Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report

This Report summarizes the proceedings of the 2015 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt with (I) new developments relevant for high precision Standard Model calculations, (II) the new PDF4LHC parton distributions, (III) issues in the theoretical description of the production of Standard Model Higgs bosons and how to relate experimental measurements, (IV) a host of phenomenological studies essential for comparing LHC data from Run I with theoretical predictions and projections for future measurements in Run II, and (V) new developments in Monte Carlo event generators.Comment: Proceedings of the Standard Model Working Group of the 2015 Les Houches Workshop, Physics at TeV Colliders, Les Houches 1-19 June 2015. 227 page

Model theory of finite and pseudofinite groups

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory

Parton distributions with scale uncertainties: a Monte Carlo sampling approach

Abstract We present the MCscales approach for incorporating scale uncertainties in parton distribution functions (PDFs). The new methodology builds on the Monte Carlo sampling for propagating experimental uncertainties into the PDF space that underlies the NNPDF approach, but it extends it to the space of factorisation and renomalisation scales. A prior probability is assigned to each scale combinations set in the theoretical predictions used to obtain each PDF replica in the Monte Carlo ensemble and a posterior probability is obtained by selecting replicas that satisfy fit-quality criteria. Our approach allows one to exactly match the scale variations in the PDFs with those in the computation of the partonic cross sections, thus accounting for the full correlations between the two. We illustrate the opportunities for phenomenological exploration made possible by our methodology for a variety of LHC observables. Sets of PDFs enriched with scale information are provided, along with a set of tools to use them.</jats:p

The top quark legacy of the LHC Run II for PDF and SMEFT analyses

Abstract We assess the impact of top quark production at the LHC on global analyses of parton distributions (PDFs) and of Wilson coefficients in the SMEFT, both separately and in the framework of a joint interpretation. We consider the broadest top quark dataset to date containing all available measurements based on the full Run II luminosity. First, we determine the constraints that this dataset provides on the large-x gluon PDF and study its consistency with other gluon-sensitive measurements. Second, we carry out a SMEFT interpretation of the same dataset using state-of-the-art SM and EFT theory cal- culations, resulting in bounds on 25 Wilson coefficients modifying top quark interactions. Subsequently, we integrate the two analyses within the SIMUnet approach to realise a simul- taneous determination of the SMEFT PDFs and the EFT coefficients and identify regions in the parameter space where their interplay is most phenomenologically relevant. We also demonstrate how to separate eventual BSM signals from QCD effects in the interpretation of top quark measurements at the LHC.</jats:p

Precision determination of the strong coupling constant within a global PDF analysis: NNPDF Collaboration

We present a determination of the strong coupling constant α s (m Z ) based on the NNPDF3.1 determination of parton distributions, which for the first time includes constraints from jet production, top-quark pair differential distributions, and the Zp T distributions using exact NNLO theory. Our result is based on a novel extension of the NNPDF methodology – th e correlated replica method – which allows for a simultaneous determination of α s and the PDFs with all correlations between them fully taken into account. We study in detail all relevant sources of experimental, methodological and theoretical uncertainty. At NNLO we find α s (m Z ) = 0.1185 ± 0. 0005 (exp) ± 0. 0001 (meth) , showing that methodological uncertainties are negligible. We conservatively estimate the theoretical uncertainty due to missing higher order QCD corrections (N 3 LO and beyond) from half the shift between the NLO and NNLO α s values, finding Δαsth=0.0011.E. S. and J. R. are supported by an European Research Council Starting Grant “PDF4BSM”. J. R. is also supposed by the Netherlands Organization for Scientific Research (NWO). The work of Z.K. is supported by the European Research Council Consolidator Grant “NNLOforLHC2” and by the Executive Research Agency (REA) of the European Commission under the Grant Agreement PITN-GA-2012-316704 (HiggsTools). S. C. is supported by the HICCUP ERC Consolidator Grant (614577). S. C. and S. F. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement no 740006). R. D. B and L. D. D. are supported by UK STFC Grants ST/L000458/1 and ST/P0000630/1

Precision determination of the strong coupling constant within a global PDF analysis: NNPDF Collaboration

We present a determination of the strong coupling constant α s (m Z ) based on the NNPDF3.1 determination of parton distributions, which for the first time includes constraints from jet production, top-quark pair differential distributions, and the Zp T distributions using exact NNLO theory. Our result is based on a novel extension of the NNPDF methodology – th e correlated replica method – which allows for a simultaneous determination of α s and the PDFs with all correlations between them fully taken into account. We study in detail all relevant sources of experimental, methodological and theoretical uncertainty. At NNLO we find α s (m Z ) = 0.1185 ± 0. 0005 (exp) ± 0. 0001 (meth) , showing that methodological uncertainties are negligible. We conservatively estimate the theoretical uncertainty due to missing higher order QCD corrections (N 3 LO and beyond) from half the shift between the NLO and NNLO α s values, finding Δαsth=0.0011.E. S. and J. R. are supported by an European Research Council Starting Grant “PDF4BSM”. J. R. is also supposed by the Netherlands Organization for Scientific Research (NWO). The work of Z.K. is supported by the European Research Council Consolidator Grant “NNLOforLHC2” and by the Executive Research Agency (REA) of the European Commission under the Grant Agreement PITN-GA-2012-316704 (HiggsTools). S. C. is supported by the HICCUP ERC Consolidator Grant (614577). S. C. and S. F. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement no 740006). R. D. B and L. D. D. are supported by UK STFC Grants ST/L000458/1 and ST/P0000630/1