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Parity-violating NN interaction from different approaches

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. Contents. Effective field theory Covariant formalism Summary.

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Parity-violating NN interaction from different approaches

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  1. Parity-violating NN interaction from different approaches Chang Ho Hyun with B. DesplanquesUniversite 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 • 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!

  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 ; 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).

  5. OPE ~ Q-1 TPE ~ Q1 CT ~ Q1 LO NNLO CHH, SA, BD, PLB651, 257 (2007) • Observable : PV asymmetry (Ag) in n p -> d g • 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 Ag at 10-8 order. • Strong interaction : Av18 • Weak interaction : Heavy baryon chiral perturbation theory

  6. Potential in momentum space

  7. Potential in configuration space We introduce form factor and cutoff : monopole form factor.

  8. CR6 r Renormalization of LEC Maximal (MX) subtraction Minimal (MN) subtraction m dependent Determination of CR6 : Usually in terms of experiment, but no available data yet in PV observables. -> Assume heavy meson limit :

  9. Numerical Result : OPE and TPE potentials ~r-3

  10. Strong interaction phenomenology : Av18 • EM operator : E1 ∝ (Siegert theorem) • Weak potential : LO, NNLO Numerical Result : PV asymmetry Ag Ag = aih1p ai Each contribution Make OPE contribution L independent ->

  11. Net value • Summary of Ag • Contribution of LEC with heavy meson limit amounts to about 30% of that of TPE. • Maximum scheme dependence amounts to 25%. • Renormalization point dependence gives about 15% uncertainty. Uncertainty due to short and intermediate range behavior of TPE and CT potentials.

  12. Covariant Formalism • Already considered in 1970’s • BD, PLB41, 461 (1972) • H.J. Pirner and D.O. Riska, PLB44, 151 (1973) • M. Chemtob and BD, NPA78, 139 (1974) Advantage of covariant formalism • 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

  13. One-pion iteration subtracted Relevant to pp scattering Relevant to np -> dg Higher order in 1/M -> Neglect them Feynman diagrams Potential in momentum space

  14. Potential in configuration space

  15. (~1/M3) (~1/M4) Relation of COV and EFT Take large nucleon mass (LM) limit from COV gA2 discrepancy can be accounted by missing D contribution in COV calculation. -> EFT is equivalent to leading 1/M term in COV.

  16. Short-intermediate Long Numerical Result : TPE potential in r-space r2v(r) • Long range : COV and LM converges. • Short range • COV : converges to a finite value, • LM : diverges proportional to r-n with n > 2. • -> No need for form factor for COV. • -> COV result will be free from cutoff uncertainty.

  17. Numerical Result : PV asymmetry Ag - OPE dominating • TPE-COV : ~5% correction • TPE-LM : ~13% correction (consistent with EFT TPE) • NNLO (EFT) : correction in the range 9~17% • D-intermediate state : negligible (N. Kaiser, PRC76, 047001 (2007))

  18. Summary Two-pion-exchange parity-violating potentials from covariant formalism and effective field theory are compared. Same TPE contribution. aLM2pw aEFT2p Higher-order corrections are contrasting. aEFTCTw 0.1 aEFT2p : Good convergence. aCOV2p w 0.3aLM2p : Significant higher 1/M corrections. h1p can be determined from measurement of Ag in n p -> d g with uncertainty about 10%. More experiments are absolutely wanted for better understanding of the PV interaction.

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