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

2018 ◽  
Vol 175 ◽  
pp. 10004 ◽  
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.

scholarly journals Determination of the charm quark mass in lattice QCD with 2 + 1 flavours on fine lattices

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jochen Heitger ◽  
Fabian Joswig ◽  
Simon Kuberski
Keyword(s):  
Lattice Qcd ◽  
Quark Mass ◽  
Charm Quark ◽  
Renormalisation Group ◽  
Tree Level ◽  
Lattice Action ◽  
Group Invariant ◽  
Quark Masses ◽  
Charm Quark Mass

Abstract We present a determination of the charm quark mass in lattice QCD with three active quark flavours. The calculation is based on PCAC masses extracted from Nf = 2 + 1 flavour gauge field ensembles at five different lattice spacings in a range from 0.087 fm down to 0.039 fm. The lattice action consists of the O(a) improved Wilson-clover action and a tree-level improved Symanzik gauge action. Quark masses are non-perturbatively O(a) improved employing the Symanzik-counterterms available for this discretisation of QCD. To relate the bare mass at a specified low-energy scale with the renormalisation group invariant mass in the continuum limit, we use the non-pertubatively known factors that account for the running of the quark masses as well as for their renormalisation at hadronic scales. We obtain the renormalisation group invariant charm quark mass at the physical point of the three-flavour theory to be Mc = 1486(21) MeV. Combining this result with five-loop perturbation theory and the corresponding decoupling relations in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme, one arrives at a result for the renormalisation group invariant charm quark mass in the four-flavour theory of Mc(Nf = 4) = 1548(23) MeV, where effects associated with the absence of a charmed, sea quark in the non-perturbative evaluation of the QCD path integral are not accounted for. In the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme, and at finite energy scales conventional in phenomenology, we quote $$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ ($$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ ; Nf = 4) = 1296(19) MeV and $$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ (3 GeV; Nf = 4) = 1007(16) MeV for the renormalised charm quark mass.

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

2014 ◽  
Author(s):  
Christian Wittemeier ◽  
Michele Della Morte ◽  
John Bulava ◽  
Jochen Heitger
Keyword(s):  
Lattice Qcd ◽  
Tree Level ◽  
Gauge Action ◽  
Wilson Fermions

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

2018 ◽  
Vol 175 ◽  
pp. 10008 ◽  
Author(s):  
Giulia Maria de Divitiis ◽  
Maurizio Firrotta ◽  
Jochen Heitger ◽  
Carl Christian Köster ◽  
Anastassios Vladikas
Keyword(s):  
Boundary Conditions ◽  
Lattice Qcd ◽  
Tree Level ◽  
Gauge Action ◽  
The Past ◽  
Functional Boundary ◽  
Functional Boundary Conditions ◽  
Mass Dependent ◽  
B Coefficients

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.

scholarly journals The renormalised $$\mathrm{O}(a)$$ improved vector current in three-flavour lattice QCD with Wilson quarks

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Jochen Heitger ◽  
◽  
Fabian Joswig
Keyword(s):  
Lattice Qcd ◽  
Gauge Coupling ◽  
Vector Current ◽  
Tree Level ◽  
Renormalisation Constant ◽  
Local Vector ◽  
The One ◽  
Smooth Dependence ◽  
Typical Range

AbstractWe present the results of a non-perturbative determination of the improvement coefficient $$c_\mathrm{V}$$ c V and the renormalisation factor $$Z_\mathrm{V}$$ Z V , which define the renormalised vector current in three-flavour $$\mathrm{O}(a)$$ O ( a ) improved lattice QCD with Wilson quarks and tree-level Symanzik-improved gauge action. In case of the improvement coefficient, we consider both lattice descriptions of the vector current, the local as well as the conserved (i.e., point-split) one. Our improvement and normalisation conditions are based on massive chiral Ward identities and numerically evaluated in the Schrödinger functional setup, which allows to eliminate finite quark mass effects in a controlled way. In order to ensure a smooth dependence of the renormalisation constant and improvement coefficients on the bare gauge coupling, our computation proceeds along a line of constant physics, covering the typical range of lattice spacings $$0.04\,\mathrm{fm}\lesssim a\lesssim 0.1\,\mathrm{fm}$$ 0.04 fm ≲ a ≲ 0.1 fm that is useful for phenomenological applications. Especially for the improvement coefficient of the local vector current, we report significant differences between the one-loop perturbative estimates and our non-perturbative results.

scholarly journals Non-perturbative improvement of the axial current in Nf=3 lattice QCD with Wilson fermions and tree-level improved gauge action

2015 ◽  
Vol 896 ◽  
pp. 555-568 ◽  
Author(s):  
John Bulava ◽  
Michele Della Morte ◽  
Jochen Heitger ◽  
Christian Wittemeier
Keyword(s):  
Lattice Qcd ◽  
Axial Current ◽  
Tree Level ◽  
Gauge Action ◽  
Wilson Fermions

scholarly journals Determination of the renormalized heavy-quark mass in lattice QCD

1996 ◽  
Vol 477 (2) ◽  
pp. 489-520 ◽  
Author(s):  
A. Bochkarev ◽  
Ph. de Forcrand
Keyword(s):  
Lattice Qcd ◽  
Heavy Quark ◽  
Quark Mass ◽  
Heavy Quark Mass

SPECTROSCOPY OF LIGHT HADRONS ON ANISOTROPIC LATTICES

2006 ◽  
Vol 21 (26) ◽  
pp. 5253-5274
Author(s):  
FRANK X. LEE
Keyword(s):  
Mass Spectrum ◽  
Lattice Qcd ◽  
Excited States ◽  
Ground State ◽  
Quark Mass ◽  
Tree Level ◽  
Mass Dependence ◽  
Anisotropic Lattices ◽  
Quark Mass Dependence ◽  
The Masses

The mass spectrum of spin-1/2 baryons in both parity channels is computed using the methods of lattice QCD in the quenched approximation. An anisotropic action with anisotropy as/at = 3 is employed, using tree-level coefficients with tadpole improvement. Clear splittings from the nucleon ground state are observed with smeared operators and 500 configurations. Methods for extracting the first excited states are investigated. Using the quark mass dependence of the masses, qualitative comparisons are made with previous calculations and experiment.

scholarly journals Exact results for $$ {Z}_m^{\mathrm{OS}} $$ and $$ {Z}_2^{\mathrm{OS}} $$ with two mass scales and up to three loops

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Matteo Fael ◽  
Kay Schönwald ◽  
Matthias Steinhauser
Keyword(s):  
Wave Function ◽  
Quark Mass ◽  
Numerical Evaluation ◽  
Large Mass ◽  
Equal Mass ◽  
Exact Results ◽  
Loop Order ◽  
Wave Function Renormalization ◽  
Shell Mass ◽  
Renormalization Constants

Abstract We consider the on-shell mass and wave function renormalization constants $$ {Z}_m^{\mathrm{OS}} $$ Z m OS and $$ {Z}_2^{\mathrm{OS}} $$ Z 2 OS up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters $$ \sqrt{1-{\tau}^2} $$ 1 − τ 2 and $$ \sqrt{1-{\tau}^2}/\tau $$ 1 − τ 2 / τ which extends the findings from ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order $$ \mathcal{O} $$ O (ϵ2) and $$ \mathcal{O} $$ O (ϵ) at two- and three-loop order which are crucial ingredients for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.

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

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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