We calculate the next-to-next-to-leading order ${\cal O}(α_s^4)$ one-loop squared corrections to the production of heavy-quark pairs in the gluon-gluon fusion process. Together with the previously derived results on the $q \bar{q}$ production channel the results of this paper complete the calculation of the one-loop squared contributions of the next-to-next-to-leading order ${\cal O}(α_s^4)$ radiative QCD corrections to the hadroproduction of heavy flavors. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in dimensional regularization.
We present a general formalism for computing the matrix-element squared for the emission of soft energy-ordered gluons beyond two loops in QCD perturbation theory at finite $N_c$. Our formalism is valid in the eikonal approximation. A Mathematica program has been developed for the automated calculation of all real/virtual eikonal squared amplitudes needed at a given loop order. For the purpose of illustration we show the explicit forms of the eikonal squared amplitudes up to the fifth-loop order. In the large-$N_c$ limit our results coincide with those previously reported in literature.
Having in mind the pre-equilibrium stage in peripheral heavy-ion collisions as a possible scenario for the production of electromagnetic radiation, we compute the two-gluon one-photon vertex in the presence of an intense magnetic field at one-loop order. The quarks in the loop are taken such that two of them occupy the lowest Landau level, with the third one occupying the first exited Landau level. When the field strength is the largest of the energy (squared) scales, the tensor basis describing this vertex corresponds to two of the three vector particles polarized in the longitudinal directio…
Next-to-next-to-leading order ${\cal O}(α^2α_s^2)$ results for top quark pair production in photon--photon collisions: The one-loop squared contributions
We present the analytic results of one-loop squared amplitudes for $tW$ production at a hadron collider. The calculation is performed using the method of differential equations. After renormalization, we have checked that the infrared divergences agree with the general structure predicted by anomalous dimensions. The finite remainder contributes to the next-to-next-to-leading order hard function, one of the essential ingredients in the factorization formula of the cross section near the infrared region, which can be used in resummation of all-order soft gluon effects or a differential next-to-…
The correspondence between the gluon density behavior of the color dipole picture and the two-Pomeron approach at low $x$ deep inelastic scattering is considered. For photon virtualities of $Q^{2}{\gtrsim}10~\mathrm{GeV}^{2}$, the results for the parametrization and CDP models are defined by the CDP asymptotic limit and are compatible with the soft and hard-Pomeron approach. These results show that the hard-Pomeron trajectory does not guarantee converging towards the asymptotic representation at low and large $Q^{2}$ ($Q^{2}{\lesssim}100~\mathrm{GeV}^{2}$) values in a wide range of the virtual…
We analyze neutrino-induced leptoquark production on atomic nuclei. A leptoquark term in the Lagrangian admits the possibility that neutrinos interact with gluons. The current lower limits on the leptoquark masses are of the order of 1 TeV depending on the leptoquark quantum numbers and couplings. Such heavy states can be produced in ultra-high energy cosmic neutrino scattering processes. The four-momentum transfer squared and the Bjorken variable simultaneously probed in these processes may reach values kinematically inaccessible at present collider experiments. We study the impact of the glu…
We consider double $gg\rightarrow g$ production in the presence of a bias on the unintegrated gluon distribution of the colliding hadron or nuclei. Such bias could be due to the selection of configurations with a greater number of gluons or higher mean transverse momentum squared or, more generally, due to a modified spectral shape of the gluon distribution in the hadrons. Hence, we consider reweighted functional averages over the stochastic ensemble of small-x gluons. We evaluate explicitly the double inclusive gluon transverse momentum spectrum in high-energy collisions, and their azimuthal …
We consider the radiation of a soft gluon ($g$) and a soft quark-antiquark ($q{\bar q}$) pair in QCD hard scattering. In the soft limit the scattering amplitude has a singular behaviour that is factorized and controlled by a soft current, which has a process-independent structure in colour space. We evaluate the soft $gq{\bar q}$ current at the tree level for an arbitrary multiparton scattering process. The irreducible correlation component of the current includes strictly non-abelian terms and also terms with an abelian character. Analogous abelian correlations appear for soft photon-lepton-a…
We provide two two-loop amplitudes relevant for precision Higgs physics. The first is the two-loop amplitude for Higgs boson production through gluon fusion with exact dependence on the top quark mass up to squared order in the dimensional regulator $ε$. The second result we provide is the two-loop amplitude for the decay of a Higgs boson into a pair of massive bottom quarks through the Higgs-to-gluon coupling in the infinite top mass limit. Both amplitudes are computed by finding canonical bases of master integrals, which we evaluate explicitly in terms of harmonic polylogarithms. We obtain t…
Production of two charm quark-antiquark pairs in single-parton scattering within the $k_t$-factorization approach
我们提出的第一个结果的$2 \to 4$单部分子散射$g g \to c \bar c c \bar c$子过程中的第一次完全在$k_t$ -因式分解方法。在这个计算中，我们使用了Kimber-Martin-Ryskin未积分胶子分布，它有效地包括了一些高阶胶子发射，以及使用最近开发的技术计算的离壳矩阵元平方。我们的结果进行了比较，较早的结果内的共线因子分解方法。只获得比共线方法稍大的截面。包含进入硬过程的胶子的横动量会导致$c c$和$\bar c \bar c$之间的方位角去相关比共线因子分解方法更强。双部分子散射（DPS）的预测结果和LHCb数据的比较强烈表明，两个完全独立的DPS（$g g \to c \bar c \otimes g g \to c \bar c$）的假设可能过于近似。
We present a calculation of the next-to-leading order (NLO) QCD corrections to gluon-induced electroweak gauge boson pair production, $gg \to ZZ$ and $gg \to W^+W^-$, matched to the PYTHIA8 parton shower in the POWHEG approach. The calculation consistently incorporates the continuum background, the Higgs-mediated $gg\to H^* \to VV$ process, and their interference. We consider leptonic decay modes of the massive vector bosons and retain offshell and non-resonant contributions. The processes considered are loop-induced at leading order and thus contain two-loop virtual contributions as well as l…
Inspired by Laughlin's theory of the fractional quantum Hall effect, we explore the topological nature of the quark-gluon plasma and the nucleons in the context of the Clifford algebra. In our model, each quark is transformed into a composite particle via the simultaneous attachment of a spin monopole and an isospin monopole. This is induced by a novel kind of meson endowed with both spin and isospin degrees of freedom. The interactions in the strongly coupled quark-gluon system are governed by the topological winding number of the monopoles, which is an odd integer to ensure that the overall …
We compute the production of prompt photons and the $v_2$ harmonic coefficient in relativistic heavy-ion collisions induced by gluon fusion in the presence of an intense magnetic field, during the early stages of the reaction. The calculations take into account several parameters which are relevant to the description of the experimental transverse momentum distribution, and elliptic flow for RHIC and LHC energies. The main imput is the strength of the magnetic field which varies in magnitude from 1 to 3 times the pion mass squared, and allows the gluon fusion that otherwise is forbidden in the…
During recent years perturbative fixed order and resummation calculations have decreased uncertainties on predictions for gluon fusion Higgs production cross sections tremendously. Most exciting results have been published just this year. In these proceedings I present an overview of recent and most recent developments of these calculations that allow theory predictions to compete with the experimental precision reached by future collider upgrades.
Next-to-next-to-leading order ${\cal O}(α_s^4)$ results for heavy quark pair production in quark--antiquark collisions: The one-loop squared contributions
We extend our previous work on scattering amplitudes [1] to hadron collisions. We provide a general formalism for the computation of eikonal amplitudes squared for the radiation of soft and energy-ordered gluons off three hard-legs at finite-N$_c$ to any order in the perturbative expansion. Examples of three-hard legs processes include vector/Higgs boson production in association with a single hard jet and dijet production in DIS. Explicit expressions for the radiation of up to four gluons are provided as an illustration of the formalism.
We calculate the transverse momentum dependent gluon-to-gluon splitting function within $k_T$-factorization, generalizing the framework employed in the calculation of the quark splitting functions in [1-3] and demonstrate at the same time the consistency of the extended formalism with previous results. While existing versions of $k_T$ factorized evolution equations contain already a gluon-to-gluon splitting function i.e. the leading order Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel or the Ciafaloni-Catani-Fiore-Marchesini (CCFM) kernel, the obtained splitting function has the important propert…
Fragmentation is the dominant mechanism for hadron production with high transverse momentum. For spin-triplet S-wave heavy quarkonium production, contribution of gluon fragmenting to color-singlet channel has been numerically calculated since 1993. However, there is still no analytic expression available up to now because of its complexity. In this paper, we calculate both polarization-summed and polarized fragmentation functions of gluon fragmenting to a heavy quark-antiquark pair with quantum number $^3S_1^{[1]}$. Our calculations are performed in two different frameworks. One is the widely …
We present the NLO (two-loop) QCD corrections to Higgs boson pair production in gluon fusion within Standard Model Effective Theory (SMEFT), including also squared dimension-6 operators and double insertions of operators. The different options to truncate the EFT expansion are contrasted to a non-linear EFT approach (HEFT) and their effects are illustrated by several phenomenological examples.
