We consider the infrared structure of hadron-hadron collisions at next-to-nextto 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 unresolved partons, denoted J ( ) 2 , are related to Catani's IR singularity operators, I ( ) ij ( ). 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.

(2017) 'Next-to-next-to leading order QCD predictions for single jet inclusive production at the LHC.', Physical review letters., 118 (7). 072002.Further information on publisher's website:https://doi.org/10.1103/PhysRevLett.118.072002Publisher's copyright statement:Reprinted with permission from the American Physical Society: Currie, J., Glover, E.W.N. Pires, J. (2017). Next-to-Next-to Leading Order QCD Predictions for Single Jet Inclusive Production at the LHC. Physical Review Letters 118(7): 072002. c 2017 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modi ed, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

The Large Hadron–Electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy-recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High-Luminosity Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron–proton and proton–proton operations. This report represents an update to the LHeC’s conceptual design report (CDR), published in 2012. It comprises new results on the parton structure of the proton and heavier nuclei, QCD dynamics, and electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics by extending the accessible kinematic range of lepton–nucleus scattering by several orders of magnitude. Due to its enhanced luminosity and large energy and the cleanliness of the final hadronic states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, this report contains a detailed updated design for the energy-recovery electron linac (ERL), including a new lattice, magnet and superconducting radio-frequency technology, and further components. Challenges of energy recovery are described, and the lower-energy, high-current, three-turn ERL facility, PERLE at Orsay, is presented, which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution, and calibration goals that arise from the Higgs and parton-density-function physics programmes. This paper also presents novel results for the Future Circular Collider in electron–hadron (FCC-eh) mode, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies.

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 increases the NNLO correction by around 10% and exhibits a p T dependence, rising from 8% at low p T to 15% at high p T . 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.