8 degrees relates the strength of the W and Z boson couplings to the EM coupling: g EM = g W sinθ W g EM = g Z sinθ W cosθ M&S use g EM = g Z cosθ W, eq. 9.8 W K.K. Gan L: Neutral Current 5

6 Neutral Current The Standard Model gives us the following for the Z boson coupling to a fermion anti-fermion pair: γ µ (c f V c f A )γ 5 = γ µ (I f 3 I f 3 γ 5 Q f sin θ W ) f c V c A I 3 Q v e,v µ,v τ 0 e,µ,τ + sin θ W d,s,b 3 sin θ W 3 In the Standard Model the masses of the W and Z are related by: M W = M Z cosθ W u,c,t 4 3 sin θ W 3 M W = g W G F / = πα G F sin θ W / 37.4 sinθ W GeV/c g Z γ µ (c V f c A f )γ 5 First order calculation Interesting new development (00) with measurement of sin θ W : NuTeV is a Fermilab neutrino experiment. NuTeV result: sin θ W = 0.77 ± 0.003(stat) ± (syst) World average: sin θ W = 0.7 ± (mainly from CERN) NuTeV result for sin θ W disagrees with previous measurements may point to physics beyond Standard Model or the structure of a proton or neutron is fundamentally modified when it is bound in a nucleus. f Z 0 f K.K. Gan L: Neutral Current 6