# Thomas Gehrmann

## Publications Authored By Thomas Gehrmann

Hadronic jets in deeply inelastic electron-proton collisions are produced by the scattering of a parton from the proton with the virtual gauge boson mediating the interaction. The HERA experiments have performed precision measurements of inclusive single jet production and di-jet production in the Breit frame, which provide important constraints on the strong coupling constant and on parton distributions in the proton. We describe the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to these processes, and assess their size and impact. Read More

We compute the order $\alpha_s^2$ QCD corrections to the $b$-quark forward-backward asymmetry in $e^+e^-\to b{\bar b}$ collisions at the $Z$ boson resonance, taking the non-zero mass of the $b$ quark into account. We determine these corrections with respect to both the $b$-quark axis and the thrust axis definition of the asymmetry. We compute also the distributions of these axes with respect to the electron beam. Read More

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. Read More

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. Read More

We present the computation of Higgs boson plus one jet production at NNLO at the LHC. The computation is carried out in the heavy-top-quark approximation and using the antenna subtraction formalism to handle the IR divergent structure of the individual contributions. All channels and all colours are included. Read More

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. Read More

The coupling of a pseudo-scalar Higgs boson to gluons is mediated through a heavy quark loop. In the limit of large quark mass, it is described by an effective Lagrangian that only admits light degrees of freedom. In this effective theory, we compute the three-loop massless QCD corrections to the form factor that describes the coupling of a pseudo-scalar Higgs boson to gluons. Read More

The rare Higgs boson decay $H\to Z\gamma$ is forbidden at tree-level. In the Standard Model, it is loop-mediated through a $W$ boson or a heavy quark. We analytically compute the QCD correction to the heavy quark loop, confirming earlier purely numerical results, that were obtained for on-shell renormalization. Read More

We compute the two-loop massless QCD corrections to the helicity amplitudes for the production of two massive vector bosons in quark-antiquark annihilation, allowing for an arbitrary virtuality of the vector bosons: $q \bar q' \to V_1V_2$. Combining with the leptonic decay currents, we obtain the full two-loop QCD description of the corresponding electroweak four-lepton production processes. The calculation is performed by projecting the two-loop diagrams onto an appropriate basis of Lorentz structures. Read More

In this article, we compute the gluon fusion Higgs boson cross-section at N3LO through the second term in the threshold expansion. This calculation constitutes a major milestone towards the full N3LO cross section. Our result has the best formal accuracy in the threshold expansion currently available, and includes contributions from collinear regions besides subleading corrections from soft and hard regions, as well as certain logarithmically enhanced contributions for general kinematics. Read More

The factorisation of QCD matrix elements in the limit of two external partons becoming collinear is described by process-independent splitting amplitudes, which can be expanded systematically in perturbation theory. Working in conventional dimensional regularisation, we compute the two-loop splitting amplitudes for all simple collinear splitting processes, including subleading terms in the regularisation parameter. Our results are then applied to derive an analytical expression for the two-loop single-real contribution to inclusive Higgs boson production in gluon fusion to fourth order (N3LO) in perturbative QCD. Read More

We compute the three-loop QCD corrections to the vertex function for the Yukawa coupling of a Higgs boson to a pair of bottom quarks in the limit of vanishing quark masses. This QCD form factor is a crucial ingredient to third-order QCD corrections for the production of Higgs bosons in bottom quark fusion, and for the fully differential decay rate of Higgs bosons to bottom quarks. The infrared pole structure of the form factors agrees with the prediction from infrared factorization in QCD. Read More

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. Read More

This article summarizes new theoretical developments, ideas and results that were presented at the 2014 Moriond "QCD and High Energy Interactions". Read More

We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes for vector boson pair production at hadron colliders, $q \bar{q} \to V V$, and thus to compute this process to next-to-next-to-leading order accuracy in QCD. The master integrals are derived using the method of differential equations, employing a canonical basis for the integrals. Read More

We describe the perturbative calculation of the transverse parton distribution functions in all partonic channels up to next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate the cancellation of light-cone divergences and show that universal process-independent transverse parton distribution functions can be obtained through a refactorization. Our results serve as the first explicit higher-order calculation of these functions starting from first principles, and can be used to perform next-to-next-to-next-to-leading logarithmic $q_T$ resummation for a large class of processes at hadron colliders. Read More

We present the cross-section for the threshold production of the Higgs boson at hadron-colliders at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. We present an analytic expression for the partonic cross-section at threshold and the impact of these corrections on the numerical estimates for the hadronic cross-section at the LHC. With this result we achieve a major milestone towards a complete evaluation of the cross-section at N3LO which will reduce the theoretical uncertainty in the determination of the strengths of the Higgs boson interactions. Read More

We study the application of the Brodsky-Lepage-Mackenzie (BLM) scale setting prescription to event shape distributions in electron-positron collisions. The renormalization scale is set dynamically according to the BLM method. We study NLO predictions and we discuss extensions of the prescription to NNLO. Read More

We present a perturbative calculation of the transverse parton distribution functions in all partonic channels up to next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate for the first time that such a definition works beyond the first non-trivial order. We extract the coefficient functions relevant for a next-to-next-to-next-to-leading logarithmic $q_T$ resummation in a large class of processes at hadron colliders. Read More

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). Read More

We present the next-to-leading order QCD corrections to the production of a photon pair in association with one or two jets. This class of processes constitutes an important background for Higgs physics at the LHC. For the one jet process we include photon fragmentation contributions and perform a comparison between different photon isolation criteria and various isolation parameters. Read More

The soft current describes the factorization behavior of quantum chromodynamics (QCD) scattering amplitudes in the limit of vanishing energy of one of the external partons. It is process-independent and can be expanded in a perturbative series in the coupling constant. To all orders in the dimensional regularization parameter, we compute the two-loop correction to the soft current for processes involving two hard partons. Read More

**Authors:**Christian Bauer, Zvi Bern, Radja Boughezal, John Campbell, Neil Christensen, Lance Dixon, Thomas Gehrmann, Stefan Hoeche, Junichi Kanzaki, Alexander Mitov, Pavel Nadolsky, Fredrick Olness, Michael Peskin, Frank Petriello, Stefano Pozzorini, Laura Reina, Frank Siegert, Doreen Wackeroth, Jonathan Walsh, Ciaran Williams, Markus Wobisch

**Category:**High Energy Physics - Phenomenology

We present a study on high-performance computing and large-scale distributed computing for perturbative QCD calculations. Read More

We compute the cross section for the production of a high-mass photon pair in association with two hadronic jets to next-to-leading order (NLO) in quantum chromodynamics (QCD). Our results allow for the first time to reliably predict the absolute normalisation of this process, and demonstrate that the shape of important kinematical distributions is modified by higher-order effects. The perturbative corrections will be an important ingredient to precision studies of Higgs boson properties from its production in association with two jets. Read More

The production of a single top quark in association with an isolated photon probes the electromagnetic coupling structure of the top quark. We investigate the sensitivity of kinematical distributions at the LHC in single-top-plus-photon production in view of a detection of anomalous electric and magnetic dipole moments of the top quark. Read More

The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master integrals by solving linear relations among them. We then use differential equations in the external invariants to compute all master integrals that are relevant to planar Feynman amplitudes. Read More

We compute the helicity amplitudes for the processes $gg\to Zg$ and $gg\to Z\gamma$ to two loops in massless QCD. The perturbative expansion of these processes starts only at the one-loop level, such that our results are a crucial ingredient to the NLO corrections to $Z\gamma$ and $Z+$jet production through gluon fusion. Read More

We report the calculation of next-to-next-to-leading order (NNLO) QCD corrections in the purely gluonic channel to dijet production and related observables at hadron colliders. Our result represents the first NNLO calculation of a massless jet observable at hadron colliders, and opens the path towards precision QCD phenomenology with the LHC. Read More

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. Read More

In the context of the dispersive model for non-perturbative corrections, we extend the leading renormalon subtraction to NNLO for the thrust distribution in $e^+e^-$ annihilation. Within this framework, using a NNLL+NNLO perturbative description and including bottom quark mass effects to NLO, we analyse data in the centre-of-mass energy range $\sqrt{s}=14-206$ GeV in view of a simultaneous determination of the strong coupling constant and the non-perturbative parameter $\alpha_0$. The fits are performed by matching the resummed and fixed-order predictions both in the R and the log-R matching schemes. Read More

We present a calculation of the perturbative quark-to-quark transverse parton distribution function at next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate for the first time that such a definition works beyond the first non-trivial order. We extract from our calculation the coefficient functions relevant for a next-to-next-to-next-to-leading logarithmic $Q_T$ resummation in a large class of processes at hadron colliders. Read More

The antenna subtraction method handles real radiation contributions in higher order corrections to jet observables. The method is based on antenna functions, which encapsulate all unresolved radiation between a pair of hard radiator partons. To apply this method to compute hadron collider observables, initial-initial antenna functions with both radiators in the initial state are required in unintegrated and integrated forms. Read More

We present a new approach to combine multiple NLO parton-level calculations matched to parton showers into a single inclusive event sample. The method provides a description of hard multi-jet configurations at next-to leading order in the perturbative expansion of QCD, and it is supplemented with the all-orders resummed modelling of jet fragmentation provided by the parton shower. The formal accuracy of this technique is discussed in detail, invoking the example of electron-positron annihilation into hadrons. Read More

In this paper we study the Sudakov form factor in N=4 super Yang-Mills theory to the three-loop order. The latter is expressed in terms of planar and non-planar loop integrals. We show that it is possible to choose a representation in which each loop integral has uniform transcendentality. Read More

The self-couplings of the electroweak gauge bosons are probed at hadron colliders through the production of a massive gauge boson and a photon. To extend the theoretical description of this type of final states towards next-to-next-to-leading order (NNLO) in QCD, we derive the two-loop QCD corrections to the helicity amplitudes describing the production of a massive gauge boson in association with a real photon. Our results are obtained by applying projectors to the general parton-level tensor structure. Read More

The antenna subtraction method handles real radiation contributions in higher order corrections to jet observables. The method is based on antenna functions, which encapsulate all unresolved radiation between a pair of hard radiator partons. To apply this method to compute hadron collider observables, initial-initial antenna functions with both radiators in the initial state are required. Read More

The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. Read More

In this talk, I review recent developments in perturbative QCD and their applications to collider physics. Read More

We present an extension of the multi-purpose Monte-Carlo event generator Sherpa for processes in deeply inelastic lepton-nucleon scattering. Hadronic final states in this kinematical setting are characterised by the presence of multiple kinematical scales, which were up to now accounted for only by specific resummations in individual kinematical regions. An extension of a known method for merging truncated parton showers with higher-order tree-level matrix elements allows to obtain predictions which are reliable in all kinematical limits. Read More

Heading towards a full automation of next-to-leading order (NLO) QCD corrections, one important ingredient is the analytical integration over the one-particle phase space of the unresolved particle that is necessary when adding the subtraction terms to the virtual corrections. We present the implementation of these integrated dipoles in the MadGraph framework. The result is a package that allows an automated calculation for the NLO real emission parts of an arbitrary process. Read More

We present a complete calculation of the electroweak O(alpha^3 alpha_s) corrections to three-jet production and related event-shape observables at electron--positron colliders. The Z-boson resonance is described within the complex-mass scheme, rendering the calculation valid both in the resonance and off-shell regions. Higher-order initial-state radiation is included in the leading-logarithmic approximation. Read More

We report on a recent calculation of the electroweak O(\alpha^3\alpha_s) corrections to 3-jet production and related event-shape observables at e+e- colliders. The calculation properly accounts for the experimental photon isolation criteria and for the corrections to the total hadronic cross section. Corrections to the normalised event-shape distributions, which are exemplarily discussed here for the thrust distribution at LEP and linear-collider energies, turn out to be at the few-per-cent level and show remnants of the radiative return to the Z pole even after inclusion of appropriate cuts. Read More

In this talk we present the extension of the antenna subtraction method to include initial states containing one hadron at NNLO. We sketch the requirements for the different necessary subtraction terms, and we explain how the antenna functions are integrated over the appropriate phase space by reducing the integrals to a small set of master integrals. Where applicable, our results for the integrated antennae were cross-checked against the known NNLO coefficient functions for deep inelastic scattering processes. Read More

We extend the multi-purpose Monte-Carlo event generator Sherpa to include processes in deeply inelastic lepton-nucleon scattering. Hadronic final states in this kinematical setting are characterised by the presence of multiple kinematical scales, which were up to now accounted for only by specific resummations in individual kinematical regions. Using an extension of the recently introduced method for merging truncated parton showers with higher-order tree-level matrix elements, it is possible to obtain predictions which are reliable in all kinematical limits. Read More

We compute the electroweak ${\cal O}(\alpha^3\alpha_s)$ corrections to three-jet production and related event-shape observables at electron-positron colliders. We properly account for the experimental photon isolation criteria and for the corrections to the total hadronic cross section. Corrections to the three-jet rate and to normalised event-shape distributions turn out to be at the few-per-cent level. Read More

In this letter we discuss a certain class of Hidden Valley models where the dynamics in the hidden sector are close to a strongly coupled conformal fixed point. We show that these models can explain the excess in cosmic ray muon events with high muon multiplicities that has been reported from cosmic ray studies with the ALEPH and DELPHI detectors. We further point out that these models can also at least partially account for the excess in multi-muon events that was found by the CDF experiment. Read More

**Authors:**Hannes Jung, Albert De Roeck, Jochen Bartels, Olaf Behnke, Johannes Blumlein, Stanley Brodsky, Amanda Cooper-Sarkar, Michal Deak, Robin Devenish, Markus Diehl, Thomas Gehrmann, Guenter Grindhammer, Gosta Gustafson, Valery Khoze, Albert Knutsson, Max Klein, Frank Krauss, Krzysztof Kutak, Eric Laenen, Leif Lonnblad, Leszek Motyka, Paul R. Newman, Fred Olness, Daniel Pitzl, Marta Ruspa, Agustin Sabio Vera, Gavin P. Salam, Thomas Schorner-Sadenius, Mark Strikman

**Category:**High Energy Physics - Phenomenology

More than 100 people participated in a discussion session at the DIS08 workshop on the topic What HERA may provide. A summary of the discussion with a structured outlook and list of desirable measurements and theory calculations is given. Read More

A summary of new experimental results and recent theoretical developments discussed in the "Hadronic Final States and QCD" working group is presented. Read More

We present the implementation of the dipole subtraction formalism for the real radiation contributions to any next-to-leading order QCD process in the MadGraph/MadEvent framework. Both massless and massive dipoles are considered. Starting from a specific (n+1)-particle process the package provides a Fortran code for all possible dipoles to all Born processes that constitute the subtraction term to the (n+1)-particle process. Read More