Calculating structure functions on the lattice

Göckeler, M.; Horsley, R.; Ilgenfritz, E. M.; Oelrich, H.; Perlt, H.; Rakow, P. E. L.; Schierholz, G.; Schiller, A.

doi:10.1088/0954-3899/22/6/005

Cited by 81 publications

(179 citation statements)

References 12 publications

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“…The renormalization factors Z O are calculated using a new method [3] to one loop order in lattice perturbation series to account for a multiplicative shift of the Wilson coefficient due replacing the M S scheme at scale µ by the lattice spacing a. Our independently derived results confirm those in the literature [1,4] and extend them where necessary. For our current set of moments the results are given in the table.…”

Section: Mentssupporting

confidence: 69%

See 1 more Smart Citation

Calculation of moments of nucleon structure functions

Brower¹,

Huang²,

Negele³

et al. 1997

Nuclear Physics B - Proceedings Supplements

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Section: Mentssupporting

confidence: 69%

“…Our methodology for calculating these operators on the lattice is similar to Göckeler et al [1]. The covariant derivative is replaced by a lattice finite difference and the operators are classified by representations of the surviving discrete subgroup H 4 of the continuum Euclidean Lorentz group SO(4) [2].…”

Section: Mentsmentioning

confidence: 99%

Calculation of moments of nucleon structure functions

Brower¹,

Huang²,

Negele³

et al. 1997

Nuclear Physics B - Proceedings Supplements

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“…For some more detailed discussions of deep inelastic scattering on the lattice, see Refs. [15][16][17][18][19][20]11] and references therein.…”

Section: Moments Of Structure Functionsmentioning

confidence: 99%

Perturbative renormalization of moments of quark momentum, helicity and transversity distributions with overlap and Wilson fermions

Capitani

2001

Nuclear Physics B

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Using overlap as well as Wilson fermions, we have computed the one-loop renormalization factors of ten non-singlet operators which measure the third moment of quark momentum and helicity distributions (the lowest two having been computed in a previous paper), as well as the lowest three moments of the g 2 structure function and the lowest two non-trivial moments of the h 1 transversity structure function (plus the tensor charge). These factors are needed to extract physical observables from Monte Carlo simulations of the corresponding matrix elements.An exact chiral symmetry is maintained in our calculations with overlap fermions, and its most important consequence here is that the operators measuring g 2 do not show any of the power-divergent mixings with operators of lower dimension which are present in the Wilson case. Many of our results for Wilson fermions are also new; for the remaining ones, we agree with the literature except in one case. The computations have been carried out using the symbolic language FORM, in a general covariant gauge, which turns out also to be useful in checking the gauge-invariance of the final results.

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“…Lattice QCD provides the only known framework for non-perturbative calculation of hadron structure, and although it cannot address the intrinsically Minkowski structure functions themselves, through the operator product expansion it is possible to calculate their moments. There have been several calculations of these moments in recent years, including calculation of all moments of the spin independent and longitudinal spin dependent structure functions through order four [1] and the tensor charge [2] by the QCDSF collaboration, as well as calculation of connected and disconnected contributions to the axial charge [3,4] and to the tensor charge [5]. These results agree qualitatively with experiment and discrepancies may plausibly be attributed to a combination of finite lattice size effects, and the omission of sea quarks and disconnected diagrams.…”

Section: Motivationmentioning

confidence: 99%

Study of instanton contributions to moments of nucleon spin-dependent structure functions

Dolgov¹,

Brower²,

Negele³

et al. 1999

Nuclear Physics B - Proceedings Supplements

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Instantons are the natural mechanism in non-perturbative QCD to remove helicity from valence quarks and transfer it to gluons and quark-antiquark pairs. To understand the extent to which instantons explain the so-called "spin crisis" in the nucleon, we calculate moments of spin-dependent structure functions in quenched QCD and compare them with the results obtained with cooled configurations from which essentially all gluon contributions except instantons have been removed. Preliminary results are presented. MOTIVATIONIn recent years there has been a major experimental effort to measure structure functions which characterize the distribution of quarks in the nucleon. The challenge for theorists is now to understand the data which already exist and to predict the structure functions which will be measured in currently planned experiments. Lattice QCD provides the only known framework for non-perturbative calculation of hadron structure, and although it cannot address the intrinsically Minkowski structure functions themselves, through the operator product expansion it is possible to calculate their moments. There have been several calculations of these moments in recent years, including calculation of all moments of the spin independent and longitudinal spin dependent structure functions through order four [1] and the tensor charge [2] by the QCDSF collaboration, as well as calculation of connected and disconnected contributions to the axial charge [3,4] and to the tensor charge [5]. These results agree qualitatively with experiment and discrepancies may plausibly be attributed to a combination of finite lattice size effects, and the omission of sea quarks and disconnected diagrams.However, in addition to showing that numeri- * Based on the poster presented by D.Dolgov. Work supported by the U.S. Department of Energy (DOE) under cooperative research agreement DE-FC02-94ER40818.cal solution of QCD reproduces the experimental results, we want to understand as fully as possible the physical origin of the observed structure. Since instantons play a major role in the physics of light quarks [6,7], we also would like to understand their role in hadron structure functions. Especially interesting from this perspective is the spin structure of a proton.is the only known vertex in QCD that directly removes helicity from valence quarks and transfers it to gluons and quark-antiquark pairs, thereby rendering instantons the natural mechanism to explain the so-called "spin crisis".Hence it is important to identify the instanton contribution to the proton spin structure functions. On the lattice, a practical way of extracting the instanton content is "cooling" [8,6], in which one sequentially minimizes the action locally on each link and iteratively approaches a stationary solution.In this work we calculate the zeroth moments of the g 1 (x) and h 1 (x) structure functions with and without cooling for u and d quarks in quenched lattice QCD. The zeroth moment of g 1 (x) is proportional to the quark's spin contribution to the total ...

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Calculating structure functions on the lattice

Abstract: We describe the methods used to calculate the nucleon structure functions from quenched lattice QCD, and present some results for moments of the polarized and unpolarized structure functions.

Cited by 81 publications

References 12 publications

Calculation of moments of nucleon structure functions

Calculation of moments of nucleon structure functions

Perturbative renormalization of moments of quark momentum, helicity and transversity distributions with overlap and Wilson fermions

Study of instanton contributions to moments of nucleon spin-dependent structure functions

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