The Higgs Boson Mass in Split Supersymmetry at Two-Loops

The mass of the Higgs boson in the Split Supersymmetric Standard Model is calculated, including all one-loop threshold effects and the renormalization group evolution of the Higgs quartic coupling through two-loops. The two-loop corrections are very small (<<1 GeV), while the one-loop threshold corrections generally push the Higgs mass down several GeV.Comment: 17 pages. 4 figures. Improved discussion and notation. Corrected typos. Added references. Added plots. Main results unchange

Neutrino mixing contribution to the cosmological constant

We show that the non-perturbative vacuum structure associated with neutrino mixing leads to a non-zero contribution to the value of the cosmological constant. Such a contribution comes from the specific nature of the mixing phenomenon. Its origin is completely different from the one of the ordinary contribution of a massive spinor field. We estimate this neutrino mixing contribution by using the natural cut--off appearing in the quantum field theory formalism for neutrino mixing and oscillation.Comment: 7 page

On the renormalization group for the interacting massive scalar field theory in curved space

The effective action for the interacting massive scalar field in curved space-time is derived using the heat-kernel method. Starting from this effective action, we establish a smooth quadratic form of the low-energy decoupling for the four-scalar coupling constant and for the nonminimal interaction parameter. The evolution of this parameter from the conformal value 1/6 at high energies down to the IR regime is investigated within the two toy models with negative and positive four-scalar coupling constants.Comment: LaTeX, 12 pages, 4 figure

Electroweak pinch technique to all orders

The generalization of the pinch technique to all orders in the electroweak sector of the Standard Model within the class of the renormalizable 't Hooft gauges, is presented. In particular, both the all-order PT gauge-boson-- and scalar--fermions vertices, as well as the diagonal and mixed gauge-boson and scalar self-energies are explicitly constructed. This is achieved through the generalization to the Standard Model of the procedure recently applied to the QCD case, which consist of two steps: (i) the identification of special Green's functions, which serve as a common kernel to all self-energy and vertex diagrams, and (ii) the study of the (on-shell) Slavnov-Taylor identities they satisfy. It is then shown that the ghost, scalar and scalar--gauge-boson Green's functions appearing in these identities capture precisely the result of the pinching action at arbitrary order. It turns out that the aforementioned Green's functions play a crucial role, their net effect being the non-trivial modification of the ghost, scalar and scalar--gauge-boson diagrams of the gauge-boson-- or scalar--fermions vertex we have started from, in such a way as to dynamically generate the characteristic ghost and scalar sector of the background field method. The pinch technique gauge-boson and scalar self-energies are also explicitly constructed by resorting to the method of the background-quantum identities.Comment: 48 pages, 8 figures; v2: typos correcte

Renormalization-Scale-Invariant PQCD Predictions for R_e+e- and the Bjorken Sum Rule at Next-to-Leading Order

We discuss application of the physical QCD effective charge $\alpha_V$, defined via the heavy-quark potential, in perturbative calculations at next-to-leading order. When coupled with the Brodsky-Lepage-Mackenzie prescription for fixing the renormalization scales, the resulting series are automatically and naturally scale and scheme independent, and represent unambiguous predictions of perturbative QCD. We consider in detail such commensurate scale relations for the $e^+e^-$ annihilation ratio $R_{e^+e^-}$ and the Bjorken sum rule. In both cases the improved predictions are in excellent agreement with experiment.Comment: 13 Latex pages with 5 figures; to be published in Physical Review

Pseudoscalar Meson Mixing in Effective Field Theory

We show that for any effective field theory of colorless meson fields, the mixing schemes of particle states and decay constants are not only related but also determined exclusively by the kinetic and mass Lagrangian densities. In the general case, these are bilinear in terms of the intrinsic fields and involve non-diagonal kinetic and mass matrices. By applying three consecutive steps this Lagrangian can be reduced into the standard quadratic form in terms of the physical fields. These steps are : (i) the diagonalization of the kinetic matrix, (ii) rescaling of the fields, and (iii) the diagonalization of the mass matrix. In case, where the dimensions of the non-diagonal kinetic and mass sub-matrices are respectively, $k\times k$ and $n\times n$, this procedure leads to mixing schemes which involve $[k(k-1)/2] + [n(n-1)/2]$ angles and $k$ field rescaling parameters. This observation holds true irrespective with the type of particle interactions presumed. The commonly used mixing schemes, correspond to a proper choice of the kinetic and mass matrices, and are derived as special cases. In particular, $\eta$-$\eta '$ mixing, requires one angle, if and only if, the kinetic term with the intrinsic fields has a quadratic form.Comment: REVTeX, 6 page

Resummation of the hadronic tau decay width with the modified Borel transform method

A modified Borel transform of the Adler function is used to resum the hadronic tau decay width ratio. In contrast to the ordinary Borel transform, the integrand of the Borel integral is renormalization--scale invariant. We use an ansatz which explicitly accounts for the structure of the leading infrared renormalon. Further, we use judiciously chosen conformal transformations for the Borel variable, in order to map sufficiently away from the origin the other ultraviolet and infrared renormalon singularities. In addition, we apply Pade approximants for the corresponding truncated perturbation series of the modified Borel transform, in order to further accelerate the convergence. Comparing the results with the presently available experimental data on the tau hadronic decay width ratio, we obtain $\alpha_s(M^z) = 0.1192 +- 0.0007_{exp.} +- 0.0010_{EW+CKM} +- 0.0009_{th.} +- 0.0003_{evol.}$. These predictions virtually agree with those of our previous resummations where we used ordinary Borel transforms instead.Comment: 32 pages, 2 eps-figures, revtex; minor changes in the formulations; a typo in Eq.(47) corrected; version as appearing in Phys. Rev.

How large could the R-parity violating couplings be?

We investigate in detail the predictions coming from the d=4 operators for proton decay. We find the most general constraints for the R-parity violating couplings coming from proton decay, taking into account all fermion mixing and in different supersymmetric scenarios.Comment: 8 pages, several corrections, to appear in J.Phys.G (2005

Can we distinguish between h^{SM} and h^0 in split supersymmetry?

We investigate the possibility to distinguish between the Standard Model Higgs boson and the lightest Higgs boson in Split Supersymmetry. We point out that the best way to distinguish between these two Higgs bosons is through the decay into two photons. It is shown that there are large differences of several percent between the predictions for \Gamma(h\to\gamma\gamma) in the two models, making possible the discrimination at future photon-photon colliders. Once the charginos are discovered at the next generation of collider experiments, the well defined predictions for the Higgs decay into two photons will become a cross check to identify the light Higgs boson in Split Supersymmetry.Comment: 8 pages, 3 Figures, typos fixed, version published in J.Phys. G31 (2005) 563-56

Yukawa Unification and the Superpartner Mass Scale

Naturalness in supersymmetry (SUSY) is under siege by increasingly stringent LHC constraints, but natural electroweak symmetry breaking still remains the most powerful motivation for superpartner masses within experimental reach. If naturalness is the wrong criterion then what determines the mass scale of the superpartners? We motivate supersymmetry by (1) gauge coupling unification, (2) dark matter, and (3) precision b-tau Yukawa unification. We show that for an LSP that is a bino-Higgsino admixture, these three requirements lead to an upper-bound on the stop and sbottom masses in the several TeV regime because the threshold correction to the bottom mass at the superpartner scale is required to have a particular size. For tan beta about 50, which is needed for t-b-tau unification, the stops must be lighter than 2.8 TeV when A_t has the opposite sign of the gluino mass, as is favored by renormalization group scaling. For lower values of tan beta, the top and bottom squarks must be even lighter. Yukawa unification plus dark matter implies that superpartners are likely in reach of the LHC, after the upgrade to 14 (or 13) TeV, independent of any considerations of naturalness. We present a model-independent, bottom-up analysis of the SUSY parameter space that is simultaneously consistent with Yukawa unification and the hint for m_h = 125 GeV. We study the flavor and dark matter phenomenology that accompanies this Yukawa unification. A large portion of the parameter space predicts that the branching fraction for B_s to mu^+ mu^- will be observed to be significantly lower than the SM value.Comment: 34 pages plus appendices, 20 figure