Flowering to bloom of PeV scale supersymmetric left–right symmetric models

Unified models incorporating right-handed neutrino in a symmetric way generically possess parity symmetry. If this is broken spontaneously, it results in the formation of domain walls in the early Universe, whose persistence is unwanted. A generic mechanism for the destabilization of such walls is a small pressure difference signalled by difference in free energy across the walls. It is interesting to explore the possibility of such effects in conjunction with the effects that break supersymmetry in a phenomenologically acceptable way. This possibility when realized in the context of several scenarios of supersymmetry breaking, leads to an upper bound on the scale of spontaneous parity breaking, often much lower than the GUT scale. In the left–right symmetric models studied, the upper bound is no higher than 10¹¹ GeV but a scale as low as 10⁵ GeV is acceptable.     

On neutrinoless double beta decay in the minimal left–right symmetric model

We analyze the general phenomenology of neutrinoless double beta decay in the minimal left–right symmetric model. We study under which conditions a New Physics dominated neutrinoless double beta decay signal can be expected in the future experiments. We show that the correlation among the different contributions to the process, which arises from the neutrino mass generation mechanism, can play a crucial role. We have found that, if no fine tuned cancelation is involved in the light–active neutrino contribution, a New Physics signal can be expected mainly from the $W_R$ – $W_R$ channel. An interesting exception is the $W_L$ – $W_R$ channel which can give a dominant contribution to the process if the right-handed neutrino spectrum is hierarchical with $M_1\lesssim $  MeV and $M_2,M_3\gtrsim $  GeV. We also discuss if a New Physics signal in neutrinoless double beta decay experiments is compatible with the existence of a successful Dark Matter candidate in the left–right symmetric models. It turns out that, although it is not a generic feature of the theory, it is still possible to accommodate such a signal with a KeV sterile neutrino as dark matter.     

Type I and new seesaw in left–right symmetric theories

We extend the Type I seesaw and suggest a new   seesaw mechanism to generate neutrino masses within the left–right symmetric theories where parity is spontaneously broken. We construct a next to minimal left–right symmetric model where neutrino masses are determined irrespective of the B−L$B-L$ breaking scale and call it the new   seesaw mechanism. In this scenario B−L$B-L$ scale can be very low. This makes B−L$B-L$ gauge boson and the quasi-Dirac heavy leptons very light. These TeV scale particles could have large impact on lepton flavor and CP violating processes. We also shed light on the phenomenological aspects of the model within the reach of the LHC.     

Linear collider test of a neutrinoless double beta decay mechanism in left–right symmetric theories

There are various diagrams leading to neutrinoless double beta decay in left?Cright symmetric theories based on the gauge group SU(2) _L ×SU(2) _R . All can in principle be tested at a linear collider running in electron?Celectron mode. We argue that the so-called ??-diagram is the most promising one. Taking the current limit on this diagram from double beta decay experiments, we evaluate the relevant cross section $e^{-} e^{-} \to W^{-}_{L} W^{-}_{R}$ , where $W^{-}_{L}$ is the Standard Model W-boson and $W^{-}_{R}$ the one from SU(2) _R . It is observable if the life-time of double beta decay and the mass of the W _R are close to current limits. Beam polarization effects and the high-energy behaviour of the cross section are also analyzed.     

Discrete random walk models for symmetric Lévy–Feller diffusion processes

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0<α⩽2), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the corresponding continuous Markovian stochastic processes which we refer to as Lévy–Feller diffusion processes.     

Higgs bosons in the left–right model

The model with the gauge group, containing one bidoublet and two triplets in the Higgs sector, is considered. The link between the constants determining the physical Higgs boson interactions and the neutrino oscillation parameters is found. It is shown that the observation of the ultrahigh-energy neutrinos with the help of the processes , gives us information on the singly charged Higgs bosons. The processes of the doubly charged Higgs bosons production, , are investigated. From the point of view of detecting the neutral Higgs bosons the process of the electron–muon recharge is studied. Received: 29 January 1999 / Revised version: 20 September 1999 / Published online: 3 February 2000     

The width of the Δ-isobar in chiral soliton models

The strong decay width Δ→πN is estimated using a linear meson-nucleon coupling derived from a constrained quantization of the ω-stabilized version of the Skyrme model. Due to the inherent gauge conditions, this coupling is subleading in N_c and differs from the one proposed by Adkins, Nappi and Witten in the context of soliton models.     

Universal seesaw from left–right and Peccei–Quinn symmetry breaking

To generate the lepton and quark masses in the left–right symmetric models, we can consider a universal seesaw scenario by integrating out heavy fermion singlets which have the Yukawa couplings with the fermion and Higgs doublets. The universal seesaw scenario can also accommodate the leptogenesis with Majorana or Dirac neutrinos. We show that the fermion singlets can obtain their heavy masses from the Peccei–Quinn symmetry breaking.     

Vacuum quark condensate,chiral Lagrangian,and Bose–Einstein statistics

In a series of articles it was recently claimed that the quantum chromodynamic (QCD) condensates are not the properties of the vacuum but of the hadrons and are confined inside them. We point out that this claim is incompatible with the chiral Lagrangian and Bose–Einstein statistics of the Goldstone bosons (pions) in chiral limit and conclude that the quark condensate must be the property of the QCD vacuum.     

Modified Eulerian–Lagrangian formulation for hydrodynamic modeling

We present the modified Eulerian–Lagrangian (MEL) formulation, based on non-divergent forms of partial differential balance equations, for simulating transport of extensive quantities in a porous medium. Hydrodynamic derivatives are written in terms of modified velocities for particles propagating phase and component quantities along their respective paths. The particles physically interpreted velocities also address the heterogeneity of the matrix and fluid properties. The MEL formulation is also implemented to parabolic Partial Differential Equations (PDE’s) as these are shown to be interchangeable with equivalent PDE’s having hyperbolic – parabolic characteristics, without violating the same physical concepts. We prove that the MEL schemes provide a convergent and monotone approximation also to PDE’s with discontinuous coefficients. An extension to the Peclet number is presented that also accounts for advective dominant PDE’s with no reference to the fluid velocity or even when this velocity is not introduced.In Sorek et al. [27], a mathematical analysis for a linear system of coupled PDE’s and an example of nonlinear PDE’s, proved that the finite difference MEL, unlike an Eulerian scheme, guaranties the absence of spurious oscillations. Currently, we present notions of monotone interpolation associated with the MEL particle tracking procedure and prove the convergence of the MEL schemes to the original balance equation also for discontinuous coefficients on the basis of difference schemes approximating PDE’s. We provide numerical examples, also with highly random fields of permeabilities and/or dispersivities, suggesting that the MEL scheme produces resolutions that are more consistent with the physical phenomenon in comparison to the Eulerian and the Eulerian–Lagrangian (EL) schemes.     

An effective chiral Lagrangian model for the τ-decay into three charged pions

An effective chiral Lagrangian for the π-ρ-A ₁-system is used to study the decayτ ^±→ν _τπ⁺π^?π^±. Demanding that the hadronic current 〈0|J _μ|3π〉 agrees at the low energy limit with the one obtained from the corresponding pseudoscalar meson Lagrangian ?(π), an ambiguity linked to free parameters in ?(π,ρ,A ₁) is eliminated. The decay spectrum and branching ratio of τ^±→ν _τπ⁺π^?π^± are calculated as functions of theA ₁-mass and compared with the experimental results. So conclusions can be drawn concerning theA ₁-parameters, which are found to be $$m_{A_1 } = (1180 \pm 50)MeV;\Gamma _{A_1 } = (450 \pm 100)MeV.$$ . The mass-value is smaller than recently published ones. This is attributed to the effect of suppressed decay channels not seen in the experiments up to now. A contribution from direct, non-(ρ ⁰π^±) resonanceA ₁-decay is obtained, being about 15%.     

Minimal supersymmetric left–right model with automatic R-parity

We revisit the minimal supersymmetric left–right model with B−L=2$B-L=2$ triplet Higgs fields and show that a self-consistent picture emerges with automatic R-parity conservation even in the absence of higher-dimensional operators. By computing the effective potential for the Higgs system including heavy Majorana neutrino Yukawa couplings we show that the global minimum of the model can lie in the charge and R-parity conserving domain. The model provides natural solutions to the SUSY phase problem and the strong CP problem and makes several interesting predictions. Quark mixing angles arise only after radiative corrections from the lepton sector are taken into account. A pair of doubly charged Higgs fields remain light below TeV with one field acquiring its mass entirely via renormalization group corrections. We find this mass to be not much above the Bino mass. In the supergravity framework for SUSY breaking, we also find similar upper limits on the stau masses. Natural solutions to the μ   problem and the SUSY CP problem entails light SUL₍₂₎$\mathit{SU}{(2)}_L$ triplet Higgs fields, leading to rich collider phenomenology.     

Why PeV scale left–right symmetry is a good thing

We report the results of in-situ characterization of ⁸⁷Rb atom cloud in a quadrupole Ioffe configuration (QUIC) magnetic trap after a radio-frequency (RF) evaporative cooling of the trapped atom cloud. The in-situ absorption images of the atom cloud have shown clear bimodal optical density (OD) profiles which indicate the Bose–Einstein condensation (BEC) phase transition in the trapped gas. Also, we report here, for the first time, the measured variation in the sizes of the condensate and thermal clouds with the final frequency selected in the frequency scan of the RF-field for evaporative cooling. These results on frequency-dependent sizes of the clouds are consistent with the theoretical understanding of the BEC phenomenon in the trap.     

Positivity constraints on the low-energy constants of the chiral pion–nucleon Lagrangian

Positivity constraints on the pion–nucleon scattering amplitude are derived in this article with the help of general S-matrix arguments, such as analyticity, crossing symmetry, and unitarity, in the upper part of the Mandelstam triangle, $\mathcal{R}$ . Scanning inside the region $\mathcal{R}$ , the most stringent bounds on the chiral low-energy constants of the pion–nucleon Lagrangian are determined. When just considering the central values of the fit results from covariant baryon chiral perturbation theory using the extended-on-mass-shell scheme, it is found that these bounds are well respected numerically both at the $O(p^3)$ and the $O(p^4)$ level. Nevertheless, when taking the errors into account, only the $O(p^4)$ bounds are obeyed in the full error interval, while the bounds on the $O(p^3)$ fits are slightly violated. If one disregards the loop contributions, the bounds always fail in certain regions of $\mathcal{R}$ . Thus, at a given chiral order these terms are not numerically negligible and one needs to consider all possible contributions, i.e., both tree-level and loop diagrams.We have provided the constraints for special points in $\mathcal {R}$ where the bounds are nearly optimal in terms of just a few chiral couplings, which can easily be implemented and employed to constrain future analyses. Some issues concerned with calculations with an explicit $\Delta $ resonance are also discussed.     

Wider frequency domain for negative refraction index in a quantized composite right–left handed transmission line

The refraction index of the quantized lossy composite right-left handed transmission line(CRLH-TL) is deduced in the thermal coherence state. The results show that the negative refraction index(herein the left-handedness) can be implemented by the electric circuit dissipative factors(i.e., the resistances R and conductances G) in a higher frequency band(1.446 GHz≤ω≤ 15 GHz), and flexibly adjusted by the left-handed circuit components(Cl, Ll) and the right-handed circuit components(Cr, Lr) at a lower frequency(ω = 0.995 GHz). The flexible adjustment for left-handedness in a wider bandwidth will be significant for the microscale circuit design of the CRLH-TL and may make the theoretical preparation for its compact applications.     

Direct CP violation in charm decays due to left–right mixing

Motivated by the 3.8σ   deviation from no CP violation hypothesis for the CP asymmetry (CPA) difference between D⁰→K⁺K⁻$D^0\to K^{+}{K}^{-}$ and D⁰→π⁺π⁻$D^0\to {\pi }^{+}{\pi }^{-}$, reported recently by LHCb and CDF, we investigate the CP violating effect due to the left–right (LR) mixing in the general LR symmetric model. In particular, we show that the large CPA difference could be explained in the non-manifest LR model.     

Maximal invariants for Lorentz–Wishart models

In this paper we consider two statistical hypotheses for the families of Wishart type distributions. These distributions are analogs of the Wishart distributions defined and parametrized over a Lorentz cone. We test these hypotheses by means of maximal invariant statistics which are explicitly derived in the paper. The testing problems, respectively, concern the hypothesis that parameters are in a sub-Lorentz-cone and the hypothesis that two observations have the same parameter.     

The extended conformal Einstein field equations with matter: The Einstein–Maxwell field

A discussion is given of the conformal Einstein field equations coupled with matter whose energy–momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to know a priori the location of the conformal boundary. In vacuum this gauge reduces to the so-called conformal Gaussian gauge. These ideas are applied to obtain (i) a new proof of the stability of Einstein–Maxwell de Sitter-like spacetimes; (ii) a proof of the semi-global stability of purely radiative Einstein–Maxwell spacetimes.