Conservation and persistence of spin currents and their relation to the Lieb-Schulz-Mattis twist operators

Systems with spin-orbit coupling do not conserve "bare" spin current $\bf{j}$. A recent proposal for a conserved spin current $\bf{J}$ [J. Shi {\it et.al} Phys. Rev. Lett. {\bf 96}, 076604 (2006)] does not flow persistently in equilibrium. We suggest another conserved spin current $\bar{\bf{J}}$ that may flow persistently in equilibrium. We give two arguments for the instability of persistent current of the form $\bf{J}$: one based on the equations of motions and another based on a variational construction using Lieb-Schulz-Mattis twist operators. In the absence of spin-orbit coupling, the three forms of spin current coincide.Comment: 5 pages; added references, simplified notation, clearer introductio

The impact of the LHCb B±B^{\pm} production cross-section on parton distribution functions and determining the mass of heavy quarks

In this work, the impact of recent measurements of heavy-flavour production in $pp$ collisions on parton distribution functions (PDFs) and their uncertainties is studied. In this regard, the absolute and normalised cross sections of beauty hadron production measured by LHCb at center-of-mass energy of 7 TeV and 13 TeV are separately included in the next-to-leading order (NLO) global QCD analysis together with the measurements of the inclusive and heavy-flavour production cross sections at HERA. It is illustrated that the heavy-flavour data of the LHCb experiment impose additional constraints on the PDFs, especially on the gluon distribution at low partonic fractions $x$ of the proton momentum. One of the most important results of the present analysis is the significant reduction of the gluon uncertainties in the region less than $x=10^{-4}$ that can play a crucial rule in many areas of high energy physics investigations.Comment: 36 pages, 8 figures, has been accepted for publication in Nuclear Physics