Nuclear effects in neutrino scattering

Transcription

1 European Graduate School Complex Systems of Hadrons and Nuclei JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN Copenhagen - Gießen - Helsinki - Jyväskylä - Torino L. Alvarez-Ruso, T. Leitner, U. Mosel Introduction Neutrino-nucleon reactions: QE and (232) Inclusive nuclear cross section In-medium modifications Final state interactions Exclusive channels: π production and nucleon knockout QE scattering at MiniBooNE Conclusions

2 Introduction Neutrino nucleus interactions are relevant for: Oscillation experiments: systematic uncertainties neutrino fluxes backgrounds detector responses Hadron structure: nucleon axial form factor N-R axial transitions strangeness in the nucleon spin In-medium modifications: form factors spectral functions nuclear correlations Experiments: MINERνA, FINeSSE with a high intensity ν beam Understanding nuclear effects is essential for the interpretation of the data and represents both a challenge and an opportunity

3 Neutrino-nucleus scattering ν l - W +. Elementary reactions: ν l N l X 2. In-medium modifications of the elementary cross sections 3. Propagation of the final state X FSI

4 Neutrino-nucleus scattering ν l - W +. Elementary reactions: ν l N l X 2. In-medium modifications of the elementary cross sections 3. Propagation of the final state X FSI

5 Elementary neutrino-nucleon reactions ν QE RES,ν ν,ν ν DIS,ν σ ν N [ -38 cm 2 ].5.3. QE RES DIS we consider QE & : νn l p νn l + νp l E ν [GeV]

6 Quasielastic scattering ν(k)+n(p) l (k )+X(p ) : d 2 σ νn dq 2 de l = dφ ( ) 64π 2 δ p 2 M 2 M 2 k p E ν matrix element for CC: M 2 = G2 F cos2 θ C L αβ H αβ 2 leptonic tensor L αβ hadronic tensor H αβ j α = ν l γ α ( γ 5 )l V A structure hadronic current: Jα X depends on the specific reaction parametrized in terms of form factors

7 Quasielastic scattering hadronic current: A α = ( γ α q/q α q 2 Jα QE = p Jα QE n =ū(p )Aαu(p) ) F V + i 2M σ αβ qβ F V 2 +γ αγ 5 F A + q αγ 5 M F P vector form factorsf,2 V (Q2 )=F p,2 Fn,2 related to electric & magnetic form factors by CVC BBA-23 parametrization axial form factorsf A (Q 2 ),F P (Q 2 ) related by PCAC dipole ansatz q/q α /q 2 extra term ensures vector current conservation for nonequal masses

8 resonance production hadronic current: J α = + J α () n = ψ β (p )B βα u(p) B βα = ψ β (p ) Rarita-Schwinger spinor ( C V 3 M (g αβ/q q β γ α )+ CV 4 M 2(g αβ q p q β p α )+ CV 5 M 2(g αβ q p q β p α)+g αβ C V 6 + CA 3 M (g αβ/q q β γα)+ CA 4 M 2(g αβq p q β p α )+CA 5 g αβ+ CA 6 M 2q βqα CVC & M + dominance PCAC Adler model ) γ 5 C4 V = M W CV 3 C 5 V = CV 6 = C V 3 e N scattering C A 6 =CA 5 M 2 Q 2 +m 2 π C5 A()= g Nπf π.2 6M C A 4 = 4 CA 5 C A 3 = dominant contribution:, C A 5 C V 3 width: p-wave Γ q CM 3 π momentum in the rest frame

9 Elementary cross sections dσ ν N /dq 2 [ -38 cm 2 /GeV 2 ] ν n -> µ - p ν p -> µ - ++ ν n -> µ Q 2 [GeV 2 ] E ν =. GeV σ ν N [ -38 cm 2 ] ν n -> µ - p ν p -> µ - ++ ν n -> µ E ν [GeV]

10 Elementary cross sections.6.4 ν µ n -> µ - p ν µ n -> µ - π p.2.3 σ [ -38 cm 2 ].8 σ [ -38 cm 2 ]. 5% error in M A E ν [GeV] 7% error in M A 5% error in C 5 A () E ν [GeV].8 ν µ p -> µ - π + p.3 ν µ n -> µ - π + n σ [ -38 cm 2 ] σ [ -38 cm 2 ]. 7% error in M A A 5% error in C 5() E ν [GeV] 7% error in M A 5% error in C 5 A () E ν [GeV]

11 Neutrino-nucleus scattering ν l - W +. Elementary reactions: ν l N l X 2. In-medium modifications of the elementary cross sections 3. Propagation of the final state X FSI

12 Neutrino-nucleus scattering ν W + l - Fermi motion Pauli blocking Nuclear binding In-medium width:. Elementary reactions: ν l N l X Γ Γ med = Γ+Γ coll 2. In-medium modifications of the elementary cross sections 3. Propagation of the final state X FSI

13 E µ [GeV] Inclusive cross section.8.8 Q 2 [GeV 2 ] d 2 σ/de µ dq 2 [ -38 cm 2 /GeV 3 ] νµ 56 Fe µ X Eν=GeV.8 Q 2 [GeV 2 ] QE.8 E µ [GeV]

14 In-medium effects νµ 56 Fe µ X E ν =GeV,Q 2 =.5GeV 2 d 2 σ/(de µ dq 2 ) [ -38 cm 2 /GeV 3 ] elementary + Fermi + Pauli + binding + in-medium width E µ [GeV]

15 Neutrino-nucleus scattering ν l - W +. Elementary reactions: ν l N l X 2. In-medium modifications of the elementary cross sections 3. Propagation of the final state X FSI

16 Neutrino-nucleus scattering ν l - W +. Elementary reactions: ν l N l X 2. In-medium modifications of the elementary cross sections 3. Propagation of the final state X FSI

17 GiBUU Transport Model Semiclassical transport model in coupled channels Previously applied to heavy-ion collisions, e A, γ A, π A reactions Particles (i=n,, π, ρ, ) propagate according to the Boltzmann-Uehling-Uhlenbeck equation: df ) i dt =( t +( p H) r ( r H) p fi ( r, p,t)=i coll [f i,f N,fπ,f,...] H = (m i +Us) 2 + p 2 Hamiltonian U s ( r, p) non-local mean field potential f i ( r, p,t) phase space density for particle species i Set of BUU equations coupled via I coll

18 GiBUU Transport Model Collision integral accounts for changes in f i : elastic and inelastic scattering Pauli blocking for fermions decay of unstable particles most important processes: NN NN NNπ NN NN N NN FSI N N πn πn πn πn ππn absorption charge exchange redistribution of energy production of new particles

19 E µ [GeV] E µ [GeV] Pion production νµ 56 Fe µ πx at Eν = GeV Q 2 [GeV 2 ].8 Q 2 [GeV 2 ] π + π π + E µ [GeV] w/o FSI E µ [GeV] w FSI.8.8 d 2 σ [ ] 38 cm2 deµdq 2 GeV 3.8 Q 2 [GeV 2 ].8 Q 2 [GeV 2 ] π

20 Pion production νµ 56 Fe µ πx σ π + [ -38 cm 2 ] w/o FSI w FSI w FSI ( ) w FSI (QE) π + σ π [ -38 cm 2 ] w/o FSI w FSI w FSI ( ) w FSI (QE) π E ν [GeV] E ν [GeV]

21 Pion Production νµ 56 Fe µ πx dσ/dt π [ -38 cm 2 /GeV] Pion kinetic energy spectrum at Eν=GeV πn strong absorption ( followed by ) side-feeding fromπ + into the π channel via charge exchange secondary pions from initial QE protons: shift to lower energies due to elastic w/o FSI w FSI w FSI ( ) w FSI (QE).8 T π [GeV] dσ/dt π [ -38 cm 2 /GeV] π + π 2 N NN pn N NNπ πn πn w/o FSI w FSI w FSI ( ) w FSI (QE).8 T π [GeV]

22 Pion Production νµ 56 Fe µ πx dσ (w FSI) /dt / dσ (w/o FSI) /dt Ratio R= (dσ/dt) w FSI (dσ/dt) w/o FSI..3.5 T [GeV] π π +

23 Pion Production νµ 56 Fe µ πx dσ (w FSI) /dt / dσ (w/o FSI) /dt Ratio R= (dσ/dt) w FSI (dσ/dt) w/o FSI..3.5 T [GeV] π π + R d R d = (dσ/dp π) A /A 2/3 (dσ/dp π ) d /2 E γ =3-4 MeV C Nb Ca Pb E γ =5-6 MeV E γ =4-5 MeV E γ =7-8 MeV Similar pattern observed in π photoproduction B. Krusche et al., Eur. Phys. J A22 (24) p π [MeV/c]

24 E µ [GeV] E µ [GeV] Nucleon Knockout νµ 56 Fe µ NXat Q 2 [GeV 2 ].8 Q 2 [GeV 2 ] p p E µ [GeV] w/o FSI E µ [GeV] w FSI.8.8 Eν=GeV.8 Q 2 [GeV 2 ].8 Q 2 [GeV 2 ] n n

25 Nucleon knockoutνµ 56 Fe µ NX σ p [ -38 cm 2 ] p 3 2 w/o FSI w FSI w FSI ( ) w FSI (QE) E ν [GeV] σ n [ -38 cm 2 ] w/o FSI w FSI w FSI ( ) w FSI (QE) n E ν [GeV] Enhancement due to secondary interactions ( NN NN, N NN, )

26 Nucleon Knockoutνµ 56 Fe µ NX Nucleon kinetic energy spectrum at large number of nucleons at low kinetic energies flux reduction of high-energy protons p n Strong side-feeding Eν=GeV dσ/dt p [ -38 cm 2 /GeV] w/o FSI w FSI w FSI ( ) w FSI (QE) p dσ/dt n [ -38 cm 2 /GeV] w/o FSI w FSI w FSI ( ) w FSI (QE) n.8 T p [GeV].8 T n [GeV]

27 QE scattering at MiniBooNE Reaction: νµ + 2 C µ + X Observables averaged over MiniBooNE ν flux Fermi motion & Pauli blocking Fraction of ν µ Flux /. GeV ν µ Flux ν e Flux Local density approximation E ν (GeV) J. Monroe, hep-ex/489 Polarization effects (nuclear RPA correlations) Following Singh & Oset NPA 542 (992) :

28 QE scattering at MiniBooNE

29 Conclusions A model for neutrino interactions with nuclei have been developed Elementary processes: both QE and (232) considered state-of-the-art form-factors (CVC & PCAC) Nuclear effects: Fermi motion, Pauli blocking, Binding Collisional broadening of the resonance FSI implemented by means of a semiclassical coupled-channel transport model (BUU) Combined description of Inclusive nuclear cross-section Exclusive channels: pion production, nucleon knockout FSI modifies considerably the distributions through rescattering, sidefeeding and absorption Nuclear correlations are important are low Q2