ν

NeutrinoNeutrino--NucleonNucleon DeepDeep InelasticInelastic ScatteringScattering

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 48 NeutrinoNeutrino--NucleonNucleon ‘‘nn aa NutshellNutshell ν • Charged - Current: W± exchange • Neutral - Current: Z0 exchange ƒ Quasi-elastic Scattering: ƒ Elastic Scattering: (Target changes but no break up) (Target unchanged) − νμ + n →μ + p νμ + N →νμ + N ƒ Nuclear Resonance Production: ƒ Nuclear Resonance Production: (Target goes to excited state) (Target goes to excited state) − 0 * * νμ + n →μ + p + π (N or Δ) νμ + N →νμ + N + π (N or Δ) n + π+ ƒ Deep-Inelastic Scattering: ƒ Deep-Inelastic Scattering (Nucleon broken up) (Nucleon broken up) − νμ + quark →μ + quark’ νμ + quark →νμ + quark

Linear rise with energy

Resonance Production

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 49 ν ScatteringScattering VariablesVariables

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

2 22 2'' 2 4-momentum Transfer : Qq=− =−( ppEE −) ≈( 4 sin (θ / 2)) Lab Energy Transfer: ν =⋅qP / M = E − E' = E − M ()ThT()()Lab Lab ' Inelasticity: yqPpPEM=⋅()()( / ⋅ =hT − / () EE h + ) Lab 22 Fractional Momentum of Struck Quark: xq=− / 2() pqQM ⋅ = / 2 Tν 22 2 2 2 Recoil Mass : WqPM=+ ( ) =TT + 2 MQν − Q2 CM Energy222 : spPM=+ ( ) = + T xy

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 50 ν

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 51 ν PartonParton InterpretationInterpretation ofof DISDIS

Mass of target quark 22222 mxPxMqT== μ ν Mass of final state quark 2 2 m q, = (xP + q)

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

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 52 SoSo whywhy isis crosscross--sectionsection soso ν large?large? • (at least compared to νe- scattering!) • Recall that for neutrino beam and target at rest

2 GGs22Qsmax ≡ σ ≈=FFdQ2 TOT ∫ π 0 π 2 sm=+ee2 mEν • But we just learned for DIS that effective mass of each target quark is mxmq = nucleon

• So much larger target mass means larger σTOT

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 53 Chirality,Chirality, ChargeCharge inin CCCC νν--qq ν ScatteringScattering

• Total spin determines * inelasticity distribution Flat in y ƒ 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 Δq ν p 2 * ♠ dσ GsF 2 =+−()xd() x xu ()(1 x y ) in scattering dxdy π νd → μ −u νu → μ +d

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 54 ν FactorizationFactorization andand PartonsPartons

• Factorization Theorem of QCD allows amplitudes for hadronic processes to be written as: A(l + h → l + X ) = dxA(l + q(x) → l + X )q (x) ∑∫ h q ƒ Parton distribution functions (PDFs) are universal ƒ Processes well described by single parton interactions ƒ Parton distribution functions not (yet) calculable from first principles in QCD • “Scaling”: parton distributions are largely independent of Q2 scale, and depend on fractional momentum, x.

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 55 ν

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 56 MomentumMomentum ofof QuarksQuarks && ν AntiquarksAntiquarks

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

qx() qx()

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 57 yy distributiondistribution inin NeutrinoNeutrino CCCC ν DISDIS dqdqσ ()νσν ( ) =∝1 dxdy dxdy dqdqσν() σν () 2 y=0: 0.14 =∝−()1 y neutrino dxdy dxdy

0.12 Quarks & antineutrino anti-quarks 0.1 y=1: Neutrino and anti-neutrino 0.08 Neutrinos see identical only quarks. 0.06 Anti-neutrinos 0.04 see only anti- quarks 0.02

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ν 1 ν σ ≈ 2 σ

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 58 TouchstoneTouchstone QuestionQuestion #4:#4: ν NeutrinoNeutrino andand AntiAnti--NeutrinoNeutrino σσνN ν 1 ν • Given: σσ CC ≈ 2 CC in the DIS regime (CC) dqdqσ ()νσν ( ) dq () σν dq () σν ==33 = and 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

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 59 MomentumMomentum ofof QuarksQuarks && ν AntiquarksAntiquarks

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

qx()

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 62 StrongStrong InteractionsInteractions amongamong ν PartonsPartons Q2 Scaling fails due to these interactions ∂qxQ(, 2 ) α ()Qdy2 1 = s 2 ∫ ∂ logQ 2π x y

⎡ ⎛⎞xx2 ⎛⎞ 2 ⎤ ⎢Pqq⎜⎟qy(),Q + P qg ⎜⎟gyQ(, )⎥ ⎣ ⎝ 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()=+− 2(1δ z ) qq 3(1− z )

1 2 Pz()=+−⎡⎤ z2 () 1 z gq 2 ⎣⎦ 12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 63 ν

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 64 ν ScalingScaling fromfrom QCDQCD

Observed quark distributions vary with Q2

Scaling well modeled by perturbative QCD with a single free

parameter (αs)

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 65 IfIf youyou findfind thisthis difficultdifficult toto ν rememberremember…… • It may help you to imagine scaling up a mountain • Perhaps after yesterday it is more intuitive that as you go up in scale ƒ the average momentum of each hiking group decreases ƒ and the number of hiking groups increases…

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 66 ν

DIS:DIS: RelatingRelating SFsSFs toto PartonParton DistributionsDistributions

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 67 ν StructureStructure FunctionsFunctions (SFs)(SFs) • A model-independent picture of these interactions can also be formed in terms of nucleon “structure functions” ƒ All Lorentz-invariant terms included ƒ 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…

ƒ Callan-Gross relationship, 2xF1=F2 ƒ Implies intermediate bosons are completely transverse Can parameterize transverse

cross-section by RL. 2 2 σ L F2 ⎛ 4M T x ⎞ •Callan-Gross violations, M R = = ⎜1+ ⎟ L ⎜ 2 ⎟ •NLO pQCD, g → qq σ T 2xF1 ⎝ Q ⎠

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 68 ν SFsSFs toto PDFsPDFs • Can relate SFs to PDFs in naïve quark-parton model by matching y dependence ƒ Assuming Callan-Gross, massless targets and partons… 2 2 2 2 ƒ 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) + cp (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) ƒ Also couplings from EW Unification ƒ And no selection by quark charge 2xFν pNC,22=+ xuuuxuxcxcx⎡ ( )()()()()( +++++ d 22 d )()()()() dxdxsxsx +++⎤ 1 ⎣ LRpppp() LRpppp( )⎦ xFν pNC,22=− xuuuxuxcxcx⎡( ) () −+−+− () () () ( d 22 d ) dxdxsxsx () −+− () () ()⎤ 3 ⎣ LRp() p p p L R() p p p p ⎦ 12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 69 ν IsoscalarIsoscalar TargetsTargets

• 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…

2()νν N 2 d σ GsF 22()νν =+−±−−{}()()1(1)()1(1)yFx23 yxFx () dxdy 2π νν()NCC , 2xF1 () x=+++++++=+ xuxdxuxdxsxsxcxcxxqxxqx (() () () () () () () () () () νν()NCC , xF3 () x=+±− xuVal () x xd Val () x 2(() x s x c ()) x

where uVal ( x )=− ux ( ) ux ( )

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 70 ν NuclearNuclear EffectsEffects inin DISDIS • Well measured effects in charged-lepton DIS ƒ Maybe the same for neutrino DIS; maybe not… all precise neutrino data is on Ca or Fe targets! ƒ Conjecture: these can be absorbed into effective nucleon PDFs in a nucleus Anti-shadowing 0.001 0.01 0.1 1 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 1.1 1.1 shadowing Fermi 1.0 1.0 motion (D) 2 0.9 0.9 (X) / F

2 NMC Ca/D F SLAC E87 Fe/D 0.8 SLAC E139 Fe/D 0.8 E665 Ca/D Parameterization Error in parameterization 0.7 0.7 EMC effect 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 0.001 0.01 0.1 1 x

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 71 ν FromFrom SFsSFs toto PDFsPDFs

• As you all know, there is a large industry in determining Parton Distributions ƒ 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 C++ software • The purpose, of course, exactly related to Chris’ point about factorization in his Friday lecture

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 72 ν FromFrom SFsSFs toto PDFsPDFs (cont(cont’’d)d)

• We just learned that…

νν()NCC , 2()()()xF1 x=+ xq x xq x νν()NCC , xFxxuxxdxxsxcx3 ()=+±−Val () Val () 2(() ())

where uVal ( x )=− ux ( ) ux ( ) • In charged-lepton DIS 2 γ p 2 2()xFx1 =+(3 ) ∑ qxqx ()() 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 ƒ the quark sea from valence quarks ƒ up quarks from down quarks 12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 73 ν

DIS:DIS: MassiveMassive QuarksQuarks andand LeptonsLeptons

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 74 ν OperaOpera atat CNGSCNGS

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?

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 75 ν LeptonLepton MassMass EffectsEffects inin DISDIS • Recall that final state mass effects enter as corrections: mm22 1-lepton →− 1 lepton sxspoint-like nucleon ƒ relevant center-of-mass energy is that of the “point-like” neutrino- parton system ƒ this is high energy approximation

•For ντ charged-current, there is a threshold of 2 smmin=+() nucleon mτ where 2 sminitial =+nucleon2 Emν nucleon (Kretzer and Reno) 2 mmmττ+ 2 nucleon • This is threshold for partons ∴Eν >≈3.5 GeV with entire nucleon momentum 2mnucleon ƒ effects big at higher Eν also "mMnucleon " is T elsewhere, 12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 76 but don't want to confuse with mτ ... TouchstoneTouchstone QuestionQuestion #5:#5: ν WhatWhat ifif TausTaus werewere Lighter?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 sm=+2 2 Em nucleon nucleonν nucleon 1 GeV10 GeV 100 GeV σ σ σ (a) Light Tau ~1.4 (b)Light Tau ~2 (c) Light Tau ~3 σ Reality σ Reality σ Reality

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 77 ν OperaOpera atat CNGSCNGS

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? 12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 80 ν HeavyHeavy QuarkQuark ProductionProduction • Scattering from heavy quarks is more complicated. ƒ 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 ≅ x⎜1+ c ⎟ kinematic suppression of ⎜ 2 ⎟ ⎝ Q ⎠ charm production 12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 81 ν NeutrinoNeutrino DileptonDilepton EventsEvents

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

⎛⎞d −+ ν μμ+ ⎜⎟→++μμνcX, c →++ X ' ⎝⎠s ⎛⎞ d +− νμμμ+ →++cX μν, c →++ X ' ⎜⎟ ⎝⎠s

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 82 ν NuTeVNuTeV atat WorkWork……

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 83 ν NeutrinoNeutrino DileptonDilepton EventsEvents

• Rate depends on:

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

figure courtesy D. Mason

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 84 ν NuTeVNuTeV DimuonDimuon SampleSample • Lots of data! • Separate data in energy, x and y (inelasticity)

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

ν ν dN2σν() μμ→ X π × dxdy 2 GMFN Eν 12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 85 QCDQCD atat Work:Work: StrangeStrange ν Asymmetry?Asymmetry? • An interesting aside… ƒ The strange sea can be generated perturbatively from g→s+sbar. ƒ 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. ƒ SO s & sbar difference probe non-perturbative (“intrinsic”) strangeness o Models: Signal&Thomas, (Brodsky & Ma, s-sbar) Brodsky&Ma, etc.

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 86 ν NuTeVNuTeV’’ss StrangeStrange SeaSea

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

Vdxcd()+→ Vsx cs () sx′ ()

Vdxcd()+→ Vsx cs () sx′ () small big ƒ Using CTEQ6 PDFs…

dx⎡⎤ x s−= s 0.0019 ± 0.0005 ± 0.0014 ∫ ⎣⎦( ) c.f., dx⎡⎤ x s+≈ s 0.02 ∫ ⎣⎦()

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 87 DeepDeep InelasticInelastic Scattering:Scattering: ν ConclusionsConclusions andand SummarySummary • Neutrino-quark scattering is elastic scattering! ƒ complicated by fact that quarks live in nucleons

• Important lepton and quark mass effects for tau neutrino appearance experiments

• Neutrino DIS important for determining parton distributions ƒ particularly valence and strange quarks

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 88 ν

NeutrinoNeutrino--NucleonNucleon DeepDeep InelasticInelastic ScatteringScattering AppliedApplied……

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 89 ν DISDIS NC/CCNC/CC RatioRatio • 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 ƒ 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

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 90 TouchstoneTouchstone QuestionQuestion #6:#6: ν PaschosPaschos--WolfensteinWolfenstein RelationRelation 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?

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 91 TouchstoneTouchstone QuestionQuestion #6:#6: ν PaschosPaschos--WolfensteinWolfenstein RelationRelation • The NuTeV experiment employed a complicated design to measure Paschos - Wolfenstein Relation σσνν− R− = NC NC =−ρ 221 sin θ νν ()2 W σσCC− CC • How did this help with the heavy quark problem of the previous question?

Hint: what to you know about the σ ()νσνqq and ( ) relationship of:

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 93 ν NuTeVNuTeV FitFit toto RRνν andand RRννbarbar

• NuTeV result:

2 (on−shell) sin θW = 0.2277 ± ±0.0013(stat.) ± 0.0009(syst.) = 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

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 95 NuTeVNuTeV Electroweak:Electroweak: ν WhatWhat doesdoes itit Mean?Mean? • If I knew, I’d tell you. • It could be BSM physics. Certainly there are no limits on a Z’ that could cause this. But why? • It could be the asymmetry of the strange sea… ƒ it would contribute because the strange sea would not cancel in ƒ but it’s been measured; not anywhere near big enough • It could be very large isospin violation

ƒ if dp(x)≠un(x) at the 5% level… it would shift charge current (normalizing) cross-sections enough. ƒ no data to forbid it. any reason to expect it? 12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 96 ν

NextNext Lecture:Lecture: GeVGeV crosscross--sections,sections,

applicationapplication toto ννμμ→ν→νee,, otherother energyenergy regimesregimes

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 97