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Register a new userLattice QCD Method To Study Proton Spin Crisis
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Gouranga C Nayak
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The proton spin crisis remains an unsolved problem in particle physics. The spin and angular momentum of the partons inside the proton are non-perturbative quantities in QCD which cannot be calculated by using the perturbative QCD (pQCD). In this paper we present the lattice QCD formulation to study the proton spin crisis. We derive the non-perturbative formula of the spin and angular momentum of the partons inside the proton from the first principle in QCD which can be calculated by using the lattice QCD method.
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In the literature it is assumed that the parton to hadron fragmentation function cannot be studied by using the lattice QCD method because of the sum over the (unobserved) outgoing hadronic states. However, in this paper we find that since the hadron formation from the partons can be studied by using the lattice QCD method, the parton to hadron fragmentation function can be studied by using the lattice QCD method by using the LSZ reduction formula for the partonic processes.
In this work we suggest a simple theoretical model of the proton able to effectively solve proton spin crisis. Within domain of applicability of this simple model proton consists only of two u quarks and one d quarks (two of which have spin opposite to proton and one identical to proton) and one neutral vector phi meson (with spin two times larger than proton spin and directed identically to proton spin). This model is in full agreement not only with existing DIS experiments, but also with spin and electric charge conservation as well as in a satisfactory agreement with rest mass-energy conservation (since phi meson mass is close to proton rest mass). Our model opens an interesting possibility of the solution of the quarks and leptons families problem (proton is not an absolutely non-strange particle, but only a particle with almost totally effectively hidden strange). Also we suggest a possible first step toward the solution of the supersymmetry crisis using so-called superexclusion principle. According to this principle usual particles (electron, neutrino,...) can exist actually and virtually, while their supersymmetric partners, s-particles (selectron, neutralino, ...) can exist (super)exclusively virtually but not actually.
We present the first chiral-continuum extrapolated up, down and strange quark spin contribution to the proton spin using lattice QCD. For the connected contributions, we use eleven ensembles of 2+1+1-flavor of Highly Improved Staggered Quarks (HISQ) generated by the MILC Collaboration. They cover four lattice spacings $a approx {0.15,0.12,0.09,0.06}$ fm and three pion masses, $M_pi approx {315,220,135}$ MeV, of which two are at the physical pion mass. The disconnected strange calculations are done on seven of these ensembles, covering the four lattice spacings but only one with the physical pion mass. The disconnected light quark calculation was done on six ensembles at two values of $M_pi approx {315,220}$ MeV. High-statistics estimates on each ensemble for all three quantities allow us to quantify systematic uncertainties and perform a simultaneous chiral-continuum extrapolation in the lattice spacing and the light-quark mass. Our final results are $Delta u equiv langle 1 rangle_{Delta u^+} = 0.777(25)(30)$, $Delta d equiv langle 1 rangle_{Delta d^+} = -0.438(18)(30)$, and $Delta s equiv langle 1 rangle_{Delta s^+} = -0.053(8)$, adding up to a total quark contribution to proton spin of $sum_{q=u,d,s} (frac{1}{2} Delta q) = 0.143(31)(36)$. The second error is the systematic uncertainty associated with the chiral-continuum extrapolation. These results are obtained without model assumptions and are in good agreement with the recent COMPASS analysis $0.13 < frac{1}{2} Delta Sigma < 0.18$, and with the $Delta q$ obtained from various global analyses of polarized beam or target data.
The exact decomposition of the proton spin has been a much debated topic, on the experimental as well as the theoretical side. In this talk we would like to report on recent non-perturbative results and ongoing efforts to explore the proton spin from lattice QCD. We present results for the relevant generalized form factors from gauge field ensembles that feature a physical value of the pion mass. These generalized form factors can be used to determine the total spin and angular momentum carried by the quarks. In addition we present first results for our ongoing effort to compute the angular momentum of the gluons in the proton.
The reweighting method is widely used in numerical studies of QCD, in particular, for the cases in which the conventional Monte-Carlo method cannot be applied directly, e.g., finite density QCD. However, the application range of the reweighing method is restricted due to several problems. One of the most severe problems here is the overlap problem. To solve it, we examine a multipoint reweighting method in which simulations at several simulation points are combined in the data analyses. We systematically study the applicability and limitation of the multipoint reweighting method in two-flavor QCD at zero density. Measuring histograms of physical quantities at a series of simulation points, we apply the multipoint reweighting method to calculate the meson masses as continuous functions of the gauge coupling $beta$ and the hopping parameters $kappa$. We then determine lines of constant physics and beta functions, which are needed in a calculation of the equation of state at finite temperature.
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