Renormalization of scalar quartic and Yukawa couplings in unified gauge theories based onE 6

Renormalization group equations for scalar and Yukawa couplings in gauge theories based on the exceptional groupE ₆ are analyzed. Asymptotic freedom is possible only for a limited set of scalar fields, and then only if several fermion generations are present. The infrared behavior of the scalar quartic coupling constants is striking: they are necessarily driven out of the region of positivity of the classical potential. Some useful group theoretic relations inE ₆ are given in an Appendix.     

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.     

Automorphisms in gauge theories and the definition of CP and P

We study the possibilities to define CP and parity in general gauge theories by utilizing the intimate connection of these discrete symmetries with the group of automorphisms of the gauge Lie algebra. Special emphasis is put on the scalar gauge interactions and the CP invariance of the Yukawa couplings.     

Dirac neutrino masses from generalized supersymmetry breaking

We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the standard model with a generalized supersymmetry breaking sector. If the superpotential neutrino Yukawa terms are forbidden by the gauge symmetry [such as a U(1)'], sub-eV scale effective Dirac mass terms can arise at tree level from hard supersymmetry breaking Yukawa couplings, or at one loop due to nonanalytic soft supersymmetry breaking trilinear scalar couplings. The radiative neutrino magnetic and electric dipole moments vanish at one-loop order.     

Effects of unparticles on running of gauge couplings

Unparticles charged under a gauge group can contribute to the running of the gauge coupling. We show that a scalar unparticle of scaling dimension d contributes to the β function a term that is (2-d) times that from a scalar particle in the same representation. This result has important implications for asymptotic freedom. An unparticle with d>2, in contrast to its matter counterpart, can speed up the approach to asymptotic freedom for a non-Abelian gauge theory and has the tendency to make an Abelian theory also asymptotically free. For not spoiling the excellent agreement of the standard model (SM) with precision tests, the infrared cut-off, m, of such an unparticle would be high but might still be reachable at colliders such as LHC and ILC. Furthermore, if the unparticle scale Λ_U is high enough, unparticles could significantly modify the unification pattern of the SM gauge couplings. For instance, with three scalar unparticles of d∼2.5 in the adjoint representation of the strong gauge group but neutral under the electroweak one, the three gauge couplings would unify at a scale of ∼ 8×10¹² GeV, which is several orders of magnitude below the supersymmetric unification scale. PACS  12.90.+b; 14.80.-j; 11.10.Hi; 12.10.Dm     

Mass of the Higgs boson from a two-loop analysis of the standard model

Using the renormalization-group equations for the various couplings of the standard model calculated to two loops, and assuming that the ratio of the quartic scalar coupling to theU(1) gauge coupling is bounded in the ultraviolet limit, we obtain an upper bound of 130 GeV on the mass of the Higgs boson and a prediction of 43 GeV in the special case where the quartic scalar coupling is assumed to be a function of the other couplings alone. The uncertainty in either value is realistically estimated at about 4 GeV.     

Two-loop renormalization group equations in a general quantum field theory: (III). Scalar quartic couplings

The two-loop β-functions for the scalar quartic couplings are computed in a general renormalizable quantum field theory with scalar, $\text{spin}\text{-}\text{1}\text{2}$, and (vector) gauge fields associated with a general gauge group G, using dimensional regularization and modified minimal subtraction (^?MS). A more explicit form is given for the two-loop β-function of the quartic coupling of the Higgs doublet in the minimal QCD electroweak theory based on SU(3) × SU(2) × U(1).     

Supersymmetric standard model from the heterotic string

We present a [FORMULA: SEE TEXT] orbifold compactification of the E8xE8 heterotic string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), whereas the Higgs fields do not form complete SO(10) multiplets. The model has large vacuum degeneracy. For generic vacua, no exotic states appear at low energies and the model is consistent with gauge coupling unification. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings, whereas the other Yukawa couplings are suppressed.     

Flavour dynamics with general scalar fields

We consider a spontaneously broken gauge theory based on the standard model (SM) group with scalar fields that carry arbitrary representations of G, and we investigate some general properties of the charged and neutral current involving these fields. In particular we derive the conditions for having real or complex couplings of the Z boson to two different neutral or charged scalar fields, and for the existence of CP-violating Z-scalar-scalar couplings. Moreover, we study models with the same fermion content as in the SM, with one SU(2) Higgs singlet, and an arbitrary number of Higgs doublets. We show that the structure of the Z-Higgs boson and of the Yukawa couplings in these models can be such that CP-violating form factors which conserve chirality are induced at the one-loop level. Received: 18 December 1998 / Published online: 22 March 1999     

From N = 1 to N = 4 extended supersymmetric Yang-Mills fields in a covariant Wess-Zumino gauge

It is assumed that N = 1 supersymmetric Yang-Mills fields coupled to chiral matter fields can be renormalized in a covariant Wess-Zumino gauge with a minimal number of subtractions so that the Ward identities of supersymmetry, ordinary gauge invariance and matter-field-flavour symmetries are satisfied. The chiral Yukawa couplings are supposed to remain unrenormalized. I show that on the basis of these assumptions an N = 4 extended manifestly O(4) invariant theory can be constructed with finite Yukawa and φ⁴ couplings. A consequence of these non-renormalizations is the vanishing of the renormalization group β function.     

Quantum Gravitational Contributions to Gauge Field Theories

We revisit quantum gravitational contributions to quantum gauge field theories in the gauge condition independent Vilkovisky-DeWitt formalism based on the background field method.With the advantage of Landau-DeWitt gauge,we explicitly obtain the gauge condition independent result for the quadratically divergent gravitational corrections to gauge couplings.By employing,in a general way,a scheme-independent regularization method that can preserve both gauge invariance and original divergent behavior of integrals,we show that the resulting gauge coupling is power-law running and asymptotically free.The regularization scheme dependence is clarified by comparing with results obtained by other methods.The loop regularization scheme is found to be applicable for a consistent calculation.     

New formulas and predictions for running masses at higher scales in MSSM

The effects of the scale dependent vacuum expectation values (VEVs) on the running masses of quarks and leptons in non-SUSY gauge theories have been considered by a number of authors. Here we use RGEs of the VEVs, and the gauge and Yukawa couplings in the MSSM to analytically derive new one loop formulas for the running masses above the SUSY breaking scale. Some of the masses exhibit a substantially different behaviour with respect to their dependence on the gauge and Yukawa couplings when compared with earlier formulas in the MSSM derived ignoring RGEs of VEVs. In particular, the masses of the first two generations are found to be independent of the Yukawa couplings of the third generation in the small mixing limit. New numerical estimates at the two loop level are also presented. Received: 30 July 1999 / Published online: 6 April 2000     

Explaining DAMPE results by dark matter with hierarchical lepton-specific Yukawa interactions

We propose to interpret the DAMPE electron excess at 1.5 Te V through scalar or Dirac fermion dark matter(DM) annihilation with doubly charged scalar mediators that have lepton-specific Yukawa couplings. The hierarchy of such lepton-specific Yukawa couplings is generated through the Froggatt-Nielsen mechanism, so that the dark matter annihilation products can be dominantly electrons. Stringent constraints from LEP2 on intermediate vector boson production can be evaded in our scenarios. In the case of scalar DM, we discuss one scenario with DM annihilating directly to leptons and another scenario with DM annihilating to scalar mediators followed by their decays. We also discuss the Breit-Wigner resonant enhancement and the Sommerfeld enhancement in the case where the s-wave annihilation process is small or helicity-suppressed. With both types of enhancement, constraints on the parameters can be relaxed and new ways for model building can be opened in explaining the DAMPE results.     

Theorems for asymptotic safety of gauge theories

We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.     

The C-theorem and chiral symmetry breaking in asymptotically free vectorlike gauge theories

We confront Cardy's suggested c-function for four-dimensional field theories with the spontaneous breaking of chiral symmetries in asymptotically free vectorlike gauge theories with fermions transforming according to different representations under the gauge group. Assuming that the infrared limit of the c-function is determined by the dimension of the associated Goldstone manifold, we find that this c-function always decreases between the ultraviolet and infrared fixed points.     

Higgs portal inflation

The Higgs sector of the Standard Model offers a unique opportunity to probe the hidden sector. The Higgs squared operator is the only dimension two operator which is Lorentz and gauge invariant. It can therefore couple both to scalar curvature and the hidden sector at the dim-4 level. We consider the possibility that a combination of the Higgs and a singlet from the hidden sector plays the role of inflaton, due to their large couplings to gravity. This implies that the quartic couplings satisfy certain constraints which leads to distinct low energy phenomenology, including Higgs signals at the LHC. We also address the unitarity issues and show that our analysis survives the unitarization procedure.     

Two-loop effect on the heavy quark mass near the fixed point

We have studied the two-loop effect on the infrared fixed point of the Yukawa couplings. The two-loop contribution to the large Yukawa coupling for the quark is found to be within 4.5% at the electroweak scale, but that for the lepton is up to 8%. It is noticed that the fixed point structure obtained by the one-loop renormalization group equations is credible enough, at least to the two-loop approximation.     

Predictions of SUSY masses in the minimal supersymmetric grand unified theory

The Minimal Supersymmetric Standard Model (MSSM) distinguishes itself from other GUT's by a successful prediction of many unrelated phenomena with a minimum number of parameters. Among them: a) Unification of the gauge couplings constants; b) Unification of the b-quark and τ-lepton masses; c) Proton stability; d) Electroweak symmetry breaking at a scale far below the unification scale and the corresponding relation between the gauge boson masses and the top quark mass. A combined fit of the free parameters in the MSSM to these low energy constraints shows that the MSSM model can satisfy these constraints simultaneously. From the fitted parameters the masses of the as yet unobserved superpartners of the SM particles are predicted, the top mass is constrained to a range between 140 and 200 GeV, and the second order QCD coupling constant is required to be between 0.108 and 0.132. The complete second order renormalization group equations for the gauge and Yukawa couplings are used and analytical solutions for the neutral gauge boson, the Higgs masses and the sparticle masses are derived, taking into account the one-loop corrections to the Higgs potential.     

Family symmetries and alignment in multi-Higgs doublet models

The exact alignment of the Yukawa structures on multi-Higgs doublet models provides cancellation of tree-level flavour changing couplings of neutral scalar fields. We show that family symmetries can provide a suitable justification for the Yukawa alignment.     

Cosmology is not a renormalization group flow

A critical examination is made of two simple implementations of the idea that cosmology can be viewed as a renormalization group (RG) flow. Both implementations are shown to fail when applied to a massless, minimally coupled scalar with a quartic self-interaction on a locally de Sitter background. Cosmological evolution in this model is not driven by any RG screening of couplings but rather by inflationary particle production gradually filling an initially empty universe with a sea of long wavelength scalars.