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Register a new userSinglet night in Feynman-ville: one-loop matching of a real scalar
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A complete one-loop matching calculation for real singlet scalar extensions of the Standard Model to the Standard Model effective field theory (SMEFT) of dimension-six operators is presented. We compare our analytic results obtained by using Feynman diagrams to the expressions derived in the literature by a combination of the universal one-loop effective action (UOLEA) approach and Feynman calculus. After identifying contributions that have been overlooked in the existing calculations, we find that the pure diagrammatic approach and the mixed method lead to identical results. We highlight some of the subtleties involved in computing one-loop matching corrections in SMEFT.
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In this paper we present the complete one-loop matching conditions, up to dimension-six operators of the Standard Model effective field theory, resulting by integrating out the two scalar leptoquarks $S_{1}$ and $S_{3}$. This allows a phenomenological study of low-energy constraints on this model at one-loop accuracy, which will be the focus of a subsequent work. Furthermore, it provides a rich comparison for functional and computational methods for one-loop matching, that are being developed. As a corollary result, we derive a complete set of dimension-six operators independent under integration by parts, but not under equations of motions, called Greens basis, as well as the complete reduction formulae from this set to the Warsaw basis.
In this paper, we propose a new method for evaluating scalar one-loop Feynman integrals in generalized D-dimension. The calculations play an important building block for two-loop and higher-loop corrections to the processes at future colliders such as the Large Hadron Collider (LHC) and the International Linear Collider (ILC). In this method, scalar one-loop N-point functions will be presented as the one-fold Mellin-Barnes representation of (N-1)-point ones with shifting space-time dimension. This representation offers a clear advantage that we can construct recursively the analytic expressions for N-point functions from the basic ones which are one-point functions. The compact formulae for scalar one-loop two-point functions with massive internal lines and three-point, four-point functions with massless internal lines are given as examples in this article. In particular, they are written in terms of generalized hypergeometric series such as Gauss, Appell F 1 functions. We also perform a sample numerical check for the analytical expressions in this report by comparing with LoopTools and AMBRE/MB. We find that the numerical results from this work are in good agreement with LoopTools at $epsilon^0$ -expansion and AMBRE/MB at higher-order of $epsilon$-expansion, at higher D-dimension.
For loop integrals, the standard method is reduction. A well-known reduction method for one-loop integrals is the Passarino-Veltman reduction. Inspired by the recent paper [1] where the tadpole reduction coefficients have been solved, in this paper we show the same technique can be used to give a complete integral reduction for any one-loop integrals. The differential operator method is an improved version of the PV-reduction method. Using this method, analytic expressions of all reduction coefficients of the master integrals can be given by algebraic recurrence relation easily. We demonstrate our method explicitly with several examples.
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed covariant diagrams. The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
Gauge singlet extensions of the Standard Model (SM) scalar sector may help remedy its theoretical and phenomenological shortcomings while solving outstanding problems in cosmology. Depending on the symmetries of the scalar potential, such extensions may provide a viable candidate for the observed relic density of cold dark matter or a strong first order electroweak phase transition needed for electroweak baryogenesis. Using the simplest extension of the SM scalar sector with one real singlet field, we analyze the generic implications of a singlet-extended scalar sector for Higgs boson phenomenology at the Large Hadron Collider (LHC). We consider two broad scenarios: one in which the neutral SM Higgs and singlet mix and the other in which no mixing occurs and the singlet can be a dark matter particle. For the first scenario, we analyze constraints from electroweak precision observables and their implications for LHC Higgs phenomenology. For models in which the singlet is stable, we determine the conditions under which it can yield the observed relic density, compute the cross sections for direct detection in recoil experiments, and discuss the corresponding signatures at the LHC.
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