Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Fluctuation study of pionisation in ultrarelativistic nucleus-nucleus interaction

The scaled factorial moments and the multifractal moments have been investigated in differentη-intervals to study the dynamical fluctuation of pions produced in 200 AGeV³²S-Ag/Br interaction. In order to investigate the detail characteristics of intermittency behaviour, theF-moments are extracted up to the eighth order of moments in differentM-intervals. The analysis indicates a non-thermal phase transition and different regime of particle production during the hadronisation process.     

Structure–activity studies on the fungitoxicity of some triorganotin(IV) compounds

Seventeen triorganotin(IV) compounds, with the general formula R₃SnX, containing symmetrical and unsymmetrical combinations of alkyl and aryl groups on tin and with a wide variation in the non-carbon-bonded anionic (X) residues, were examined along with three formally pentacoordinated adducts of triaryltin chlorides with triphenylphosphine oxide for their antifungal activity against nine plant pathogenic and saprophytic fungi. The in vitro tests included inhibitory studies on radial growth, mycelial growth, spore germination, and germ tube elongation. A significant finding was the dependence of fungitoxicity on the nature of the X group in both the tributyltin and triaryltin series, in contrast to earlier published reports on the negligible influence of the X groups on overall toxicity relative to the R group. This suggests that the X group is significantly involved in transporting the biocide to the reactive sites, and that the X group which tends to confer increased solubility to the triorganotin compound gives rise to increased activity. In studies of R group variations, tri-iso-butyltin bromide was found to be much less fungitoxic than tri-n-butyltin compounds, a result which is reconcilable in terms of increased steric encumbrance at the tin site in the former case. The steric factor is also implicated in the reduced activities observed for tris(p-tolyl)tin and tris(p-chlorophenyl)tin compounds relative to (Ph₃SnX) towards most of the fungi screened in this study. In general, it was also noted that the triaryltins were more selective in their antifungal action than the trialkyltins, which exhibited broad spectral activity when applied at the concentration level of 10 μg cm^?3.     

Bounds on the inverses of nonnegative triangular matrices with monotonicity properties

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.     

4f-electric quadrupolar anomalies in PrCu2Si2 and its pseudoternary solid solutions

Experimental observations for possible presence of 4f quadrupolar Kondo effect in PrCu₂Si₂ are critically discussed. A comparison of the low temperature properties of the alloys, Pr _x Y_1–x Cu₂Si₂ (x=0.05, 0.2 and 0.4), seems to signal the existence of 4f electric quadrupolar glass phenomenon around 4K forx=0.2.     

A shape-optimization technique for the capillary surface problem

Summary The problem of the construction of an equilibrium surface taking the surface tension into account leads to Laplace-Young equation which is a nonlinear elliptic free-boundary problem. In contrast to Orr et al. where an iterative technique is used for direct solution of the equation for problems with simple geometry, we propose here an alternative approach based on shape optimization techniques. The shape of the domain of the liquid is varied to attain the optimality condition. Using optimal control theory to derive expressions for the gradient, a numerical scheme is proposed and simple model problems are solved to validate the scheme.     

Relativistic bilocal lattice meson fields,divergence-free Green's functions and parton confinement

A bilocal lattice meson field equation which is invariant underP ₄×SO ₂×SO ₂×SO ₂×SO ₂, is investigated. A class of general solutions in terms of the Laguerre polynomials (products of 2-dimensional hydrogen atom wave-functions) is presented. The “atomic” wave-functions in “momentum”-space indicate that two particles (patrons) are in bound orconfined state and moving along elliptical orbits in “momentum”-space. Four Green's functions for the (bilocal lattice scalar) partialdifference equation are obtained. Theconvergence of one Green's function is rigorously proved and the convergence of others are conjectured.