Interactions of Neutrinos ν Kevin McFarland University of Rochester SUSSP 70/INSS 2014 St. Andrews, Scotland 11-13 August 2014 ν Outline • Brief Motivation for and History of Measuring Interactions . Key reactions and thresholds • Weak interactions and neutrinos . Elastic and quasi-elastic processes, e.g., νe scattering . Complication of Targets with Structure . Deep inelastic scattering (νq) and UHE neutrinos . Quasielastic and nearly elastic scattering • Special problems at accelerator energies . Nuclear Effects . Generators, theory and experimental data • Conclusions 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 2 ν Focus of These Lectures • This is not a comprehensive review of all the interesting physics associated with neutrino interactions • Choice of topics will focus on: . Cross-sections useful for studying neutrino properties . Estimating cross-sections . Understanding the most important effects qualitatively or semi-quantitatively . Understanding how we use our knowledge of cross-sections in experiments 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 3 ν Weak Interactions • Current-current interaction G F µ w = µ Fermi, Z. Physik, 88, 161 (1934) 2 . Paper famously rejected by Nature: “it contains speculations too remote from reality to be of interest to the reader” • Prediction for neutrino interactions − + . If n→ pe ν , then ν p→ en . Better yet, it is robustly predicted by Fermi theory o Bethe and Peirels, Nature 133, 532 (1934) . For neutrinos of a few MeV from a reactor, a typical cross-section was found to be −44 2 σν p 5× 10 cm This is wrong by a factor of two (parity violation) 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 4 ν How Weak is This? • σ~5x10-44cm2 compared with -25 2 . σγp~10 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 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 5 Extreme Measures to Overcome ν Weakness (Reines and Cowan, 1946) ν p→ en+ • 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. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 6 ν Discovery of the Neutrino • Reines and Cowan (1955) . Chose a constant source, nuclear reactor (Savannah River) . 1956 message to Pauli: ”We are happy to inform you [Pauli] that we have definitely detected neutrinos…” . 1995 Nobel Prize for Reines ν p→ en+ 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 7 ν Better than the Nobel Prize? Thanks for the message. Everything comes to him who knows how to wait. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 8 Another Neutrino ν 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 −− ννµµee→ ν Gargamelle, event from neutral weak force 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 9 ν 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 ν σν()µµNX→ ν R = − σν()µ NX→ µ • But this discovery was complicated for 12- 18 months by a lack of understanding of neutrino interactions . backgrounds from neutrons induced by neutrino interactions outside the detector . not understanding fragmentation to high energy hadrons which then “punched through” to fake muons Great article: P. Gallison, Rev Mod Phys 55, 477 (1983) 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 10 The Future: Interactions and ν Oscillation Experiments • Oscillation experiments point us to a rich physics potential at L/E~400 km/GeV (and L/E~N∙(400 km/GeV) as well) . mass hierarchy, CP violation • But there are difficulties . transition probabilities as a function of energy must be precisely measured for mass hierarchy and CP violation . the neutrinos must be at difficult energies of 1-few GeV for electron appearance experiments, few-many GeV for atmospheric neutrino and τ appearance experiments. or use neutrinos from reactors… “past is prologue” – B.S. • Our generations lack neutrino flavor measurements in which distinguishing 1 from 0 or 1/3 buys a trip to Stockholm . Difficulties are akin to neutral current experiments . Is there a message for us here? 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 11 What are the potential ν problems from interactions? • As you will learn shortly, for a fixed baseline oscillation experiment, the relationship between oscillation parameters and event rate depends on flavor and Eν which we measure from the final state • Energy reconstruction . Final state particles and their production from a nuclear target determine ability to reconstruct Eν • Signal rate for different flavors • Backgrounds . Copiously produced pions have an annoying habit of faking leptons (π0→e or π±→μ) in realistic detectors . Important to understand rate and spectrum of pions 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 12 ν Kinematics of Neutrino Reactions 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 13 ν 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 Lepton 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 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 14 ν Thresholds and Processes Process Considerations Threshold (typical) νN→νN (elastic) Target nucleus is free and recoil is none very small - νen→e p In some nuclei (mostly metastable None for free ones), this reaction is exothermic if neutron & some proton not ejected other nuclei. νe→νe (elastic) Most targets have atomic electrons ~ 10eV – 100 keV - anti-νep→e n mn>mp & me. Typically more to 1.8 MeV (free p). make recoil from stable nucleus. More in nuclei. - νℓn→ℓ p Final state nucleon is ejected from ~ 10s MeV for νe (quasielastic) nucleus. Massive lepton +~100 MeV for νμ - νℓN→ℓ X Must create additional hadrons. ~ 200 MeV for νe (inelastic) Massive lepton. +~100 MeV for νμ • Energy of neutrinos determines available reactions, and therefore experimental technique 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 15 ν Calculating Neutrino Interactions from Electroweak Theory 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 16 ν Weak Interactions Revisited • Current-current interaction (Fermi 1934) • Modern version: G µ = F γν−−γ γ γ + H weak lcµ (1 55) fh(VA) f .. 2 • P L = 1/2 ( 1 − γ 5 ) is a projection operator onto left-handed states for fermions and right- handed states for anti-fermions 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 17 ν Helicity and Chirality • Helicity is projection • However, chirality of spin along the (“handedness”) is particle’s direction Lorentz-invariant . Operator: σ●p • Operator: PLR()=1/2( 1 γ 5) . Frame dependent for – Only same as helicity massive particles for massless particles • Textbook example is pion decay to leptons π++(0)()()()J=→= µν eJ11 J = right-helicity left-helicity 22µ ()e + µν()e ←• → ⇐⇐ 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 18 ν Helicity and Chirality • Helicity is projection • However, chirality of spin along the (“handedness”) is particle’s direction Lorentz-invariant . Operator: σ●p • Operator: PLR()=1/2( 1 γ 5) • Neutrinos only interact weakly with a (V-A) interaction G µ = F γν−−γ γ γ + H weak lcµ (1 55) fh(VA) f .. 2 . All neutrinos are left-handed . All antineutrinos are right-handed o Determined at time of the weak reaction that produces the neutrino 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 19 ν Helicity and Chirality • Helicity is projection • However, chirality of spin along the (“handedness”) is particle’s direction Lorentz-invariant . Operator: σ●p • Operator: PLR()=1/2( 1 γ 5) • Since neutrinos have mass then the left-handed neutrino is: – Overwhelmingly left-helicity – Then small right-helicity component ∝ m/E but it can almost always be safely neglected for energies of interest 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 20 ν 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 ⇒ν l + l ⇒ν l 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 21 ν Electroweak Theory • Standard Model . SU(2) ⊗ U(1) gauge theory unifying weak/EM ⇒ weak NC follows from EM, Weak CC . Physical couplings related to mixing parameter for the interactions in the high energy theory int µµgg+− µ L=EW−+QAe e µµγ e W νγLL e + W µ eLLγν 22 Charged-Current 1 νγνµ LL 2 g 021 µ +Zµ +−sin θγWee LL cosθW 2 +sin2 θγeeµ WR R Neutral-Current 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 22 ν Electroweak Theory • Standard Model . SU(2) ⊗ U(1) gauge theory unifying weak/EM ⇒ weak NC follows from EM, Weak CC . Measured physical parameters related to mixing parameter for the couplings. Z Couplings gL gR g 2 2 M ν ν , ν 1/2 0 W e , µ τ e = g sin θW , GF = 2 , = cosθW 2 2 8MW M Z e , µ , τ −1/2 + si n θW si n θW u , c , t 1/2 − 2/3 2θ − 2/3 2θ si n W si n W Charged-Current 2 2 d , s , b −1/2 + 1/3 si n θW 1/3 si n θW • Neutrinos are special in SM .