Proton polarizabilities from Compton data using covariant chiral effective field theory

Abstract

We present a fit of the spin-independent electromagnetic polarisabilities of the proton to lowenergy Compton scattering data in the framework of covariant baryon chiral effective field theory. Using the Baldin sum rule to constrain their sum, we obtain αE1 = [10.6 ± 0.25(stat) ± 0.2(Baldin) ± 0.4(theory)] × 10 −4 fm 3 and βM1 = [3.2 ∓ 0.25(stat) ± 0.2(Baldin) ∓ 0.4(theory)] × 10 −4 fm 3 , in excellent agreement with other chiral extractions of the same quantities.PACS numbers: 12.39. Fe, 13.60.Fz, 14.20.Dh The electromagnetic polarisabilities of the proton have been a subject of investigation for many years; the earliest extractions from low-energy Compton scattering data were carried out in the 1950s, and the relevant database was greatly expanded in the 1990s. In the very lowenergy regime one can make an expansion of the cross section which deviates from the Thomson scattering only through the inclusion of the two spin-independent polarisabilities α E1 and β M 1 . However, since very few measurements have been taken below 80 MeV, almost all extractions require theoretical input to describe the evolution of the cross section with energy. Historically, dispersion relation (DR) approaches were used, with input from pion photoproduction data. A model-independent constraint can be obtained from the Baldin sum rule, most recently evaluated to give α E1 + β M 1 = 13.8 ± 0.4 in units of 10 −4 fm 3 [1], so typically the parameter extracted is α E1 − β M 1 . In 2001 Olmos de León et al. published the most comprehensive data set yet, obtained with the TAPS detector at MAMI, and in a DR framework analysed it together with other "modern" data to give α E1 − β M 1 = 10.5 ± 0.9 ± 0.7 in the same units [1]. For some time this was regarded as the definitive result.However, chiral effective field theories (χEFT) can also be used to describe Compton scattering amplitudes. These are field theories in which the interactions of lowenergy degrees of freedom are governed by the symmetries of QCD, and scattering amplitudes can be systematically expanded in powers of the ratio of light to heavy scales. The former are typically external particle momenta of the order of the pion mass, and the latter are governed by those particles such as the ρ meson which are not included explicitly in the theory but whose effects, along with other short distance physics, are encoded in low energy constants. At leading one-loop order in the theory with pion and nucleons these predictions are parameter-free, but beyond leading order α E1 and β M 1 are free parameters which can be fit to data. The first attempt to do this was the work of Beane et al. [2,3], working in heavy baryon (HB) chiral perturbation theory. The absence of a dynamical Delta isobar restricted the fit to relatively low momentum transfer, and as a result the statistical errors were large. However, the inclusion of the Delta followed shortly [4][5][6]. Most recently, the result α E1 − β M 1 = 7.5 ± 0.7 ± 0.6 has been obtained by McGovern et al. in ref. [7]. Although this value is comp...

Compton Scattering Program Studying Nucleon Polarizabilities

“…To make room for the detectors, however, the polarizing magnet needs to be removed, at which point a weaker holding coil is energized to maintain the polarization. The Mainz FST has been online since 2009, achieving polarizations up to 90%, with relaxation times of over 1000 h. [9], dispersion relation calculations HDPV [10] and DPV [11][12], chiral Lagrangian calculation L χ [13], heavy baryon and covariant chiral perturbation theory calculations HBχPT [3] and BχPT [14].…”

Generalized polarizabilities of the nucleon in baryon chiral perturbation theory

“…It is important to note, however, that the error of the scalar polarizabilities α E1 (Q 2 ) and β M1 (Q 2 ) in the static limit Q 2 = 0 is defined by the error of the corresponding static (real) polarizabilities. This error was argued to be small [37] due to the fact that these polarizabilities are very close at NLO to the results obtained in Bχ PT fits to real Compton scattering data [52], and that there are contact terms at NNLO that will in any case compensate changes in α E1 and β M1 coming from other higher-order mechanisms. The static errors are estimated as error(α E1 , static) error(β M1 , static) ∼ 0.7 × 10 −4 fm 3 (see Ref.…”

“…Our Bχ PT prediction is substantially larger [35,37]: β M1 = 3.9(7) in the usual units. Fits of Compton scattering data based on χ PT also tend to yield a larger value [52,57]:…”

Magnetic structure of light nuclei from lattice QCD

“…The primary focus of this article is on the magnetic polarizabilities and the cross-section for the radiative capture process np → dγ at low energies which is dominated by the M 1 multipole. While the magnetic polarizability of the proton 1 , β exp p = (3.15 ± 0.35 ± 0.20 ± 0.30) × 10 −4 fm 3 , is well determined experimentally [3][4][5][6][7][8], the magnetic polarizability of the neutron β exp n = (3.65 ± 1.25 ± 0.20 ± 0.80) × 10 −4 fm 3 remains quite uncertain [6,7,[9][10][11]. This uncertainty is largely a consequence of the lack of a free neutron target; the neutron polarizability must be determined from that of light nuclei, primarily the deuteron (see Ref.…”