Gauge coupling beta functions in the Standard Model
We report about the computation of three-loop corrections to the gauge coupling beta functions in the Standard Model.
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arXiv subjects
Matthias Steinhauser
Publications and source records attributed to Matthias Steinhauser.
Decoupling constant for $α_s$ and the effective gluon-Higgs coupling to three loops in supersymmetric QCD
We compute the three-loop QCD corrections to the decoupling constant for $α_s$ which relates the Minimal Supersymmetric Standard Model to Quantum Chromodynamics with five or six active flavours. The new results can be used to study the stability of $α_s$ evaluated at a high scale from the knowledge of its value at $M_Z$. We furthermore derive a low-energy theorem which allows the calculation of the coefficient function of the effective Higgs boson-gluon operator from the decoupling constant. This constitutes the first independent check of the matching coefficient to three loops.
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Supersymmetric next-to-next-to-leading order corrections to Higgs boson production in gluon fusion
We compute the total cross section for the production of a light CP even Higgs boson within the framework of supersymmetric QCD up to next-to-next-to-leading order. Technical subtleties in connection to the evaluation of three-loop Feynman integrals with many mass scales are discussed in detail and explicit results for the counterterms of the evanescent couplings are provided. The new results are applied to several phenomenological scenarios which are in accordance with the recent discovery at the LHC. In a large part of the still allowed parameter space the $K$ factor of the supersymmetric theory is close to the one of the Standard Model. However, for the case where one of the top squarks is light, a deviation of more than 5% in the next-to-next-to-leading order prediction of the cross section can be observed where at the same time the predicted Higgs boson mass has a value of about 125 GeV.
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Towards Higgs boson production in gluon fusion to NNLO in the MSSM
We consider the Higgs boson production in the gluon-fusion channel to next-to-next-to-leading order within the Minimal Supersymmetric Standard Model. In particular, we present analytical results for the matching coefficient of the effective theory and study its influence on the total production cross section in the limit where the masses of all MSSM particles coincide. For supersymmetric masses below 500 GeV it is possible to find parameters leading to a significant enhancement of the Standard Model cross section, the $K$-factors, however, change only marginally.
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Moments of heavy quark correlators with two masses: exact mass dependence to three loops
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.
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Gauge Coupling Beta Functions in the Standard Model to Three Loops
In this paper we compute the three-loop corrections to the beta functions of the three gauge couplings in the Standard Model of particle physics using the minimal subtraction scheme and taking into account Yukawa and Higgs self couplings.
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Simultaneous decoupling of bottom and charm quarks
Parameters and light fields of the QCD Lagrangian with two heavy flavours, b and c, are related to those in the low-energy effective theory without these flavours, to three-loop accuracy taking into account the exact dependence on m_c/m_b. Similar relations for bilinear quark currents are also considered.
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CRunDec: a C++ package for running and decoupling of the strong coupling and quark masses
In this paper we present the {\tt C++} package {\tt CRunDec} which implements all relevant formulae needed for the running and decoupling for the strong coupling constant and light quark masses. Furthermore, several formulae are implemented which can be used to transform the heavy quark masses among different renormalization schemes. {\tt CRunDec} is the {\tt C++} version on the {\tt Mathematica} package {\tt RunDec} containing several updates and improvements.
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Gluino Pair Production at the LHC: The Threshold
The next-to-leading order analysis of the cross section of hadronic gluino pair production close to threshold is presented. Within the framework of non-relativistic QCD a significant enhancement compared to fixed order perturbation theory is observed which originates from the characteristic remnant of the 1S peak below the nominal pair threshold. This enhancement is similar to the corresponding one for top production. However, as a consequence of the larger colour factor of the QCD potential the effect is significantly enhanced. The analysis includes all colour configurations of S-wave gluino pairs, i.e. singlet, symmetric and antisymmetric octet, decuplet and twenty-seven representation. Matching coefficients involving real and virtual radiation are separately evaluated for all colour and spin configurations and initial states. We concentrate on the case of gluino decay rates comparable to the gluino binding energy. The non-relativistic dynamics of the gluino pair is solved by calculating the Green's function in NLO. Numerical results for the Large Hadron Collider at sqrt(s)=14 TeV and 7 TeV are presented for various characteristic scenarios.
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Heavy quark and gluino potentials to two loops
The static potentials for systems of a heavy quark and anti-quark, two gluinos and a quark and a gluino are computed for all possible colour configurations of a $SU(N_c)$ gauge group.
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Simultaneous decoupling of bottom and charm quarks
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 $m_c/m_b$. 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 $α_s$.
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Production of scalar and pseudo-scalar Higgs bosons to next-to-next-to-leading order at hadron colliders
We consider the production of intermediate-mass CP-even and CP-odd Higgs bosons in proton-proton and proton-anti-proton collisions. We extend the recently published results for the complete next-to-next-to-leading order calculation for a scalar Higgs boson to the pseudo-scalar case and present details of the calculation that might be useful for similar future investigations. The result is based on an expansion in the limit of a heavy top quark mass and a subsequent matching to the expression obtained in the limit of infinite energy. For a Higgs boson mass of 120 GeV the deviation from the infinite-top quark mass result is small. For 300 GeV, however, the next-to-next-to-leading order corrections for a scalar Higgs boson exceed the effective-theory result by about 9% which increases to 22% in the pseudo-scalar case. Thus in this mass range the effect on the total cross section amounts to about 2% and 6%, respectively, which may be relevant in future precision studies.
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Three-loop anomalous dimensions for squarks in supersymmetric QCD
In this paper we evaluate the renormalization constants and anomalous dimensions for the squark wave function and mass within supersymmetric QCD. These results complement the ones obtained in Ref. \cite{Harlander:2009mn} and thus provide further confirmation on the applicability of dimensional reduction to supersymmetric QCD at three-loop order. The three-loop anomalous dimension constitute important input to precision predictions of the supersymmetric mass spectrum as obtained from the evolution from the GUT to the TeV energy scale.
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Complete next-to-leading order gluino contributions to b--> s gamma and b--> s g
We present the first complete order alpha_s corrections to the Wilson coefficients (at the high scale) of the various versions of magnetic and chromomagnetic operators which are induced by a squark-gluino exchange. For this matching calculation, we work out the on-shell amplitudes b--> s gamma and b --> s g, both in the full and in the effective theory up to order alpha_s^2. The most difficult part of the calculation is the evaluation of the two-loop diagrams in the full theory; these can be split into two classes: a) diagrams with one gluino and a virtual gluon; b) diagrams with two gluinos or with one gluino and a four-squark vertex. Accordingly, the Wilson coefficients can be split into a part a) and a part b). While part b) of the Wilson coefficients is presented in this paper for the first time, part a) was given in (Bobeth et al.). We checked their results for the coefficients of the magnetic operators and found perfect agreement. Moreover, we work out the renormalization procedure in great detail. Our results for the complete next-to-leading order Wilson coefficients are fully analytic, but far too long to be printed. We therefore publish them in the form of a C++ program. They constitute a crucial building block for the phenomenological next-to-leading logarithmic analysis of the branching ratio Bbar --> X_s gamma in a supersymmetric model beyond minimal flavor violation.
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Moments of heavy-light current correlators up to three loops
We consider moments of the non-diagonal vector, axial-vector, scalar and pseudo-scalar current correlators involving two different massive quark flavours up to three-loop accuracy. Expansions around the limits where one mass is zero and the equal-mass case are computed. These results are used to construct approximations valid for arbitrary mass values.
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Heavy-light current-current correlators
The current-current correlator method has been used successfully to obtain very accurate results for quark masses and the coupling alpha_s. The calculations were done using Highly Improved Staggered Quarks (HISQ) and heavy-heavy meson correlators. We now extend this work to the significantly more challenging heavy-light case, reporting the first results here. The aim is to determine nonperturbative Z factors for NRQCD heavy-light currents, but first we test the method in the HISQ case where Z=1.
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The static quark potential to three loops in perturbation theory
The static potential constitutes a fundamental quantity of Quantum Chromodynamics. It has recently been evaluated to three-loop accuracy. In this contribution we provide details on the calculation and present results for the 14 master integrals which contain a massless one-loop insertion.
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Beyond Heavy Top Limit In Higgs Boson Production At LHC
QCD corrections to inclusive Higgs boson production at the LHC are evaluated at next-to-next-to leading order. By performing asymptotic expansion of the cross section near the limit of infinitely heavy top quark we obtained a few first top mass-suppressed terms. The corrections to the hadronic cross sections are found to be small compared to the scale uncertainty, thus justifying the use of heavy top quark approximation in many published results.
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