Stabilization of the Electroweak Vacuum by a Scalar Threshold Effect

We show how a heavy scalar singlet with a large vacuum expectation value can evade the potential instability of the Standard Model electroweak vacuum. The quartic interaction between the heavy scalar singlet and the Higgs doublet leads to a positive tree-level threshold correction for the Higgs quartic coupling, which is very effective in stabilizing the potential. We provide examples, such as the see-saw, invisible axion and unitarized Higgs inflation, where the proposed mechanism is automatically implemented in well-defined ranges of Higgs masses.Comment: 18 pages, 5 figure

Theoretical Implications of the Higgs Discovery

El reciente descubrimiento de la partícula Higgs en el Large Hadron Collider (LHC) es un hito en la física de partículas. Dicho descubrimiento abre la posibilidad de explorar el Standard Model (SM) y posible nueva física más alla del SM (BSM, i.e. beyond the SM ) a través de las interacciones del Higgs con las demás partículas del SM. Es decir, el interés real no consiste en el mero hecho de explorar los aspectos puramente fenomenol'gicos del Higgs y del SM sino en entender cual es la física y principios detrás de la rotura de la fuerza electrodébil. La física del Higgs tiene lugar a la escala de energía más alta explorada hasta la fecha y es por lo tanto muy importante que la investiguemos a fondo. En la primera parte de la tesis discuto las implicaciones que tiene el valor de la masa del Higgs para la estabilidad del vacío electrodébil. En primer lugar, presento el análisis de orden N 2LLog del potencial del Higgs del SM. Este análisis permite reducir a 1 GeV la incertidumbre en el valor crítico de la masa Higgs Mh para la estabilidad del vacío electrodébil. Aunque el parametro del acoplo cuártico del Higgs evaluado en la escala de energía de Planck es muy próximo a zero, el N 2LLog análisis muestra que la estabilidad absoluta del vacío electrodébil es incompatible con los valores centrales de las medidas experimentales de las masas del Higgs y top quark. También muestro que un escalar pesado puede inducir una corrección relativamente grande al acoplo cuártico de Higgs y por lo tanto estabilizar el vaco electrodébill. Varios ejemplos relevantes de física BSM donde el mecanismo puede estar operativo son discutidos. En la segunda parte de la tesis discutimos como operadores de dimensión superior, que parametrizan física BSM pesada, afecta las interacciones del Higgs. Bajo ciertas asump-ciones, 8 CP-par y 3 CP-impart Wilson coefficients parametrizan el impacto principal en la física del Higgs, ya que todos los demás Wilson coefficients están constreñidos por experimentos previos al LHC. Calculamos las dimensiones anómalas más relevantes para la física del Higgs. Esta dimensiones anómalas describen como se mezclan los operadores de dimension superior bajo correcciones cuánticas perturbativas. Esto permite encontrar las correcciones logarítmicas principales a las predicciones de las interacciones del Higgs en varios modelos específicos como el MSSM o el modelo del Higgs compuesto. Tales correcciones pueden ser relevantes en varios casos. Finalmente, en la última parte estudiamos el patrón sorprendente que tienen las dimen¬siones anómalas de los operadores de dimensión seis. El patrón consiste en que la matriz de dimensiones anómalas presenta muchas entradas nulas, lo cuál no es evidente ya que aparentemente dichas entradas no esta prohibidas por ninguna simetría. Un argumento, basado en el uso de supersimetría como simetría espúrea, es presentado.The discovery of the Higgs at the Large Hadron Collider has triggered a renewed inte- rest on understanding the physical mechanism behind electroweak symmetry breaking. The Higgs boson has opened a new window to probe possible new physics Beyond de Standard Model (BSM) through the measurements of its couplings and its mass value. The Higgs physics is the current energy frontier and it is therefore very important that we explore it thoroughly. In the rst part of the thesis we discuss the implications of the Higgs mass value Mh for the stability of the electroweak (EW) vacuum. We present the next-to-next-to-leading order analysis of the Standard Model Higgs potential. This analysis allows to reduce the theoretical uncertainty in the determination of the critical value of Mh for stability of the EW vacuum to 1 GeV. While the Higgs quartic coupling at the Planck scale is remarkably close to zero, absolute stability of the EW vacuum is excluded for the central experimental values of the Higgs and top quark masses. Next, we show that a heavy scalar singlet can induce a relatively large and positive tree-level threshold correction to the Higgs quartic coupling and stabilize the EW vacuum. We provide examples, such as the see-saw and the invisible axion, where the proposed mechanism is automatically implemented. In the second part we investigate how dimension-six operators, parametrizing heavy BSM physics, a ect the Higgs couplings. Under certain well-motivated assumptions, we nd that 8 CP-even plus 3 CP-odd Wilson coe cients parametrize the main impact in Higgs physics, as all other coe cients are constrained by non-Higgs SM measurements. We calculate the most relevant anomalous dimensions for these Wilson coe cients, which describe operator mixing from the heavy BSM scale down to the EW scale. This allows us to nd the leading-log corrections to the predictions for the Higgs couplings in speci c models, such as the MSSM or composite Higgs, which we nd to be signi cant in certain cases. Finally, in the third part we study the striking structure of the dimension-six anomalous dimension matrix. We present an argument, partly based on the use of supersymmetry as a spurious symmetry, that gives an explanation to the plethora of vanishing entries in the anomalous dimension matrix that are not forbidden by symmetries otherwise

Higgs mass implications on the stability of the electroweak vacuum

We update instability and metastability bounds of the Standard Model electroweak vacuum in view of the recent ATLAS and CMS Higgs results. For a Higgs mass in the range 124--126 GeV, and for the current central values of the top mass and strong coupling constant, the Higgs potential develops an instability around $10^{11}$ GeV, with a lifetime much longer than the age of the Universe. However, taking into account theoretical and experimental errors, stability up to the Planck scale cannot be excluded. Stability at finite temperature implies an upper bound on the reheat temperature after inflation, which depends critically on the precise values of the Higgs and top masses. A Higgs mass in the range 124--126 GeV is compatible with very high values of the reheating temperature, without conflict with mechanisms of baryogenesis such as leptogenesis. We derive an upper bound on the mass of heavy right-handed neutrinos by requiring that their Yukawa couplings do not destabilize the Higgs potential.Comment: 14 pages, 8 figure

Higgs mass and vacuum stability in the Standard Model at NNLO

We present the first complete next-to-next-to-leading order analysis of the Standard Model Higgs potential. We computed the two-loop QCD and Yukawa corrections to the relation between the Higgs quartic coupling (lambda) and the Higgs mass (Mh), reducing the theoretical uncertainty in the determination of the critical value of Mh for vacuum stability to 1 GeV. While lambda at the Planck scale is remarkably close to zero, absolute stability of the Higgs potential is excluded at 98% C.L. for Mh < 126 GeV. Possible consequences of the near vanishing of lambda at the Planck scale, including speculations about the role of the Higgs field during inflation, are discussed.Comment: 35 pages, 8 figures. Final published version, misprints fixed, figures update

Comparing the utility of clinical risk scores and integrated clinical judgement in patients with suspected acute coronary syndrome

Aims The utility of clinical risk scores regarding the prediction of major adverse cardiac events (MACE) is uncertain. We aimed to directly compare the prognostic performance of five established clinical risk scores as well as an unstructured integrated clinical judgement (ICJ) of the treating emergency department (ED) physician. Methods and results Thirty-day MACE including all-cause death, life-threatening arrhythmia, cardiogenic shock, acute myocardial infarction (including the index event), and unstable angina requiring urgent coronary revascularization were centrally adjudicated by two independent cardiologists in patients presenting to the ED with acute chest discomfort in an international multicentre study. We compared the prognostic performance of the HEART score, GRACE score, T-MACS, TIMI score, and EDACS, as well as the unstructured ICJ of the treating ED physician (visual analogue scale to estimate the probability of acute coronary syndrome, ranging from 0 to 100). Among 4551 eligible patients, 1110/4551 patients (24.4%) had at least one MACE within 30 days. Prognostic accuracy was high and comparable for the HEART score, GRACE score, T-MACS, and ICJ [area under the receiver operating characteristic curve (AUC) 0.85–0.87] but significantly lower and only moderate for the TIMI score (AUC 0.79, P &lt; 0.001) and EDACS (AUC 0.74, P &lt; 0.001), resulting in sensitivities for the rule-out of 30-day MACE of 93–96, 87 (P &lt; 0.001), and 72% (P &lt; 0.001), respectively. Conclusion The HEART score, GRACE score, T-MACS, and unstructured ICJ of the treating physician, not the TIMI score or EDACS, performed well for the prediction of 30-day MACE and may be considered for routine clinical use. Trial registration ClinicalTrials.gov number NCT0047058

Theoretical Implications of the Higgs Discovery

El reciente descubrimiento de la partícula Higgs en el Large Hadron Collider (LHC) es un hito en la física de partículas. Dicho descubrimiento abre la posibilidad de explorar el Standard Model (SM) y posible nueva física más alla del SM (BSM, i.e. beyond the SM ) a través de las interacciones del Higgs con las demás partículas del SM. Es decir, el interés real no consiste en el mero hecho de explorar los aspectos puramente fenomenol´gicos del Higgs y del SM sino en entender cual es la física y principios detrás de la rotura de la fuerza electrodébil. La física del Higgs tiene lugar a la escala de energía más alta explorada hasta la fecha y es por lo tanto muy importante que la investiguemos a fondo. En la primera parte de la tesis discuto las implicaciones que tiene el valor de la masa del Higgs para la estabilidad del vacío electrodébil. En primer lugar, presento el análisis de orden N 2LLog del potencial del Higgs del SM. Este análisis permite reducir a 1 GeV la incertidumbre en el valor crítico de la masa Higgs Mh para la estabilidad del vacío electrodébil. Aunque el parametro del acoplo cuártico del Higgs evaluado en la escala de energía de Planck es muy próximo a zero, el N 2LLog análisis muestra que la estabilidad absoluta del vacío electrodébil es incompatible con los valores centrales de las medidas experimentales de las masas del Higgs y top quark. También muestro que un escalar pesado puede inducir una corrección relativamente grande al acoplo cuártico de Higgs y por lo tanto estabilizar el vaco electrodébill. Varios ejemplos relevantes de física BSM donde el mecanismo puede estar operativo son discutidos. En la segunda parte de la tesis discutimos como operadores de dimensión superior, que parametrizan física BSM pesada, afecta las interacciones del Higgs. Bajo ciertas asump-ciones, 8 CP-par y 3 CP-impart Wilson coefficients parametrizan el impacto principal en la física del Higgs, ya que todos los demás Wilson coefficients están constre˜nidos por experimentos previos al LHC. Calculamos las dimensiones anómalas más relevantes para la física del Higgs. Esta dimensiones anómalas describen como se mezclan los operadores de dimension superior bajo correcciones cuánticas perturbativas. Esto permite encontrar las correcciones logarítmicas principales a las predicciones de las interacciones del Higgs en varios modelos específicos como el MSSM o el modelo del Higgs compuesto. Tales correcciones pueden ser relevantes en varios casos. Finalmente, en la última parte estudiamos el patrón sorprendente que tienen las dimen¬siones anómalas de los operadores de dimensión seis. El patrón consiste en que la matriz de dimensiones anómalas presenta muchas entradas nulas, lo cuál no es evidente ya que aparentemente dichas entradas no esta prohibidas por ninguna simetría. Un argumento, basado en el uso de supersimetría como simetría espúrea, es presentado.The discovery of the Higgs at the Large Hadron Collider has triggered a renewed inte- rest on understanding the physical mechanism behind electroweak symmetry breaking. The Higgs boson has opened a new window to probe possible new physics Beyond de Standard Model (BSM) through the measurements of its couplings and its mass value. The Higgs physics is the current energy frontier and it is therefore very important that we explore it thoroughly. In the rst part of the thesis we discuss the implications of the Higgs mass value Mh for the stability of the electroweak (EW) vacuum. We present the next-to-next-to-leading order analysis of the Standard Model Higgs potential. This analysis allows to reduce the theoretical uncertainty in the determination of the critical value of Mh for stability of the EW vacuum to 1 GeV. While the Higgs quartic coupling at the Planck scale is remarkably close to zero, absolute stability of the EW vacuum is excluded for the central experimental values of the Higgs and top quark masses. Next, we show that a heavy scalar singlet can induce a relatively large and positive tree-level threshold correction to the Higgs quartic coupling and stabilize the EW vacuum. We provide examples, such as the see-saw and the invisible axion, where the proposed mechanism is automatically implemented. In the second part we investigate how dimension-six operators, parametrizing heavy BSM physics, a ect the Higgs couplings. Under certain well-motivated assumptions, we nd that 8 CP-even plus 3 CP-odd Wilson coe cients parametrize the main impact in Higgs physics, as all other coe cients are constrained by non-Higgs SM measurements. We calculate the most relevant anomalous dimensions for these Wilson coe cients, which describe operator mixing from the heavy BSM scale down to the EW scale. This allows us to nd the leading-log corrections to the predictions for the Higgs couplings in speci c models, such as the MSSM or composite Higgs, which we nd to be signi cant in certain cases. Finally, in the third part we study the striking structure of the dimension-six anomalous dimension matrix. We present an argument, partly based on the use of supersymmetry as a spurious symmetry, that gives an explanation to the plethora of vanishing entries in the anomalous dimension matrix that are not forbidden by symmetries otherwise

Nonperturbative Methods in Quantum Field Theory

Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory non-perturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant operator of scaling dimension ∆. In this talk I will review the HT techniques and emphasise few key open problems. I will also discuss the recent efforts to extend these ideas to higher dimensions (d > 2) and for UV divergent relevant operators (d/2 <= ∆ < d)