Mass Insertions vs. Mass Eigenstates calculations in Flavour Physics

We present and prove a theorem of matrix analysis, the Flavour Expansion Theorem (or FET), according to which, an analytic function of a Hermitian matrix can be expanded polynomially in terms of its off-diagonal elements with coefficients being the divided differences of the analytic function and arguments the diagonal elements of the Hermitian matrix. The theorem is applicable in case of flavour changing amplitudes. At one-loop level this procedure is particularly natural due to the observation that every loop function in the Passarino-Veltman basis can be recursively expressed in terms of divided differences. FET helps to algebraically translate an amplitude written in mass eigenbasis into flavour mass insertions, without performing diagrammatic calculations in flavour basis. As a non-trivial application of FET up to a third order, we demonstrate its use in calculating strong bounds on the real parts of flavour changing mass insertions in the up- squark sector of the MSSM from neutron Electric Dipole Moment (nEDM) measurements, assuming that CP-violation arises only from the CKM matrix.Comment: 23 page

Rare Top-quark Decays to Higgs boson in MSSM

In full one-loop generality and in next-to-leading order in QCD, we study rare top to Higgs boson flavour changing decay processes $t\to q h$ with $q=u,c$ quarks, in the general MSSM with R-parity conservation. Our primary goal is to search for enhanced effects on $Br(t\to q h)$ that could be visible at current and high luminosity LHC running. To this end, we perform an analytical expansion of the amplitude in terms of flavour changing squark mass insertions that treats both cases of hierarchical and degenerate squark masses in a unified way. We identify two enhanced effects allowed by various constraints: one from holomorphic trilinear soft SUSY breaking terms and/or right handed up squark mass insertions and another from non-holomorphic trilinear soft SUSY breaking terms and light Higgs boson masses. Interestingly, even with $\mathcal{O}(1)$ flavour violating effects in the, presently unconstrained, up-squark sector, SUSY effects on $Br(t\to q h)$ come out to be unobservable at LHC mainly due to leading order cancellations between penguin and self energy diagrams and the constraints from charge- and colour-breaking minima (CCB) of the MSSM vacuum. An exception to this conclusion may be effects arising from non-holomorphic soft SUSY breaking terms in the region where the CP-odd Higgs mass is smaller than the top-quark mass but this scenario is disfavoured by recent LHC searches. Our calculations for $t\to q h$ decay are made available in SUSY_FLAVOR numerical library.Comment: 32 pages, 6 figures; version accepted for publication in JHEP: additional comparison with literature added, minor misprints correcte

Effective Field Theories in R_xi gauges

In effective quantum field theories, higher dimensional operators can affect the canonical normalization of kinetic terms at tree level. These contributions for scalars and gauge bosons should be carefully included in the gauge fixing procedure, in order to end up with a convenient set of Feynman rules. We develop such a setup for the linear R_xi-gauges. It involves a suitable reduction of the operator basis, a generalized gauge fixing term, and a corresponding ghost sector. Our approach extends previous results for the dimension-six Standard Model Effective Field Theory to a generic class of effective theories with operators of arbitrary dimension.Comment: 16 pages, no figure

SmeftFR v3 -- Feynman rules generator for the Standard Model Effective Field Theory

We present version 3 of SmeftFR, a Mathematica package designed to generate the Feynman rules for the Standard Model Effective Field Theory (SMEFT) including the complete set of gauge invariant operators up to dimension-6 and the complete set of bosonic operators of dimension-8. Feynman rules are generated with the use of FeynRules package, directly in the physical (mass eigenstates) basis for all fields. The complete set of interaction vertices can be derived, including all or any chosen subset of SMEFT operators. As an option, the user can also choose preferred gauge fixing, generating Feynman rules in unitary or $R_\xi$-gauges. The novel feature in version-3 of SmeftFR is its ability to calculate SMEFT interactions consistently up to dimension-8 in EFT expansion (including quadratic dimension-6 terms) and express the vertices directly in terms of user-defined set of input-parameters. The derived Lagrangian in the mass basis can be exported in various formats supported by FeynRules, such as UFO, FeynArts etc. Initialisation of numerical values of Wilson coefficients of higher dimension operators is interfaced to WCxf format. The package also includes a dedicated Latex generator allowing to print the result in clear human-readable form. The SmeftFR v3 is publicly available at www.fuw.edu.pl/smeft.Comment: 51 pages, version accepted for publication in Computer Physics Communications. arXiv admin note: substantial text overlap with arXiv:1904.0320

Searching for Secluded Dark Matter via Direct Detection of Recoiling Nuclei as well as Low Energy Electrons

Motivated by recent cosmic ray experimental results there has been a proposition for a scenario where a secluded dark matter particle annihilates, primarily, into Standard Model leptons through a low mass mediator particle. We consider several varieties of this scenario depending on the type of mixing among gauge bosons and we study the implications in novel direct dark matter experiments for detecting low energy recoiling electrons. We find significant event rates and time modulation effects, especially in the case where the mediator is massless, that may be complementary to those from recoiling nuclei.Comment: 27 pages, references added, published versio