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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
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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
Outline • Background • : One-meson exchange • Effective field theory • up to next-to-leading order • Summary n p→d g n p→d g → →
Background PC vertex p, r, w, ... PV vertex * One-meson exchange PV interactions WeakMNNcoupling constants ; pNN(h1p), rNN (h0r, h1r, h2r), wNN (h0w, h1w)…
* DDH potential : one-meson exchange PV potential ofp, r, wmesons S, D, … ↔ P, F, … Background
* 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
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
: 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)
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
* Result with one-meson exchange Aγ = aph1p+ arh1r+ awh1w Ifhi’s ~10-7, more than 97% of Aγ from pion. One-meson exchange
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
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
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
LO NLO Effective Field Theory
Need control at highq • Form factor and cutoff :exp(-q2/L2) • Dispersion relation Fourier transformation Effective Field Theory
Form factor and cutoff C0PV Effective Field Theory
Dispersion relation Effective Field Theory
OPEP + TPEP OPE OPE+TPE Effective Field Theory
OPEP + TPEP + CT OPE+TPE OPE+TPE+CT Effective Field Theory
up to next-to-leading order np→dg → ap Aγ = aph1p ± 10 % sub 1 %
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
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