Satoshi Nakamura (Osaka University) Extracting low-energy h-nucleon scattering amplitude from g d  h n p data Satoshi Nakamura (Osaka University) Collaborators : H. Kamano (KEK), T. Ishikawa (Tohoku Univ.)

Introduction

h N scattering length (ahN) Fundamental quantity in hadron physics Important relevance to the existence of h-mesic nuclei B.E. of various h-mesic nuclei from theoretical calculations Q. Haider and L. Liu, Int.J.Mod.Phys. E24 1530009 (2015)

h N scattering length (ahN) Fundamental quantity in hadron physics Important relevance to the existence of h-mesic nuclei But not well-known Current status Several combined analyses of p N  h N and g N  h N data Re[ahN] = 0.2 ~ 1.1 fm Im[ahN] = 0.2 ~ 0.3 fm (optical theorem) pn  dh data (WASA/PROMICE@COSY) Eur. Phys. J. A 38, 209 (2008) Re[ahN] = 0.4 ~ 0.6 fm ahN determined with indirect information  model dependence Need process that sensitively probes h N  h N scattering but not contaminated by others

Proposed experiment at ELPH@Tohoku Univ. g d  h n p at Eg ~ 0.95 GeV and proton detected at 0o An ideal kinematical setting for extracting h N scattering length h is produced almost at rest  strong h n  h n rescattering is expected p n  h n and NN rescatterings are expected to be suppressed Data still need to be analyzed with reliable model to extract ahN

Dynamical Coupled-Channels (DCC) model for meson productions Kamano, SXN, Lee, Sato, PRC 88, 035209 (2013) PRC 94, 015201 (2016) Developed through fully combined analysis of gN, pN  pN, hN, KL, KS data, W < 2.1 GeV This talk Show DCC model meets requirements to extract ahN from ELPH data Develop g d  h n p reaction model with DCC model as building block Demonstrate model prediction agrees well with g d  h n p data Predict g d  h n p cross sections at ELPH kinematics Study sensitivity of ELPH exp. to ahN and rhN

Dynamical Coupled-Channels model for meson productions

Both on- and off-shell amplitudes are calculated Kamano et al., PRC 88, 035209 (2013) Coupled-channel Lippmann-Schwinger equation for meson-baryon scattering , By solving the LS equation, coupled-channel unitarity is fully taken into account Both on- and off-shell amplitudes are calculated

Kamano et al., PRC 88, 035209 (2013) Coupled-channel Lippmann-Schwinger equation for meson-baryon scattering 1 or 2 bare N* in each partial wave ,

In addition, gN channels are included perturbatively Kamano et al., PRC 88, 035209 (2013) Coupled-channel Lippmann-Schwinger equation for meson-baryon scattering T V , By solving the LS equation, coupled-channel unitarity is fully taken into account In addition, gN channels are included perturbatively T

DCC analysis of gN, pN  pN, hN, KL, KS

DCC analysis of meson production data Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Fully combined analysis of gN, pN  pN, hN, KL, KS data and polarization observables (W ≤ 2.1 GeV) ~ 23,000 data points are fitted by adjusting parameters (N* mass, N*  MB couplings, cutoffs)

Eta production reactions Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Relevant to p n  h n rescattering in g d  h n p reaction

Relevant to p n  h n rescattering in g d  h n p reaction γp  π0p dσ/dΩ for W < 2.1 GeV Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Kamano, Nakamura, Lee, Sato, 2012 Relevant to p n  h n rescattering in g d  h n p reaction

Tested important elementary amplitudes for g d  h n p g p  h p Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Tested important elementary amplitudes for g d  h n p relevant to impulse and h n  h n rescattering mechanisms

Application of DCC model to g d reactions

Model for g d  h n p Impulse NN rescattering pN & hN rescattering TNN p, h g d d d g N  p N, h N amplitude  DCC model p N, h N  h N amplitude  DCC model TNN , deuteron w.f.  CD-Bonn potential (PRC 63, 024001 (2001) ) Off-shell effects are taken into account

Numerical results for g d  h n p

Comparison with data for h angular distribution in g d  h X Very near threshold Data: Hejny et al. Eur. Phys. J. A 13 493 (2002) Significant underestimate of data  Missing contributions Mechanisms Small IA contribution (momentum mismatch) Very large NN rescattering contribution h rescattering effect is also significant Coherent process 3-body hNN correlations  possible virtual pole

Comparison with data for h angular distribution in g d  h X Data: Krusche et al., Phys. Lett. B 358 40 (1995) Prediction is good agreement with data Mechanisms Coherent contribution is small Soundness of model demonstrated ! IA term dominates NN rescattering contribution is small h rescattering effect is not large but important

Numerical results for g d  h n p at ELPH kinematics

g d  h n p at proposed ELPH experiment Kinematics : Eg = 950 MeV, proton at 0o One-to-one relation between Mh n and proton momentum Impulse current dominates h n rescattering (mostly s-wave) gives sizable contribution pN  hN rescattering are small but visible; NN rescattering negligible for Mh n< 1.5 GeV h production suppressed in intermediate Mh n　 deuteron wave function

g d  h n p at proposed ELPH experiment Kinematics : Eg = 950 MeV, proton at 0o hn  hn rescattering (mostly s-wave) gives sizable (-40% ~ +20% ) contribution pN  hN rescattering are smaller but visible; data exist  controllable contribution NN rescattering negligible for Mh n< 1.5 GeV  more multiple rescattering expected for Mh n> 1.5 GeV Data for Mh n< 1.5 GeV will be useful to study hN scattering

h n  h n s-wave amplitude Definition Effective range expansion (ERE) a : scattering length r : effective range a = 0.7 + 0.3 i fm r = –1.9 – 0.5 i fm (DCC model) ERE is valid for W < 1550 MeV where h n rescattering is important off-shell-ness of h n  h n s-wave amplitude turns out to be small effect on g d  h n p at ELPH kinematics hn  hn amplitude in g d  h n p can be replaced with ERE and study ER parameter dependence ~

Re[ahN]-dependence of g d  h n p at ELPH exp. Kinematics : Eg = 950 MeV, proton at 0o Im[a]=0.25 fm, r = 0 g d  h n p at ELPH exp. kinematics has a good sensitivity to Re[ahN] D (Re[ahN]) ~ 0.2 fm seems possible with 5% precision cross section measurement Well-tested elementary amplitudes for g p  h p and p N  hN are essential

Im[ahN]-dependence of g d  h n p at ELPH exp. Kinematics : Eg = 950 MeV, proton at 0o Re[a]=0.6 fm, r = 0 Im[ahN] seems difficult to determine better than before with g d  h n p at ELPH kinematics ; Im[ahN] has been already determined better than 0.1 fm

Re[rhN]-dependence of g d  h n p at ELPH exp. Kinematics : Eg = 950 MeV, proton at 0o a = 0.75 + 0.25 i fm, Im[r] = 0 g d  h n p at ELPH exp. kinematics has some sensitivity to Re[rhN] D (Re[rhN]) ~ 1 fm seems possible with 5% precision cross section measurement

Conclusion

Conclusion ✓ Dynamical coupled-channels (DCC) model developed  analysis of g N, pN  pN, hN, KL, KS data ✓ DCC model applied to photo-reactions on the deuteron * impulse, NN and meson-nucleon rescattering mechanisms * g d  h n p data well reproduced for Eg = 700 ~ 800 MeV ✓ g d  h n p at ELPH exp. kinematics studied with the DCC model * impulse dominates; g p  h p elementary amplitude needs solid validation * h n  h n rescattering effect is sizable (-40% ~ +20%) at low Mh n * p n  h n effect is small and NN rescattering effect is negligible for Mh n < 1.5 GeV * g d  h n p at ELPH setup has sensitivity to h n scattering length & effective range better than the current range ~

BACKUP

Partial wave amplitudes of p N scattering Real part Kamano, Nakamura, Lee, Sato, PRC 88 (2013) Previous model (fitted to pN  pN data only) [PRC76 065201 (2007)] Imaginary part Data: SAID pN amplitude

g d  p N N Purpose : test the soundness of the model Data: EPJA 6, 309 (1999) Data: NPB 65, 158 (1973) Model prediction is reasonably consistent with data Large NN (small pN) rescattering effect for p0 production orthogonality between deuteron and pn scattering wave functions Small rescattering effect for p- production

h n  h n s-wave amplitude Re[a]-dependence of FhN Im Re Q : Can we discriminate h n scattering length with g d  h n p data from ELPH ?

Resonance region (single nucleon) gN  X 2nd 3rd D (MeV) Multi-channel reaction  2p production is comparable to 1p  h, K productions (n case: background of proton decay exp.)

“Δ” resonances (I=3/2) “N” resonances (I=1/2) JP(L2I 2J) Kamano, Nakamura, Lee, Sato, PRC 88 (2013) JP(L2I 2J) -2Im(MR) (“width”) Re(MR) PDG: 4* & 3* states assigned by PDG2012 AO : ANL-Osaka J : Juelich (DCC) [EPJA49(2013)44, Model A] BG : Bonn-Gatchina (K-matrix) [EPJA48(2012)5]