Huber, Tobias
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Publication Access status: Metadata only , Feynman integral reduction using Gröbner basesWe investigate the reduction of Feynman integrals to master integrals using Gröbner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal. The problem of reducing a given family of integrals to master integrals can then be solved once and for all by computing the Gröbner basis of the left ideal formed by the IBP relations. We demonstrate this explicitly for several examples. We introduce so-called first-order normal-form IBP relations which we obtain by reducing the shift operators in Y modulo the Gröbner basis of the left ideal of IBP relations. For more complicated cases, where the Gröbner basis is computationally expensive, we develop an ansatz based on linear algebra over a function field to obtain the normal-form IBP relations.Source Type:Article1 - Some of the metrics are blocked by yourconsent settings
Publication Access status: Metadata only , Inclusive $$\overline{B}\to {X}_s{\ell}^{+}{\ell}^{-}$$ at the LHC: theory predictions and new-physics reachWe present theoretical predictions for observables in inclusive $\overline{B}\to {X}_s{\ell}^{+}{\ell}^{-}$ suitable for measurements at hadron colliders through a sum-over-exclusive approach. At low $q^{2}$ we calculate the branching ratio and three angular observables. At high $q^{2}$ we provide the branching ratio and the ratio of the $\overline{B}\to {X}_s{\ell}^{+}{\ell}^{-}$ rate with respect to the inclusive $\overline{B}\to {X}_u\ell \overline{\nu}$ rate with the same phase-space cut. We compare our predictions to the B factory measurements and also to an extraction of the experimental rate through a sum-over-exclusive method using branching ratios of the exclusive $\overline{B}\to {K}^{\left(\ast \right)}{\mu}^{+}{\mu}^{-}$ modes measured at LHCb. We find a consistent picture comparing Standard Model theory and experiment. As such, our analysis does not support a recent claim about a deficit in the inclusive branching ratio in the high- $q^{2}$ region. Finally, we present current model-independent bounds on new physics and emphasize the potential of complementary analyses of $\overline{B}\to {X}_s{\ell}^{+}{\ell}^{-}$ at Belle II and the LHC.Source Type:Article2
