Bjorken Sum Research Articles

New COMPASS results on [formula omitted] and [formula omitted] and QCD fit

During its 2011 data taking campaign, the COMPASS experiment at CERN has collected data of 200 GeV polarised muons scattering off a target with polarised protons. These data allow the extension of the phase-space coverage of the COMPASS data obtained in 2007 with a beam of 160 GeV polarised muons, namely to access lower values of x for any given value of Q2.The data in the DIS region were used to extract the longitudinal double spin asymmetry A1p and the spin dependent structure function g1p. Thereafter, our world data NLO QCD fits of polarised parton distributions were updated. It was also possible to improve our test on the Bjorken sum rule.The asymmetries A1p and the structure function g1p were likewise extracted from the two beam energy data sets for Q2<1(GeV/c)2, thus complementing our extraction of similar quantities in the non-perturbative region for the deuteron.

Flux tube zero-point motion, hadronic charge radii, and hybrid meson production cross sections

Flux tube zero-point motion produces quark displacements transverse to the flux tube which make significant contributions to hadronic charge radii. In heavy quark systems, these contributions can be related by Bjorken's sum rule to the rates for semileptonic decay to hybrid mesons. This connection can be generalized to other leptoproduction processes, where transverse contributions to elastic form factor slopes are related to the cross sections for the production of the associated hybrid states. I identify the flux tube overlap integral responsible for these effects as the strong QCD analogue of the Sudakov form factor of perturbative QCD.

Nonresonant semileptonic heavy quark decay

In both the large N_c limit and the valence quark model, semileptonic decays are dominated by resonant final states. Using Bjorken's sum rule in an "unquenched" version of the quark model, I demonstrate that in the heavy quark limit nonresonant final states should also be produced at a significant rate. By calculating the individual strengths of a large number of exclusive two-body nonresonant channels, I show that the total rate for such processes is highly fragmented. I also describe some very substantial duality-violating suppression factors which reduce the inclusive nonresonant rate to a few percent of the total semileptonic rate for the finite quark masses of B decay, and comment on the importance of nonresonant decays as testing grounds for very basic ideas on the structure, strength, and significance of the quark-antiquark sea and on quark-hadron duality in QCD.

Quantitative predictions forBsemileptonic decays intoD,D*,and the orbitally excitedD**in quark models in the manner of Bakamjian and Thomas

Once chosen the dynamics in one frame, the rest frame in this paper, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the infinite quark mass limit, fully covariant current form factors as matrix elements of the quark current operator. In this paper we use the rest frame dynamics fitted from the meson spectrum by various authors, already shown to provide a reasonable value for $\rho^2$. From the general formulae for the scaling invariant form factors $\xi^{(n)}(w)$, $\tau_{1/2}^{(n)}(w)$ and $\tau_{3/2}^{(n)}(w)$, we predict quantitavely the $B$ semileptonic branching ratios to the ground state and orbitally excited charmed mesons $D, D^\ast$ and $D^{\ast\ast}$. We check Bjorken's sum rule and discuss the respective contributions to it. We find $\xi(w)\simeq (2/(1+w)) ^2$, resulting from the fact that the ground state wave function is Coulomb-like. We also find $\tau_{3/2}\simeq 0.5 (2/(1+w))^3$ and $\tau_{1/2}(w)\ll \tau_{3/2}(w)$. Very small branching ratios into $j=1/2$ orbitally excited $D$'s results. The overall agreement with experiment is rather good within the present accuracy which is poor for the orbitally excited charmed mesons. We predict a ratio $Br(B\to D^\ast_2 l \nu)/Br(B\to D_1 l \nu)=1.55\pm 0.15$ as a mere consequence of the heavy quark symmetry. If some faint experimental indications that $Br(B\to D_1 l \nu)\simeq Br(B\to D^\ast_2 l \nu)$ were confirmed, it would indicate a sizeable $O(1/m_c)$ correction.

Fixing the renormalization scheme in NNLO perturbative QCD using conformal limit arguments.

We discuss how the renormalization scheme ambiguities in QCD can be fixed, when two observables are related, by requiring the coefficients in the perturbative expansion relating the two observables to have their conformal limit values, i.e., to be independent of the $\ensuremath{\beta}$ function of the renormalized coupling. We show how the next-to-leading order BLM automatic scale-fixing method can be extended to next-to-next-to-leading order to fix both the renormalization scale and ${\ensuremath{\beta}}_{2}$ in a unique way. As an example we apply the method to the relation between Bjorken's sum rule and ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ and compare with experimental data as well as other scheme-fixing methods.