Renormalization of the chromomagnetic operator on the lattice

Constantinou, Martha; Costa, Marios; Frezzotti, R.; Martinelli, G.; Meloni, Davide; Panagopoulos, H.; Simula, Silvano

doi:10.1103/physrevd.92.034505

Cited by 18 publications

(35 citation statements)

References 29 publications

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“…In lattice QCD one calculates matrix elements of fermion operators between the relevant hadron states and unless these operators correspond to a conserved current they must be renormalized in order to extract the physical information one is after. In many cases, calculation of renormalization functions (RFs) can be carried out using lattice perturbation theory, which proves to be extremely helpful in cases where there is a mixing with operators of equal or lower dimension, such as the chromomagnetic operator [7,8] and the operator measuring the glue of the nucleon [9,10]. However, perturbation theory is reliable for a limited range of values of the coupling constant, g, and of the renormalization scale, µ.…”

Section: Introductionmentioning

confidence: 99%

Renormalization functions for Nf=2 and Nf=4 twisted mass fermions

2017

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We present results on the renormalization functions of the quark field and fermion bilinears with up to one covariant derivative. For the fermion part of the action we employ the twisted mass formulation with N f =2 and N f =4 degenerate dynamical quarks, while in the gluon sector we use the Iwasaki improved action. The simulations for N f =4 have been performed for pion masses in the range of 390 MeV -760 MeV and at three values of the lattice spacing, a, corresponding to β=1.90, 1.95, 2.10. The N f =2 action includes a clover term with csw=1.57551 at β=2.10, and three ensembles at different values of mπ.The evaluation of the renormalization functions is carried out in the RI ′ scheme using a momentum source. The non-perturbartive evaluation is complemented with a perturbative computation, which is carried out at one-loop level and to all orders in the lattice spacing, a. For each renormalization function computed non-perturbatively we subtract the corresponding lattice artifacts to all orders in a, so that a large part of the cut-off effects is eliminated.The renormalization functions are converted to the MS scheme at a reference energy scale of µ=2 GeV after taking the chiral limit.

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Section: Introductionmentioning

confidence: 99%

Renormalization functions for Nf=2 and Nf=4 twisted mass fermions

2017

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“…The setup of this process is extensively described in Refs. [34,35] and is briefly outlined below. As is common practice, we will consider mass-independent renormalization schemes, so that fermion renormalized masses will be vanishing; for the one-loop lattice calculations this implies that the Lagrangian masses must be set to zero.…”

Section: Renormalization Prescriptionmentioning

confidence: 99%

Perturbative renormalization of quasi-parton distribution functions

2017

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In this paper we present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one-loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions.The extended nature of such 'long-link' operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors.On the lattice there is also mixing among certain subsets of these nonlocal operators; we calculate the corresponding finite mixing coefficients, which are necessary in order to disentangle individual matrix elements for each operator from lattice simulation data. Finally, extending our perturbative setup, we present non-perturbative prescriptions to extract the linearly divergent contributions.

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“…The MS-renormalized Green's functions are already known in dimensional regularization, see Ref. [4]. Equations (2.9) and (2.10) now take the form:…”

Section: Lattice Regularization -Renormalization Functions In the Ms mentioning

confidence: 99%

Perturbative and non-perturbative renormalization results of the Chromomagnetic Operator on the Lattice

Constantinou¹,

Costa²,

Frezzotti³

et al. 2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing pattern, the CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO. Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory. On the other hand using a lattice regularization further operators with d ≤ 5 will mix; choosing the lattice action in a manner as to preserve certain discrete symmetries, a minimul set of 3 additional operators (all with d < 5) will appear. In order to compute all relevant mixing coefficients, we calculate the quark-antiquark (2-pt) and the quark-antiquark-gluon (3-pt) Green's functions of the CMO at nonzero quark masses. These calculations were performed in the continuum (dimensional regularization) and on the lattice using the maximally twisted mass fermion action and the Symanzik improved gluon action. In parallel, non-perturbative measurements of the K − π matrix element are being performed in simulations with 4 dynamical (N f = 2 + 1 + 1) twisted mass fermions and the Iwasaki improved gluon action.

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Renormalization of the chromomagnetic operator on the lattice

Cited by 18 publications

References 29 publications

Renormalization functions for Nf=2 and Nf=4 twisted mass fermions

Renormalization functions for Nf=2 and Nf=4 twisted mass fermions

Perturbative renormalization of quasi-parton distribution functions

Perturbative and non-perturbative renormalization results of the Chromomagnetic Operator on the Lattice

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