Two-loop renormalization group equations in the standard model

Two-loop renormalization group equations in the standard model are recalculated. A new coefficient is found in the beta function of the quartic coupling and a class of gauge invariants is found to be absent in the beta functions of hadronic Yukawa couplings. The two-loop beta function of the Higgs mass parameter is presented in complete form.     

Two-loop renormalization group restrictions on the standard model and the fourth chiral family

In the framework of the two-loop renormalization group, the restrictions on the Higgs mass from the electroweak vacuum stability and from the absence of the strong coupling are refined, while the more precise value of the top mass is taken into account. When the SM cutoff is equal to the Planck scale, the Higgs mass must be GeV and GeV, where the corridor is the theoretical one and the errors are due to the top-mass uncertainty. The SM two-loop functions are generalized to the case with massive neutrinos from extra families. The requirement of self-consistency of the perturbative SM as an underlying theory up to the Planck scale excludes a fourth chiral family. Under the precision-experiment restriction GeV, the fourth chiral family, if alone, is excluded even when the SM is regarded as an effective theory. Nevertheless a pair of chiral families constituting a vector-like one could exist. Received: 2 September 1998 / Revised version: 4 January 1999 / Published online: 28 September 1999     

One-loop amplitudes on orbifolds and the renormalization of coupling constants

We consider three-point one-loop amplitudes for strings propagating on orbifolds that preserve a supersymmetry. For three external gauge bosons, we compute the explicit wave-function renormalization of the external legs and show that it leads to the correct value for the Yang-Mills β-function. For two gauge bosons and a graviton, we show that there is no renormalization of the coupling, but if the graviton is replaced with an antisymmetric tensor, then the coupling is renormalized.     

The Higgs sector of the minimal supersymmetric standard model including radiative corrections

We discuss the Higgs sector of the minimal supersymmetric standard model including effects of radiative corrections. The formalism is explained in detail for computing radiative corrections to the masses and the coupling constants of the Higgs bosons. The radiative corrections to the masses are studied in the on-shell renormalization scheme. The radiative corrections to the mixing angles between the two CP-even Higgs bosons and the Higgs self-coupling constants are investigated in a simple procedure. The explicit analytic expressions are given for the radiative corrections due to the loops containing the top and bottom quarks and their superpartners. Simple approximate formulae are derived from the analytic expressions obtained in the on-shell renormalization scheme. We numerically study the effects of radiative corrections on the mass of the lighter Higgs boson and the mixing angles between the two CP-even Higgs bosons.     

Unitarizing high-energy scattering amplitudes in field theories I: QED

Using a procedure which incorporates the s-channel unitarity and t-channel unitarity at every step, we calculate the scattering amplitudes of QED in the high-energy limit. We find that all scattering amplitudes, elastic and inelastic, are summarized by a single eikonal formula which is explicitly unitary.     

The one-loop renormalization of the MSSM Higgs sector and its application to the neutral scalar Higgs masses

The structure of the Higgs sector in the minimal supersymmetric standard model is reviewed at the oneloop level. An on-shell renormalization scheme of the MSSM Higgs sector is presented in detail together with the complete list of formulae for the neutral Higgs masses at the one-loop level. The results of a complete one-loop calculation for the mass spectrum of the neutral MSSM Higgs bosons and the quality of simpler Born-like approximations are discussed for sfermion and gaugino masses in the range of the electroweak scale.     

Two-loop renormalization of tanβ and its gauge dependence

Renormalization of two-loop divergent corrections to the vacuum expectation values (v₁,v₂) of the two Higgs doublets in the minimal supersymmetric standard model, and their ratio tanβ=v₂/v₁, is discussed for general R_ξ gauge fixings. When the renormalized (v₁,v₂) are defined to give the minimum of the loop-corrected effective potential, it is shown that, beyond the one-loop level, the dimensionful parameters in the R_ξ gauge fixing term generate gauge dependence of the renormalized tanβ. Additional shifts of the Higgs fields are necessary to realize the gauge-independent renormalization of tanβ.     

The Higgs sector of supersymmetric theories and the implications for high-energy colliders

One of the main motivations for low-energy supersymmetric theories is their ability to address the hierarchy and naturalness problems in the Higgs sector of the standard model. In these theories, at least two doublets of scalar fields are required to break the electroweak symmetry and to generate the masses of the elementary particles, resulting in a rather rich Higgs spectrum. The search for the Higgs bosons of supersymmetry and the determination of their basic properties is one of the major goals of high-energy colliders and, in particular, the LHC, which will soon start operation. We review the salient features of the Higgs sector of the minimal supersymmetric standard model and of some of its extensions and summarize the prospects for probing them at the LHC and at the future ILC. In memoriam of Julius Wess, 1934–2007.     

Two-loop renormalization of the Finkel’stein theory: The specific heat

We explore the two-loop renormalization of the specific heat for an interacting disordered electron system in the case of broken time reversal symmetry. Within the nonlinear sigma model approach we derive the two-loop result for the anomalous dimension which controls scaling of the specific heat with temperature. As an example, we elaborate the metal-insulator transition in d=2+?$d=2+?$ dimensions for the case of broken time reversal and spin rotational symmetries and in the presence of Coulomb interaction. In this situation scaling of the specific heat is determined by the anomalous dimension of the Finkel’stein operator which is the eigenoperator of the renormalization group complementary to the eigenoperator corresponding to the second moment of the local density of states. We find that the absolute values of the anomalous dimensions of these operators differ beyond one-loop approximation contrary to the noninteracting case.     

Signatures of lower-scale gauge coupling unification in the standard model due to extended Higgs sector

The gauge coupling unification can be achieved at a unification scale around 5×10¹³ GeV if the Standard Model scalar sector is extended with extra Higgs-like doublets. The relevant new scalar degrees of freedom in the form of chiral Z* and W* vector bosons might “be visible” already at about 700 GeV. Their eventual preferred coupling to the heavy quarks explains the non observation of these bosons in the first LHC run and provides promising expectation for the second LHC run.     

The renormalization flow in the adjoint SU(2) lattice Higgs model

Applying the Monte Carlo renormalization group method we investigate the flow of coupling constants for the 8⁴ and 16⁴ SU(2) lattice Higgs model with triplet Higgs fields. The couplings of the renormalized actions are determined using Schwinger-Dyson equations. From the flow we find new evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β but no indication for a discontinuity fixed point.     

Probing the Higgs sector of $$$$ Higgs triplet model at LHC

In this paper, we investigate the Higgs Triplet Model with hypercharge \(Y_{\varDelta }=0\) (HTM0), an extension of the Standard model, caracterized by a more involved scalar spectrum consisting of two CP even Higgs \(h^0, H^0\) and two charged Higgs bosons \(H^\pm \). We first show that the parameter space of HTM0, usually delimited by combined constraints originating from unitarity and BFB as well as experimental limits from LEP and LHC, is severely reduced when the modified Veltman conditions at one loop are also imposed. Then, we perform an rigorous analysis of Higgs decays either when \(h^0\) is the SM-like or when the heaviest neutral Higgs \(H^0\) is identified to the observed 125 GeV Higgs boson at LHC. In these scenarios, we perform an extensive parameter scan, in the lower part of the scalar mass spectrum, with a particular focus on the Higgs to Higgs decay modes \(H^0 \rightarrow h^0h^0, H^\pm \,H^\mp \) leading predominantly to invisible Higgs decays. Finally, we also study the scenario where \(h^0, H^0\) are mass degenerate. We thus find that consistency with LHC signal strengths favours a light charged Higgs with a mass about 176–178 GeV. Our analysis shows that the diphoton Higgs decay mode and \(H \rightarrow Z \gamma \) are not always positively correlated as claimed in a previous study. Anti-correlation is rather seen in the scenario where h is SM like, while correlation is sensitive to the sign of the potential parameter \(\lambda \) when H is identified to 125 GeV observed Higgs.