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

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.

Download Full-text

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

EPJ Web of Conferences ◽

10.1051/epjconf/201817510008 ◽

2018 ◽

Vol 175 ◽

pp. 10008 ◽

Cited By ~ 2

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.

Download Full-text

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

Journal of High Energy Physics ◽

10.1007/jhep05(2021)288 ◽

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.

Download Full-text

Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $$N_\mathrm {f}=3$$ QCD with Wilson quarks

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09387-z ◽

2021 ◽

Vol 81 (7) ◽

Author(s):

Jochen Heitger ◽

Fabian Joswig ◽

Pia L. J. Petrak ◽

Anastassios Vladikas

Keyword(s):

Quark Mass ◽

Tree Level ◽

Lattice Action ◽

Quark Masses ◽

Current Quark Mass ◽

Functional Boundary ◽

Normalisation Factor ◽

Functional Boundary Conditions ◽

Current Quark ◽

Wilson Fermions

AbstractWe determine non-perturbatively the normalisation factor $$r_{\mathrm{m}}\equiv Z_{\mathrm{S}}/Z_{\mathrm{S}}^{0}$$ r m ≡ Z S / Z S 0 , where $$Z_{\mathrm{S}}$$ Z S and $$Z_{\mathrm{S}}^{0}$$ Z S 0 are the renormalisation parameters of the flavour non-singlet and singlet scalar densities, respectively. This quantity is required in the computation of quark masses with Wilson fermions and for instance the renormalisation of nucleon matrix elements of scalar densities. Our calculation involves simulations of finite-volume lattice QCD with the tree-level Symanzik-improved gauge action, $$N_{\mathrm{f}}= 3$$ N f = 3 mass-degenerate $${\mathrm{O}}(a)$$ O ( a ) improved Wilson fermions and Schrödinger functional boundary conditions. The slope of the current quark mass, as a function of the subtracted Wilson quark mass is extracted both in a unitary setup (where nearly chiral valence and sea quark masses are degenerate) and in a non-unitary setup (where all valence flavours are chiral and the sea quark masses are small). These slopes are then combined with $$Z \equiv Z_{\mathrm{P}}/(Z_{\mathrm{S}}Z_{\mathrm{A}})$$ Z ≡ Z P / ( Z S Z A ) in order to obtain $$r_{\mathrm{m}}$$ r m . A novel chiral Ward identity is employed for the calculation of the normalisation factor Z. Our results cover the range of gauge couplings corresponding to lattice spacings below $$0.1\,$$ 0.1 fm, for which $$N_{\mathrm{f}}= 2+1$$ N f = 2 + 1 QCD simulations in large volumes with the same lattice action are typically performed.

Download Full-text

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

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09037-4 ◽

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.

Download Full-text

Determination of quark masses from nf=4 lattice QCD and the RI-SMOM intermediate scheme

Physical Review D ◽

10.1103/physrevd.98.014513 ◽

2018 ◽

Vol 98 (1) ◽

Cited By ~ 12

Author(s):

A. T. Lytle ◽

C. T. H. Davies ◽

D. Hatton ◽

G. P. Lepage ◽

C. Sturm ◽

...

Keyword(s):

Lattice Qcd ◽

Quark Masses

Download Full-text

Non-perturbative determination of improvement coefficients $$b_\mathrm{m}$$ and $$b_\mathrm{A}-b_\mathrm{P}$$ and normalisation factor $$Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$$ with $$N_\mathrm{f}= 3$$ Wilson fermions

The European Physical Journal C ◽

10.1140/epjc/s10052-019-7287-1 ◽

2019 ◽

Vol 79 (9) ◽

Cited By ~ 2

Author(s):

Giulia Maria de Divitiis ◽

Patrick Fritzsch ◽

Jochen Heitger ◽

Carl Christian Köster ◽

Simon Kuberski ◽

...

Keyword(s):

Large Volume ◽

Quark Mass ◽

Gauge Coupling ◽

Perturbative Calculation ◽

Quark Masses ◽

Functional Scheme ◽

Normalisation Factor ◽

Mass Renormalisation ◽

Wilson Fermions

Abstract We determine non-perturbatively the normalisation parameter $$Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$$ZmZP/ZA as well as the Symanzik coefficients $$b_\mathrm{m}$$bm and $$b_\mathrm{A}-b_\mathrm{P}$$bA-bP, required in $$\mathrm{O}(a)$$O(a) improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in $$N_\mathrm{f}=3$$Nf=3 QCD with $$\mathrm{O}(a)$$O(a) improved massless sea and non-degenerate valence quarks in the finite-volume Schrödinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume $$N_\mathrm{f}=2+1$$Nf=2+1 QCD simulations with Wilson fermions at lattice spacings below $$0.1\,\mathrm{fm}$$0.1fm, are of particular use for the non-perturbative calculation of $$\mathrm{O}(a)$$O(a) improved renormalised quark masses.

Download Full-text

PHASE DIAGRAM OF THE STRONG INTERACTION SYSTEM FROM LATTICE QCD

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194511000079 ◽

2011 ◽

Vol 01 ◽

pp. 28-33

Author(s):

SEYONG KIM

Keyword(s):

Phase Diagram ◽

Thermodynamic Properties ◽

Lattice Qcd ◽

Strong Interaction ◽

Accurate Determination ◽

Baryon Density ◽

Quark Masses ◽

Interaction System ◽

Sign Problem

We briefly review recent progresses in studying QCD thermodynamics from lattice QCD. Investigation of QCD in zero baryon density shows a rapid cross-over with realistic (u, d, s) quark masses. Various improvements of lattice QCD action leads to more accurate determination of QCD thermodynamic properties. Although simulating QCD in non-zero baryon density is difficult due to "sign problem", steady progress is also achieved.

Download Full-text

Baryon interactions from lattice QCD with physical masses — strangeness S = -1 sector —

EPJ Web of Conferences ◽

10.1051/epjconf/201817505030 ◽

2018 ◽

Vol 175 ◽

pp. 05030 ◽

Cited By ~ 14

Author(s):

Hidekatsu Nemura ◽

Sinya Aoki ◽

Takumi Doi ◽

Shinya Gongyo ◽

Tetsuo Hatsuda ◽

...

Keyword(s):

Lattice Qcd ◽

Large Volume ◽

Correlation Functions ◽

Large Scale ◽

Phase Shifts ◽

Quark Masses ◽

Scattering Phase ◽

Scattering Phase Shifts ◽

Computer Resources ◽

Comprehensive Study

We present our recent results of baryon interactions with strangeness S = −1 based on Nambu-Bethe-Salpeter (NBS) correlation functions calculated fromlattice QCD with almost physical quark masses corresponding to (mk,mk) ≈ (146, 525) MeV and large volume (La)4 ≈ (96a)4 ≈ (8.1 fm)4. In order to perform a comprehensive study of baryon interactions, a large number of NBS correlation functions from NN to ΞΞ are calculated simultaneously by using large scale computer resources. In this contribution, we focus on the strangeness S = −1 channels of the hyperon interactions by means of HAL QCD method. Four sets of three potentials (the 3S1 − 3 D1 central, 3S1 − 3 D1 tensor, and the 1S0 central potentials) are presented for the ∑N − ∑N (the isospin I = 3/2) diagonal, the ∧N − ∧N diagonal, the ∧N → ∑N transition, and the ∑N − ∑N (I = 1/2) diagonal interactions. Scattering phase shifts for ∑N (I = 3/2) system are presented.

Download Full-text

Recent highlights with baryons from lattice QCD

EPJ Web of Conferences ◽

10.1051/epjconf/202024102004 ◽

2020 ◽

Vol 241 ◽

pp. 02004

Author(s):

Colin Morningstar

Keyword(s):

Lattice Qcd ◽

Percent Level ◽

Form Factors ◽

Distribution Functions ◽

Electromagnetic Form Factors ◽

Parton Distribution Functions ◽

Quark Masses ◽

Proton Mass ◽

Key Points

Highlights from recent computations in lattice QCD involving baryons are presented. Calcula tions of the proton mass and spin decompositions are discussed, a percent level determination of the nucleon axial coupling is described, and determinations of the proton and neutron electromagnetic form factors and light-cone parton distribution functions are outlined. Recent results applying the so-called Luscher method to meson-baryon systems are presented. Key points emphasized are that much better precision with disconnected diagrams is being achieved, incorporating multi-hadron operators is now feasible, and more and more studies are being done with physical quark masses.

Download Full-text