Subleading corrections to parity-violating pion photoproduction

We compute the photon asymmetry for near threshold parity violating (PV) pion photoproduction through sub-leading order. We find a potentially significant contribution from new PV low-energy constants not considered previously. We observe that a measurement of this asymmetry may help clarify the theoretical intepretation of backward angle PV electron-proton scattering, provided that the PV πNN Yukawa coupling is determined from nonradiative nuclear PV experiments. PACS Indices: 11.30.Er, 11.30.Rd, 13.60.Le. The parity violating (PV) πNN Yukawa coupling constant hπ is a key ingredient to the understanding of the PV nuclear interaction[1, 2, 3, 4, 5]. There have been a number of past attempts to extract this coupling from PV reactions[2, 5, 6, 7, 8, 9], and there are a slate of new experiments, suggested or being planned, with this goal in mind, e.g., ~np → dγ at LANSCE [10], γd → np at Jefferson Lab [11], the rotation of polarized neutrons in helium at NIST [9] as well as polarized Compton scattering processes [12, 13]. Recently, Chen and Ji (CJ) suggested using PV π photoproduction near threshold in order to extract hπ [14]. Specifically, the process considered by these authors is −→γ (q; ǫ) + p(P i ) → π(k) + n(P μ f ) , (1) where q = (ω,q), P i , k μ = (ωπ,k), and P μ f are the center-of-mass four-momenta of photon, proton, pion and neutron, respectively, and ǫ is the photon polarization vector. In the threshold region, the pion and photon as well as the nucleon momenta are much smaller than the chiral symmetry breaking scale Λχ = 4πFπ ∼ 1 GeV and CJ demonstrated that the use of heavy baryon chiral perturbation theory [15, 16] yields a low energy theorem for the threshold PV photon-helicity asymmetry at lowest order of the chiral expansion: Aγ (ωth, θ) = √ 2Fπ(μp − μn) gAmN hπ , (2) The corrections from terms higher order in the chiral expansion were estimated to be around 20% [14]. This process has been studied from the point of view of a more conventional meson exchange approach in [17, 18], and the same hπ dominance of the asymmetry at threshold was found [18]. In this note we present the first order sub-leading result for the aysmmetry. Contrary to the naive expectation that such higher order corrections are small, the subleading correction from the PV πNN vector coupling hV (defined below) is of order unity, as previously found in the radiative corrections to hπ [19] and to the nucleon anapole moment [20]. We further argue that the proposed parity violating photoproduction process is more suitable for constraining hV rather than h 1 π. In contrast, other – nonradiative – processes[9, 10, 11] may be most appropriate for the determination of hπ, since vector current conservation implies the contributions from hV are suppressed in such cases. Finally we observe that the contribution from hV to the nucleon anapole moment introduces significant theoretical uncertainty into the axial vector radiative correction RA for backward angle PV ep scattering[20]. The SAMPLE collaboration has recently reported an result for this correction which appears to differ from the theoretical estimate [21]. A new constraint on hV from PV pion photoproduction would reduce the theoretical uncertainty in RA and may help resolve the apparent difference between theory and experiment. The motivation behind the use of heavy baryon chiral perturbation theory (HBCPT) is explained in detail in [14], so we follow the notations of this reference. Since we work in the near-threshold region, we use the so-called “small-scale” expansion [22], i.e., we treat ω, ωπ, |k|,mπ, δ = m∆−mN , etc. as small quantities and characterize amplitudes by the number of powers of these terms, e.g., we count the term ωπ/q · k as being O(p−1). The photon asymmetry arises from the interference of the parity conserving (PC) and PV amplitudes. In Ref. [14] the asymmetry was truncated at leading order, i.e., O(p). In the present work we include the O(p) correction, which arises dominantly from the PV vector πNN