Non-perturbative pion matrix element of a twist-2 operator from the lattice

We give a continuum limit value of the lowest moment of a twist-2 operator in pion states from non-perturbative lattice calculations. We find that the non-perturbatively obtained renormalization group invariant matrix element is \(\langle x\rangle_{\mathrm{RGI}} = 0.179(11)\), which corresponds to \...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2005-03, Vol.40 (1), p.69-80
Main Author: The Zeuthen-Rome (Zero) Collaboration
Format: Article
Language:English
Subjects:
Computer simulation
Invariants
Mathematical analysis
Pions
Size effects
Systematic errors
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Summary:We give a continuum limit value of the lowest moment of a twist-2 operator in pion states from non-perturbative lattice calculations. We find that the non-perturbatively obtained renormalization group invariant matrix element is \(\langle x\rangle_{\mathrm{RGI}} = 0.179(11)\), which corresponds to \(\langle x \rangle^{\overline{\mathrm{MS}}}(2\mathrm{ GeV}) = 0.246(15)\). In obtaining the renormalization group invariant matrix element, we have controlled important systematic errors that appear in typical lattice simulations, such as non-perturbative renormalization, finite size effects and effects of a non-vanishing lattice spacing. The crucial limitation of our calculation is the use of the quenched approximation. Another question that remains not fully clarified is the chiral extrapolation of the numerical data.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s2005-02121-5