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νNeutrino-NucleonDeep Inelastic Scattering12-15 August 2006Kevin McFarland: Interactions of Neutrinos48

Neutrino-Nucleon‘n a Nutshellν Charged - Current: W exchange Neutral - Current: Z0 exchange Quasi-elastic Scattering: Elastic Scattering:(Target changes but no break up)(Target unchanged) νμ n μ pνμ N ν μ N Nuclear Resonance Production: Nuclear Resonance Production:(Target goes to excited state)(Target goes to excited state)νμ n μ p π0 (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 νμ quarkνμ quark μ quark’Linear rise with energyResonance Production12-15 August 2006Kevin McFarland: Interactions of Neutrinos49

νScattering VariablesScattering variables given interms of invariants More general than just deepinelastic (neutrino-quark)scattering, althoughinterpretation may change.() ( 4EE' sin (θ / 2))ν ( q P) / M ( E E' ) ( E M )y ( q P ) / ( p P ) ( E M ) / ( E E' )4-momentum Transfer : Q q p' p2Energy Transfer:2222LabThLabInelasticity:hTFractional Momentum of Struck Quark: x q / 2 ( p q ) Q / 2M TνRecoil Mass 2 : W 2 (q P) 2 M T 2 2 M Tν Q 2Q2222CM Energy : s ( p P) M T xy212-15 August 2006Kevin McFarland: Interactions of NeutrinosTLabhLab250

ν12-15 August 2006Kevin McFarland: Interactions of Neutrinos51

νParton Interpretation of DISMass of target quarkμνmq x P x M22Mass of final state quark22m q , ( xP q )q pν p μ12-15 August 20062T2In “infinite momentumframe”, x is momentum ofpartons inside the nucleon2Neutrino scatters off aparton inside the nucleon22QQx 2 P q 2 M TνKevin McFarland: Interactions of Neutrinos52

So why is cross-section solarge?ν (at least compared to νe- scattering!) Recall that for neutrino beam and target at restσ TOT 22 Qmax sFG πdQ 202FG sπs me 2me Eν2 But we just learned for DIS that effective mass of eachtarget quark is m q xm nucleon So much larger target mass means larger σTOT12-15 August 2006Kevin McFarland: Interactions of Neutrinos53

Chirality, Charge in CC ν-qScattering Total spin determinesinelasticity distribution*Flat in y Familiar from neutrinoelectron scattering dσν p GF2 s * xd (x) xu(x)(1 y)2dxdy π dσν p GF2 s * xd (x) xu(x)(1 y)2dxdy πν 1/4(1 cosθ )2 (1-y)2()() (1-y)2dy 1/3 Neutrino/Anti-neutrino CCeach produce particular Δqin scatteringνd μ uνu μ d 12-15 August 2006Kevin McFarland: Interactions of Neutrinos54

Factorization and Partonsν Factorization Theorem of QCD allows amplitudes for hadronicprocesses to be written as:A(l h l X ) dx A(l q ( x) l X )q ( x)hq Parton distribution functions (PDFs) are universal Processes well described by single parton interactions Parton distribution functions not (yet) calculable from first principles inQCD “Scaling”: parton distributions are largely independent of Q2scale, and depend on fractional momentum, x.12-15 August 2006Kevin McFarland: Interactions of Neutrinos55

ν12-15 August 2006Kevin McFarland: Interactions of Neutrinos56

Momentum of Quarks &Antiquarksν Momentum carried by quarksmuch greater than anti-quarksin nucleonq( x)q ( x)12-15 August 2006Kevin McFarland: Interactions of Neutrinos57

y distribution in Neutrino CCDISy 0:dσ (ν q ) dσ (ν q ) 1dxdydxdydσ (ν q ) dσ (ν q )2 (1 y )dxdydxdy0.14neutrinoQuarks &anti-quarks0.12antineutrinoy 1:0.1Neutrino andanti-neutrinoidenticalνNeutrinos seeonly quarks.0.080.06Anti-neutrinossee only antiquarks0.040.02012-15 August 200600.10.20.30.40.50.60.70.80.9Kevin McFarland: Interactions of Neutrinos1νσ σ12ν58

νTouchstone Question #4:Neutrino and Anti-Neutrino σνNνν1σ σ Given: CCin the DIS regime (CC)2 CCdσ (ν q) dσ (ν q )dσ (ν q )dσ (ν q) 3 3dxdxdxdxandfor CC scattering from quarks or anti-quarks of agiven momentum,and that cross-section is proportional to partonmomentum, what is the approximate ratio of antiquark to quark momentum in the nucleon?(a) q / q 1/ 312-15 August 2006(b) q / q 1/ 5Kevin McFarland: Interactions of Neutrinos(c) q / q 1/ 859

Momentum of Quarks &Antiquarksν Momentum carried by quarksmuch greater than anti-quarksin nucleonq( x) Rule of thumb: at Q2 of 10 GeV2: total quark momentum is 1/3q ( x)12-15 August 2006Kevin McFarland: Interactions of Neutrinos62

νStrong Interactions amongPartonsQ Scaling fails due to these interactions2 q( x, Q 2 ) α s (Q 2 ) dy 22π x y log Q1 Pqq x 2q( y , Q ) Pqg y x 2 g ( y, Q ) y Pqq(x/y) probability of finding a quark withmomentum x within a quark with momentum y Pqq(x/y) probability of finding a q withmomentum x within a gluon with momentum y4 1 z2Pqq ( z ) 2δ (1 z )3 (1 z )12Pgq ( z ) z 2 (1 z ) 2 12-15 August 2006Kevin McFarland: Interactions of Neutrinos63

ν12-15 August 2006Kevin McFarland: Interactions of Neutrinos64

Scaling from QCDνObserved quarkdistributions varywith Q2Scaling wellmodeled byperturbative QCDwith a single freeparameter (αs)12-15 August 2006Kevin McFarland: Interactions of Neutrinos65

If you find this difficult toremember ν It may help you to imagine scaling up amountain Perhaps after yesterday it is more intuitivethat as you go up in scale the average momentum of each hiking groupdecreases and the number of hiking groups increases 12-15 August 2006Kevin McFarland: Interactions of Neutrinos66

νDIS: Relating SFs to PartonDistributions12-15 August 2006Kevin McFarland: Interactions of Neutrinos67

Structure Functions (SFs)ν A model-independent picture of these interactions canalso be formed in terms of nucleon “structure functions” All Lorentz-invariant terms included Approximate zero lepton mass (small correction) M xy dσ ν ,ν 2 y 2 xF1 ( x, Q 2 ) 2 2 y T F2 ( x, Q 2 ) y (2 y )xF3 ( x, Q 2 ) E dxdy For massless free spin-1/2 partons, one simplification Callan-Gross relationship, 2xF1 F2 Implies intermediate bosons are completely transverseCan parameterize transversecross-section by RL. Callan-Gross violations, M NLO pQCD, g q q12-15 August 2006F2 4M T2 x 2 σL 1 RL 2Q σ T 2 xF1 Kevin McFarland: Interactions of Neutrinos68

νSFs to PDFs Can relate SFs to PDFs in naïve quark-parton model bymatching y dependence Assuming Callan-Gross, massless targets and partons F3: 2y-y2 (1-y)2-1 , 2xF1 F2: 2-2y y2 (1-y)2 1νp ,CC2 xF1νp ,CCxF3[ x[d]( x) u ( x) s ( x) c ( x)] x d p ( x) u p ( x) s p ( x) c p ( x)pppp In analogy with neutrino-electron scattering, CC onlyinvolves left-handed quarks However, NC involves both chiralities (V-A and V A) Also couplings from EW Unification And no selection by quark charge(())(() ) 2 xF1ν p , NC x (uL2 uR2 ) u p ( x) u p ( x) c p ( x) c p ( x) ( d L2 d R2 ) d p ( x) d p ( x) s p ( x) s p ( x) xF3ν p , NC x (uL2 uR2 ) u p ( x) u p ( x) c p ( x) c p ( x) (d L2 d R2 ) d p ( x) d p ( x) s p ( x) s p ( x) 12-15 August 2006Kevin McFarland: Interactions of Neutrinos69

νIsoscalar Targets Heavy nuclei are roughly neutron-proton isoscalar Isospin symmetry implies u p d n , d p u n Structure Functions have a particularly simpleinterpretation in quark-parton model for this case d 2σ ν (ν ) N GF2 s 1 (1 y ) 2 F2 ( x) 1 (1 y ) 2 xF3ν (ν ) ( x)2πdxdy2 xF1ν (ν ) N ,CC ( x) x(u ( x) d ( x) u ( x) d ( x) s( x) s ( x) c( x) c( x) xq( x) xq( x)xF3ν (ν ) N ,CC ( x) xuVal ( x) xdVal ( x) 2 x( s ( x) c( x))where uVal ( x) u ( x) u ( x){(12-15 August 2006)()Kevin McFarland: Interactions of Neutrinos}70

νNuclear Effects in DIS 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 effectivenucleon PDFs in a nucleus Anti-shadowing0.0011.1234 5 670.01234 5 670.1234 5 6711.1shadowing1.0F2(X) / F2(D)1.00.90.9NMC Ca/DSLAC E87 Fe/DSLAC E139 Fe/DE665 Ca/DParameterizationError in parameterization0.80.70.001Fermimotion0.80.7234 5 670.01234 5 670.1234 5 67EMC effect1x12-15 August 2006Kevin McFarland: Interactions of Neutrinos71

From SFs to PDFsν As you all know, there is a large industry in determiningParton Distributions to the point where some of my colleagues on colliderexperiments might think of parton distributions as anannoying piece of FORTRAN code in their C software The purpose, of course, exactly related to Chris’point about factorization in his Friday lecture12-15 August 2006Kevin McFarland: Interactions of Neutrinos72

From SFs to PDFs (cont’d)ν We just learned that 2 xF1ν (ν ) N ,CC ( x) xq ( x) xq ( x)xF3ν (ν ) N ,CC ( x) xuVal ( x) xdVal ( x) 2 x( s( x) c( x))where uVal ( x) u ( x) u ( x) In charged-lepton DIS2 xF1 ( x) (γp23)2 ( 13 ) q ( x) q ( x)up type quarks2 q ( x) q( x)down type quarks So you begin to see how one can combine neutrino andcharged lepton DIS and separate the quark sea from valence quarks up quarks from down quarks12-15 August 2006Kevin McFarland: Interactions of Neutrinos73

νDIS: Massive Quarksand Leptons12-15 August 2006Kevin McFarland: Interactions of Neutrinos74

νOpera at CNGSGoal: ντ appearance 0.15 MWatt source high energy νμ beam 732 km baseline handfuls of events/yr1 mmτν1.8kTonPbEmulsion layersfigures courtesy D. Autierooscillation probabilitybut what is this effect?12-15 August 2006Kevin McFarland: Interactions of Neutrinos75

Lepton Mass Effects in DIS νRecall that final state mass effectsenter as corrections:1-2mleptonspoint-like 1 2mleptonxsnucleon relevant center-of-mass energy isthat of the “point-like” neutrinoparton system this is high energy approximation For ντ charged-current, there is athreshold ofsmin (mnucleon mτ ) 2where2sinitial mnucleon 2 Eν mnucleonmτ 2 2mτ mnucleon Eν 3.5 GeV2mnucleon" mnucleon " is M T elsewhere,but don't want to confuse with mτ .12-15 August 2006(Kretzer and Reno) This is threshold for partonswith entire nucleon momentum effects big at higher Eν alsoKevin McFarland: Interactions of Neutrinos76

Touchstone Question #5:What if Taus were Lighter?ν Imagine we lived in a universe where the tau mass wasnot 1.777 GeV, but was 0.888 GeV By how much would the tau appearance cross-sectionfor an 8 GeV tau neutrino increase at OPERA?masssuppression:1 2mleptonxsnucleon2snucleon mnucleon 2 Eν mnucleon1 GeV10 GeV 100 GeVσ Light Tauσ Light Tau 1.4 (b)(a) 2σ Realityσ Reality12-15 August 2006Kevin McFarland: Interactions of Neutrinosσ Light Tau(c) 3σ Reality77

νOpera at CNGSGoal: ντ appearance 0.15 MWatt source high energy νμ beam 732 km baseline handfuls of events/yr1 mmτν1.8kTonPbEmulsion layersfigures courtesy D. Autierowhat else is copiously produced inneutrino interactions with cτ 100μmand decays to hadrons?12-15 August 2006Kevin McFarland: Interactions of Neutrinos80

Heavy Quark Productionν Scattering from heavy quarks is morecomplicated. Charm is heavier than proton; hints that itsmass is not a negligible effect (q ζp )2 p'2 mc 2q 2 2ζp q ζ 2 M 2 mc2 q 2 mcTherefore ζ 2p q2Q 2 mcQ 2 mc ζ 2MυQ2 / x2 mc 2 ζ x 1 2 Q 12-15 August 20062“slow rescaling” leads tokinematic suppression ofcharm productionKevin McFarland: Interactions of Neutrinos81

Neutrino Dilepton Events νNeutrino 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 νμ μ c X ,c μ ν μ X ' s d c μ ν μ X 'ν μ μ c X , s 12-15 August 2006Kevin McFarland: Interactions of Neutrinos82

NuTeV at Work 12-15 August 2006Kevin McFarland: Interactions of Neutrinosν83

Neutrino Dilepton Eventsν Rate depends on: d, s quark distributions, Vcd Semi-leptonic branching ratios of charm Kinematic suppression and fragmentationfigure courtesy D. Mason12-15 August 2006Kevin McFarland: Interactions of Neutrinos84

NuTeV Dimuon Sample νLots of data!Separate data in energy, x and y (inelasticity) Energy important for charm threshold, mc x important for s(x)ννd 2σ (ν N μμ X )π dxdyGF2 M N Eν12-15 August 2006Kevin McFarland: Interactions of Neutrinos85