Single-pion contribution to the Gerasimov--Drell--Hearn sum rule and related integrals

Abstract

Phenomenological amplitudes obtained in partial-wave analyses (PWA) of single-pion photoproduction are used to evaluate the contribution of this process to the Gerasimov-Drell-Hearn (GDH), Baldin and Gell-Mann-Goldberger-Thirring (GGT) sum rules, by integrating up to 2 GeV in photon energy. Our study confirms that the single-pion contribution to all these sum rules converges even before the highest considered photon energy, but the levels of saturation are very different in the three cases. Single-pion production almost saturates the GDH sum rule for the proton, while a large fraction is missing in the neutron case. The Baldin integrals for the proton and the neutron are both saturated to about four fifths of the predicted total strength. For the GGT sum rule, the wide variability in predictions precludes any definitive statement.

First concurrent extraction of the leading-order scalar and spin proton polarizabilities

“…The obtained value of both α E1 + β M 1 and γ 0 are in agreement, within the quoted errors, with the available estimates of the Baldin and GGT sum rule values listed in Refs. [57,58]. This gives a confirmation of the validity of our overall procedure.…”

“…The last term, γ π , is the sum of the dispersive contribution γ disp π , to be fitted to the data, and the pion-pole contribution, fixed to γ π 0 −pole π = −46.7 [40]. The choice of the fit parameters allows for a direct comparison, as a consistency check, of the fit results for α E1 + β M 1 and γ 0 to the available experimental predictions of the Baldin [39,[56][57][58] and Gellmann-Goldberger-Thirring (GGT) [56][57][58][59] sum rule values, respectively, obtained using pion photoproduction data. When present, point-to-point systematic errors were added in quadrature to the statistical errors, while common systematic scale factors were treated as in the previous bootstrap extractions by Pasquini et al [14,21], namely they are assumed to follow a uniform distribution, unless otherwise specified in the original publication.…”

Results on spin sum rules and polarizabilities at low Q2

“…The sum rule expectation I n LT (0) = 0 agrees with the E97-110 data once they are guided to Q 2 = 0 using the expected behavior of I LT (Q 2 ) from the Gerasimov-Drell-Hearn (GDH) sum rule [24] and elastic form factors. Since the GDH sum rule is solid, with its validity verified to good accuracy [25], and the form factors are well measured, the agreement strengthens confidence in the data quality. Yet, it cannot entirely rule out possible issues with the low-x extrapolation (important in I LT while suppressed in δ LT ) or high-x contamination from elastic/quasi-elastic reactions (enhanced in δ LT compared to I LT ).…”

“…1 is the datum at Q 2 = 0 from MAMI [26]. At first, it may seem incompatible with the E03006 data but their extrapolation to Q 2 = 0 assuming either the results of Bernard et al or Alarcón et al shows that under this assumption, the data of JLab and MAMI agree within uncertainties [25]. The Hall A E97110 data on γ n 0 agree with the earlier EG1 (Hall B) and E94010 (Hall A) data, but not with the predictions except at higher Q 2 for Alarcón et al and MAID.…”

“…A possibility to advance further, even if no new experiments measuring these observables are foreseen and calculating the next order of the χEFT series is very difficult, is to compute the observables with other non-perturbative approaches, e.g. that based on the Dyson-Schwinger Equations, Lattice QCD, Gauge-Duality (AdS/QCD) or global phenomenological analyses like MAID or SAID [25]. It is important to resolve this issue: it challenges our search for a description of Nature at all level since χEFT is the leading approach to manage the first level of complexity arising above the strong force sector of the Standard Model.…”