New Measurements of the Beam Normal Spin Asymmetries at Large Backward Angles with Hydrogen and Deuterium Targets

Abstract

New measurements of the beam normal single spin asymmetry in the electron elastic and quasielastic scattering on the proton and deuteron, respectively, at large backward angles and at hQ 2 i ¼ 0.22 ðGeV=cÞ The exchange of two hard virtual photons in the elastic electron-nucleon scattering beyond the one-photon exchange Born approximation has been the subject of recent investigation [1,2]. Two complementary methods, a determination from a measurement of a differential cross section using unpolarized electrons (Rosenbluth separation) and the measurement of the polarization transfer to the proton final state, gave significantly different results forThe two-photon exchange has been addressed as the explanation for such a discrepancy. Other observables in which the two-photon exchange physics plays a role are: neutron form factors, resonance electroproduction, the pion form factor and the elastic electron-nucleus cross section, in particular deuteron and 3 He [1]. The exchange of two virtual photons implies the excitation of nucleon intermediate states offering the possibility of testing models of hadronic structure [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In contrast to previous measurements at forward [23,24] and close to right angles [25], the A4 measurements presented in this work have been performed at large backward angles. The A4 measurements explore a new important parameter region of the virtualities of the exchanged virtual photons, involved in the theoretical calculation of the nucleon intermediate states, see Fig. 2 from Ref. [11]. Moreover, in contrast to the SAMPLE measurement [26], at similar backward scattering angle, the A4 measurements have improved the precision by a factor ∼4. The A4 measurements have been performed at larger beam energies, probing the πN and Δ resonance inelastic intermediate states.The two-photon exchange physics affects the parity violating asymmetry through the normalization to the electromagnetic amplitude [27] and it is of special relevance in precision measurements of the weak charge of the proton at low Q 2 like Q weak [28] and P2 [29]. It is also useful in the theoretical determination of the γZ box diagrams which also takes part in the proton weak charge radiative corrections [30][31][32][33].Two-photon exchange effects can be observed in radiative corrections to the cross section, the ratio in e − p and e þ p elastic scattering cross sections, the depolarization tensor, and the target and beam normal single spin asymmetries [34][35][36][37]. Six generalized form factors depending on two kinematic variables parametrize the elastic electron-proton scatteringG M ðs; Q 2 Þ,G E ðs; Q 2 Þ, [10]. There are also partonic calculations which resort to generalized parton distributions of the nucleon and are able to resolve the discrepancy at large Q 2 [12,16]. The T-odd observables target and beam normal spin asymmetries arise from the interference of the one-photon and two-photon exchange amplitudes, see Fig. 1 in Ref. [39]. The target normal spi...

Study of Two-Photon Exchange via the Beam Transverse Single Spin Asymmetry in Electron-Proton Elastic Scattering at Forward Angles over a Wide Energy Range

“…The correction coefficients c i (i = 1...6) are determined through a multiple linear regression analysis. After this correction, the asymmetries measured in different datataking periods, when the half-wave plate was either in or out of the laser optics of the polarized electron source, are consistent with each other, as in our previous investigations [63,64,[71][72][73][74]. The corrected asymmetry A corr is then normalized by the beam polarization P e , which was measured approximately once per day using a Mott polarimeter located at the beam injection line.…”

“…The γ p → πN amplitudes are taken from the latest MAID analyses of single π electroproduction observables [78]. This calculation has given results which agree well with our backward-angle data [64]. As shown in Fig.…”

“…At the time when the interest on the two-photon exchange was revived by the polarization-Rosenbluth discrepancy, the techniques as well as expertise for measuring asymmetries of part per million (ppm) had been developed at several facilities like MIT-Bates, JLab and MAMI, aiming at measuring parity-violating asymmetries in electron scattering [56]. With these facilities, investigations of transverse beam spin asymmetries in various kinematic regions have been performed with transversely polarized electrons scattering off different targets [57][58][59][60][61][62], including A4 measurements [63,64] with both hydrogen and deuterium targets at the A4 experiment. In this letter, we report new results of the beam transverse spin asymmetry A ep ⊥ in ep elastic scattering at forward angles over a wide energy range, measured with a full azimuthal-angle detector at the A4 experiment.…”

Beam normal spin asymmetry for the ep→eΔ(1232) process

“…This behavior for the ep → e∆ process is unlike the corresponding B n for the elastic process. The measured value for B n for the elastic ep → ep process ranges from a few ppm in the forward angular range to around a hundred ppm in the backward angular range for beam energies below and around 1 GeV [31][32][33][34][35][36][37], in good agreement with theoretical TPE expectations [29]. For the inelastic process ep → e∆, we expect an enhancement of B n in the forward angular range, corresponding with low Q 2 , since the OPE process which enters the denominator of B n , is suppressed by one power of Q 2 relative to its elastic counterpart, as seen from Eqs.…”

“…We see that the corresponding asymmetries become large at forward angles. In [32,33]. The curves denote the contributions from different intermediate states: nucleon (dashed-dotted red curve); ∆(1232) (dashed blue curve); S11(1535) + D13(1520) (dotted violet curve); N + ∆ + S11(1535) + D13(1520) (solid black curve).…”