Structure Functions on the Lattice

Guagnelli, M.; Palombi, Filippo; Petronzio, R.; Jansen, Karl; Shindler, Andrea; Wetzorke, I.

doi:10.1142/9789812705167_0009

Cited by 24 publications

(47 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…the renormalized matrix element at the scale µ 0 . The final result for the renormalized matrix element of the pion that we are going to provide here, was made possible by a number of theoretical and conceptual developments that we could achieve over the last years [6][7][8][9]. The methods developed there can immediately be taken over to other matrix elements than the lowest twist case of the pion considered here and to the unquenched situation.…”

Section: Renormalized Matrix Elementmentioning

confidence: 93%

“…In the course of our work [6][7][8][9][10][11] to reach a reliable value for a moment of a parton distribution function we eliminated important sources of systematic errors besides the quenched approximation (see [12][13][14] for summaries of these works). The transition to full dynamical simulations is undertaken world-wide today [15] and the next years will see the exciting results of such calculations.…”

Section: Introductionmentioning

confidence: 99%

“…In this way, all quantities could be extrapolated to their continuum value in a controlled way performing a constrained continuum limit [8,11]. In particular in this work we have used this strategy to control the continuum limit of the renormalized matrix element.…”

Section: Introductionmentioning

confidence: 99%

“…For the matrix elements, a careful test of finite size effects has been performed [21] with the somewhat surprising result that such effects are rather large for the pion matrix element at a point where the pion mass itself shows no effects. Since this was done for pion matrix elements only, it will be very important to repeat the analysis for baryon matrix elements, where such effects are expected to be even larger [22].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

et al. 2005

View full text Add to dashboard Cite

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 x RGI = 0.179(11), which corresponds to x MS (2 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.

show abstract

Section: Renormalized Matrix Elementmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

et al. 2005

View full text Add to dashboard Cite

show abstract

“…For applications to similar problems in applying the lattice to construct matrix elements relevant in deep inelastic scattering see, for instance, [28,29]. It is also worth drawing attention to an alternative lattice approach to constructing moments of the parton distribution functions, [30]. This uses the Schrödinger functional technique of [31] and is non-perturbative.…”

Section: Introductionmentioning

confidence: 99%

Three loop anomalous dimension of the second moment of the transversity operator in the and RI′ schemes

Gracey

2003

Nuclear Physics B

View full text Add to dashboard Cite

Abstract. We compute the anomalous dimension of the second moment of the transversity operator,ψσ µν D ρ ψ, at three loops in both the MS and RI ′ schemes. As a check on the result we also determine the O(1/N f ) critical exponent of the n-th moment of the transversity operator in d-dimensions in the large N f expansion and determine leading order information on the n dependence of the anomalous dimension at three and four loops in MS. In addition the RI ′ anomalous dimension of the non-singlet twist-2 operator,ψγ µ D ν ψ, is also determined. LTH 5801

show abstract

Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks

Karpie

Orginos

Rothkopf

et al. 2019

J. High Energ. Phys.

126

View full text Add to dashboard Cite

The computation of the parton distribution functions (PDF) or distribution amplitudes (DA) of hadrons from first principles lattice QCD constitutes a central open problem. In this study, we present and evaluate the efficiency of a selection of methods for inverse problems to reconstruct the full x-dependence of PDFs. Our starting point are the so called Ioffe time PDFs, which are accessible from Euclidean time calculations in conjunction with a matching procedure. Using realistic mock data tests, we find that the ill-posed incomplete Fourier transform underlying the reconstruction requires careful regularization, for which both the Bayesian approach as well as neural networks are efficient and flexible choices.

show abstract

Structure Functions on the Lattice

Cited by 24 publications

References 0 publications

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

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

Three loop anomalous dimension of the second moment of the transversity operator in the and RI′ schemes

Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks

Contact Info

Product

Resources

About