Transcription
IntroductionIntroduction toto NeutrinoNeutrino InteractionInteraction PhysicsPhysicsNUFACT08NUFACT08 SummerSummer SchoolSchool11-13 June 2008Benasque, SpainPaul Soler
4. Quasi-elastic, resonant, coherent anddiffractive scattering4.1 Motivation4.2 Charged current quasi-elastic scattering4.3 Neutral current elastic scattering4.4 Resonant pion production4.5 Coherent pion production4.6 ExperimentsNeutrino Interaction PhysicsNUFACT08 Summer School2
4.1 Motivation Many neutrino oscillation experiments need to achieveE/L 10-3 GeV/km, so for distances 1000 km, we need interactionsaround 1 GeV.For example, T2K, MINOS, atmospheric experiments requireknowledge of cross-section between 0.4 and 2 GeV/c to performaccurate m223 and θ23 analysisT2KNeutrino Interaction PhysicsNUFACT08 Summer School3
4.1 Motivation Around 1 GeV there is a complicated region where deep inelasticscattering (DIS), quasi-elastic (QEL) scattering and resonanceproduction (for example, 1π production) co-existNeutrino Interaction PhysicsNUFACT08 Summer School4
4.2 Charged current quasi-elastic scattering Quasi-elastic neutrino-nucleon scattering reactions (small q2):affects nucleon as a wholeνµ n µ pνµ p µ nνµνµµ Wµ W pnpnM µ , p H eff ν µ , n GF cosθ cµ γ µ (1 γ 5 )ν µ pγ µ FV (q 2 ) FA (q 2 )γ 5 n2FV (q 2 ) vector form factorcosθ C 0.975 (Cabbibo angle)FA (q 2 ) axial vector form factor[][ (Neutrino Interaction PhysicsNUFACT08 Summer School)]5
4.2 Charged current quasi-elastic scattering In reality, it is more complicated and we need Llewelyn-Smithformalism to calculate QE differential cross-sections:dσ ν ,ν GF2M 2 (s u )(s u ) 2 AmB C 22 24dQMM8πEν (s u ) 4MEν Q 2 mµ2 A, B, C are complicated functions of two vector form factorsF1V(Q2), F2V(Q2), the axial form factor FA(Q2) and the pseudoscalarform factor FP(Q2).See Zeller, hep-ex/0312061, for details2 (mµ2 Q2 ) m Q2 2 µ22222 A (F F2 ) (FA 2FP ) 2 4 FP (1 τ )FA (1 τ )F1 τ (1 τ )F2 4τF1F2 22 1M4M M 2Q1 τ (1 µ p µ n ) F V (Q 2 ) 1 τ (1 µ p µn )V2B 2 FA (F1 F2 )2F1 (Q ) 222M2 Q Q (1 τ ) 1 2 (1 τ ) 1 2 1 222mV C FA F1 τF22 mV 2M224gF(Q) F(Q)2A2PA22FA (Q ) Qm Q2π2τ NeutrinoInteractionPhysics Q2Form factors: assume 1 A (0) g A 1.2573 0.028 6 SummerFSchool4MNUFACT082 dipole approximationµ p 1.793 µN and µ n 1.913 µN mA ()
4.2 Charged current quasi-elastic scattering Form factors introduced since proton, neutron not elementary.Depends on vector and axial weak charges of the proton and neutron.Conservation of Vector Current (CVC) relates form factors to electronscatteringMain physics to be extracted from QE scattering data are empirical formfactor parameters (fits to mA, mV, deviations from dipole approximation)FV (q 2 ) FA (q 2 ) FV (0)(1 q/mFA (0)(1 q2/ mA2mV 0.84 GeV2σ (ν e n ) σ (ν e p ) Neutrino InteractionPhysics E 38 0.975 10 SummerNUFACT08School 1 GeV )2 2V2mA 1.032 GeV7)2
4.3 Neutral current elastic scattering ( )Neutral current elastic neutrino-nucleon scattering reactions arerelated to the CC quasielastic (small q2): about 15% of CC QEL( )ν µ p ν µ p( )ννν µ n ν µ nµν( )νµµZ0Z0p( )( )( )µ( )pnnAlso need tocalculate formfactorsNeutrino Interaction PhysicsNUFACT08 Summer School8
4.4 Resonant pion production Between the elastic and inelastic region is an area associated withpion production through the excitation of baryon resonancesν l N l N * and N* π N'Invariant mass squared:W 2 MT2 2MTν (1 x ) If x 1 then quasi-elastic scattering but if x 1then you can excite different pion states:W 2 (MT mπ )2 , (MT 2mπ )2 ,. Rein and Sehgal’s model describes low energy pion production by acoherent superposition of all possible resonancesdσ112Cross-section:2dQ dWwith: 2T (νN lN *) 232MEspins1Γ0Γ(W M )Neutrino Interaction Physics2π (W MSchool)2 Γ 2 / 4NUFACT08SummerΓ(W M )9
4.4 Resonant pion production For example, possible resonances are or ν µ N µ µ p π ν µ N µ µ n π All possible channels: 3 in CC and 4 in NCVery little data, has large statisticalerrors, mainly from old bubblechamber experimentsNeutrino Interaction PhysicsNUFACT08 Summer School10
4.4 Resonant pion production For example, possible resonances are or ν µ N µ µ p π ν µ N µ µ n π All possible channels: 3 in CC and 4 in NCNC data is even worse!Neutrino Interaction PhysicsNUFACT08 Summer School11
4.4 Resonant pion production Duality: use electronscattering data to improveprecision of modelCan observe individualresonances with goodagreement data and modelBodek and YangNeutrino Interaction PhysicsNUFACT08 Summer School12
4.5 Coherent pion production Neutrinos can also produce pions coherently (low Q2 and high ν)The neutrino coherently scatters off the whole nucleus with negligibleenergy transfer to the whole nucleus of mass AThis results in a forward scattered single pion (background inoscillation searches because forward peaked)Neutral and charged current processes are possible:ν µ A ν µ A π 0νµ A µ A π Rein and Sehgal’s model also describes coherent pion production:Cross-section:22 b t2dσGM 2 21mπN2A e Fabsf A Eν (1 y )σ tot (1 r ) 2 22 π2 dQ dydt2π16π mA Q Re[fπN (0)]fπN (0) pion - nucleon scattering amplituder Im[fπN (0)]f 0.93m pion decay constant2ππ x /λ( )t (q pπ )2 ( (E) ( ( p ))2 pi ) iiFabs e pion absorptionNeutrino Interaction Physicsin t distributionNUFACT08 SummerExponentialSchoolb (1/ 3)R 2 / 3 impact parameter13i i2
4.5 Coherent pion production Charged current single pion coherent cross-section: 1 coh σ CCNC cross-section is half of CC: σ2Neutrino Interaction PhysicscohNCNUFACT08 Summer School14
4.6 Experiments Recent experiments carrying out measurementsin the 1GeV region:––––K2K near detectors (ie. SciBar): completedMINOS near detector: runningMiniBoone: runningSciBoone: moved SciBar to Fermilab, operating at theBooster beamline– Minerva (under construction)– T2K (under construction)Neutrino Interaction PhysicsNUFACT08 Summer School15
4.6 Experiments K2K SciBar and SciBooneObserved CC QE interactionνµ n µ pNeutrino Interaction PhysicsNUFACT08 Summer School16
4.6 Experiments MiniBoone: measurement of CCQE scattering– Fitted form factor, effective axial mass:π0 event– NC π0 measurement: 28,000 eventsRatio coherent/non-coherent:Neutrino Interaction PhysicsNUFACT08 Summer School17
4.6 Experiments Minerνa: a detector for precision interaction physics at FermilabScintillator bar wavelength shifting fibreNeutrino Interaction PhysicsNUFACT08 Summer SchoolResonance event18 CCQE event ν µ n µ p
5. Nuclear Effects5.1 Fermi smearing and Pauli blocking5.2 Nuclear re-interactionsNeutrino Interaction PhysicsNUFACT08 Summer School19
5.1 Fermi smearing and Pauli blocking Nuclear effects in neutrino scattering:– In a nucleus, the target nucleon has a momentumwhich modifies scattering– Modelled as “Fermi gas” that fills up all availablestates until some initial state Fermi momentum, kF– The Pauli exclusion principle ensures that states cannot occupystates that are already filled (Pauli blocking)– Particles that escape nuclear medium may be re-scattered anddeflected by the Fermi momentum, especially at low energies.– We need better understanding of the Fermi motion– For example, MiniBoone have already published a paper suggestinga modification to the Fermi gas model based on matching QEscattering in all values of Q2 with their data.Neutrino Interaction PhysicsNUFACT08 Summer School20
5.1 Fermi smearing and Pauli blocking Effects on Structure Functions:– In charged lepton scattering, have observed shadowing andmodifications to PDFs due to nucleons.– At small x, coherent interaction of a hadronic component of the virtualphoton with target nucleus - shadowing– It is not clear if this is also present in neutrino structure functionsThese effects need to besince at low x, dominated by axial currentAnti-shadowingShadowingstudied in detail with highstatistics neutrino scatteringFermi motionEMC effectNeutrino Interaction PhysicsNUFACT08 Summer School21
5.2 Re-interactions Nuclear effects in resonanceregion:– Production of resonance may beaffected by nuclear medium (see plotof photoabsorption data)– Resonant structure gets washed out– Pions may either rescatter or beabsorbed. This needs to be measuredNeutrino Interaction PhysicsNUFACT08 Summer School22
Conclusions Neutrino interactions have provided valuable insight into thetheory of weak interactions– Maximal parity violation, V-A theory and finally the Glashow-WeinbergSalam electroweak theory were developed in part from information onneutrino interactions– Neutrino interaction data is used to probe the electroweak theory, suchas in the measurements of sin2θW. Neutrino interactions have also provided information on thestructure of nucleons– Structure function measurements and scaling violations have beenobserved (F3 is only accessible through neutrino interactions) Neutrino oscillations allow us to probe the grand unificationenergy scale, but it is crucial that we understand further the 1 GeV energy region to be able to exploit oscillationexperiments to the maximumA new generation of experiments is commencing to lead theway towards a new precision era in neutrino interaction physicsNeutrino Interaction PhysicsNUFACT08 Summer School23
EMC effect Fermi motion These effects need to be studied in detail with high statistics neutrino scattering. Neutrino Interaction Physics NUFACT08 Summer School 22 . Neutrino interactions have provided valuable insight into the theory of weak interactions – Maximal parity vi
