All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology

Recent progress on scattering amplitudes has benefited from the mathematical technology of symbols for efficiently handling the types of polylogarithm functions which frequently appear in multi-loop computations. The symbol for all two-loop MHV amplitudes in planar SYM theory is known, but explicit analytic formulas for the amplitudes are hard to come by except in special limits where things simplify, such as multi-Regge kinematics. By applying symbology we obtain a formula for the leading behavior of the imaginary part (the Mandelstam cut contribution) of this amplitude in multi-Regge kinematics for any number of gluons. Our result predicts a simple recursive structure which agrees with a direct BFKL computation carried out in a parallel publication.Comment: 20 pages, 2 figures. v2: minor correction

Imaginary parts and discontinuities of Wilson line correlators

We introduce a notion of position-space cuts of eikonal diagrams, the set of diagrams appearing in the perturbative expansion of the correlator of a set of straight semi-infinite Wilson lines. The cuts are applied directly to the position-space representation of any such diagram and compute its imaginary part to the leading order in the dimensional regulator. Our cutting prescription thus defines a position-space analog of the standard momentum-space Cutkosky rules. Unlike momentum-space cuts which put internal lines on shell, position-space cuts constrain a number of the gauge bosons exchanged between the energetic partons to be lightlike, leading to a vanishing and a non-vanishing imaginary part for space- and timelike kinematics, respectively.Comment: 5 pages, 2 figures; minor changes; version published in PR

Position-space cuts for Wilson line correlators

We further develop the formalism for taking position-space cuts of eikonal diagrams introduced in [Phys.Rev.Lett. 114 (2015), no. 18 181602, arXiv:1410.5681]. These cuts are applied directly to the position-space representation of any such diagram and compute its discontinuity to the leading order in the dimensional regulator. We provide algorithms for computing the position-space cuts and apply them to several two- and three-loop eikonal diagrams, finding agreement with results previously obtained in the literature. We discuss a non-trivial interplay between the cutting prescription and non-Abelian exponentiation. We furthermore discuss the relation of the imaginary part of the cusp anomalous dimension to the static interquark potential.Comment: 39+18 pages, 16 figures; elaborated the discussion of the comparison of numerical and analytic results for the three-gluon vertex diagram in the caption of fig. 16; version to be published in JHE

Beam normal spin asymmetry in the quasi-RCS approximation

The two-photon exchange contribution to the single spin asymmetries with the spin orientation normal to the reaction plane is discussed for elastic electron-proton scattering in the equivalent photon approximation. In this case, hadronic part of the two-photon exchange amplitude describes real Compton scattering (RCS). We show that in the case of the beam normal spin asymmetry, this approximation selects only the photon helicity flip amplitudes of RCS. At low energies, we make use of unitarity and estimate the contribution of the $\pi N$ multipoles to the photon helicity flip amplitudes. In the Regge regime, QRCS approximation allows for a contribution from two pion exchange, and we provide an estimate of such contributions. We furthermore discuss the possibility of the quark and gluon GPD's contributions in the QRCS kinematics.Comment: 10 pages, 5 figures, revtex, submitted to Phys. Rev. C; new version: references adde

Single spin asymmetry in DVCS

In the following note, we will present an estimation of the single spin asymmetry in deeply virtual Compton scattering (DVCS) which directly allows one to test predictions of the ratio of the imaginary part of the amplitude in DIS to DVCS, as well as access the skewed parton distributions at small $x$ in the DGLAP region. We find it to be large for the HERA kinematics to be accessible in forthcoming runs with polarized electrons.Comment: 6 pages, 2 figures in eps format. Submitted to Phys. Rev. D's Rapid Communication