arXiv subjects

Sebastian Steinbeißer

Publications and source records attributed to Sebastian Steinbeißer.

13 recordsLinked to original sources

arXiv2026

Strong coupling constant from the 1-loop improved static energy

The static energy is an excellent observable for extracting the strong coupling $α_s$ on the lattice. For short distances, the static energy can be calculated both on the lattice using Wilson line correlators, and with perturbation theory up to three loop accuracy with leading ultrasoft log resummation. Comparing the perturbative expression and lattice data allows for precise determination of $α_s$. We present early results for 1-loop lattice perturbation theory improvement of the Wilson loop and show how it improves the $α_s$ extraction. We present a preliminary reanalysis of the TUMQCD (2+1)-flavor QCD data.

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arXiv2025

Strong coupling in (2+1+1)-flavor QCD

The strong coupling $α_\mathrm{s}$ can be obtained from the static energy as shown in previous lattices studies. For short distances, the static energy can be calculated both on the lattice with the use of Wilson line correlators, and with the perturbation theory up to three loop accuracy with leading ultrasoft log resummation. Comparing the perturbative expression and lattice data allows for precise determination of $α_\mathrm{s}(m_Z)$. We will present preliminary results for the determination of $α_\mathrm{s} {(M_Z)}$ in (2+1+1)-flavor QCD using the configurations made availableby the MILC-collaboration with smallest lattice spacing reaching 0.0321fm.

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arXiv2023

Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects

We present results for the static energy in ($2+1+1$)-flavor QCD over a wide range of lattice spacings and several quark masses, including the physical quark mass, with ensembles of lattice-gauge-field configurations made available by the MILC Collaboration. We obtain results for the static energy out to distances of nearly $1$~fm, allowing us to perform a simultaneous determination of the scales $r_{1}$ and $r_{0}$, as well as the string tension $σ$. For the smallest three lattice spacings we also determine the scale $r_{2}$. Our results for $r_{0}/r_{1}$ and $r_{0}\sqrtσ$ agree with published ($2+1$)-flavor results. However, our result for $r_{1}/r_{2}$ differs significantly from the value obtained in the ($2+1$)-flavor case, which is most likely due to the effect of the charm quark. We also report results for $r_{0}$, $r_{1}$, and $r_{2}$ in~fm, with the former two being slightly lower than published ($2+1$)-flavor results. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest two lattices with the previously published ($2+1$)-flavor QCD results at similar lattice spacing. We find that for $r > 0.2$~fm our results on the static energy agree with the ($2+1$)-flavor result, implying the decoupling of the charm quark for these distances. For smaller distances, on the other hand, we find that the effect of the dynamical charm quark is noticeable. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects. This is the first time that the decoupling of the charm quark is observed and quantitatively analyzed on lattice data of the static energy.

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arXiv2022

Charm mass effects in the static energy computed in 2+1+1 flavor lattice QCD

We report our analysis for the static energy in (2+1+1)-flavor QCD over a wide range of lattice spacings and several quark masses. We obtain results for the static energy out to distances of nearly 1 fm, allowing us to perform a simultaneous determination of the lattice scales $r_2$, $r_1$ and $r_0$ as well as the string tension, $σ$. While our results for ${r_0}/{r_1}$ and $r_0$ $\sqrtσ$ agree with published (2+1)-flavor results, our result for ${r_1}/{r_2}$ differs significantly from the value obtained in the (2+1)-flavor case, likely due to the effect of the charm quark. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest lattices with the previously published (2+1)-flavor QCD results at similar lattice spacing. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects.

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arXiv2022

QuantumFDTD -- A computational framework for the relativistic Schrödinger equation

We extend the publicly available quantumfdtd code. It was originally intended for solving the time-independent three-dimensional Schrödinger equation via the finite-difference time-domain (FDTD) method and for extracting the ground, first, and second excited states. We (a) include the case of the relativistic Schrödinger equation and (b) add two optimized FFT-based kinetic energy terms for the non-relativistic case. All the three new kinetic terms are computed using Fast Fourier Transform (FFT). We release the resulting code as version 3 of quantumfdtd. Finally, the code now supports arbitrary external file-based potentials and the option to project out distinct parity eigenstates from the solutions. Our goal is quark models used for phenomenological descriptions of QCD bound states, described by the three-dimensional Schrödinger equation. However, we target any field where solving either the non-relativistic or the relativistic three-dimensional Schrödinger equation is required.

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arXiv2021

The Relativistic Schrödinger Equation through FFTW3: An Extension of quantumfdtd

In order to solve the time-independent three-dimensional Schrödinger equation, one can transform the time-dependent Schrödinger equation to imaginary time and use a parallelized iterative method to obtain the full three-dimensional eigenstates and eigenvalues on very large lattices. In the case of the non-relativistic Schrödinger equation, there exists a publicly available code called quantumfdtd which implements this algorithm. In this paper, we (a) extend the quantumfdtd code to include the case of the relativistic Schrödinger equation and (b) add two optimized FFT-based kinetic energy terms for non-relativistic cases. The new kinetic energy terms (two non-relativistic and one relativistic) are computed using the parallelized Fast Fourier Transform (FFT) algorithm provided by the FFTW library. The resulting quantumfdtd v3 code, which is publicly released with this paper, is backwards compatible with version 2, supporting explicit finite differences schemes in addition to the new FFT-based schemes. Finally, the original code has been extended so that it supports arbitrary external file-based potentials and the option to project out distinct parity eigenstates from the solutions. Herein, we provide details of the quantumfdtd v3 implementation, comparisons and tests of the three new kinetic energy terms, and code documentation.

hep-ph↗

arXiv2021

Chromo-electric screening length in 2+1 flavor QCD

We study Polyakov loop as well as correlators of real and imaginary parts of the Polyakov loop in 2+1 flavor QCD at finite temperature. We use hypercubic (HYP) smearing to improve the signal in the lattice calculations and to obtain reliable results for the correlators at large distances. From the large distance behavior of the correlators we estimate the chromo-electric screening length to be (0.38-44)/T. Furthermore, we show that the short distance distortions due to HYP smearing do not affect the physics of interest

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arXiv2021

The static energy in 2+1+1-flavor QCD

We report on the status of the analysis of the static energy in $2+1+1$-flavor QCD. The static energy is obtained by measuring Wilson line correlators in Coulomb gauge using the HISQ action, yielding the scales $r_{0}/a$, $r_{1}/a$, $r_{2}/a$, their ratios, and the string tension $σr_{i}^{2}$. We put emphasis on the possible effects due to the dynamical charm-quark by comparing the lattice results to continuum results of the static energy with and without a massive flavor at two-loop accuracy. We employ gauge-field ensembles from the HotQCD and MILC Collaborations.

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arXiv2019

Electric dipole transitions of $1P$ bottomonia

We compute the electric dipole transitions $χ_{bJ}(1P)\to γΥ(1S)$, with $J=0,1,2$, and $h_{b}(1P)\to γη_{b}(1S)$ in a model-independent way. We use potential non-relativistic QCD (pNRQCD) at weak coupling with either the Coulomb potential or the complete static potential incorporated in the leading order Hamiltonian. In the last case, the perturbative series shows very mild scale dependence and a good convergence pattern, allowing predictions for all the transition widths. Assuming $Λ_{\text{QCD}} \ll mv^2$, the precision that we reach is $k_γ^{3}/(mv)^{2} \times \mathcal{O}(v^{2})$, where $k_γ$ is the photon energy, $m$ is the mass of the heavy quark and $v$ its relative velocity. Our results are: $Γ(χ_{b0}(1P)\to γΥ(1S)) = 28^{+2}_{-2}~\text{keV}$, $Γ(χ_{b1}(1P)\to γΥ(1S)) = 37^{+2}_{-2}~\text{keV}$, $Γ(χ_{b2}(1P)\to γΥ(1S)) = 45^{+3}_{-3}~\text{keV}$ and $Γ(h_b(1P)\to γη_b(1S)) = 63^{+6}_{-6}~\text{keV}$.

hep-ph↗

arXiv2019

Heavy quarkonium electric dipole transitions in non-relativistic quantum field theory

In this work we use the low-energy EFT called potential non-relativistic QCD (pNRQCD) to calculate the partial decay width of different $b\bar{b}$-states undergoing an electric dipole transition at next-to-next-to leading order (NNLO). Explicitly, the $χ_{b J}$, for $J=0,1,2$, and the $h_b$ are investigated by computing the processes $χ_{b J} \to Υ+ γ$ and $h_b \to η_b + γ$. Relativistic corrections of relative order $v^2$ to the leading electric dipole operator are included. The analysis separates those contributions that account for the electromagnetic interaction terms in the pNRQCD Lagrangian, which are $v^2$ suppressed, and those that account for quarkonium state corrections of relative order $v$ and $v^2$. Within the last ones, corrections come from higher order potentials ($\frac{1}{m}$ and $\frac{1}{m^2}$ terms), and from higher order Fock states which account for the coupling of the quark-antiquark state to other low-energy degrees of freedom and thus demand non-perturbative input. Finally, the experimentally known branching fractions are used to predict the total decay with of the respective initial states.

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arXiv2018

Color screening in $2+1$ flavor QCD at large distances

We study correlation functions of spatially separated static quark-antiquark pairs in $2+1$ flavor QCD in order to investigate the nature of color screening at high temperatures. We perform lattice calculations in a wide temperature range, $116~\text{MeV} \leq T \leq 5814~\text{MeV}$, using the highly improved staggered quark (HISQ) action and several lattice spacings to control discretization effects. We alleviate the UV noise problem through the use of four dimensional hypercubic (HYP) smearing, which enables the reconstruction of correlators and determination of screening properties even at low temperatures and at large distances.

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arXiv2017

Determination of electric dipole transitions in heavy quarkonia using potential non-relativistic QCD

The electric dipole transitions $χ_{bJ}(1P)\to γΥ(1S)$ with $J=0,1,2$ and $h_{b}(1P)\to γη_{b}(1S)$ are computed using the weak-coupling version of a low-energy effective field theory named potential non-relativistic QCD (pNRQCD). In order to improve convergence and thus give firm predictions for the studied reactions, the full static potential is incorporated into the leading order Hamiltonian; moreover, we must handle properly renormalon effects and re-summation of large logarithms. The precision we reach is $k_γ^{3}/(mv)^{2} \times \mathcal{O}(v^{2})$, where $k_γ$ is the photon energy, $m$ is the mass of the heavy quark and $v$ its velocity. Our analysis separates those relativistic contributions that account for the electromagnetic interaction terms in the pNRQCD Lagrangian which are $v^{2}$ suppressed and those that account for wave function corrections of relative order $v^{2}$. Among the last ones, corrections from $1/m$ and $1/m^2$ potentials are computed, but not those coming from higher Fock states since they demand non-perturbative input and are $Λ_{\text{QCD}}^{2}/(mv)^{2}$ or $Λ_{\text{QCD}}^{3}/(m^{3}v^{4})$ suppressed, at least, in the strict weak coupling regime. These proceedings are based on the forthcoming publication \cite{steinbeisser}

hep-ph↗

arXiv2017

pNRQCD determination of E1 radiative transitions

This contribution contains the first numerical computation of the complete set of relativistic corrections of relative order $v^{2}$ for electric dipole (E1) transitions in heavy quarkonium; in particular, for the processes $χ_{bJ}(1P) \to Υ(1S) + γ$ with $J=0,\,1,\,2$. We assume that the momentum transfer of the heavy mesons involved in the reactions lies in the weak-coupling regime of the low-energy effective field theory potential non-relativistic QCD (pNRQCD) and thus a full perturbative calculation can be performed.

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