arXiv subjects

Jochen Heitger

Publications and source records attributed to Jochen Heitger.

At least 19 recordsLinked to original sources

arXiv2026

Precision renormalisation and improvement of $N_{\rm f}=3$ lattice QCD with Wilson fermions

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 Schr\"odinger functional boundary conditions and resolutions $8\leq L/a\leq 64$ to lines of constant physics with massless quarks and fixed gradient flow coupling $\bar{g}_\mathrm{GF}^2(L_i),\; i=0,1,2$, corresponding to $L_0 \approx 0.25$ 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 $Z_{\rm A}$, 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 $Z_{\rm A},Z_{\rm V}$. We provide an explanation for the strong suppression of their statistical variances.

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arXiv2026

Heavy quark masses from step-scaling

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.

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arXiv2026

Ground-State Extraction of Heavy-Light Meson Semileptonic Decay Form Factors

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 $\mbox{O}(a)$-improved Wilson fermions (presently) at the $\mathrm{SU}(3)$-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 $B \to \pi \ell \nu$ and $B_s \to K \ell \nu$ semileptonic form factors, combining the continuum-limit relativistic results with static-limit calculations.

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arXiv2025

$\mathrm{O}(a)$ improvement of the flavour singlet scalar density in a setup with Wilson fermions

We report on our Ward identity determination of the $\mathrm{O}(a)$ improvement coefficient for the flavour singlet scalar density, namely $g_\mathrm{S}$, from three-flavour lattice QCD with Wilson-clover fermions and the tree-level Symanzik improved gauge action. We employ five couplings, $g_0^2 \in [1.5,1.77]$, that cover the range used in large-volume CLS simulations. While $g_\mathrm{S}$ itself is for instance relevant for the $\mathrm{O}(a)$ improvement of meson and baryon sigma terms, a relation to $b_\mathrm{g}$, the $\mathrm{O}(a)$ improvement parameter of the gauge coupling, can also be established, allowing for its non-perturbative extraction as well. With Wilson fermions, $b_\mathrm{g}$ is in principle required for full $\mathrm{O}(a)$ improvement at non-vanishing sea quark masses. We outline our procedure for extracting $b_\mathrm{g}$.

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arXiv2024

The hadronic decay of vector charmonium

The extraction of decay parameters using lattice techniques is a computationally expensive task, requiring several volumes and group irreps to relate the spectrum on a lattice simulation to the infinite volume scattering. In this project we employ an alternative method based on a narrow-width approximation to extract the hadronic mixing $<\bar{D}D|\psi(3770)>$, which is needed to compute the decay $\Gamma(\psi(3770)\to\bar{D}D)$ between the second excited state of vector charmonium and a pair of $D$-mesons in a $p$-wave. We carry out our lattice simulations on two CLS ensembles at $m_\pi \sim 440~\text{MeV}$ and $a\sim 0.066~\text{fm}$ and obtain results compatible with experiment. Furthermore, we interpret our results analytically using the ${}^3P_0$ quark model.

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arXiv2024

Hadronic decay of vector charmonium from the lattice

Estimating decay parameters in lattice simulations is a computationally demanding problem, requiring several volumes and momenta. We explore an alternative approach, where the transition amplitude can be extracted from the spectral decomposition of particular ratios built from correlation functions. This so-called ratio method has the advantage of not needing various irreducible representations or volumes, and it allows us to predict the decay width $\Gamma$ and the energy shift $\epsilon$ of the spectrum directly. In this work, we apply this method to study the hadronic decay $\psi(3770)\to \bar{D}D$ on two CLS $N_\text{f}=2$ ensembles. This approach requires close to on-shell kinematics to work, and we employ twisted boundary conditions to precisely tune the on-shell point. Although our study is yet to approach the continuum limit, we find a value of $\Gamma$ fully compatible to the physical result, and $\epsilon$ informs us by how much our spectrum would shift in a fully dynamical simulation. Besides lattice calculations, many analytical tools have been proposed to understand decay processes. A relatively simple, early example is the ${}^3P_0$ quark model, which provides a physical insight of the decay process.

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arXiv2024

$\mathrm{D}$ and $\mathrm{D_s}$ decay constants in $N_{\rm f}=2+1$ QCD with Wilson fermions

We present results for the leptonic decay constants of the D and D$_{\rm s}$ mesons from $N_{\rm f}=2+1$ lattice QCD. We employ a set of 49 high statistics gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort utilising non-perturbatively improved Wilson fermions and the tree-level Symanzik improved gauge action at six values of the lattice spacing in the range $a = 0.098\,$fm down to $a = 0.039\,$fm, with pion masses varying from around $420\,$MeV down to below the physical point. The ensembles lie on three trajectories in the quark mass plane, two trajectories intersecting close to the physical quark mass point and the third one approaching the SU(3) chiral limit, enabling tight control of the light and strange quark mass dependence. We obtain $f_{\mathrm{D_s}}=246.8(1.3)\,$MeV, $f_\mathrm{D}=208.4(1.5)\,$MeV and $f_{\mathrm{D_s}}/f_\mathrm{D}=1.1842(36)$, where the precision of our results is mostly limited by the determination of the scale.

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arXiv2024

Optimized Distillation Profiles for Heavy-Light Spectroscopy

It has been demonstrated that distillation profiles can be employed to build optimized quarkonium interpolators for spectroscopy calculations in lattice QCD. We test their usefulness for heavy-light systems on (3+1)-flavor ensembles with mass-degenerate light and a charm quark in the sea in preparation for a future $D\bar{D}$-scattering analysis. The additional cost of light inversions naturally leads to the question if knowledge of optimal profiles can be used to avoid superfluous computations. We show such optimal profiles for different lattice sizes and pion masses and discuss general trends. Furthermore, we discuss the handling of momenta in this framework.

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arXiv2024

Towards charm physics with stabilised Wilson fermions

We report on a first study towards the use of stabilised Wilson fermions in heavy flavour physics. In particular, we are interested in fixing the charm quark mass via various physical observables and to inspect cut-off effects arising from different choices. This is done on large-volume OpenLat ensembles with periodic boundary conditions. Two different ways of fixing the charm quark mass are explored, namely using the mass of the $D$- and $\eta_{\rm c}$-meson as physical inputs. We furthermore give an update on our determination of the non-singlet axial current improvement coefficient $c_{\rm A}$.

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arXiv2023

A strategy for B-physics observables in the continuum limit

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, $m_{\rm charm}$ to $m_{\rm bottom}$. All quantities are first continuum extrapolated and then interpolated in $1/m_h=1/m_{\rm heavy}$. Large volume computations are combined with finite volume ones where a relativistic bottom quark is accessible with small $am_{\rm bottom}$. 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 $m_h\to\infty$ is approached with power corrections O$(1/m_h)$ only. Perturbative corrections $\sim\alpha_s(m_h)^{\gamma+n}$ 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].

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arXiv2023

$m_B$ and $f_{B^{(\star)}}$ in $2+1$ flavour QCD from a combination of continuum limit static and relativistic results

We present preliminary results for B-physics from a combination of non-perturbative results in the static limit with relativistic computations satisfying $am_{\mathrm{heavy}}\ll 1$. Relativistic measurements are carried out at the physical b-quark mass using the Schr\"{o}dinger Functional in a $0.5 \ \mathrm{fm}$ 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 $\alpha_s(m_{\mathrm{heavy}})^{n+\gamma}$ 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.

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arXiv2023

Sigma terms of the baryon octet in $N_\mathrm{f} = 2+1$ QCD with Wilson quarks

A lot of progress has been made in the direct determination of nucleon sigma terms. Using similar methods, we consider the sigma terms of the other octet baryons as well. These are determined on CLS gauge field ensembles employing the L\"uscher-Weisz gluon action and the Sheikholeslami-Wohlert fermion action with $N_\mathrm{f} = 2 + 1$. The ensembles have pion masses ranging from ${410}\,\mathrm{MeV}$ down to the physical value and lattice spacings covering a range between ${0.098}\,\mathrm{fm}$ and ${0.039}\,\mathrm{fm}$. We present some preliminary results for the pion and strange sigma terms and compare to indirect determinations. To do so, we discuss multi-state fits to tackle the well-known problem of excited state contamination comparing the ratio and summation methods also including priors.

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arXiv2022

On improvement of the axial-vector current with stabilised Wilson fermions

We report on the determination of the improvement coefficient $c_{\rm A}$ for the non-singlet axial-vector current $A^{a}_{\mu}(x)$ in the framework of stabilised Wilson-Clover fermions within three flavour lattice QCD. This is done by requiring the PCAC relation to hold for two different pseudo-scalar states. To generate these states, wavefunctions altering spatial structures on the boundaries of a Schr\"odinger functional lattice are employed and some variations of the (previously applied) wavefunction method are explored. The improvement coefficient is determined on a few ensembles for a range of gauge couplings that is potentially useful for future applications. Preliminary results on the renormalisation constants $Z_{\rm V}$ for the vector current and $Z_{\rm A}$ for the axial-vector current are also presented.

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arXiv2022

Direct access to hadronic decay parameters with twisted boundary conditions

Our exploratory study looks for direct access to the resonant hadronic transition amplitude without resorting to the L\"uscher formalism. We study the decay $\Psi(3770)\to\bar{D}D$ by applying partially twisted boundary conditions to the quenched charm quark, circumventing possible problems with final state interactions. If successful, we could compute the dependence of the transition amplitude on the charm-quark mass and test the predictions made by phenomenological quark-pair-creation models. Finally, we study if and to what extent an extraction of the excited state $\Psi(3770)$ is necessary for this analysis.

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arXiv2022

A lattice QCD perspective on weak decays of b and c quarks Snowmass 2022 White Paper

Lattice quantum chromodynamics has proven to be an indispensable method to determine nonperturbative strong contributions to weak decay processes. In this white paper for the Snowmass community planning process we highlight achievements and future avenues of research for lattice calculations of weak $b$ and $c$ quark decays, and point out how these calculations will help to address the anomalies currently in the spotlight of the particle physics community. With future increases in computational resources and algorithmic improvements, percent level (and below) lattice determinations will play a central role in constraining the standard model or identifying new physics.

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arXiv2021

Towards the determination of sigma terms for the baryon octet on $N_\mathrm{f} = 2+1$ CLS ensembles

A lot of progress has been made in the determination of nucleon sigma terms. In this work we consider the sigma terms of the other octet baryons as well. These are determined on CLS gauge field ensembles employing the L\"uscher-Weisz gluon action and the Sheikholeslami-Wohlert fermion action with $N_\mathrm{f} = 2 + 1$. The ensembles have pion masses ranging from ${410}\,\mathrm{MeV}$ down to the physical value and lattice spacings covering a range between ${0.09}\,\mathrm{fm}$ and ${0.04}\,\mathrm{fm}$. We present some preliminary results for $a\approx 0.06$ fm along a trajectory where the sum of the sea quark masses is kept constant, focusing on the quark mass dependence. We discuss multi-state fits to tackle the well-known problem of excited state contamination and detail how we analyse connected and disconnected contributions.

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arXiv2021

$B_s \to D^{(*)}_s$ form factors from lattice QCD with ${ N_f}=2$ Wilson-clover quarks

We report on a two-flavour lattice QCD determination of the $B_s\to D_s$ and $B_s\to D_s^*$ transitions, which in the heavy quark limit can be parameterised by the form factors $\mathcal{G}$, and $h_{\text A_1}$, $h_{\text A_2}$ and $h_{\text A_3}$. In the search of New Physics through tests of lepton-flavour universality, $B_s$ decay channels are complementary to $B$ decays and widely studied at $B$ factories and LHCb. The purpose of our study is to explore a suitable method to extract form factors associated with $b\to c$ currents from lattice QCD. In particular, we present numerical results for $\mathcal{G}$ and $h_{\text A_1}$.

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arXiv2021

Precision $B^*B\pi$ coupling from three-flavor lattice QCD

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.

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