Jens Hoff

On the Higgs boson pair production at the LHC

We compute the production cross section of a pair of Standard Model Higgs bosons at the LHC at next-to-leading order in QCD, including corrections in inverse powers of the top quark mass. We calculate these power corrections through O(1/Mt8) and study their relevance for phenomenology of the double Higgs production. We find that power corrections are significant, even for moderate values of partonic center-of-mass energies, and that convergence of the 1/Mt1/Mt expansion can be dramatically improved by factorizing the leading order cross section with full MtMt-dependence.

Higgs boson production at the LHC: NNLO partonic cross sections through order

We consider Higgs boson production at hadron colliders in the gluon fusion channel and compute higher order terms in the regularization parameter ǫ. In particular, the next-to-next-to-leading order cross section is evaluated including order ǫ terms. These results are used to compute all convolutions with the splitting functions entering the next-to-next-to-next-to-leading order cross section.

\epsilon

We compute next-to-next-to-leading order QCD corrections to the gluon-induced production cross section of Higgs boson pairs in the large top quark mass limit using the soft-virtual approximation. In the limit of infinitely-heavy top quark we confirm the results in the literature. We add two more expansion terms in the inverse top quark mass to the Mt → ∞ result. Since the 1/Mt expansion converges poorly, we try to improve on it by factorizing the exact leading order cross section. We discuss two ways of doing that and conclude that the finite top quark mass effects shift the cross section at most by about 10% at next-to-leading order and by about 5% at next-to-next-to-leading order.

and convolutions with splitting functions to N

A bstractWe study master integrals needed to compute the Higgs boson production cross section via gluon fusion in the infinite top quark mass limit, using a canonical form of differential equations for master integrals, recently identified by Henn, which makes their solution possible in a straightforward algebraic way. We apply the known criteria to derive such a suitable basis for all the phase space master integrals in afore mentioned process at next-to-next-to-leading order in QCD and demonstrate that the method is applicable to next-to-next-to-next-to-leading order as well by solving a non-planar topology. Furthermore, we discuss in great detail how to find an adequate basis using practical examples. Special emphasis is devoted to master integrals which are coupled by their differential equations.

^3

We compute the decoupling relations for the strong coupling, the light quark masses, the gauge-fixing parameter, and the light fields in QCD with heavy charm and bottom quarks to three-loop accuracy taking into account the exact dependence on mc/mb. The application of a low-energy theorem allows the extraction of the three-loop effective Higgs-gluon coupling valid for extensions of the Standard Model with additional heavy quarks from the decoupling constant of αs.

LO

A bstractWe compute the contribution to the total cross section for the inclusive production of a Standard Model Higgs boson induced by two quarks with different flavour in the initial state. Our calculation is exact in the Higgs boson mass and the partonic center-of-mass energy. We describe the reduction to master integrals, the construction of a canonical basis, and the solution of the corresponding differential equations. Our analytic result contains both Harmonic Polylogarithms and iterated integrals with additional letters in the alphabet.

Higgs boson pair production: Top quark mass effects at NLO and NNLO

A bstractWe compute the contribution to the total cross section for the inclusive production of a Standard Model Higgs boson induced by two quarks with different flavour in the initial state. Our calculation is exact in the Higgs boson mass and the partonic center-of-mass energy. We describe the reduction to master integrals, the construction of a canonical basis, and the solution of the corresponding differential equations. Our analytic result contains both Harmonic Polylogarithms and iterated integrals with additional letters in the alphabet.

Adequate bases of phase space master integrals for gg → h at NNLO and beyond

Abstract We compute moments of non-diagonal correlators with two massive quarks. Results are obtained where no restriction on the ratio of the masses is assumed. Both analytical and numerical methods are applied in order to evaluate the two-scale master integrals at three loops. We provide explicit results for the latter which are useful for other calculations. As a by-product we obtain results for the electroweak ρ parameter up to three loops which can be applied to a fourth generation of quarks with arbitrary masses.

Simultaneous decoupling of bottom and charm quarks

Abstract We introduce the Mathematica package MT which can be used to compute, both analytically and numerically, convolutions involving harmonic polylogarithms, polynomials or generalized functions. As applications contributions to next-to-next-to-next-to leading order Higgs boson production and the Drell–Yan process are discussed. Program summary Title of program: MT Available from: http://www-ttp.physik.uni-karlsruhe.de/Progdata/ttp13/ttp13-27/ Computer for which the program is designed and others on which it is operable: Any computer where Mathematica versionxa06 or higher is running. Operating system or monitor under which the program has been tested: Linux No. of bytes in distributed program including test data etc.: approximately 50 000 bytes, and tables of approximately 60 megabytes Distribution format: source code Keywords: Convolution of partonic cross sections and splitting functions, Mellin transformation, harmonic sums, harmonic polylogarithms, Higgs boson production, Drell–Yan process Nature of physical problem: For the treatment of collinear divergences connected to initial-state radiation it is necessary to consider convolutions of partonic cross sections with splitting functions. MT can be used to compute such convolutions. Method of solution: MT is implemented in Mathematica and we provide several functions in order to perform transformations to Mellin space, manipulations of the expressions, and inverse Mellin transformations. Restrictions on the complexity of the problem: In case the weight of the input quantities is too high the tables for the (inverse) Mellin transforms have to be extended. In the current implementation the tables contain expressions up to weight eight, code for the generation of tables of even higher weight is provided, too. MT can only handle convolutions of expressions involving harmonic polylogarithms, plus distributions and polynomials in the partonic variable x . Typical running time: In general the run time for the individual operations is at most of the order of a few minutes (depending on the speed and memory of the computer).

Exact N

We consider power corrections due to a finite top quark mass M_t to the production of a Higgs boson pair within the Standard Model at next-to-leading order (NLO) in QCD. Previous calculations for this process and at this precision were done in the limit of an inifinitely heavy top quark. Our results for the inclusive production cross section at NLO include terms up to O(1/M_t^12). We present the Mathematica package TopoID which for arbitrary processes aims to perform the necessary steps from Feynman diagrams to unrenormalized results expressed in terms of master integrals. We employ it for advancing in this process towards next-to-next-to-leading order (NNLO) where further automatization is needed.