Vacuum stability and the Cholesky decomposition

We discuss how the Cholesky decomposition may be used to ascertain whether a critical point of the field theory scalar potential provides a stable vacuum configuration. We then use this method to derive the stability conditions in a specific example.Comment: 7 page

Anatomy of Mixing-Induced CP Asymmetries in Left-Right-Symmetric Models with Spontaneous CP Violation

We investigate the pattern of CP violation in K, B_d and B_s mixing in a symmetrical SU(2)_R x SU(2)_L x U(1) model with spontaneous CP violation. We calculate the phases of the left and right quark mixing matrices beyond the small phase approximation and perform a careful analysis of all relevant restrictions on the model's parameters from Delta m_K, Delta m_B, epsilon, epsilon'/epsilon and the CP asymmetry in B->J/psi K_S. We find that, with current experimental data, the mass of the right-handed charged gauge boson, M2, is restricted to be in the range 2.75 to 13 TeV and the mass of the flavour-changing neutral Higgs boson, MH, in 10.2 to 14.6 TeV. This means in particular that the decoupling limit M2, MH -> infinity is already excluded by experiment. We also find that the model favours opposite signs of epsilon and sin 2beta and is excluded if sin 2beta > 0.1.Comment: 33 pages Latex with 11 Postscript-Figures (included

The Minimal Left-Right Symmetric Model and Radiative Corrections to the Muon Decay

A self-consistent version of the left-right (LR) symmetric model is used to examine tree- as well as one-loop level radiative corrections to the muon decay. It is shown that constraints on the heavy sector of the model parameters are different when going beyond tree-level physics. In fact, in our case, the only useful constraints on the model can be obtained from the one-loop level calculation. Furthermore, corrections coming from the subset of SM particles within the LR model have a different structure from their SM equivalent, e.g. the top quark leading term contribution to $\Delta \rho$ within the LR model is different from its SM counterpart. As a consequence, care must be taken in fitting procedures of models beyond the SM, where usually, only tree-level couplings modified by the SM radiative corrections are considered. This procedure is not always correct.Comment: small corrections, final version for proceeding

Muon Decay to One Loop Order in the Left-Right Symmetric Model

One loop corrections to the muon decay are studied in a popular and self-consistent version of the Left-Right symmetric model. It is shown quantitatively, that the corrections do not split into those that come from the Standard Model sector and some decoupling terms. For a heavy Spontaneous Symmetry Breaking (SSB) scale of the order of a least 1 TeV, the contributions from the top quark have a logarithmic behaviour and there is a strong quadratic dependence on the heavy Higgs scalar masses. The dependence on the light Higgs boson mass is small. The heavy neutrinos are shown to play an important role, although secondary in comparison with the heavy scalar particles as long as the heavy neutrinos' Majorana Yukawa coupling matrix $h_M$ obeys unitarity bounds.Comment: 20 pages, 7 figure

Higgs Sector of the Minimal Left-Right Symmetric Model

We perform an exhaustive analysis of the most general Higgs sector of the minimal left-right symmetric model (MLRM). We find that the CP properties of the vacuum state are connected to the Higgs spectrum: if CP is broken spontaneously, the MLRM does not approach the Standard Model in the limit of a decoupling left-right symmetry breaking scale. Depending on the size of the CP phases scenarios with extra non-decoupling flavor-violating doublet Higgses or very light SU(2) triplet Higgses emerge, both of which are ruled out by phenomenology. For zero CP phases the non-standard Higgses decouple only if a very unnatural fine-tuning condition is fulfilled. We also discuss generalizations to a non-minimal Higgs sector.Comment: brief discussion of non-minimal Higgs sectors added, journal versio

On Neutrino Masses and a Low Breaking Scale of Left-Right Symmetry

In left-right symmetric models (LRSM) the light neutrino masses arise from two sources: the seesaw mechanism and a VEV of an SU(2)$_L$ triplet. If the left-right symmetry breaking, $v_R$, is low, v_R\lsim15\TeV, the contributions to the light neutrino masses from both the seesaw mechanism and the triplet Yukawa couplings are expected to be well above the experimental bounds. We present a minimal LRSM with an additional U(1) symmetry in which the masses induced by the two sources are below the eV scale and the two-fold problem is solved. We further show that, if the U(1) symmetry is also responsible for the lepton flavor structure, the model yields a small mixing angle within the first two lepton generations.Comment: 18 pages references added published versio

Spontaneous CP violation in the left-right model and the kaon system

A left-right model with spontaneous CP breakdown, consistent with the particle physics phenomenology, is presented. Constraints on free parameters of the model: mass of the new right handed gauge boson M2 and ratio r of the two vacuum expectation values of the bidoublet, are found from the measurement of ϵ in the kaon system. For most of the parameter space, M2 is restricted to be below 10 TeV. Higher masses can be achieved only by fine tuning of Kobayashi-Maskawa matrix elements, quark masses, r and the phase α which is the unique source of CP-violation in the model. Large number of combinations of signs of quark masses, which are observables of the model, are found to be not allowed since they contradict with data. The range of ϵ′/ϵ the model predicts is around 10−4 in magnitude

Two Higgs Bi-doublet Left-Right Model With Spontaneous P and CP Violation

A left-right symmetric model with two Higgs bi-doublet is shown to be a consistent model for both spontaneous P and CP violation. The flavor changing neutral currents can be suppressed by the mechanism of approximate global U(1) family symmetry. We calculate the constraints from neural $K$ meson mass difference $\Delta m_K$ and demonstrate that a right-handed gauge boson $W_2$ contribution in box-diagrams with mass well below 1 TeV is allowed due to a cancellation caused by a light charged Higgs boson with a mass range $150 \sim 300$ GeV. The $W_2$ contribution to $\epsilon_K$ can be suppressed from appropriate choice of additional CP phases appearing in the right-handed Cabbibo-Kobayashi-Maskawa matrix. The model is also found to be fully consistent with $B^0$ mass difference $\Delta m_B$, and the mixing-induced CP violation quantity $\sin2\beta_{J/\psi}$, which is usually difficult for the model with only one Higgs bi-doublet. The new physics beyond the standard model can be directly searched at the colliders LHC and ILC.Comment: 25 pages, 6 figures, typos corrected, 1 figure added, published versio

Minimal SUSY SO(10) model and predictions for neutrino mixings and leptonic CP violation

We discuss a minimal Supersymmetric SO(10) model where B-L symmetry is broken by a {\bf 126} dimensional Higgs multiplet which also contributes to fermion masses in conjunction with a {\bf 10} dimensional superfield. This minimal Higgs choice provides a partial unification of neutrino flavor structure with that of quarks and has been shown to predict all three neutrino mixing angles and the solar mass splitting in agreement with observations, provided one uses the type II seesaw formula for neutrino masses. In this paper we generalize this analysis to include arbitrary CP phases in couplings and vevs. We find that (i) the predictions for neutrino mixings are similar with $U_{e3}\simeq 0.18$ as before and other parameters in a somewhat bigger range and (ii) that to first order in the quark mixing parameter $\lambda$ (the Cabibbo angle), the leptonic mixing matrix is CP conserving. We also find that in the absence of any higher dimensional contributions to fermion masses, the CKM phase is different from that of the standard model implying that there must be new contributions to quark CP violation from the supersymmetry breaking sector. Inclusion of higher dimensional terms however allows the standard model CKM phase to be maintained.Comment: 22 pages, 6 figure

Bounds of the mass of Z' and the neutral mixing angles in general SU(2)_L x SU(2)_R x U(1) models

We consider phenomenological constraints on the mass $M_{Z^{\prime}}$ and the two mixing angles $\theta_R$ and $\xi$ of the neutral sector in a very general class of $SU(2)_L \times SU(2)_R \times U(1)$ models using electroweak data. We do not make any specific assumptions such as left-right symmetry or the Higgs structure. The analysis of the neutral sector has the advantage that it has relatively fewer parameters compared to the charged sector since the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements in the right-handed sector do not enter into the analysis, hence the number of various possibilities from a big parameter space is reduced. We utilize theoretical considerations on the masses of the gauge particles and the mixing angles. We combine the precision electroweak data from LEP I and the low-energy neutral-current experimental data to constrain the parameters introduced in the model. It turns out that $M_{Z^{\prime}}> 400$ GeV, $-0.0028 <\xi <0.0065$ with little constraint on $\theta_R$. In the left-right symmetric theory, $M_{Z^{\prime}}$ should be larger than 900 GeV. With these constraints, we compare the values for $\sigma (e^+ e^- \to \mu^+ \mu^-)$, $\sigma (e^+ e^- \to b\bar{b})$ and $A_{FB}^{\ell}$ at LEP II with experimental values.Comment: 34 pages, a LaTeX file with macros elsart and pictex. 4 Figure