Parity violating neutron spin asymmetry of process in pionless effective theory Jae Won Shin Collaborators: Shung-Ichi Ando 1), Chang Ho Hyun 1), Seung-Woo Hong Department of Physics, Sungkyunkwan University, Korea 1) Department of Physics Education, Daegu University, Korea The 5 th Asia-Pacific Conference on Few-Body Problems in Physics 2011(APFB 2011)

OUTLINE 1. Introduction 2. Effective Lagrangian 3. Results 4. Summary

1. Introduction Radiative neutron capture on a proton at BBN energies 1) neutron-neutron fusion 2) neutral pion production in proton-proton collision near threshold 3) proton-proton fusion 4) 1) S. Ando et al., Phys. Rev. C 74, (2006). 2) S. Ando and K. Kubodera, Phys. Lett. B 633, 253 (2006). 3) S. Ando, Eur. Phys. J. A 33, 185 (2007). 4) S. Ando et al., Phys. Lett. B 668, 187 (2008). Pionless Effective Field Theory with dibaryon field (dEFT) approach  Pion (heavy degree of freedom) → integrate out  Expansion of Q/Λ (Q: light, Λ: heavy)  fast conversions Applications for low energy nuclear physics

Extend the dEFT works, “parity violating (PV) interaction” was considered. 5) M. J. Savage, Nucl. Phys. A 695, 365 (2001). 6) C. H. Hyun, J. W. Shin and S. Ando, Modern Phys. Lett. A 24, 827 (2009). 7) S. Ando, C. H. Hyun and J. W. Shin, Nucl. Phys. A 844, 165c (2010). 8) J. W. Shin, S. Ando and C. H. Hyun, Phys. Rev. C 81, (2010). 9) S. Ando et al., Phys. Rev. C 83, (2011). - Neutron spin polarization P y’ [P x’, P z’ = 0 (chosen coordinate)] - Only parity conserving part contribute ! However, -P x’ and P z’ ≠ 0 with parity violating interactions -P z’ ( in this work) Recent work PV asymmetry in Neutron spin polarization in From these works, unknown LEC h 0t dNN, h 0s dNN and h 1 dNN are appearing. Not yet were determined ! at thermal energies 5) PV polarization inat threshold 6-8) 9)

In this work, We consider the two-nucleon weak interactions with a pionless effective field theory. Introducing a di-baryon field for the deuteron, we can facilitate the convergence of the theory better than the one without di-baryon fields. dEFT Standard way Contact interactions (LEC) Exchange of π, ω, ρ meson Weak interactions The weak interactions are accounted for with the parity-violating di-baryon- nucleon-nucleon vertices, which contain unknown weak coupling constants. We calculate the parity-violating neutron spin asymmetry in process, where we consider incident photon energies up to 30~MeV.

a) Parity conserving part of the Lagrangian 2. Effective Lagrangian

b) Parity violating part of the Lagrangian 1 S 0 ↔ 3 P 0 3 S 1 ↔ 1 P 1 3 S 1 ↔ 3 P 1 : Odd at a PV vertex : Even Unknown LECs

3. Results Leading order (Q 0 ) PV diagrams Single solid line : nucleon Wavy line : photon Double line with a filled circle : dressed dibaryon Blue circle : PC dNN vertex Circle with a cross : PV dNN vertex ∨ PC dNN vertex ∝ Q 1/2 ∨ Photon, derivative ∝ Q 1 ∨ Nucleon, Dibaryon propagator ∝ Q -2 ∨ Loop ∝ Q 5 * Counting rules

Amplitude χ 1, χ 2 : nucleon spinors ɛ (d) : deuteron polarization vector ɛ (γ) : photon polarization vector

A = A PC + A PV |A PC* A PV | interference term |A PC | 2 term * |A PV | 2 terms are ignored. PV LECs ∝ |A PV | 2 term ∝ P z’

 Coefficients of h010, h001 shows same feature. As the angle (lab) increase, dependency of the incident photon energies (lab) of neutron spin polarization decrease.  But, coefficient of h100 seem to be seen angle (lab) independent. h100 : Coefficient of h 0t dNN h010 : Coefficient of h 0s dNN h001 : Coefficient of h 1 dNN Preliminary results

Θ lab increase → E1 contribution increase → M1 contribution decrease (go to zero) For Θ lab = 90° → E1 contribution dominants ! Cancelation between E1 and M1 ~ nearly constant h100 : Coefficient of h 0t dNN Preliminary results

Θ lab increase → E1 contribution increase → M1 contribution decrease For Θ lab = 90° → E1 contribution (65% ?) h010 : Coefficient of h 0s dNN Preliminary results

Θ lab increase → E1 contribution increase → M1 contribution decrease (go to zero) For Θ lab = 90° → E1 contribution dominants ! For Θ lab = 30° → M1 contribution dominants ! h001 : Coefficient of h 1 dNN Preliminary results

The weak interactions are accounted for with the parity-violating di-baryon- nucleon-nucleon vertices, which contain unknown weak coupling constants. We calculate the parity-violating neutron spin asymmetry in process, where we consider incident photon energies up to 30~MeV. 4. Summary Overall characteristics, Θ lab increase and E1 contribution increase but M1 contribution decrease. M1 contribution gives significant role for PV neutron spin polarization. A possible experiment or theory from which one can get information about the unknown weak coupling constants and hadronic weak interactions is discussed.

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