Lepton Number Violation in Supersymmetric Grand Unified Theories

We argue that the nature of the global conservation laws in Supersymmetric Grand Unified Theories is determined by the basic vacuum configuration in the model rather than its Lagrangian. It is shown that the suppression of baryon number violation in a general (R-parity violating) superpotential can naturally appear in some extended SU(N) SUSY GUTs which, among other degenerate symmetry-breaking vacua, have a missing VEV vacuum configuration giving a solution to the doublet-triplet splitting problem. We construct SU(7) and SU(8) GUTs where the effective lepton number violating couplings immediately evolve, while the baryon number non-conserving ones are safely projected out as the GUT symmetry breaks down to that of the MSSM. However at the next stage, when SUSY breaks, the radiative corrections shift the missing VEV components to some nonzero values of order M_{SUSY}, thereby inducing the ordinary Higgs doublet mass, on the one hand, and tiny baryon number violation, on the other. So, a missing VEV solution to the gauge hierarchy problem leads at the same time to a similar hierarchy of baryon vs lepton number violation.Comment: 15 page LaTeX fil

Deriving Gauge Symmetry and Spontaneous Lorentz Violation

We consider a class of field theories with a four-vector field $A_{\mu}(x)$ in addition to other fields supplied with a global charge symmetry - theories which have partial gauge symmetry in the sense of only imposing it on those terms in the Lagrangian density which have derivatives as factors in them. We suppose that spontaneous Lorentz invariance breaking occurs in such a theory due to the four-vector field taking a non-zero vacuum expectation value. Under some very mild assumptions, we show that this Lorentz violation is not observable and the whole theory is practically gauge invariant. A very important presupposition for this theorem is that an initial condition is imposed on the no-derivative expressions corresponding to the early Universe being essentially in a vacuum state. This condition then remains true forever and can be interpreted as a gauge constraint. We formulate the conditions under which the spontaneous Lorentz violation becomes observable. Spontaneously broken Lorentz invariance could be seen by some primordially existing or created "fossil" charges with the property of moving through the Universe with a fixed velocity.Comment: Extended versio

Standard Model with Partial Gauge Invariance

We argue that an exact gauge invariance may disable some generic features of the Standard Model which could otherwise manifest themselves at high energies. One of them might be related to the spontaneous Lorentz invariance violation (SLIV) which could provide an alternative dynamical approach to QED and Yang-Mills theories with photon and non-Abelian gauge fields appearing as massless Nambu-Goldstone bosons. To see some key features of the new physics expected we propose partial rather than exact gauge invariance in an extended SM framework. This principle applied, in some minimal form, to the weak hypercharge gauge field B_{mu} and its interactions leads to SLIV with B field components appearing as the massless Nambu-Goldstone modes, and provides a number of distinctive Lorentz beaking effects. Being naturally suppressed at low energies they may become detectable in high energy physics and astrophysics. Some of the most interesting SLIV processes are considered in significant detail.Comment: 32 pages, extended version, to appear in Eur.Phys.J.

Spontaneously Generated Tensor Field Gravity

An arbitrary local theory of a symmetric two-tensor field $H_{\mu \nu}$ in Minkowski spacetime is considered, in which the equations of motion are required to be compatible with a nonlinear length-fixing constraint $H_{\mu \nu}^{2}=\pm M^{2}$ leading to spontaneous Lorentz invariance violation, SLIV ($M$ is the proposed scale for SLIV). Allowing the parameters in the Lagrangian to be adjusted so as to be consistent with this constraint, the theory turns out to correspond to linearized general relativity in the weak field approximation, while some of the massless tensor Goldstone modes appearing through SLIV are naturally collected in the physical graviton. In essence the underlying diffeomophism invariance emerges as a necessary condition for the tensor field $H_{\mu \nu}$ not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in the theory is chosen by SLIV. The emergent theory appears essentially nonlinear, when expressed in terms of the pure Goldstone tensor modes and contains a plethora of new Lorentz and $CPT$ violating couplings. However, these couplings do not lead to physical Lorentz violation once this tensor field gravity is properly extended to conventional general relativity.Comment: 27 pages, published version, to appear in Nuclear Physics

Constrained Gauge Fields from Spontaneous Lorentz Violation

Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type $A_{\mu}A^{\mu}=M^{2}$ ($M$ is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory proves to be QED with a massless vector Goldstone boson naturally associated with the photon, while the non-Abelian symmetry case results in a conventional Yang-Mills theory. These theories, both Abelian and non-Abelian, look essentially nonlinear and contain particular Lorentz (and $CPT$) violating couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical Lorentz violation due to the simultaneously generated gauge invariance.Comment: 15 pages, minor corrections, version to be published in Nucl. Phys.

Towards the Non-Chiral Extension of SM and MSSM

We show that in some SU(N) type GUTs with the complementary pairs of the conjugated fermion multiplets there naturally appear the relatively light ($M\ll M_{GUT}$) vectorlike fermions which considerably modify the desert physics. In the non-SUSY case they can provide for the unification of the standard coupling constant $\alpha_1$, $\alpha_2$ and $\alpha_S$ whereas in the SUSY case they can increase the unification point up to the string unification limit and decrease $\alpha_S(M_Z)$ down to the value predicted from the low energy physics.Comment: LaTeX, 1 figur

Minimal Mixing of Quarks and Leptons in the SU(3) Theory of Flavour

We argue that flavour mixing, both in the quark and lepton sector, follows the minimal mixing pattern, according to which the whole of this mixing is basically determined by the physical mass generation for the first family of fermions. So, in the chiral symmetry limit when the masses of the lightest ($u$ and $d$) quarks vanish, all the quark mixing angles vanish. This minimal pattern is shown to fit extremely well the already established CKM matrix elements and to give fairly distinctive predictions for the as yet poorly known ones. Remarkably, together with generically small quark mixing, it also leads to large neutrino mixing, provided that neutrino masses appear through the ordinary ``see-saw'' mechanism. It is natural to think that this minimal flavour mixing pattern presupposes some underlying family symmetry, treating families of quarks and leptons in a special way. Indeed, we have found a local chiral $SU(3)_{F}$ family symmetry model which leads, through its dominant symmetry breaking vacuum configuration, to a natural realization of the proposed minimal mechanism. It can also naturally generate the quark and lepton mass hierarchies. Furthermore spontaneous CP violation is possible, leading to a maximal CP violating phase $\delta =\frac{\pi}{2}$, in the framework of the MSSM extended by a high-scale $SU(3)_{F}$ chiral family symmetry.Comment: 52 pages, LaTex, no figures; some typos corrected; journal versio

Spontaneous Lorentz Violation via QED with Non-Exact Gauge Invariance

We reconsider an alternative theory of the QED with the photon as a massless vector Nambu-Goldstone boson and show that the underlying spontaneous Lorentz violation caused by the vector field vacuum expectation value, while being superficial in gauge invariant theory, becomes physically significant in the QED with a tiny gauge non-invariance. This leads, through special dispersion relations appearing for charged fermions, to a new class of phenomena which could be of distinctive observational interest in particle physics and astrophysics. They include a significant change in the GZK cutoff for UHE cosmic-ray nucleons, stability of high-energy pions and W bosons, modification of nucleon beta decays, and some others.Comment: 15 pages, to appear in Eur.Phys.J.

Spontaneous Lorentz Violation: Non-Abelian Gauge Fields as Pseudo-Goldstone Vector Bosons

We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstone vector bosons caused by spontaneous Lorentz invariance violation (SLIV). To this end, the SLIV which evolves in a general Yang-Mills type theory with the nonlinear vector field constraint Tr(% \boldsymbol{A}_{\mu }\boldsymbol{A}^{\mu})=\pm M^{2} ($M$ is a proposed SLIV scale) imposed is considered in detail. With an internal symmetry group $G$ having $D$ generators not only the pure Lorentz symmetry SO(1,3), but the larger accidental symmetry $SO(D,3D)$ of the SLIV constraint in itself appears to be spontaneously broken as well. As a result, while the pure Lorentz violation still generates only one genuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosons related to the $SO(D,3D)$ breaking also come into play in the final arrangement of the entire Goldstone vector field multiplet. Remarkably, they remain strictly massless, being protected by gauge invariance of the Yang-Mills theory involved. We show that, although this theory contains a plethora of Lorentz and $CPT$ violating couplings, they do not lead to physical SLIV effects which turn out to be strictly cancelled in all the lowest order processes considered. However, the physical Lorentz violation could appear if the internal gauge invariance were slightly broken at very small distances influenced by gravity. For the SLIV scale comparable with the Planck one the Lorentz violation could become directly observable at low energies.Comment: Invited talk given at Caucasian-German School and Workshop in Hadron Physics (4-7 September 2006, Tbilisi, Georgia

Where does Flavour Mixing come from?

We argue that flavour mixing, both in the quark and charged lepton sector, is basically determined by the lightest family mass generation mechanism. So, in the chiral symmetry limit when the up and down quark masses vanish, all the quark mixing angles vanish. This mechanism is not dependent on the number of quark-lepton families nor on any ``vertical'' symmetry structure, unifying quarks and leptons inside a family as in Grand Unified Theories. Together with a hypothesis of maximal CP violation, the model leads to a completely predictive ansatz for all the CKM matrix elements in terms of the quark masses. Some implications for neutrino masses and oscillations are briefly discussed.Comment: 13 page LaTeX file, minor changes in fourth paragraph of Conclusion and in Reference