Titles and Abstracts:
Dmitry Chicherin: Multi-Regge Limit of the Non-Planar Two-Loop Five-Particle Amplitudes in N = 4 super Yang-Mills and N = 8 Supergravity
Multi-loop scattering amplitudes for multi-particle processes are starting to play an important role given the increasing precision of the collider physics experiments. The non-planar corrections for five-particle massless scattering at Next-to-Next-to-Leading-Order in the coupling are at the frontier of these studies. The full-color two-loop five-particle amplitude in N = 4 super Yang-Mills calculated at the symbol level was the very first analytic result in this direction. This maximally supersymmetric theory, which is endowed with a large amount of symmetries and has the simplest organization of the amplitudes among all 4D gauge theories, serves as an ideal theoretical laboratory for testing the machinery aimed at two-loop five-particle QCD amplitudes. The next natural step in revealing the analytic properties of the five-particle amplitudes, which are multi-variable functions, is to study certain limits. The multi-Regge limit describes a high-energy scattering regime that is both important for phenomenology and of great theoretical relevance. In this limit the picture of the scattering process simplifies significantly. This leads to enormous simplifications of the amplitudes and helps to reveal their structure and symmetries of the underlying theory. The symbol of the non-planar part of the N = 4 super Yang-Mills two-loop five-particle amplitude vanishes in the multi-Regge limit. We study the beyond-the-symbol contributions and restore the complete functional dependence of the amplitude in the multi-Regge kinematics. We also carry out the same analysis for the two-loop five-particle amplitude in N = 8 supergravity, which is intrinsically non-planar.
Lance Dixon: Hexagon Scattering Amplitude at the Origin
Six-gluon scattering in planar N=4 super-Yang-Mills theory is known for any kinematics through seven loops, and to all loop orders in single collinear limits, which are controlled by an operator product expansion in terms of flux tube excitations. By resumming a class of these excitations, we move to a kind of “triple collinear limit” where the three traditional cross ratios all vanish. At this kinematical origin, the MHV amplitude simplifies to three anomalous dimensions multiplying kinematical logarithms, and one constant term. Based on this resummation, we propose all orders (finite coupling) results for all four quantities, which match the seven loops of data at weak coupling, and also agree with strong coupling results where available. Mysteriously, some of these quantities also appear in the light-like limit of the recently studied large R charge correlator dubbed the “octagon”.
Giulio Falcioni: Wilson-line geometries in amplitude and splitting function factorisation
Gauge theories feature infrared singularities that are generated by the exchange of particles that are collinear to the massless external states or that are soft. These long-distance contributions decouple from scattering processes and are isolated in universal factors, expressed by Wilson-line correlators. In this talk I will discuss a simple relation between the long-distance singularities of the gauge theory form factors and those of the DGLAP splitting functions in the elastic limit. Such relation is dictated by the Wilson-line geometries that capture the soft singularities of these two quantities.
Massimiliano Grazzini: Recent development in the qt-subtraction formalism
I review the qt-subtraction method and its application to the computation of NNLO QCD corrections to the production of a colourless high-mass system in hadronic collisions. I then discuss the extension of the method to heavy-quark production, and present some recent developments on the study of power suppressed contributions. I also discuss possible applications to the computation of mixed QCD-EW corrections to the Drell-Yan process.
Lorenzo Magnea: Infrared Factorisation and Subtraction beyond NLO
I will discuss some recent work on the infrared subtraction problem beyond NLO, focusing in particular on the general definition of local subtraction counterterms for real radiation. The first step to build a subtraction algorithm is the analysis of singular regions for real radiation matrix elements, with special attention for overlapping singularities: at this level, it is possible to build a formal subtraction formula valid to all orders in perturbation theory. Next, I will use the factorisation properties of virtual corrections to fixed-angle scattering amplitudes to define local soft and collinear counterterms in terms of matrix elements of field operators and Wilson lines, again to all orders in perturbation theory. I will then discuss some details about the structure of counterterms at NNLO and N3LO.
Tiziano Peraro: Complex multi-loop results via finite-field techniques
I will describe recent developments in the calculation of multi-loop amplitudes and form factors using finite fields and functional reconstruction techniques. I will show several applications of these techniques within the public FiniteFlow framework, such as results for two-loop five-point scattering and the four-loop cusp anomalous dimension.
Vladimir Smirnov: Expansion by regions: a review
If a given Feynman integral depends on kinematic invariants and masses which essentially differ in scale, a natural idea is to expand it in ratios of small and large parameters. As a result, the integral can be written as a series of quantities which are simpler than the original integral itself and can be substituted by a sufficiently large number of terms of such an expansion. The universal strategy of expansion by regions enables us to write down terms of expansion of any given Feynman integral in any given limit. It can be described in a nice geometrical language, where regions correspond to special facets of the Newton polytope associated with polynomials corresponding to a given graph. Various results on expansion by regions and various examples illustrating expansion by regions and subtle points of its application are presented.
Emeri Sokatchev: Correlation functions and event shapes in gauge theories
We discuss a method for calculating event shapes based on correlation functions of conserved currents in a generic gauge theory. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. We consider the simplest example of a charge-charge correlation at leading order. We compute the correlation function of four electromagnetic currents and extract the event shape from it. The result is compared to the standard amplitude calculation. We also comment on a new conformal anomaly specific to parity-odd operators like the gauge topological term.
Lorenzo Tancredi: Physical projectors for multiloop scattering amplitudes
I’ll discuss a method for extract form factors for multiloop scattering amplitudes valid in ’t Hooft-Veltman scheme and that makes use of the simplifications arising from treating external states in d=4 space-time dimensions.
Gabriele Travaglini: From scattering amplitudes to Newton’s potential…and beyond
Stefan Weinzierl: Infrared properties of the integrands of loop amplitudes
The infrared properties of loop amplitudes after loop momentum integration are at low loop orders relatively well understood. Less is known for the integrands of the loop amplitudes before loop momentum integration. In this talk I will discuss the integrand of loop amplitudes. Understanding the integrand is a prerequisite to derive infrared subtraction terms. The latter are needed in an approach, where loop amplitudes are evaluated with Monte Carlo methods.
Christopher White: Journeys beyond the soft approximation
The soft, or eikonal, approximation is widely used in both collider physics and gravity, in order to classify the behaviour of scattering amplitudes to all orders in perturbation theory. Recent developments in both areas of physics have started to go beyond this approximation, and to look at the impact of “next-to-soft” effects. This talk will review these developments, and outline various open questions.
Kai Yan: Soft-gluon Factorization at Two-loop in Full Color
The factorization properties of gauge-theory amplitudes in the infrared kinematic regime is of great theoretical interests. Understanding the universal factorization behaviors at fixed-order is central to the subjects of IR subtraction in phase-space integrals, resummation of large logarithms in physical observables and bootstrapping the complete scattering amplitudes. Recently we computed the two-loop soft gluon emission factor which captures the leading-power behavior of multi-point scattering amplitude with a single soft gluon in the final state. At two loop it exhibits a new “tripole” structure due to soft gluon coupling to three hard partons. The full tripole contribution is linear combination of single-valued harmonic polylogarithms, and a smooth function in the physical scattering regime. In the limit where the soft gluon is collinear to an incoming hard parton, we observe collinear-factorization violating terms. Our analytic result provides evidence of the breakdown of the naive picture of factorization of cross section in hadron collisions, at the perturbative level of N^3LO.
Alexander Zhiboedov: Event shapes with spinning targets
I will review recent developments in our understanding of light-ray operators in CFTs and their application to event shapes. In particular, I will discuss the OPE for light-ray operators and various subtleties associated with it.
Simone Zoia: Implications of conformal symmetry for scattering amplitudes
Particle collisions occur in accelerators at extremely high energies. As a consequence, the particle masses can sometimes be neglected, in which case the Standard Model Lagrangian and the tree-level amplitudes become conformally invariant. Although the implications of this powerful symmetry have been extensively explored in position space, much less is known about its consequences for scattering amplitudes, where it is obscured by ultraviolet and infrared divergences. Even for finite loop integrals, the way conformal symmetry manifests itself may be subtle, e.g. in the form of anomalous Ward identities. On top of all this, there is also a practical complication: the generator of special conformal transformations becomes second-order in momentum space. In my talk I address these issues and show that there is hope to overcome them. Recent work has shown that conformal symmetry retains a surprising predictive power even at loop level. For instance, it allows for the computation of certain Feynman integrals by solving anomalous Ward identities. Moreover, I present the first example of conformally invariant loop amplitude, the one-loop n-gluon all-plus amplitude in Yang-Mills theory. Through on-shell methods I show that the conformal invariance of the latter implies that of certain rational factors in the two-loop all-plus amplitude.
