Operator product expansion on the lattice: a numerical test in the two-dimensional non-linear sigma-model

Caracciolo, Sergio; Montanari, Andrea; Pelissetto, Andrea

doi:10.1088/1126-6708/2000/09/045

Cited by 7 publications

(5 citation statements)

References 81 publications

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“…Due to the explicit breaking of chiral symmetry induced by the Wilson term, fourfermion ∆F = 2 and ∆I = 3/2 operators mix with operators of the same dimension but of different "naive" chirality [1,42]. 7 In order to define the complete basis of dimension-six four-fermion operators which mix under renormalization we introduce the notation…”

Section: Four-fermion Operatorsmentioning

confidence: 99%

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Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action

Bečirević

Gimenez

Lubicz

et al. 2004

J. High Energy Phys.

115

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We present the results of an extensive lattice calculation of the renormalization constants of bilinear and four-quark operators for the non-perturbatively O(a)improved Wilson action. The results are obtained in the quenched approximation at four values of the lattice coupling by using the non-perturbative RI/MOM renormalization method. Several sources of systematic uncertainties, including discretization errors and final volume effects, are examined. The contribution of the Goldstone pole, which in some cases may affect the extrapolation of the renormalization constants to the chiral limit, is non-perturbatively subtracted. The scale independent renormalization constants of bilinear quark operators have been also computed by using the lattice chiral Ward identities approach and compared with those obtained with the RI-MOM method. For those renormalization constants the non-perturbative estimates of which have been already presented in the literature we find an agreement which is typically at the level of 1%.PACS numbers: 11.15.Ha, 12.38.Gc, 11.10.Gh.1 See also ref.[7] for a related study in the context of the lattice non-linear σ-model.• Finite volume effects have been examined by comparing the results of two independent simulations performed, at the same value of the lattice coupling (β = 6.0), on different lattice volumes.• Goldstone pole contributions: power suppressed contributions coming from the Goldstone pole, which may affect the extrapolation to the chiral limit of the RCs of the pseudoscalar density and of the four-fermion operators coupled to the Goldstone boson, have been non-perturbatively subtracted.The scale independent RCs of the vector and axial-vector currents, Z V and Z A , and the ratio Z P /Z S , have also been determined in this study by using the lattice chiral WI approach, and the results are compared with those obtained with the RI/MOM method. We also compare our determinations of these constants with those obtained by the AL-PHA [16,17] and LANL [18] Collaborations by using the WI method, and our determination of Z P with the one obtained by ALPHA [19] within the SF approach. We find an agreement which is typically at the level of 1%. Since the systematics involved in these approaches are different, these comparisons provide additional confidence on the high level of accuracy reached in the implementation of the RI/MOM non-perturbative method.Our final results for the RCs of bilinear quark operators and four-fermion operators are collected in tables 2-7. Preliminary results of the present study have been presented at the Lattice 2002 conference [5,20].The plan of this paper is as follows. In sec. 2 we give the details of the numerical simulation and briefly review the non-perturbative RI/MOM method used to determine lattice RCs. The various sources of systematic errors involved in the calculation are discussed in sec. 3, where we also provide estimates of the corresponding uncertainties. The results for the RCs of bilinear quark operators obtained with the RI/MOM method are summarized i...

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Section: Four-fermion Operatorsmentioning

confidence: 99%

“…and, in order to minimize discretization effects, we select momenta with components [4,7]) (L ν is the lattice size in the direction ν).…”

Section: Details Of the Lattice Calculationmentioning

confidence: 99%

Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action

Bečirević

Gimenez

Lubicz

et al. 2004

J. High Energy Phys.

115

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“…In leading order we get 10) which can be further simplified with the help of (A.20), (A.22), (2.3) and (2.7) leading to 11) where the constants G l are equal to V l and T l for the spin and current cases respectively given in (A.21) and (A.23), and further 12) which can also be written as 13) where the Adler functions A (r) were defined in (2.9). The final results for the complete structure functions are…”

Section: Structure Functions Momentsmentioning

confidence: 99%

“…in refs. [3], [11]. So far too little is rigorously known about the detailed structure of the OPE from the general principles of the bootstrap approach to obtain the explicit results below.…”

Section: The Operator Product Expansionmentioning

confidence: 99%

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Structure functions of the 2d non-linear sigma models

Balog

Weisz

2005

Nuclear Physics B

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We investigate structure functions in the 2-dimensional (asymptotically free) nonlinear O(n) σ-models using the non-perturbative S-matrix bootstrap program. In particular the exact small (Bjorken) x behavior is derived. Structure functions in the special case of the n = 3 model are accurately computed over the whole x range for −q 2 /M 2 < 10 5 , and some moments are compared with results from renormalized perturbation theory. Some results concerning the structure functions in the 1/n approximation are also presented.

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Energy-momentum tensor in QCD: nucleon mass decomposition and mechanical equilibrium

Lorcé

Metz

Pasquini

et al. 2021

J. High Energ. Phys.

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We review and examine in detail recent developments regarding the question of the nucleon mass decomposition. We discuss in particular the virial theorem in quantum field theory and its implications for the nucleon mass decomposition and mechanical equilibrium. We reconsider the renormalization of the QCD energy-momentum tensor in minimal-subtraction-type schemes and the physical interpretation of its components, as well as the role played by the trace anomaly and Poincaré symmetry. We also study the concept of “quantum anomalous energy” proposed in some works as a new contribution to the nucleon mass. Examining the various arguments, we conclude that the quantum anomalous energy is not a genuine contribution to the mass sum rule, as a consequence of translation symmetry.

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Operator product expansion on the lattice: a numerical test in the two-dimensional non-linear sigma-model

Cited by 7 publications

References 81 publications

Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action

Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action

Structure functions of the 2d non-linear sigma models

Energy-momentum tensor in QCD: nucleon mass decomposition and mechanical equilibrium

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