A technique recently developed for inelastic electron proton scattering is applied for inelastic electron pion scattering. It is found that all the derivatives of off-shell form factor of pion nears=m_π² and for largeQ² are bounded from above, provided that the dispersion relation for the form factor requires no more than one subtraction. The elastic pion form factor is bounded by [lnQ²]^c/Q², wherec is any positive constant.

Using unitarity, analyticity and the hypothesis of Bjorken scaling inequalities have been derived for the upper bounds on the wave function renormalization constant of pion.

Ifμ-e universality is assumed, there are 17 neutral-current parameters of current experimental interest, including the parity-violating nuclear force sector. We deduce the general relations among these parameters implied by gauge models. In single-Z boson models, there are 10 relations, while two-boson models lead to 4 relations. Ifμ-e universality is abandoned, the number of parameters increases to 31, while the number of relations becomes 21 in single-boson models and 12 in two-boson models. We derive all these relations.

Using recent data on pion structure function and a rigorous inequality obtained recently using unitarity analyticity and Bjorken scaling a numerical upper bound on the wave-function-renormalisation constant of pion is computed. By the (somewhat drastic) act of neglecting the sea, it is shown that the bare part of the pion can be no more than 38%.

A phenomenological representation for differential cross-section recently proposed using Mandelstam analyticity and convergent polynomial expansion (CPE) which has been found to be successful in describing scaling of the differential cross-section-ratio data for several elastic diffractive and inelastic nondiffractive processes is used to analyse the energy dependence of the slope-parameter data at high energies, extrapolate the slope parameter and predict the differential cross-section ratio as a function of |t| at higher energies forπ^±pndK⁺p scattering. Following the method of Hansen and Krisch it is found that, in spite of the existence of rather widely varying data points for nearbys values, a more systematic trend in the energy dependence of the slope parameter emerges when a statistical average of the existing high-energy data is used. Extrapolating the fits to the average data ontos → ∞ provides strong evidence in favour of a model-independent result that asymptotically theπ^±p slopes may be equal. There is also a strong indication to the effect that each of these two slopes may be equal to theK⁺p slope fors → ∞. Using the scaling curves generated by the existing data on differential cross-section ratio and extrapolated values of the slope parameter, the differential cross-section ratio for each of the three processes is predicted as a function of |t| for higher energies.

Existing data on the differential cross-section ratio at high energies for pp,$$\bar p$$p, π^±p andK^±p scatering have been fitted by the proposed convergent polynomial expansion to determine the unknown coefficients in the scaling function. It is found that the data are very well represented within and somewhat outside the peak regions by only four or five terms in the proposed series in terms of Laguerre polynomials.

Using suitable factorisation relations and factorisation dependent neutralcurrent parameters of Hung and Sakurai, the neutral current contributions to the parity violating parameters in nuclear force are estimated. Using Cabbibo rotation and Fierz transformation, the charge current contribution is added. It is found that three out of four parity violating parameters can be calculated with respect to their signs and magnitudes. The range of values of the other parameter appears to be small.

Without assuming any symmetry amongμ, e andτ leptons, we consider several neutral current processes involving 73 physical parameters and deduce general relations among them implied by different classes of gauge models with one, two and three neutralZ bosons. In the single-Z boson model there are 60 general relations while the two (three)-boson model leads to 48 (36) relations. If onlyμ-e universality is imposed, the physical parameters reduce to 41 and the single (two)-Z boson model yields 31 (22) relations, while only 13 relations exist for the threeZ boson model. Imposingμ-e-τ universality decreases the number of physical parameters to 18, while the number of relations in the single- and two-Z boson models reduces to 11 and 5, respectively. In these relations are contained those obtained by Hung and Sakurai and Parida and Rajasekaran in the corresponding cases. In addition we obtain some new inequalities among the observable parameters which are to be satisfied by all gauge models.

A modifiedN/D method is applied for the cases of³He charge and magnetic form factors. Anomalous cut positions are computed using possible exchanges at the photon-³He electromagnetic vertex. and one of them is found att_a=0.0618 GeV². TheD-function is used to parametrize the two-pion cut while theN-function is taken to represent the effect of an anomalous or the three-pion cut. Excellent fits to the available experimental data on charge and magnetic form factors are obtained and several useful information on the form factors computed.

Using fits to the available data on the pion and deuteron electromagnetic form factors and the Chou-Yang model, the computed values of differential cross-sections for high-energy pion-deuteron elastic scattering agree reasonably well with the available experimental data. Whereas only a shoulder is expected to appear up to energies of several hundreds of GeV, a dip and a secondary maximum are predicted to be conspicuous only forP_lab≫400 GeV/C. The position of the dip starts at a much lower value, |t_d| ≅ 0.5–0.6 GeV², as compared to the corresponding position in thepp scattering. The positions of the first dip are plotted against total cross-section which can be verified by future high-energy experiments. Limitations of the model predictions for ultrahigh energies are pointed out.

We review general results on threshold effects and their implications on GUTs in the context of LEP data. Among the blooming grand-desert models, threshold effects are computed in the presence of a single real scalar ζ (3, 0, 8) with M_ζ≃10¹⁰ GeV leading to experimentally testable predictions on the proton lifetimeτ_p in SU (5) and, in addition, small neutrino masses in SO (10) needed for the solar neutrino flux and the dark matter of the universe. The fine structure constant matching at M_Z is ensured by including threshold effects on the unification coupling. In the minimal SUSY SU (5) such effects at the GUT scale modify the prediction of the supersymmetric mass threshold near the TeV scale and the precision measurments of the Standard Model couplings at M_Z probe into the superheavy mass spectrum. Consequences of theorems proved very useful for threshold, compactification and multiloop effects are discussed. It is noted that in a class of GUTs the highest intermediate scale M_I above which G_224P becomes a good symmetry is not affected by the GUT threshold or compactification effects or multiloop contributions in the range M_I-M_U. But spontaneous compatification effects can decrease the intermediate scale drastically in models where parity and SU(2)_R breakings are decoupled. Low mass W_R-bsosns are permitted in models with decoupled parity and SU (2)_R breakings.

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.