An inverse problem for the wave equation with source and receiver at distinct points

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results

Reconciling GA/GV,<rn2>G_A/G_V, <r_n^2> and μp,n\mu_{p,n} in Chiral Quark Model with one Gluon Generated Configuration Mixing

The spin polarization functions $(\Delta u, ~\Delta d, ~\Delta s)$ for proton are calculated in the chiral quark model ($\chi$QM) with SU(3) symmetry breaking as well as configuration mixing generated by one gluon exchange forces for the NMC and the most recent E866 data. Besides reproducing the spin polarization functions $\Delta u,\Delta d, \Delta s$ as well as $G_A/G_V$, it can accomodate nucleon magnetic moments and neutron charge radius as well, thus resolving the compatibility problem of these parameters which could not be achieved in constituent quark models.Comment: 10 latex pages with 2 tables, revised in the light of latest dat

Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\sqrt{\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotropic wave equation perturbed by a divergence with respect to $x$ of a vector whose components are quadratics with respect to $\nabla_x u(t,x)$ by ignoring the terms with smallness $O(|\nabla_x u(t,x)|^3)$. We will show that we can uniquely determine $\gamma(x)$ and the coefficients of these quadratics by many boundary measurements at the boundary of the spacial domain over finite time interval. More precisely the boundary measurements are given as the so-called the hyperbolic Dirichlet to Neumann map

Strangeness Content of the Nucleon in the \chiCQM_{config}

Several parameters characterizing the strangeness content of the nucleon have been calculated in the chiral constituent quark model with configuration mixing (\chiCQM_{config}) which is known to provide a satisfactory explanation of the ``proton spin problem'' and related issues. In particular, we have calculated the strange spin polarization \Delta s, the strangeness contribution to the weak axial vector couplings \Delta_8 etc., strangeness contribution to the magnetic moments \mu(p)^s etc., the strange quark flavor fraction f_s, the strangeness dependent quark ratios \frac{2 \bar s}{u+d} and \frac{2 \bar s}{\bar u+\bar d} etc.. Our results show in general excellent agreement with the recent experimental observations.Comment: 14 pages, 3 table

What is inside the nucleon?

We briefly review the structure of nucleon in the context of QCD, Constituent Quark Model and Chiral Quark Model.Comment: LateX, 23 pages, 3 figures and 5 Table

Implications of Configuration Mixing in The Chiral Quark Model With SU(3) and Axial U(1) Breakings for Nucleon Spin-Flavor Structure

The implications of Chiral Quark Model with SU(3) and axial U(1) symmetry breakings as well as configuration mixing generated by one gluon exchange forces ($\chi$QM$_{gcm}$) are discussed in context of proton flavor and spin structure as well as hyperon $\beta$-decay data. Apart from reproducing the success of $\chi$QM with symmetry breaking, it is able to improve upon the agreement with data in several cases such as, $G_A/G_V, \Delta_8,$ dependent on spin polarization functions and ($\frac{2 \bar s}{u+d}$), ($\frac{2 \bar s}{\bar u+\bar d}$) and f_s involving the quark distribution functions.Comment: 11 pages and 3 table

Constructing "Reference" Triangle through Unitarity of CKM Matrix

Motivated by the possibility of the low value of sin2\beta in the measurements of BABAR and BELLE collaborations, a reference unitarity triangle is constructed using the unitarity of the CKM matrix and the experimental values of the well known CKM elements, without involving any inputs from the processes which might include the new physics effects. The angles of the triangle are evaluated by finding the CP violating phase \delta through the Jarlskog's rephasing invariant parameter J. The present data and the unitarity of the CKM matrix gives for \delta the range 28^o to 152^o, which for sin2\beta translates to the range 0.21 to 0.88. This range is broadly in agreement with the recent BABAR and BELLE results. However, a value of sin2\beta \leq 0.2, advocated by Silva and Wolfenstein as a benchmark for new physics, would imply a violation in the three generation unitarity and would hint towards the existence of a fourth generation Further, the future refinements in the CKM elements will push the lower limit on sin2\beta still higher.Comment: Latex, 10 pages, 1 eps figur

Octet magnetic moments and the violation of CGSR in χ\chiQM with configuration mixing

Octet baryon magnetic moments are calculated within \chiQM, respecting color spin spin forces (Szczepaniak et al., PRL 87, 072001(2001)), incorporating the orbital angular momentum as well as the quark sea contribution through the Cheng and Li mechanism (PRL 80, 2789(1998)). Using configuration mixing generated by color spin spin forces as well as the concept of ``effective'' quark mass to include the effects of confinement, we are able to get an excellent fit to the octet magnetic moments as well as the violation of Coleman Glashow Sum Rule (CGSR) without any further input except for the ones already used in \chiQM as well as in NRQM. Specifically, in the case of p, \Sigma^+, \Xi^o, and violation of CGSR we get a perfect fit whereas in almost all the other cases the results are within 5% of the data.Comment: 5 pages, 1 Table, RevTe

Strangeness in the Nucleon

There are several different experimental indications, such as the strangeness contribution to the magnetic moment of the proton, sigma_{\pi N} term, strange spin polarization, ratio of strange and non strange quark flavor distributions which suggest that the nucleon contains a hidden strangeness component which is contradictory to the naive constituent quark model. Chiral constituent quark model with configuration mixing (\chiCQM_{{\rm config}}) is known to provide a satisfactory explanation of the ``proton spin problem'' and related issues. In the present work, we have extended the model to carry out the calculations for the parameters pertaining to the strange quark content of the nucleon, for example, the strange spin polarization \Delta s, strange components of the weak axial vector form factors \Delta \Sigma and \Delta_8 as well as F and D, strangeness magnetic moment of the proton \mu_p^s, the strange quark content in the nucleon f_s coming from the \sigma_{\pi N} term, the ratios between strange and non-strange quarks \frac{2 s}{u+d} and \frac{2 s}{\bar u+ \bar d}, contribution of strangeness to angular momentum sum rule etc.. Our result demonstrates the broad consistency with the experimental observations as well as other theoretical considerations.Comment: 4 pages, To appear in the Proceedings of International Workshop on Theoretical High Energy Physics, 15-20 March 2007, Roorkee, Indi

Flavor mixings and textures of the fermion mass matrices

A comprehensive review of several aspects of fermion mixing phenomenon and texture specific mass matrices have been presented. Regarding fermion mixings, implications of unitarity and certain new developments for the CKM paradigm have been discussed. In the leptonic sector, the question of possibility of CP violation has been discussed in detail from the unitarity triangle perspective. In the case of texture specific mass matrices, the issues of viability of Fritzsch-like as well as non Fritzsch-like mass matrices have been detailed for both the quark and leptonic sectors. The relationship of textures, naturalness and weak basis rotations has also been looked into. The issue of the compatibility of texture specific mass matrices with the SO(10) based GUT mass matrices has also been discussed.Comment: 100 pages, 19 figure