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 021 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 . Right-handed neutrino has NO

interactions! Neutral-Current

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 23 ν Why “Weak”? • Weak interactions are weak because of the massive W and Z boson exchanged 1 dσ ∝ q is 4-momentum carried by exchange particle dq2 (q2 − M 2 )2 M is mass of exchange particle

At HERA see W and Z propagator effects - Also weak ~ EM strength

• Explains dimensions of Fermi “constant” 2 2  g  =  W  GF   8  MW  −5 2 =1.166×10 / GeV (gW ≈ 0.7)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 24 ν Neutrino-Electron Scattering μ- • Inverse µ−decay: − − νμ θ* e- νµ + e → µ + νe . Total spin J=0 νe (Assuming massless muon, helicity=chirality) 2 2 Qe≡−( −ν e )

2 Qmax 1 σ ∝ dQ2 TOT ∫ 2 2 2 0 (Q + MW ) 2 Qmax ≈ 4 MW

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 25 Lecture Question #1 ν 2 What is Q max? μ- − − νµ + e → µ + ν ν * - e μ θ e

2 2 νe Qe≡−( −ν e ) Work in the center-of-mass frame and assume, for now, that we can neglect the masses.

Hint: if you want to know the range of Q2, there’s only one variable (θ*) in the 2→2 process

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 26 Lecture Question #1 ν 2 What is Q max? μ- − − νµ + e → µ + ν ν * - e μ θ e

2 2 νe Qe≡−( −ν e ) Work in the center-of-mass ** eE≈−(vv ,0,0, E ) frame and assume, for now, ν≈−** θθ * − * * that we can neglect the masses. e (EEvv , sin ,0, Ev cos ) 2 2 22 Qe=−+−( νν ee2 e ) ≈− −*2 − θ * 2Ev ( 1 cos ) 2 2* 2 02rest frame) s() pννµ pe m ee 2 mE • Proportionality to energy is a generic feature of point-like scattering! . because dσ/dQ2 is constant (at these energies)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 28 ν Neutrino-Electron (cont’d) • Elastic scattering: − − νµ + e → νµ + e . Recall, EW theory has coupling to left or right- handed electron Z Couplings gL gR . νe , νµ , ντ 1/2 0 Total spin, J=0,1 2 2 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 0 2 2 • Electron-Z coupling d , s , b −1/2 + 1/3 si n θW 1/3 si n θW 2 2 . Left-handed: -1/2 + sin θW GF s  1 2 4  σ ∝  − sin θW + sin θW  π  4 

2 2 . Right-handed: sin θW G s σ ∝ F (sin 4 θ ) π W 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 29 ν Neutrino-Electron (cont’d) • What are relative contributions of scattering from left and right-handed electrons?

ν ν f fLH RH ν ν θ θ

ff RH fLH 2 dσ dσ 1+ cosθ  = const = const ×  d cosθ d cosθ  2  11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 30 ν Neutrino-Electron (cont’d) 2 0 GF s  1 2 4  • Electron-Z coupling σ ∝  − sin θW + sin θW  2 π  4  . (LH, V-A): -1/2 + sin θW 2 GF s 4 . 2θ σ ∝ (sin θW ) (RH, V+A): sin W π Let y denote inelasticity. Recoil energy is related to  CM scattering angle by dσ LH: ∫ dy = 1 dy =  Ee ∫ 2 y = ≈1− 1 (1− cosθ ) dy RH: (1−=y ) dy 1 2  ∫ 3 Eν

2 GsF 142 4 −42 2 σTOT = −+sin θθW sinW =× 1.4 10cm / GeV ⋅ Eν ( GeV ) π 43

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 31 Lecture Question #2: ν Flavors and νe Scattering The reaction − − νµ + e → νµ + e has a much smaller cross-section than − − νe + e → νe + e Why?

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 32 Lecture Question #2: ν Flavors and νe Scattering The reaction − − νe νe νµ + e → νµ + e has a much smaller cross-section than Z − − νe + e → νe + e e e Why?

ν − − e e νe + e → νe + e has a second contributing W reaction, charged current e νe

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 33 Lecture Question #2: ν Flavors and νe Scattering Let’s show that this increases the rate (Recall from the previous pages… 2 dσ LH LH σ = σ TOT ∝ total coupling - TOT ∫ dy e dy For electron… LH coupling RH coupling dσ LH dσ RH  = + Weak NC -1/2+ sin2θ sin2θ ∫ dy  W W  dy dy  Weak CC -1/2 0 = σ LH + 1 σ RH TOT 3 TOT )

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

2 There are two LH couplings: NC coupling is -1/2+sin θW ≈ -1/4 and the CC 2 coupling is -1/2. We add the associated amplitudes… and get -1+sin θW ≈ -3/4

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 34 Who Cares about ν-e ν Elastic Scattering? • I just spent ~10-6 of your life span telling you about a reaction whose rate is 500x10-6 of the leading reaction for accelerator neutrinos . Was this a good deal? . I’ll argue yes… maybe… • This reaction, as we will see, is nearly unique in being predicted to a fraction of a % precision

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 35 ν Who Cares… (cont’d)

• Not easy to do. Reaction is rare and the detector is filled with photons from π0 decays which can be easily confused with electrons . But electrons from ν + e− → ν + e− are very forward 2 (because of small Q max) and electromagnetic showers from photons & electrons are subtly different

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 36 ν Who Cares… (cont’d)

• In this example (MINERvA) the number of events is small, so impact on the uncertainty of neutrino flux is modest today . ~10%→6%

• But for NOvA-era and LBNF-era beams, another order of magnitude in events makes this the leading method for measuring neutrino flux 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 37 ν Lepton Mass Effects • Let’s return to Inverse µ−decay: − − νµ + e → µ + νe

. What changes in the presence 2 Qmax of final state mass? 2 1 σ ∝ dQ TOT ∫ 2 22 o pure CC so always left-handed 2 ()QM+ Qmin W 2 o BUT there must be finite Q to 22 QQmax− min create muon in final state! ≈ 4 22 MW Qmmin = µ Gsm22()− σ = F µ . see a suppression scaling with TOT π (mass/CM energy)2 m2 = σ (massless)  µ o This can be generalized…  TOT  1-  s  11 -13 August 2014 Kevin McFarland: Interactions of Neutrinos 38 ν What about other targets? νany νany

• Imagine now a proton target Z . Neutrino-proton elastic scattering: p p ν + p → ν + p + e e νe e . “Inverse beta-decay” (IBD): + W νe + p → e + n p n . and “stimulated” beta decay: - νe + n → e + p . Recall that IBD was the Reines and Cowan discovery signal

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 39 ν Proton Structure

• How is a proton different from an electron? g − 2 . anomalous magnetic moment, κ ≡≠1 2 . “form factors” related to finite size Determined proton RMS charge radius to be (0.7±0.2) x10-13 cm

McAllister and Hofstadter 1956 188 MeV and 236 MeV electron beam from linear accelerator at Stanford

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 40 ν Final State Mass Effects

+ • In IBD, νe + p → e + n, have to pay a mass ν + penalty twice e e . M -M ≈1.3 MeV, M ≈0.5 MeV n p e W • What is the threshold? p n

. kinematics are simple, at least to zeroth order in Me/Mn  heavy nucleon kinetic energy is zero 22 sinitial =+=+() pνν pp M pp 2 ME (proton rest frame) 2 22 sfinal =() pen + p ≈ M n ++ m e 2 ME n( ν −( M n − M p)) 2 (Mm+−) M2 • Solving… E min ≈≈ne p1.806 MeV ν 2M p 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 41 Final State Mass Effects ν (cont’d) min • Define δE as Eν-Eν , then s=++ M2 2 Mδ EEmin initial pp( ν ) 222 =+Mp2δ EM ×+p( M ne + m) − M p 2 =2δ EM ×+p( M ne + m) • Remember the suppression generally goes as 2 m 2 (Mm+ ) final ne ξmass =−=−11 2 s (Mm++×) 2 Mδ E ne p  2M p  δ E × 2 low energy 2ME×δ  (Mmne+ ) = p ≈ 2  2 (Mm++×) 2 Mδ E (Mm+ ) M ne p 1− ne p high energy  2 δ  2MEp 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 42 ν Putting it all together… 2 GsF 2 22 σTOT =×cos ϑξCabibbo ×( mass ) ×+( ggVA3 ) π proton form quark mixing! final state mass factors (vector, suppression axial) ν + • mass suppression is proportional to e e δE at low Eν, so quadratic near threshold W • vector and axial-vector p n form factors (for IBD usually referred to as f and g, respectively)

gV, gA ≈ 1, 1.26.

. FFs, θCabibbo, best known from τn

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 43 Lecture Question #3: ν Quantitative Lepton Mass Effect • Which is closest to the minimum beam energy in which the reaction

− − νµ + e → µ + νe

can be observed?

(a) 100 MeV (b) 1 GeV (c) 10 GeV

22 (It might help you to remember that Qm min = µ or you might just want to think about the total CM energy required to produce the particles in the final state.)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 44 Lecture Question #3: ν Quantitative Lepton Mass Effect • Which is closest to the minimum beam energy in which the reaction

− − νµ + e → µ + νe

can be observed?

22 Qmmin = µ(a) 100 MeV (b) 1 GeV (c) 10 GeV 22 Qspp<=()e +ν 2 22 2 =(mEe++νν ,0,0, E−≈ mνν ) mee 2m E 2 mµ ∴Eν >≈10.9 GeV 11-13 August 2014 2me Kevin McFarland: Interactions of Neutrinos 45 Summary of First Lecture… ν and Next Topic • We calculated νe- scattering and Inverse Beta Decay (IBD) cross-sections! • In point-like weak interactions, key features are: . dσ/dQ2 is ≈ constant.

o Integrating gives σ∝Eν . LH coupling enters w/ dσ/dy∝1, RH w/ dσ/dy∝(1-y)2 o Integrating these gives 1 and 1/3, respectively . Lepton mass effect gives minimum Q2 2 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 ν-quark scattering 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 46 ν

Neutrino-Nucleon Deep Inelastic Scattering

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 47 Neutrino-Nucleon Scattering ν

• Charged - Current: W± exchange • Neutral - Current: Z0 exchange . CC Elastic Scattering (sometimes . Elastic Scattering: called “quasi-elastic” since neutron (Target unchanged) targets are only found in nuclei) νµ + N → νµ + N (Target changes but no break up) . Baryon Resonance Production: − νµ + n → µ + p (Target goes to excited state) * . Baryon Resonance Production: νµ + N → νµ + N + π (N or ∆) (Target goes to excited state) . Deep-Inelastic Scattering − 0 * νµ + n → µ + p + π (N or ∆) (Nucleon broken up) + π+ n νµ + quark → νµ + quark . Deep-Inelastic Scattering: (Nucleon broken up) − νµ + quark → µ + quark’ Linear rise with energy

Resonance Production

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 48 ν Scattering Variables

Scattering variables given in terms of invariants •More general than just deep inelastic (neutrino-quark) scattering, although interpretation may change.

2 4-momentum Transfer22 : Q=−=−− q 2( p'' p) ≈(4 EE sin2 (θ / 2)) Lab Energy Transfer: ν =⋅=−=−(qP) / M E E' ( E M) T( ) hTLab Lab Inelasticity: y=⋅ qP / pP ⋅= E − M/ E + E' ( ) ( ) ( hT) ( h ) Lab 22 Fractional Momentum of Struck Quark: x=− q/2( pq ⋅=) Q /2 MTν 22 2 2 2 Recoil Mass : W=+=+ ( qP ) MTT 2 Mν − Q Q2 CM Energy2 : s=+=+ ( pP )22 M T xy

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 49 Parton Interpretation of High ν Energy Limit Mass of target quark 22222 mqT= xP = xM µ ν Mass of final state quark 2 2 m q, = (xP + q)

qp=νµ − p In “infinite momentum frame”, xP is momentum of partons inside the nucleon Q2 Q2 x = = Neutrino scatters off a 2P ⋅q 2M Tν parton inside the nucleon

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 50 So why is cross-section so ν large? • (at least compared to νe- scattering!) • Recall that for neutrino beam and target at rest

Qs2 ≡ G22max Gs σ ≈=FF2 TOT ∫ dQ ππ0 2 s= mee + 2 mEν • But we just learned for DIS that effective mass of each target quark is mq = xmnucleon

• So much larger target mass means larger σTOT

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 51 Chirality, Charge in CC ν-q ν Scattering

• Total spin determines *

inelasticity distribution Flat in y . Familiar from neutrino- electron scattering ♠

1/4(1+cosθ∗)2 = (1-y)2 ν p 2 * ♠ ∫(1-y)2dy=1/3 dσ GsF 2 =( xd() x +− xu ()(1 x y )) • Neutrino/Anti-neutrino CC dxdy π each produce particular ∆q dσ ν p Gs2 * ♠ =F ( xd() x +− xu ()(1 x y )2 ) in scattering dxdy π νd → µ −u νu → µ +d

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 52 ν Factorization and Partons • Factorization Theorem of QCD allows cross-sections for hadronic processes to be written as:

σ ()lh+ →+ lX

=∑∫ dxσ ( l + q () x →+ l X ) q () x q h

. qh(x) is the probability of finding a parton, q, with momentum fraction x inside the hadron, h. It is called a parton distribution function (PDF). . PDFs are universal . PDFs are not (yet) calculable from first principles in QCD • “Scaling”: parton distributions are largely independent of Q2 scale, and depend on fractional momentum, x.

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 53 Brief Summary of Neutrino- ν Quark Scattering so Far 2 • x≡Q /2MTν is the fraction of the nucleon 4-momentum carried by a quark in the infinite momentum frame 2 . Effective mass for struck quark, MqT=() xP = xM . Parton distribution functions, q(x), incorporate information about the “flux” of quarks inside the hadron • Quark and anti-quark scattering from neutrinos or anti- neutrinos defines total spin . vq and vq are spin 0, isotropic . vq and vq are spin 1, backscattering is suppressed • Neutrinos and anti-neutrinos pick out definite quark and anti-quark flavors (charge conservation) 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 54 Momentum of Quarks & ν Antiquarks

• Momentum carried by quarks much greater than anti-quarks in nucleon

qx() qx()

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 55 y distribution in Neutrino CC ν

DIS dqdσν() σν ( q ) = ∝1 dxdy dxdy dqdσν() σν () q 2 = ∝−(1 y) At y=0: dxdy dxdy At y=1: Quarks & anti-quarks Neutrinos see only quarks. Neutrino and anti-neutrino Anti-neutrinos identical see only anti- quarks Averaged over protons and neutrons,

νν1 σσ≈ 2 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 56 ν Structure Functions (SFs) • A model-independent picture of these interactions can also be formed in terms of nucleon “structure functions” . All Lorentz-invariant terms included . Approximate zero lepton mass (small correction) ν ,ν dσ  2 2  M T xy  2 2  ∝ y 2xF1(x,Q ) + 2 − 2y − F2 (x,Q ) ± y(2 − y)xF3 (x,Q ) dxdy   E   • For massless free spin-1/2 partons, one simplification…

. Callan-Gross relationship, 2xF1=F2 . Implies intermediate bosons are completely transverse Can parameterize longitudinal cross-section by RL. σ F  4M 2 x2  = L = 2  + T  Callan-Gross violations result RL 1 2  g→ qq σ from MT, NLO pQCD, T 2xF1  Q 

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 57 ν SFs to PDFs • Can relate SFs to PDFs in naïve quark-parton model by matching y dependence . Assuming Callan-Gross, massless targets and partons… 2 2 2 2 . F3: 2y-y =(1-y) -1 , 2xF1=F2: 2-2y+y =(1-y) +1 νp,CC 2xF1 = x[d p (x) + u p (x) + s p (x) + c p (x)] νp,CC xF3 = x[d p (x) − u p (x) + s p (x) − c p (x)] • In analogy with neutrino-electron scattering, CC only involves left-handed quarks • However, NC involves both chiralities (V-A and V+A) . Also couplings from EW Unification . And no selection by quark charge 2xFν p, NC = xuuuxuxcxcx ( 22 + ) () + () + () + () ++ ( d2 d 2 ) dxdxsxsx () + () + () + () 1 LRpppp( ) LRpppp( ) xFν p, NC = xuuuxuxcxcx( 22 − ) () − () + () − () +− ( d2 d 2 ) dxdxsxsx () − () + () − () 3 LRpppp( ) LRpppp( ) 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 58 ν Isoscalar Targets

• Heavy nuclei are roughly neutron-proton isoscalar • Isospin symmetry implies u p = dn ,d p = un • Structure Functions have a particularly simple interpretation in quark-parton model for this case…

2νν ()N 2 d σ GsF 2 2νν () =(1 +− (1y )) F23 ( x ) ±−−( 1 (1 y )) xF ( x ) dxdy 2π { } νν()N , CC 2xF1 () x= xux (() + dx () ++ ux () dx () ++++= sx () sx () cx () cx () xqx () + xqx () νν()N , CC xF3 () x=+±− xuVal () x xdVal () x 2(() xsxcx ())

where uVal () x= ux () − ux ()

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 59 Lecture Question #4: Neutrino ν and Anti-Neutrino σνN ννNN1 • Given that σσ CC ≈ 2 CC in the DIS regime (CC) dqdqσν()()()() σν dq σν dq σν = =33 = and that dx dx dx dx for CC scattering from quarks or anti-quarks of a given momentum,

and that cross-section is proportional to parton momentum, what is the approximate ratio of anti- quark to quark momentum in the nucleon?

(a) qq/ ~1/3 (b) qq/ ~1/5 (c) qq/ ~1/8

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 60 Lecture Question #4: Neutrino ν and Anti-Neutrino σνN ννNN1 • Given that σσ CC ≈ 2 CC in the DIS regime (CC) dqdqσν()()()() σν dq σν dq σν = =33 = and that dx dx dx dx for CC scattering from quarks or anti-quarks of a given momentum,

and that cross-section is proportional to parton momentum, what is the approximate ratio of anti- quark to quark momentum in the nucleon?

(a) qq/ ~1/3 (b) qq/ ~1/5 (c) qq/ ~1/8

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 61 Lecture Question #4: Neutrino ν and Anti-Neutrino σνN ννNN1 • Given: σσ CC ≈ 2 CC in the DIS regime (CC) dqdqσν()()()() σν dq σν dq σν = =33 = and dx dx dx dx dqdqσν() σν () σ = + ν ∫ dx qq, dx dx dqdqσν() σν ( ) dqσν () dq σν () σ = += +3 ν ∫∫dxdx qq,,dx dx qq 3dx dx dqdqσν() σν ()  dqσν ()3 dq σν ()  ∴∫∫dx += 2 dx +  qq,,dx dx qq 3dx dx  1dqσν () dq σν ()5 dq σν () ∫∫dx = 5 dx = ∫ dx 33qqdx dx q dx

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 62 Momentum of Quarks & ν Antiquarks

• Momentum carried by quarks much greater than anti-quarks in nucleon qx(). Rule of thumb: at Q2 of 10 GeV2: . total quark momentum is 1/3, . total anti-quark is 1/15. qx()

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 63 ν From SFs to PDFs

• As you all know, there is a large industry in determining Parton Distributions for hadron collider simulations. . to the point where some of my colleagues on collider experiments might think of parton distributions as an annoying piece of FORTRAN code in their software package • The purpose, of course, is to use factorization to predict cross-sections for various processes . combining deep inelastic scattering data from various sources together allows us to “measure” parton distributions . which then are applied to predict hadron-hadron processes at colliders, and can also be used in predictions for neutrino scattering, as we shall see.

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 64 ν From SFs to PDFs (cont’d)

• We just learned that… νν()N , CC 2xF1 () x= xq () x + xq () x νν()N , CC =+±− xF3 () x xuVal () x xdVal () x 2(() xsxcx ()) where u ( x)= ux () − ux () Val • In charged-lepton DIS 2 γ p = 2 + 2xF1 () x ( 3 ) ∑ qx() qx () up type quarks 2 ++1 ( 3 ) ∑ qx() qx () down type quarks • So you begin to see how one can combine neutrino and charged lepton DIS and separate . the quark sea from valence quarks . up quarks from down quarks 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 65 Deep Inelastic Scattering: ν Conclusions and Summary • Neutrino-quark scattering is elastic scattering! . complicated by fact that quarks live in nucleons . and, as we will discuss later, nucleons in nuclei! • Neutrino DIS important for determining parton distributions • Supplemental material: . scaling violations of partons (more partons with lower mometum at higher Q2) . mass effects for tau neutrino interactions and production of charm quarks

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 66 ν

Ultra-High Energy Cross-Sections

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 67 ν Ultra-High Energies • At energies relevant for UHE Cosmic Ray studies (e.g., IceCube, Antares, ANITA) . ν-parton cross-section is dominated by high Q2, since dσ/dQ2 is constant o at high Q2, gluon radiation and splitting lead to more sea quarks at fewer high x partons (see supplemental material: scaling violations)

o see a rise in σ/ Eν from growth of sea at low x o neutrino & anti-neutrino cross-sections nearly equal 1 . Q2»M 2, then propagator dσ ∝ Until W 2 2 2 2 term starts decreasing and dq (q − M ) cross-section stops growing linearly with energy

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 68 Lecture Question #5: ν Where does σ Level Off?

2 2 • Until Q »MW , then propagator 1 dσ ∝ term starts decreasing and dq2 (q2 − M 2 )2 cross-section becomes constant • To within a few orders of magnitude, at what beam energy for a target at rest will this happen?

(a) Eν  10TeV (b) Eν  10,000TeV (c) Eν  10,000,000TeV

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 69 Lecture Question #5: ν Where does σ Level Off?

2 2 • Until Q »MW , then propagator 1 dσ ∝ term starts decreasing and dq2 (q2 − M 2 )2 cross-section becomes constant • To within a few orders of magnitude, at what beam energy for a target at rest will this happen?

(a) Eν  10TeV (b) Eν  10,000TeV (c) Eν  10,000,000TeV

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 70 Lecture Question #5: ν Where does σ Level Off?

2 2 • Until Q »MW , then propagator 1 dσ ∝ term starts decreasing and dq2 (q2 − M 2 )2 cross-section becomes constant • At what beam energy for a target at rest will this happen? Bonus point realization… 22 Q<= snucleon m nucleon +2 Emν nucleon In reality, that is only correct for 2 a parton at x=1. Typical quark x Q<≈ snucleon 2 Emν nucleon 2 is much less, say ~0.03 M 2 W Q limit is s. 2 < Eν So won’t start to MW 2mnucleon < 2 Eν 2 plateau until s>Mw 2mx (80.4) GeV2 nucleon ∴>Eν  3000GeV 3000GeV  2(.938)GeV ∴>Eν  100TeV  0.03

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 71 ν Ultra-High Energies • ν-parton cross-section is dominated by high Q2, since dσ/dQ2 is constant . at high Q2, scaling violations have made most of nucleon momentum carried by sea quarks

. see a rise in σ/ Eν from growth σ∝E of sea at low x ν . neutrino & anti-neutrino cross-sections nearly equal 2 2 • Until Q »MW , then propagator actual cross-section term starts decreasing and (Reno, hep-ph/0410109) cross-section becomes constant 1 dσ ∝ dq2 (q2 − M 2 )2 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 72 Example: Ultra-High ν Energies • At UHE, can we reach thresholds of non-SM processes? . E.g., structure of quark or leptons, black holes from extra dimensions, etc. . Then no one knows what to expect…

Fodor et al. PLB 561 (2003)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 73 ν

Motivation for Understanding GeV Cross-Sections

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 74 What’s special about it? ν Why do we care? • Remember this picture? . 1-few GeV is exactly where these additional processes are turning on 1 GeV is here . It’s not DIS yet! Final states & threshold effects matter • Why is it important? Examples from T2K, ICAL Goals:

1. νµ→νe

2. νµ disappearance

Eν is 0.4-2.0 GeV (T2K) or 3-10 GeV (INO ICAL) 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 75 How do cross-sections effect ν oscillation analysis?

• νμ disappearance (low energy) . at Super-K reconstruct these events by muon angle and momentum

(proton below Cerenkov threshold in H2O) . other final states with more particles below threshold (“non-QE”) will disrupt this reconstruction • T2K must know these events at few % level to do disappearance analysis to measure 2 ∆m 23, θ23

(fig. courtesy Y. Hayato)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 76 ν How do cross-sections effect µ oscillation analysis?

• νμ disappearance (high energy) • Visible Energy in a calorimeter is π NOT the ν energy transferred to the hadronic system 23 ,1993  π absorption, π re-scattering, final state rest mass effect the calorimetric response  Can use external data to constrain et et PRCal,

Ashery D.

MINOS Near Det. Anti-ν,  At very high energies, particle A. Souza, 25/8/2012 multiplicities are high and these effects will average out  Low energy is more difficult 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 77 How do cross-sections effect ν oscillation analysis?

• In the case of INO ICAL, need good energy and angle resolution to separate normal and inverted hierarchy

. Best sensitivity requires survival probability in both Eν and L

• Interaction models are understanding of detector response both needed to optimize resolution Petcov, Schwetz, hep-ph/0511277

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 78 How do cross-sections effect ν oscillation analysis?

signal • νe appearance . different problem: signal rate is very low so even rare backgrounds contribute! π0 background from E >peak • Remember the end goal of electron ν

neutrino appearance experiments Minakata & • Want to compare two signals with Nunokawa JHEP 2001 two different sets of backgrounds and signal reactions . with sub-percent precision . Requires precise knowledge of background and signal reactions 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 79

ν

Models for GeV Cross-Sections

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 80 ν (Quasi-)Elastic Scattering • Elastic scattering leaves a single nucleon in the final state . CC quasi-elastic (“quasi” since neutrons ν n→ lp− are in nuclei) is easier to observe ν p→ ln+ ()−− () ννNN→ • State of data on “free-ish”

neutrons (D2) is marginal . No free neutrons implies nuclear corrections . Low energy statistics poor • Cross-section is calculable . But depends on incalculable form- factors of the nucleon • Theoretically and experimentally constant at high energy . 1 GeV2 is ~ a limit in Q2 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 81

What was that last cryptic ν remark? • Theoretically and experimentally constant at high energy 2 2 2 . 1 GeV is ~ a limit in Q Qmax 1 σ ∝ dQ2 TOT ∫ 2 2 2 • Inverse µ−decay: 0 (Q + MW ) ν + − → µ− + ν 2 µ e e Qmax ≈ 4 2 a maximum Q independent of MW beam energy ⇒ constant σTOT

2 • OK, but why does cross-section have a Q max limit? . If Q2 is too large, then the probability for the final state nucleon to stay intact (elastic scattering) becomes low . This information is encoded in “form factors” of the nucleons

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 82 ν Elastic Scattering (cont’d) • As with IBD, nucleon structure alters cross-section − . ν n→ lp Can write down in terms of all possible “form factors” + of the nucleon allowed by Lorentz invariance ν p→ ln ()−− () C.H. Llewellyn Smith, Phys. Rep. 3C, 261 (1972) ννNN→ Occupants of the form factor zoo: 1 2 F V, F V are vector form factors;

FA is the axial vector form factor;

FP is the pseudo- scalar form factor; 3 3 F V and F A are form factors related to currents requiring G-parity violation, small? 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 83 ν Elastic Scattering (cont’d) 3 • Form factors representing second class currents, F V and 3 F A, are usually assumed to be zero

• Pseduoscalar form factor, FP, can be calculated from FA with reasonable assumptions (Adler’s theorem and the Goldberger-Treiman relation) 1 2 • The leading form factors, F V, F V and FA, are approximately dipole in form

“dipole approximation”

MV ≈0.71 GeV parameters MA≈1.01 GeV determined from data FA(0) ≈-1.267 n.b.: we’ve seen Fv(0) and FA(0) FV(0) is charge of proton before in IBD discussion (g and g ) V A • Note that those masses which “cut off” the form factor are of order 1 GeV, so form factors are low beyond 1 GeV2 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 84 ν Elastic Scattering (cont’d)

Vector form factors Axial vector form factors • Measured in charged • Measured in pion electro- lepton scattering production & neutrino scattering

Not quite dipole at high Q2

e.g., Bradford-Bodek-Budd-Arrington (“BBBA”), Bodek, Avvakumov, Bradford and Budd, Nucl.Phys.Proc.Suppl.159:127-132,2006 J. Phys. Conf. Ser. 110, 082004 (2008).

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 85 Low W, the Baryon ν Resonance Region • Intermediate to elastic and DIS regions is a region of resonance production . Recall mass2 of hadronic final state is given by 2 2 2 2 W = M T + 2M Tν − Q = M T + 2M Tν (1− x) . At low energy, nucleon-pion states dominated by N* and Δ resonances • Leads to cross-section with significant structure in W just

above Mnucleon . Low ν, high x

2 W photoabsorption vs Eγ. } Line shows protons. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos More later… 86 ν The Resonance Region • Models of the resonance region are complicated . In principle, many baryon resonances can be excited in the scattering and they all can contribute . They de-excite mostly by radiating pions

D. Rein and L. Sehgal, Ann. Phys. 133, 79 (1981) 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 87 ν Quark-Hadron Duality • Bloom-Gilman Duality is the relationship between quark and hadron descriptions of reactions. It reflects: . link between confinement and asymptotic freedom . transition from non-perturbative to perturbative QCD

σ (ee+−→ hadrons) R ≡ σ()ee+−→ µµ + −

quark-parton model calculation: 2 =EM ++αα RNC ∑ ( Qq ) O()EM S but of course, final state is really sums ∋>′ 2 qsmq over discrete hadronic systems

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 88 ν Duality and ν  1  W 2 = M 2 + Q2  −1 T  x  Low Q2 data DIS-Style PDF prediction • Governs transition between resonance and DIS region • Sums of discrete resonances approaches DIS cross-section • Bodek-Yang: Observe in electron scattering data; apply to ν cross-sections 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 89 ν Duality’s Promise

• In principle, a duality based approach can be applied over the entire kinematic region • The problem is that duality gives “averaged” differential cross-sections, and not details of a final state

• Microphysical models may lack important physics, but duality models may not predict all we need to know . How to scale the mountain between the two? 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 90 Lecture Question #6: ν Duality meets Reality

A difficulty in relating cross-sections of electron scattering (photon exchange) to charged-current neutrino scattering (W± exchange) is that some e- scatting reactions have imperfect ν-scattering analogues.

Write all possible νµ CC reactions involving the same target particle and isospin rotations of the final state for each of the following… (a) en−−→ en + (b) ep−−→ ep π − −+ n 0 (c) ep→ enπ  π − −− p (d) en→ epπ  − π 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 91 Lecture Question #6: ν Duality meets Reality

Write all possible ν reactions involving the same target particle and isospin rotations of the final state for each of the following… − −+ (a) en−−→ en (c) ep→ enπ − −+ νµµ np→ νµ pp→ µπ

−− (b) ep→ ep (d) en−→ ep −−π there are none! −+ νµ nn→ µπ − 0 νµ np→ µπ

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 92 ν Building a Unified Model

• In the relevant energy regime around 1 GeV, need a model that smoothly manages exclusive (elastic, resonance) to inclusive (DIS) transition • Duality argues that the transition from the high W part of the resonance region (many resonances) to deep inelastic scattering should be smooth.

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 93 Summary of Second ν Lecture… and Next Topics • We (slowly) extended what we learned about νe- scattering to (anti)ν-(anti)quark scattering and calculated in the inelastic high energy limit . Fully predicted cross-section, up to quark distributions inside nucleon (PDFs) . Discussed implications for Ice Cube energy neutrinos • We then tried to build the elastic and barely-inelastic neutrino-nucleon cross-sections ab initio . Lots of form factors and baryon resonances. Complex! • Duality between quark and hadron pictures can help extend calculations in deep inelastic limit to Δ resonance dominated regime

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 94 Exclusive Resonance ν Models and Duality Models • Duality models agree with inclusive data by construction . However, in a generator context, have to add details of final state • Typical approach (GENIE, NEUT and NUANCE) is to use a resonance model (Rein & Sehgal) below W<2 GeV, and duality + string fragmentation model for W>2 GeV . This is far from an idea solution . Discrete resonance model (probably) disagrees with total cross- section data below W<2 GeV and is difficult to tune . Average cross-section at high W does agree with data, but final state simulation is of unknown quality and difficult to tune also.

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 95 ν

From Nucleons to Nuclei

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 96 ν Why are Nuclei So Difficult?

• 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. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 97 ν

Coherent Neutrino-Nucleus Scattering

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 98 ν Coherent and Elastic

• Here is a limit in which, in principle, we can calculate scattering from the nucleus ν

ν • Why? If probe is long wavelength, then • Also, coherent implies significant enhancement of rate

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 99 ν Coherence Condition • Wavelength of probe, must be much larger than target, so momentum transfer: QR1/ • If coherent, amplitudes from nucleons add . Therefore rate goes as (#nucleons)2 • Limited momentum transfer, means limited 2 kinetic energy of recoil: Tmax 1/ MRA . Typical nuclear size in “natural” Q2 T ≈ for Q M units ~ 100 MeV, so maximum  A 2M A recoil energy is ~100 keV or less for 40Ar 2 σ 2 2 d GFA22MT =NZ −−(1 4sinθW )  1 − (FQ ( )) dT 42π E 2 ν Form factor with coherence Weak NC coupling : nearly zero for proton condition… goes to 0 except for very low Q2 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 100 Comments on Coherent ν Nuclear Scattering • No one has ever observed this because of the difficulties of finding such low recoils in nuclear matter . Most promising approaches have much in common with dark matter detectors • Very useful practically if this can be overcome since it is a reaction perfect for “counting” neutrinos from a beam, a reactor, etc.

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 101 ν Lecture Question #7 I would be willing to assert at high confidence that the discovery of neutrinos from the big bang would earn you a Nobel prize. Coherent scattering has no threshold, so can use it to detect neutrinos with energies ~1 meV What makes this difficult? 11Q2 ⇒ ≈ QTmax 2 T for Q M A R MRA 2M A

2 dσ G 2 MT 2 =FANZ −−1 4sin22θ 1 − FQ ( ) ( W ) 2 ( ) dT 42π Eν

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 102 ν Lecture Question #7 I would be willing to assert at high confidence that the discovery of neutrinos from the big bang would earn you a Nobel prize. Coherent scattering has no threshold, so can use it to detect neutrinos with energies ~1 meV What makes this difficult to detect? The maximum momentum that 2 can be transferred to a heavy Q T ≈ for Q M A stationary target is no more than 2M A twice the lab frame momentum. Q2 2 p 2 So T ≈< < ν 10−15 eV

2MMAA Bummer! I was looking forward to that sauna. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 103 ν Coherent and Inelastic? • What does that even mean? • A long wavelength probe of the nucleus can interact with an off- shell W or Z, turning it into a pion! . Firing a gun at a bubble, leaving it intact, but breaking apart the bullet? • Problematic background for oscillation experiments if pion fakes a single lepton • MINERvA and other experiments have seen this happen! . MINERvA data shows current models are poor

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 104 ν

Inverse Beta Decay and Related Reactions in Nuclei

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 105 ν Recall: Inverse Beta Decay

2 dσ GsF 2 22βe =×cos ϑCabibbo ××( ξ mass ) ggVe(1 + βθ cos) + 3 A 1 − cosθ d cosθπ 3 proton form quark mixing! final state mass factors (vector, suppression axial) ν + • mass suppression is proportional to e e δE at low Eν, so quadratic near threshold W • vector and axial-vector p n form factors (for IBD usually referred to as f and g, respectively)

gV, gA ≈ 1, 1.26.

. FFs, θCabibbo, best known from τn (neutron beta decay)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 106 ν Inside a Nucleus • Near threshold, have to account for discrete excitations of final state nucleus . If reaction is inclusive, then this is a sum over states . That can be difficult if many states are involved • Exclusive reactions behave like free nucleon beta decay, but with a different threshold ν 12Ce→ − 12 N e ( )ground state + ν e p→ en

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 107 ν Nuclei for Solar Neutrinos

• Here are some nuclei historically important for Solar neutrino experiments. Low thresholds.

Experiment Nuclear Target Reaction σo ∆Enucl [10-46cm2] [MeV] (no det. Thres.) GALLEX/GNO 71 71 − 71 8.611 ± 0.4% Ga33 v + Ga → e + Ge 0.2327 SAGE e (GT)

HOMESTAKE 37 37 − 37 1.725 Cl17 v + Cl → e + Ar 0.814 e (F) SNO 2 2 − (GT) 1.442 H1 ve + H → e + p + p

ICARUS 40 40 − 40 ∗ 148.58 (F) Ar18 ve + Ar → e + K … 44.367 (GT2) 1.505 + …

41.567 (GT6) …

table courtesy F. Cavana 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 108 ν SNO • Three reactions for observing ν from sun (Eν ~ few MeV

. 2H, 16O binding energies are 13.6eV, ~1 keV. - . Therefore, e are “free”. σ∝Eν

Deuteron binding energy is 2.2 MeV . Energy threshold of a few MeV for neutral current. Less for the charged

current because mn>mp+me (Bahcall, Kubodara, 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos Nozawa, PRD38 1030) 109 ν

GeV Cross-Sections on Nucleons in a Nucleus

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 110 ν Elastic? Fantastic!

• Last time, we showed that the elastic scattering of neutrinos from nucleons is (nearly) predicted . Charged-current reaction allows tagging of neutrino flavor and reconstruction of energy • Unfortunately, practical neutrino experiments have these nucleons inside nuclei

μ Does it matter that I started my ν new life inside a nucleus?

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 111 Fermi Motion, Binding and ν Pauli “Blocking” • In a nucleus, target nucleon has some initial momentum which modifies the observed scattering . Simple model is a “Fermi Gas” model of nucleons filling

available states up to some initial state Fermi momentum, kF

Motion of target Initial state nucleon changes p μ ν Final state n kinematics of reaction

• The nucleon is bound in the nucleus, so it take energy to remove it • Pauli blocking for nucleons not

escaping nucleus… states are already B kF filled with identical nucleon

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 112 ν “Final State” Interactions

ν µ- • The outgoing nucleon could create µ another particle as it travels in nucleus W . If it is a pion, event would appear inelastic π+ • Also other final states can contribute n p to apparent “quasi-elastic” scattering n through absorption in the nucleus… . kinematics may or may not distinguish nucleus the reaction from elastic • Theoretical uncertainties in these reactions are large . At least at the 10% level. More on this later. . If precise knowledge is needed for target (e.g., water, liquid argon, hydrocarbons), dedicated measurements will be needed o Most relevant for low energy experiments, i.e., T2K 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 113 ν “Final State” Interactions

ν µ- • The outgoing nucleon could create µ another particle as it travels in nucleus W . If it is a pion, event would appear inelastic π+ • Also other final states can contribute n ∆+ to apparent “quasi-elastic” scattering n through absorption in the nucleus… . kinematics may or may not distinguish nucleus the reaction from elastic • Theoretical uncertainties in these reactions are large . At least at the 10% level. More on this later. . If precise knowledge is needed for target (e.g., water, liquid argon, hydrocarbons), dedicated measurements will be needed o Most relevant for low energy experiments, i.e., T2K 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 114 Measurements of CCQE on ν Nuclei: Backgrounds • K2K famously observed a “low Q2 deficit” in its analysis K2K SciFi • MiniBooNE originally had (Oxygen target) a significant discrepancy PRD74 052002 (2006) at low Q2 as well . Original approach was to enhance Pauli blocking MiniBooNE to “fix” low Q2 . Was resolved by tuning single pion background

to data w/ pions PRL100 032301 (2008)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 115 ν MiniBooNE (Phys. Rev. D81 092005, 2010) • Oil Cerenkov detector (carbon), views only muon • Fit to observables, muon energy & angle find a discrepancy with expectation from free nucleons • It looks like a distortion of the Q2 distribution • MiniBooNE fits for an “effective”

axial mass, MA, higher than expected . Good consistency between total cross-section and this Q2 shape in

this high MA explanation

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 116 ν NOMAD (Eur.Phys.J.C63:355-381,2009)

• Like MiniBooNE, target is mostly carbon (drift chamber walls) • Reconstruct both recoiling proton and muon • Total cross-section and Q2 distribution are both consistent with expectation from free nucleon • Two experiments, same target, but different energies and reconstruction… … incompatible results?

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 117 ν MiniBooNE and NOMAD • Current data cannot be fit by a single prediction for low energy data (BooNEs) and high energy data (NOMAD)

. In effective dipole form-factor picture, different “MA”

. Free nucleon MA is ~1 GeV from both pion electroproduction and neutrino scattering on deuterium • Recall: MiniBooNE measures μ only, NOMAD μ+p

Plot courtesy of T. Katori

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 118 ν MINERvA CCQE on Carbon • MINERvA has measured CCQE in neutrino and anti-neutrino beams . Flux integrated from 1.5 to 10 GeV. It’s a measurement “near” 3.5 GeV • Sample is selected by muon and “low” calorimetric recoil away from vertex

Module number

Vertex Energy Recoil Energy Region TRACKER ECAL HCAL

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 119 ν dσ/dQ2 Shape

RFG, SF RFG, SF

MA = 1.35 MA = 1.35 TEM TEM

2 • Q distribution doesn’t agree well with “high effective MA”, but there is a clear disagreement with free nucleon result • Best fit is to “transverse enhancement model” 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 120 6-8 August 2013 Kevin McFarland: Interactions of Neutrinos 120 ν MINERvA μ+proton CCQE

• MINERvA has also done a NOMAD-like measurement requiring the proton • And… agrees with NOMAD data’s preferred model instead of model disagreement seen in MINERvA μ only CCQE TEM • Maybe (likely?) this is because of interactions of the proton leaving the nucleus? 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 121 ν Multi-Nucleon Correlations • Inclusion of correlations among nucleons in nucleus would add another quasielastic like process knocking two nucleons from nucleus . Could alter kinematics and rate in a way that would make a better fit to the data muon inclusive CCQE data • How to implement? . Microphysical models don’t yet give complete final state description . “Ad hoc” enhancement scaled from electron scattering dagta? (Carlson & Bodek, Budd, Christy) 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 122 ν Vertex Region Energy • Vertex region ignored in MINERvA recoil cut . Therefore selection is mostly insensitive to low energy nucleons in the final state • Study energy near vertex . Vertex is precisely located, so distance of energy from vertex is sensitive to range of extra protons

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 123 6-8 August 2013 Kevin McFarland: Interactions of Neutrinos 123 ν MINERvA: Vertex Energy

• A trend toward higher vertex energy is observed in the neutrino data, but not in anti-neutrino data • Red band represents uncertainties on energy reconstruction and final state interactions • Assume extra energy is due to additional protons 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 124 6-8 August 2013 Kevin McFarland: Interactions of Neutrinos 124 ν Extra Protons in MINERvA?

• Data wants to add low energy protons in 25±9% of neutrino events, but prefers 10±7% fewer protons in anti-neutrino • Suggests correlated pairs are dominantly n+p in initial state, and therefore p+p or n+n in CCQE 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 125 6-8 August 2013 Kevin McFarland: Interactions of Neutrinos 125 ν

One model to fit them all? C. Wilkinson, NuFact2014 preview

• T2K has been working to do exactly this • MiniBooNE and

MINERvA MINERvA have some tension between them

• Reasonable fit for Fermi Gas model and some (but not full) MiniBooNE multi-nucleon effect • This fit is also

consistent with D2 and vector form factors

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 126 Summary of CCQE in ν Nuclear Targets • There is evidence for nuclear modification of quasielastic neutrino-nucleon reactions . Kinematics of nucleons: Fermi motion, Pauli blocking . Multi-nucleon processes seem to also be present • There are other possible effects . More complete nucleon kinematics (spectral function) . A suppression is expected at low Q2 (long probe wavelength) from interactions of probe with multiple nuclei in “random phase approximation” calculations • Some of these effects contain overlapping physics! A challenge for the prediction. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 127 Nuclear Effects in Resonance ν

Region - νµ µ • An important reaction like W νnp→ µπ− 0 µ π0 ∆+ (νe background) can be modified in n a nucleus p • Production kinematics are modified nucleus by nuclear medium . at right have photoabsorption showing resonance structure . line is proton; data is 12C . except for first Δ peak, the structure is washed out . Fermi motion and interactions of resonance inside nucleus

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 128 Nuclear Effects in Resonance ν model of Region- (cont’d) νµ µ E. Paschos, NUINT04 νnp→ µπ− 0 W µ π+ π0 n ∆+ before interactions p after interactions nucleus

• How does nucleus affect π0 after production? π0 • “Final State Interactions”: migration of one state to another and pion absorption

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 129 Approaches to Final State ν Interactions • Propagate final state particles through the nuclear medium with varying degrees of sophistication where they interact according the measured cross-sections or models • Issues: . Are the hadrons modified by the nuclear medium? . Are hadrons treated as only on-shell or is off-shell transport allowed? . How to cleanly separate the initial state particles from their final state interactions? . How to relate scattering of external pions or nucleons from nuclei to scattering of particle created in nucleus? 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 130 ν Lecture Question #8 • Two questions with (hint) related answers… 1. Remember that W2 is… 22 2 WM=+−PP2 Mν Q 2 =+−MM21ν ( x) 2 PP } W the square of the invariant mass of the hadronic system. (ν=Eν-Eµ; x is the parton fractional momentum) It can be measured, as you see above with only leptonic quantities (neutrino and muon 4-momentum). In neutrino scattering on a scintillator target, you observe an event with a recoiling proton and with W reconstructed (perfectly) from leptonic variables =+ PP21 Mν ( − x) can only be true if x>1. That means the fractional momentum by the struck target parton is >1! This can only happen for in a nucleon boosted towards the collision in the CM frame by interactions within the nucleus (“Fermi momentum”) µ- νµ 12 −− 3.ν µ C→ µπp + remnant nucleus W is nonsense in a free nucleon picture. p It is forbidden to occur off of a proton or a n ∆+ neutron target by charge conservation! π0 But remember… reinteraction of pions! nucleus π- 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 132 ν Single Pion Production Data

−+ − 0 0 νµ NN→ µπ νµ NN→ µπ ′ νµµNN→ νπ P. Rodrigues, NuINT12

• Comparison of models to MiniBooNE single pion

production on CH2 • Some models do better on one process than another, but no model reproduces features of all processes • That’s crazy! These are processes related by isospin! 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 133 ν What is Failing Here? • The honest answer: we don’t know . Comparison at right is: (1) the best model for pion production tuned to electron scattering + (2) a sophisticated final state model tuned to photoproduction • This disagreement is large compared to precision needed for current oscillation experiments

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 134 Adding Confusion to ν Confusion MINERVA

MiniBooNE

• Data from MINERvA on CC1π+ MINERVA shape . No obvious evidence for the shape disagreement seen by MiniBooNE. . MINERvA rate appears different . Difficult to draw unifying conclusions

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 135 ν D2 : Disappointing Data? • Ideally to resolve our pion conundrum, we would go to Understanding reliable nucleon level data . Unfortunately, we don’t have it.

Data on Hernandez nucleons

• eN vs. eA data: our only hope for exclusive states? (MINERvA is

proposing a D2 target, but for DIS.) 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 136 ν

Nuclear Effects in Deep Inelastic Scattering

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 137 For Inclusive Scattering, ν Does Nucleus Matter? • In high energy limit, calculate of strongly coupled system should be “easy”. However… • Nucleon are not at rest in nucleus (Fermi motion) • Nuclear medium may modify the structure of free nucleon . Evidence of this from inclusive charged lepton scattering • Less important: final state interactions, since you don’t care about exclusive final states 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 138 ν Is the DIS Limit Simple? • Well measured effects in charged-lepton DIS . Maybe the same for neutrino DIS; maybe not… all precise neutrino data is on Ca or Fe targets! . Conjecture: these can be absorbed into effective nucleon PDFs in a nucleus Anti-shadowing

shadowing Fermi motion

EMC effect

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 139 But that conjecture may be ν wrong…

Curves from: Ingo Schienbein et al., Phys.Rev.D80(2009)094004; PRD77(2008)054013 • Only answer is to measure… red points would have been precision of MINERvA experiment if it could have added a deuterium target in the NOvA running of NuMI beamline. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 140 Comparing Light and Heavy ν

Nuclei? B. Tice et al, Phys. Rev. Lett. 112 231801 (2014) • Can’t compare to D2 data, but can compare different nuclei • MINERvA has an analysis on CH, Fe and Pb targets . This is at low energies and includes substantial elastic contribution . Remember that this can be confusing from the duality discussion… . Repeating now in NOvA-era beam with more inelastic events • That said, this data is not explained by nuclear effects seen in charged lepton scattering 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 141 ν

Thoughts on Effective Models and Neutrino Interaction Generators

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 142 The Problem of the Nucleus is ν Very, Very Hard

Measurements (Neutrino Effective scattering or Model related processes)

• Our iterative process uses data to improve models • Our models are effective theories, ranging from pure parameterizations of data to microphysical models with simplifying assumptions. . “Effective” has both positive and negative meanings, but in particular here I mean that these are not first-principles calculations from QCD. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 143 ν The Mosel Paradox

We don’t have models which fit (all) the available data, although many models provide valuable insight into features of this data Theorist’s paradigm: “A good generator does not have to fit the data, provided [its model] is right” Experimentalist’s paradigm: “A good generator does not have to be right, provided it fits the data” Ulrich Mosel, first articulated at NuINT11 conference 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 144

ν Feynman Weighs In...

“It doesn't matter how beautiful your theory is; it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.” — Richard Feynman This is surely true, but invalidating one side of an argument doesn’t make the other side correct!

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 145 ν Counter Argument

• Experimentalists can do (and have done, and will do) shameful things when confronted with data and model disagreements! • MiniBooNE oscillation analysis approach: . Modify the dipole axial - νμn→μ p mass and Pauli blocking PRD 81, 092005 (2010) until model fits data. . But there is nothing fundamental backing this approach. It’s a mechanical convenience to parameterize the data for the oscillation analysis.

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 146 ν Counter Argument (cont’d) • What we now believe about the MiniBooNE oscillation analysis approach: - - . In a simplistic view, there νμn→μ p + νμ(np)corr.→μ pp are neglected contributions from multi-nucleon pairs. . Those pairs alter the Martini et al, Δσ PRC 81, 045502 (2010) kinematics. Nieves, Nieves, . MiniBooNE got its energy by demonstrated Also

reconstruction wrong by NuINT12 at

picking the wrong physics Lalakulich & Mosel, Ankowski arXiV:208.3678 to modify.

.

OK within uncertainties? here If so, only by luck. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 147 ν Counter Argument (cont’d) P. Rodrigues, NuFact 2012 and NuINT12 Rein-Sehgal [Ann. Phys. 133, 79-153 (1981)] implementation in NEUT “Tuned” Rein-Sehgal to modify Q2 distribution, pion spectrum, rate

• But what else can experimentalists do? Mea culpa. • T2K finds poor agreement between Rein-Sehgal and - (+)0 (´) 0 MiniBooNE νμN→μ π N and νμN→νμπ N data. • Ad hoc tuning “breaks” assumptions of underlying model, e.g. CC-NC universality of process and relation among resonances, to force good agreement. 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 148

ν

Conclusions

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 149 What Should I Remember from ν These Lectures?

• Understanding neutrino interactions is necessary for precision measurements of neutrino oscillations • Point like scattering: weak interactions couple differently to each chirality of fermions, neutrino scattering rate proportional to energy (until real boson exchange) • Target (proton, nucleus) structure is a significant complication to theoretical prediction of cross-section . Particularly problematic near inelastic thresholds • Our best models are incomplete, and even those best models often aren’t the ones in generators • Resolving differences between data and models is a major conceptual challenge 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 150 ν

Supplemental Slides

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 151 ν

SUPPLEMENT: Scaling Violations of Partons

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 152 Strong Interactions among ν Partons Q2 Scaling fails due to these interactions ∂qxQ(, 2 ) α ()Q2 1 dy = s 2 ∫ ∂ logQ 2π x y

xx2  2 Pqq qy(),Q + Pqg g(, yQ )   yy 

•Pqq(x/y) = probability of finding a quark with momentum x within a quark with momentum y

•Pqq(x/y) = probability of finding a q with momentum x within a gluon with momentum y

41+ z2 Pz() = +−2δ (1z ) qq 3 (1− z )

1 2 Pz()= z2 +−( 1 z) gq 2  11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 153 ν Scaling from QCD

Observed quark distributions vary with Q2

Scaling well modeled by perturbative QCD with a single free

parameter (αs)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 154 ν

SUPPLEMENT: Massive Leptons (Taus) and Quarks (Charm) in DIS

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 155 ν Opera at CNGS

1 mm Goal: ντ appearance • 0.15 MWatt source τ ν • high energy νµ beam • 732 km baseline • handfuls of events/yr 1.8kTon Pb Emulsion layers

figures courtesy D. Autiero oscillation probability but what is this effect?

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 156 ν Lepton Mass Effects in DIS • Recall that final state mass effects enter as corrections: mm22 1-lepton →− 1 lepton s xs point-like nucleon . relevant center-of-mass energy is that of the “point-like” neutrino- parton system . this is high energy approximation • For ντ charged-current, there is a threshold of 2 smmin=() nucleon + mτ where 2 sinitial = mnucleon + 2 Emν nucleon (Kretzer and Reno) 2 mττ+ 2 mmnucleon • This is threshold for partons ∴>Eν ≈3.5 GeV with entire nucleon momentum 2mnucleon . effects big at higher Eν also "mMnucleon " is T elsewhere, 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 157 but don't want to confuse with m ... τ Lecture Question: ν What if Taus were Lighter?

• Imagine we lived in a universe where the tau mass was not 1.777 GeV, but was 0.888 GeV • By how much would the tau appearance cross-section for an 8 GeV tau neutrino increase at OPERA?

m2 mass 1− lepton suppression: xsnucleon s= m2 + 2 Em nucleon nucleon ν nucleon 1 GeV 10 GeV 100 GeV

σ Light Tau σ σ (a) ~ 1.4 (b) Light Tau ~2 (c) Light Tau ~3 σ Reality σ Reality σ Reality

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 158 Lecture Question: ν What if Taus were Lighter?

• Imagine we lived in a universe where the tau mass was not 1.777 GeV, but was 0.888 GeV • By how much would the tau appearance cross-section for an 8 GeV tau neutrino increase at OPERA?

m2 mass 1− lepton suppression: xsnucleon s= m2 + 2 Em nucleon nucleon ν nucleon 1 GeV 10 GeV 100 GeV

σ Light Tau σ σ (a) ~ 1.4 (b) Light Tau ~2 (c) Light Tau ~3 σ Reality σ Reality σ Reality

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 159 Lecture Question: ν What if Taus were Lighter?

• By how much would the tau appearance cross-section for an 8 GeV tau neutrino increase at OPERA?

m2 mass 1− lepton suppression: xsnucleon Numerator goes down by factor of four. Equivalent to denominator 1 GeV 10 GeV 100 GeV increasing by factor of four and tau mass unchanged… s= m2 + 2 Em nucleon nucleon ν nucleon σ Light Tau ~3 energy term dominates… σ Reality so set energy a factor of four higher

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 160 ν Opera at CNGS

1 mm Goal: ντ appearance • 0.15 MWatt source τ ν • high energy νµ beam • 732 km baseline • handfuls of events/yr 1.8kTon Pb Emulsion layers

figures courtesy D. Autiero what else is copiously produced in neutrino interactions with cτ ~ 100μm and decays to hadrons? 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 161 ν Heavy Quark Production • Production of heavy quarks modifies kinematics of our earlier definition of x. . Charm is heavier than proton; hints that its mass is not a negligible effect…

2 2 2 (q +ζp) = p' = mc 2 2 2 2 q + 2ζp • q +ζ M = mc − q2 + m 2 Therefore ζ ≅ c 2 p • q Q2 + m 2 Q2 + m 2 ζ ≅ c = c 2Mυ Q2 / x  m 2  “slow rescaling” leads to ζ ≅  + c  x1 2  kinematic suppression of  Q  charm production 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 162 ν Neutrino Dilepton Events

• Neutrino induced charm production has been extensively studied . Emulsion/Bubble Chambers (low statistics, 10s of events). Reconstruct the charm final state, but limited by target mass. . “Dimuon events” (high statistics, 1000s of events)

d −+ νµµ+ → µ ++cX, c →µν + + X' s  d +− νµµ+ → µ ++ →µν + +  cX, c X' s

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 163 ν

SUPPLEMENT: NuTeV Measurement of Strange Sea

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 164 ν Neutrino Dilepton Events

• Rate depends on:

. d, s quark distributions, |Vcd| . Semi-leptonic branching ratios of charm . Kinematic suppression and fragmentation

figure courtesy D. Mason

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 165 ν NuTeV Dimuon Sample • Lots of data! • Separate data in energy, x and y (inelasticity)

. Energy important for charm threshold, mc . x important for s(x)

ν ν dN2σ() ν→ µµ X π × dxdy 2 GMFN Eν 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 166 QCD at Work: Strange ν Asymmetry? • An interesting aside… . The strange sea can be generated perturbatively from g→s+sbar. . BUT, in perturbative generation the momenta of strange and anti- strange quarks is equal o well, in the leading order splitting at least. At higher order get a vanishingly small difference. . SO s & sbar difference probe non-perturbative (“intrinsic”) strangeness o Models: Signal&Thomas, (Brodsky & Ma, s-sbar) Brodsky&Ma, etc.

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 167 ν NuTeV’s Strange Sea

• NuTeV has tested this . NB: very dependent on what is assumed about non-strange sea . Why? Recall CKM mixing…

Vcd dx()+→ Vsxcs () s′ () x +→′ Vdxcd () Vsxcs () sx () small big . Using CTEQ6 PDFs… −= ± ± ∫ dx x( s s) 0.0019 0.0005 0.0014 +≈ c.f., ∫ dx x( s s) 0.02

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 168 ν

SUPPLEMENT: 2 NuTeV sin θW

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 169 ν NuTeV at Work…

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 170 ν DIS NC/CC Ratio • Experimentally, it’s “simple” to measure ratios of neutral to charged current cross-sections on an isoscalar target to extract NC couplings

W-q coupling is I 2 3 Z-q coupling is I3-Qsin θW

• Holds for isoscalar targets of u and d Llewellyn Smith Formulae quarks only . Heavy quarks, differences between u σ ν (ν )  σ ν (ν )  Rν (ν ) = NC = (u 2 + d 2 )+ CC (u 2 + d 2 ) and d distributions are corrections ν (ν )  L L ν (ν ) R R  • Isospin symmetry causes PDFs to σ  σ CC  CC drop out, even outside of naïve quark-parton model

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 171

Lecture Question: ν Paschos-Wolfenstein Relation Charged-Current Neutral-Current

• If we want to measure electroweak parameters from the ratio of charged to neutral current cross-sections, what problem will we encounter from these processes?

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 172 Lecture Question: ν Paschos-Wolfenstein Relation Charged-Current Neutral-Current

• CC is suppressed due to final state charm quark

⇒ Need strange sea and mc

. Remember heavy quark mass threshold set by mc effect: 2 mc xx→=ξ 1 + 2 Q 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 173 Lecture Question: ν Paschos-Wolfenstein Relation • The NuTeV experiment employed a complicated design to measure Paschos - Wolfenstein Relation σσνν− − =NC NC =ρθ221 − R νν ( 2 sin W ) σσCC− CC • How did this help with the heavy quark problem of the previous question?

Hint: what to you know about the σν(qq ) and σν ( ) relationship of:

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 174 Lecture Question: ν Paschos-Wolfenstein Relation • The NuTeV experiment employed a complicated design to measure Paschos - Wolfenstein Relation σσνν− − =NC NC =ρθ221 − R νν ( 2 sin W ) σσCC− CC • How did this help with the heavy quark problem of the previous question? σν(qq )= σν ( ) ∴−σν()qq σν ( )0 = σν(qq )= σν ( ) So any quark-antiquark symmetric part is not in difference, e.g., strange sea.

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 175 ν NuTeV Fit to Rν and Rνbar

• NuTeV result:

− sin 2 θ (on shell) = 0.2277 ± ±0.0013(stat.) ± 0.0009(syst.) W = 0.2277 ± 0.0016 (Previous neutrino measurements gave 0.2277 ± 0.0036) • Standard model fit (LEPEWWG): 0.2227 ± 0.00037 A 3σ discrepancy…

ν Rexp = 0.3916 ± 0.0013 (SM : 0.3950) ⇐ 3σ difference ν Rexp = 0.4050 ± 0.0027 (SM : 0.4066) ⇐ Good agreement

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 176 NuTeV Electroweak: ν What does it Mean? • If I knew, I’d tell you. • It could be BSM physics. Certainly there is no exclusive of a Z’ that could cause this. But why? • It could be the asymmetry of the strange sea… . it would contribute because the strange sea would not cancel in . but it’s been measured; not anywhere near big enough • It could be very large isospin violation

. if dp(x)≠un(x) at the 5% level… it would shift charge current (normalizing) cross-sections enough. . no data to forbid it. any reason to expect it? 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 177 ν

SUPPLEMENT: Inclusive Scattering on Heavy Targets

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 178 Measuring Inclusive ν Interactions • Much of the data we have is at high energies . Neutrino flux is usually poorly known. Common wideband technique is “low recoil” method which uses

the observation that lim is independent of Eν 𝑑𝑑𝜎𝜎 . Cross-section normalized𝜈𝜈→0 𝑑𝑑𝜈𝜈 from narrow band expt’s which counted secondary particles to measure flux • Typical goal is to extract structure functions 2 2 2 2xF1(x,Q ), F2(x,Q ), xF3(x,Q ) from dependence in y and Eν. • Most recently, NuTeV, CHORUS, NOMAD, MINOS

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 179 NuTeV CC Differential ν Cross-Sections Phys.Rev.D74:012008,2006 • NuTeV has a very large data sample on iron . High energies, precision calibration from testbeam • Uses:

. pQCD fits for ΛQCD . Extract structure functions for comparisons with other experiments

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 180 ν CHORUS and NOMAD

CHORUS νPb cross-sections Phys.Lett..632(2006) 65 NOMAD νC CC total cross-sections Phys.Lett.B660:19-25,2008

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 181 Nuclear Corrections and ν High-x PDFs CTEQ global fit compared to neutrinos

Figures No attempt to apply After “Kulgain-Petti style” courtesy nuclear corrections nuclear corrections J. Morfín

 There are two confusing aspect of these comparisons  We observed problems before in nuclear corrections from models  Also, some strange behavior at high x… difficult to incorporate both data sets in one model

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 182 ν MINOS Total Cross-Section

• Attempt to bravely extend low recoil technique to very low energies . “Low recoil” sample is visible hadronic energy below 1 GeV, so a fair fraction of the cross-section at the lowest energy (3 GeV)

Phys.Rev.D81:072002,2010 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 183 ν

SUPPLEMENT: Experiments to Measure GeV Cross-Sections

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 184 Energies and Targets of ν Cross-Section Measurements

recent results and/or currently analyzing and publishing new cross- section data

(Compilation from D. Schmitz)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 185 Energies and Targets of ν Cross-Section Measurements

(Compilation from D. Schmitz)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 186 Technologies of “Old” ν Experiments • BooNE and K2K: both have Cerenkov and Scintillator Bar detectors for measuring neutrino interactions . Cerenkov detectors have uniform acceptance, but high thresholds for massive particles . Scintillator bar detectors usually have a directional bias, typically smaller and may not contain interaction, but thresholds are lower than Cerenkov and particles can be identified by dE/dx • NOMAD: drift chambers in an analyzing magnet . Good momentum measurement and possibly better particle identification by dE/dx, but diffuse material makes photon reconstruction difficult • MINOS: coarse sampling iron detector . Difficult to distinguish particles other than muons, but very high rate

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 187 Technologies: Cerenkov ν Detectors • Cerenkov gives efficient muon or e/γ identification • Also, tag soft pions by decay

Figures from M. Wascko

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 188 Technologies: Segmented ν Scintillator • Lower thresholds, particle ID by dE/dx, calorimetric energy reconstruction . i.e., vertex activity • But detectors must be smaller (cost), so escaping particles • Reconstruction not uniform in angle

Figures from M. Wascko

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 189 Current and Near Future ν Experiments

• MINERνA: in NuMI at Fermilab . Fine-grained scintillator detector

. Nuclear targets of He, C, H2O, Fe, Pb • T2K 280m Near Detector at J-PARC . Fine-grained scintillator, water, and TPC’s in a magnetic field MINERνA • NOνA near detector: to run in 2014 . Segmented Liquid scintillator in off-axis beam T2K ND280 • MicroBooNE: to run in 2014 . Liquid Argon TPC in FNAL Booster Beam . Some data from ArgoNeuT, a test in NuMI 11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 190 MINERνA Detector ν

• 120 modules VetoWall Cryotarget Side HCAL . Finely segmented scintillator (OD)

planes read out by WLS fibers

. Fully Side calorimetry LHe Active ECAL • Signals to 64-anode PMT’s HCAL Targets Target Nuclear Downstream Downstream Downstream

• Front End Electronics using Side ECAL Trip-t chips (thanks to D0) • Side and downstream EM and hadron calorimetry • MINOS Detector gives muon momentum and charge Kevin McFarland: Interactions of Neutrinos 191 11-13 August 2014 ν Events in MINERνA ν

• So what does an event look like in MINERνA… Particle leaves the inner detector, 3 stereo views, X—U —V , shown separately and stops in outer beam direction DATA iron calorimeter

looking down on detector +60° -60°

color = energy

Muon leaves the back of the detector headed X views twice as dense, UX,VX,UX,VX,… toward MINOS 11-13 August 2014 192 ν Events in MINERνA ν

• Charged-current Quasi-elastic candidate

MeV

DATA • Single Electron Candidate

MeV

11-13 August 2014 Kevin McFarland: Interactions193 of Neutrinos ν Events in MINERνA ν

• Charged-current DIS candidate

MeV

DATA • Charged-current DIS candidate

MeV

11-13 August 2014 Kevin McFarland: Interactions194 of Neutrinos ν T2K Near Detectors

slide courtesy of R. Terri

Kevin McFarland: Interactions of 195 11-13 August 2014 Neutrinos ν Off-Axis Detector

• Multiple technologies for different final

states See Dytman talk

slide courtesy of R. Terri

Kevin McFarland: Interactions of 196 11-13 August 2014 Neutrinos ν NOvA Near Detector

• Scintillator extrusion cross section of 3.87cm x 6cm , but with added muon range stack to see 2 GeV energy peak •Range stack: 1.7 Veto region, fiducial region meters long, steel Shower containment, muon catcher interspersed with 10 active planes of 4.5m liquid scintillator

•First located on the surface, then moved to final underground location

Kevin McFarland: Interactions of Neutrinos 197 11-13 August 2014 ν MicroBooNE

TPC: • Liquid Argon TPC (2.5m)2x10.4m long . 150/89 tons 3mm wire pitch total/active To go on . 30 PMT’s for Booster Neutrino scintillation Beam light Axis

Kevin McFarland: Interactions of Neutrinos 198 11-13 August 2014 ν Technologies: Liquid Argon

• Very low threshold, excellent particle ID . Even electron/photon separation!

• Reconstruction is not always so straightforward with this level of detail available Figures from G. Barker

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 199 Future Experiments at a ν Neutrino Factory

• Early on in the consideration of neutrino factories, this possibility was pointed out by a number of groups . Concepts for experiments tried to leverage flux in high energy beams . Precision weak interaction physics through νe→ νe . Separated flavor structure functions through neutrino and anti-

neutrino scattering on H2 and D2 targets • Expect proposals for these experiments, or sensible versions thereof, to match parameters of whatever we eventually build D. Harris, KSM, AIP Conf.Proc.435:376-383,1998; AIP Conf.Proc.435:505-510,1998, R. Ball, D. Harris, KSM, hep-ph/0009223 M. Mangano et al. CERN-TH-2001-131, 2001 I.I. Bigi et al, Phys.Rept.371:151-230,2002.

Kevin McFarland: 200 11-13 August 2014 Interactions of Neutrinos ν

Slides with Animations (not good for PDF)

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 201 Nuclear Effects in Elastic ν Scattering • Several effects: . In a nucleus, target nucleon has some initial momentum which modifies the observed scattering o Simple model is a “Fermi Gas” model of nucleons filling available

states up to some initial state Fermi momentum, kF

ν

. The nucleon is bound in the nucleus, so it take energy to remove it . Pauli blocking for nucleons not escaping nucleus… states are already

filled with identical nucleon B kF . Outgoing nucleon can interact with the target

11-13 August 2014 Kevin McFarland: Interactions of Neutrinos 202