Applied lattice gauge calculations: diquark content of the nucleon
As an example of an application of lattice QCD we describe a computation of four-quark operators in the nucleon. The results are interpreted in a diquark language.
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arXiv subjects
B. Klaus
Publications and source records attributed to B. Klaus.
A lattice evaluation of four-quark operators in the nucleon
Nucleon matrix elements of various four-quark operators are evaluated in quenched lattice QCD using Wilson fermions. Some of these operators give rise to twist-four contributions to nucleon structure functions. Furthermore, they bear valuable information about the diquark structure of the nucleon. Mixing with lower-dimensional operators is avoided by considering appropriate representations of the flavour group. We find that for a certain flavour combination of baryon structure functions, twist-four contributions are very small. This suggests that twist-four effects for the nucleon might be much smaller than m_p^2/Q^2.
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Four-quark operators in hadrons
We present calculations of matrix elements of 4-quark operators in the pion and in the nucleon extracted from quenched Monte Carlo simulations at beta = 6.0 using Wilson fermions. These operators are relevant for higher-twist effects. We are particularly careful to avoid mixing with lower-dimensional operators by choosing appropriate flavour structures.
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Higher-Twist Contribution to Pion Structure Function: 4-Fermi Operators
We present quenched lattice QCD results for the contribution of higher-twist operators to the lowest non-trivial moment of the pion structure function. To be specific, we consider the combination $F_2^{π^+} + F_2^{π^-} - 2 F_2^{π^0}$ which has $I = 2$ and receives contributions from 4-Fermi operators only. We introduce the basis of lattice operators. The renormalization of the operators is done perturbatively in the $\bar{\rm{MS}}$ scheme using the 't Hooft-Veltman prescription for $γ_5$, taking particular care of mixing effects. The contribution is found to be of $O(f_π^2/Q^2)$, relative to the leading contribution to the moment of $F_2^{π^+}$.
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Higher-twist contributions to the Structure Functions coming from 4-fermion operators
We evaluate the contribution of a class of higher-twist operators to the lowest moment of the Structure Functions, by computing appropriate matrix elements of six four-fermion operators in the quenched approximation. Their perturbative renormalization constants and mixing coefficients are calculated in the 't Hooft-Veltman scheme of dimensional regularization, using codes written in the algebraic manipulation computer language FORM.
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Light quark masses from the lattice
A completely non-perturbative estimate is given for the u/d and strange quark masses in quenched QCD using O(a) improved fermions and, for comparison, Wilson fermions. For improved fermions we find m_{u/d}^MSbar(μ=2 GeV) = 4.4(2) MeV, m_s^MSbar(μ=2 GeV) = 105(4) MeV when using r_0 to set the physical scale.
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Nucleon form factors and O(a) Improvement
Nucleon form factors have been extensively studied both experimentally and theoretically for many years. We report here on new results of a high statistics quenched lattice QCD calculation of vector and axial-vector nucleon form factors at low momentum transfer within the Symanzik improvement programme. The simulations are performed at three kappa and three beta values allowing first an extrapolation to the chiral limit and then an extrapolation in the lattice spacing to the continuum limit. The computations are all fully non-perturbative. A comparison with experimental results is made.
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$O(a)$ Improvement for Quenched Wilson Fermions
We briefly describe some of our recent results for the mass spectrum and matrix elements using $O(a)$ improved fermions for quenched QCD. Where possible a comparison is made between improved and Wilson fermions.
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