Parity violating neutron spin asymmetry of process

in pionless effective theory

Jae Won Shin

Collaborators:Shung-Ichi Ando1), Chang Ho Hyun1), Seung-Woo Hong

Department of Physics, Sungkyunkwan University, Korea 1)Department of Physics Education, Daegu University, Korea

The 5th Asia-Pacific Conference on Few-Body Problems in Physics 2011(APFB 2011)

pn dγ

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, 025809 (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, 055501 (2010).

9)S. Ando et al., Phys. Rev. C 83, 064002 (2011).

- Neutron spin polarization Py’ [Px’, Pz’ = 0 (chosen coordinate)]- Only parity conserving part contribute !

However, -Px’ and Pz’ ≠ 0 with parity violating interactions-Pz’ (in this work)

Recent work

• PV asymmetry in

• Neutron spin polarization in

dγ pn

np γd

pn γd

From these works, unknown LEC h0tdNN, h0s

dNN and h1dNN are appearing.

Not yet were determined !

at thermal energies 5)

• PV polarization in at 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.

pn γd

a) Parity conserving part of the Lagrangian

2. Effective Lagrangian

b) Parity violating part of the Lagrangian

1S0 ↔ 3P0

3S1 ↔ 1P1

3S1 ↔ 3P1

)( ISL L : Odd at a PV vertex

: Even

Unknown

LECs

3. ResultsLeading order (Q0) 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

χ1, χ2 : nucleon spinors

ɛ(d) : deuteron polarization vector

ɛ(γ) : photon polarization vector

A = APC + APV

|APC*APV| interference term

|APC|2 term

* |APV|2 terms are ignored.

PV LECs ∝ 10-5

|APV|2 term ∝ 10-10

Pz’

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 h0tdNN

h010 : Coefficient of h0sdNN

h001 : Coefficient of h1dNN

Preliminary results

Θlab increase

→ E1 contribution increase

→ M1 contribution decrease (go to zero)

For Θlab = 90°

→ E1 contribution dominants !

Cancelation between E1 and M1 ~ nearly constant

h100 : Coefficient of h0tdNN

Preliminary results

Θlab increase

→ E1 contribution increase

→ M1 contribution decrease

For Θlab = 90°

→ E1 contribution (65% ?)

h010 : Coefficient of h0sdNN

Preliminary results

Θlab increase

→ E1 contribution increase

→ M1 contribution decrease (go to zero)

For Θlab = 90°

→ E1 contribution dominants !

For Θlab = 30°

→ M1 contribution dominants !

h001 : Coefficient of h1dNN

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

pn γd

Overall characteristics, Θlab 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.

Thank you for your attention !