Renormalization group constraints on unified gauge theories

Renormalization group constraints on the behavior of Yukawa and scalar quartic couplings in unified gauge theories are examined. Yukawa couplings are generally asymptotically free whenever the gauge couplings are, but scalar quartic couplings can be asymptotically free only for simple scalar multiplets in large groups with large fermion content. The infrared behavior of Yukawa and scalar quartic couplings implied by the renormalization group equations has interesting and phenomenologically useful consequences: infrared fixed points (or quasifixed points) lead to bounds on masses of fermions and scalars, while scalar quartic couplings can be driven out of the domain of positivity of the classical potential, with possible implications for patterns of symmetry breaking.     

A convergent scheme for one-loop evolutions of the Yukawa couplings in the MSSM

Integrated forms of the one-loop evolution equations are given for the Yukawa couplings in the MSSM, valid for any value of , generalizable to virtually any number of Yukawa fermions, and including all gauge couplings. These forms turn out to have nice mathematical convergence properties which we prove, and we determine the ensuing convergence criteria. Furthermore, they allow one to write down general sufficient and necessary conditions to avoid singularities in the evolution of the Yukawa couplings over physically relevant energy ranges. We also comment briefly on the possible use of these features for physics issues and give a short numerical illustration. Received: 28 July 1999 / Published online: 16 November 1999     

Higgs boson couplings to bottom quarks: two-loop supersymmetry-QCD corrections

We present two-loop supersymmetry (SUSY) QCD corrections to the effective bottom Yukawa couplings within the minimal supersymmetric extension of the standard model (MSSM). The effective Yukawa couplings include the resummation of the nondecoupling corrections Deltam_{b} for large values of tanbeta. We have derived the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-quark-induced SUSY-electroweak contributions to Deltam_{b}. The scale dependence of the resummed Yukawa couplings is reduced from O(10%) to the percent level. These results reduce the theoretical uncertainties of the MSSM Higgs branching ratios to the accuracy which can be achieved at a future linear e;{+}e;{-} collider.     

Analytic approach to the MSSM mass spectrum in the large tan β regime

In various unified extensions of the Minimal Supersymmetric Standard Model, the Yukawa couplings of the third generation are predicted to be of the same order. As a result, low energy measured mass ratios require large ratios of the standard model Higgs vacuum expectation values, corresponding to a large value of the parameter tan β. We present analytic solutions for the Yukawa couplings and the Higgs and third generation squark masses, in the case of large top and bottom Yukawa couplings. We examine regions of these Yukawas which give predictions for the top mass compatible with the present experimentally determined top mass and provide useful approximate formulae for the scalars. We discuss the implications on the radiative symmetry breaking mechanism and derive constraints on the undetermined initial conditions of the scalars.     

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     

Yukawa Couplings in Heterotic Compactification

We present a practical, algebraic method for efficiently calculating the Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau three-folds with non-standard embeddings. Our methodology covers all of, though is not restricted to, the recently classified positive monads over favourable complete intersection Calabi-Yau three-folds. Since the algorithm is based on manipulating polynomials it can be easily implemented on a computer. This makes the automated investigation of Yukawa couplings for large classes of smooth heterotic compactifications a viable possibility.     

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.     

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.     

Third generation Yukawa couplings unification in supersymmetric SO(10) model

In the minimal supersymmetric standard model (MSSM) contained in SUSY SO(10), top-- Yukawa unification is achieved at the intermediate mass scale GeV using the recent world average experimental value of the top-quark mass, GeV, which has been directly established by CDF and D0 experiments at the Tevatron Collider. It is also observed that the Yukawa couplings unification scale can be further decreased by taking lower input values of the top-quark mass. This trend indicates the possible existence of an intermediate symmetry breaking scale in SUSY SO(10). The present finding does not agree with the earlier notion that the third generation Yukawa couplings unification should occur at the GUT scale . Received: 22 September 1997 / Revised version: 22 January 1998 / Published online: 24 March 1998     

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.     

Neutrino masses and lepton-flavor-violating τ decays in the supersymmetric left-right model

In the supersymmetric left-right model,the light neutrino masses are given by the Type-II seesaw mechanism.A duality property of this mechanism indicates that there exist eight possible Higgs triplet Yukawa couplings which result in the same neutrino ma6s matrix.In this paper,we work out the one-loop renormalization group equations for the effective neutrino mass matrix in the supersymmetric left-right model.The stability of the Type-II seesaw scenario is briefly discussed.We also study the lepton-flavor-violating processes (τ→μγ and τ→eγ)by using the reconstructed Higgs triplet Yukawa couplings.     

Supersymmetry breaking in warped geometry

We examine the soft supersymmetry breaking parameters in supersymmetric theories on a slice of AdS₅ which generate the hierarchical Yukawa couplings by dynamically quasi-localizing the bulk matter fields in an extra dimension. Such models can be regarded as the AdS dual of the recently studied 4-dimensional models which contain a supersymmetric CFT to generate the hierarchical Yukawa couplings. In such models, if supersymmetry breaking is mediated by the bulk radion superfield and/or some brane chiral superfields, potentially dangerous flavor-violating soft parameters are suppressed with an appropriate correlation with the Yukawa coupling suppression, thereby avoiding the SUSY flavor problem in a natural manner. We present some models of radion-dominated supersymmetry breaking which yield a highly predictive form of soft parameters in this framework, and discuss the constraints from flavor-changing rare processes. Most of the discussions in this paper can be applied also to models with a flat extra dimension in which the Yukawa hierarchy is generated by quasi-localizing the bulk matter fields in the extra dimension.Received: 21 October 2003, Revised: 12 January 2004, Published online: 5 May 2004     

Mirror symmetry,mirror map and applications to Calabi-Yau hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.On leave of absence from Dept. of Math., Toyama Univ., Toyama 930, Japan (address after Sept. 1, 1993)Address after Oct. 1, 1993: Dept. of Math., Harvard Univ., Cambridge, MA 02138, USA. after April 1, 1994: CERN, Theory Division, CH-1211 Geneva 23, Switzerland     

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.     

Hermitian flavor violation

The fundamental constraint on two Higgs doublet models comes from the requirement of sufficiently suppressing flavor-changing neutral currents. There are various standard approaches for dealing with this problem, but they all tend to share a common feature; all of the Higgs doublets couple very weakly to the first generation quarks. Here we consider a simple two Higgs doublet model which is able to have large couplings to the first generation, while also being safe from flavor constraints. We assume only that there is an SUf(3) flavor symmetry which is respected by the couplings of one of the Higgs doublets, and which is broken by Hermitian Yukawa couplings of the second doublet. As a result of the large permitted couplings to the first generation quarks, this scenario may be used to address the excess in W+dijet events recently observed by CDF at the Tevatron. Moreover, Hermitian Yukawa coupling matrices arise naturally in a broad class of solutions to the strong CP problem, providing a compelling context for the model.     

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.     

Mirror symmetry,mirror map and applications to complete intersection Calabi-Yau spaces

We extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton corrected Yukawa couplings and the topological one-loop partition function to the case of complete intersections with higher dimensional moduli spaces. We will develop a new method of obtaining the instanton corrected Yukawa couplings through a study of the solutions of the Picard-Fuchs equations. This leads to closed formulas for the prepotential for the Kähler moduli fields induced from the ambient space for all complete intersections in nonsingular weighted projective spaces. As examples we treat part of the moduli space of the phenomenologically interesting three-generation models which are found in this class. We also apply our method to solve the simplest model in which a topology change was observed and discuss examples of complete intersections in singular ambient spaces.     

Electroweak Chiral Lagrangian for Neutral Higgs Boson

A neutral Higgs boson is added into the traditional electroweak chiral Lagrangian by writing down all possible high dimension operators. The matter part of the Lagrangian is investigated in detail. We find that if Higgs field dependence of Yukawa couplings can be factorized out, there will be no flavour changing neutral couplings; neutral Higgs can induce coupling between light and heavy neutrinos.     

Neutrino masses, mixing angles and the unification of couplings in the MSSM

In the light of the gathering evidence for neutrino oscillations, coming in particular from the Super-Kamiokande data on atmospheric neutrinos, we re-analyze the unification of gauge and Yukawa couplings within the minimal supersymmetric extension of the Standard Model (MSSM). Guided by a range of different grand-unified models, we stress the relevance of large mixing in the lepton sector for the question of bottom-tau Yukawa coupling unification. We also discuss the dependence of the favoured value of on the characteristics of the high-energy quark and lepton mass matrices. In particular, we find that, in the presence of large lepton mixing, Yukawa unification can be achieved for intermediate values of that were previously disfavoured. The renormalization-group sensitivity to the structures of different mass matrices may enable Yukawa unification to serve as a useful probe of GUT models. Received: 22 June 1999 / Published online: 10 December 1999     

Gauge coupling beta functions in the standard model to three loops

In this Letter, we compute the three-loop corrections to the beta functions of the three gauge couplings in the standard model of particle physics using the minimal subtraction scheme and taking into account Yukawa and Higgs self-couplings.