Neutrino Experiments Lecture I

Transcription

1 Neutrino Experiments Lecture I Deborah Harris Fermilab CINVESTAV Course September 4-7, 018 Mexico City, MEXICO 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 1

2 Goals of this Course 1 st : To give you an understanding of how to make measurements of a particle that is Neutral Almost never interacts Physics requires these measurements to be: Over many orders of magnitude of energy Over many orders of magnitude of distance Many experiments out there to describe Solar, Reactor, Atmospheric, Accelerator-based Absolute Mass measurements Tests of neutrinos being their own antiparticles nd : To explain why goal #1 is worth doing! 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments

3 Brief History of the Neutrino in 1930 there was a crisis in particle physics! proton neutron (A, Z) è (A, Z+1) + e +ν e observed electron expected It was well known that nuclei could change from one variety to another by emitting a beta (electron). Some were ready to abandon Conservation of Energy to explain this missing energy ν e... until W. Pauli proposed his desperate remedy,the neutrino, which invisibly carried away the missing energy and the neutrino was born. electron energy April September Deborah Harris, Fermilab: Neutrino Experiments 3 Slide courtesy D. Schmitz

4 6 years later, 1 st Observation of neutrino Reactors make huge fluxes of neutrinos Reines and Cowan can t see a neutrino directly since they are neutral method for observation was called inverse beta decay electron antineutrino from power reactor Water Target plus CdCl proton in water mol. antielectron annihilates on normal electron in water and releases photons inverse beta decay neutron photon 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments gets captured by Cadmium nucleus and releases one 4

5 What makes the Sun Shine? Sun is prolific producer of neutrinos Goal was to test solar models of fusion: what makes the sun shine? Ray Davis looked for ν +37 Clà 37 Ar+e - Found neutrinos, but 1/3 the number expected Ray Davis Experiment Homestake Mine, USA 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 5

6 Created in the sun and any star Created when nuclei decay Created at the birth of the universe A billion times more of them than protons But they only feel the weak force Only 3 talk to the Z boson Neutrinos 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 6

7 How weak is weak? Average distance between interactions: mean free path Probability of interaction/particle Number of particles/kg Number of kg/m 3 ν-n crosssection atomic mass unit 1.66x10-7 kg d lead = (σ x-n m )(11400 kg/m 3 ) neutrinos produced in a reactor typically have a few MeV of energy d 1.5 x m density of lead neutrinos produced at an accelerator typically have a few GeV of energy d 1.5 x 10 1 m (1.5 billion km!) What about a proton with a few GeV of energy? d 10cm in lead 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 7

8 Smoking Gun for Neutrinos Changing over time Measurements of neutrinos from the atmosphere: 80 to 10,000km Muon Neutrinos from above don t disappear Muon Neutrinos from below disappear Electron neutrinos don t seem to disappear! e-like Super- Kamiokande Results Neutrino 010 µ-like 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 8

9 Minimum Oscillation Formalism If neutrino mass eigenstates: ν 1, ν, ν 3, etc. are not flavor eigenstates: ν e, ν µ, ν τ then one has, e.g., ν α = cosπ ν sin π 4 i + ν 4 time ν α cosθ sinθ ν i = ν β sinθ cosθ ν j j take only two generations for now! ν β = sin π ν cosπ 4 i + ν September 018 Deborah Harris, Fermilab: Neutrino Experiments 9 Slide courtesy K. McFarland different masses alter time evolution j

10 Acoustic Analogy (for musicians ) wave 1 wave wave 1 + wave 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 10

11 Neutrino Oscillations If neutrinos are waves of slightly different frequencies: Over time, they disappear and reappear The bigger the frequency difference, the faster the disappearance Lots of ν e No ν e Time or distance Lots of ν e 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments Particles are like waves particle mass determines its frequency Measuring neutrinos oscillating: Measuring mass differences If one kind of neutrino disappears, another kind must appear 11

12 Schedule Lecture 1 (4 September) What do we want to measure about neutrinos? What neutrino sources are available? How do neutrinos interact in matter? Lecture (5 September) How do non-neutrino particles interact in matter? What neutrino detectors are out there? Lecture 3 (6 September) Absolute Mass and Majorana Mass Measurements Lecture 4 (7 September) Oscillation Measurements 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 1

13 What are the parameters we want to measure? 1. Neutrino Masses A. Absolute B. Relative (this is easier remember?). Are neutrinos their own anti-particle? 3. Neutrino Mixing Matrix 1. Not as simple as one mass difference and one mixing angle when you have 3 generations 4. Maybe there is more to neutrinos than 3 generations? 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 13

14 What happens if there are 3 neutrinos? Simplistic way of describing mixing matrix 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 14

15 Additional Complication: Matter Effects The oscillation probability changes differently for electron neutrinos vs antineutrinos when they propagate through matter: Wolfenstein, PRD (1978) Can t treat neutrinos propagating through earth simply as mass eigenstates, have to take into account electron flavor This would give an apparent CP violation just because the earth is not CP-symmetric 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 15

16 Additional Complication: Matter Effects, with math Remember the -generation formula? P( ν µ ν ) τ = sin θ sin ( m m 4E 1 ) L Wolfenstein, PRD (1978) x n = = υ GFneE Δm e - density sin Θ M = sin sin Θ + ( ± x Θ cos Θ) L M = L sin Θ + ( ± x cosθ) 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 16

17 ν Oscillation Probabilities ν µ Disappearance: 1-sin θ 3 sin (Δm 3 L/4E) ν e Disappearance: ν e appearance in a ν µ beam: even more complicated P(ν µ ν e )=P 1 +P +P 3 +P September 018 Deborah Harris, Fermilab: Neutrino Experiments 17 Minakata & Nunokawa JHEP 001

18 What do we know now? Mass differences: One is large eV One is small eV LSND signal 1-0.1eV, not consistent with oscillations (thanks to MiniBooNE results) Mixing angles: one is around ~45o one is ~35o one is around 8o 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 18

19 What don t we know? We have yet to learn if neutrinos and antineutrinos oscillate differently Could this be why the universe is dominated by matter? We have yet to learn if their masses are like the quark masses, or not figures courtesy B. Kayser Δm sol à δm 1 8x10-5 ev Δm atm à δm 3.5x10-3 ev 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 19

20 To measure probabilities, need Neutrino Flavor Distance between creation and detection Neutrino Energy No source we can use today is monochromatic! Initial state: neutrino plus nucleus or electron Final state: a bunch of stuff you only measure so well, sometimes you only measure the charged lepton Neutrino or Antineutrino? Accelerator-based beams are always a mixture of both Atmospheric neutrinos are also a mixture Reactors and the sun are only one or the other 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 0

21 Measuring Oscillation Probabilities For a given number of signal ν x events in a detector, Assuming you are starting with a source of ν y : N = ϕ ν y σ ν x P(ν y ν x )ε x M φ=flux, σ= cross section ε=efficiency M=detector mass P(ν µ ν x ) = N ϕ νµ σ ν x ε x M 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 1

22 Key Parameters: Flux Energy Neutrino Sources Baseline(s) available Neutrino Beam Flavor and Helicity Composition Sensitive to Matter Effects? What do the neutrinos travel through between production and detection 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments

23 How does the Sun Shine? A Helium nucleus is produced by the fusion of 4 Hydrogen nuclei; 4 p He + e + flux 1 4πR = 6 10 ( L 10 ν sun e / + cm ν This reaction produces about 7 MeV energy. Then, the total neutrino flux on the Earth is; = Lsun 7MeV e ν / sec e = erg / sec) Observing neutrinos from the sun is direct proof that the generation of the energy in the Sun is due to nuclear fusion. 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments T. Kajita, INSS 013 3

24 Solar Neutrino Energy Spectrum However, in reality, 4 protons cannot make a Helium nucleus at a time T. Kajita, INSS September 018 Deborah Harris, Fermilab: Neutrino Experiments 4

25 Other Beam Parameters Baselines Available: all close to 10 8 km Distance to sun changes based on the season Day/night asymmetry changes whether or not ν s went through the earth before detection Beam Composition ν e Matter effects 8 B ν s feel matter effects from sun x can be close to 1! sin Θ M = sin sin Θ + ( ± x Θ cos Θ) 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 5

26 Experimental Challenges with Solar Neutrino Measurements Neutrinos are very low in energy Very few interactions are accessible Cannot make final state muons or taus, so only neutral current or ν e charged current interactions are available Different detectors have different energy thresholds, most neutrinos from sun not visible by most techniques Cannot turn off the sun to measure backgrounds in the detector Standard Solar Model had many tunable parameters flux predictions were suspect for a long time. 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 6

27 Neutrinos from a Reactor Like the sun, but backwards: fission instead of fusion 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 7

28 Energy Spectrum from Reactors Several processes occurring during the fuel cycle of a reactor, with different yields and energy spectra 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 8

29 Baselines available Reactors send out neutrinos in all directions, so you could put detectors at any baseline you chose Different physics can be reached at different baselines 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 9

30 Extreme Example of Long baseline Kamland experiment: sees neutrinos from large array of reactors in Japan Ichimura, ν September 018 Deborah Harris, Fermilab: Neutrino Experiments 30

31 Shorter Baselines used Daya Bay: 3 cores, 3 halls, baselines of km Reno: 6 reactor cores, halls, baseline(s) ~1.3km Double Chooz: cores, halls at 0.4 and 1.0km 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 31

32 Experimental Challenges with Reactor Fluxes Flux changes over time because of fuel cycle Double Chooz (ν014) at right Have several cores, not all at the same distance from the detector Energy deposited in detector is so low you can t possibly figure out original direction of neutrino Hard to determine backgrounds since reactors are always on (usually), signal rates very different between near and far detectors 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 3

33 What do reactor experiments see? Remember Events=flux* cross section? Flux at reactors falls with energy Cross section rises with energy 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 33

34 How well is Reactor Flux Known? As much as we know about radioactivity rates, 3 reactor experiments see a slightly different spectrum than predicted even before oscillations But that excess persists at all detectors, cancels in near/far ratio Yu, Intae. (018, June). Recent Results from RENO. Zenodo /zenodo September 018 Deborah Harris, Fermilab: Neutrino Experiments 34

35 Atmospheric Neutrinos Atmosphere 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 35

36 From Cosmic Rays to Neutrinos Measured cosmic ray proton flux Carrying out the calculation all over the Earth + solar activity + geomagnetic field + (p+nucleon) int. + decay of π or K 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 36 T.Kajita, INSS 013

37 What is known well (ν µ + ν µ )/(ν e + ν e ) HKKM11 M. Honda et al., PRD 83, (011) ü ν µ /ν e ratio is calculated to an accuracy of about % below ~5GeV. ü ν and anti-ν ratios also accurately calculated. T.Kajita, INSS September 018 Deborah Harris, Fermilab: Neutrino Experiments 37

38 What else is known well: up/down Zenith (Japan) Up-going Down cosθ zenith Up/down ratio very close to 1.0 and accurately calculated (1% or better) above a few GeV. 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 38 38

39 Experimental Challenges with Atmospheric Fluxes Absolute rates are hard to predict Overall rates are low and steeply falling in energy Near equal mix of neutrino and antineutrino means CP violation measurement is near impossible Homework question: how might you be able to see matter effects using atmospheric neutrinos? Do you NEED a magnetic field in your detector? 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 39

40 Neutrinos from Accelerators Atmospheric Neutrino Beam: High energy protons strike atmosphere Pions and kaons are produced Pions decay before they interact Muons also decay Conventional Neutrino Beam: very similar! 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 40

41 Example: NuMI beamline at Fermilab Major Components: Proton Beam Pion Production Target Focusing System Decay Region Absorber Shielding Most ν µ s from -body decays: π + µ + ν µ K + µ + ν µ Most ν e s from 3-body decays: µ + e + ν e ν µ K + π 0 e + ν e 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 41

42 Proton beam Basics Rules of Thumb number of pions produced is roughly a function of proton power (or total number of protons on target x proton energy) The higher energy ν beam you want, the higher energy p you need Proton Source Experiment Proton Energy (GeV) 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 4 p/yr Power (MW) KEK KK / FNAL Booster MiniBooNE FNAL Main Injector MINOS and NOvA to 0.7 CNGS OPERA J-PARC TK to 0.75 Neutrino Energy (GeV)

43 1.E+14 1.E+13 ANL FNAL Main Ring BNL CERN PS LSND Nomad/ Chorus CNGS goal CERN SPS Beam Dose (Joules) 1.E+1 1.E+11 1.E+10 IHEP LAMPF KEK FNAL Booster FNAL NuMI FNAL TeV MINOS goal First MINOS Restults (10 0 ) ν flavors 1.E+09 1.E+08 Discovery of NC s Year KK MiniBooNE Plot courtesy Sacha Kopp September 018 Deborah Harris, Fermilab: Neutrino Experiments 43

44 Neutrino Production Targets Have to balance many competing needs: The longer the target, the higher the probability the protons will interact The longer the target, the more the produced particles will scatter The more the protons interact, the hotter the target will get targeting above ~1MW not easy! Rule of thumb: want target to be 3 times wider than +- 1 sigma of proton beam size MiniBooNE TK CNGS NuMI 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 44

45 Hadron Production This is tricky stuff, hard to predict with theory alone Copious thin target measurements available, but neutrino targets are usually long NA61 data from CERN: thin and thick target data used for TK analysis New this year: MIPP hadron production results (Fermilab), using same target as used for MINOS, and 10GeV protons (at right) Ref: J.M.Paley, M.D.Messier, R.Raja et al, arxiv: September 018 Deborah Harris, Fermilab: Neutrino Experiments 45

46 Focusing Systems Want to focus as many particles as possible for highest neutrino flux Typical transverse momentum of secondaries: approximately Λ QCD, or about 00MeV Minimize material in the way of the pions you ve just produced What kinds of magnets are there? Dipoles no, they won t focus Quadrupoles done with High Energy neutrino beams focus in vertical or horizontal, need pairs of them they will focus negative and positive pions simultaneously 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 46

47 What focusing works best? Imagine particles flying out from a target: When particle gets to front face of horn, it has transverse momentum proportional to radius at which it gets to horn B Field from line source of current is in the Φ direction but has a size proportional to 1/r How do you get around this? (hint: pt B l ) 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 47

48 What should the B field be? FROM TO Make the particles at high radius go through a field for longer than the particles at low radius. (B 1/r, but make dl r ) Horn: a -layered sheet conductor No current inside inner conductor, no current outside outer conductor Between conductors, toroidal field proportional to 1/r δp t eµ I r l 0 πcr r outer p tune θ 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 48

49 Horn Photo Album Length (m) Diameter (m) KK.4,.7 0.6,1.5 MBooNE ~1.7 ~0.5 1 NuMI 3,3 0.3,0.7 CNGS 6.5m 0.7 TK 1.4,,.5.47,.9,1.4 3 # in beam MiniBooNE CNGS NUMI TK Horn September 018 Deborah Harris, Fermilab: Neutrino Experiments 49

50 Designing what provides the 180kA is almost as important as designing the horn itself! 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 50

51 Decay Regions How long a decay region you need (and how wide) depends on what the energy of the pions you re trying to focus. The longer the decay region, the more muon decays you ll get (per pion decay) and the larger ν e contamination you ll have What is better: air, vacuum window, or Hefilled decay pipe? Does it depend on energy? Length Diameter BNB 50m 1.8m NuMI 675m m CNGS 1000m.45m TK 130m Up to 5.4m NUMI TK CNGS 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 51

52 Beamline Decay Pipe Comparison Can show that neglecting things hitting the side of the decay pipe Φ( ν ) Φ( ν Lmµ c Eπτ µ e e 1 1 = + 1 yπ µ ) 1 yπ y π =the number of pion lifetimes in one decay pipe y π = Lm E π π c cτ π Length E π (GeV) y π y µ Φ(ν e )/Φ(ν µ ) (theoretical) BNB 50m % 0.15% MINOS 675m % 0.8% CNGS 1000m % 0.15% TK 130m % 0.10% 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 5

53 Off-Axis Technique 1-1 relationship between neutrino energy and pion energy+angle between neutrino and pion (derive) Off axis neutrino beams: aim pions and kaons AWAY from detector Ref: D. Beavis et al, BNL No. 5459, 4/95 TK and NOvA both use this TK NOvA 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 53

54 Experimental Challenges with Accelerator-based Neutrinos Operations Target and horns must be robust Still working on a target that can survive 1MW beam power Composition Can never make pure beam, always some contamination of anti-neutrinos or ν e s in what you designed as ν µ beam Flux Predictions Hadron production uncertainties still at the 5% level even with new data Using different hadron shower models to predict flux gives even higher differences Beamline optics can also introduce uncertainties Question: what are the advantages of a neutrino beam made of muon decays? 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 54

55 Neutrino Source Summary Source Flux ν Energy Composition Baseline Matter Effects? Sun 6x10 10 ν/ cm /sec Reactor 10 0 ν/ sec/gw Atmosphere 1 ν/cm / sec Accelerator 6x10 5 ν/ cm MeV ν e (ν ) 10 8 km yes 1-10MeV Anti-ν e 1-180km Not yet GeV ν e +ν µ and anti GeV ν µ +%ν e or antiν µ +%ν e km yes km yes * NuMI beamline low energy tune, on axis, currently x3 higher! 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 55

56 NEUTRINO INTERACTIONS 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 56

57 Thresholds and Processes We detect neutrino interactions only in the final state, and often with poor knowledge of the incoming neutrinos Creation of that final state may require energy to be transferred from the neutrino ν Target Recoil In charged-current reactions, where the final state lepton is charged, this lepton has mass The recoil may be a higher mass object than the initial state, or it may be in an excited state Lepton K. McFarland, INSS September 018 Deborah Harris, Fermilab: Neutrino Experiments 57

58 Thresholds and Processes Process Considerations Threshold (typical) νn νn (elastic) ν e n e - p Target nucleus is often free (recoil is very small) In some nuclei (mostly metastable ones), this reaction is exothermic if proton not ejected none None for free neutron some others. νe νe (elastic) Most targets have atomic electrons ~ 10eV 100 kev anti-ν e p e - n ν l n l - p (quasielastic) ν l N l - X (inelastic) m n >m p & m e. Typically more to make recoil from stable nucleus. Final state nucleon is ejected from nucleus. Massive lepton Must create additional hadrons. Massive lepton. 1.8 MeV (free p). More for nuclei. ~ 10s MeV for ν e +~100 MeV for ν μ ~ 00 MeV for ν e +~100 MeV for ν μ Energy of neutrinos determines available reactions, and therefore experimental technique K. McFarland, INSS September 018 Deborah Harris, Fermilab: Neutrino Experiments 58

59 Why is the interaction so 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) K. McFarland, INSS September 018 Deborah Harris, Fermilab: Neutrino Experiments 59

60 Neutrino-Electron Scattering Inverse µ-decay: ν µ + e - µ - + ν e Total spin J=0 (Assuming massless muon, helicity=chirality) ν µ ν e Q e ν e ( ) µ e σ 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 60 TOT Q max dq 0 Q M max 4 W ( Q + 1 M W ) K. McFarland, INSS 013

61 Neutrino-Electron Scattering σ = σ TOT Qmax s TOT Gs F = π = cm / GeV Eν ( GeV ) Why is it proportional to ν µ ν e µ e beam energy? - s= ( p + p ) = m + m E ν µ e e e ν (e rest frame) Proportionality to energy is a generic feature of point-like scattering! because dσ/dq is constant (at these energies) K. McFarland, INSS September 018 Deborah Harris, Fermilab: Neutrino Experiments 61

62 Neutrino Electron Elastic Scattering Elastic scattering: ν µ + e - ν µ + e - Recall, EW theory has coupling to left or righthanded electron Total spin, J=0,1 Z Couplings g L g R ν e, ν µ, ν τ 1/ 0 Electron-Z 0 coupling Left-handed: -1/ + sin θ W Right-handed: sin θ W σ σ 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 G F s π G π 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 6 s F 1 4 sin ( 4 sin θ ) W θ W + sin 4 θ W K. McFarland, INSS 013

63 Neutrino Electron Scattering, cont d What are relative contributions of scattering from left and right-handed electrons? ν f LH θ ν ν f RH θ ν f LH dσ dσ = const = d cosθ d cosθ 1+ cosθ const 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 63 K. McFarland, INSS 013 f RH

64 What about ν e scattering off e s? The reaction ν µ + e - ν µ + e - has a much smaller cross-section than ν e + e - ν e + e - ν e e Z ν e e Why? ν e + e - ν e + e - has a second contributing reaction, charged current ν e e W e ν e K. McFarland, INSS September 018 Deborah Harris, Fermilab: Neutrino Experiments 64

65 Muon Neutrino thresholds: Inverse muon decay: Need enough energy to create a final state muon Question: how much energy do you need for this process? ν µ ν e µ e 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 65

66 What about other targets? Imagine now a proton target Neutrino-proton elastic scattering: ν e + p ν e + p Inverse beta-decay (IBD): anti-ν e + p e + + n and stimulated beta decay: ν e + n e - + p IBD was the Reines and Cowan discovery signal Cross section much higher Think of what s is here K. McFarland, INSS 013 n ν any p ν e p ν e p ν any Z p e + W n e - e - W n p 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 66

67 Final State Mass Effects In IBD, ν e + p e + + n, have to pay a mass penalty twice ν e 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 à heavy nucleon kinetic energy is zero sinitial = ( pν + pp) = Mp + MpEν (proton rest frame) Solving E min ν ( ) M + m M n e p M What is threshold for neutrino analog? MeV 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 67 p W p n ( ( )) ν s p p M m M E M M final = ( e + n) n + e + n n p K. McFarland, INSS 013

68 Neutrino-Nucleon Scattering Charged - Current: W ± exchange Quasi-elastic Scattering: (Target changes but no break up) ν µ + n µ - + p Nuclear Resonance Production: (Target goes to excited state) ν µ + n µ - + p + π 0 (N * or Δ) n + π + Deep-Inelastic Scattering: (Nucleon broken up) ν µ + quark µ - + quark Neutral - Current: Z 0 exchange Elastic Scattering: (Target unchanged) ν µ + N ν µ + N Nuclear Resonance Production: (Target goes to excited state) ν µ + N ν µ + N + π (N * or Δ) Deep-Inelastic Scattering (Nucleon broken up) ν µ + quark ν µ + quark Linear rise with energy Resonance Production K. McFarland, INSS September 018 Deborah Harris, Fermilab: Neutrino Experiments 68

69 Scattering off Nuclei The fundamental theory allows a complete calculation of neutrino scattering from quarks But those quarks are in nucleons (PDFs), and those nucleons are in a strongly interacting tangle Imagine calculating the excitations of a pile of coupled springs. Very hard in general. To be discussed in 4 th lecture 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 69

70 Summary for Neutrino Interactions Total cross section proportional to neutrino energy Angular dependence because of ν helicity and conservation of spin Consequence: Neutrinos have higher cross section than anti-neutrinos ν-e scattering is the ONLY perfectly known cross section Everything else is more complicated: NEED BETTER THEORY PREDICTIONS! The higher the ν energy, the more final state particles produced Those particles can produce backgrounds to your oscillation analysis! Source ν Energy Composition Reactions Sun MeV ν e (ν ) ν-e or CCQE Reactor MeV Anti-ν e CCQE Atmosphere GeV ν e +ν µ CCQE+RES+DI S Accelerator GeV ν µ +%ν e or antiν µ +%ν e CCQE+RES+DI S 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 70

71 Questions from Lecture Given the luminosity of the sun,, how long would the sun last if it was simply burning chemical energy instead of nuclear energy Sun s luminosity is 4x10 6 Joules/second Sun weighs x10 30 kg Think of how many joules you get from a kg of gas a million? How might you be able to see matter effects using atmospheric neutrinos? Do you NEED a magnetic field in your detector? Hint: take advantage of a matter resonance What is better: air, vacuum window, or He-filled decay pipe? Does it depend on pion energy? (recall multiple scattering formula) Derive the relationship between the neutrino energy and the pion energy and angle between neutrino and pion What is threshold for ν e +n -> e - + p? Hint: where do you find neutrons? What about for ν µ? What about for ν τ? 4-7 September 018 Deborah Harris, Fermilab: Neutrino Experiments 71