Radiative Electroweak Breaking with Pseudogoldstone Higgs Doublets

We consider a realistic example of supersymmetric grand unification based on $SU(3)_c \times SU(3)_L \times SU(3)_R$ in which the electroweak (EW) higgs doublets are `light' as a consequence of the `pseudogoldstone' mechanism. We discuss radiative EW breaking in this model, exploring in particular the `small' (order unity) and `large' $(\approx m_t/m_b)$ $\tan \beta$ regions by studying the variations of $r (\equiv \sqrt{\mu^2_{1,2}/\mu^2_3})$, where $\mu^2_{1,2,3}$ are the well known MSSM parameters evaluated at the GUT scale. For $r$ sufficiently close to unity the quantity $\tan \beta$ can be of order unity, but the converse is not always true.Comment: 18 pages plain LaTeX (to be run twice) and 11 figures available separately from uuencoded file

Infra-red fixed points in supersymmetry

Model independent constraints on supersymmetric models emerge when certain couplings are drawn towards their infra-red (quasi) fixed points in the course of their renormalization group evolution. The general principles are first reviewed and the conclusions for some recent studies of theories with R-parity and baryon and lepton number violations are summarized.Comment: 5 pages Latex with 2 figures embedded as eps files Talk given at WHEPP6, Chennai, India, January 3-15, 2000, to appear in special issue of Praman

Constraining Form Factors with the Method of Unitarity Bounds

The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also to isolate domains on the real axis and in the complex energy plane where zeros are excluded. In this lecture note, we review the mathematical techniques of this formalism in its standard form, known as the method of unitarity bounds, and recent developments which allow us to include information on the phase and modulus along a part of the unitarity cut. We also provide a brief summary of some results that we have obtained in the recent past, which demonstrate the usefulness of the method for precision predictions on the form factors.Comment: 12 pages, 2 figures; Lecture given at the DAE-BRNS Workshop on Hadron Physics, Bhabha Atomic Research Centre, Mumbai, India, October 31-November 4, 2011, submitted to Proceeding

Top Yukawa coupling measurement with indefinite CP Higgs in e+e−→ttˉΦe^+e^-\to t\bar{t}\Phi

We consider the issue of the top quark Yukawa coupling measurement in a model in dependent and general case with the inclusion of CP-violation in the coupling. Arguably the best process to study this coupling is the associa ted production of Higgs boson along with a $t\bar t$ pair in a machine like the International Linear Collider (ILC). While detailed analyses of the sensitivity of the measurement assuming a Standard Model (SM) - like coupling are available in the context of ILC, conclude that th e coupling could be pinned down at about 10\% level with modest luminosity, our investigations show that the scenario could be different in case of a more general coupling. The modified Lorentz structure resulting in a changed functional dependence of the cross section on the couplin g, along with the difference in the cross section itself leads to considerable deviation in the sensitivity. Our studies with an ILC of center of mass energies of 500 GeV, 800 GeV and 1000 GeV show that moderate CP-mixing in the Higgs sector could change the sensitivity to about 20\ %, while it could be worsened to 75\% in cases which could accommodate more dramatic changes in the coupling. While detailed considerations of the decay distributions point to a need for a relook at the analysis strategy followed for the case of SM such as for a model independent analysis of the top quark Yukawa coupling measurement. This study strongly suggests that, a joint analysis of the CP properties and the Yukawa coupling measurement would be the way forward at the ILC and that caution must be excercised in the measurem ent of the Yukawa couplings and the conclusions drawn from it.Comment: 18 pages, 7 figures, uses revte

Probing SO(10) symmetry breaking patterns through sfermion mass relations

We consider supersymmetric SO(10) grand unification where the unified gauge group can break to the Standard Model gauge group through different chains. The breaking of SO(10) necessarily involves the reduction of the rank, and consequent generation of non-universal supersymmetry breaking scalar mass terms. We derive squark and slepton mass relations, taking into account these non-universal contributions to the sfermion masses, which can help distinguish between the different chains through which the SO(10) gauge group breaks to the Standard Model gauge group. We then study some implications of these non-universal supersymmetry breaking scalar masses for the low energy phenomenology.Comment: 13 pages, latex using revtex4, contains 2 figures, replaced with version accepted for publicatio

Infrared Fixed Point Structure in Minimal Supersymmetric Standard Model with Baryon and Lepton Number Violation

We study in detail the renomalization group evolution of Yukawa couplings and soft supersymmetry breaking trilinear couplings in the minimal supersymmetric standard model with baryon and lepton number violation. We obtain the exact solutions of these equations in a closed form, and then depict the infrared fixed point structure of the third generation Yukawa couplings and the highest generation baryon and lepton number violating couplings. Approximate analytical solutions for these Yukawa couplings and baryon and lepton number violating couplings, and the soft supersymmetry breaking couplings are obtained in terms of their initial values at the unification scale. We then numerically study the infrared fixed surfaces of the model, and illustrate the approach to the fixed points.Comment: 16 pages REVTeX, figures embedded as epsfigs, replaced with version to appear in Physical Review D, minor typographical errors eliminated and references reordered, figures correcte

Large tanβtan \beta from SU(2)RSU(2)_R Gauge Symmetry

Sufficient conditions for the relation $tan \beta \simeq m_t/m_b$ to hold in supersymmetric grand unified theories are formulated. Essential ingredients are the $SU(2)_R$ gauge symmetry and a discrete matter parity. The applicability of our conditions is illustrated by specific examples. Implications for neutrino masses are discussed.Comment: 13 pages, LaTeX, UT-STPD-1-9

Yukawa Unification, b --> s gamma and Bino-Stau Coannihilation

The minimal supersymmetric standard model with universal boundary conditions and "asymptotic" Yukawa unification is considered. The full one-loop effective potential for radiative electroweak symmetry breaking as well as the one-loop corrections to the charged Higgs boson, b-quark and tau lepton masses are included. The CP-even Higgs boson masses are corrected to two-loops. The relic abundance of the lightest supersymmetric particle (bino) is calculated by including its coannihilations with the next-to-lightest supersymmetric particle (lightest stau) consistently with Yukawa unification. The branching ratio of b --> s gamma is evaluated by incorporating all the applicable next-to-leading order QCD corrections. The bino-stau coannihilations reduce the bino relic abundance below the upper bound from cold dark matter considerations in a sizable fraction of the parameter space allowed by b --> s gamma for mu>0. Thus, the mu>0 case, which also predicts an acceptable b-quark mass, is perfectly compatible with data.Comment: 16 pages including 3 figures, Revtex, major revisions are mad

Nonminimal Supersymmetric Standard Model with Baryon and Lepton Number Violation

We carry out a comprehensive analysis of the nonminimal supersymmetric standard model (NMSSM) with baryon and lepton number violation. We catalogue the baryon and lepton number violating dimension four and five operators of the model. We then study the renormalization group evolution and infrared stable fixed points of the Yukawa couplings and the soft supersymmetry breaking trilinear couplings of this model with baryon and lepton number (and R-parity) violation involving the heaviest generations. We show analytically that in the Yukawa sector of the NMSSM there is only one infrared stable fixed point. This corresponds to a non-trivial fixed point for the top-, bottom-quark Yukawa couplings and the $B$ violating coupling $\lambda_{233}''$, and a trivial one for all other couplings. All other possible fixed points are either unphysical or unstable in the infrared region. We also carry out an analysis of the renormalization group equations for the soft supersymmetry breaking trilinear couplings, and determine the corresponding fixed points for these couplings. We then study the quasi-fixed point behaviour, both of the third generation Yukawa couplings and the baryon number violating coupling, and those of the soft supersymmetry breaking trilinear couplings. From the analysis of the fixed point behaviour, we obtain upper and lower bounds on the baryon number violating coupling $\lambda_{233}''$, as well as on the soft supersymmetry breaking trilinear couplings. Our analysis shows that the infrared fixed point behavior of NMSSM with baryon and lepton number violation is similar to that of MSSM.Comment: 35 pages, Revtex, 6 eps fig

Squark and slepton masses as probes of supersymmetric SO(10) unification

We carry out an analysis of the non-universal supersymmetry breaking scalar masses arising in SO(10) supersymmetric unification. By considering patterns of squark and slepton masses, we derive a set of sum rules for the sfermion masses which are independent of the manner in which SO(10) breaks to the Standard Model gauge group via its SU(5) subgroups. The phenomenology arising from such non-universality is unaffected by the symmetry breaking pattern, so long as the breaking occurs via any of the SU(5) subgroups of the SO(10) group.Comment: 15 pages using RevTe