Reconstructing Rational Functions with FireFly\texttt{FireFly}

We present the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use $\texttt{FireFly}$ in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program $\texttt{Kira}$.Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio

Higgs mass prediction in the MSSM at three-loop level in a pure DR‾\overline{\text{DR}} context

The impact of the three-loop effects of order $\alpha_t\alpha_s^2$ on the mass of the light CP-even Higgs boson in the MSSM is studied in a pure $\overline{\text{DR}}$ context. For this purpose, we implement the results of Kant et al. into the C++ module Himalaya and link it to FlexibleSUSY, a Mathematica and C++ package to create spectrum generators for BSM models. The three-loop result is compared to the fixed-order two-loop calculations of the original FlexibleSUSY and of FeynHiggs, as well as to the result based on an EFT approach. Aside from the expected reduction of the renormalization scale dependence with respect to the lower order results, we find that the three-loop contributions significantly reduce the difference from the EFT prediction in the TeV-region of the SUSY scale $M_S$. Himalaya can be linked also to other two-loop $\overline{\text{DR}}$ codes, thus allowing for the elevation of these codes to the three-loop level.Comment: 32 pages, 8 figures, 1 table [version submitted to EPJC

Integral Reduction with Kira 2.0 and Finite Field Methods

We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly. This procedure can be parallelized on computer clusters with MPI. Furthermore, the support for user-provided systems of equations has been significantly improved. This mode provides the flexibility to integrate Kira into projects that employ specialized reduction formulas, direct reduction of amplitudes, or to problems involving linear system of equations not limited to relations among standard Feynman integrals. We show examples from state-of-the-art Feynman integral reduction problems and provide benchmarks of the new features, demonstrating significantly reduced main memory usage and improved performance w.r.t. previous versions of Kira

vh@nnlo-v2: new physics in Higgs Strahlung

Introducing version 2 of the code vh@nnlo [1], we study the effects of a number of new-physics scenarios on the Higgs-Strahlung process. In particular, the cross section is evaluated within a general 2HDM and the MSSM. While the Drell-Yan-like contributions are consistently taken into account by a simple rescaling of the SM result, the gluon-initiated contribution is supplemented by squark-loop mediated amplitudes, and by the s-channel exchange of additional scalars which may lead to conspicuous interference effects. The latter holds as well for bottom-quark initiated Higgs Strahlung, which is also included in the new version of vh@nnlo. Using an orthogonal rotation of the three Higgs CP eigenstates in the 2HDM and the MSSM, vh@nnlo incorporates a simple means of CP mixing in these models. Moreover, the effect of vector-like quarks in the SM on the gluon-initiated contribution can be studied. Beyond concrete models, vh@nnlo allows to include the effect of higher-dimensional operators on the production of CP-even Higgs bosons. Transverse momentum distributions of the final state Higgs boson and invariant mass distributions of the Vϕ final state for the gluon- and bottom-quark initiated contributions can be studied. Distributions for the Drell-Yan-like component of Higgs Strahlung can be included through a link to MCFM. vh@nnlo can also be linked to FeynHiggs and 2HDMC for the calculation of Higgs masses and mixing angles. It can also read these parameters from an SLHA-file as produced by standard spectrum generators. Throughout the manuscript, we highlight new-physics effects in various numerical examples, both at the inclusive level and for distributions

ZH production in gluon fusion: two-loop amplitudes with full top quark mass dependence

We present results for the two-loop helicity amplitudes entering the NLO QCD corrections to the production of a Higgs boson in association with a Z -boson in gluon fusion. The two-loop integrals, involving massive top quarks, are calculated numerically. Results for the interference of the finite part of the two-loop amplitudes with the Born amplitude are shown as a function of the two kinematic invariants on which the amplitudes depend

Transcriptome profiling of ontogeny in the acridid grasshopper Chorthippus biguttulus

Acridid grasshoppers (Orthoptera:Acrididae) are widely used model organisms for developmental, evolutionary, and neurobiological research. Although there has been recent influx of orthopteran transcriptomic resources, many use pooled ontogenetic stages obscuring information about changes in gene expression during development. Here we developed a de novo transcriptome spanning 7 stages in the life cycle of the acridid grasshopper Chorthippus biguttulus. Samples from different stages encompassing embryonic development through adults were used for transcriptomic profiling, revealing patterns of differential gene expression that highlight processes in the different life stages. These patterns were validated with semi-quantitative RT-PCR. Embryonic development showed a strongly differentiated expression pattern compared to all of the other stages and genes upregulated in this stage were involved in signaling, cellular differentiation, and organ development. Our study is one of the first to examine gene expression during post-embryonic development in a hemimetabolous insect and we found that only the fourth and fifth instars had clusters of genes upregulated during these stages. These genes are involved in various processes ranging from synthesis of biogenic amines to chitin binding. These observations indicate that post-embryonic ontogeny is not a continuous process and that some instars are differentiated. Finally, genes upregulated in the imago were generally involved in aging and immunity. Our study highlights the importance of looking at ontogeny as a whole and indicates promising directions for future research in orthopteran development

Precision calculations for Higgs physics in the standard model and beyond

At least since the discovery of the Higgs boson at the Large Hadron Collider at CERN, the Higgs sector of the Standard Model of particle physics has become one of the central research areas of high energy physics. Deviations between measurement and theoretical prediction within this sector have the potential to become a window on the quantum field theories describing nature. Besides the increasing precision of measurements, high-precision predictions are required to become sensitive on possible deviations. The focus of this work is on precise predictions of observables within the Higgs sector. On the one hand, studies of Higgs mass calculations within the context of the minimal supersymmetric extension of the Standard Model are presented, which include partial three-loop contributions. Different kinds of calculational methods are introduced, which, when combined, yield a reliable prediction of the light CP-even Higgs mass for in principle arbitrary parameter configurations. Utilizing the results of this work, the relative uncertainty of the predicted mass of the light CP-even Higgs can be reduced below the 1% level. Additionally, all corresponding results are implemented in an open-source program, which allows for further studies. Moreover, Higgs production in association with a vector boson at the Large Hadron Collider at CERN is studied. By exploiting a symmetry connecting the final state gauge bosons, a particular observable can be defined, that leads to the cancellation of various sources of uncertainty in both measurement and prediction. For illustration, an experimental analysis for this observable is performed, which demonstrates an increased sensitivity to possible deviations between measurement and prediction, and, in addition, yields to evidence for the production of a Higgs boson associated with a Z boson through gluon fusion. Finally, the recent progress in the calculation of two-loop corrections to Higgs-Z production via gluon fusion including the full top-quark mass dependence are presented. To include these quark-mass effects, novel algebraic methods are developed and provided with an implementation into an open-source program, that can find wide application in the calculation of multi-loop Feynman diagrams

The light CP-even MSSM Higgs mass including N

We present a calculation of the light neutral CP-even Higgs boson pole mass in the real MSSM which combines state-of-the-art EFT and fixed-order results, including the three-loop fixed-order QCD corrections as well as the resummation of logarithmic terms in the ratio of the weak to the SUSY scale up to fourth logarithmic order. This hybrid calculation should be valid for arbitrary SUSY scales above the weak scale. Comparison to the pure fixed-order and EFT results provides an estimate of their individual validity range.Comment: 20 pages, 4 figures, 1 table; changed uncertainty estimate of fixed-order calculation; v2 matches version published in EPJ