198 research outputs found

### Two-loop QCD corrections to gluon-gluon scattering

We present the virtual QCD corrections to gluonâgluon scattering due to the interference of tree- and two-loop amplitudes. We work in conventional dimensional regularisation and give analytic expressions renormalised in the scheme. The structure of the infrared divergences agrees with that predicted by Catani while formulae for the finite remainder are given in terms of logarithms and polylogarithms that are real in the physical region. These results, together with those previously obtained for quarkâquark and quarkâgluon scattering, complete the two-loop matrix elements needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders

### Real-virtual corrections for gluon scattering at NNLO

We use the antenna subtraction method to isolate the mixed real-virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In a previous paper, we derived the subtraction term that rendered the double real radiation tree-level process finite in the single and double unresolved regions of phase space. Here, we show how to construct the real-virtual subtraction term using antenna functions with both initial- and final-state partons which removes the explicit infrared poles present in the one-loop amplitude, as well as the implicit singularities that occur in the soft and collinear limits. As an explicit example, we write down the subtraction term that describes the single unresolved contributions from the five-gluon one-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space prior to integration, leaving a finite remainder that can be safely evaluated numerically in four-dimensions. We show numerically that the subtraction term correctly approximates the matrix elements in the various single unresolved configurations

### The singular behavior of massive QCD amplitudes

We discuss the structure of infrared singularities in on-shell QCD amplitudes
with massive partons and present a general factorization formula in the limit
of small parton masses. The factorization formula gives rise to an all-order
exponentiation of both, the soft poles in dimensional regularization and the
large collinear logarithms of the parton masses. Moreover, it provides a
universal relation between any on-shell amplitude with massive external partons
and its corresponding massless amplitude. For the form factor of a heavy quark
we present explicit results including the fixed-order expansion up to three
loops in the small mass limit. For general scattering processes we show how our
constructive method applies to the computation of all singularities as well as
the constant (mass-independent) terms of a generic massive n-parton QCD
amplitude up to the next-to-next-to-leading order corrections.Comment: version to appear in JHEP (sec. 3 with expanded discussion and
appendix with added results

### NNLO QCD corrections to event orientation in e+e- annihilation

We present a new implementation of the NNLO QCD corrections to three-jet final states and related event-shape observables in electronâpositron annihilation. Our implementation is based on the antenna subtraction method, and is performed in the NNLOjet framework. The calculation improves upon earlier results by taking into account the full kinematical information on the initial state momenta, thereby allowing the event orientation to be computed to NNLO accuracy. We find the event-orientation distributions at LEP and SLC to be very robust under higher order QCD corrections

### The two-loop scalar and tensor pentabox graph with light-like legs

We study the scalar and tensor integrals associated with the pentabox
topology: the class of two-loop box integrals with seven propagators - five in
one loop and three in the other. We focus on the case where the external legs
are light-like and use integration-by-parts identities to express the scalar
integral in terms of two master-topology integrals and present an explicit
analytic expression for the pentabox scalar integral as a series expansion in
ep = (4-D)/2. We also give an algorithm based on integration by parts for
relating the generic tensor integrals to the same two master integrals and
provide general formulae describing the master integrals in arbitrary dimension
and with general powers of propagators.Comment: Detailed expansions of intermediate results adde

### Double virtual corrections for gluon scattering at NNLO

We use the antenna subtraction method to isolate the double virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In previous papers, we derived the subtraction terms that rendered (a) the double real radiation tree-level process finite in the single and double unresolved regions of phase space and (b) the mixed single real radiation one-loop process both finite and well behaved in the unresolved regions of phase space. Here, we show how to construct the double virtual subtraction term using antenna functions with both initial- and final-state partons which remove the explicit infrared poles present in the two-loop amplitude. As an explicit example, we write down the subtraction term for the four-gluon two-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space leaving a finite remainder that can be safely evaluated numerically in four-dimensions

### Precise QCD predictions for the production of a Z boson in association with a hadronic jet

We compute the cross section and differential distributions for the production of a Z boson in association with a hadronic jet to next-to-next-to-leading order (NNLO) in perturbative QCD, including the leptonic decay of the Z boson. We present numerical results for the transverse momentum and rapidity distributions of both the Z boson and the associated jet at the LHC. We find that the NNLO corrections increase the NLO predictions by approximately 1% and significantly reduce the scale variation uncertainty

### Single photon production at hadron colliders at NNLO QCD with realistic photon isolation

Isolated photons at hadron colliders are defined by permitting only a limited amount of hadronic energy inside a fixed-size cone around the candidate photon direction. This isolation criterion admits contributions from collinear photon radiation off QCD partons and from parton-to-photon fragmentation processes. We compute the NNLO QCD corrections to isolated photon and photon-plus-jet production, including these two contributions. Our newly derived results allow us to reproduce the isolation prescription used in the experimental measurements, performing detailed comparisons with data from the LHC experiments. We quantify the impact of different photon isolation prescriptions, including no isolation at all, on photon-plus-jet cross sections and discuss possible measurements of the photon fragmentation functions at hadron colliders

### The NNLO QCD corrections to Z boson production at large transverse momentum

The transverse momentum distribution of massive neutral vector bosons can be measured to high accuracy at hadron colliders. The transverse momentum is caused by a partonic recoil, and is determined by QCD dynamics. We compute the single and double-differential transverse momentum distributions for fully inclusive Z/Îłâ production including leptonic decay to next-to-next-to-leading order (NNLO) in perturbative QCD. We also compute the same distributions normalised to the cross sections for inclusive Z/Îłâ production, i.e. integrated over the transverse momentum of the lepton pair. We compare our predictions for the fiducial cross sections to the 8 TeV data set from the ATLAS and CMS collaborations, which both observed a tension between data and NLO theory predictions, using the experimental cuts and binning. We find that the inclusion of the NNLO QCD effects does not fully resolve the tension with the data for the unnormalised pZT distribution. However, we observe that normalising the NNLO Z-boson transverse momentum distribution by the NNLO Drell-Yan cross section substantially improves the agreement between experimental data and theory, and opens the way for precision QCD studies of this observable

### Precise predictions for the angular coefficients in Z-boson production at the LHC

The angular distributions of lepton pairs in the Drell-Yan process can provide rich information on the underlying QCD production mechanisms. These dynamics can be parameterised in terms of a set of frame dependent angular coefficients, Ai=0,âŠ,7, which depend on the invariant mass, transverse momentum, and rapidity of the lepton pair. Motivated by recent measurements of these coefficients by ATLAS and CMS, and in particular by the apparent violation of the Lam-Tung relation A0âA2=0, we perform a precision study of the angular coefficients at O(Î±3s) in perturbative QCD. We make predictions relevant for pp collisions at sâ=8 TeV, and perform comparisons with the available ATLAS and CMS data as well as providing predictions for a prospective measurement at LHCb. To expose the violation of the Lam-Tung relationship we propose a new observable ÎLT=1âA2/A0 that is more sensitive to the dynamics in the region where A0 and A2 are both small. We find that the O(Î±3s) corrections have an important impact on the pT,Z distributions for several of the angular coefficients, and are essential to provide an adequate description of the data. The compatibility of the available ATLAS and CMS data is reassessed by performing a partial Ï2 test with respect to the central theoretical prediction which shows that Ï2/Ndata is significantly reduced by going from O(Î±2s) to O(Î±3s)

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