1. Parity-violating NN interaction from different approaches Chang Ho Hyun with B. Desplanques Universite Joseph Fourier S. Ando Manchester C.-P. Liu Wisconsin-Madison 13 November, 2007

2. Contents Effective field theory Covariant formalism Summary

3. 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 amount of terms (diagrams) not considered.  Low energy constants (LECs) : Make the prediction model- independent 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

4. 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 ; Q 1 ) : 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).

5. 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 LONNLO OPE ~ Q -1 TPE ~ Q 1 CT ~ Q 1

6. 

7.  We introduce form factor and cutoff : monopole form factor.

8. 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

9.  ~  -3

10.  A  A  = a i  1  aiai I.Strong interaction phenomenology : Av18 II.EM operator : E1 ∝ (Siegert theorem) III.Weak potential : LO, NNLO Each contribution Make OPE contribution  independent ->

11. 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.

12.  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)

13.  One-pion iteration subtracted  Relevant to np -> d  Relevant to pp scattering Higher order in 1/M -> Neglect them

15. 

16.  Take large nucleon mass (LM) limit from COV  A 2 discrepancy can be accounted by missing  contribution in COV calculation. -> EFT is equivalent to leading 1/  term in COV. (~1/  3 ) (~1/  4 )

17.  Short-intermediateLong 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 ()2 ()

18. Weak pot.OPETPE-COVTPE-LMTPE+CT(EFT) aa -0.1120.0040.0140.010~0.019 - 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 

19. Summary Two-pion-exchange parity-violating potentials from covariant formalism and effective field theory are compared. Same TPE contribution. a LM 2   a EFT 2  Higher-order corrections are contrasting. a EFT CT  0.1 a EFT 2  : Good convergence. a COV 2   0.3  a LM 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.