arXiv subjects
Publications and source records attributed to Elliot Leader.
We show that the recent claim that the expression 1/2 \int x dx [ H_q (x,0,0) + E_q(x,0,0)], involving the generalized parton distributions H and E, measures the transverse angular momentum of quarks in a transversely polarized nucleon, is incorrect.
Lin and Liu evaluate the nucleon expectation value of the non gauge-invariant canonical quark momentum operator on a lattice, and obtain zero. They conclude that my argument that, despite the non gauge-invariance of the operator, its physical matrix elements \emph{are} gauge-invariant, cannot be correct. I show that their result has no bearing on the question of gauge-invariance, and also point to an amusing lattice paradox.
I derive a rigorous relation between the expectation value of the transverse component of the angular momentum of a quark in a transversely polarized nucleon in terms of the Generalized Parton Distributions H and E, namely = 1/2M [P_0 \int dx x E_q(x,0,0) + M \int dx x H_q(x,0,0)] where P_0 is the energy of the nucleon and where "quark" implies the sum of quark and antiquark of a given flavor. A similar relation holds for gluons. The result is remarkably similar to Ji's relation for the case of longitudinal polarization. In this revised version, I have rectified some misleading statements, introduced a more precise notation and specified mpre clearly the meaning of the terms in both the Ji and the new tranverse relation.
The strange quark polarization puzzle, i.e. the contradiction between the negative polarized strange quark density obtained from analyses of inclusive DIS data and the positive values obtained from combined analyses of inclusive and semi-inclusive SIDIS data using de Florian et. al. (DSS) fragmentation functions, is discussed. To this end the results of a new combined NLO QCD analysis of the polarized inclusive and semi-inclusive DIS data, using the Hirai et. al. (HKNS) fragmentation functions, are presented. It is demonstrated that the polarized strange quark density is very sensitive to the kaon fragmentation functions, and if the set of HKNS fragmentation functions is used, the polarized strange quark density obtained from the combined analysis turns out to be negative and well consistent with values obtained from the pure DIS analyses.
A major controversy has arisen in QCD as to how to split the total angular momentum into separate quark and gluon contributions, and as to whether the gluon angular momentum can itself be split, in a gauge invariant way, into a spin and orbital part. Several authors have proposed various answers to these questions and offered a variety of different expressions for the relevant operators. I argue that none of these is acceptable and suggest that the canonical expression for the momentum and angular momentum operators is the correct and physically meaningful one. It is then an inescapable fact that the gluon angular momentum operator cannot, in general, be split in a gauge invariant way into a spin and orbital part. However, the projection of the gluon spin onto its direction of motion i.e. its helicity is gauge invariant and is measured in deep inelastic scattering on nucleons. The Ji sum rule, relating the quark angular momentum to generalized parton distributions, though not based on the canonical operators, is shown to be correct, if interpreted with due care. I also draw attention to several interesting aspects of QED and QCD, which, to the best of my knowledge, are not commented upon in the standard textbooks on Field Theory.
We compare and contrast the implications of gauge invariance for the structure of scattering amplitudes in QED and QCD. We derive the most general analogue for QCD of the famous QED rule that the scattering amplitude must be invariant if the polarization vectors $ε^{μ_j}(k_j)$ of any number of photons undergo the replacement $ ε^{μ_j}(k_j) \rightarrow ε^{μ_j}(k_j) + c \, k_j^{μ_j} $, where $c$ is an arbitrary constant.
A new combined NLO QCD analysis of the polarized inclusive and semi-inclusive DIS data is presented. In contrast to previous combined analyses, the 1/Q^2 terms (kinematic - target mass corrections, and dynamic - higher twist corrections) in the expression for the nucleon spin structure function g1 are taken into account. The new COMPASS data are included in the analysis. The impact of the semi-inclusive (SIDIS) data on the polarized parton densities (PDFs) and on the higher twist corrections is demonstrated. The controversial behavior of the polarized strange quark density obtained from the fit to the DIS data alone, and a combined analysis of DIS and SIDIS data is discussed.
A new combined next to leading order QCD analysis of the polarized inclusive and semi-inclusive deep inelastic lepton-hadron scattering (DIS) data is presented. In contrast to previous combined analyses, the $1/Q^2$ terms (kinematic - target mass corrections, and dynamic - higher twist corrections) in the expression for the nucleon spin structure function $g_1$ are taken into account. The new COMPASS data are included in the analysis. The impact of the semi-inclusive data on the polarized parton densities (PDFs) and on the higher twist corrections is discussed. The new results for the PDFs are compared to our (Leader, Sidorov, Stamenov) LSS'06 PDFs, obtained from the fit to the inclusive DIS data alone, and to those obtained from the de Florian, Sassot, Stratmann, and Vogelsang global analysis.
In a recent analysis of the world data on polarized DIS, Blumlein and Bottcher conclude that there is no evidence for higher twist contributions, in contrast to the claim of the LSS group, who find evidence for significant higher twist effects. We explain the origin of the apparent contradiction between these results.
We show that the difference cross sections in unpolarized SIDIS e+N\to e+h+X and pp hadron production p+p\to h+X determine, uniquely and in any order in QCD, the two FFs: D_u^{h-\bar h} and D_d^{h-\bar h}, h=π^\pm, K^\pm. If both K^\pm and K_s^0 are measured, then e+e-\to K+X, e+N\to e+K+X and p+p\to K+X yield independent measurements of (D_u-D_d)^{K^+ +K^-}. In a combined fit to K^\pm and K^0_s production data from e+e- collisions, (D_u-D_d)^{K^++K^-} is obtained and compared to conventional parametrizations.
The results on polarized parton densities (PDFs) obtained using different methods of QCD analysis of the present polarized DIS data are discussed. Their dependence on the method used in the analysis, accounting or not for the kinematic and dynamic 1/Q^2 corrections to spin structure function g_1, is demonstrated. It is pointed out that the precise data in the preasymptotic region require a more careful matching of the QCD predictions to the data in this region in order to determine the polarized PDFs correctly.
The present status of the longitudinal polarized parton densities (PDFs) and the contribution of their first moments to the nucleon spin is discussed. Special attention is paid to the role of higher twist effects in determining the PDFs and to the polarized strange quark and gluon densities, which are still not well determined from the present data.
We show that the difference cross sections in unpolarized SIDIS e+N\to e+h+X and pp hadron production p+p\to h+X determine independently in a model independent way, in any order in QCD, the two FFs: D_u^{h-\bar h} and D_d^{h-\bar h}, h=π^\pm, K^\pm or a sum over charged hadrons. If both K^\pm and K_s^0 are measured, then e+e-\toK+X, e+N\to e+K+X and p+p\to K+X present independent measurements of just one FF: D_{u-d}^{K^++K^-}. The above results allow to test the existing parametrizations, obtained with various different assumptions about the FFs, and to test the $Q^2$ evolution and factorization.
We explain the origin of the controversy about the existence of a transverse angular momentum sum rule, and show that it stems from utilizing an incorrect result in the literature, concerning the expression for the expectation values of the angular momentum operators. We demonstrate a new, short and direct way of obtaining correct expressions for these expectation values, from which a perfectly good transverse angular momentum sum rule can be deduced. We also introduce a new classification of sum rules into primary and secondary types. In the former all terms occurring in the sum rule can be measured experimentally; in the latter some terms cannot be measured experimentally.
We examine the influence of the recent CLAS and COMPASS experiments on our understanding of higher twist (HT) effects and the gluon polarization, and show how EIC could discriminate between negative and positive gluon polarizations. We comment on the issue of HT and the recent DSSV analysis.
We consider semi-inclusive unpolarized DIS for the production of charged Kaons and the different possibilities, both in LO and NLO, to test the conventionally used assumptions s-\bar s=0, Δs-Δ\bar s=0 and D_d^{K+ - K-}=0. The considered tests have the advantage that they do not require any knowledge of the fragmentation functions.
The impact of the recent very precise CLAS and COMPASS g1/F1 data on polarized parton densities and higher twist effects is discussed. It is demonstrated that the low Q^2 CLAS data improve essentially our knowledge of higher twist corrections to the spin structure function g1, while the large Q^2 COMPASS data influence mainly the strange quark and gluon polarizations. It is also shown that the uncertainties in the determination of the polarized parton densities are significantly reduced. We find also that the present inclusive DIS data cannot rule out a negative polarized and changing in sign gluon densities. The present status of the proton spin sum rule is discussed.
The impact of the recent very precise CLAS and COMPASS g_1/F_1 data on polarized parton densities and higher twist effects is discussed. We demonstrate that the low Q^2 CLAS data improve essentially our knowledge of higher twist corrections to the spin structure function g1, while the large Q^2 COMPASS data influence mainly the strange quark and gluon polarizations which slightly decrease. We find also that the present inclusive DIS data cannot rule out a negative polarized and changing in sign gluon densities.