arXiv subjects

Claude Duhr

Publications and source records attributed to Claude Duhr.

At least 109 records · Page 6Linked to original sources

arXiv2018

Gluon-fusion Higgs production in the Standard Model Effective Field Theory

We provide the complete set of predictions needed to achieve NLO accuracy in the Standard Model Effective Field Theory at dimension six for Higgs production in gluon fusion. In particular, we compute for the first time the contribution of the chromomagnetic operator $ \bar Q_L Φσq_R G$ at NLO in QCD, which entails two-loop virtual and one-loop real contributions, as well as renormalisation and mixing with the Yukawa operator $Φ^\dagger Φ\, \bar Q_L Φq_R$ and the gluon-fusion operator $Φ^\dagger Φ\, GG$. Focusing on the top-quark-Higgs couplings, we consider the phenomenological impact of the NLO corrections in constraining the three relevant operators by implementing the results into the MadGraph5_aMC@NLO framework. This allows us to compute total cross sections as well as to perform event generation at NLO that can be directly employed in experimental analyses.

hep-ph↗

arXiv2018

Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case

We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the dimensional regulator are multiple polylogarithms (MPLs). Our main result is the conjecture that this diagrammatic coaction reproduces the combinatorics of the coaction on MPLs order by order in the Laurent expansion. We show that our conjecture holds in a broad range of nontrivial one-loop integrals. We then explore its consequences for the study of discontinuities of Feynman integrals, and the differential equations that they satisfy. In particular, using the diagrammatic coaction along with information from cuts, we explicitly derive differential equations for any one-loop Feynman integral. We also explain how to construct the symbol of any one-loop Feynman integral recursively. Finally, we show that our diagrammatic coaction follows, in the special case of one-loop integrals, from a more general coaction proposed recently, which is constructed by pairing master integrands with corresponding master contours.

hep-th↗

arXiv2017

Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.

hep-th↗

arXiv2017

The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy

We study some analytic properties of the BFKL ladder at next-to-leading logarithmic accuracy (NLLA). We use a procedure by Chirilli and Kovchegov to construct the NLO eigenfunctions, and we show that the BFKL ladder can be evaluated order by order in the coupling in terms of certain generalised single-valued multiple polylogarithms recently introduced by Schnetz. We develop techniques to evaluate the BFKL ladder at any loop order, and we present explicit results up to five loops. Using the freedom in defining the matter content of the NLO BFKL eigenvalue, we obtain conditions for the BFKL ladder in momentum space at NLLA to have maximal transcendental weight. We observe that, unlike in moment space, the result in momentum space in N = 4 SYM is not identical to the maximal weight part of QCD, and moreover that there is no gauge theory with this property. We classify the theories for which the BFKL ladder at NLLA has maximal weight in terms of their field content, and we find that these theories are highly constrained: there are precisely four classes of theories with this property involving only fundamental and adjoint matter, all of which have a vanishing one-loop beta function and a matter content that fits into supersymmetric multiplets. Our findings indicate that theories which have maximal weight are highly constrained and point to the possibility that there is a connection between maximal transcendental weight and superconformal symmetry.

hep-th↗

arXiv2017

Bootstrapping the QCD soft anomalous dimension

The soft anomalous dimension governs the infrared singularities of scattering amplitudes to all orders in perturbative quantum field theory, and is a crucial ingredient in both formal and phenomenological applications of non-abelian gauge theories. It has recently been computed at three-loop order for massless partons by explicit evaluation of all relevant Feynman diagrams. In this paper, we show how the same result can be obtained, up to an overall numerical factor, using a bootstrap procedure. We first give a geometrical argument for the fact that the result can be expressed in terms of single-valued harmonic polylogarithms. We then use symmetry considerations as well as known properties of scattering amplitudes in collinear and high-energy (Regge) limits to constrain an ansatz of basis functions. This is a highly non-trivial cross-check of the result, and our methods pave the way for greatly simplified higher-order calculations.

hep-ph↗

arXiv2017

Cuts from residues: the one-loop case

Using the multivariate residue calculus of Leray, we give a precise definition of the notion of a cut Feynman integral in dimensional regularization, as a residue evaluated on the variety where some of the propagators are put on shell. These are naturally associated to Landau singularities of the first type. Focusing on the one-loop case, we give an explicit parametrization to compute such cut integrals, with which we study some of their properties and list explicit results for maximal and next-to-maximal cuts. By analyzing homology groups, we show that cut integrals associated to Landau singularities of the second type are specific combinations of the usual cut integrals, and we obtain linear relations among different cuts of the same integral. We also show that all one-loop Feynman integrals and their cuts belong to the same class of functions, which can be written as parametric integrals.

hep-th↗

arXiv2017

The algebraic structure of cut Feynman integrals and the diagrammatic coaction

We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g. to hypergeometric functions. The coaction also applies to generic one-loop Feynman integrals with any configuration of internal and external masses, and in dimensional regularization. In this case, we demonstrate that it can be given a diagrammatic representation purely in terms of operations on graphs, namely contractions and cuts of edges. The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they admit. In particular, the differential equations for any one-loop integral are determined by the diagrammatic coaction using limited information about their maximal, next-to-maximal, and next-to-next-to-maximal cuts.

hep-th↗

arXiv2016

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

hep-th↗

arXiv2016

Long-distance singularities in multi-leg scattering amplitudes

We report on the recent completion of the three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes. This brings the state-of-the-art knowledge of long-distance singularities in multi-leg QCD amplitudes with any number of massless particles to three loops. The result displays some novel features: this is the first time non-dipole corrections appear, which directly correlate the colour and kinematic degrees of freedom of four coloured partons. We find that non-dipole corrections appear at three loops also for three coloured partons, but these are independent of the kinematics. The final result is remarkably simple when expressed in terms of single-valued harmonic polylogarithms, and it satisfies several non-trivial constraints. In particular, it is consistent with the high-energy limit behaviour and it satisfies the expected factorization properties in two-particle collinear limits.

hep-ph↗

arXiv2016

Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions

We present the CoLoRFulNNLO method to compute higher order radiative corrections to jet cross sections in perturbative QCD. We apply our method to the computation of event shape observables in electron-positron collisions at NNLO accuracy and validate our code by comparing our predictions to previous results in the literature. We also calculate for the first time jet cone energy fraction at NNLO.

hep-ph↗

arXiv2016

Three-loop corrections to the soft anomalous dimension in multi-leg scattering

We present the three-loop result for the soft anomalous dimension governing long-distance singularities of multi-leg gauge-theory scattering amplitudes of massless partons. We compute all contributing webs involving semi-infinite Wilson lines at three loops and obtain the complete three-loop correction to the dipole formula. We find that non-dipole corrections appear already for three coloured partons, where the correction is a constant without kinematic dependence. Kinematic dependence appears only through conformally-invariant cross ratios for four coloured partons or more, and the result can be expressed in terms of single-valued harmonic polylogarithms of weight five. While the non-dipole three-loop term does not vanish in two-particle collinear limits, its contribution to the splitting amplitude anomalous dimension reduces to a constant, and it only depends on the colour charges of the collinear pair, thereby preserving strict collinear factorization properties. Finally we verify that our result is consistent with expectations from the Regge limit.

hep-ph↗

arXiv2016

CP-even scalar boson production via gluon fusion at the LHC

In view of the searches at the LHC for scalar particle resonances in addition to the 125 GeV Higgs boson, we present the cross section for a CP-even scalar produced via gluon fusion at N3LO in perturbative QCD assuming that it couples directly to gluons in an effective theory approach. We refine our prediction by taking into account the possibility that the scalar couples to the top-quark and computing the corresponding contributions through NLO in perturbative QCD. We assess the theoretical uncertainties of the cross section due to missing higher-order QCD effects and we provide the necessary information for obtaining the cross section value and uncertainty from our results in specific scenarios beyond the Standard Model. We also give detailed results for the case of a 750 GeV scalar, which will be the subject of intense experimental studies.

hep-ph↗

arXiv2016

Three-jet production in electron-positron collisions using the CoLoRFulNNLO method

We introduce a subtraction method for jet cross sections at next-to-next-to-leading order (NNLO) accuracy in the strong coupling and use it to compute event shapes in three-jet production in electron-positron collisions. We validate our method on two event shapes, thrust and C-parameter, which are already known in the literature at NNLO accuracy and compute for the first time oblateness and the energy-energy correlation at the same accuracy.

hep-ph↗

arXiv2016

High precision determination of the gluon fusion Higgs boson cross-section at the LHC

We present the most precise value for the Higgs boson cross-section in the gluon-fusion production mode at the LHC. Our result is based on a perturbative expansion through N$^3$LO in QCD, in an effective theory where the top-quark is assumed to be infinitely heavy, while all other Standard Model quarks are massless. We combine this result with QCD corrections to the cross-section where all finite quark-mass effects are included exactly through NLO. In addition, electroweak corrections and the first corrections in the inverse mass of the top-quark are incorporated at three loops. We also investigate the effects of threshold resummation, both in the traditional QCD framework and following a SCET approach, which resums a class of $π^2$ contributions to all orders. We assess the uncertainty of the cross-section from missing higher-order corrections due to both perturbative QCD effects beyond N$^3$LO and unknown mixed QCD-electroweak effects. In addition, we determine the sensitivity of the cross-section to the choice of parton distribution function (PDF) sets and to the parametric uncertainty in the strong coupling constant and quark masses. For a Higgs mass of $m_H = 125~{\rm GeV}$ and an LHC center-of-mass energy of $13~{\rm TeV}$, our best prediction for the gluon fusion cross-section is \[ σ= 48.58\,{\rm pb} {}^{+2.22\, {\rm pb}\, (+4.56\%)}_{-3.27\, {\rm pb}\, (-6.72\%)} \mbox{ (theory)} \pm 1.56 \,{\rm pb}\, (3.20\%) \mbox{ (PDF+$α_s$)} \]

hep-ph↗

arXiv2015

Computing decay rates for new physics theories with FeynRules and MadGraph5/aMC@NLO

We present new features of the FeynRules and MadGraph5/aMC@NLO programs for the automatic computation of decay widths that consistently include channels of arbitrary final-state multiplicity. The implementations are generic enough so that they can be used in the framework of any quantum field theory, possibly including higher-dimensional operators. We extend at the same time the conventions of the Universal FeynRules Output (or UFO) format to include decay tables and information on the total widths. We finally provide a set of representative examples of the usage of the new functions of the different codes in the framework of the Standard Model, the Higgs Effective Field Theory, the Strongly Interacting Light Higgs model and the Minimal Supersymmetric Standard Model and compare the results to available literature and programs for validation purposes.

hep-ph↗

arXiv2015

Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N$^3$LO

We present methods to compute higher orders in the threshold expansion for the one-loop production of a Higgs boson in association with two partons at hadron colliders. This process contributes to the N$^3$LO Higgs production cross section beyond the soft-virtual approximation. We use reverse unitarity to expand the phase-space integrals in the small kinematic parameters and to reduce the coefficients of the expansion to a small set of master integrals. We describe two methods for the calculation of the master integrals. The first was introduced for the calculation of the soft triple-real radiation relevant to N$^3$LO Higgs production. The second uses a particular factorization of the three body phase-space measure and the knowledge of the scaling properties of the integral itself. Our result is presented as a Laurent expansion in the dimensional regulator, although some of the master integrals are computed to all orders in this parameter.

hep-ph↗

arXiv2015

Higgs boson gluon-fusion production in N3LO QCD

We present the cross-section for the production of a Higgs boson at hadron-colliders at next-to- next-to-next-to-leading order (N3LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross-section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N3LO in the large top-mass limit. For renormalisation and factorisation scales equal to half the Higgs mass, the N3LO corrections are of the order of +2.2%. The total scale variation at N3LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of three.

hep-ph↗

arXiv2015

Higgs boson decay into b-quarks at NNLO accuracy

We compute the fully differential decay rate of the Standard Model Higgs boson into b-quarks at next-to-next-to-leading order (NNLO) accuracy in alpha_S. We employ a general subtraction scheme developed for the calculation of higher order perturbative corrections to QCD jet cross sections, which is based on the universal infrared factorization properties of QCD squared matrix elements. We show that the subtractions render the various contributions to the NNLO correction finite. In particular, we demonstrate analytically that the sum of integrated subtraction terms correctly reproduces the infrared poles of the two-loop double virtual contribution to this process. We present illustrative differential distributions obtained by implementing the method in a parton level Monte Carlo program. The basic ingredients of our subtraction scheme, used here for the first time to compute a physical observable, are universal and can be employed for the computation of more involved processes.

hep-ph↗