Neutrino-Nucleon Deep Inelastic Scattering
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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 Quasi-elastic Scattering: Elastic Scattering: (Target changes but no break up) (Target unchanged) − νμ + n →μ + p νμ + N →νμ + N Nuclear Resonance Production: 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+ Deep-Inelastic Scattering: 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 4-momentum Transfer22 : Qq=− 2 =− ppEE'' − ≈ 4 sin 2 (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 Familiar from neutrino- electron scattering ♠ 1/4(1+cosθ∗)2 = (1-y)2 ν p 2 * ♠ ∫(1-y)2dy=1/3 dσ Gs 2 =+−F xd() x xu ()(1 x y ) • Neutrino/Anti-neutrino CC dxdy π () each produce particular Δq dσν p Gs2 * ♠ =+−F xd() x xu ()(1 x y )2 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 Parton distribution functions (PDFs) are universal Processes well described by single parton interactions 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 ()νσνσνσν ( ) dq () dq () ==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 Rule of thumb: at Q2 of 10 GeV2: 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 the average momentum of each hiking group decreases 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” 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 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 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) + 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) Also couplings from EW Unification 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… d 2()σ νν N Gs2 =+−±−−F 1(1)()1(1)yFx22() yxFxνν () dxdy 2π {}()()23 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 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 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 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 the quark sea from valence quarks 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.