Regularization Independent Analysis of the Origin of Two Loop Contributions to N=1 Super Yang-Mills Beta Function

We present a both ultraviolet and infrared regularization independent analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out whilst the beta function receives contributions of infrared modes.Comment: 7 pages, 2 figures, typos correcte

Naturalness and theoretical constraints on the Higgs boson mass

Arbitrary regularization dependent parameters in Quantum Field Theory are usually fixed on symmetry or phenomenology grounds. We verify that the quadratically divergent behavior responsible for the lack of naturalness in the Standard Model (SM) is intrinsically arbitrary and regularization dependent. While quadratic divergences are welcome for instance in effective models of low energy QCD, they pose a problem in the SM treated as an effective theory in the Higgs sector. Being the very existence of quadratic divergences a matter of debate, a plausible scenario is to search for a symmetry requirement that could fix the arbitrary coefficient of the leading quadratic behavior to the Higgs boson mass to zero. We show that this is possible employing consistency of scale symmetry breaking by quantum corrections. Besides eliminating a fine-tuning problem and restoring validity of perturbation theory, this requirement allows to construct bounds for the Higgs boson mass in terms of $\delta m^2/m^2_H$ (where $m_H$ is the renormalized Higgs mass and $\delta m^2$ is the 1-loop Higgs mass correction). Whereas $\delta m^2/m^2_H<1$ (perturbative regime) in this scenario allows the Higgs boson mass around the current accepted value, the inclusion of the quadratic divergence demands $\delta m^2/m^2_H$ arbitrarily large to reach that experimental value.Comment: 6 pages, 4 figure

Symmetry preserving regularization with a cutoff

A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimension based on momentum cutoff. We use the conditions of gauge invariance or freedom of shift of the loop-momentum to define the evaluation of the terms carrying Lorentz indices, e.g. proportional to k_{\mu}k_{\nu}. The remaining scalar integrals are calculated with a four dimensional momentum cutoff. The finite terms (independent of the cutoff) are unambiguous and agree with the result of dimensional regularization.Comment: 12 pages, 1 figure, v2 references adde

On the equivalence between Implicit Regularization and Constrained Differential Renormalization

Constrained Differential Renormalization (CDR) and the constrained version of Implicit Regularization (IR) are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods which have rather distinct basis have been successfully applied to several calculations which show that they can be trusted as practical, symmetry invariant frameworks (gauge and supersymmetry included) in perturbative computations even beyond one-loop order. In this paper, we show the equivalence between these two methods at one-loop order. We show that the configuration space rules of CDR can be mapped into the momentum space procedures of Implicit Regularization, the major principle behind this equivalence being the extension of the properties of regular distributions to the regularized ones.Comment: 16 page

ABC₂-SPH risk score for in-hospital mortality in COVID-19 patients:development, external validation and comparison with other available scores

Objectives: The majority of available scores to assess mortality risk of coronavirus disease 2019 (COVID-19) patients in the emergency department have high risk of bias. Therefore, this cohort aimed to develop and validate a score at hospital admission for predicting in-hospital mortality in COVID-19 patients and to compare this score with other existing ones. Methods: Consecutive patients (≥ 18 years) with confirmed COVID-19 admitted to the participating hospitals were included. Logistic regression analysis was performed to develop a prediction model for in-hospital mortality, based on the 3978 patients admitted between March–July, 2020. The model was validated in the 1054 patients admitted during August–September, as well as in an external cohort of 474 Spanish patients. Results: Median (25–75th percentile) age of the model-derivation cohort was 60 (48–72) years, and in-hospital mortality was 20.3%. The validation cohorts had similar age distribution and in-hospital mortality. Seven significant variables were included in the risk score: age, blood urea nitrogen, number of comorbidities, C-reactive protein, SpO2/FiO2 ratio, platelet count, and heart rate. The model had high discriminatory value (AUROC 0.844, 95% CI 0.829–0.859), which was confirmed in the Brazilian (0.859 [95% CI 0.833–0.885]) and Spanish (0.894 [95% CI 0.870–0.919]) validation cohorts, and displayed better discrimination ability than other existing scores. It is implemented in a freely available online risk calculator (https://abc2sph.com/). Conclusions: An easy-to-use rapid scoring system based on characteristics of COVID-19 patients commonly available at hospital presentation was designed and validated for early stratification of in-hospital mortality risk of patients with COVID-19.</p