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Abstract We present a NNLO QCD accurate event generator for direct photon pair production at hadron colliders, based on the MiNNLO PS formalism, within the Powheg Box Res framework. Despite the presence of the photons requires the use of isolation criteria, our generator is built such that no technical cuts are needed at any stage of the event generation. Therefore, our predictions can be used to simulate kinematic distributions with arbitrary fiducial cuts. Furthermore, we describe a few modifications of the MiNNLO PS formalism in order to allow for a setting of the renormalization and factorization scales more similar to that of a fixed-order computation, thus reducing the numerical impact of higher-order terms beyond the nominal accuracy. Finally, we show several phenomenological distributions of physical interest obtained by showering the generated events with Pythia8, and we compare them with the 13 TeV data from the ATLAS Collaboration.

A number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum (qT) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-x logarithms. In this paper, we initiate the study of rapidity logarithms, and the associated rapidity divergences, at subleading order in the power expansion. This is accomplished using the soft collinear effective theory (SCET). We discuss the structure of subleading-power rapidity divergences and how to consistently regulate them. We introduce a new pure rapidity regulator and a corresponding MS¯\\[ \\overline{\\mathrm{MS}} \\]-like scheme, which handles rapidity divergences while maintaining the homogeneity of the power expansion. We find that power-law rapidity divergences appear at subleading power, which give rise to derivatives of parton distribution functions. As a concrete example, we consider the qT spectrum for color-singlet production, for which we compute the complete qT2/Q2 suppressed power corrections at Oαs\\[ \\mathcal{O}\\left({\\alpha}_s\\right) \\], including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.

Abstract We consider the production of a pair of heavy quarksQQ̅ ̅in association with a generic colour singlet system V at lepton colliders, and present the first analytic calculation of the two-loop soft function differential in the total momentum of the real radiation. The calculation is performed by reducing the relevant Feynman integrals into a canonical basis of master integrals by means of integration-by-parts identities. The resulting integrals are then evaluated by solving a system of differential equations in the kinematic invariants, whose boundary conditions are determined analytically with some care due to the presence of Coulomb singularities. The fully differential soft function is expressed in terms of Goncharov polylogarithms. This result is an essential ingredient for a range of N3LL resummations for key collider observables at lepton colliders, such as theQQ̅ ̅Vproduction cross section at threshold and observables sensitive to the total transverse momentum of the radiation in heavy-quark final states. Moreover, it constitutes the complete final-final dipole contribution to the fully differential soft function needed for the description ofQQ̅ ̅Vproduction at hadron colliders, which plays an important role in the LHC physics programme.

Abstract We present a formulation to give renormalon-free predictions consistently with fixed order perturbative results. The formulation has a similarity to Lee’s method in that the renormalon-free part consists of two parts: one is given by a series expansion which does not contain renormalons and the other is the real part of the Borel integral of a singular Borel transform. The main novel aspect is to evaluate the latter object using a dispersion relation technique, which was possible only in the large-β 0 approximation. Here, we introduce an “ ambiguity function,” which is defined by inverse Mellin transform of the singular Borel transform. With the ambiguity function, we can rewrite the Borel integral in an alternative formula, which allows us to obtain the real part using analytic techniques similarly to the case of the large-β 0 approximation. We also present detailed studies of renormalization group properties of the formulation. As an example, we apply our formulation to the fixed-order result of the static QCD potential, whose closest renormalon is already visible.

Typically, a production of a particle with a small transverse momentum in hadron-hadron collisions is described by CSS-based TMD factorization at moderate Bjorken xB 1 and by kT-factorization at small xB. A uniform description valid for all xB is provided by rapidity-only TMD factorization developed in a series of recent papers at the tree level. In this paper the rapidity-only TMD factorization for particle production by gluon fusion is extended to the one-loop level.

Abstract We present results for SCET and bHQET matching coefficients and jet functions in the large-β 0 limit. Our computations exactly predict all terms of the form α s n + 1 n f n α_(s)ⁿ⁺¹n_(f)ⁿ for any n ≥ 0, and we find full agreement with the coefficients computed in the full theory up to O α s 4 𝓞\\left{(}{α}{_(s)}⁴\\right) . We obtain all-order closed expressions for the cusp and non-cusp anomalous dimensions (which turn out to be unambiguous) as well as matrix elements (with ambiguities) in this limit, which can be easily expanded to arbitrarily high powers of α s using recursive algorithms to obtain the corresponding fixed-order coefficients. Examining the poles laying on the positive real axis of the Borel-transform variable u we quantify the perturbative convergence of a series and estimate the size of non-perturbative corrections. We find a so far unknown u = 1/2 renormalon in the bHQET hard factor H m that affects the normalization of the peak differential cross section for boosted top quark pair production. For ambiguous series the so-called Borel sum is defined with the principal value prescription. Furthermore, one can assign an ambiguity based on the arbitrariness of avoiding the poles by contour deformation into the positive or negative imaginary half-plane. Finally, we compute the relation between the pole mass and four low-scale short distance masses in the large-β 0 approximation (MSR, RS and two versions of the jet mass), work out their μ- and R-evolution in this limit, and study how their implementation improves the convergence of the position-space bHQET jet function, whose three-loop coefficient in full QCD is numerically estimated.

Parton distribution functions (PDFs) at large x are challenging to extract from experimental data, yet they are essential for understanding hadron structure and searching for new physics beyond the Standard Model. Within the framework of the large momentum Pz expansion of lattice quasi-PDFs, we investigate large x PDFs, where the matching coefficient is factorized into the hard kernel, related to the active quark momentum xPz, and the threshold soft function, associated with the spectator momentum (1 − x)Pz. The renormalization group equation of the soft function enables the resummation of the threshold double logarithms αk ln2k(1 − x), which is crucial for a reliable and controllable calculation of large x PDFs. Our analysis with pion valence PDFs indicates that perturbative matching breaks down when the spectator momentum (1 − x)Pz approaches ΛQCD, but remains valid when both xPz and (1 − x)Pz are much larger than ΛQCD. Additionally, we incorporate leading renormalon resummation within the threshold framework, demonstrating good perturbative convergence in the region where both spectator and active quark momenta are perturbative scales.

A bstract We critically examine the magnitude of theoretical uncertainties in perturbative calculations of fist-order phase transitions, using the Standard Model effective field theory as our guide. In the usual daisy-resummed approach, we find large uncertainties due to renormalisation scale dependence, which amount to two to three orders-of-magnitude uncertainty in the peak gravitational wave amplitude, relevant to experiments such as LISA. Alternatively, utilising dimensional reduction in a more sophisticated perturbative approach drastically reduces this scale dependence, pushing it to higher orders. Further, this approach resolves other thorny problems with daisy resummation: it is gauge invariant which is explicitly demonstrated for the Standard Model, and avoids an uncontrolled derivative expansion in the bubble nucleation rate.

A bstract Typically, a production of a particle with a small transverse momentum in hadron-hadron collisions is described by CSS-based TMD factorization at moderate Bjorken x B ~ 1 and by k T -factorization at small x B . A uniform description valid for all x B is provided by rapidity-only TMD factorization developed in a series of recent papers at the tree level. In this paper the rapidity-only TMD factorization for particle production by gluon fusion is extended to the one-loop level.