1,741 research outputs found

    Renormalization constants of local operators within the Schr\"odinger functional scheme

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    We define, within the Schr\"odinger functional (SF) scheme, the matrix elements of the twist-2 operators corresponding to the first two moments of non-singlet parton density, and the first moment of singlet parton densities. We perform a lattice one-loop calculation that fixes the relation between the SF scheme and other common schemes and shows the main source of lattice artefacts. Few remarks on the improvement case are added.Comment: Presented at LATTICE99, 3 page

    Perturbative Renormalization of Improved Lattice Operators

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    We derive bases of improved operators for all bilinear quark currents up to spin two (including the operators measuring the first moment of DIS Structure Functions), and compute their one-loop renormalization constants for arbitrary coefficients of the improvement terms. We have thus control over O(a) corrections, and for a suitable choice of improvement coefficients we are only left with errors of O(a^2).Comment: 4 pages, LaTeX + 1 eps file + epscrc2.sty (included). Talk given to the Lattice 97 International Symposium, 22-26 July 1997, Edinburgh, UK. Minor changes in notatio

    Large pion pole in Z_{S}^{MOM}/Z_{P}^{MOM} from Wilson action data

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    We show that, contrarily to recent claims, data from the Wilson (unimproved) fermionic action at three different beta values demonstrate the presence of a large Goldstone boson contribution in the quark pseudoscalar vertex, quantitatively close to our previous estimate based on the SW action with c_{SW}=1.769. We show that discretisation errors on Z_{S}^{MOM}/Z_{P}^{MOM} seem to be much smaller than the Goldstone pole contribution over a very large range of momenta. The subtraction of this non perturbative contribution leads to numbers close to one-loop BPT.Comment: 12 pages, 5 figures, laTeX, minor corrections of typos, beta dependence made more explicit, added one table giving the contribution of the Goldstone vs. the discretisation errors at ap=

    3-point functions from twisted mass lattice QCD at small quark masses

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    We show at the example of the matrix element between pion states of a twist-2, non-singlet operator that Wilson twisted mass fermions allow to compute this phenomenologically relevant quantitiy at small pseudo scalar masses of O(270 MeV). In the quenched approximation, we investigate the scaling behaviour of this observable that is derived from a 3-point function by applying two definitions of the critical mass and find a scaling compatible with the expected O(a^2) behaviour in both cases. A combined continuum extrapolations allows to obtain reliable results at small pion masses, which previously could not be explored by lattice QCD simulations.Comment: 6 pages, 2 figures, talk presented at Lattice 200

    Renormalization of minimally doubled fermions

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    We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Borici-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Borici-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.Comment: 23 pages, 1 figur

    Moments of Structure Functions in Full QCD

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    Moments of the quark density distribution, moments of the quark helicity distribution, and the tensor charge are calculated in full QCD. Calculations of matrix elements of operators from the operator product expansion have been performed on 163×3216^3 \times 32 lattices for Wilson fermions at β=5.6\beta = 5.6 using configurations from the SESAM collaboration and at β=5.5\beta = 5.5 using configurations from SCRI. One-loop perturbative renormalization corrections are included. Selected results are compared with corresponding quenched calculations and with calculations using cooled configurations.Comment: Lattice 2000 (Hadronic Matrix Elements), 4 pages, 5 figure

    Moments of parton evolution probabilities on the lattice within the Schroedinger functional scheme

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    We define, within the Schroedinger functional scheme (SF), the matrix elements of the twist-2 operators corresponding to the first two moments of non-singlet parton densities. We perform a lattice one-loop calculation that fixes the relation between the SF scheme and other common schemes and shows the main source of lattice artefacts. This calculation sets the basis for a numerical evaluation of the non-perturbative running of parton densities.Comment: Latex file, 4 figures, 15 page

    Higher-Twist Contribution to Pion Structure Function: 4-Fermi Operators

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    We present quenched lattice QCD results for the contribution of higher-twist operators to the lowest non-trivial moment of the pion structure function. To be specific, we consider the combination F2π++F2π2F2π0F_2^{\pi^+} + F_2^{\pi^-} - 2 F_2^{\pi^0} which has I=2I = 2 and receives contributions from 4-Fermi operators only. We introduce the basis of lattice operators. The renormalization of the operators is done perturbatively in the MSˉ\bar{\rm{MS}} scheme using the 't Hooft-Veltman prescription for γ5\gamma_5, taking particular care of mixing effects. The contribution is found to be of O(fπ2/Q2)O(f_\pi^2/Q^2), relative to the leading contribution to the moment of F2π+F_2^{\pi^+}.Comment: Version to appear in Nucl. Phys.

    Power Corrections to Perturbative QCD and OPE in Gluon Green Functions

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    We show that QCD Green functions in Landau Gauge exhibit sizable O(1/μ2)O(1/\mu^2) corrections to the expected perturbative behavior at energies as high as 10 GeV. We argue that these are due to a -condensate which does not vanish in Landau gauge.Comment: 3 pages 1 figure lattice2001 (gaugetheories
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