arXiv subjects
Publications and source records attributed to Rahul Basu.
In this talk I review the low x QCD experimental results from HERA and their theoretical underpinnings. In particular, I discuss the structure function $F_2$, large rapidity gap events, pomeron structure functions and $J/ψ$ production.
In this paper we check the validity of the ideas of double scaling as given by Ball and Forte in a semi inclusive process like $J/ψ$ production at HERA, in different kinematical regions, for low values of the Bjorken variable $x$. In particular, we study $J/ψ$ production in the inelastic and diffractive (elastic) regimes using the double scaling form of the gluon distribution functions. We compare these predictions with data (wherever available) and with other standard parameterisations. We find that double scaling holds in the inelastic regime over a larger kinematic region than that given by the analysis of the proton structure function $F_2^p$. However, in the diffractive region, double scaling seems to suggest an admixture of hard pomeron boundary conditions for the gluon distribution, while predicting a steeper rise in the cross section than that suggested by present data.
In the kinematic region of small $x$ and large $Q^2$ in deep inelastic scattering, presently being explored by HERA, we present an analysis of the evolution of the longitudinal structure function $F_L^{p}(x, Q^2)$ in the double scaling limit of Ball and Forte. We fit the evolution to a $1/x^λ$ behaviour and extract the value of $λ$. We also study the behaviour of $R=F_2/2xF_1 -1$. We present comparisons of both $F_L$ and $R$ with the corresponding MRS fits in this region of $x$ and $Q^2$.
We propose a mechanism for instanton induced chiral symmetry breaking in QCD with fundamental scalars. The model Lagragian that we use has the same symmetry properties as QCD. The scalar fields develop vacuum expectation values at a non-trivial minimum and generate masses for thhe light quarks. The minimization condition is also used to break the $SU(N_f)$ flavour symmetry in order to make the $s$ quark heavier than the two lighter ones. Thus a vacuum of the theory that is not chirally invariant is obtained.
One of the most debated issues related to high-$T_c$ superconductivity is the symmetry of the Cooper pair or the gap function. In this report, we present numerical results regarding the gap function in strongly correlated electron systems using $t-J$ and Hubbard models in one and two dimensions. To this end, we use exact diagonalization to study the ground states of 8- and 16-site clusters consisting of single or coupled layers. We calculate a reduced two-particle density matrix in momentum space which is a measure of the gap function. We then analyze the eigenvectors of this density matrix, which display the possible Cooper pair symmetries. The eigenvector corresponding to the largest eigenvalue indicates a vanishing gap on the Fermi surface (which is in favour of odd-gap pairing) although $d_{x^2-y^2}$ symmetry is seen to be a very close contestant in many of the cases.
Electron correlation in cuprates leads to a global constraint $\sum_{\bf k} Δ_{\bf k} = 0$ on the gap function $Δ_{\bf k}$ resulting in a gap nodal surface. We give physical arguments supported by numerical results and discuss some experimental results to argue that correlations also lead to a local constraint on charge fluctuations in ${\bf k}$-space close to the Fermi surface, which may result in a substantial overlap of the Fermi surface with the gap nodal surface.
We present physical arguments as well as numerical evidence to show that the Cooper pair (gap) function vanishes on the Fermi surface in strongly correlated electron systems such as \tJ and \lU Hubbard models in one and two dimensions. Using exact diagonalization, we study a correlation function which is a measure of the gap function even in a finite system, and present numerical results for this correlation function on small clusters of 8 (Hubbard) and 16 ($t-J$) sites.
A chromoelectric vacuum that confines both gluon and quark degrees of freedom (in the sense that they do not exist as asymptotic states) is constructed. However some degrees of freedom still exist as asymptotic states thereby allowing colour singlets to propagate.