Physics From Breit-Frame Regularization Of a Lattice Hamiltonian

Abstract

We suggest a Hamiltonian formulation on a momentum lattice using a physically motivated regularization using the Breit-frame which links the maximal parton number to the lattice size. This scheme restricts parton momenta to positive values in each spatial direction. This leads to a drastic reduction of degrees of freedom compared to a regularization in the rest frame (center at zero momentum). We discuss the computation of physical observables like (i) mass spectrum in the critical region, (ii) structure and distribution functions, (iii) $S$-matrix, (iv) finite temperature and finite density thermodynamics in the Breit-frame regularization. For the scalar ${\varphi }_{3+1}^4$ theory we present numerical results for the mass spectrum in the critical region. We observe scaling behavior for the mass of the ground state and for some higher lying states. We compare our results with renormalization group results by Lüscher and Weisz. Using the Breit-frame, we calculate for $QCD$ the relation between the $W^{\mu \nu }$ tensor, structure functions (polarized and unpolarized) and quark distribution functions. We use the improved parton-model with a scale dependence and take into account a non-zero parton mass. In the Bjorken limes we find the standard relations between $F_1$, $F_2$, $g_1$ and the quark distribution functions. We discuss the rôle of helicity. We present numerical results for parton distribution functions in the scalar model. For the ${\varphi }^4$-model we find no bound state with internal parton structure. For the ${\varphi }^3$-model we find a distribution function with parton structure similar to Altarelli-Parisi behavior of $QCD$.

20 pages, four figures

References in corpus (10)

• Polarized and Unpolarized Nucleon Structure Functions from Lattice QCD
• Improved Hamiltonian for Minkowski Yang-Mills Theory
• Core -- a New Computational Technique for Lattice Systems
• Estimate for the $0^{++}$ glueball mass in QCD
• Universality for SU(2) Yang-Mills Theory in (2+1)D
• Glueball Masses in Quantum Chromodynamics
• Working Group Report on the Structure of the Proton
• COMBINING MCRG AND FOURIER ACCELERATED LANGEVIN ALGORITHM
• Scattering of Glueballs and Mesons in Compact $QED$ in $2+1$ Dimensions
• Momentum Lattice Simulation on a Small Lattice Using Stochastic Quantization

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