Non-perturbative determination of improvement b-coefficients in Nf = 3

We present our preliminary results of the non-perturbative determination of the valence mass dependent coefficients bA - bP and bm as well as the ratio ZPZm=ZA entering the flavour non-singlet PCAC relation in lattice QCD with Nf = 3 dynamical flavours. We apply the method proposed in the past for quenched approximation and Nf = 2 cases, employing a set of finite-volume ALPHA configurations with Schrödinger functional boundary conditions, generated with O(a) improved Wilson fermions and the tree-level Symanzik-improved gauge action for a range of couplings relevant for simulations at lattice spacings of about 0.09 fm and below.

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Ward identity determination of $$Z_{\mathrm {S}}/Z_{\mathrm {P}}$$ for $$N_{\mathrm {f}}=3$$ lattice QCD in a Schrödinger functional setup

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8266-2 ◽

2020 ◽

Vol 80 (8) ◽

Author(s):

Jochen Heitger ◽

Fabian Joswig ◽

Anastassios Vladikas

Keyword(s):

Lattice Qcd ◽

Large Volume ◽

Ward Identity ◽

Tree Level ◽

Quark Masses ◽

Axial Variation ◽

Functional Boundary ◽

Functional Boundary Conditions ◽

Typical Range

Abstract We derive chiral Ward identities for lattice QCD with Wilson quarks and $$N_{\mathrm{f}}\ge 3$$Nf≥3 flavours, on small lattices with Schrödinger functional boundary conditions and vanishingly small quark masses. These identities relate the axial variation of the non-singlet pseudoscalar density to the scalar one, thus enabling the non-perturbative determination of the scale-independent ratio $$Z_{\mathrm {S}}/Z_{\mathrm {P}}$$ZS/ZP of the renormalisation parameters of these operators. We obtain results for $$N_{\mathrm{f}}=3$$Nf=3 QCD with tree-level Symanzik-improved gluons and Wilson-Clover quarks, for bare gauge couplings which cover the typical range of large-volume $$N_{\mathrm{f}}= 2+1$$Nf=2+1 simulations with Wilson fermions at lattice spacings below $$0.1\,$$0.1fm. The precision of our results varies from 0.3 to 1%, except for the coarsest lattice, where it is 2%. We discuss how the $$Z_{\mathrm {S}}/Z_{\mathrm {P}}$$ZS/ZP ratio can be used in the non-perturbative calculations of $${\mathrm {O}}(a)$$O(a) improved renormalised quark masses.

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Schrödinger functional boundary conditions and improvement of the SU(N) pure gauge action for $N>3$

10.22323/1.187.0328 ◽

2014 ◽

Author(s):

Tuomas Karavirta ◽

Ari Hietanen ◽

Pol Vilaseca

Keyword(s):

Boundary Conditions ◽

Gauge Action ◽

Pure Gauge ◽

Functional Boundary ◽

Functional Boundary Conditions

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Determination of $c_A$ in three-flavour lattice QCD with Wilson fermions and tree-level improved gauge action

10.22323/1.187.0311 ◽

2014 ◽

Author(s):

Christian Wittemeier ◽

Michele Della Morte ◽

John Bulava ◽

Jochen Heitger

Keyword(s):

Lattice Qcd ◽

Tree Level ◽

Gauge Action ◽

Wilson Fermions

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Non-perturbative determination of cV, ZV and ZS/ZP in Nf = 3 lattice QCD

EPJ Web of Conferences ◽

10.1051/epjconf/201817510004 ◽

2018 ◽

Vol 175 ◽

pp. 10004 ◽

Cited By ~ 5

Author(s):

Jochen Heitger ◽

Fabian Joswig ◽

Anastassios Vladikas ◽

Christian Wittemeier

Keyword(s):

Lattice Qcd ◽

Quark Mass ◽

Numerical Evaluation ◽

Vector Current ◽

Tree Level ◽

Gauge Action ◽

Renormalization Factor ◽

Preliminary Results ◽

Renormalization Constants

We report on non-perturbative computations of the improvement coefficient cV and the renormalization factor ZV of the vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action. To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the Schrödinger functional setup, which also allow deriving a new method to extract the ratio ZS/ZP of scalar to pseudoscalar renormalization constants. We present preliminary results of a numerical evaluation of ZV and cV along a line of constant physics with gauge couplings corresponding to lattice spacings of about 0:09 fm and below, relevant for phenomenological applications.

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Nontrivial Solutions of Systems of Perturbed Hammerstein Integral Equations with Functional Terms

Mathematics ◽

10.3390/math9040330 ◽

2021 ◽

Vol 9 (4) ◽

pp. 330

Author(s):

Gennaro Infante

Keyword(s):

Fixed Point ◽

Boundary Conditions ◽

Integral Equations ◽

General Class ◽

Fixed Point Index ◽

Nontrivial Solutions ◽

Point Index ◽

Hammerstein Integral Equations ◽

Functional Boundary ◽

Functional Boundary Conditions

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the components of the system and their derivatives. The results are applicable to systems of nonlocal second order ordinary differential equations subject to functional boundary conditions, this is illustrated in an example. Our approach is based on the classical fixed point index.

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