Interactions of Neutrinos at High and Low Energies. Kevin McFarland University of Rochester Neutrinos at SUSSP August 2006

Transcription

1 Interactions of Neutrinos at High and Low Energies Kevin McFarland University of Rochester Neutrinos at SUSSP August 006

2 Neutrino Interaction Outline Motivations for and History of Measuring Neutrino Interactions Weak interactions and neutrinos Elastic and quasi-elastic processes, e.g., e scattering Deep inelastic scattering, (q scattering) The difficulties of being in near thresholds Current & future cross-section knowledge What we need to learn and how to learn it 1-15 August 006 Kevin McFarland: Interactions of Neutrinos

3 Tone of These Lectures Focus will be on Cross-sections useful for experiments Estimating cross-sections Understanding qualitatively the key effects Therefore, it should therefore go without saying that I am the second experimentalist lecturing at SUSSP 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 3

4 The Birth of the Neutrino Wolfgang Pauli 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 4

5 Translation from the German, Please? 4th December 1930 Dear Radioactive Ladies and Gentlemen, As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the wrong statistics of the N and 6 Li nuclei and the continuous beta spectrum, I have hit upon a desperate remedy to save the exchange theorem of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass (and in any event not larger than 0.01 proton masses). The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant... From now on, every solution to the issue must be discussed. Thus, dear radioactive people, look and judge. Unfortunately I will not be able to appear in Tübingen personally, because I am indispensable here due to a ball which will take place in Zürich during the night from December 6 to 7. Your humble servant, W. Pauli 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 5

6 The True Source of Slow Progress in Neutrino Physics From now on, every solution to the issue must be discussed. Thus, dear radioactive people, look and judge. Unfortunately I will not be able to appear in Tübingen personally, because I am indispensable here due to a ball which will take place in Zürich during the night from December 6 to 7. Your humble servant, W. Pauli 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 6

7 Translation from the Archaic Physics Terms, Please? To save the law of conservation of energy? β-decay The Energy of the β If the above picture is complete, conservation of energy in this two body decay predicts monochromatic β but a continuous spectrum had been observed (since 1914) Pauli suggests neutron takes away energy! The exchange theorem of statistics, by the way, refers to the fact that a spin½ neutron can t decay to an spin½ proton + spin½ electron 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 7

8 Weak Interactions Current-current interaction GF w = Fermi, Z. Physik, 88, 161 (1934) Paper rejected by Nature because it contains speculations too remote from reality to be of interest to the reader Prediction for neutrino interactions If n pe +, then p e n Better yet, it is robustly predicted by Fermi theory o Bethe and Peirels, Nature 133, 53 (1934) For neutrinos of a few MeV from a reactor, a typical cross-section was found to be (Actually wrong by a factor of two (parity violation) 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 8 μ H J J μ σ p 5 10 cm 44

9 How Weak is This? σ~5x10-44 cm compared with σ γp ~10-5 cm at similar energies, for example The cross-section of these few MeV neutrinos is such that the mean free path in steel would be 10 light-years I have done something very bad today by proposing a particle that cannot be detected; it is something no theorist should ever do. Wolfgang Pauli 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 9

10 Extreme Measures to Overcome Weakness (Reines and Cowan, 1946) p + e n Why inverse neutron beta decay? clean prediction of Fermi weak theory clean signature of prompt gammas from e + plus delayed neutron signal. o Latter not as useful with bomb source August 006 Kevin McFarland: Interactions of Neutrinos 10

11 Discovery of the Neutrino Reines and Cowan (1955) Chose a constant source, nuclear reactor (Savannah River) 1956 message to Paul: We are happy to inform you [Pauli] that we have definitely detected neutrinos 1995 Nobel Prize for Reines p + e n 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 11

12 Better than the Nobel Prize? Thanks for the message. Everything comes to him who knows how to wait August 006 Kevin McFarland: Interactions of Neutrinos 1

13 Interactions and Flavor 196 Lederman, Schwartz, Steinberger at Brookhaven Nat l Lab One neutrino was known (beta decay) Question: if μ + e +, why not μ + e + γ? First accelerator neutrino beam 5 GeV protons on Be Target (3.5x10 17 of them) π + μ + μ in a 1m decay region Found 34 single-μ events, 5 background, but NO e-like events! 1988 Nobel citation: for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muonneutrino 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 13

14 Another Flavor Example Radiochemical Solar Neutrino Detector Ray Davis (Nobel prize, 00) +n p+e - (stimulated β-decay) Use this to produce an unstable isotope, +37 Cl 37 Ar+e -, which has 35 day half-life Put 615 tons of Perchloroethylene in a gold mine o expect one 37 Ar atom every 17 hours August 006 Kevin McFarland: Interactions of Neutrinos 14

15 Another Flavor (cont d) Confirmed that sun shines from fusion, but 1/3 of! Of course this is oscillation and flavor selection of interaction + 37 Cl 37 Ar+e August 006 Kevin McFarland: Interactions of Neutrinos 15

16 Another Neutrino Interaction Discovery Neutrinos only feel the weak force a great way to study the weak force! Search for neutral current arguably the most famous neutrino interaction ever observed is shown at right μe μe Gargamelle, event from neutral weak force 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 16

17 An Illuminating Aside The discovery signal for the neutral current was really neutrino scattering from nuclei usually quoted as a ratio of muon-less interactions to events containing muons σ ( N X R ) μ μ = σ ( N μ X) 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 17 μ But this discovery was complicated for 1-18 months by a lack of understanding of neutrino interactions backgrounds from neutrons induced by neutrino interactions outside the detector not understanding probability of fragmentation to high E hadrons which then punched through to fake muons

18 The Future: Interactions and Oscillation Experiments Boris has elegantly described a situation where muon oscillation appearance experiments at L/E~300 km/gev have rich physics potential mass hierarchy, CP violation, τ appearance (sterile s) What Boris hasn t worried about (at least in front of you) transition probabilities are small, must be precisely measured for mass hierarchy and CP violation the neutrinos must be at difficult energies of 1-few GeV for electron appearance, many GeV (> charm threshold) for τ We are not looking for neutrino flavor measurements in which distinguishing 1 from 0 or 1 from 1/3 buys a ticket to Stockholm Difficulties are akin to neutral current experiments Is there a message for us here? 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 18

19 Present View of Weak Interactions 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 19

20 Weak Interactions Revisited F μ Current-current interaction Hw = J J μ (Fermi 1934) Paper rejected by Nature because it contains speculations too remote from reality to be of interest to the reader Modern version: G F l ( 1 ) ( ) 5 f μ H V A 5 f h.. c weak = γμ γ γ γ + P = 1/ 1 γ ( ) L 5 is a projection operator onto left-handed states for fermions and righthanded states for anti-fermions 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 0 G

21 Helicity and Chirality Helicity is projection of spin along the particles direction Frame dependent (if massive) However, chirality ( handedness ) is Lorentzinvariant Only same as helicity for massless particles. right-helicity left-helicity Neutrinos only interact weakly with a (V-A) interaction All neutrinos are left-handed All antineutrinos are righthanded o because of production! Weak interaction maximally violates parity + π J If neutrinos have mass then left-handed neutrino is: Mainly left-helicity But also small right-helicity component m/e Only left-handed charged-leptons (e,μ,τ ) interact weakly but mass brings in right-helicity: + 1 ( = 0) μ ( J = 1 ) ( J = μ ) μ August 006 Kevin McFarland: Interactions of Neutrinos

22 Two Weak Interactions W exchange gives Charged-Current (CC) events and Z exchange gives Neutral-Current (NC) events In charged-current events, Flavor of outgoing lepton tags flavor of neutrino Charge of outgoing lepton determines if neutrino or antineutrino l l + l l 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 3

23 Electroweak Theory Standard Model SU() U(1) gauge theory unifying weak/em weak NC follows from EM, Weak CC Measured physical parameters related to mixing parameter for the couplings, g =g tanθ W Charged-Current Neutral-Current 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 4

24 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 5

25 Electroweak Theory Standard Model SU() U(1) gauge theory unifying weak/em weak NC follows from EM, Weak CC Measured physical parameters related to mixing parameter for the couplings, g =g tanθ W Z Couplings g L g R e, μ, τ 1/ 0 e, μ, τ 1/ + sin θ W sin θ W u, c, t 1/ /3 sin θ W /3 sin θ W d, s, b 1/ + 1/3 sin θ W 1/3 sin θ W e = g g sinθw, GF = 8MW M, M W Z Charged-Current = cosθ W Neutrinos are special in SM Right-handed neutrino has NO interactions! Neutral-Current 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 6

26 Why Weak? Weak interactions are weak because of the massive W and Z bosons exchange dσ dq ( q 1 M ) q is 4-momentum carried by exchange particle M is mass of exchange particle At HERA see W and Z propagator effects - Also weak ~ EM strength Explains dimensions of Fermi constant G F = 8 g M W W = / GeV ( g W 0.7) 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 7

27 Neutrino-Electron Scattering Inverse μ decay: μ + e μ + e Total spin J=0 (Assuming massless muon, helicity=chirality) μ e e μ σ TOT Q max dq 0 Q M max 4 W ( Q + 1 M W ) 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 8

28 Touchstone Question #1 What is Q max? μ μ + e μ + e ( ) Q e e Let s work in the center-ofmass frame. Assume, for now, we can neglect the masses μ e e 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 9

29 σ Neutrino-Electron (cont d) σ = TOT Qmax s TOT Gs F = π = cm / GeV E ( GeV ) Why is it proportional to beam energy? s = ( p + p ) = m + m E μ μ e e - e e e (e rest frame) Proportionality to energy is a generic feature of point-like scattering! because dσ/dq is constant (at these energies) μ 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 31

30 Neutrino-Electron (cont d) Elastic scattering: μ + e μ + e Coupling to left or righthanded electron Total spin, J=0,1 Electron-Z 0 coupling (LH, V-A): -1/ + sin θ W σ G π s F 1 4 sin θ W + sin 4 θ W (RH, V+A): sin θ W σ G π s F ( 4 sin θ ) W 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 3

31 Neutrino-Electron (cont d) What are relative contributions of left and right-handed scattering from electron? f LH θ f RH θ f LH dσ = const d cosθ dσ = d cosθ 1+ cosθ const 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 33 f RH

32 Neutrino-Electron (cont d) Electron-Z 0 coupling (LH, V-A): -1/ + sin θ W (RH, V+A): sin θ W y Let y denote inelasticity. Recoil energy is related to CM scattering angle by = E E e 1 1 (1 cosθ ) σ G π σ 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 34 s F G π 1 4 s F sin θ W ( 4 sin θ ) W + sin Gs F σtot = sin θw + sin θw = cm / GeV E ( GeV ) π θ dσ = dy dy W LH: dy 1 = RH: (1 y) dy = 1 3

33 Touchstone Question #: Flavors and e e Scattering The reaction μ + e μ + e has a much smaller cross-section than Why? e + e e + e ) 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 35

34 Touchstone Question #: Flavors and e e Scattering The reaction μ + e μ + e has a much smaller cross-section than Why? e + e e + e e e Z e e e + e e + e has a second contributing reaction, charged current e e W e e 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 36

35 Touchstone Question #: Flavors and e e Scattering Show that this increases the rate σ (Recall from the previous pages TOT = = = σ dσ dy dy dσ dy dy LH TOT LH σ RH TOT dσ + dy RH LH σ TOT 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 37 For electron Weak NC Weak CC LH total coupling e - LH coupling -1/+ sin θ W -1/ ) RH coupling sin θ W We have to show the interference between CC and NC is constructive. The total RH coupling is unchanged by addition of CC because there is no RH weak CC coupling There are two LH couplings: NC coupling is -1/+sin θ W -1/4 and the CC coupling is -1/. We add the associated amplitudes and get -1+sin θ W -3/4 0

36 Lepton Mass Effects Let s return to Inverse μ decay: μ + e μ + e What changes in the presence of final state mass? o pure CC so always left-handed o BUT there must be finite Q to create muon in final state! Q min = m μ see a suppression scaling with (mass/cm energy) o can be generalized = (massless) μ σ TOT 1- s 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 38 σ σ TOT TOT Q Q max Q min max min GF ( s mμ ) = π dq ( Q + M W ) Q M 4 W 1 m

37 What about other targets? Imagine now a proton target Neutrino-proton elastic scattering: e + p e + p Inverse beta-decay (IBD): e + p e + + n and its close cousin: e + n e - + p Recall that IBD was the Reines and Cowan discovery signal any p e p any Z p e + W n 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 39

38 Proton Structure How is a proton different from an electron? anomalous magnetic moment, κ form factors related to finite size g 1 Determined proton RMS charge radius to be (0.7±0.) x10-13 cm McAllister and Hofstadter MeV and 36 MeV electron beam from linear accelerator at Stanford 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 40

39 Final State Mass Effects In IBD, e + p e + + n, have to pay a mass penalty twice e M n -M p 1.3 MeV, M e 0.5 MeV What is the threshold? kinematics are simple, at least to zeroth order in M e /M n heavy nucleon kinetic energy is zero sinitial = p + p = M + M E (proton rest frame) sfinal = ( p + p ) M + m + M E M M Solving ( p) p p e n n e n n p E min ( ) M + m M n e p M MeV 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 41 p e + W p n ( ( ))

40 Final State Mass Effects (cont d) Define δe as E -E min, then initial ( δ ) s = M + M E+ E min p p = M p + δ E M p + ( Mn + me) M p = δ E M p + ( Mn + me) Remember the suppression generally goes as mfinal ( Mn + me) ξmass = 1 = 1 s ( M + m ) + M δ E n e p M p δ E low energy M ( ) p δ E Mn + me = ( Mn + me) + M p δ E ( Mn + me) M p 1 high energy M p δ E 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 4

41 Putting it all together Gs σ ϑ ξ π F TOT = cos Cabibbo V + 3 A quark mixing! mass suppression is proportional to δe at low E, so quadratic near threshold vector and axial-vector form factors (for IBD usually referred to as f and g, respectively) g V, g A 1, 1.6. FFs, θ Cabibbo, best known from τ n ( ) ( ) mass g g final state mass suppression e p proton form factors (vector, axial) W e + n 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 43

42 Touchstone Question #3: Quantitative Lepton Mass Effect Which is closest to the minimum beam energy in which the reaction μ + e μ + e can be observed? (a) 100 MeV (b) 1 GeV (c) 10 GeV = m μ (It might help you to remember that min or you might just want to think about the total CM energy required to produce the particles in the final state.) Q 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 44

43 Summary and Outlook We know e - scattering and IBD cross-sections! In point-like weak interactions, key features are: dσ/dq is constant. o Integrating gives σ E LH coupling enters w/ dσ/dy 1, RH w/ dσ/dy (1-y) o Integrating these gives 1 and 1/3, respectively Lepton mass effect gives minimum Q o Integrating gives correction factor in σ of (1-Q min /s) Structure of target can add form factors Deep Inelastic Scattering is also a point-like limit where interaction is -quark scattering 1-15 August 006 Kevin McFarland: Interactions of Neutrinos 46