In cross sections with angular cuts, an intricate pattern of enhanced higher-order corrections known as nonglobal logarithms arises. The leading logarithmic terms were computed numerically two decades ago, but the resummation subleading remained a challenge that we solve in this Letter using renormalization group methods effective field theory. To achieve next-to-leading accuracy, implement two-loop anomalous dimension governing into large-N_{c} parton shower framework, together one-loop...

Phase separation (PS) proteins form droplets to regulate myriad membraneless organelles (MLOs) and cellular pathways such as transcription, signaling transduction protein degeneration. PS are usually liquid-like can convert hydrogel/solid-like under certain conditions. The behavior of is regulated by co-PS partners mutations, modifications, oligomerizations, repeat regions alternative splicing the proteins. With growing interest in condensates associated proteins, we established PhaSepDB...

A bstract We revisit the calculation of perturbative quark transverse momentum de- pendent parton distribution functions and fragmentation using exponential regulator for rapidity divergences. show that provides a consistent framework various ingredients in dependent factorization. Compared to existing regulators literature, has couple advantages which we explain detail. As result, calcula- tion is greatly simplified are able obtain next-to-next-to-leading order results up O ( E 2 )...

Canonical Feynman integrals are of great interest in the study scattering amplitudes at multi-loop level. We propose to construct $d\log$-form hypergeometric type, treat them as a representation integrals, and project into master using intersection theory. This provides constructive way build canonical whose differential equations can be solved easily. use our method investigate both maximally cut uncut ones one two loops, demonstrate its applicability problems with multiple scales.

A bstract new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows the consistent inclusion of scale dependence strong coupling, thereby providing more reliable estimates uncertainties theoretical predictions. The key idea to rearrange relevant RG...

Since the discovery of Higgs boson at Large Hadron Collider, a future electron-position collider has been proposed for precisely studying its properties. We investigate production such an ${e}^{+}{e}^{\ensuremath{-}}$ associated with $Z$ boson, and calculate first time mixed QCD-electroweak corrections to total cross sections. provide approximate analytic formula section show that it reproduces exact numeric results rather well energies up 350 GeV. also $\sqrt{s}=500\text{ }\text{...

The soft radiation emitted in jet cross sections can resolve the directions and colors of individual hard partons, leading to a complicated pattern logarithmically enhanced terms perturbative series. Starting from factorization theorem solving renormalization group equations for its ingredients, these large logarithms be resummed. In this paper, we extract two-loop anomalous dimension governing resummation subleading other non-global observables. This obtained by considering limits...

In this work, we present for the first time a calculation of complete next-to-leading order corrections to gg→ZH process. We use method small mass expansion tackle most challenging two-loop virtual amplitude, in which top quark dependence is retained throughout calculations. show that our provides reliable numeric results all kinematic regions, and phenomenological predictions total differential cross sections at Large Hadron Collider its future upgrades. Our are necessary ingredients...

A bstract The resummation of the “Glauber series” in non-global LHC observables is extended to processes with gluons initial state. This series simultaneously incorporates large double-logarithmic corrections, so-called “super-leading logarithms”, together higher-order exchanges pairs Glauber associated numerical factor ( iπ ) 2 . On a technical level, main part this work devoted systematic reduction appearing color traces and construction basis structures, which consist thirteen elements...

A bstract It is well-known that all Feynman integrals within a given family can be expressed as finite linear combination of master integrals. The naturally group into sectors. Starting from two loops, there exist sectors made up more than one integral. In this paper we show such may have additional symmetries. First all, self-duality, which was first observed in related to Calabi-Yau geometries, often carries over non-Calabi-Yau Secondly, addition Galois symmetries relating the simplest...

A bstract The Glauber series for non-global jet observables at hadron colliders simultaneously includes the super-leading logarithms alongside an arbitrary number of phases. Building on formalism [1], it is shown that leading terms in this large N c can be resummed closed form renormalization-group improved perturbation theory. This remarkable observation suggests large- methods might also helpful to study other aspects colliders, and combine our analytic results with amplitude-level parton showers.

We propose that loop integrals with internal heavy particles can be evaluated by expanding in the limit of small external masses. This provides a systematically improvable approximation to entire phase space, and works particularly well for high energy tails kinematic distributions (where usual $1/M$ expansions cease valid). demonstrate our method using Higgs boson pair production as an example. find at both one-loop two-loop, good approximations appearing scattering amplitudes. Comparing...

We present a precise and efficient computation of the two-loop amplitudes entering Higgs boson pair production process via gluon fusion. Our approach is based on small-Higgs-mass expansion while keeping full dependence top quark mass other kinematic invariants. compare our results to up-to-date predictions combination sector decomposition high-energy expansion. find that method provides precision numeric in entire phase space, at same time highly as can be easily performed normal desktop or...

A bstract To separate the energetic photons produced in hard scattering processes from those other sources, measurements impose isolation requirements which restrict hadronic radiation inside a cone around photon. In this paper, we perform detailed factorization analysis of QCD effects associated with photon isolation. We show that for small radius R , can be captured by fragmentation function describing decay parton into accompanied radiation. compute different criteria and solve...

We report on an exact calculation of lattice correlation functions a finite four-dimensional with either Euclidean or Minkowskian signature. The are calculated by the method differential equations. This can be used for and signature alike. have power series expansion in $1/\sqrt{\lambda}$, where $\lambda$ is coupling. show that this convergent all non-zero values $\lambda$. At small coupling we quantify accuracy perturbative approximations. technical level systematically investigate...

We present the first calculation of next-to-next-to-leading order threshold soft function for top quark pair production at hadron colliders, with full velocity dependence massive quarks. Our results are fully analytic, and can be entirely written in terms generalized polylogarithms. The scale-dependence our result coincides well-known two-loop anomalous dimension matrix including three-parton correlations, which only appear when more than one partons involved scattering process. In boosted...

We consider the two-loop corrections to $HW^+W^-$ vertex at order $\alpha\alpha_s$. construct a canonical basis for integrals using Baikov representation and intersection theory. By solving $\epsilon$-form differential equations, we obtain fully analytic expressions master in terms of multiple polylogarithms, which allow fast accurate numeric evaluation arbitrary configurations external momenta. apply our results decay process $H \to \nu_e e W$, study both integrated rates. Our can also be...

We calculate analytically the two-loop triangle integrals entering $\mathcal{O}(\alpha\alpha_s)$ corrections to $HZV$ vertex with $V=Z^*,\gamma^*$ using method of differential equations. Our result provides a prototype study analytic properties multi-loop multi-scale Feynman integrals, and also allows fast numeric evaluation for phenomenological studies. apply our results leptonic decay Higgs boson $ZH$ production at electron-positron colliders. Besides top quark loop, we include bottom loop...

We investigate top quark pair production near the threshold where invariant mass $$ {M}_{t\overline{t}} approaches 2mt, which provides sensitive observables to extract mt. Using effective field theory methods, we derive a factorization and resummation formula for kinematic distributions in limit up next-to- leading power, resums higher order Coulomb corrections all orders strong coupling constant. Our is similar those literature but differs several important aspects. apply our distribution,...

Symbol letters are crucial for analytically calculating Feynman integrals in terms of iterated integrals. We present a novel method to construct the symbol given integral family without prior knowledge canonical differential equations. provide program package implementing our algorithm, and demonstrate its effectiveness solving non-trivial problems with multiple loops legs. Using method, we successfully bootstrap equations two-loop five-point two external masses three-loop four-point masses,...

A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows the consistent inclusion of scale dependence strong coupling, thereby providing more reliable estimates uncertainties theoretical predictions. The key idea to rearrange relevant RG evolution...

The Glauber series for non-global jet observables at hadron colliders simultaneously includes the super-leading logarithms alongside an arbitrary number of phases. Building on formalism arXiv:2405.05305, it is shown that leading terms in this large $N_c$ can be resummed closed form renormalization-group improved perturbation theory. This remarkable observation suggests large-$N_c$ methods might also helpful to study other aspects colliders, and combine our analytic results with...

Abstract In this study, we investigate the invariant-mass distribution of top-quark pairs near 2 m t threshold, which strongly influences determination mass . Higher-order non-relativistic corrections lead to large contributions, are not included in state-of-the-art theoretical predictions. A factorization formula is derived resum such all orders strong-coupling, and necessary ingredients calculated perform resummation at next-to-leading power. We combine with fixed-order results present...

In cross sections with angular cuts, an intricate pattern of enhanced higher-order corrections known as non-global logarithms arises. The leading logarithmic terms were computed numerically two decades ago, but the resummation subleading remained a challenge that we solve in this Letter using renormalization group methods effective field theory. To achieve next-to-leading accuracy, implement two-loop anomalous dimension governing into large-$N_c$ parton shower framework, together one-loop...

The soft radiation emitted in jet cross sections can resolve the directions and colors of individual hard partons, leading to a complicated pattern logarithmically enhanced terms perturbative series. Starting from factorization theorem solving renormalization group equations for its ingredients, these large logarithms be resummed. In this paper, we extract two-loop anomalous dimension governing resummation subleading other non-global observables. This obtained by considering limits...