We use general arguments to show that coloured QCD states when restricted to gauge invariant local observables are mixed. This result has important implications for confinement: a pure colourless state can never evolve into two coloured states by unitary evolution. Furthermore, the mean energy in such a mixed coloured state is infinite. Our arguments are confirmed in a matrix model for QCD that we have developed using the work of Narasimhan and Ramadas and Singer. This model, a $(0+1)$-dimensional quantum mechanical model for gluons free of divergences and capturing important topological aspects of QCD, is adapted to analytical and numerical work. It is also suitable to work on large $N$ QCD. As applications, we show that the gluon spectrum is gapped and also estimate some low-lying levels for $N=2$ and 3 (colors).
Incidentally the considerations here are generic and apply to any non-abelian gauge theory.
We calculate the complete set of two-loop leading-colour QCD helicity amplitudes for $γγj$-production at hadron colliders. Our results are presented in a compact, fully-analytical form.
In our world the standard model of particle physics contains within it the fairly intractable theory called QCD. A toy version with two colours is often studied as a model confining and chiral symmetry breaking field theory. Here we investigate the cascade of changes at various distance scales if we make this change within the standard model. It is possible to limit the changes at the hadronic scale. However, the minor changes that occur actually cascade down to the far infrared, into nuclear and atomic physics, and chemistry. Through this it also possibly affects the evolution of stars and ga…
We present the master integrals relevant for computing the complete set of leading-colour analytic helicity amplitudes for top-quark pair production via gluon fusion at two-loops in QCD. We include corrections due to massive fermion loops which give rise to integrals involving elliptic curves. We also elaborate on the structure of singularities that play an important role in the numerical evaluation of the iterated integrals and their analytic continuation.
We compute the two-loop QCD helicity amplitudes for the production of a Higgs boson in association with a bottom-quark pair at a hadron collider. We take the approximations of leading colour and work in the five flavour scheme, where the bottom quarks are massless while the Yukawa coupling is non-zero. We extract analytic expressions from multiple numerical evaluations over finite fields and present the results in terms of an independent set of special functions that can be reliably evaluated over the full phase space.
We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves. We present the results of the missing master integrals needed to compute the amplitude and obtain an analytic form for the finite remainders in terms of iterated integrals using rationalised kinematics and finite field sampling. We also study the numerical evaluation of the iterated integrals.
We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their …
We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the epsilon-regime of chiral perturbation theory at small mu, where mu^2 mult…
We report on recent progress in understanding confinement of colour in $QCD$ as dual superconductivity of the vacuum. A gauge invariant version of the creation operator of monopoles is constructed whose vacuum expectation value is the order parameter. This order parameter is gauge-invariant from scratch, has no infrared divergences, is finite in the confined phase and vanishes in the deconfined phase. A natural explanation also emerges of why the electric field lines in the flux tubes keep no memory of the colour orientation of the condensing monopoles. A further by-product is that the order p…
We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finite remainders from numerical evaluations over finite fields including all colour contributions. Compact expressions are found using the pentagon function basis. We provide a fast and stable implementation for the colour- and helicity-summed interference between the one-loop and two-loop finite remainders in C++ as part of the NJet library.
Two-loop QCD amplitudes for $t\bar{t}W$ production at the LHC in the leading-colour approximation
Università di Bologna and INFN, Sezione di Bologna（博洛尼亚大学与意大利国家核物理研究所博洛尼亚分部）；Universität Zürich（苏黎世大学）；University of Oxford（牛津大学）；CERN（欧洲核子研究中心）；Max-Planck-Institut für Physik, Werner-Heisenberg-Institut（马克斯·普朗克物理研究所韦纳·海森堡研究所）；Technical University of Munich（慕尼黑工业大学）
We study a bottom-up holographic description of the QCD colour superconducting phase in the presence of higher derivative corrections. We expand this holographic model in the context of Gauss-Bonnet (GB) gravity. The Cooper pair condensate has been investigated in the deconfinement phase for different values of the GB coupling parameter $λ_{G B}$, we observe a change in the value of the critical chemical potential $μ_c$ in comparison to Einstein gravity. We find that $μ_c$ grows as $λ_{G B}$ increases. We add four fermion interactions and show that in the presence of these corrections the main…
Transverse-momentum resummation at mixed QCD$\otimes$QED NNLL accuracy for Z boson production at hadron colliders
Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València（粒子物理研究所（IFIC），西班牙瓦伦西亚大学）；CERN（欧洲核子研究中心）；Tif Lab, Dipartimento di Fisica, Universitá di Milano and INFN, Sezione di Milano（米兰大学物理系及意大利国家核物理研究院米兰分部）；Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca（萨拉曼卡大学基础物理系）
