theory of pion production for nu-d - Neutrino induced pion production reaction on deuteron -

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1 theory of pion production for nu-d - Neutrino induced pion production reaction on deuteron - Toru Sato RCNP,Osaka University Collaborators: νd, γd: S.X. Nakamura, H. Kamano, T. -S. H. Lee pion angular distribution: J. E. Sobczyk, E. Hernandez, S. X. Nakamura, J. Nieves T. Sato (Osaka U.) νd June / 33

2 contents Motivation Models of neutrino induced pion production reactions Neutrino deuteron reaction and extraction of elementary cross section Summary T. Sato (Osaka U.) νd June / 33

3 Motivation CC Neutrino-nucleon reaction (building block to describe neutrino-nucleus reaction) ν + N l + N l + N + π l + N + η l + Y + K l + N + π + π... l + Y l + N + K... T. Sato (Osaka U.) νd June / 33

4 Neutrino-nucleon cross section σ/e ν [ -38 cm 2 /GeV] CC ν µ µ - p µ - π N µ - M N σ/e ν [ -38 cm 2 /GeV] CC anti-ν µ µ + n µ + π N µ + M N E ν [GeV] E ν [GeV] cross section of single pion production is as large as non-meson production ( model, S. X. Nakamura et al.) non negligible contribution of 2π, K, η production channels( ν). T. Sato (Osaka U.) νd June / 33

5 Single pion production ν µ + p µ + π + + p, ν µ + n µ + π + + n, ν µ + n µ + π + p, ν µ + n µ + + π + n ν µ + p µ + + π + p ν µ + p µ + + π + n Cross sections σ(e ν), dσ dq 2, dσ dw πn, dσ dw πn dq 2 dω π T. Sato (Osaka U.) νd June / 33

6 Data on single pion production Data on Neutrino induced Single pion production ( π 2π GGM Lerche 978 ν Propane - Bolognese 979 ν Propane-Freon -7.5 BEBC Allen 986 ν p -8 Allasia 99 ν, ν d 5-5 BNL Kitagaki 986 ν d ANL Barish 979 ν p,d.4-6 Radecky 982 ν d Day 983 ν d FNAL Bell 978 ν p 5-4 SKAT Ammosov 988 ν Freon(CF 3 Br) 4-8 Grabosch 989 ν, ν Freon(CF 3 Br) Reanalysis of ANL/BNL data (C. Wilkinson et al. PRD9 (24), P. Rodrigues, C. Wilkinson, K. McFarland, EPJC76 (26)) T. Sato (Osaka U.) νd June / 33

7 models of pion production are tested against ANL/BNL data. σ [ 38 cm 2 ] HNV ν μ p μ pπ +, W πn <.4 GeV E ν [GeV] 2 σ [ 38 cm 2 ] BNL ν μ p μ pπ +, W πn < 2 GeV E ν [GeV] Events/.5GeV Q 2 [GeV 2 ] σ(νn) exp are extracted from νd data without taking into account FSI. < F j µ CC I > < (πnn) P LW j µ CC d > T. Sato (Osaka U.) νd June / 33

8 It is well known FSI is important for γd π pn and not so important for γd π pp. (channel dependent role of FSI ) dσ more than 3% effects of FSI on pion angular distribution around QE de µdω µdω π production kinematics have been pointed out. Jia-jun Wu, T. -S. H. Lee, T. Sato PRC9 (25) in this talk Extend our previous analysis to cover whole phase space of µ πnn to examine how important final state interaction in ν + d l + π + N + N. Try to extract σ(νn) from νd data without full microscopic calculation. T. Sato (Osaka U.) νd June / 33

9 Model of meson production < MB J α N µ > J em µ = V µ 3 + V µ IS J µ CC = V µ +i2 Aµ +i2 ( S = current without CKM) J µ NC = V µ 3 Aµ 3 2 sin2 θ W J µ em 2 sγµ ( γ 5 )s meson production through resonance excitation and non-resonant mechanisms. model should be constrained as much as possible by existing data on pion, photon and electron induced reactions. T. Sato (Osaka U.) νd June / 33

10 ANL-Osaka model Model developed for N physics: spectrum of N, (W < 2GeV ),transition form factors Fock-Space:isobar(N, ), Meson-Baryon (πn, ηn, KΛ, KΣ, ππn(π, ρn, σn)) Coupled-channel(Lippmann-Schwinger)equation is solved numerically. s-channel u-channel t-channel contact coupledchannels effect N* bare analyze available data on pion, photon, electron induced meson production πp πn, ηn, KΛ, KΣ γp/n πn, ηn, KΛ, KΣ ep e πn resonance spectrum and coupling constants, form factors at resonance pole are extracted from the analytic continuation of the amplitude. neutrino reaction: Axial vector current : ga NN from gπ NN assuming PCAC and dipole form factor, except (232). T. Sato (Osaka U.) νd June / 33

11 dσ/dw πn of single pion production E ν = 4GeV 6 Axial Vector Neutrino anti-neutrino BEBC NP343,285(99) (232) gives most important contribution for all channels. One can make only qualitative test of model for W dependence. T. Sato (Osaka U.) νd June / 33

12 comparison of models I : total cross section of single pion production J. E. Sobczyk, E. Hernandez, S. X. Nakamura, J. Nieves, T. Sato : ANL-Osaka HNV: E. Hernandez, J. Nieves, M. Valverde single pion production in region non-resonant interaction from chiral Lagrangian Unitarity (Satisfy Watson theorem for P 33 ) T. Sato (Osaka U.) νd June / 33

13 σ [ 38 cm 2 ] HNV ν μ p μ pπ +, W πn <.4 GeV E ν [GeV] σ [ 38 cm 2 ] ν μ p μ pπ +, W πn < 2 GeV E ν [GeV] σ [ 38 cm 2 ] σ [ 38 cm 2 ] HNV ν μ n μ nπ +, W πn <.4 GeV E ν [GeV] HNV ν μ n μ pπ, W πn <.4 GeV E ν [GeV] σ [ 38 cm 2 ] σ [ 38 cm 2 ] ν μ n μ nπ +, W πn < 2 GeV E ν [GeV] ν μ n μ pπ, W πn < 2 GeV E ν [GeV].9g AN T. Sato (Osaka U.) νd June / 33

14 comparison of models II : Angular distribution of pion production off nucleons dσ CC dw πn dq 2 dω π = G2 F W πn [A + B cos ϕπ + C cos 2ϕπ + Dsin ϕπ + Esin 2ϕπ] 4πMk2 T.Sato, D. Uno, T. -S. H. Lee (23), E. Hernandez, J.Nieves, M. Valverde, PRD76, 335 (27) parity violating T-odd angular distributions are generated. angular distribution pion may reveal differences among models that are not seen well in integrated cross sections. k π Y * φ* π X * k θ θ* π Z * k q PV: sin ϕ π k k k π T. Sato (Osaka U.) νd June / 33

15 A [MeV] E= GeV W πn=.23 GeV Q 2 =. GeV 2 /c 2 ν ep e pπ + ν en e nπ + ν en e pπ HNV 2 HNV 24 HNV 9 22 SL 8 8 SL SL B [MeV] HNV SL HNV SL HNV SL C [MeV] HNV 4 SL HNV HNV SL 5 5 SL D [MeV] 2 5 HNV 5 SL HNV 4 2 SL HNV SL E [MeV] 35 HNV 3 25 SL cos θ π HNV 2 4 SL cos θ π HNV SL cos θ π T. Sato (Osaka U.) νd June / 33

16 φ π HNV ν e p e pπ HNV ν e n e nπ HNV ν e n e pπ φ π ν e p e pπ cos θ π Nr of events ν e n e nπ cos θ π ANL ν μp μ pπ + Nr of events ν e n e pπ.5.5 cos θ π cos θ π φ π Nr of events HNV HNV 8 HNV BNL ν μp μ pπ + Nr of events cos θ π φ π T. Sato (Osaka U.) νd June / 33

17 Neutrino induced pion production on deuteron how important final state interaction in ν + d l + π + N + N? simple recipe to extract σ(νn) from νd data? T. Sato (Osaka U.) νd June / 33

18 leading order terms of FSI [πnn] P LW > ( + G T NN + G T πn ) [πnn] P LW > (IA) NN resc. πn resc. note: Above rescattering terms are the leading order of multiple scattering theory(faddeev Eq.). More elaborate description of three-body(πnn) dynamics may be possible( A. Matsuyama T.-S.H.Lee PRC34(986), M. Schwamb Phys. Rep. 485(2)) Meson exchange current is not considered. TS,K.Koshigiri, H. Ohtsubo,Z.Phys.A32(985) T. Sato (Osaka U.) νd June / 33

19 Example of NN rescattering amplitude J NN resc µ = < [πnn] P LW t NN G J CC µ d >= spin,isospin N (p ) N 2 (p 2 ) t NN (M N N 2 ) Ñ (q k + l) N 2( l) π(k) Ñ (q k + l) Jµ(W, q) N (l) E E N (q k + l) E N ( l) E π(k) + iϵ N (l) N 2 ( l) Ψ d(s d ) dl ANL-Osaka model: J µ CC, t πn Bonn-NN-potential: t NN 3dim loop integration + 7-dim phase space(monte-carlo) T. Sato (Osaka U.) νd June / 33

20 Effects of FSI on γd πnn S. X. Nakamura et al. arxiv E γ = 35 MeV E γ = 53 MeV (x 3) E γ = 66 MeV (x 5) dσ/dω c (µb/sr) 3 2 dσ/dω c (µb/sr) E γ = 75 MeV E γ = 765 MeV E γ = MeV θ π, c (deg) θ π, c (deg) θ π, c (deg) 2 E γ = 3 MeV E γ = 5 MeV E γ = 7 MeV dσ/dω (µb/sr) E γ = 95 MeV E γ = 5 MeV θ π (deg) dσ/dω (µb/sr) θ π (deg) θ π (deg) Large FSI for π production. 3 S scattering state is orthogonal to deuteron bound state. (in DW, deuteron component is eliminated from NN PLW.) T. Sato (Osaka U.) νd June / 33

21 4 dσ/dω c (µb/sr) 3 2 E γ = 35 MeV E γ = 53 MeV (x 3) E γ = 66 MeV (x 5) dσ/dω c (µb/sr) cos θ π, c cos θ π, c E γ = 75 MeV E γ = 765 MeV E γ = MeV - cos θ π, c E γ = 3 MeV E γ = 5 MeV E γ = 7 MeV dσ/dω (µb/sr) 2 E γ = 95 MeV E γ = 5 MeV cos θ π dσ/dω (µb/sr) 5 - cos θ π cos θ π - T. Sato (Osaka U.) νd June / 33

22 momentum distribution of spectator nucleon (ν + d µ + π + + p + n) separate proton and neutron π + production reaction dσ/dp n ( -38 cm 2 /GeV) Fermi motion in d IA(ν µ p --> µ - π + p) p n (MeV) /dp p(-38cm2/gev) d.2 IA p p (MeV) neutron spectator(p π + p) proton spectator(n π + n) p π + p (n π + n) mechanism is dominated in p n < 5MeV (p p < 5MeV ). ( momentum of muon and pion are integrated) T. Sato (Osaka U.) νd June / 33

23 Effects of FSI ν µ + d µ + π + + p + n (E ν =.5GeV ) neutron spectator proton spectator dσ/dp n ( -38 cm 2 /GeV) p n (MeV) dσ/dp p ( -38 cm 2 /GeV) p p (MeV).2.9. σ x /σ IA IA+NN/IA IA+NN+piN/IA p n (MeV) σ x /σ IA IA+NN/IA IA+NN+piN/IA p p (MeV) T. Sato (Osaka U.) νd June / 33

24 Effects of FSI ν µ + d µ + π + + p + n (E ν = GeV ) neutron spectator 7 proton spectator.2 dσ/dp n ( -38 cm 2 /GeV) p n (MeV) IA/IA (IA+NN)/IA (IA+NN+πN)/IA dσ/dp p ( -38 cm 2 /GeV) p p (MeV) about (5 3) % FSI effects depending on E ν, p s and channel. T. Sato (Osaka U.) νd June / 33

25 ) N α (E ν ) parametrization of FSI dσ νd (E ν) N dσ νn α(e ν) dp s dp s dσ νn = p 2 s dω ps σ α(ẽν) ψ d( p s) 2 dp s.95 N (E E (GeV) Ideally, one fit data using amplitude with FSI calculated by model of elementary amplitude. N α : fitting our spectator distribution with FSI for p s < 5MeV by using our convoluted cross section. T. Sato (Osaka U.) νd June / 33

26 Summary Pion angular distribution in region is discussed in ANL-Osaka model and HNV model. angular distribution is sensitive to interference among partial wave amplitudes, phase of amplitudes, non-resonant mechanism. parity violating T-odd correlation shows up with non-negligible strength. Role of FSI is examined within the first order rescattering correction. pion photoproduction on deuteron is reasonably well described in model+fsi. FSI for the spectator momentum distribution of νd: FSI can be as large as 3% effect depending on E ν, p s, channel. Main mechanism of FSI: NN rescattering(pπ +, nπ + ) πn rescattering (nπ + ) FSI is small for π production. Acknowledgments KAKENHI JP255,JP6K T. Sato (Osaka U.) νd June / 33

27 Backup T. Sato (Osaka U.) νd June / 33

28 Full amplitude is needed, not res-only P 33 P W[Mev] fort. u :2:5 f-p u :2:5 W[Mev] T. Sato (Osaka U.) νd June / 33

29 Approximate relation between structure functions F CC 3 and F γz 3 (F α i = (F α ip + F α in )/2) 2F γz 3 = F3 CC V IV (A IV ) 2F γz 3 F3 CC u ū + d d PDF * W γn 3 can be used to test F CC 3 for neutrino reaction. T. Sato (Osaka U.) νd June / 33

30 e 2 C ex(e e =.96,.,.3 GeV,θ e = 37.5 o ) A d 2 σ/dωde (nb/gev sr) A d 2 σ/dωde (nb/gev sr) A d 2 σ/dωde (nb/gev sr) W [GeV] W [GeV] A - d 2 σ/dω de ( -38 cm 2 /GeV sr) W [GeV].8.6 θ= o W [GeV] B. Szczerbinska, T. Sato, K. Kubodera, T.-S. H. Lee, PLB649(27) 32 T. Sato (Osaka U.) νd June / 33

31 L µν W µν = Q 2 [R T + ϵr L + 2ϵ( + ϵ)r LT cos ϕ π + ϵr T T cos 2ϕ π ϵ 2 s N,s N + 2ϵ( + ϵ)r LT sin ϕ π + ϵr T T sin 2ϕ π] where R T = jx c 2 + j y c 2 2 ϵ 2 Im(j x c j y c ), R L = Q2 qc 2 j c 2, Q R LT = 2 ϵ qc 2 [ Re( j c jc x ) ± + ϵ Im( j c jc y )], R T T = ( jx c 2 jc y 2 ), 2 Q R LT = 2 ϵ qc 2 [Re( j c jy c ) ± + ϵ Im( j c jx c )], R T T = Re(j x c jy c ), ϵ = + 2 q 2 Q 2 tan 2 θ l 2 T. Sato (Osaka U.) νd June / 33

32 Axial vector current at Q 2 = Axial Vector current F2 CC at Q 2 = Proton Neutron Total Using PCAC, F CC 2 (Q 2 = ) = 2f 2 π π σ(virtualπ + N) open box, green cross are data. pi-n final T. Sato (Osaka U.) νd June / 33

33 Vector current at large Q LO Parton Model CLAS data J JJJJJJJJ J Our RES Model JJ J J J JJJ J J J JJJJ JJ J J J JJ JJJJJJJJJ J JJJ J JJ J JJJJJJJ d σ/d Ω d E (µb/sr GeV).2. Q 2 = (GeV/c) 2 θ e =2.45 o W (GeV) description of ep in RES, smoothly connected to DIS 2pi pi T. Sato (Osaka U.) νd June / 33