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Register a new userAnalytic integration of soft and collinear radiation in factorised QCD cross sections at NNLO
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Within the framework of local analytic sector subtraction, we present the full analytic integration of double-real and real-virtual local infrared counterterms that enter NNLO QCD computations with any number of massless final-state partons. We show that a careful choice of phase-space mappings leads to simple analytic results, including non-singular terms, that can be obtained with conventional integration techniques.
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We consider QCD radiative corrections to $W^+W^-$ production at the LHC and present the first fully differential predictions for this process at next-to-next-to-leading order (NNLO) in perturbation theory. Our computation consistently includes the leptonic decays of the $W$ bosons, taking into account spin correlations, off-shell effects and non-resonant contributions. Detailed predictions are presented for the different-flavour channel $pptomu^+e^- u_mu {bar u}_e+X$ at $sqrt{s}=8$ and $13$ TeV. In particular, we discuss fiducial cross sections and distributions in the presence of standard selection cuts used in experimental $W^+W^-$ and $Hto W^+W^-$ analyses at the LHC. The inclusive $W^+W^-$ cross section receives large NNLO corrections, and, due to the presence of a jet veto, typical fiducial cuts have a sizeable influence on the behaviour of the perturbative expansion. The availability of differential NNLO predictions, both for inclusive and fiducial observables, will play an important role in the rich physics programme that is based on precision studies of $W^+W^-$ signatures at the LHC.
When the energy of the heavy quark is comparable with its mass, it is natural to attribute this heavy quark to the hard part of the reaction. At large energies, this approach is impractical due to large logarithms from intensive QCD radiation affecting both inclusive and differential observables. We present a formalism for all-order summation of such logarithms and reliable description of heavy-quark distributions at all energies. As an illustration, we calculate angular distributions of B-mesons produced in neutral-current events at large momentum transfers at the ep collider HERA.
We demonstrate how to efficiently expand cross sections for color-singlet production at hadron colliders around the kinematic limit of all final state radiation being collinear to one of the incoming hadrons. This expansion is systematically improvable and applicable to a large class of physical observables. We demonstrate the viability of this technique by obtaining the first two terms in the collinear expansion of the rapidity distribution of the gluon fusion Higgs boson production cross section at next-to-next-to leading order (NNLO) in QCD perturbation theory. Furthermore, we illustrate how this technique is used to extract universal building blocks of scattering cross section like the N-jettiness and transverse momentum beam function at NNLO.
It is well-known that direct analytic continuation of DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as splitting functions are not analytic function of external momenta. However, splitting functions can be constructed from square of (generalized) splitting amplitudes. We establish the rule of analytic continuation for splitting amplitudes, and use them to determine the analytic continuation of certain holomorphic and anti-holomorphic part of splitting functions and transverse-momentum dependent distributions. In this way we derive the time-like splitting functions at three loops without ambiguity. We also propose a reciprocity relation for singlet splitting functions, and provide non-trivial evidence that it holds in QCD at least through three loops.
The cross sections of ultra-soft x-ray bremsstrahlung in at electron scattering by Ar, Kr and Xe are theoretically calculated. The results are consistent with the absolute values of the differential cross sections measured by Gnatchenko et al [Phys. Rev. A 80, 022707 (2009)] for scattering electrons with an energy of 600 eV on these atoms.
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