Atomic parity violation in the economical 3–3–1 model

The deviation δQW$\delta Q_{\mathrm{W}}$ of the weak charge from its standard model prediction due to the mixing of the W boson with the charged bilepton Y as well as of the Z   boson with the neutral Z^′$Z^{\prime }$ and the real part of the non-Hermitian neutral bilepton X   in the economical 3–3–1 model is established. Additional contributions to the usual δQW$\delta Q_{\mathrm{W}}$ expression in the extra U(1)$\mathrm{U}(1)$ models and the left–right models are obtained. Our calculations are quite different from previous analyzes in this kind of the 3–3–1 models and give the limit on mass of the Z^′$Z^{\prime }$ boson, the Z–Z^′$Z\text{–}{Z}^{\prime }$ and W–Y$W\text{–}Y$ mixing angles with the more appropriate values: MZ^′>564 GeV$M_{Z^{\prime }}>564\text{GeV}$, −0.018<sinφ<0$-0.018<\sin \phi <0$ and |sinθ|<0.043$|\sin \theta |<0.043$.     

Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo–Kobayashi–Maskawa (CKM) unitarity triangle, α≈90°$\alpha \approx 90\text{°}$. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5)$\mathit{SU}(5)$, a discrete family symmetry such as A₄$A_4$ or S₄$S_4$, a shaping symmetry including products of Z₂${\mathbb{Z}}_2$ and Z₄${\mathbb{Z}}_4$ groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of α≈90°$\alpha \approx 90\text{°}$ by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1–3 texture zeros that satisfy the “phase sum rule” and lepton mass matrices that satisfy the “lepton mixing sum rule” together with a new prediction that the leptonic CP violating oscillation phase is close to either 0°, 90°, 180°, or 270° depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.     

Right unitarity triangles,stable CP-violating phases and approximate quark–lepton complementarity

Current experimental data indicate that two unitarity triangles of the CKM quark mixing matrix V   are almost the right triangles with α≈90°$\alpha \approx 90°$. We highlight a very suggestive parametrization of V and show that its CP-violating phase ? is nearly equal to α   (i.e., ?−α≈1.1°$?-\alpha \approx 1.1°$). Both ? and α   are stable against the renormalizaton-group evolution from the electroweak scale MZ$M_Z$ to a superhigh energy scale MX$M_X$ or vice versa, and thus it is impossible to obtain α=90°$\alpha =90°$ at MZ$M_Z$ from ?=90°$?=90°$ at MX$M_X$. We conjecture that there might also exist a maximal CP-violating phase φ≈90°$\phi \approx 90°$ in the MNS lepton mixing matrix U. The approximate quark–lepton complementarity relations, which hold in the standard parametrizations of V and U, can also hold in our particular parametrizations of V and U   simply due to the smallness of |V_ub|$|V_{ub}|$ and |V_e3|$|V_{e3}|$.     

Realistic neutrinogenesis with radiative vertex correction

We propose a new model for naturally realizing light Dirac neutrinos and explaining the baryon asymmetry of the universe through neutrinogenesis. To achieve these, we present a minimal construction which extends the Standard Model with a real singlet scalar, a heavy singlet Dirac fermion and a heavy doublet scalar besides three right-handed neutrinos, respecting lepton number conservation and a Z₂$Z_2$ symmetry. The neutrinos acquire small Dirac masses due to the suppression of weak scale over a heavy mass scale. As a key feature of our construction, once the heavy Dirac fermion and doublet scalar go out of equilibrium, their decays induce the CP asymmetry from the interference of tree-level processes with the radiative vertex corrections (rather than the self-energy corrections). Although there is no lepton number violation, an equal and opposite amount of CP asymmetry is generated in the left-handed and the right-handed neutrinos. The left-handed lepton asymmetry would then be converted to the baryon asymmetry in the presence of the sphalerons, while the right-handed lepton asymmetry remains unaffected.     

Parity doubling among the baryons

We study the evidence for and possible origins of parity doubling among the baryons. First we explore the experimental evidence, finding a significant signal for parity doubling in the non-strange baryons, but little evidence among strange baryons. Next we discuss potential explanations for this phenomenon. Possibilities include suppression of the violation of the flavor singlet axial symmetry (U(1_)A$U(1{)}_A$) of QCD, which is broken by the triangle anomaly and by quark masses. A conventional Wigner–Weyl realization of the SU(2_)L×SU(2_)R$\mathit{SU}(2{)}_L\times \mathit{SU}(2{)}_R$ chiral symmetry would also result in parity doubling. However this requires the suppression of families of chirally invariant   operators by some other dynamical mechanism. In this scenario the parity doubled states should decouple from pions. We discuss other explanations including connections to chiral invariant short distance physics motivated by large _Nc$N_c$ arguments as suggested by Shifman and others, and intrinsic deformation of relatively rigid highly excited hadrons, leading to parity doubling on the leading Regge trajectory. Finally we review the spectroscopic consequences of chiral symmetry using a formalism introduced by Weinberg, and use it to describe two baryons of opposite parity.     

Universal extra dimensions on real projective plane

We propose a six-dimensional Universal Extra Dimensions (UED) model compactified on a real projective plane RP²${\mathit{RP}}^2$, a two-sphere with its antipodal points being identified. We utilize the Randjbar-Daemi–Salam–Strathdee spontaneous sphere compactification with a monopole configuration of an extra UX₍₁₎$U{(1)}_X$ gauge field that leads to a spontaneous radius stabilization. Unlike the sphere and the S²/Z₂$S^2/Z_2$ orbifold compactifications, the massless UX₍₁₎$U{(1)}_X$ gauge boson is safely projected out. We show how a compactification on a non-orientable manifold results in a chiral four-dimensional gauge theory by utilizing 6D chiral gauge and Yukawa interactions. The resultant Kaluza–Klein mass spectra are distinct from the ordinary UED models compactified on torus. We briefly comment on the anomaly cancellation and also on a possible dark matter candidate in our model.     

Multiple seesaw mechanisms of neutrino masses at the TeV scale

In pursuit of a balance between theoretical naturalness and experimental testability, we propose two classes of multiple seesaw mechanisms at the TeV scale to understand the origin of tiny neutrino masses. They are novel extensions of the canonical and double seesaw mechanisms, respectively, by introducing even and odd numbers of gauge-singlet fermions and scalars. It is thanks to a proper implementation of the global U(1)×Z_2N$\mathrm{U}(1)\times {\mathbb{Z}}_{2N}$ symmetry that the overall neutrino mass matrix in either class has a suggestive nearest-neighbor-interaction pattern. We briefly discuss possible consequences of these TeV-scale seesaw scenarios, which can hopefully be explored in the upcoming Large Hadron Collider and precision neutrino experiments, and present a simple but instructive example of model building.     

Hypermagnetic baryogenesis

We study a new scenario for baryogenesis due to the spontaneous breaking of the CPT   invariance through the interaction between a baryon current and a hypermagnetic helicity. The hypermagnetic helicity (Chern–Simons number) of UY₍₁₎$U{(1)}_Y$ provides a CPT violation background for the generation of baryons via sphaleron processes, which protects these baryons from the sphaleron wash-out effect in thermal equilibrium. It is shown that if the present amplitude of the resultant magnetic fields are sufficiently large, for a wide range mass scale (from TeV to the Planck scale), the observational magnitude of the baryon asymmetry of the Universe can be realized.     

Number-theory dark matter

We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)_B–L gauge symmetry, Z₂(B–L)$Z_2(\mathrm{B}\text{–}\mathrm{L})$. We introduce a set of chiral fermions charged under the U(1)_B–L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1)_B–L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z₂(B–L)$Z_2(\mathrm{B}\text{–}\mathrm{L})$.     

Worldsheet instantons,torsion curves and non-perturbative superpotentials

As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov–Witten invariants for a Calabi–Yau threefold with fundamental group π₁(X)=Z₃×Z₃${\pi }_1(X)={\mathbb{Z}}_3\times {\mathbb{Z}}_3$. We find that the curves fall into homology classes in H₂(X,Z)=Z³⊕(Z₃⊕Z₃)$H_2(X,\mathbb{Z})={\mathbb{Z}}^3\oplus ({\mathbb{Z}}_3\oplus {\mathbb{Z}}_3)$. The unexpected appearance of the finite torsion subgroup in the homology group complicates our analysis. However, we succeed in computing the complete genus-0 prepotential. Expanding it as a power series, the number of instantons in any integral homology class can be read off. This is the first explicit calculation of the Gromov–Witten invariants of homology classes with torsion. We find that some curve classes contain only a single instanton. This ensures that the contribution to the superpotential from each such instanton cannot cancel.     

A realistic world from intersecting D6-branes

We describe a three-family Pati–Salam model from intersecting D6-branes in type IIA string theory on the T⁶/(Z₂×Z₂)${\mathbf{T}}^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ orientifold which is of strong phenomenological interest. In the model, the gauge coupling unification is achieved naturally at the string scale, and the gauge symmetry can be broken down to the Standard Model (SM) close to the string scale. Moreover, we find that it is possible to obtain the correct SM quark masses and mixings, and the tau lepton mass. Additionally, neutrino masses and mixings may be generated via the seesaw mechanism. Furthermore, we calculate the supersymmetry breaking soft terms, and the corresponding low-energy supersymmetric particle spectra which may potentially be tested at the Large Hadron Collider (LHC), and provide the observed dark matter density.     

Gauge coupling unification in the exceptional supersymmetric Standard Model

We consider the renormalisation group flow of gauge couplings within the so-called exceptional supersymmetric Standard Model (E₆SSM) based on the low-energy matter content of 27-dimensional representations of the gauge group E₆$E_6$, together with two additional non-Higgs doublets. The two-loop beta functions are computed, and the threshold corrections are studied in the E₆SSM. Our results show that gauge coupling unification in the E₆SSM can be achieved for phenomenologically acceptable values of α₃(MZ)${\alpha }_3(M_Z)$, consistent with the central measured low-energy value, unlike in the minimal supersymmetric Standard Model (MSSM) which, ignoring the effects of high energy threshold corrections, requires significantly higher values of α₃(MZ)${\alpha }_3(M_Z)$, well above the experimentally measured central value.     

μ–τ symmetry in Zee–Babu model

We study the Zee–Babu two-loop neutrino mass generation model and look for a possible flavor symmetry behind the tri-bimaximal neutrino mixing. We find that there probably exists the μ–τ   symmetry in the case of the normal neutrino mass hierarchy, whereas there may not be in the inverted hierarchy case. We also propose a specific model based on a Froggatt–Nielsen-like Z₅$Z_5$ symmetry to naturally accomplish the μ–τ symmetry on the neutrino mass matrix for the normal hierarchy case.