The Higgs System in and Beyond the Standard Model

After the discovery of the Higgs boson particle on the 4th of July of 2012 at the Large Hadron Collider, sited at the european CERN laboratory, we are entering in a fascinating period for Particle Physics where both theorists and experimentalists are devoted to fully understand the features of this new particle and the possible consequences for High Energy Physics of the Higgs system both within and beyond the Standard Model of fundamental particle interactions. This paper is a summary of the lectures given at the third IDPASC school (Santiago de Compostela, Feb. 2013, Spain) addressed to PhD students, and contains a short introduction to the main basic aspects of the Higgs boson particle in and beyond the Standard Model.Comment: 62 pages, 31 figures, Lectures of the IDPASC School at Santiago de Compostela, Spain, February 201

Next-to-leading Corrections to the Higgs Boson Transverse Momentum Spectrum in Gluon Fusion

We present a fully analytic calculation of the Higgs boson transverse momentum and rapidity distributions, for nonzero Higgs $p_\perp$, at next-to-leading order in the infinite-top-mass approximation. We separate the cross section into a part that contains the dominant soft, virtual, collinear, and small-$p_\perp$-enhanced contributions, and the remainder, which is organized by the contributions due to different parton helicities. We use this cross section to investigate analytically the small-$p_\perp$ limit and compare with the expectation from the resummation of large logarithms of the type $\ln{m_H/p_\perp}$. We also compute numerically the cross section at moderate $p_\perp$ where a fixed-order calculation is reliable. We find a $K$-factor that varies from $\approx1.6-1.8$, and a reduction in the scale dependence, as compared to leading order. Our analysis suggests that the contribution of current parton distributions to the total uncertainty on this cross section at the LHC is probably less than that due to uncalculated higher orders.Comment: 40 pages, 10 figures, JHEP style (minor changes, added reference

A viability criterion for modified gravity with an extra force

A recently proposed theory of modified gravity with an explicit ``anomalous'' coupling of the Ricci curvature to matter is discussed, and an inequality is derived which expresses a necessary and sufficient condition to avoid the notorius Dolgov-Kawasaki instability.Comment: 4 latex pages, to appear in Phys. Rev.

The mediating role of comorbid conditions in the association between type 2 diabetes and cognition: a cross-sectional observational study using the UK Biobank cohort

Aims: Using the UK Biobank cohort, a large sample of middle aged and older adults in the UK, the present study aimed to examine the cross-sectional association between type 2 diabetes and cognition and to assess the hypothesised mediating role of common comorbid conditions, whilst controlling for important demographic and lifestyle factors. Methods: Using regression models and general structural equation models, we examined the cross-sectional association between type 2 diabetes status and: fluid intelligence; reaction time; visual memory; digit span and prospective memory; and the hypothesised mediating role of common comorbid conditions: visceral obesity; sleep problems; macrovascular problems; respiratory problems,; cancer and depressive symptoms in 47,468 participants from the UK Biobank cohort, of whom 1,831 have type 2 diabetes. We controlled for ethnicity, sex, age, deprivation, smoking status, alcohol consumption, physical activity levels and use of diabetes medication. Results: Participants with type 2 diabetes had a significantly shorter digit span, b = -0.14, 99.2% CIs [-0.27, -0.11] than those without type 2 diabetes. Those with type 2 diabetes did not differ from those without type 2 diabetes on fluid intelligence, reaction time, visual memory and prospective memory. The associations that do exist between type 2 diabetes and cognition are consistently mediated via macrovascular problems, depressive symptoms, and to a lesser extent visceral obesity. Respiratory problems, sleep disturbances and cancer did not mediate the association between type 2 diabetes status and measures of cognition. Conclusions: Comorbid conditions explain some of the observed association between type 2 diabetes and cognitive deficits. This suggests that prevention, management or treatment of these comorbid conditions may be important to reduce the likelihood of cognitive decline. Treatment studies with long follow-ups are needed to examine this. Tweet: Comorbid conditions explain the association between type 2 diabetes and cognitive deficits. Prevention, management or treatment of these comorbid conditions may prevent or delay the onset of cognitive decline in people with type 2 diabetes

Higgs Radiation off Top Quarks at the Tevatron and the LHC

Higgs bosons can be searched for in the channels $p\bar p/pp\to t\bar tH+X$ at the Tevatron and the LHC. We have calculated the QCD corrections to these processes in the Standard Model at next-to-leading order. The higher-order corrections reduce the renormalization and factorization scale dependence considerably and stabilize the theoretical predictions for the cross sections. At the central scale $\mu=(2m_t+M_H)/2$ the properly defined $K$ factors are slightly below unity for the Tevatron ($K \sim 0.8$) and slightly above unity for the LHC ($K \sim 1.2$).Comment: 5 pages, latex, 2 figure

Gravitation Interaction and Electromagnetic Interaction in the Relativistic Universe with Total Zero and Local Non-Zero Energy

In the model of flat expansive homogeneous and isotropic relativistic universe with total zero and local non-zero energy the gravitation energy of bodies and the elecromagnetic energy of charged bodies can be localised.Comment: LaTeX, 10 pages, 1 figur

Probing the Higgs mechanism via γγ→W+W−\gamma\gamma\to W^+W^-

We investigate the sensitivity of the reaction $\gamma\gamma\to W^+W^-$ to the Higgs sector based on the complete one-loop corrections in the minimal Standard Model and the gauged non-linear $\sigma$-model. While this sensitivity is very strong for the suppressed cross-section of equally polarized photons and longitudinal W bosons, it is only marginal for the dominant mode of transverse polarizations. The corrections within the $\sigma$-model turn out to be UV-finite in accordance with the absence of \log\MH terms in the Standard Model with a heavy Higgs boson.Comment: 12 pages uuencoded postscrip

Bloch-Nordsieck Violation in Spontaneously Broken Abelian Theories

We point out that, in a spontaneously broken U(1) gauge theory, inclusive processes, whose primary particles are mass eigenstates that do not coincide with the gauge eigenstates, are not free of infrared logarithms. The charge mixing allowed by symmetry breaking and the ensuing Bloch-Nordsieck violation are here analyzed in a few relevant cases and in particular for processes initiated by longitudinal gauge bosons. Of particular interest is the example of weak hypercharge in the Standard Model where, in addition, left-right mixing effects arise in transversely polarized fermion beams.Comment: 4 pages, 1 figur

RNA secondary structure formation: a solvable model of heteropolymer folding

The statistical mechanics of heteropolymer structure formation is studied in the context of RNA secondary structures. A designed RNA sequence biased energetically towards a particular native structure (a hairpin) is used to study the transition between the native and molten phase of the RNA as a function of temperature. The transition is driven by a competition between the energy gained from the polymer's overlap with the native structure and the entropic gain of forming random contacts. A simplified Go-like model is proposed and solved exactly. The predicted critical behavior is verified via exact numerical enumeration of a large ensemble of similarly designed sequences.Comment: 4 pages including 2 figure

The Triple Higgs Boson Self-Coupling at Future Linear e+e- Colliders Energies: ILC and CLIC

We analyzed the triple Higgs boson self-coupling at future $e^{+}e^{-}$ colliders energies, with the reactions $e^{+}e^{-}\to b \bar b HH, t \bar t HH$. We evaluate the total cross-sections for both $b\bar bHH$ and $t\bar tHH$, and calculate the total number of events considering the complete set of Feynman diagrams at tree-level. We vary the triple coupling $\kappa\lambda_{3H}$ within the range $\kappa=-1$ and +2. The numerical computation is done for the energies expected to be available at a possible Future Linear $e^{+}e^{-}$ Collider with a center-of-mass energy $800, 1000, 1500$ $GeV$ and a luminosity 1000 $fb^{-1}$. Our analysis is also extended to a center-of-mass energy 3 $TeV$ and luminosities of 1000 $fb^{-1}$ and 5000 $fb^{-1}$. We found that for the process $e^{+}e^{-}\to b \bar b HH$, the complete calculation differs only by 3% from the approximate calculation $e^{+}e^{-}\to ZHH(Z\to b\bar b)$, while for the process $e^{+}e^{-}\to t \bar tHH$, the expected number of events, considering the decay products of both $t$ and $H$, is not enough to obtain an accurate determination of the triple Higgs boson self-coupling.Comment: 19 pages, 12 figure