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Register a new userHigh-energy amplitudes in the next-to-leading order
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Authors
Ian Balitsky
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I review the calculation of the next-to-leading order behavior of high-energy amplitudes in N=4 SYM and QCD using the operator expansion in Wilson lines.
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We develop further an approach to computing energy-energy correlations (EEC) directly from finite correlation functions. In this way, one completely avoids infrared divergences. In maximally supersymmetric Yang-Mills theory ($mathcal{N}=4$ sYM), we derive a new, extremely simple formula relating the EEC to a triple discontinuity of a four-point correlation function. We use this formula to compute the EEC in $mathcal{N}=4$ sYM at next-to-next-to-leading order in perturbation theory. Our result is given by a two-fold integral representation that is straightforwardly evaluated numerically. We find that some of the integration kernels are equivalent to those appearing in sunrise Feynman integrals, which evaluate to elliptic functions. Finally, we use the new formula to provide the expansion of the EEC in the back-to-back and collinear limits.
The energy-energy correlation (EEC) between two detectors in $e^+e^-$ annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of EEC in the collinear and back-to-back regions through to next-to-leading power, information which should aid resummation in these regions.
We determine an approximate expression for the O(alpha_s^3) contribution chi_2 to the kernel of the BFKL equation, which includes all collinear and anticollinear singular contributions. This is derived using recent results on the relation between the GLAP and BFKL kernels (including running-coupling effects to all orders) and on small-x factorization schemes. We present the result in various schemes, relevant both for applications to the BFKL equation and to small-x evolution of parton distributions.
We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers $n$, $ell$, $s$ and $j$, up to ${cal O}(alpha_s^5 m)$ and ${cal O}(alpha_s^5 m log alpha_s)$ in perturbative QCD. The QCD Bethe logarithm is given in a one-parameter integral form. The rest of the formula is given as a combination of rational numbers, transcendental numbers ($pi$, $zeta(3)$, $zeta(5)$) and finite sums (besides the 3-loop constant $bar{a}_3$ of the static potential whose full analytic form is still unknown). A derivation of the formula is given.
We compute the hydrodynamic relaxation times $tau_pi$ and $tau_j$ for hot QCD at next-to-leading order in the coupling with kinetic theory. We show that certain dimensionless ratios of second-order to first-order transport coefficients obey bounds which apply whenever a kinetic theory description is possible; the computed values lie somewhat above these bounds. Strongly coupled theories with holographic duals strongly violate these bounds, highlighting their distance from a quasiparticle description.
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