We assume that New Physics effects are parametrized within the Standard Model Effective Field Theory (SMEFT) written in a complete basis of gauge invariant operators up to dimension 6, commonly referred to as "Warsaw basis". We discuss all steps necessary to obtain a consistent transition to the spontaneously broken theory and several other important aspects, including the BRST-invariance of the SMEFT action for linear R ξ -gauges. The final theory is expressed in a basis characterized by SM-like propagators for all physical and unphysical fields. The effect of the non-renormalizable operators appears explicitly in triple or higher multiplicity vertices. In this mass basis we derive the complete set of Feynman rules, without resorting to any simplifying assumptions such as baryon-, lepton-number or CP conservation. As it turns out, for most SMEFT vertices the expressions are reasonably short, with a noticeable exception of those involving 4, 5 and 6 gluons. We have also supplemented our set of Feynman rules, given in an appendix here, with a publicly available Mathematica code working with the FeynRules package and producing output which can be integrated with other symbolic algebra or numerical codes for automatic SMEFT amplitude calculations.

Assuming that new physics effects are parametrized by the Standard-Model Effective Field Theory (SMEFT) written in a complete basis of up to dimension-6 operators, we calculate the CP-conserving one-loop amplitude for the decay h → γγ in general R ξ -gauges. We employ a simple renormalisation scheme that is hybrid between on-shell SM-like renormalised parameters and running MS Wilson coefficients. The resulting amplitude is then finite, renormalisation scale invariant, independent of the gauge choice (ξ) and respects SM Ward identities. Remarkably, the S-matrix amplitude calculation resembles very closely the one usually known from renormalisable theories and can be automatised to a high degree. We use this gauge invariant amplitude and recent LHC data to check upon sensitivity to various Wilson coefficients entering from a more complete theory at the matching energy scale. We present a closed expression for the ratio R h→γγ , of the Beyond the SM versus the SM contributions as appeared in LHC h → γγ searches. The most important contributions arise at tree level from the operators Q ϕB , Q ϕW , Q ϕW B , and at one-loop level from the dipole operators Q uB , Q uW . Our calculation shows also that, for operators that appear at tree level in SMEFT, one-loop corrections can modify their contributions by less than 10%. Wilson coefficients corresponding to these five operators are bounded from current LHC h → γγ data -in some cases an order of magnitude stronger than from other searches. Finally, we correct results that appeared previously in the literature. *

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.

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.

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 → qh with q = u, c quarks, in the general MSSM with R-parity conservation. Our primary goal is to search for enhanced effects on B(t → qh) 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 O(1) flavour violating effects in the, presently unconstrained, up-squark sector, SUSY effects on B(t → qh) 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 → qh decay are made available in SUSY FLAVOUR numerical library.