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James Currie

Publications and source records attributed to James Currie.

33 records · Page 2Linked to original sources
arXiv2016

A family of formulas with reversal of high avoidability index

We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting due to its size and the simple structure of its members. For each $k\in\{4,5\}$, there are several previously known avoidable formulas (without reversal) of avoidability index $k$, but they are small in number and they all have rather complex structure.

math.CO↗
arXiv2016

Precise QCD predictions for the production of dijet final states in deep inelastic scattering

The production of two-jet final states in deep inelastic scattering is an important QCD precision observable. We compute it for the first time to next-to-next-to-leading order (NNLO) in perturbative QCD. Our calculation is fully differential in the lepton and jet variables and allows one to impose cuts on the jets both in the laboratory and the Breit frame. We observe that the NNLO corrections are moderate in size, except at kinematical edges, and that their inclusion leads to a substantial reduction of the scale variation uncertainty on the predictions. Our results will enable the inclusion of deep inelastic dijet data in precision phenomenology studies.

hep-ph↗
arXiv2014

Second order QCD corrections to gluonic jet production at hadron colliders

We report on the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to the production of two gluonic jets at hadron colliders. In previous work, we discussed gluonic dijet production in the gluon-gluon channel. Here, for the first time, we update our numerical results to include the leading colour contribution to the production of two gluonic jets via quark-antiquark scattering.

hep-ph↗
arXiv2013

NNLO QCD corrections to dijet production at hadron colliders

In this talk we present the calculation of next-to-next-to-leading order (NNLO) QCD corrections to dijet production and related observables at hadron colliders in the purely gluonic channel. Results for this channel are obtained keeping all orders of $N_C$ in the colour expansion. We show that the NNLO correction significantly reduces the scale uncertainty compared to next-to-leading order (NLO). We present the NNLO double-differential single jet inclusive cross section where jets are reconstructed using the anti-$k_T$ jet algorithm and show the dependence on the jet resolution parameter $R$.

hep-ph↗
arXiv2013

Colourful antenna subtraction for gluon scattering

In this talk I discuss the application and generalization of the antenna subtraction method to processes involving incoherent interferences of partial amplitudes, which are generically present for the sub-leading colour contributions to processes involving more than five partons. The approach makes use of the known infrared (IR) singularity structure of one- and two-loop matrix elements to guide the construction of the subtraction terms. A set of integrated dipoles are defined which can be used to express the poles of one- and two-loop matrix elements in terms of integrated antennae. The unintegrated counterparts of these subtraction terms are then inferred to construct the double real and real-virtual subtraction terms. The method has been tested by computing the NNLO sub-leading colour contribution dijet production via gluon scattering. The double real and real virtual matrix elements for this process can be written purely in terms of incoherent interferences and so the successful removal of all singularities and divergences demonstrates the ability of the antenna subtraction method to handle general sub-leading colour contributions

hep-ph↗
arXiv2013

NNLO QCD corrections to jet production at hadron colliders from gluon scattering

We present the next-to-next-to-leading order (NNLO) QCD corrections to dijet production in the purely gluonic channel retaining the full dependence on the number of colours. The sub-leading colour contribution in this channel first appears at NNLO and, as expected, increases the NNLO correction by around 10% and exhibits a pT dependence, rising from 8% at low pT to 15% at high pT . The present calculation demonstrates the utility of the antenna subtraction method for computing the full colour NNLO corrections to dijet production at the Large Hadron Collider.

hep-ph↗
arXiv2013

Infrared Structure at NNLO Using Antenna Subtraction

We consider the infrared structure of hadron-hadron collisions at next-to-next-to leading order using the antenna subtraction method. The general form of the subtraction terms is presented for double real, real-virtual and double virtual contributions. At NLO and NNLO it is shown that the virtual and double virtual subtraction terms can be written in terms of integrated dipoles, formed by systematically combining the mass factorisation contributions and integrated antenna functions. The integrated dipoles describing $\ell$ unresolved partons, denoted $\bs{J}_{2}^{(\ell)}$, are related to Catani's IR singularity operators, $\bs{I}_{ij}^{(\ell)}(\eps)$. It is shown that the IR pole structure of the virtual and double virtual contributions can be written as a sum over integrated dipoles within the antenna subtraction formalism and the master expressions analogous to Catani's one- and two-loop factorisation formulae are derived. To demonstrate the techniques described in this paper, we apply antenna subtraction to the production of two gluon jets via quark-antiquark scattering at NLO and NNLO. Double real, real-virtual and double virtual subtraction terms are explicitly derived for the leading colour NNLO contribution.

hep-ph↗
arXiv2011

Antenna Subtraction in pQCD at NNLO

In this talk I discuss the antenna subtraction method for isolating infrared (IR) singularities of jet cross sections in perturbative QCD. The method is applied at next-to-next-to-leading order (NNLO) to dijet production in hadron collisions at the LHC. The double real radiative corrections to the dijet cross section are considered and their IR behaviour is examined. IR subtraction terms are constructed to absorb numerical divergences of the cross section in the single and double unresolved regions of phase space using the antenna subtraction method. A pictorial representation of matrix elements and antenna functions is presented with specific examples of how such diagrams can be used in practical calculations.

hep-ph↗
arXiv2009

Dejean's conjecture holds for n>=27

We show that Dejean's conjecture holds for n>=27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

math.CO↗
arXiv2009

A proof of Dejean's conjecture

We prove Dejean's conjecture. Specifically, we show that Dejean's conjecture holds for the last remaining open values of n, namely 15 <= n <= 26.

math.CO↗
arXiv2008

There are k-uniform cubefree binary morphisms for all k >= 0

A word is cubefree if it contains no non-empty subword of the form xxx. A morphism h : Sigma^* -> Sigma^* is k-uniform if h(a) has length k for all a in Sigma. A morphism is cubefree if it maps cubefree words to cubefree words. We show that for all k >= 0 there exists a k-uniform cubefree binary morphism.

math.CO↗
arXiv2008

Cubefree words with many squares

We construct infinite cubefree binary words containing exponentially many distinct squares of length n. We also show that for every positive integer n, there is a cubefree binary square of length 2n.

math.CO↗