The Isgur-Wise function in a relativistic model for qQˉq\bar Q system

We use the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz scalar) linear '' potential to estimate the light quark wavefunction for $q\bar Q$ mesons in the limit $m_Q\to \infty$. We use these wavefunctions to calculate the Isgur-Wise function $\xi (v.v^\prime )$ for orbital and radial ground states in the phenomenologically interesting range $1\leq v.v^ \prime \leq 4$. We find a simple expression for the zero-recoil slope, $\xi^ \prime (1) =-1/2- \epsilon^2 /3$, where $\epsilon$ is the energy eigenvalue of the light quark, which can be identified with the $\bar\Lambda$ parameter of the Heavy Quark Effective Theory. This result implies an upper bound of $-1/2$ for the slope $\xi^\prime (1)$. Also, because for a very light quark $q (q=u, d)$ the size $\sqrt {}$ of the meson is determined mainly by the ``confining'' term in the potential $(\gamma_\circ \sigma r)$, the shape of $\xi_{u,d}(v.v^\prime )$ is seen to be mostly sensitive to the dimensionless ratio $\bar \Lambda_{u,d}^2/\sigma$. We present results for the ranges of parameters $150 MeV <\bar \Lambda_{u,d} <600 MeV$ $(\bar\Lambda_s \approx \bar\Lambda_{u,d}+100 MeV)$, $0.14 {GeV}^2 \leq \sigma \leq 0.25 {GeV}^2$ and light quark masses $m_u, m_d \approx 0, m_s=175 MeV$ and compare to existing experimental data and other theoretical estimates. Fits to the data give: ${\bar\Lambda_{u,d}}^2/\sigma =4.8\pm 1.7$, $-\xi^\prime_{u,d}(1)=2.4\pm 0.7$ and $\vert V_{cb} \vert \sqrt {\frac {\tau_B}{1.48 ps}}=0.050\pm 0.008$ [ARGUS '93]; ${\bar\Lambda_{u,d}}^2/\sigma = 3.4\pm 1.8$, $-\xi^\prime_{u,d}(1)=1.8\pm 0.7$ and $\vert V_{cb} \vert \sqrt { \frac {\tau_B}{1.48 ps}}=0.043\pm 0.008$ [CLEO '93]; ${\bar\Lambda_{u,d}}^2/Comment: 22 pages, Latex, 4 figures (not included) available by fax or via email upon reques

Neutron structure function and inclusive DIS from H-3 and He-3 at large Bjorken-x

A detailed study of inclusive deep inelastic scattering (DIS) from mirror A = 3 nuclei at large values of the Bjorken variable x is presented. The main purpose is to estimate the theoretical uncertainties on the extraction of the neutron DIS structure function from such nuclear measurements. On one hand, within models in which no modification of the bound nucleon structure functions is taken into account, we have investigated the possible uncertainties arising from: i) charge symmetry breaking terms in the nucleon-nucleon interaction, ii) finite Q**2 effects neglected in the Bjorken limit, iii) the role of different prescriptions for the nucleon Spectral Function normalization providing baryon number conservation, and iv) the differences between the virtual nucleon and light cone formalisms. Although these effects have been not yet considered in existing analyses, our conclusion is that all these effects cancel at the level of ~ 1% for x < 0.75 in overall agreement with previous findings. On the other hand we have considered several models in which the modification of the bound nucleon structure functions is accounted for to describe the EMC effect in DIS scattering from nuclei. It turns out that within these models the cancellation of nuclear effects is expected to occur only at a level of ~ 3%, leading to an accuracy of ~ 12 % in the extraction of the neutron to proton structure function ratio at x ~ 0.7 -0.8$. Another consequence of considering a broad range of models of the EMC effect is that the previously suggested iteration procedure does not improve the accuracy of the extraction of the neutron to proton structure function ratio.Comment: revised version to appear in Phys. Rev. C; main modifications in Section 4; no change in the conclusion