Three-loop \beta-functions for top-Yukawa and the Higgs self-interaction in the Standard Model

We analytically compute the dominant contributions to the \beta-functions for the top-Yukawa coupling, the strong coupling and the Higgs self-coupling as well as the anomalous dimensions of the scalar, gluon and quark fields in the unbroken phase of the Standard Model at three-loop level. These are mainly the QCD and top-Yukawa corrections. The contributions from the Higgs self-interaction which are negligible for the running of the top-Yukawa and the strong coupling but important for the running of the Higgs self-coupling are also evaluated.Comment: 22 pages, 7 figures. Few extra citations are added; the plots are improved. Results in computer readable form can be retrieved from http://www-ttp.particle.uni-karlsruhe.de/Progdata/ttp12/ttp12-012

Direct Detection of Electroweak-Interacting Dark Matter

Assuming that the lightest neutral component in an SU(2)L gauge multiplet is the main ingredient of dark matter in the universe, we calculate the elastic scattering cross section of the dark matter with nucleon, which is an important quantity for the direct detection experiments. When the dark matter is a real scalar or a Majorana fermion which has only electroweak gauge interactions, the scattering with quarks and gluon are induced through one- and two-loop quantum processes, respectively, and both of them give rise to comparable contributions to the elastic scattering cross section. We evaluate all of the contributions at the leading order and find that there is an accidental cancellation among them. As a result, the spin-independent cross section is found to be O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio

The order of the quantum chromodynamics transition predicted by the standard model of particle physics

We determine the nature of the QCD transition using lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities.No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.Comment: 7 pages, 4 figure

The gradient flow running coupling with twisted boundary conditions

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.Comment: 27 pages. LaTe

Impact of massive neutrinos on the Higgs self-coupling and electroweak vacuum stability

The presence of right-handed neutrinos in the type I seesaw mechanism may lead to significant corrections to the RG evolution of the Higgs self-coupling. Compared to the Standard Model case, the Higgs mass window can become narrower, and the cutoff scale become lower. Naively, these effects decrease with decreasing right-handed neutrino mass. However, we point out that the unknown Dirac Yukawa matrix may impact the vacuum stability constraints even in the low scale seesaw case not far away from the electroweak scale, hence much below the canonical seesaw scale of 10^15 GeV. This includes situations in which production of right-handed neutrinos at colliders is possible. We illustrate this within a particular parametrization of the Dirac Yukawas and with explicit low scale seesaw models. We also note the effect of massive neutrinos on the top quark Yukawa coupling, whose high energy value can be increased with respect to the Standard Model case.Comment: 17 pages, 7 figures, minor revisions, version to appear in JHE

Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.Comment: 20 pages, no figure

Light hadron, Charmonium(-like) and Bottomonium(-like) states

Hadron physics represents the study of strongly interacting matter in all its manifestations and the understanding of its properties and interactions. The interest on this field has been revitalized by the discovery of new light hadrons, charmonium- and bottomonium-like states. I review the most recent experimental results from different experiments.Comment: Presented at Lepton-Photon 2011, Mumbai, India; 21 pages, 18 figures; add more references; some correctio

Dimension-Six Terms in the Standard Model Lagrangian

When the Standard Model is considered as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian. Dimension-six terms have been enumerated in the classical article by Buchmueller and Wyler [3]. Although redundance of some of those operators has been already noted in the literature, no updated complete list has been published to date. Here we perform their classification once again from the outset. Assuming baryon number conservation, we find 15 + 19 + 25 = 59 independent operators (barring flavour structure and Hermitian conjugations), as compared to 16 + 35 + 29 = 80 in Ref.[3]. The three summed numbers refer to operators containing 0, 2 and 4 fermion fields. If the assumption of baryon number conservation is relaxed, 4 new operators arise in the four-fermion sector.Comment: 16 pages, no figures, v3: Redundant B-violating operator remove

Vacuum stability of asymptotically safe

We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatrix, and the Coleman-Weinberg effective potential. Classical and quantum stability of the vacuum is established

Three-loop HTL QCD thermodynamics

The hard-thermal-loop perturbation theory (HTLpt) framework is used to calculate the thermodynamic functions of a quark-gluon plasma to three-loop order. This is the highest order accessible by finite temperature perturbation theory applied to a non-Abelian gauge theory before the high-temperature infrared catastrophe. All ultraviolet divergences are eliminated by renormalization of the vacuum, the HTL mass parameters, and the strong coupling constant. After choosing a prescription for the mass parameters, the three-loop results for the pressure and trace anomaly are found to be in very good agreement with recent lattice data down to $T \sim 2-3\,T_c$, which are temperatures accessible by current and forthcoming heavy-ion collision experiments.Comment: 27 pages, 11 figures; corresponds with published version in JHE