1 / 21

Next-to-Leading Order Parity-Violating Potential and

n p → d γ. →. Next-to-Leading Order Parity-Violating Potential and. Chang Ho Hyun Sungkyunkwan University In collaboration with S. Ando and B. Desplanques PAVI06 Milos, Greece May 19, 2006. Outline. Background : One-meson exchange Effective field theory

alka
Download Presentation

Next-to-Leading Order Parity-Violating Potential and

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. n p→dγ → Next-to-Leading Order Parity-Violating Potential and Chang Ho Hyun Sungkyunkwan University In collaboration with S. Ando and B. Desplanques PAVI06 Milos, Greece May 19, 2006

  2. Outline • Background • : One-meson exchange • Effective field theory • up to next-to-leading order • Summary n p→d g n p→d g → →

  3. Background PC vertex p, r, w, ... PV vertex * One-meson exchange PV interactions WeakMNNcoupling constants ; pNN(h1p), rNN (h0r, h1r, h2r), wNN (h0w, h1w)…

  4. * DDH potential : one-meson exchange PV potential ofp, r, wmesons S, D, … ↔ P, F, … Background

  5. * Weak MNNcoupling constants : Theory * Quark model : B. Desplanques et al., Ann. Phys. 124 (1980) * Soliton : N. Kaiser, U.G. Meissner, Nucl. Phys. A499 (1989) * QCD sum rule : E. M. Henley et al., Phys. Lett. B 367 (1996) Background

  6. np→dg → * Weak MNNcoupling constants : Experiment h1p Forbidden decay of 18F : | h1p | ≤ 1.4 × 10-7 Anapole moment of 133Cs : h1p ~ 9.5 × 10-7 * Measurement of PV asymmetry in Aγ = - (0.6 ± 2.7) × 10-7 Cavaignac et al., Phys. Lett. B 67 (1977) Aγ = - (1.5 ± 4.8) × 10-8 Alberi et al., Can. J. Phys 66 (1988) In 1998 : Proposal to measure Ag with the accuracy at the order of 10-9 Background

  7. : One-meson exchange ds ∝ 1 + Aγ cosq dq Photon momentum Neutron polarization q Neutron momentum np→dg → Non-zeroAγ: PV E1 transition E1operator :OE = i (tz1-tz2) r (DI = 1, DL = 1, DS = 0) wg 4 CHH, T.-S. Park, D.-P. Min, PLB516 (2001) CHH, S.J. Lee, J. Haidenbauer, S.W. Hong, EPJA24 (2005)

  8. Scattering :1S0, 3S1+3D1 Deuteron:3S1+3D1 * PC transition : 1S0→3S1+3D1 (M1 isovector) 3S1+3D1→3S1+3D1 (M1 isoscalar) * PV transition :3PJ5→3S1+3D1 3S1+3D1→3PJ5 ( E1 : DL = 1, DS = 0) * Isovector PV potential produces 3PJ5 admixture to 3S1+3D1. → Aγ determined byh1p, h1r, h1w One-meson exchange

  9. * Result with one-meson exchange Aγ = aph1p+ arh1r+ awh1w Ifhi’s ~10-7, more than 97% of Aγ from pion. One-meson exchange

  10. Effective Field Theory * Heavy baryon chiral perturbation theory • Lagrangian satisfying the symmetries of QCD • Nucleon treated as a heavy field • SSB : pion is a Goldstone boson • Expansion in powers ofq/Lc • Counting rule : systematic expansion in powers ofq/Lc Counting rule * Meson propagator ~ q-2 * Nucleon propagator ~ q-1 * Loop integral ~ q4 * Derivative or external field ~ q1

  11. q q-2 q-1 q q q q0 q q-1 q q4 q-2 … … q-2 q-2 q-2 q4 q-2 C0PVq q-2 q4 q0 q-1 q q0 q-1 q q0 q-1 q Two-pion exchange (TPE) Contact term(CT) * PV potential : Isovector Thorough EFT derivation : Zhu et al. NPA748, 435 (2005) LO ~ q-1 NLO ~ q1 Effective Field Theory

  12. q +••• q-2 q-2 q-2 q4 q-2` q4 q q q q-1 NNLO ~ q2 • Contact term • Calculated from underlying theory or • Adjusted to experiments No calculation, no experiment Approximation : (q2 + m2V)-1 ~ m-2V + O(q2) CT term at LO Effective Field Theory

  13. LO NLO Effective Field Theory

  14. Need control at highq • Form factor and cutoff :exp(-q2/L2) • Dispersion relation Fourier transformation Effective Field Theory

  15. Form factor and cutoff C0PV Effective Field Theory

  16. Dispersion relation Effective Field Theory

  17. OPEP + TPEP OPE OPE+TPE Effective Field Theory

  18. OPEP + TPEP + CT OPE+TPE OPE+TPE+CT Effective Field Theory

  19. up to next-to-leading order np→dg → ap Aγ = aph1p ± 10 % sub 1 %

  20. Summary • PV potential calculated with heavy baryon chiral perturbation theory up to next-to-leading order • Aγ calculated with OME and effective NLO potentials • Heavy OME to Aγ : ~ 1 % • TPE to Aγ: ~ 10 % • CT toAγ :sub 1 % • How to achieve cutoff independence ; V low k? • One-pion exchange ; Dominant with 10% uncertainty • Measurement of Aγ; Crucial for h1p

  21. q q-1 C0PC ~ q0 q-2 q4 q-1 q0 Other NLO diagram Can be absorbed in CT term by redefiningC0PV 1/mN correction at LO ` B† (v∙∂pS∙D) B→v∙qs ∙p ~ p2/mN ~ 10-2 eV Backup

More Related