Hexagon bootstrap in the double scaling limit

We study the six-particle amplitude in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory in the double scaling (DS) limit, the only nontrivial codimension-one boundary of its positive kinematic region. We construct the relevant function space, which is significantly constrained due to the extended Steinmann relations, up to weight 13 in coproduct form, and up to weight 12 as an explicit polylogarithmic representation. Expanding the latter in the collinear boundary of the DS limit, and using the Pentagon Operator Product Expansion, we compute the non-divergent coefficient of a certain component of the Next-to-Maximally-Helicity-Violating amplitude through weight 12 and eight loops. We also specialize our results to the overlapping origin limit, observing a general pattern for its leading divergences.

Algebraic branch points at all loop orders from positive kinematics and wall crossing

There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar $$ \mathcal{N} $$ N = 4 SYM. A long-standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.

Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation

In this paper, we use the re-summation procedure, suggested in Ducloué et al. (JHEP 1904:081, 2019), Salam (JHEP 9807:019 1998), Ciafaloni et al. (Phys Rev D 60:1140361999) and Ciafaloni et al. (Phys Rev D 68:114003, 2003), to fix the BFKL kernel in the NLO. However, we suggest a different way to introduce the non-linear corrections in the saturation region, which is based on the leading twist non-linear equation. In the kinematic region: $$\tau \,\equiv \,r^2 Q^2_s(Y)\,\le \,1$$ τ ≡ r 2 Q s 2 ( Y ) ≤ 1 , where r denotes the size of the dipole, Y its rapidity and $$Q_s$$ Q s the saturation scale, we found that the re-summation contributes mostly to the leading twist of the BFKL equation. Assuming that the scattering amplitude is small, we suggest using the linear evolution equation in this region. For $$\tau \,>\,1$$ τ > 1 we are dealing with the re-summation of $$(\bar{\alpha }_S\,\ln \tau )^n$$ ( α ¯ S ln τ ) n and other corrections in NLO approximation for the leading twist. We find the BFKL kernel in this kinematic region and write the non-linear equation, which we solve analytically. We believe the new equation could be a basis for a consistent phenomenology based on the CGC approach.

Investigation of abnormal absorption of cosmic-ray hadrons in lead calorimeters

A phenomenon of abnormally weak absorption of very high energy cosmic ray hadrons in thick lead blocks is discussed. This phenomenon was first observed in a Tien Shan high altitude experiment to study hadronic cores of extensive air showers (EAS) with a deep ionization calorimeter and encouraged researchers to introduce the hypothesis of the so-called long-flying or penetrating cosmic ray component. A similar effect was detected later with deep uniform lead X-ray emulsion chambers (XREC) at the Pamirs, which we discuss in detail. To establish the nature of the phenomenon we are have carried out dedicated experiments at the Tien Shan and at the Pamirs by exposing two-storey XRECs with large air gaps. According to detailed simulation of the chamber response, these experiments are very sensitive to the production of charmed hadrons in the forward kinematic region and can prove a hypothesis that the phenomenon under study can be explained on the assumption of very high values of charm particle production cross section at 〈ELab〉 ~ 75 TeV in the forward kinematic region at xLab ≳ 0.1 which are near the upper limit of recent results of collider experiments, i.e., σpp→c¯c ~ 8 mb. The same factor makes it possible to fit all the features of the experimental hadron absorption curve observed by means of deep uniform lead XRECs, including its bending at a depth of ~ 70 c.u.

Nucleon Partonic Spin Structure to be Explored by the Unpolarized Drell-Yan Program of COMPASS Experiment at CERN

The observation of the violation of Lam-Tung relation in the [Formula: see text] Drell-Yan process triggered many theoretical speculations. The TMD Boer-Mulders functions characterizing the correlation of transverse momentum and transverse spin for partons in unpolarized hadrons could nicely account for the violation. The COMPASS experiment at CERN will measure the angular distributions of dimuons from the unpolarized Drell-Yan process over a wide kinematic region and study the beam particle dependence. Significant statistics is expected from a successful run in 2015 which will bring further understanding of the origin of the violation of Lam-Tung relation and of the partonic transverse spin structure of the nucleon.

On the polarized DIS spin structure function g1 at small x

In the present paper we summarize our recent results on the structure function g1 and present explicit expressions for the nonsinglet and singlet components of g1, which can be also used at arbitrary x and Q2. These expressions combine the well-known DGLAP-results for the anomalous dimensions and coefficient functions with the total resummation of the leading logarithmic contributions and the shift of Q2 →Q2 + μ2. In contrast to DGLAP, these expressions do not require the introduction of singular parametrizations for the initial parton densities. We have also applied our results to describe the experimental data in the kinematic region of the COMPASS experiment, which is beyond the reach of DGLAP. For a more detailed review of our results see Ref. 1.

PARTONIC INTERPRETATION OF GENERALIZED PARTON DISTRIBUTIONS

Dispersion relations have been applied to hard exclusive processes suggesting that generalized parton distributions can be fully determined from their values on a kinematical ridge. We show significant pitfalls associated that vitiate this approach. We suggest an improved treatment of this assumption. Secondly, in order for a partonic interpretation to hold throughout the accessible kinematic region, semi-disconnected diagrams should not contribute. We show, however, that this condition is not satisfied for non-forward kinematics at leading order. Lastly we present our recent flexible parameterization of GPDs and indicate its application to neutral pseudoscalar electroproduction.

PROGRESS IN SMALL x RESUMMATION

I review recent theoretical progress in the resummation of small x contributions to the evolution of parton distributions, in view of its potential significance for accurate phenomenology at future colliders. I show that a consistent perturbative resummation of collinear and energy logs is now possible, and necessary if one wishes to use recent NNLO results in the HERA kinematic region.