Pion production in nucleon-nucleon collisions at low energies: status and perspectives

Transcription

1 Pion production in nucleon-nucleon collisions at low energies: status and perspectives Vadim Baru Forschungszentrum Jülich, Institut für Kenphysik (Theorie), D-545 Jülich, Germany ITEP, B. Cheremushkinskaya 5, 78 Moscow, Russia INT, Seattle, April 3, in collaboration with E. Epelbaum, A. Filin, J. Haidenbauer, C. Hanhart, A. Kudryavtsev, V. Lensky and U.-G. Meißner Related works: EPJA 7, 37 (6); PRC 8, (9) 443; Phys. Lett. B 68, (9) 43

2 NN NNπ. Motivation Study of π production in NN collisions: test of ChPT in the process with large momentum transfer allows for determination of LECs ((N N) π contact term) = direct connection to other low-energy processes key to dispersive corrections to πd scattering: πd NN πd (our work 7) = extraction of s-wave πn scattering lengths from data on π p and π d atoms (V.B., C.Hanhart, M.Hoferichter, B.Kubis, A.Nogga, D.Phillips ()) accurate data are available due to COSY; IUCF; TRIUMF, Uppsala Isospin Conserving π-production: necessary for studying isospin violation (IV) pn dπ : Opper et al. (3), v.kolck et al (), Bolton and Miller (9), A. Filin et al. (9) dd απ : Stephenson et al.(3),gårdestig et al.(4); Nogga et al.(6),fonseca et al. (9)

3 CSB effects and neutron-proton mass difference δm str N and δm em N Possibilities to determine δm str N δm N = m n m p = δm str N + δmn em =.9 MeV contribute to different low-energy reactions and δm em N : Cottingham sum rule provides an electromagnetic contribution to the nucleon self mass: δmn em = (.7 ±.3) MeV = δmn str = (. ±.3) MeV (Gasser, Leutwyler (98)) Weinberg s idea (977): large CSB effects in π processes, e.g., a π p a π n a π p a π n = 4π( + M π/m N )fπ δmn str + O(q 4 ) (Meißner, Steininger (998)) However, experimentally very difficult, if possible! Forward-backward assymetry in pn dπ can serve to pin down δmn str δmn em (v.kolck, Miller, Niskanen ()) dd απ (Stephenson et al.,gårdestig et al.; Nogga et al.,fonseca et al. ) lattice calculations (Beane et al. (7)) and

4 CSB effects in pn dπ dσ dω (θ) = C + C P (cos θ) +... A fb = π/ π/ ( dσ dσ dω (θ) dω (π θ)) sin θdθ ( dσ dσ dω (θ) + dω (π θ)) sin θdθ dσ dσ (θ) (π θ) dω dω = C C experiment: (Opper et al., TRIUMF (3)) measurement at T lab = 79.5 MeV (threshold T lab = 75. MeV), η = k π/m π =.7 A fb = (7. ± 8 ± 5.5) 4

5 CSB effects in pn dπ. Theory A fb = C C Near threshold regime (η =.7) = s- and p-wave pion productions only: IC 3 P 3 S s IV P 3 S s S 3 S p D 3 S p 3 S 3 S p 3 D 3 S p 3 D 3 S p M pn dπ = M IC,s [ S n] ε d +M IC,p (ˆk S π ε d )+M»( nˆk IC,p D π)( n ε d ) 3 (ˆk π ε d ) +Ms IV ( n ε d ) + theory: C Re M IV s wavem IC p wave + Re M IV p wavem IC s wave LO... N LO... C total cross section, basically 3 P 3 S s

6 Pion reactions on few-nucleon systems ChPT treatment (Weinberg 99) expand the transition operator using ChPT. Include irreducible graphs only. ChPT natural expansion parameter χ q Λ ChPT Mπ m N ; each graph gets its chiral order according to the counting rules; A = C + C χ + C χ + + non-analytic terms convolute with the (non-perturbative) wave functions A is perturbative Ψ i A Ψ f Ψ i/f are treated non perturbatively successful application to many low-momentum transfer reactions, for instance: πd πd Weinberg, Gasser et al, Beane et al, Meißner et al, our works π 3 He π 3 He, π 4 He π 4 He our works γd πnn our works πd γnn Gårdestig and Phillips γd π d Beane et al, Krebs et al.

7 Power Counting, NN NNπ Ψ i A Ψ f Naive application of the Weinbergs s P.C. (with q M π) to NNπ = disaster! (Park et al. (996), Hanhart et al. (998)) NLO corrections increase discrepancy with the data N LO terms are larger than those at NLO. Modified power counting Cohen et al. (996); Hanhart et al. () new small scale in the production operator: p M πm N initial NN momentum in c.m.s s-wave pion: χ p m N r Mπ m N p-wave pion: k π M π χ kπ p p m N r Mπ m N

8 s-wave pion production up to NLO p LO p p p p p p p a b c c d d NLO reducible pp dπ + : pp ppπ : NLO contribution Hanhart, Kaiser () A a+b+c dπ + = g3 A q ( σ 56fπ 5 + σ ) q, A a+b+c = ppπ q = p p Ψ d A a+b+c dπ + growing operator = large sensitivity to the NN w. f. Gårdestig, Phillips, Elster (5) p

9 pp dπ +, s-wave pion production (our work 6) σ/η [µb] 3 p m π LO p p p p p a b c c NLO contribution A a+b+c+d(irr)+d(irr) = g3 A q ( σ dπ + 56fπ 5 + σ ) q Koltun and Reitan PSI 998 (pionic deuterium) PSI 9 (pionic deuterium).5..5 η=k π /m π NLO p d p d «= 4 Theoretical uncertainty is O( mπ m N ) 3%. N LO calculation is necessary to reduce the uncertainty important for IV. N LO pp ppπ in progress (our group, Kim et. al (9))

10 p-wave pion production in NN NNπ (our work (9)) LO NLO N LO first calculation: pp pnπ + channel (Hanhart, Miller, v.kolck ()) Our goals: to study different channels: pp dπ +, pp pnπ + and pn ppπ to see if it is possible to describe them simultaneousely with only one unknown (N N) π LEC d to investigate convergence of the chiral expansion to obtain accurate p-wave amplitudes necessary for CSB studies L () =» L () = N ga τ σ π N + h h A N (T S π)ψ i + h.c. +, f π f π + 8m N fπ (in τ (π π) N + h.c.) fπ c 4 + 4M N N» c 3 ( π) «ε ijk ε abc σ k τ c i π a j π b N d f π N (τ σ π)n N N +.

11 p-wave pion production and (N N) π LEC ΝΝ ΝΝ π Hanhart et al. () Nakamura (8) this study (9) π d γ ΝΝ o Gardestig,Phillips (6) γ d πνν our work (6) ΝΝ d e ν o Gardestig, Phillips (6) Park et al. (3) Nakamura (8) pd pd Epelbaum () Nogga et al. (6) Gazit et al. (9) Low-momentum transfer: NN deν, µd ν µnn, πd γnn, γd πnn, pd pd,... Large-momentum transfer: NN NNπ Nakamura (8): pp de + ν, pp pnπ + Conclusion: failure of simultaneous description

12 (N N) π LEC d in NN NNπ pp dπ +, pp pn + π pn pp π p p p p S p large 3 3 S S S Ψ d(λ) p p p small large small Ψ (r = ) d(λ) Ψ (r = ) (r = ) Ψ (r = ) Ψ q(r = ) + m N Description with the same LEC d non trivial test of consistency Z Why do we expect this to work? 8 >< d 3 T (p, q, q) p A = C(Λ) exp q p + i >: π energy dependence of Ψ q() model independent C(Λ) model dependent C S (Λ) and C3 S (Λ) are absorbed in d Z 4m N 9 >= ds δ NN (s ) s s(q) + i >;

13 p-wave pion production mechanism LO NLO N LO d: S 3 S p in pp pnπ + /dπ + d: ( 3 D 3 S ) S p in pn ppπ d=d(λ) depends on the regularization scheme and type of NN interaction d absorbs the short-range part of the production operator c3 A ci + c 4 + «( p ) const + O(N 4 LO) 4m N ( p ) + Mπ LEC d absorbs A ci

14 NN NNπ, Results (our work (9)) pp dπ + Ay d=3 d=-3 d= η= θ π Ay (9) Korkmaz Mathie Heimberg Positive d 3 is clearly preferred..4 η

15 NN NNπ, Results (our work (9)) pp dπ + Ay d=3 d=-3 d= η=.4 Ay (9) θ π η pn ppπ (η =.6), M pp.5 MeV ( 3 S 3 D ) S p Korkmaz Mathie Heimberg d σ/dο π dm pp [pb/mev sr] TRIUMF (998) 3-3 A y TRIUMF (998) PSI () our theory (9) θ cos θ π π New measurement of pn ppπ at different energies (ANKE at COSY ) IMPORTANT! Positive d 3 is clearly preferred

16 pn ppπ, Measurement at COSY Analyzing power at Tlab MeV (ANKE (), S.Dymov et al.: PRELIMINARY).5 A y Positive d 3 is clearly preferred -.5 ANKE (PRELIMINARY) our theory (9) cos θ π Prediction for double polarization observables A xz -.4 A xx -.5 d=3 d= d= θ θ Measurement: dσ/dω( A xx ) C C /3 sin (θ) direct access to p-wave amplitudes C (d) and C (d). ( V.B., S.Dymov, C. Hanhart, A. Kacharava, Yu. Uzikov, C. Wilkin)

17 pp pnπ +, Results (our work (9)) A y (9 ) C C «dσ dω = C + C P (cos θ) +... C = a + a + a + C I=, 4 C = a Re[a a ], 4 = 4 ( Im[a a ] + Im[a a ]). a : S 3 S p a : D 3 S p a : 3 P 3 S s IUCF, Flammang et al. (998) C (µb). -A y (9 o ) (C -C /) η influence of Pp states needs to be understood η We can describe all channels of NN NNπ with the same LEC d!

18 pp pnπ +, Partial wave analysis Flammang et al (998) Drawbacks of PWA old pp ppπ data were used to extract C I=. New data (COSY 3) are 5% larger! C I= is not corrected for the difference between pp and pn interactions at low energies: a pp 7.8 fm a pn 3.7 fm Integrated ratio of the Jost functions: No Pp states R dτ3 F pn(p) R = R.5 for η =. dτ3 F pp(p) a Nakamura η Nakamura s result: failure of bridging program between pp fusion and NNπ Conclusion is based on wrong PWA!

19 s- and p-wave isospin conserving pion production is under control. Next goal: Charge Symmetry Breaking effects

20 CSB effects in pn dπ. Power counting CSB operators for s-wave pion up to N LO +... (a) (b) L () IV LO N LO» L () IC = N τ ( π π) + g A τ σ 4Fπ F π N +, π = δm N N τ 3 N δmstr N 4F π N τ ππ 3 N δmem N 4Fπ N (τ 3 π τ ππ 3 )N +... No terms at NLO = theoretical uncertainty of LO calculation is χ Mπ m N 5% IV p-wave pion starts from N LO.

21 CSB effects in pn dπ. Additional IV operator at LO. New contribution from diagram (b) at LO (our work (9)) πn Lagrangians relevant at LO: L () iv (a) = δmstr N 4Fπ (b) N τ ππ 3 N δmem N 4Fπ L () WT = N τ ( π π)n 4Fπ N (τ 3 π τ ππ 3 )N WT Lagrangian is time-dependent = vertex q + M π depends on δm N through q π n π p V WT = i 4f π 3mπ δm N π p π + n V WT = i 3mπ 4fπ δm N p (b ) n n (b ) Terms δm N add up! p

22 CSB effects in pn dπ. Our results Filin et al. (9) Strategy: To minimize the theoretical uncertainty of IC amplitudes as much as possible using data! IC p-wave (N LO) calculation very good description of data take C directly from data on pionic deuterium atom σ(nn dπ ) = 5 +5 η [µb] perform complete LO calculation of CSB amplitudes + δm str N «δmem N + δmstr N + δm em N 3 δmstr N Our LO result: A fb = (.5 ± 3.5) 4 δm str N δmn str = (.5 ±.8 (exp.) ±.5 (th.)) MeV pn dπ at LO δmn str = (. ±.3) MeV Gasser and Leutwyler δmn str = (.6 ±.57 ±.4 ±.) MeV lattice data Beane et al.(7)

23 CSB effects in pn dπ. Comparison to other works 7 6 v.kolck, Miller, Niskanen () 5 Bolton, Miller (9) A fb x our results (9) δm str N =. MeV TRIUMF (3) CSB at LO (Bolton and Miller): main origins of discrepancies with our results s- and p-wave IC amplitudes are calculated at NLO = 3% +5% uncertainties in A fb -isobar contribution at NLO to the p-wave amplitudes is too large = phenom. formfactors with Λ 4 MeV are introduced. Still A y in pp dπ + is overestimated by about 3%.

24 NN NNπ. Summary and Outlook s-wave production, NLO calculation quantitative understanding of pp dπ + with 5% uncertainty in the amplitude p-wave production, N LO calculation studying different channels of NNπ simultaneously good test for LEC (N N) π in different kinematic regimes good overall description of all channels with the same LEC! chiral expansion indeed converges in accordance to power counting CSB effects in pn dπ, LO calculation unique opportunity to extract δm str N δm str N from a dynamical process: = (.5 ±.8 (exp.) ±.5 (th.)) MeV Non-trivial consistency with the Cottingham sum rule and lattice results

25 NN NNπ. Outlook We are on the way to control pion dynamics in NN NNπ Further steps and future plans pp ppπ still needs to be understood. N LO is in progress (Kim et al. (8), our group) N LO calculation for pp dπ + (in progress) and CSB effects for pn dπ together with dd απ NN NNπ + pp de + ν + within the same framework is interesting! results from ANKE are highly awaited pn ppπ at low energies is the best chance to fix 4Nπ CT in NN NNπ planned measurements of spin-correlation coefficients, A y and dσ/dω for pn ppπ and pp ppπ would allow for a partial wave analysis extension of ChPT NN interaction above pion threshold