We investigate constraints that the requirements of perturbativity and gauge coupling unification impose on extensions of the Standard Model and of the MSSM. In particular, we discuss the renormalization group running in several SUSY left-right symmetric and Pati-Salam models and show how the various scales appearing in these models have to be chosen in order to achieve unification. We find that unification in the considered models occurs typically at scales below M^{min}_{B violation} = 10^16 GeV, implying potential conflicts with the non-observation of proton decay. We emphasize that extending the particle content of a model in order to push the GUT scale higher or to achieve unification in the first place will very often lead to non-perturbative evolution. We generalize this observation to arbitrary extensions of the Standard Model and of the MSSM and show that the requirement of perturbativity up to M^{min}_{B violation}, if considered a valid guideline for model building, severely limits the particle content of any such model, especially in the supersymmetric case. However, we also discuss several mechanisms to circumvent perturbativity and proton decay issues, for example in certain classes of extra dimensional models.
We discuss gauge and Yukawa unification in the context of a supersymmetric model with bilinear R-parity violation. We show that this model allows $b-τ$ Yukawa unification for any value of $\tanβ$ while satisfying perturbativity of the couplings. We also find the $t-b-τ$ Yukawa unification easier to achieve than in the MSSM, occurring in a wider high $\tanβ$ region. Finaly, we also discuss the compatibility between the predicted and the measured values for $α_s(M_Z)$
The unification of gauge coupling constants in the minimal supersymmetric model (MSSM) is unaffected at the one-loop level by the inclusion of additional mass-degenerate SU(5) multiplets. Perturbativity puts an upper limit on the number of additional fields. We analyse the evolution of the gauge coupling constants in all models satisfying these criteria using two-loop $β$ functions and including low energy threshold effects. We find that similarly to the minimal supersymmetric model (MSSM) unification takes place within the theoretical and experimental errors. The dominant proton decay mode is…
We consider the low-energy signatures of, and high-energy motivations for, scenarios of semi-perturbative gauge coupling unification. Such scenarios can leave striking imprints on the low-energy sparticle spectrum, including novel gaugino mass ratios (including $M_2/M_1\approx1$), substantial compression of the intra-generational squark-to-slepton mass ratios, and an overall lifting of scalar masses relative to the gauginos. We also demonstrate that the unification scale can be raised to $M_X \approx 4\times10^{17}$ GeV while still in the perturbative regime -- close to the 1-loop heterotic st…
We suggest a minimal extension of the standard model, which can explain current experimental data of the dark matter, small neutrino masses and baryon asymmetry of the universe, inflation, and dark energy, and achieve gauge coupling unification. The gauge coupling unification can explain the charge quantization, and be realized by introducing six new fields. We investigate the vacuum stability, coupling perturbativity, and correct dark matter abundance in this model by use of current experimental data.
We look for minimal extensions of Standard Model with vector like fermions leading to precision unification of gauge couplings. Constraints from proton decay, Higgs stability and perturbativity are considered. The simplest models contain several copies of vector fermions in two different (incomplete) representations. Some of these models encompass Type III seesaw mechanism for neutrino masses whereas some others have a dark matter candidate. In all the models, at least one of the candidates has non-trivial representation under $SU(3)_{color}$. In the limit of vanishing Yukawa couplings, new QC…
Supersymmetric models have traditionally been assumed to be perturbative up to high scales due to the requirement of calculable unification. In this note I review the recently proposed `Fat Higgs' model which relaxes the requirement of perturbativity. In this framework, an NMSSM-like trilinear coupling becomes strong at some intermediate scale. The NMSSM Higgses are meson composites of an asymptotically-free gauge theory. This allows us to raise the mass of the Higgs, thus alleviating the MSSM of its fine tuning problem. Despite the strong coupling at an intermediate scale, the UV completion a…
We present an update of the most stringent experimental bounds on the trilinear R-parity violating couplings. We then analyse bounds on the R-parity violating couplings at the unification scale by renormalising the weak scale bounds. We derive unification scale upper bounds upon the couplings which are broadly independent of the fermion mass texture assumed. The R-parity violating couplings are factors of two to five more severely bounded at the unification scale than at the electroweak scale. In the presence of quark mixing, a few of the bounds are orders of magnitude stronger than their weak…
We derive perturbativity constraints on beyond standard model scenarios with extra gauge groups, such as $SU(2)$ or $U(1)$, whose generators contribute to the electric charge, and show that there are both upper and lower limits on the additional gauge couplings, from the requirement that the couplings remain perturbative up to the grand unification theory (GUT) scale. This leads to stringent constraints on the masses of the corresponding gauge bosons and their collider phenomenology. We specifically focus on the models based on $SU(2)_L\times U(1)_{I_{3R}} \times U(1)_{B-L}$ and the left-right…
We suggest two types of extension of the standard model, which are the so-called next to new minimal standard model (NNMSM) type-II and -III. They can achieve gauge coupling unification as well as suitable dark matter abundance, small neutrino masses, baryon asymmetry of the universe, inflation, and dark energy. The gauge coupling unification can be realized by introducing extra two or three new fields, and could explain the charge quantization. We also show that there are regions in which the vacuum stability, coupling perturbativity, and correct dark matter abundance can be realized with cur…
We analyze two minimal supersymmetric constrained models with low-energy vector-like matter preserving gauge coupling unification. In one we add to the MSSM spectrum a pair of 5-plets of SU(5), in the other a pair of 10-plets. We show that the muon g-2 anomaly can be explained in these models while retaining perturbativity up to the unification scale, satisfying electroweak and flavor precision tests and current LHC data. We examine also some related phenomenological features of the models, including Higgs mass, fine-tuning, dark matter and several LHC signatures. We stress that, at least for …
We investigate the effects of messenger-matter mixing on the lightest CP-even Higgs boson mass m_h in gauge-mediated supersymmetry breaking models. It is shown that with such mixings m_h can be raised to about 125 GeV, even when the superparticles have sub-TeV masses, and when the gravitino has a cosmologically preferred sub-keV mass. In minimal gauge mediation without messenger-matter mixing, realizing m_h = 125 GeV would require multi-TeV SUSY spectrum. The increase in $m_h$ due to messenger-matter mixing is maximal in the case of messengers belonging to 10+\bar{10} of SU(5) unification, whi…
Quarks whose left- and right-handed chiral components are both singlets with respect to the SU(2) weak-isospin gauge group, offer interesting physics possibilities beyond the Standard Model (SM) already studied in many contexts. We here address some further aspects. We first collect and update the constraints from present data on their masses and mixings with conventional quarks. We discuss possible effects on $b\to sγ$ and $Z\to b\bar b$ decays and give fresh illustrations of CP asymmetries in $B^0$ decays differing dramatically from SM expectations. We analyse singlet effects in grand unific…
In the minimal supersymmetric standard model, the three gauge couplings appear to unify at a mass scale near $2 \times 10^{16}$ GeV. We investigate the possibility that intermediate scale particle thresholds modify the running couplings so as to increase the unification scale. By requiring consistency of this scenario, we derive some constraints on the particle content and locations of the intermediate thresholds. There are remarkably few acceptable solutions with a single cleanly defined intermediate scale far below the unification scale.
We test the consistency of several independent astrophysical measurements of fundamental dimensionless constants. In particular, we compare direct measurements of the fine-structure constant $α$ and the proton-to-electron mass ratio $μ=m_p/m_e$ (mostly in the optical/ultraviolet) with combined measurements of $α$, $μ$ and the proton gyromagnetic ratio $g_p$ (mostly in the radio band). We point out some apparent inconsistencies, which suggest that hidden systematics may be affecting some of the measurements. These findings demonstrate the importance of future more precise measurements with ALMA…
The minimal supersymmetric standard model, and extensions, have stringent upper bounds on the mass of the lightest Higgs boson if perturbativity up to the Planck scale is assumed. We argue that these bounds are softened tremendously if the Higgs is charged under an asymptotically free gauge group. We present a model with an additional SU(2) gauge group which easily produces Higgs masses above 200 GeV while avoiding electroweak constraints. If one allows some fine-tuning of the high-scale value of the gauge coupling, Higgs masses greater than 350 GeV are achieved. Unification of couplings is pr…
Building up on previous work we propose a Dark Matter (DM) model with gauged matter parity and dynamical gauge coupling unification, driven by the same physics responsible for scotogenic neutrino mass generation. Our construction is based on the extended gauge group \3311, whose spontaneous breaking leaves a residual conserved matter parity, $M_{P}$, stabilizing the DM particle candidates of the model. A key role is played by the Majorana ${\rm SU(3)_{L}}$-octet leptons, in allowing successful gauge coupling unification and one-loop scotogenic neutrino mass generation. Theoretical consistency …
The possibility of grand unification of the standard model (SM) with fermion spectrum extended to include mirror fermions is examined. SM gauge couplings do not automatically unify. SO(10) grand unification is studied with one intermediate scale. Renormalization group equations (RGE) for fermion Yukawa couplings and the scalar self-coupling are studied numerically at one and two loop level. Strong restrictions for mirror fermion masses are obtained assuming perturbative unification. Mirror masses much smaller than the tree unitarity bounds are required. In particular mirror leptons have to be …
We suggest that quintessential vacuum energy could be the source of right handed neutrino masses that feed the seesaw mechanism, which may provide observed small masses to light standard neutrinos. This idea is naturally implemented in the Cosmological Unification model based on the global $SO(1,1)$ symmetry, where early inflation and late accelerated expansion of the Universe are driven by the degrees of freedom of a doublet scalar field. In this model, the $SO(1,1)$ custodial symmetry naturally provides the quintessence to standard model singlet fermion couplings that source neutrino masses.…
We point out that models where gauge and charged matter fields live on the world volume of D3 branes can provide a weak string coupling description of the gauge coupling unification in the supersymmetric standard model at a scale of order $10^{16}$ GeV. In the D3 brane picture, the string and unification scales coincide, while the size of the extra dimensions is somewhat larger than the string length. We then construct a quasirealistic "three generation" model with D3 branes at orbifold fixed points. We point out that placing D3 branes at different orbifold fixed points provides a geometric de…
The unification of gauge and Yukawa couplings within the minimal supersymmetric standard model is studied at the two loop level. We derive an expression for the effective scale, $T_{SUSY}$, which characterizes the supersymmetric particle threshold corrections to the gauge couplings, and demonstrate that $T_{SUSY}$ is only slightly dependent on the squark and slepton masses, and strongly dependent on the Higgsino masses as well as on the mass ratio of the gauginos of the strong and weak interactions. Moreover, the value of the top quark Yukawa coupling necessary to achieve the unification of bo…
We examine various predictions of the minimal supersymmetric standard model coupled to minimal supergravity. The model is characterised by a small set of parameters at the unification scale. The supersymmetric particle spectrum at low energy and the spontaneous breaking of the standard model itself are then generated radiatively. The previously considered predictions of the model now include the neutralino relic density which in turn provides bounds on the scale parameters. We find a remarkable consistency among several different constraints which imply all supersymmetric particle masses prefe…
We propose a theory of chiral fermion dark matter (DM) with an isospin-3/2 fermion of a dark sector $SU(2)_D$ gauge symmetry, which is arguably the simplest chiral theory. An isospin-3 scalar breaks $SU(2)_D$ down to a discrete non-Abelian group $T'$ and generates the DM mass. The $SU(2)_D$ gauge symmetry protects the DM mass and guarantees its stability. We derive consistency conditions for the theory and study its DM phenomenology. In some regions of parameters of the theory a two-component DM scenario is realized, consisting of a fermion and a boson, with the boson being the lightest $T'$ n…
Consistency of trans-unification RG evolution is used to discuss the domain of definition of the New Minimal Supersymmetric SO(10) GUT (NMSGUT). We compute the 1-loop RGE $β$ functions, simplifying generic formulae using constraints of gauge invariance and superpotential structure. We also calculate the 2 loop contributions to the gauge coupling and gaugino mass and indicate how to get full 2 loop results for all couplings. Our method overcomes combinatorial barriers that frustrate computer algebra based attempts to calculate SO(10) $β$ functions involving large irreps. Use of the RGEs identif…
We present an updated assessment of the viability of t-b-tau Yukawa coupling unification in supersymmetric models. For the superpotential Higgs mass parameter mu>0, we find unification to less than 1% is possible, but only for GUT scale scalar mass parameter m_{16}~8-20 TeV, and small values of gaugino mass m_{1/2}<400 GeV. Such models require that a GUT scale mass splitting exists amongst Higgs scalars with m_{H_u}^2<m_{H_d}^2. Viable solutions lead to a radiatively generated inverted scalar mass hierarchy, with third generation and Higgs scalars being lighter than other sfermions. These mode…
We examine the influence of gauge kinetic mixing on the couplings of a TeV scale $Z'$ in both $E_6$ and SO(10) models. The strength of such mixing, which arises due to the existence of incomplete matter representations at low scale, can be described by a single parameter, $δ$. The value of this parameter can significantly influence the ability of both hadron and lepton colliders to detect a $Z'$ using conventional search techniques. In addition, $δ\neq 0$ also adds to the complexities involved in separating $E_6$ $Z'$ models from those arising from alternative scenarios. Employing a reasonable…
Talk given at the 26th Workshop: ``From Superstrings to Supergravity" Erice - Sicily, 5-12 December 1992: In this talk we discuss string consistency requirements on four dimensional string models, namely the cancellation of target space duality anomalies. The analysis is explicitly performed for (hypothetical) orbifold models assuming the massless spectrum of the supersymmetric standard model. In addition, some phenomenological properties of four-dimensional strings, like the unification of the standard model gauge coupling constants and soft supersymmetry breaking parameters, are investigated…
Recently type II seesaw dominance in a supersymmetric SO(10) framework has been found useful in explaining large solar and atmospheric mixing angles as well as larger values of $theta_{13}$ while unifying quark and lepton masses. An important question in these models is whether there exists consistency between coupling unification and type II seesaw dominance. Scenarios where this consistency can be demonstrated have been given in a SUSY framework. In this paper we give examples where type II dominance occurs in SO(10) models without supersymmetry but with additional TeV scale particles and al…
An Extra-Dimensional Axion in a 5D Warped Orbifold GUT
William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota（明尼苏达大学物理与天文学院威廉·I·芬理论物理研究所）；School of Physics and Astronomy, University of Minnesota（明尼苏达大学物理与天文学院）
We make a complete analysis of radiative symmetry breaking in the MSSM and its $SU(5)$ extensions including low- and high-energy threshold effects in the framework of the two-loop renormalization group. In particular, we consider minimal $SU(5)$, the ``missing-doublet'' $SU(5)$, a Peccei-Quinn invariant version of $SU(5)$ as well as a version with light adjoint remnants. We derive permitted ranges for the parameters of these models in relation to predicted $α_{s}$ and $M_G$ values within the present experimental accuracy. The parameter regions allowed under the constraints of radiative symmetr…
A review is given on the consistency checks of GUT, which unify the electroweak and strong nuclear forces into a single theory. Such theories predict a new kind of force, which could provide answers to several open questions in cosmology. The possible role of such a ``primeval'' force will be discussed in the framework of the Big Bang Theory. Although such a force cannot be observed directly, there are several predictions of GUT's, which can be verified at low energies. The MSSM distinguishes itself from other GUT's by a successful prediction of many unrelated phenomena with a minimum number o…
The three theoretical and historical components of the Standard Model are the exact chiral gauge theory of weak interactions, electroweak unification, and the Higgs mechanism for spontaneous symmetry breaking. I put into historical perspective my 1958 invention of the first gauge theory of weak interactions, predicting weak neutral currents, and show how the fundamental differences between global and gauge symmetries and between partial flavour and exact gauge symmetries, emerged in the strong and weak interactions. Although renormalizability is necessary for theoretical consistency, electrowe…
We study different phenomenological aspects of compact, D=4, N=1 Type IIB orientifolds considered as models for unification of the standard model and gravity. We discuss the structure of the compactification, string and unification scales depending on the different possible D-brane configurations. It is emphasized that in the context of Type I models the $M_W/M_{Planck}$ hierarchy problem is substantially alleviated and may be generated by geometrical factors. We obtain the effective low-energy supergravity Lagrangian and derive the form of soft SUSY-breaking terms under the assumption of dila…
We consider a non-exotic gauged U(1)$_X$ extension of the Standard Model (SM), where the U(1)$_X$ charge of a SM field is given by a linear combination of its hypercharge and Baryon-minus-Lepton ($B-L$) number. All the gauge and mixed gauge-gravitational anomalies are cancelled in this model with the introduction of three right-handed neutrinos (RHNs). Unlike the conventional minimal U(1)$_X$ model, where a universal U(1)$_X$ charge of $-1$ is assigned to three RHNs, we consider an alternative charge assignment, namely, two RHNs ($N_R^{1,2}$) have U(1)$_X$ charge $-4$ while one RHN ($N_R$) has…
Type IIB superstring models with the standard model gauge group on D3-branes and with massless matter associated with open strings joining D3-branes to D3-branes or D3-branes to ${\rm D}7_3$-branes are studied. Models with gauge coupling constant unification at an intermediate scale between about $10^{10}$ and $10^{12}$GeV and consistency with the observed value of $\sin^2 θ_W (M_Z)$ are obtained. Extra vector-like states and extra pairs of Higgs doublets play a crucial role.
We consider various bulk fields with general dilaton couplings in the linear dilaton background in five dimensions as the continuum limit of clockwork models. We show that the localization of the zero modes of bulk fields and the mass gap in the KK spectrum depend not only on the bulk dilaton coupling, but also on the bulk mass parameter in the case of a bulk fermion. The consistency from universality and perturbativity of gauge couplings constrain the dilaton couplings to the brane-localized matter fields as well as the bulk gauge bosons. Constructing the Clockwork Standard Model (SM) in the …
General features of the spectra of matter states in all 175 models found in a previous work by the author are discussed. Only twenty patterns of representations are found to occur. Accomodation of the Minimal Supersymmetric Standard Model (MSSM) spectrum is addressed. States beyond those contained in the MSSM and nonstandard hypercharge normalization are shown to be generic, though some models do allow for the usual hypercharge normalization found in SU(5) embeddings of the Standard Model gauge group. The minimum value of the hypercharge normalization consistent with accomodation of the MSSM i…
We investigate the field dependence of the gauge couplings of locally supersymmetric effective quantum field theories. We find that the Weyl rescaling of supergravity gives rise to Wess-Zumino terms that affect the gauge couplings at the one-loop level. These Wess-Zumino terms are crucial in assuring supersymmetric consistency of both perturbative and non-perturbative gauge interactions. At the perturbative level, we distinguish between the holomorphic Wilsonian gauge couplings and the physically-measurable momentum-dependent effective gauge couplings; the latter are affected by the Konishi an…
The supersymmetric extension of the standard model suffers from a problem of baryon-number violation. Discrete (and global) symmetries introduced to protect the proton are unstable under gravitational effects. We add a gauged $U(1)_X$ to the standard model gauge group $G_{SM}$ and require it to be anomaly-free. As new (chiral) superfields we only allow $G_{SM}$-singlets in order to maintain the good unification predictions. We find the most general set of solutions for the rational singlet charges. We embed our models in {\it local} supersymmetry and study the breaking of supersymmetry and $U(…
A remarkable achievement of the realistic superstring standard--like models is the successful prediction of the top quark mass, assuming the Minimal Supersymmetric Standard Model spectrum below the string scale. Recently it was shown that string scale unification requires the existence of additional matter, in vector--like representations, at intermediate energy scales and that certain string models contain the needed representations in their massless spectrum. I obtain the top, bottom and tau lepton Yukawa couplings in these models, by calculating tree level string amplitudes, in terms of the…
We study the general patterns of SUSY-breaking soft terms arising under the assumption of Kahler moduli dominated SUSY-breaking in string theory models. Insisting that all MSSM gauginos get masses at leading order and that the top Yukawa coupling is of order the gauge coupling constant identifies the class of viable models. These are models in which the SM fields live either in the bulk or at the intersection of local sets of Type IIB D7-branes or their F-theory relatives. General arguments allow us to compute the dependence of the Kahler metrics of MSSM fields on the local Kahler modulus of t…
