There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Theory and phenomenology of two-Higgs-doublet models

We review the present status of QCD corrections to weak decays beyond the leading-logarithmic approximation, including particle-antiparticle mixing and rare and $\mathrm{CP}$-violating decays. After presenting the basic formalism for these calculations we discuss in detail the effective Hamiltonians of all decays for which the next-to-leading-order corrections are known. Subsequently, we present the phenomenological implications of these calculations. The values of various parameters are updated, in particular the mass of the newly discovered top quark. One of the central issues in this review are the theoretical uncertainties related to renormalization-scale ambiguities, which are substantially reduced by including next-to-leading-order corrections. The impact of this theoretical improvement on the determination of the Cabibbo-Kobayashi-Maskawa matrix is then illustrated. [S0034-6861(96)00304-2]

Weak decays beyond leading logarithms

Annals of physics

Theories with Gauge-Mediated Supersymmetry Breaking

We examine the predictions of the conventional SU(2${)}_{\mathit{L}}$\ensuremath{\bigotimes}SU(2${)}_{\mathit{R}}$\ensuremath{\bigotimes}U(1${)}_{\mathit{B}\mathrm{\ensuremath{-}}\mathit{L}}$ left-right-symmetric model in the case where the minimal Higgs sector (containing one bidoublet, one L-triplet, and one R-triplet Higgs field) and the standard lepton representations (incorporating right-handed partners for the observed neutrinos) are adopted. We show that a complete analysis of spontaneous symmetry breaking for the Higgs sector leads to a highly restrictive range of possibilities for global minima that are simultaneously consistent with all experimental observations (such as lepton masses, ${\mathit{K}}_{\mathit{L}}$-${\mathit{K}}_{\mathit{S}}$ mixing, etc.). As a result, the possible phenomenologies for the gauge and Higgs bosons of the model are very limited. For instance, we demonstrate that in the absence of explicit CP violation in the Higgs potential, spontaneous CP violation does not arise and the fermion couplings exhibit ``manifest'' left-right symmetry. Further, we find no entirely natural solutions other than ones in which all of the extra (non-standard-model) gauge and Higgs bosons associated with the left-right-symmetric extension are extremely heavy (typically, more massive than ${10}^{7}$ GeV). Only by ``fine-tuning'' certain parameters of the Higgs potential is it possible to bring these extra particles down to an observable mass scale. Alternatively, symmetries can be introduced to eliminate the terms in the Higgs potential associated with these parameters, but only at the sacrifice of introducing undesirable consequences for fermion masses. Many of the pitfalls and problems are illustrated using a simplified model. Overall, we emphasize the necessity of performing a complete minimization of the Higgs sector before extracting phenomenology.

Left-right-symmetric electroweak models with triplet Higgs field

Prediction of B-->K gamma as a test of the standard model.

We consider background to the rare decay modes b\ensuremath{\rightarrow}${\mathrm{sl}}^{+}$${l}^{\mathrm{\ensuremath{-}}}$, B\ensuremath{\rightarrow}${K}^{\mathrm{*}}$${l}^{+}$${l}^{\mathrm{\ensuremath{-}}}$, and B\ensuremath{\rightarrow}${\mathrm{Kl}}^{+}$${l}^{\mathrm{\ensuremath{-}}}$ arising from the process b\ensuremath{\rightarrow}${\mathrm{sV}}_{i}$ followed by on- and off-resonance transition ${V}_{i}$\ensuremath{\rightarrow}${l}^{+}$${l}^{\mathrm{\ensuremath{-}}}$. We obtain dilepton mass spectrum including short-distance effects and then suggest cuts to enhance the signal over background.

Resonance background to the decays b-->sl+l-, B-->Kl+l-, and B-->Kl+l-

On noncommutative spacetime, the Standard Model allows new, usually Standard Model forbidden, triple gauge boson interactions. In this letter we propose the Standard Model strictly forbidden Z -> gamma gamma and Z -> gg decay modes coming from the gauge sector of the Noncommutative Standard Model as a place where noncommutativity could be experimentally discovered.

The Z -> gamma gamma, gg Decays in the Noncommutative Standard Model

On non-commutative spacetime, the standard model (SM) allows new, usually SM forbidden, triple gauge boson interactions to occur. In this letter we propose the SM strictly forbidden $Z\rightarrow \gamma\gamma$
 and $Z\rightarrow gg$
 decay modes coming from the gauge sector of the non-commutative standard model (NCSM) as a place where non-commutativity could be experimentally discovered.

N. G. Deshpande

Papers

Left-right-symmetric electroweak models with triplet Higgs field

Prediction of B-->K gamma as a test of the standard model.

Resonance background to the decays b-->sl+l-, B-->Kl+l-, and B-->Kl+l-

The Z -> gamma gamma, gg Decays in the Noncommutative Standard Model

The $Z \rightarrow \gamma \gamma,\;gg$ decays in the non-commutative standard model