We analyze the neutrino mass spectrum and discuss the extra-dimensional interpretation of a three-site Pati-Salam model which i) unifies all families of quark and leptons, ii) provides a natural description of the Standard Model Yukawa couplings, iii) could account for the recent $B$-physics anomalies. The key feature of the model is a breaking of the Pati-Salam and electroweak gauge symmetries localized on opposite sites, communicated to the other sites in an attenuated manner via nearest-neighbor interactions. We show that in this context gauge-singlet fermions localized on each site, receiving hierarchical Majorana masses, can allow the implementation of an inverse seesaw mechanism leading to light anarchic neutrino masses consistent with data. The continuum limit of this three-site setup has a natural interpretation in terms of a warped extra dimension with three defects, where the required exponential hierarchies can be achieved from $\mathcal{O}(1)$ differences in the bulk field masses.
We present a framework of underlying SU(3) x SU(3) family symmetries consistent with Pati-Salam unification and discuss advantages that can justify introducing multiple non-Abelian factors. Advantages include improved vacuum alignment and increased predictivity. We explore in this framework deviations from tri-bi-maximal neutrinos, such as relatively large theta13.
We provide what we believe is the minimal three family ${\cal N} = 1$ SUSY and conformal Pati-Salam Model from type IIB superstring theory. This $Z_3$ orbifolded AdS$\otimes S^5$ model has long lived protons and has potential phenomenological consequences for LHC.
We investigate models where gauge unification (GUT) proceeds in steps that include Pati-Salam symmetry. Beyond the Standard Model, we allow for a well-defined set of small representations of the GUT gauge group. We show that all possible chains of Pati-Salam symmetry breaking can be realized in accordance with gauge-coupling unification. We identify, in particular, models with unification near the Planck scale, with intermediate left-right or SU(4) quark-lepton symmetries that are relevant for flavor physics, with new colored particles at accessible energies, and with an enlarged electroweak H…
We demonstrate to two-loop order that an intermediate symmetrically embedded Pati-Salam $SU(2)_L \times SU(2)_R \times SU(4)$ level of symmetry is all that is necessary to accommodate empirical values of $α(M_z), α_s(M_z)$ and $\sin^2θ_w(M_z)$ within a grand unification context but with a high (10^{14} GeV) intermediate mass scale and with a concomitant higher GUT scale.
We investigate the phase space of parameters in the Pati-Salam model derived in the context of D-branes scenarios, requiring low energy string scale. We find that a non-supersymmetric version complies with a string scale as low as 10 TeV, while in the supersymmetric version the string scale raises up to ~2 x 10^7 TeV. The limited energy region for RGE running demands a large tan(beta) in order to have experimentally acceptable masses for the top and bottom quarks.
Recent neutrino oscillation experiments suggest that the PMNS matrix in the lepton sector has a $CP$ violating phase as the CKM matrix in the quark sector. However, origin of these phases in both matrices are not clarified by now. Although complex Yukawa couplings could induce these phases, they remain as free parameters of the model even in that case. If the $CP$ symmetry is considered to be spontaneously broken, they are expected to be determined by some physics at a much lower energy scale than the Planck scale. We study such a possibility in a framework of Pati-Salam type unification. We a…
In this work we demonstrate how Scotogenic model can arise naturally from an $SU(7)$ grand unified theory. Our model also includes a low scale Pati-Salam $SU(4)_c\times SU(2)_L\times U(1)_R$ symmetry which unifies quarks and leptons. $\mathbb{Z}_2$ symmetry needed for the realization of Scotogenic scenario is a residual symmetry and not $ad$ $hoc$. A short fermion masses and dark matter analysis is included.
We show the scalar potential in the spectral Pati-Salam model does not provide a suitable vacuum to break to the standard model. We see this potential is proton decay free although diquark and leptoquark vertices exist.
We analyze the running at one-loop of the gauge couplings in the spectral Pati-Salam model that was derived in the framework of noncommutative geometry. There are a few different scenario's for the scalar particle content which are determined by the precise form of the Dirac operator for the finite noncommutative space. We consider these different scenarios and establish for all of them unification of the Pati-Salam gauge couplings. The boundary conditions are set by the usual RG flow for the Standard Model couplings at an intermediate mass scale at which the Pati-Salam symmetry is broken.
We analyze the compatibility of the unified left-right symmetric Pati-Salam models motivated by non-commutative geometry and the TeV scale right-handed W boson suggested by recent LHC data. We find that the unification/matching conditions place conflicting demands on the symmetry breaking scales and that generating the required W_R mass and coupling is non-trivial.
I discuss the implementation of the Peccei-Quinn mechanism in a minimal realization of the Pati-Salam partial unification scheme. The axion mass is shown to be related to the Pati-Salam breaking scale and it is predicted via a two-loop renormalization group analysis to be in the window $m_a \in [10^{-11}, \, 3 \times 10^{-7}]$ eV, as a function of a sliding Left-Right symmetry breaking scale. This parameter space will be fully covered by the late phases of the axion Dark Matter experiments ABRACADABRA and CASPEr-Electric. A Left-Right symmetry breaking scenario as low as 20 TeV is obtained for…
We consider models built on $AdS_5\otimes S^5/Γ$ orbifold compactifications of the type $IIB$ superstring, where $Γ$ is the abelian group $Z_n$. An attractive three family $\mathcal{N}=0$ SUSY model is found for $n=7$ that is a modified Pati--Salam Model which reduced to the Standard Model after symmetry breaking.
We explore the potential of ultimate unification of the Standard Model matter and gauge sectors into a single $E_8$ superfield in ten dimensions via an intermediate Pati-Salam gauge theory. Through a consistent realisation of a $\mathbb{T}^6/(\mathbb{Z}_6\times \mathbb{Z}_2)$ orbifolding procedure accompanied by the Wilson line breaking mechanism and Renormalisation Group evolution of gauge couplings, we have established several benchmark scenarios for New Physics that are worth further phenomenological exploration.
Attempts to incorporate in a coherent picture the $B$-decay anomalies presumably observed in $b\rightarrow c$ and $b\rightarrow s$ semi-leptonic decays have to face the absence of signals in other related experiments, both at low and at high energies. By extending and making more precise the content of Ref. [1], we describe one such attempt based on the Pati-Salam SU(4) group, that unifies colour and the $B$-$L$ charge, in the context of a new strongly interacting sector, equally responsible for producing a pseudo-Goldstone Higgs boson.
A brief review of the assignment of elementary fermions and bosons to irreducible multiplets in grand unified $E_6$ models is followed by a discussion of different, hierarchical symmetry breaking chains from $E_6$ down to $SU(3)_C \times U(1)_{EM}$. We concentrate here on a model with an intermediate Pati-Salam symmetry for which $(B-L)$ is conserved. In particular, the mass/mixing matrix of electrically neutral fermions (i.e.neutrinos) that would be derived from Yukawa couplings is constructed. The pattern of neutrino masses and some bounds on mixing parameters are discussed.
Recently one of the authors proposed a dual theory of a Supersymmetric Standard Model (SSM), in which it is naturally understood that at least one quark (the top quark) should be heavy, i.e., almost the same order as the weak scale, and the supersymmetric Higgs mass parameter $μ$ can naturally be expected to be small. However, the model cannot have Yukawa couplings of the lepton sector. In this paper, we examine a dual theory of a Supersymmetric Model with the Pati-Salam gauge group $SU(4)_{PS}\times SU(2)_L\times SU(2)_R $ with respect to the gauge group $SU(4)_{PS}$. In this scenario, Yukawa…
We analyse the experimental limits on the breaking scale of Pati-Salam extensions of the Standard Model. These arise from the experimental limits on rare-meson decay processes mediated at tree-level by the vector leptoquark in the model. This leptoquark ordinarily couples to to both left- and right-handed SM fermions and therefore the meson decays do not experience a helicity suppression. We find that the current limits vary from $\mathcal{O}(80-2500)$ TeV depending on the choice of matrix structure appearing in the relevant three-generational charged-current interactions. We extensively analy…
In supersymmetric theories with extra dimensions, the Higgs and matter fields can be part of the gauge multiplet, so that the Yukawa interactions can arise from the gauge interactions. This leads to the possibility of gauge-Yukawa coupling unification, g_i=y_f, in the effective four dimensional theory after the initial gauge symmetry and the supersymmetry are broken upon orbifold compactification. We consider gauge-Yukawa unified models based on a variety of four dimensional symmetries, including SO(10), SU(5), Pati-Salam symmetry, trinification, and the Standard Model. Only in the case of Pat…
In this talk I discuss a supersymmetric Pati-Salam model of fermion masses and mixing angles which fits low energy data. The model is then extended to include an inflationary sector which is shown to be consistent with Bicep2-Keck-Planck data. The energy scale during inflation is associated with the PS symmetry breaking scale. Finally, the model is shown to be consistent with the observed baryon-to-entropy ratio necessary for Big Bang Nucleosynthesis. It turns out that only the heaviest right-handed neutrino decays produce the correct sign of the baryon-to-entropy ratio. Nevertheless, we obtai…
In this talk, we discuss a simplified version of a recently proposed twin Pati-Salam (PS) theory of flavour broken to the $G_{4321}$ gauge group at high energies, then to the Standard Model at low energies, yielding a TeV scale vector leptoquark $U^μ_1(3,1,2/3)$ which may be used to address the lepton universality anomalies $R_{K^{(*)}}$ and $R_{D^{(*)}}$ in $B$ decays. The model also accounts for quark and lepton mass hierarchies, providing a link between the flavour anomalies and a theory of flavour.
Both discrete flavour symmetries and Grand Unified symmetries explain apparent structures in the mass sector of the Standard Model. A model that combines both symmetries is therefore very appealing. We construct a model with the $S_4$ flavour symmetry and the Pati-Salam unification. We show that this model can indeed explain many observable relations between the masses of the quarks and leptons and that it is predictive in the neutrino sector. However, the combination of the two symmetries leads to new complications in the Higgs sector and in the running of the renormalisation group equations.
We systematically study the minimal supersymmetric Pati-Salam theory, paying special attention to the unification constraints. We find that the SU(4)_c scale M_c and the Left-Right scale M_R lie in the range 10^{10} GeV < M_c < 10^{14} GeV, 10^{3} GeV < M_R <10^{10} GeV (with single-step breaking at 10^{10} GeV), giving a potentially accessible scale of parity breaking. The theory includes the possibility of having doubly-charged supermultiplets at the supersymmetry breaking scale; color octet states with mass of order M_R^2/M_c; magnetic monopoles of intermediate mass that do not conflict wit…
Combining Pati-Salam (PS) and flavour symmetries in a renormalisable setup, we devise a scenario which produces realistic masses for the charged leptons. Flavour-symmetry breaking scalar fields in the adjoint representations of the PS gauge group are responsible for generating different flavour structures for up- and down-type quarks as well as for leptons. The model is characterised by new heavy fermions which mix with the Standard Model quarks and leptons. In particular, the partners for the third fermion generation induce sizeable sources of flavour violation. Focusing on the charged-lepton…
We perform a complete global phenomenological analysis of a realistic string-inspired model based on the supersymmetric Pati-Salam $SU(4)\times SU(2)_L \times SU(2)_R$ gauge group supplemented by a U(1) family symmetry, and present predictions for all observables including muon $g-2$, $τ\to μγ$, and the CHOOZ angle. Our analysis demonstrates the compatibility of such a model with all laboratory data including charged fermion masses and mixing angles, LMA MSW and atmospheric neutrino masses and mixing angles, and $b \to s γ$, allowing for small deviations from third family Yukawa unification. W…
We explore supersymmetric Type I string-motivated three-family scenarios in which the Standard Model is embedded within two sets of intersecting D branes with U(1)-extended Pati-Salam gauge groups. We study a model inspired by the Shiu-Tye Type IIB orientifold, in which a three-family scenario is obtained by assuming that the gauge symmetry breaking takes place in two stages; the Pati-Salam group arises from diagonal breaking of the U(N) gauge groups, which is then broken to the SM gauge group. We investigate the diagonal breaking scenario in detail and find that generically there are difficul…
We propose a Pati-Salam extension of the standard model incorporating a flavor symmetry based on the $Δ\left( 27\right)$ group. The theory realizes a realistic Froggatt-Nielsen picture of quark mixing and a predictive pattern of neutrino oscillations. We find that, for normal neutrino mass ordering, the atmospheric angle must lie in the higher octant, CP must be violated in oscillations, and there is a lower bound for the $0νββ$ decay rate. For the case of inverted mass ordering, we find that the lower atmospheric octant is preferred, and that CP can be conserved in oscillations. Neutrino mass…
We construct an extension of the Standard Model (SM) which is based on grand unification with Pati-Salam symmetry. The setup is supplemented with the idea of spontaneous flavour symmetry breaking which is mediated through flavon fields with renormalizable couplings to new heavy fermions. While we argue that the new gauge bosons in this approach can be sufficiently heavy to be irrelevant at low energies, the fermionic partners of the SM quarks, in particular those for the third generation, can be relatively light and provide new sources of flavour violation. The size of the effects is constrain…
The low-energy manifestations of a minimal extension of the electroweak standard model based on the quark-lepton symmetry $SU(4)_V \otimes SU(2)_L \otimes G_R$ of the Pati-Salam type are analyzed. Given this symmetry the third type of mixing in the interactions of the $SU(4)_V$ leptoquarks with quarks and leptons is shown to be required. An additional arbitrariness of the mixing parameters could allow, in principle, to decrease noticeably the indirect lower bound on the vector leptoquark mass originated from the low-energy rare processes, strongly suppressed in the standard model.
In this paper, we consider a lopsided flavor texture compatible with thermal leptogenesis in partially composite Pati--Salam unification. The Davidson--Ibarra bound $M_{νR1} \gtrsim 10^9$ GeV for the successful thermal leptogenesis can be recast to the Froggatt--Nielsen (FN) charge of the lopsided texture. We found the FN charge $n_{\nu1}$ of the lightest right-handed neutrino $ν_{R1}$ can not be larger than a upper bound, $n_{\nu1} \lesssim 4.5$. From the viewpoint of unification, the FN charges of the neutrinos $n_{νi}$ should be the same to that of other SM fermions. Then, two cases $n_{νi}…
Grand Unified Theories based on an E6 gauge group embed all Higgs- and matter fields within one 27 dimensional fundamental representation. In addition each 27 contains a right handed neutrino, an NMSSM-like standard model singlet and a pair of exotic particles, that couple quarks to leptons. The extended particle content spoils simple gauge unification as in the MSSM. By embedding the SM into a Pati-Salam gauge group above 10^16 GeV, one obtains a unification below the Planck-scale. We present a Markov chain Monte-Carlo algorithm to systematically scan the high dimensional parameter space and …
The gauge bosons of Pati-Salam do not mediate proton decay at the renormalisable level, and for this reason it is possible to construct scenarios in which $SU(4) \otimes SU(2)_{R}$ is broken at relatively low scales. In this Letter we show that such low-scale models generate dimension-5 operators that can give rise to nucleon decays at unacceptably large rates, even if the operators are suppressed by the Planck scale. We find an interesting complementarity between the nucleon-decay limits and the usual meson-decay constraints. Furthermore, we argue that these operators are generically present …
The B anomalies, by their distinctive flavour structure i.e. $U(2)^5$, bring a new piece to the long-standing flavour puzzle. The three-site flavour non-universal Pati-Salam (PS) model, which unifies quarks and leptons, provides through the ratios of vacuum expectation values (VEV) acquired at different scales, a combined explanation of the charged and neutral current B anomalies as well as of the mass hierarchies of the Standard Model (SM). The mixings, in new, flavour non-universal, gauge interactions, as well as in the Yukawa couplings, are obtained through suppressed nearest-neighbour inte…
We show how an accidental $U(1)$ Peccei-Quinn (PQ) symmetry can arise from a discrete $A_4$ family symmetry combined with a discrete flavour symmetry $ \mathbb{Z}_3 \times \mathbb{Z}_5^2 $, in a realistic Pati-Salam unified theory of flavour. Imposing only these discrete flavour symmetries, the axion solution to the strong $ CP $ problem is protected from PQ-breaking operators to the required degree. A QCD axion arises from a linear combination of $ A_4 $ triplet flavons, which are also responsible for fermion flavour structures due to their vacuum alignments. We find that the requirement of a…
We provide a combined explanation of the increasingly tantalizing $B$-meson anomalies, both in $R_{K^{(*)}}$ and $R_{D^{(*)}}$, in the Pati-Salam model with minimal matter content. This well-known model, based on the gauge group $SU(4)_{LC} \times SU(2)_L \times SU(2)_R$, naturally contains a variety of scalar leptoquarks with related and restricted couplings. In particular we show that the seesaw-motivated scalar leptoquark within the representation $(\overline{10}, 3, 1)$ and its right-handed parity partner $(\overline{10}, 1, 3)$ can solve both anomalies while making testable predictions fo…
We propose a twin Pati-Salam (PS) theory of flavour broken to the $G_{4321}$ gauge group at high energies, then to the Standard Model at low energies, yielding a TeV scale vector leptoquark $U^μ_1(3,1,2/3)$ which has been suggested to address the lepton universality anomalies $R_{K^{(*)}}$ and $R_{D^{(*)}}$ in $B$ decays. Quark and lepton masses are mediated by vector-like fermions, with personal Higgs doublets for the second and third families, which may be replaced by a two Higgs doublet model (2HDM). The twin PS theory of flavour successfully accounts for all quark and lepton (including neu…
One or more scalar leptoquarks with masses around a few TeV may provide a solution to some of the flavor anomalies that have been observed. We discuss the impact of such new degrees on baryon number violation when the theory is embedded in a Pati-Salam model. The Pati-Salam embedding can suppress renormalizable and dimension-five baryon number violation in some cases. Our work extends the results of Assad, Grinstein, and Fornal who considered the same issue for vector leptoquarks.
We propose an elegant theory of flavour based on $A_4\times Z_5$ family symmetry with Pati-Salam unification which provides an excellent description of quark and lepton masses, mixing and CP violation. The $A_4$ symmetry unifies the left-handed families and its vacuum alignment determines the columns of Yukawa matrices. The $Z_5$ symmetry distinguishes the right-handed families and its breaking controls CP violation in both the quark and lepton sectors. The Pati-Salam symmetry relates the quark and lepton Yukawa matrices, with $Y^u=Y^ν$ and $Y^d\sim Y^e$. Using the see-saw mechanism with very …
We analyse the gravitational wave and low energy signatures of a Pati-Salam phase transition. For a Pati-Salam scale of $M_{PS} \sim 10^5$ GeV, we find a stochastic power spectrum within reach of the next generation of ground-based interferometer experiments such as the Einstein Telescope, in parts of the parameter space. We study the lifetime of the proton in this model, as well as complementarity with low energy constraints including electroweak precision data, neutrino mass measurements, lepton flavour violation, and collider constraints.
We discuss non-perturbative corrections to the neutrino sector, in the context of a D-brane Pati-Salam-like model, that can be obtained as a simple alternative to $SO(10)$ GUT's in theories with open and unoriented strings. In such D-brane models, exotic stringy instantons can correct the right-handed neutrino mass matrix in a calculable way, thus affecting mass hierarchies and modifying the see-saw mechanism to what we name exotic see-saw. For a wide range of parameters, a compact spectrum of right-handed neutrino masses can occur that gives rise to a predictive scenario for low energy observ…
In this paper, we extend the analysis of a Pati-Salam subcritical hybrid $F$-term inflation model, proposed by two of us, by studying the reheating and the baryogenesis (via leptogenesis) of the model. This SUSY GUT model is able to fit low energy electroweak precision data, LHC data, $b$-physics data, in addition to inflation observables such as the tensor-to-scalar ratio and the scalar spectral index. The reheating mechanism of this model is instant preheating due to the bosonic and fermionic broad parametric resonance, while the baryon-to-entropy ratio is obtained from the CP asymmetric rig…
In this paper, we show an explicit way to realize a TeV-scale vector leptoquark from the Pati-Salam (PS) unification with extra vectorlike families. The leptoquark mass is constrained to be heavier than PeV-scale by the measurement of a flavor violating kaon decay, $K_L \to μe$, in conventional models. This strong constraint can be avoided by introducing vectorlike families consistently with the quark and lepton masses and CKM and PMNS matrices. The other flavor violating processes are also suppressed. In this model, the vector leptoquark can be sufficiently light to explain the recent $b\to s…
If right-handed neutrinos are {\em not} singlets under the electroweak gauge group as it was proposed in a recent model, they can acquire electroweak scale masses and are thus accessible experimentally in the near future. When this idea is combined with quark-lepton unification à la Pati-Salam, one is forced to introduce new neutral particles which are singlets under the Standard Model (SM). These "sterile neutrinos" which exist in both helicities and which are different in nature from the popular particles with the same name can have their own seesaw with masses in the keV range for the light…
We analyze the gauge unification in minimal supersymmetric SO(10) grand unified theories in 5 dimensions. The single extra spatial dimension is compactified on the orbifold S^1/(Z_2 x Z_2') reducing the gauge group to that of Pati-Salam SU(4)_c x SU(2)_L x SU(2)_R. The Standard Model gauge group is achieved by the further brane-localized Higgs mechanism on one of the fixed points. There are two main different approaches developed in literature. Higgs mechanism can take place on the Pati Salam brane, or on the SO(10) preserving brane. We show, both analytically and numerically, that in the firs…
In this paper we present a model of subcritical hybrid inflation with a Pati-Salam [PS] symmetry group. Both the inflaton and waterfall fields contribute to the necessary e-foldings of inflation, while only the waterfall field spontaneously breaks PS hence monopoles produced during inflation are diluted during the inflationary epoch. The model is able to produce a tensor-to-scalar ratio, $r < 0.09$ consistent with the latest BICEP2/Keck and Planck data, as well as scalar density perturbations and spectral index, $n_s$, consistent with Planck data. For particular values of the parameters, we fi…
We present a model of quark and lepton masses and mixings based on A4 family symmetry, a discrete subgroup of an SO(3) flavour symmetry, together with Pati-Salam unification. It accommodates tri-bimaximal neutrino mixing via constrained sequential dominance with a particularly simple vacuum alignment mechanism emerging through the effective D-term contributions to the scalar potential.
All the possible three-family ${\cal N}=1$ supersymmetric Pati-Salam models constructed with intersecting D6-branes from Type IIA orientifolds on $T^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ are recently presented in arXiv: 2112.09632. Taking models with largest wrapping number $5$ and approximate gauge coupling unification at GUT scale as examples, we show string scale gauge coupling unification can be realized through two-loop renormalization group equation running by introducing seven pairs of vector-like particles from ${\cal N}=2$ sector. The number of these introduced vector-like particles ar…
We analyse the low energy predictions of the minimal supersymmetric standard model (MSSM) arising from a GUT scale Pati-Salam gauge group further constrained by an $A_4 \times Z_5$ family symmetry, resulting in four soft scalar masses at the GUT scale: one left-handed soft mass $m_0$ and three right-handed soft masses $m_1,m_2,m_3$, one for each generation. We demonstrate that this model, which was initially developed to describe the neutrino sector, can explain collider and non-collider measurements such as the dark matter relic density, the Higgs boson mass and, in particular, the anomalous …
Post-sphaleron baryogenesis, a fresh and profound mechanism of baryogenesis accounts for the matter-antimatter asymmetry of our present universe in a framework of Pati-Salam symmetry. We attempt here to embed this mechanism in a non-SUSY SO(10) grand unified theory by reviving a novel symmetry breaking chain with Pati-Salam symmetry as an intermediate symmetry breaking step and as well to address post-sphaleron baryogenesis and neutron-antineutron oscillation in a rational manner. The Pati-Salam symmetry based on the gauge group $SU(2)_L \times SU(2)_{R} \times SU(4)_C$ is realized in our mode…
In this manuscript, based on arXiv:2209.00276, I present a model which can simultaneously explain and connect the flavour hierarchies of the Standard Model with flavour anomalies in $B$-physics. I will briefly introduce the model and highlight the main features, including a common origin of Yukawa couplings and vector leptoquark $U_{1}$ couplings to Standard Model fermions. A GIM-like mechanism allows for large leptoquark couplings which can explain the $B$-anomalies, while protecting from the most dangerous FCNCs that could be mediated by a heavy coloron and $Z'$. Finally, I will highlight so…
Leptogenesis and Planck-scale black hole remnants in a Pati-Salam cosmology
School of Advanced Sciences, Vellore Institute of Technology（维洛尔理工学院高级科学学院）；Department of Physics and Institute of Basic Science, Sungkyunkwan University（成均馆大学物理系与基础科学研究院）；School of Physical Sciences, Indian Institute of Technology Goa（印度戈阿理工学院物理科学学院）
In this paper we construct supersymmetric Pati-Salam (PS) models containing the minimal supersymmetric standard model and an invisible axion. The models include two discrete symmetries, $\mathbb{Z}_4^R \times \mathbb{Z}_N$, which maintain the $quality$ of the accidental Peccei-Quinn (PQ) symmetry and thus the solution to the strong CP problem. We require that the discrete anomaly conditions are satisfied for both $\mathbb{Z}_4^R \times G_{\rm PS}^2$ and $ \mathbb{Z}_N \times G_{\rm PS}^2$. The vacuum expectation value of the PQ field spontaneously breaks all the discrete symmetries. R-parity i…
We compute the complete gauge and chiral superheavy mass spectrum and couplings of the Minimal Susy GUT (based on the $ \bf {210- \oot- 126-10}$ irreps as the Higgs system) by decomposing SO(10) labels in terms of Pati Salam subgroup labels. The spectra are sensitive functions of the single complex parameter that controls MSGUT symmetry breaking. We scan for the dependence of the threshold corrections to the Weinberg angle and Unification scale as functions of this parameter. We find that for generic values of the GUT scale parameters the modifications are within 10% of the one loop values and…
I report the recent studies\cite{1,2} on the low--energy manifestations of a minimal extension of the Standard Model based on the quark-lepton symmetry $SU(4)_V \otimes SU(2)_L \otimes G_R$ of the Pati-Salam type. Given this symmetry the third type of mixing in the interactions ot the $SU(4)_V$ leptoquarks with quarks and leptons is shown to be required. An additional arbitrariness of the mixing parameters could allow, in principle, to decrease noticeably the lower bound on the vector leptoquark mass originated from the low-energy rare processes. The decays $μ\rightarrow e γ$, $μ\rightarrow e …
