Flavor-Singlet g A from Lattice QCD

Recent developments in lattice QCD calculation of flavor singlet nucleon matrix elements are reviewed. Substantial sea quark contributions are found in the π-N σ term and the quark spin content of the nucleon such that the total magnitude including valence contributions is in reasonable agreement with experiments. Some problems with flavor non-singlet nucleon matrix elements are pointed out. Recent work on lattice QCD calculation of hadron scattering length is also discussed.

“…1(b)) has been made in quenched QCD using both the wall source method without gauge fixing [11,12] and the Z 2 source method [14,15]. In Fig.…”

Section: π-N σ Term -Recent Lattice Resultsmentioning

confidence: 99%

“…However, concrete applications of the method [14,15] show that the number of quark propagators L has to be large, generally exceeding 100. Thus the method becomes harder to use for lighter quarks for which a substantial computer time is necessary to obtain even a single quark propagator.…”

Section: Z 2 Source Methodsmentioning

confidence: 99%

New developments in lattice QCD: Calculation of flavor singlet nucleon matrix elements and hadron scattering lengths

Okawa

1996

“…Whether we do lattice calculation for quenched or dynamical QCD, these quark loops contribute significantly to various hadronic matrix elements. For example, for nucleonic scalar (πN N -σ term) [1], vector (strange magnetic moment) [2,3], flavor-singlet axial (quark spin) [4], and tensor (quark orbital angular momentum) [5] channels, it is absolutely essential to consider disconnected quark loops. In particular, the strangeness content of the nucleon comes exclusively from these disconnected loops.…”

Section: Introductionmentioning

confidence: 99%

Study of stochastic estimates of quark loops with unbiased subtraction

Mathur¹,

Dong

2003

Stochastic noise estimator method is a powerful tool to calculate the disconnected insertion involving quark loops. We study the variance reduction technique with unbiased subtraction. We use the complex Z2 noise to calculate the quark loops on a 16 3 × 24 lattice with β = 6.0 and κ = 0.154. Unbiased subtraction method is performed by using hoping parameter expansion. We report on the variance reduction for the point-split vector current as a function of the number of subtraction terms and the number of noise used.

“…For strange quark contribution we follow the same procedure as in ref. [4]. •: unsubtracted From DI calculation, we find that J DI q , like the DI part of the quark spin 1 2 Σ DI , is also flavor symmetric, i.e., J DI u = J DI d ≃ J DI s = −0.047 ± 0.013.…”

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confidence: 99%

“…Experimental [2], [3] and lattice results [4], [5] suggest that the quark contribution ( 1 2 Σ) to the proton spin is about 25 ± 10%. But to date, we have very little knowledge about the remaining part of the proton spin.…”

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confidence: 99%

Proton spin content from lattice QCD

Mathur¹,

Dong²,

Liu³

et al. 2000

We calculate the form factor of the quark energy momentum tensor and thereby extract the quark orbital angular momentum of the nucleon. The calculation is done on a quenched 16 3 × 24 lattice at β = 6.0 and with Wilson fermions at κ = 0.148, 0.152, 0.154 and 0.155. We calculate the disconnected insertion stochastically which employs the Z2 noise with an unbiased subtraction. This proves to be an efficient method of reduce the error from the noise. We find that the total quark contribution to the proton spin is 0.29 ± 0.07. From this we deduce that the quark orbital angular momentum is 0.17 ± 0.08 and predict the gluon spin to be 0.21 ± 0.07, i.e. about 40% of the proton spin is due to the glue. To understand the spin content of the proton remains a challenging problem in QCD [1]. Experimental [2], [3] and lattice results [4], [5]suggest that the quark contribution ( 1 2 Σ) to the proton spin is about 25 ± 10%. But to date, we have very little knowledge about the remaining part of the proton spin. We do not have reliable estimate about the spin contribution from the gluons or the orbital angular momentum of the quark. In this talk, I will show our lattice results on the total angular momentum of the quarks and thereby deduce the quark orbital angular momentum and predict the gluon contribution to the proton spin.Recently it was shown [6] that one can decompose the total angular momentum of QCD in a gauge invariant way, i.e.The forward matrix element of this operator in the proton defines the decomposition of the proton spin 1 2 = 1 2 Σ + L q + J g , where 1 2 Σ is the quark spin contribution, L q is the quark orbital angular momentum and J g is the total angular momentum of the glue. To calculate the angular momentum of the quark and the gluon in the * Talk presented by N. Mathur at Lattice '99, Pisa, Italy proton, one first notices that the gauge invariant quark-gluon energy momentum tensor [6] iswhere the first part is the quark energy momentum tensor and the second one is that of the gluon. Form factors of this energy momentum tensor current can be defined aswherep µ = (p µ + p ′ µ )/2, q µ = p µ − p ′ µ and u(p) is the nucleon spinor. It is proved [6] that the total angular momentum of the quark or gluon is related to the sum of the T 1 and T 2 form factors at zero momentum transfer, i. e.