Parity-violating Parity-violating NNNN interaction interaction from different approachesfrom different approaches

Chang Ho Hyun with

B. Desplanques Universite Joseph Fourier

S. Ando Manchester

C.-P. Liu Wisconsin-Madison

13 November, 2007

Contents

Effective field theory

Covariant formalism

Summary

• Effective field theory (EFT) in nuclear physics : Successful in describing various strong and electromagnetic few body (2N, 3N, …) processes at low energies.

• Advantage of EFT Perturbative expansion scheme : We can (roughly) estimate the amo

unt of terms (diagrams) not considered. Low energy constants (LECs) : Make the prediction model-independe

nt without the knowledge of short range dynamics.

-> A natural extension of EFT to other realm of interaction :

Parity-violating (PV) interaction from order by order expansion of EFT!

Effective Field Theory

• The first derivation PV two-nucleon (2N) potential from EFT :S.-L. Zhu, C.M. Maekawa, B.R. Holstein, M.J. Ramsey-Musolf, U. van Kolck, NPA748, 435 (2005). Leading order (LO ; Q-1) : one-pion-exchange (OPE) Next-to-next-to leading order (NNLO ; Q1) : two-pion-exchange (TPE) + 4N contact term (CT)

• Re-derivation of the PV potential up to NNLO :

CHH, SA and BD, PLB652, 257 (2007),

and

• Application to physical processes :

CHH, SA and BD, PLB652, 257 (2007),

CPL, PRC75, 065501 (2007).

CHH, SA, BD, PLB651, 257 (2007)

• Observable : PV asymmetry (A) in n p -> d

• Last measurement : (1.5 +- 4.8)x10-8 (Cavainag et al. Can. J. Phys. ’88)

• On-going experiment at SNS aims at unambiguous measurement of A at 10-8 order.

• Strong interaction : Av18• Weak interaction : Heavy baryon chiral perturbation theory

LO NNLO

OPE ~ Q-1 TPE ~ Q1 CT ~ Q1

We introduce form factor and cutoff : monopole form factor.

Maximal (MX) subtraction

Minimal (MN) subtraction

Determination of : Usually in terms of

experiment, but no available data yet in PV observables.-> Assume heavy meson limit :

dependent

~-3

A

A = ai 1

ai

I. Strong interaction phenomenology : Av18

II. EM operator : E1 ∝ (Siegert theorem)

III. Weak potential : LO, NNLO

r

Each contribution

Make OPE contribution

independent ->

Net value

A

1. Contribution of LEC with heavy meson limit amounts to about 30% of that of TPE.

2. Maximum scheme dependence amounts to 25%.

3. Renormalization point dependence gives about 15% uncertainty.

Uncertainty due to short and intermediate range behavior of TPE

and CT potentials.

• No unknown parameter (no LEC)

• Well defined at short range (form factor and cutoff not necessary)

• Can give hints to the magnitude of LECs and their contributions to observables

• Can be a guideline to the behavior of TPE potential in the intermediate range

Covariant Formalism

’• BD, PLB41, 461 (1972)• H.J. Pirner and D.O. Riska, PLB44, 151 (1973)• M. Chemtob and BD, NPA78, 139 (1974)

One-pion iteration subtracted

Relevant to np -> d

Relevant to pp scattering

Higher order in 1/M -> Neglect them

Take large nucleon mass (LM) limit from COV

A2 discrepancy can be accounted by missing

contribution in COV calculation.

-> EFT is equivalent to leading 1/ term in COV.

(~1/3)

(~1/4)

Short-intermediate

Long

1. Long range : COV and LM converges.2. Short range• COV : converges to a finite value,• LM : diverges proportional to - with > 2.-> No need for form factor for COV. -> COV result will be free from cutoff uncertainty.

2 ()

Weak pot.

OPE TPE-COV TPE-LM TPE+CT(EFT)

a -0.112 0.004 0.014 0.010~0.019

- OPE dominating

- TPE-COV : ~5% correction

- TPE-LM : ~13% correction (consistent with EFT TPE)

- NNLO (EFT) : correction in the range 9~17%

※ -intermediate state : negligible (N. Kaiser, PRC76, 047001 (2007))

A

Summary

Two-pion-exchange parity-violating potentials from covariant formalism and effective field theory are compared.

Same TPE contribution. aLM2 aEFT

2

Higher-order corrections are contrasting.

aEFTCT 0.1 aEFT

2: Good convergence.

aCOV20.3aLM

2 : Significant higher corrections.

1 can be determined from measurement of A in n p -> d

with uncertainty about 10%.

More experiments are absolutely wanted for better understanding of the PV interaction.