Spin dependence of high energy proton scattering

Abstract

Motivated by the need for an absolute polarimeter to determine the beam polarization for the forthcoming RHIC spin program, we study the spin dependence of the proton-proton elastic scattering amplitudes at high energy and small momentum transfer. In particular, we examine experimental evidence for the existence of an asymptotic part of the helicity-flip amplitude φ 5 which is not negligible relative to the largely imaginary average non-flip amplitude φ + = 1 2 (φ 1 + φ 3 ). We discuss theoretical estimates of r 5 = m φ 5 / √ −t Im φ + based upon several approaches: extrapolation of low and medium energy Regge phenomenological results to high energies, models based on a hybrid of perturbative QCD and non-relativistic quark models, and models based on eikonalization techniques. We also apply the rigorous, model-independent methods of analyticity and unitarity. We find the preponderence of evidence at currently available energy indicates that r 5 is small, probably less than 10%. The best available experimental limit comes from Fermilab E704: combined with rather weak theoretical assumptions those data indicate that |r 5 | < 15%. These bounds are important because rigorous methods allow much larger values. Furthermore, in contradiction to a widelyheld prejudice that r 5 decreases with energy, general principles allow it to grow as fast as ln s asymptotically, and some of the models we consider show an even faster growth in the RHIC range. One needs a more precise measurement of r 5 or to bound it to be smaller than 5% in order to use the classical Coulomb-nuclear interference technique for RHIC polarimetry. Our results show how important the measurements of spin dependence at RHIC will be to our understanding of proton structure and scattering dynamics. As part of this study, we demonstrate the surprising result that protonproton elastic scattering is self-analysing, in the sense that all the helicity amplitudes can, in principle, be determined experimentally at small momentum transfer without a knowledge of the magnitude of the beam and target polarization.

Azimuthal asymmetries in unpolarized Drell–Yan events on nuclear targets

“…The problem of estimating r so is, therefore, translated into the determination of the typical size of A N . In the literature, recent measurements and attempts of theoretical interpretations have been published for elastic scatterings at energies beyond 10 GeV with proton-proton [39,40], proton-12 C [41,42,43], and antiproton-proton [39] systems (for a collection of older experimental data, see Ref. [40] and references therein).…”

“…In the literature, recent measurements and attempts of theoretical interpretations have been published for elastic scatterings at energies beyond 10 GeV with proton-proton [39,40], proton-12 C [41,42,43], and antiproton-proton [39] systems (for a collection of older experimental data, see Ref. [40] and references therein). Results for A N with proton and 12 C targets are similar in magnitude and shape and they show a steep decrease from 10% at 10 GeV down to 2÷4% at 20 GeV, with somewhat higher values at larger energies around 30 GeV but with large error bars.…”

Single Spin Asymmetries from a Single Wilson Loop

“…The spin-dependent odderon has been considered in this way in [58] and in many studies of elastic scattering, but without reference to TMDs, e.g. [59][60][61].…”

Diffractive effects in spin-flipppamplitudes and predictions for relativistic energies

“…Since the differential cross section (dσ/dt) at ISR energies is usually assumed to be dominated by the spin-non-flip amplitude, many of the models describing the diffraction in pp scattering do not take into account the contribution from spin-flip amplitudes [2,3,4]. Others do [5,6,7,8] but in this case they use data at lower energies [9]. However, the study of diffraction in spin-flip amplitudes began many years before that when one of us [10] noticed that polarization data at πp scattering suggested a diffractive contribution in the spin-flip πp amplitude at high energy which becomes evident when the kinematical zero is removed.…”

“…In Ref. [7] the magnitudes of φ 2 and φ 4 with respect to the spin-non-flip amplitude were analyzed and reasonable arguments were given concerning the linear dependence on t for φ 2 (φ 2 ∝ t when t → 0) [15], while in the case of φ 4 the relation φ 4 ∝ t is consequence of angular momentum conservation.…”