We extend our algorithm for automating the calculation of two-loop dijet soft functions to observables that do not obey the non-Abelian exponentiation theorem, i.e. to those that require an independent calculation of the uncorrelated-emission contribution. As the singularity structure of uncorrelated double emissions differs substantially from the one for correlated emissions, we introduce a novel phase-space parametrisation that isolates the corresponding divergences. The resulting integrals are implemented in SoftSERVE 1.0, which we release alongside of this work, and which we supplement by a regulator that is consistent with the rapidity renormalisation group framework. Using our automated setup, we confirm existing results for various jet-veto observables and provide a novel prediction for the soft-drop jet-grooming algorithm.
We extend our framework for the automated calculation of dijet soft functions to observables that do not obey the non-Abelian exponentiation theorem, like jet-veto or grooming soft functions that are sensitive to clustering effects of the jet algorithm. Although the matrix element for uncorrelated double emissions has a simpler structure than the one for correlated emissions, we argue that its singularity structure poses more stringent constraints on the required phase-space parametrisation. Our algorithm applies to both SCET-1 and SCET-2 soft functions and it is implemented in the novel progr…
We present compact integral representations for the calculation of two-loop anomalous dimensions for a generic class of soft functions that are defined in terms of two light-like Wilson lines. Our results are relevant for the resummation of Sudakov logarithms for e+ e- event-shape variables and inclusive hadron-collider observables at next-to-next-to-leading logarithmic accuracy within Soft-Collinear Effective Theory (SCET). Our formalism applies to both SCET-1 and SCET-2 soft functions and we clarify the relation between the respective soft anomalous dimension and the collinear anomaly expone…
We make progress towards resummation of power-suppressed logarithms in dijet event shapes such as thrust, which have the potential to improve high-precision fits for the value of the strong coupling constant. Using a newly developed formalism for Soft-Collinear Effective Theory (SCET), we identify and compute the anomalous dimensions of all the operators that contribute to event shapes at order $1/Q^2$. These anomalous dimensions are necessary to resum power-suppressed logarithms in dijet event shape distributions, although an additional matching step and running of observable-dependent soft f…
We present a systematic algorithm for the perturbative computation of soft functions that are defined in terms of two light-like Wilson lines. Our method is based on a universal parametrisation of the phase-space integrals, which we use to isolate the singularities in Laplace space. The observable-dependent integrations can then be performed numerically, and they are implemented in the new, publicly available package SoftSERVE that we use to derive all of our numerical results. Our algorithm applies to both SCET-1 and SCET-2 soft functions, and in the current version it can be used to compute …
We study the exclusive heavy quark dijet cross section from $e^+e^-$-annihilation using soft-collinear effective theory. In order to resum the large logarithms of small jet veto parameter $β$ and jet radius $R$, we factorize the cross section into the hard, hard-soft, collinear, and collinear-soft parts. Compared with the case of a massless quark, the jet sector with the collinear and collinear-soft parts can be modified to include the heavy quark mass. The factorization of the jet sector can be systematically achieved through matching onto the boosted heavy quark effective theory. Heavy quark…
We investigate the impact of soft gluon resummation on the azimuthal angle correlation between the total and relative momenta of two energetic final state particles (jets). We show that the initial and final state radiations induce sizable $\cos(ϕ)$ and $\cos (2ϕ)$ asymmetries in single jet and dijet events, respectively. We numerically evaluate the magnitude of these asymmetries for a number of processes in collider experiments, including diffractive dijet and dilepton production in ultraperipheral $pA$ and $AA$ collisions, inclusive and diffractive dijet production at the EIC and inclusive d…
Diffractive dijet production at the electron-ion collider (EIC) has been proposed to study the gluon Wigner distribution at small-$x$. We investigate the soft gluon radiation associated with the final state jets and an all order resummation formula is derived. We show that the soft gluon resummation plays an important role to describe E791 data on $π$-induced diffractive dijet production at Fermilab. Predictions for the EIC are presented, and we emphasize that the soft gluon resummation is an important aspect to explore the nucleon/nucleus tomography through these processes.
The factorization theorem for the dijet cross section is presented in hadron-hadron collisions with a cone-type jet algorithm. We also apply the beam veto to the beam jets consisting of the initial radiation. The soft-collinear effective theory is employed to see the factorization structure transparently when there are four distinct lightcone directions involved. There are various types of divergences such as the ultraviolet and infrared divergences. And when the phase space is divided to probe the collinear and the soft parts, there appears an additional divergence called rapidity divergence.…
We discuss central-forward dijet production at LHC energies within the framework of high energy factorization. In our study, we profit from the recent progress on consistent merging of Sudakov resummation with small-$x$ effects, which allows us to compute two different gluon distributions which depend on longitudinal momentum, transverse momentum and the hard scale of the process: one for the quark channel and one for the gluon channel. The small-$x$ resummation is included by means of the BK equation supplemented with a kinematic constraint and subleading corrections. We test the new gluon di…
Using Soft-Collinear Effective Theory, we develop the transverse-momentum-dependent factorization formalism for heavy flavor dijet production in polarized-proton-electron collisions. We consider heavy flavor mass corrections in the collinear-soft and jet functions, as well as the associated evolution equations. Using this formalism, we generate a prediction for the gluon Sivers asymmetry for charm and bottom dijet production at the future Electron-Ion Collider. Furthermore, we compare theoretical predictions with and without the inclusion of finite quark masses. We find that the heavy flavor m…
We study factorization in single transverse spin asymmetries for dijet production in proton-proton collisions, by considering soft gluon radiation at one-loop order. We show that the associated transverse momentum dependent (TMD) factorization is valid at the leading logarithmic level. At next-to-leading-logarithmic (NLL) accuracy, however, we find that soft gluon radiation generates terms in the single transverse spin dependent cross section that differ from those known for the unpolarized case. As a consequence, these terms cannot be organized in terms of a spin independent soft factor in th…
We discuss the measurement of gluon transverse momentum distribution (TMD) in dijet and heavy hadron pair (HHP) production in semi-inclusive deep inelastic scattering. The factorization of these processes in impact parameter space shows the appearance of a specific new soft factor matrix element on top of angular a complex valued anomalous dimensions. We show in detail how these features can be treated consistently and we discuss a scale prescription for the evolution kernel of the dijet soft function. As a result we obtain phenomenological predictions for unpolarized and angular modulated cro…
We consider the central exclusive production of high $E_T$ jets $pp\to p+(X+{\rm dijet})+p$. In particular we study the possible contamination of the purely exclusive signal by semi-exclusive production where no other secondaries are emitted in one hemisphere, between the highest $E_T$ dijet and the recoil proton, while in the other hemisphere a third jet, plus possibly additional hadron activity, is allowed, but still separated from the incoming proton by a large rapidity gap. This process arising from the fusion of a hard and a soft Pomeron has not been considered before. It turns out that i…
We study a transverse momentum dependent (TMD) factorization framework for the processes of di-jet and heavy meson pair production in deep-inelastic-scattering in an electron-proton collider, considering the measurement of the transverse momentum imbalance of the two hard probes in the Breit frame. For the factorization theorem we employ soft-collinear and boosted-heavy-quark effective field theories. The factorized cross-section for both processes is sensitive to gluon unpolarized and linearly polarized TMD distributions and requires the introduction of a new soft function. We calculate the n…
We present an operator based factorization formula for the transverse energy-energy correlator (TEEC) hadron collider event shape in the back-to-back (dijet) limit. This factorization formula exhibits a remarkably symmetric form, being a projection onto a scattering plane of a more standard transverse momentum dependent factorization. Soft radiation is incorporated through a dijet soft function, which can be elegantly obtained to next-to-next-to-leading order (NNLO) due to the symmetries of the problem. We present numerical results for the TEEC resummed to next-to-next-to-leading logarithm (NN…
Using the CGC effective theory together with the hybrid factorisation, we study forward dijet production in proton-nucleus collisions beyond leading order. In this paper, we compute the "real" next-to-leading order (NLO) corrections, i.e. the radiative corrections associated with a three-parton final state, out of which only two are being measured. To that aim, we start by revisiting our previous results for the three-parton cross-section presented in our previous paper. After some reshuffling of terms, we deduce new expressions for these results, which not only look considerably simpler, but …
The PYTHIA Monte Carlo (PMC), first introduced more than thirty years ago, remains a popular simulation tool both for analysis of $p$-$p$ collision dynamics and for detector design and calibration. The PMC assumes that almost all produced hadrons result from parton-parton scatterings (interactions) described by pQCD (a hard component), and that multiple parton interactions per collision event (MPIs) are a common occurrence. In contrast, a two-component (soft + hard) model (TCM) of high-energy collisions, inferred inductively from a variety of data formats, attributes a majority of final-state …
Resummed azimuthal decorrelation and transverse momentum imbalance of dijets at the LHC
Fudan University（复旦大学）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（NSFC与复旦大学上海理论核物理研究中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；University of Vienna（维也纳大学）；Nikhef（尼赫夫国家粒子物理研究所）；University of Amsterdam（阿姆斯特丹大学）；Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学加利西亚高能物理研究所）
We present a systematic framework for the calculation of soft functions that are defined in terms of $N\geq2$ light-like Wilson lines. The formalism represents an extension of a method that we developed earlier for the calculation of dijet soft functions to the general $N$-jet case. We discuss the technical aspects of this generalisation, focussing on SCET-1 soft functions that obey the non-Abelian exponentiation theorem in this contribution. As a first application of our method, we consider the $N$-jettiness observable and present numerical results for the $1$-jettiness and $2$-jettiness hadr…
We demonstrate that hard dijet production via coherent inelastic diffraction is a promising channel for probing gluon saturation at the Electron-Ion Collider. By $inelastic$ diffraction we mean a process in which the two hard jets - a quark-antiquark pair generated by the decay of the virtual photon - are accompanied by a softer gluon jet, emitted by the quark or the antiquark. This process can be described as the elastic scattering of an effective gluon-gluon dipole. The cross section takes a factorised form, between a hard factor and a unintegrated ("Pomeron") gluon distribution describing t…
