Lattice computation of structure functions

Recent lattice calculations of hadron structure functions are described.Comment: Plenary talk presented at LATTICE96, LaTeX, 7 pages, 5 figures, espcrc2.sty and epsfig.sty include

Perturbative Renormalization of Lattice Bilinear Quark Operators

Our aim is to compute the lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon on the lattice. The theoretical basis of the calculation is the operator product expansion. To construct operators with the appropriate continuum behavior out of the bare lattice operators one must absorb the effects of momentum scales far greater than any physical scale into a renormalization of the operators. In this work we compute the renormalization constants of all bilinear quark operators of leading twist and spin up to four. The calculation is done for Wilson fermions and in the quenched approximation where dynamical quark loops are neglected.Comment: 28 pages, uuencoded Z-compressed postscript file. Also available from http://www.desy.de/pub/preprints/desy/199

Polarized and Unpolarized Nucleon Structure Functions from Lattice QCD

We report on a high statistics quenched lattice QCD calculation of the deep-inelastic structure functions $F_1$, $F_2$, $g_1$ and $g_2$ of the proton and neutron. The theoretical basis for the calculation is the operator product expansion. We consider the moments of the leading twist operators up to spin four. Using Wilson fermions the calculation is done for three values of $\kappa$, and we perform the extrapolation to the chiral limit. The renormalization constants, which lead us from lattice to continuum operators, are calculated in perturbation theory to one loop order.Comment: 17 pages, uuencoded postscript file. Renormalization constant of now include

Nonperturbative Renormalisation of Composite Operators in Lattice QCD

We investigate the nonperturbative renormalisation of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.Comment: LaTeX, 41 pages, 24 figure

Moments of Nucleon Light Cone Quark Distributions Calculated in Full Lattice QCD

Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through the operator product expansion have been performed on $16^3 \times 32$ lattices for Wilson fermions at $\beta = 5.6$ using configurations from the SESAM collaboration and at $\beta = 5.5$ using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac Sea are small. Close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play a dominant role. Naive linear extrapolation of the full QCD calculation to the physical pion mass yields results inconsistent with experiment. Extrapolation to the chiral limit including the physics of the pion cloud can resolve this discrepancy and the requirements for a definitive chiral extrapolation are described.Comment: 53 Pages Revtex, 26 Figures, 9 Tables. Added additional reference and updated referenced data in Table I

Reliability of forced internal rotation and active internal rotation to assess lateral instability of the biceps pulley

PURPOSE: the aim of this study was to investigate the relationship between positive painful forced internal rotation (FIR) and lateral pulley instability in the presence of a pre-diagnosed posterosuperior cuff tear. The same investigation was conducted for painful active internal rotation (AIR). METHODS: a multicenter prospective study was conducted in a series of patients scheduled to undergo arthroscopic posterosuperior cuff repair. Pain was assessed using a visual analog scale (VAS) and the Disabilities of the Arm, Shoulder and Hand questionnaire (DASH) was administered. The VAS score at rest, DASH score, and presence/absence of pain on FIR and AIR were recorded and their relationships with lesions of the lateral pulley, cuff tear patterns and shape of lesions were analyzed. RESULTS: the study population consisted of 115 patients (mean age: 55.1 years) recruited from 12 centers. The dominant arm was affected in 72 cases (62.6%). The average anteroposterior extension of the lesion was 1.61 cm. The mean preoperative VAS and DASH scores were 6.1 and 41.8, respectively. FIR and AIR were positive in 94 (81.7%) and 85 (73.9%) cases, respectively. The lateral pulley was compromised in 50 cases (43.4%). Cuff tears were partial articular in 35 patients (30.4%), complete in 61 (53%), and partial bursal in 19 (16.5%). No statistical correlation between positive FIR or AIR and lateral pulley lesions was detected. Positive FIR and AIR were statistically associated with complete lesions. Negative FIR was associated with the presence of partial articular tears. CONCLUSIONS: painful FIR in the presence of a postero-superior cuff tear does not indicate lateral pulley instability. When a cuff tear is suspected, positive FIR and AIR are suggestive of full-thickness tear patterns while a negative FIR suggests a partial articular lesion. LEVEL OF EVIDENCE: level I, validating cohort study with good reference standards

Deep inelastic scattering in improved lattice QCD (II): the second moment of structure functions

In this paper we present the 1-loop perturbative computation of the renormalization constants and mixing coefficients of the lattice quark operators of rank three whose hadronic elements enter in the determination of the second moment of Deep Inelastic Scattering (DIS) structure functions.We have employed in our calculations the nearest-neighbor improved ''clover-leaf'' lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order a (a being the lattice spacing) have been demonstrated to be absent from on-shell hadronic lattice matrix elements. We have limited our computations to the quenched case, in which quark operators do not mix with gluon operators.We have studied the transformation properties under the hypercubic group of the operators up to the rank five (which are related to moments up to the fourth of DIS structure functions), and we discuss the choice of the operators considered in this paper together with the feasibility of lattice computations for operators of higher ranks.To perform the huge amount of calculations required for the evaluation of all the relevant Feynman diagrams, we have extensively used the symbolic manipulation languages Schoonschip and Form