We renormalise (and improve) the flavour non-singlet axial current, pseudo-scalar density, vector current and tensor current, as well as quark masses, in O(a) improved lattice QCD with three massless flavours and lattice spacings down to 0.01 fm. To this end, we tune a number of lattices with Schrödinger functional boundary conditions and resolutions 8≤ L/a≤ 64 to lines of constant physics with massless quarks and fixed gradient flow coupling g̅_GF^2(L_i), i=0,1,2, corresponding to L_0 ≈ 0.25 fm, L_1=2L_0 and L_2=4L_0. We further renormalise and improve the quark mass of additional heavy quarks for use in the B-physics programme of the collaboration (arXiv:2312.09811). Our somewhat technical results enable first-principles strategies for solving multi-scale problems involving, e.g., the b-quark mass (arXiv:2312.10017) or a large temperature (arXiv:2501.11603). Comparing also to other determinations of the axial current renormalisation constant Z_ A, we have a precise confirmation of how renormalisation and the restoration of chiral symmetry work out with Wilson fermions at small a. In particular, the accurate restoration of chiral symmetry and the exact flavour symmetry lead to practically negligible uncertainties in observables determined from Ward identities: four to five significant digits are achieved for Z_ A,Z_ V. We provide an explanation for the strong suppression of their statistical variances.

We present a determination of the charm- and bottom-quark masses using the heavy-quark step-scaling strategy. Renormalization is performed in small volumes where relativistic bottom quarks can be simulated directly. A sequence of finite-volume simulations connects this calculation to large-volume CLS ensembles, where simulations at physical light and strange quark masses provide reliable control over low-energy hadronic physics. In all but the smallest volume, the B-scale is reached by interpolating between relativistic heavy-quark data and the static limit. The resulting quark masses are obtained with good precision, with subdominant systematic uncertainties that differ from, and thus complement, those of standard large-volume determinations.

We discuss the extraction of heavy-light pseudo-scalar to light pseudo-scalar decay form factors from finite time correlation functions. We place particular emphasis on the contamination from excited states employing summed ratios and input from chiral perturbation theory. The analysis is performed on four CLS ensembles with N_f = 2+1 flavours of (a)-improved Wilson fermions (presently) at the SU(3)-symmetric point with relativistic heavy-quark masses in the charm region and above. The study presented here is part of the analysis aimed at the computation of the B → πℓ ν and B_s → K ℓ ν semileptonic form factors, combining the continuum-limit relativistic results with static-limit calculations.

In this proceeding contribution we discuss the status and progress towards a modernised and extended International Lattice Data Grid (ILDG), which has seen major developments, updates, and upgrades over the last year. In particular, metadata and file schemata have been extended. Moreover, the registration and authentication services have been modernised, and the file and metadata catalogues re-implemented.

We discuss how to perform interpolations between relativistic and static computations in order to extract heavy-light B-physics observables in the continuum. This strategy can be carried out entirely in large volume, but its predictivity is enhanced by the following step scaling approach. Relativistic computations are carried out at the physical b-quark mass using the Schrödinger Functional in a box, where small $am$ is accessible. They are connected to large volume observables through step scaling functions that trace the mass dependence between the physical charm region and the static limit, such that B-physics results can be obtained by interpolation. We discuss the extraction of relativistic large volume observables entering the computation, focusing on leptonic and semi-leptonic transition amplitudes. We review in detail our numerical results first presented in [1] for leptonic decays from CLS $N_f=2+1$ ensembles at $m_u=m_d=m_s$, and with five values of the lattice spacing down to $0.039 \ \mathrm{fm}$.

In a somewhat forgotten paper [1] it was shown how to perform interpolations between relativistic and static computations in order to obtain results for heavy-light observables for masses from, say, m_ charm to m_ bottom. All quantities are first continuum extrapolated and then interpolated in 1/m_h=1/m_ heavy. Large volume computations are combined with finite volume ones where a relativistic bottom quark is accessible with small am_ bottom. We discuss how this strategy is extended to semi-leptonic form factors and other quantities of phenomenological interest. The essential point is to form quantities where the limit m_h→∞ is approached with power corrections O(1/m_h) only. Perturbative corrections ∼α_s(m_h)^γ+n are cancelled in the construction of the observables. We also point out how such an approach can help to control systematics in semi-leptonic decays with just large volume data. First numerical results with N_f = 2 + 1 and lattice spacings down to 0.039 fm are presented in [2].

The International Lattice Data Grid (ILDG) is a community-wide initiative to realize the sharing of primary data from lattice QCD simulations according to the principles of FAIR data. We recall the basic concepts of ILDG as a federation of autonomous regional grids with common standards for (meta-)data and services, and report on current activities, progress, and plans to restore and extend the usability of ILDG.

We present preliminary results for B-physics from a combination of non-perturbative results in the static limit with relativistic computations satisfying am_heavy≪ 1. Relativistic measurements are carried out at the physical b-quark mass using the Schrödinger Functional in a 0.5 fm box. They are connected to large volume observables through step scaling functions that trace the mass dependence between the physical charm region and the static limit, such that B-physics results can be obtained by interpolation; the procedure is designed to exactly cancel the troublesome α_s(m_heavy)^n+γ corrections to large mass scaling. Large volume computations for both static and relativistic quantities use CLS N_f=2+1 ensembles at m_u=m_d=m_s, and with five values of the lattice spacing down to 0.039 fm. Our preliminary results for the b-quark mass and leptonic decay constants have competitive uncertainties, which are furthermore dominated by statistics, allowing for substantial future improvement. Here we focus on numerical results, while the underlying strategy is discussed in a companion contribution.

PUNCH4NFDI (Particles, Universe, NuClei and Hadrons for the NFDI) aims at developing concepts and tools for the efficient management of digital research products in fundamental physics research. At the heart of the research products are scientific data sets that should be made interoperable and available to a broad scientific community and the public for a sustainable usage (“open data”). The first PUNCH4NFDI “Open Data Workshop” gave the opportunity for an initial survey of existing and planned open data initiatives within the PUNCH science field. The paper addresses the conceptual differences and commonalities of the participating communities presented in the workshop. Existing open data collections were presented and discussed. This is an inquiry into the community’s requirements for a better use of open data and in this context also of “Open Science”.

We consider three-flavor QCD and perform a determination of the low-energy coupling $\hat{g}_\chi$ of SU(2) Heavy Meson Chiral Perturbation Theory. It is the $B^*B\pi$ coupling in the limit of static heavy and chiral light quarks and has not been determined with precision thus far. The calculation is performed on a large set of the $2+1$ flavor CLS ensembles with pion masses from 420 MeV down to 130 MeV. This allows us to significantly reduce the systematic uncertainty from the chiral extrapolation compared to previous works. Only a weak dependence on the lattice spacing is visible in our results.

We discuss the extraction of the ground state 〈K(p)|Vμ(0)|Bs(0)〉 matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings 0.075, 0.05 fm and pion masses 330, 270 MeV are used from the O(a)-improved CLS 2-flavour simulations and the final state momentum is |p| = 0.5 GeV. The b-quark is treated in HQET including the 1/mb corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is not limited by the 1/mb corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

We discuss the extraction of the ground state < K(p)vertical bar V-mu(0)vertical bar B-s(0)> matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings 0.075, 0.05 fm and pion masses 330, 270 MeV are used from the O(a)-improved CLS 2-flavor simulations and the final state momentum is vertical bar p vertical bar = 0.5 GeV. The b-quark is treated in HQET including the 1/m(b) corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is not limited by the 1/m(b) corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

We discuss the extraction of the ground state ⟨K ( p)|V_μ(0)|B ( 0)⟩ matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings 0.075, 0.05 fm and pion masses 330, 270 MeV are used from the O(a)- improved CLS 2-flavour simulations and the final state momentum is | p|=0.5 GeV. The b-quark is treated in HQET including the 1/m_b corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2 1/m_b corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

We discuss the extraction of the ground state [Formula: see text] matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings 0.075, 0.05 fm and pion masses 330, 270 MeV are used from the O[Formula: see text]-improved CLS 2-flavor simulations and the final state momentum is [Formula: see text] GeV. The b-quark is treated in HQET including the [Formula: see text] corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is not limited by the [Formula: see text] corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

We compute semi-leptonic Bs decay form factors using Heavy Quark Effective Theory on the lattice. To obtain good control of the 1 /mb expansion, one has to take into account not only the leading static order but also the terms arising at O (1/mb): kinetic, spin and current insertions. We show results for these terms calculated through the ratio method, using our prior results for the static order. After combining them with non-perturbative HQET parameters they can be continuum-extrapolated to give the QCD form factor correct up to O (1/mb2) corrections and without O (αs(mb)n) corrections.

We present a lattice determination of the Λ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from 0.2 to 70 GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain Λ_{MS[over ¯]}^{(3)}=341(12)  MeV. The nonperturbative running up to very high energies guarantees that systematic effects associated with perturbation theory are well under control. Using the four-loop prediction for Λ_{MS[over ¯]}^{(5)}/Λ_{MS[over ¯]}^{(3)} yields α_{MS[over ¯]}^{(5)}(m_{Z})=0.11852(84).

Based on a non-perturbative matching strategy between Heavy Quark Effective Theory (HQET) at O(1/m_h) and finite-volume QCD, we report on our determination of the effective theory parameters of all components of the HQET heavy-light axial and vector currents in two-flavour lattice QCD. These parameters, which can be fixed by matching conditions between suitable QCD and HQET observables evaluated through numerical simulations, are required to absorb the power divergences of lattice HQET, as, for instance, encountered in an effective theory computation of form factors for semi-leptonic decays of B- and B_s-mesons.

We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at α∼>0.2 and at the same time has the physical scales small compared to the cutoff 1/a in all stages of the computation. The result ΛMS‾(3)=332(14)MeV is translated to αMS‾(mZ)=0.1179(10)(2) by use of (high order) perturbative relations between the effective theory couplings at the charm and beauty quark “thresholds”. The error of this perturbative step is discussed and estimated as 0.0002.

Mattia Bruno, Mattia Dalla Brida, Patrick Fritzsch, Tomasz Korzec, Alberto Ramos, Stefan Schaefer, Hubert Simma, Stefan Sint, and Rainer Sommer 7 Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA Dipartimento di Fisica, Università di Milano-Bicocca and INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland Department of Physics, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany John von Neumann Institute for Computing (NIC), DESY, Platanenallee 6, 15738 Zeuthen, Germany School of Mathematics and Hamilton Mathematics Institute, Trinity College Dublin, Dublin 2, Ireland Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany (Dated: July 13, 2017)