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Casimir vacuum energy is divergent. It needs to be regularized. The regularization introduces a renormalization scale which may lead to a scale dependent cosmological constant. We show that the requirement of physical cosmological constant is renormalization scale independent provides important constraints on possible particle contents and their masses in particle physics models. In the Standard Model of strong and electroweak interactions, besides the Casimir vacuum energy there is also vacuum energy induced from spontaneous symmetry breaking. The requirement that the total vacuum energy to be scale independent dictates the Higgs mass to be where the summation is over fermions and N_i equals to 3 and 1 for quarks and leptons, respectively. The Higgs mass is predicted to be approximately 382 GeV.

We propose a phenomenological solution to the electroweak hierarchy problem. It predicts no new particles beyond those in the Standard Model. The Higgs is arbitrarily massive and slow-roll inflation can be implemented naturally. Loop corrections will be negligible even for large cutoffs.

We update the upper bound on the lightest CP-even Higgs mass in the NMSSM, which is given as a function of tan β and λ. It is pointed out that large values of tan β, with λ not too small, imply a large value for the MSSM-like parameter M_A. We include the available one- and two-loop corrections to the NMSSM Higgs masses, and constraints from the absence of Landau singularities below the GUT scale as well as from the stability of the NMSSM Higgs potential. For m_top varying between 171.4 and 178 GeV, squark masses of 1 TeV and maximal mixing the upper bound is assumed near tan β ~ 2 and varies between 139.9 and 141.4 GeV.

The universe exhibits two striking manifestations, (a) immense complexity and (b) an astonishingly high scale-free precision. Since a cryptographic system based on the modular arithmetic of a finite field can provide a mathematical structure matching these two cardinal characteristics, it is natural to evaluate the theoretical possibilities of a cryptographic analysis of physical phenomena. The organization of the particle mass scale provides a particularly suitable test of this idea, since the cryptographic approach also has the inherent feature that divergences are fully barred, thereby eliminating the need for ad hoc procedures of renormalization. This article (1) shows how such a cryptographic concept can be implemented and (2) demonstrates its surprising ability to synthesize the description of a broad range of phenomena through the development of an interlocking set of quantitative findings. It is found that a cryptographic theoretical framework based solely on two physically anchored parameters, a modulus P_α and a corresponding primitive root g_α, can simultaneously achieve six goals. Specifically, it (α) unites the concepts of mass and space, (β) organizes the physical mass scale in a group structure, (γ) produces a quantitative concordance of findings linking the cosmic and micro-scales that includes values for the fine structure constant α and the unified strong-electroweak coupling constant α*, (δ) respectively gives prospective magnitudes of 0.808 meV and 27.68 meV for the rest masses m_νe and m_νμ of the electron (ν_e) and muon (ν_μ) neutrinos, (∊) specifies a symmetry condition that yields an exact predicted value for the Higgs particle mass that lies above 10¹⁸ GeV, and (ζ) enables the formulation of a direct physical connection between the anomalous flavor (ν_e/ν_μ) transforming propagation of solar neutrinos and the existence of a positive cosmological constant Λ. These results are uniformly in agreement with all corresponding observational data.

Unification ideas motivate the formulation of field equations on an extended matrix-spin space. Demanding that the Poincaré symmetry be maintained, one derives scalar symmetries that are associated with flavor and gauge groups. Boson and fermion solutions are obtained with a fixed representation. A field theory can be equivalently written and interpreted in terms of elements of such a space and is similarly constrained. At 5+1 dimensions, one obtains isospin and hypercharge SU(2)_L×U(1) symmetries, their vector carriers, two-flavor charged and chargeless leptons, and scalar particles. Mass terms produce breaking of the symmetry to an electromagnetic U(1), a Weinberg's angle with sin²(θ_W)=0.25, and additional information on the respective coupling constants. The particles' underlying spin symmetry gives information on their masses; one reproduces the Standard Model ratio M_Z/M_W, and predicts possible Higgs masses of M_H≈114 and M_H≈161 GeV, at tree level.

The construction of specific supersymmetric grand unified models based on the Pati–Salam gauge group and leading to a set of Yukawa quasi-unification conditions which can allow an acceptable b-quark mass within the constrained minimal supersymmetric standard model with μ > 0 is briefly reviewed. Imposing constraints from the cold dark matter abundance in the universe, B physics, and the mass m_h of the lighter neutral CP-even Higgs boson, we find that there is an allowed parameter space with, approximately, 44 ≤ tan β ≤ 52, -3 ≤ A₀/M_1/2 ≤ 0.1, 122 ≤ m_h/GeV ≤ 127, and mass of the lightest sparticle in the range (0.75–1.43) TeV. Such heavy lightest sparticle masses can become consistent with the cold dark matter requirements on the lightest sparticle relic density thanks to neutralino–stau coannihilations which are enhanced due to stau–antistau coannihilation to down type fermions via a direct-channel exchange of the heavier neutral CP-even Higgs boson. Restrictions on the model parameters by the muon anomalous magnetic moment are also discussed.

The Higgs mass value is derived from a Hamiltonian on the Lie group U(3) where we relate strong and electroweak energy scales. The baryon states of nucleon and delta resonances originate in specific Bloch wave degrees of freedom coupled to a Higgs mechanism which also gives rise to the usual gauge boson masses. The derived Higgs mass is around 125 GeV. From the same Hamiltonian, we derive the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict scarce neutral flavor baryon singlets that should be visible in scattering cross-sections for negative pions on protons, in photoproduction on neutrons, in neutron diffraction dissociation experiments and in invariant mass spectra of protons and negative pions in B-decays. The fundamental predictions are based on just one length scale and the fine structure constant. More particular predictions rely also on the weak mixing angle and the up–down quark flavor mixing matrix element. With differential forms on the measure-scaled wave function, we could generate approximate parton distribution functions for the u and d valence quarks of the proton that compare well with established experimental analysis.

We discuss a new mechanism of D-term dynamical supersymmetry breaking in the context of Dirac gaugino scenario. The existence of a nontrivial solution of the gap equation for D-term is shown. It is also shown that an observed 126 GeV Higgs mass is realized by tree level D-term effects in a broad range of parameters.

With no conclusive signal till date of the minimal supersymmetric and extra-dimensional models at the Large Hadron Collider (LHC), the issue of naturalness of the Higgs mass still calls for attention. One way to achieve that is to introduce additional bosonic degrees of freedom and rely on fine-tuning thereafter. That is, to arrange for a cancellation between various parameters so that the coefficient of the quadratically divergent term in the Higgs mass is vanishing or small to a manageable level. In this work, we explore the possibility of doing so using two- and three-Higgs doublet models. We consider different versions of the same and fold in various relevant constraints accordingly. The study reveals that the quadratically divergent mass term of the 125 GeV Higgs can be exactly canceled in most of the models considered here. However, the same does not hold for the nonstandard scalars owing to the applied constraints.

We study the renormalization group flow for the Higgs self-coupling in the presence of gravitational correction terms. We show that the resulting equation is equivalent to a singular linear ODE, which has explicit solutions in terms of hypergeometric functions. We discuss the implications of this model with gravitational corrections on the Higgs mass estimates in particle physics models based on the spectral action functional.

We discuss a new mechanism of D-term dynamical supersymmetry breaking in the context of Dirac gaugino scenario. The existence of a nontrivial solution of the gap equation for D-term is shown. It is also shown that an observed 126 GeV Higgs mass is realized by tree level D-term effects in a broad range of parameters.