Recent Results on the Nucleon Structure Functions from Lattice QCD
We report on recent results of a high statistics lattice calculation of the unpolarized and polarized structure functions of the nucleon.
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arXiv subjects
G. Schierholz
Publications and source records attributed to G. Schierholz.
Non-Perturbative versus Perturbative Renormalization of Lattice Operators
Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory.
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A Lattice Evaluation of the Deep-Inelastic Structure Functions of the Nucleon
The lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon are calculated on the lattice. The calculation is done with Wilson fermions and for three values of the hopping parameter $κ$, so that we can perform the extrapolation to the chiral limit. Particular emphasis is put on the renormalization of lattice operators. The renormalization constants, which lead us from lattice to continuum operators, are computed perturbatively to one loop order as well as non-perturbatively.
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Polarized and Unpolarized Nucleon Structure Functions from Lattice QCD
We report on a high statistics quenched lattice QCD calculation of the deep-inelastic structure functions $F_1$, $F_2$, $g_1$ and $g_2$ of the proton and neutron. The theoretical basis for the calculation is the operator product expansion. We consider the moments of the leading twist operators up to spin four. Using Wilson fermions the calculation is done for three values of $κ$, and we perform the extrapolation to the chiral limit. The renormalization constants, which lead us from lattice to continuum operators, are calculated in perturbation theory to one loop order.
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On the Structure of the Yang-Mills Vacuum
In this talk I will discuss the current picture of color confinement. In particular, I will show how it can be tested microscopically. It is stressed that the color magnetic monopoles in this picture are dyons. Furthermore, the role of instantons is illuminated.
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Hadronic Coupling Constants in Lattice QCD
We calculate the hadronic coupling constants $g_{NNπ}$ and $g_{ρππ}$ in QCD, including dynamical quarks in the framework of staggered fermions in the lattice approach. For the nucleon--pion coupling we obtain $g_{NNπ} = 13.8 \pm 5.8$, to be compared with the experimental value $13.13 \pm 0.07$. The $ρππ$ coupling has been analysed for two different sets of operators with the averaged result $g_{ρππ} = 4.2 \pm 1.9$ which is to be compared with the experimental value $6.06 \pm 0.01$.
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Effective Yukawa Couplings in Noncompact Lattice QED
We investigate effective Yukawa couplings of mesons to the elementary fermions in noncompact lattice QED. The couplings are extracted from suitable fermion-antifermion-meson three-point functions calculated by Monte Carlo simulations with dynamical staggered fermions. The scaling behaviour is compatible with expectations from perturbation theory, thus indicating triviality of QED. The lines of constant Yukawa coupling are compared to flows of other quantities. Consistency is seen, at most, for weak coupling.
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Theta Vacua, Confinement and the Continuum Limit
We investigate the dependence of the CP^3 model and of the SU(2) Yang-Mills theory on the vacuum angle theta. The CP^3 model exhibits a first order deconfining phase transition in theta. The critical value of theta runs from pi in the strong coupling limit towards zero as beta is taken to infinity. Qualitatively the same behavior is found in the SU(2) Yang-Mills theory in four dimensions. We discuss the renormalization group trajectories. Only the line with theta = 0 allows the cut-off to go to infinity, while the lines with theta > 0 end on the line of first order phase transitions. Thus theta is forced to zero in the continuum limit.
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Towards a Lattice Calculation of the Nucleon Structure Functions
We have initiated a programme to compute the lower moments of the unpolarised and polarised deep inelastic structure functions of the nucleon in the quenched approximation. We review our progress to date.
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Probing the Continuum Limit in Non-Compact QED: New Results on Large Lattices
We present new Monte Carlo results in non-compact lattice QED with staggered fermions down to m_0 = 0.005. This extends our previous investigations on the nature of the continuum limit of QED.
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A Solution to the Strong CP Problem
One may argue that QCD solves the strong CP problem by itself, without having to introduce new symmetries and particles. To test this idea, a lattice simulation is performed. The problem is investigated in the CP$^3$ model first. It is found that the model has a first order phase transition in $θ$ from a confining phase at small $θ$ to a deconfining phase at large $θ$, and that the critical value of $θ$ decreases towards zero as $β$ is taken to infinity. This suggests that $θ$ is tuned to zero in the continuum limit. Preliminary studies of the SU(2) Yang-Mills theory in four dimensions show a phase transition in $θ$ as well, so that it is quite likely that the strong CP problem in QCD is solved along the same line.
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Towards a Dynamical Solution of the Strong CP Problem
It is argued that QCD might solve the strong CP problem on its own. To test this idea, a lattice simulation suggests itself. In view of the difficulty of such a calculation we have, as a first step, investigated the problem in the $CP^3$ model. The $CP^3$ model is in many respects similar to QCD. In this talk I shall present some first results of our calculation. Among other things it is shown that the model has a first order deconfining phase transition in $θ$ and that the critical value of $θ$ decreases towards zero as $β$ is taken to infinity. This suggests that $θ$ is tuned to zero in the continuum limit.
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Spectroscopy and Renormalisation Group Flow of a Lattice Nambu-Jona-Lasinio Model
We investigate a lattice Nambu--Jona-Lasinio model both by the Monte Carlo method and Schwinger-Dyson equations. A comparison allows the discussion of finite size effects and the extrapolation to infinite volume. We pay special attention to the identification of particles and resonances. This enables us to discuss renormalisation group flows in the neighbourhood of the critical coupling where the chiral symmetry breaking phase transition takes place. In no region of the bare parameter space do we find renormalisability for the model.
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The Nambu-Jona-Lasinio model with staggered fermions
We investigate the neighbourhood of the chiral phase transition in a lattice Nambu--Jona-Lasinio model, using both Monte Carlo methods and lattice Schwinger-Dyson equations.
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Hadronic coupling constants in lattice QCD
We report on calculations of the hadronic coupling constants $g_{ρππ}$ and $g_{nnπ}$ based on lattice QCD with four flavors of dynamical staggered fermions. By computing 2--point and 3--point Green's functions we have been able to determine these coupling constants ab initio from QCD; the results are compatible with the experimental values.
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The present status of non-compact lattice QED
We give a 1993 update of non-compact lattice QED, in particular the chiral condensate, finite size effects and meson mass ratios. We compare descriptions of the phase transition. Our previous conclusions remain valid.
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Three-point functions in noncompact lattice QED
We calculate fermion-antifermion-"meson" three-point functions in noncompact lattice QED with dynamical staggered fermions and use them to extract effective Yukawa couplings. The results are consistent with the hypothesis that QED is trivial.
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On the existence of a first order phase transition at small vacuum angle $θ$ in the $CP^3$ model
We examine the phase structure of the $CP^3$ model as a function of $θ$ in the weak coupling regime. It is shown that the model has a first order phase transition at small $θ$. We pay special attention to the extrapolation of the data to the infinite volume. It is found that the critical value of $θ$ decreases towards zero as $β$ is taken to infinity.
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