arXiv subjects

Nikolai Husung

Publications and source records attributed to Nikolai Husung.

14 recordsLinked to original sources

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 $B \to π\ell ν$ and $B_s \to K \ell ν$ semileptonic form factors, combining the continuum-limit relativistic results with static-limit calculations.

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arXiv2025

opbasis -- a Python package to derive minimal operator bases

Finding a complete and yet minimal on-shell basis of operators of a given mass-dimension that are compatible with a specific set of transformation properties is the first step in any Effective Field Theory description. This step is the main bottleneck for systematic studies of leading logarithmic corrections to integer-power lattice artifacts in Symanzik Effective Field Theory targeting various local fields and lattice actions. The focus on discrete symmetry transformations in lattice field theory, especially reduced hypercubic spacetime symmetry with Euclidean signature, complicates the use of standard continuum field theory tools. Here, a new Python package is being presented that targets the typical lattice field-theorist's use cases. While the main target lies on continuum EFTs describing 4D non-Abelian lattice gauge theories, the applicability can be extended beyond Effective Field Theories. New discrete symmetries, twisted masses, or the introduction of boosts are just a few examples of possible extensions that can be easily implemented by the user. This should allow for a wider range of theories and applications beyond the initial focus of this package. The general functionality of the package is explained along the lines of three examples: The $\mathrm{O}(a)$ operator basis of the axial-vector in Wilson QCD, operator bases compatible with the symmetries of unrooted Staggered quarks as well as a pedestrian derivation of a $B^*(\mathbf{p})π(-\mathbf{p})$ operator with pseudo-scalar quantum numbers. Each example makes use of an increasing range of features and requires user-defined extensions show-casing the versatility of the package.

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arXiv2025

Logarithmic corrections to O($a^2$) effects in lattice QCD with unrooted Staggered quarks

We derive the asymptotic lattice-spacing dependence $a^2[2b_0\bar{g}^2(1/a)]^{\hatγ_i}$ relevant for spectral quantities of lattice QCD, when using unrooted Staggered quarks. Without taking any effects from matching into account we find $\min_i\hatγ_i\approx -0.273, -0.301, -0.913, -2.614$ for $N_\mathrm{f}=0,4,8,12$ respectively. Common statements in the literature on the absence of mass-dimension~5 operators from the on-shell basis of the Symanzik Effective Field Theory action are being clarified for a description using strictly local tastes, here playing the role of continuum quark flavours. Potential impact of $\mathrm{O}(a)$ EOM-vanishing terms beyond spectral quantities is being discussed.

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arXiv2025

SymEFT for local tastes of staggered lattice QCD

The applicability of Symanzik Effective Field Theory (SymEFT) for the description of lattice artifacts assumes a local formulation of the lattice theory. We discuss the symmetries realised by tastes local in spacetime of unrooted staggered quarks, approaching mass-degenerate 4-flavour QCD in the continuum limit. An outlook on some implications for the asymptotic lattice-spacing dependence is given for spectral quantities as well as local composite fields.

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arXiv2024

The asymptotic approach to the continuum of lattice QCD spectral observables

We consider spectral quantities in lattice QCD and determine the asymptotic behavior of their discretization errors. Wilson fermion with O$(a)$-improvement, (Möbius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height $M_5=1+{\rm O}(g_0^2)$ have the same, approximate, form of the asymptotic cutoff effects: $ K\,a^2\left[\bar g^2(a^{-1})\right]^{0.760}$. A domain wall height $M_5=1.8$, as often used, introduces large mass-dependent $K'(m)\,a^2\left[\bar g^2(a^{-1})\right]^{0.518}$ effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is included. For their mass-dependent cutoff effects we have information on the exponents $\hatΓ_i$ of $\bar g^2(a^{-1})$ but not for the pre-factors. For staggered fermions there is only partial information on the exponents. We propose that tree-level ${\rm O}(a^2)$ improvement, which is easy to do [2], should be used in the future -- both for the fermion and the gauge action. It improves the asymptotic behavior in all cases.

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arXiv2024

Lattice artifacts of local fermion bilinears up to $\mathrm{O}(a^2)$

Recently the asymptotic lattice spacing dependence of spectral quantities in lattice QCD has been computed to $\mathrm{O}(a^2)$ using Symanzik Effective theory [1,2]. Here, we extend these results to matrix elements and correlators of local fermion bilinears, namely the scalar, pseudo-scalar, vector, axial-vector, and tensor. This resembles the typical current insertions for the effective Hamiltonian of electro-weak or BSM contributions, but is only a small fraction of the local fields typically considered. We again restrict considerations to lattice QCD actions with Wilson or Ginsparg-Wilson quarks and thus lattice formulations of QCD without flavour-changing interactions realising at least $\mathrm{SU}(N_\mathrm{f})_\mathrm{V}\times\mathrm{SU}(N_\mathrm{b}|N_\mathrm{b})_\mathrm{V}$ flavour symmetries for $N_\mathrm{f}$ sea-quarks and $N_\mathrm{b}$ quenched valence-quarks respectively in the massless limit. Overall we find only few cases $\hatΓ$, which worsen the asymptotic lattice spacing dependence $a^n[2b_0\bar{g}^2(1/a)]^{\hatΓ}$ compared to the classically expected $a^n$-scaling. Other than for trivial flavour quantum numbers, only the axial-vector and much milder the tensor may cause some problems at $\mathrm{O}(a)$, strongly suggesting to use at least tree-level Symanzik improvement of those local fields.

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arXiv2024

SymEFT predictions for local fermion bilinears

Beyond spectral quantities, Symanzik Effective Theory (SymEFT) predictions of the asymptotic lattice-spacing dependence require the inclusion of an additional minimal basis of higher-dimensional operators for each local field involved in the matrix element of interest. Adding the proper bases for fermion bilinears of mass-dimension 3 allows to generalise previous predictions to matrix elements of those bilinears. These results can be incorporated in ansätze used in continuum extrapolations and should allow improved control of the associated systematic uncertainties. Potential difficulties and pitfalls are being highlighted. The current work is limited to the use of Wilson or Ginsparg-Wilson quarks in both sea and valence.

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arXiv2022

Asymptotic lattice spacing dependence of spectral quantities in lattice QCD with Wilson or Ginsparg-Wilson quarks

One major systematic uncertainty of lattice QCD results is due to the continuum extrapolation. For an asymptotically free theory like QCD one finds corrections of the form $a^{n_\mathrm{min}}[2b_0\bar{g}^2(1/a)]^{\hatΓ_i}$ with lattice spacing $a$, where $\bar{g}(1/a)$ is the running coupling at renormalisation scale $μ=1/a$ and $n_\mathrm{min}$ is a positive integer. $\hatΓ_i$ can take any positive or negative value, but is computable by next-to-leading order perturbation theory. It will impact convergence towards the continuum limit. Balog, Niedermayer and Weisz first pointed out how problematic such corrections can be in their seminal work for the O(3) model. Based on Symanzik Effective Theory for lattice QCD with Ginsparg-Wilson and Wilson quarks, various powers $\hatΓ_i$ are found due to lattice artifacts from the discretised lattice action. Those powers are sufficient when describing spectral quantities, while non-spectral quantities will require additional powers originating from corrections to each of the discretised local fields involved. This new input should be incorporated into ansätze used for the continuum extrapolation.

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arXiv2022

Log-enhanced discretization errors in integrated correlation functions

Integrated time-slice correlation functions $G(t)$ with weights $K(t)$ appear, e.g., in the moments method to determine $α_s$ from heavy quark correlators, in the muon g-2 determination or in the determination of smoothed spectral functions. For the (leading-order-)normalised moment $R_4$ of the pseudo-scalar correlator we have non-perturbative results down to $a=10^{-2}$ fm and for masses, $m$, of the order of the charm mass in the quenched approximation. A significant bending of $R_4$ as a function of $a^2$ is observed at small lattice spacings. Starting from the Symanzik expansion of the integrand we derive the asymptotic convergence of the integral at small lattice spacing in the free theory and prove that the short distance part of the integral leads to $\log(a)$-enhanced discretisation errors when $G(t)K(t) \sim\, t $ for small $t$. In the interacting theory an unknown, function $K(aΛ)$ appears. For the $R_4$-case, we modify the observable to improve the short distance behavior and demonstrate that it results in a very smooth continuum limit. The strong coupling and the $Λ$-parameter can then be extracted. In general, and in particular for $g-2$, the short distance part of the integral should be determined by perturbation theory. The (dominating) rest can then be obtained by the controlled continuum limit of the lattice computation.

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arXiv2022

Logarithmic corrections to O($a$) and O($a^2$) effects in lattice QCD with Wilson or Ginsparg-Wilson quarks

We derive the asymptotic lattice spacing dependence $a^n[2b_0\bar{g}^2(1/a)]^{\hatΓ_i}$ relevant for spectral quantities of lattice QCD, when using Wilson, O$(a)$ improved Wilson or Ginsparg-Wilson quarks. We give some examples for the spectra encountered for $\hatΓ_i$ including the partially quenched case, mixed actions and using two different discretisations for dynamical quarks. This also includes maximally twisted mass QCD relying on automatic O$(a)$ improvement. At O$(a^2)$, all cases considered have $\min_i\hatΓ_i\gtrsim -0.3$ if $N_\mathrm{f}\leq 4$, which ensures that the leading order lattice artifacts are not severely logarithmically enhanced in contrast to the O$(3)$ non-linear sigma model [1,2]. However, we find a very dense spectrum of these leading powers, which may result in major pile-ups and cancellations. We present in detail the computational strategy employed to obtain the 1-loop anomalous dimensions already used in [3].

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arXiv2022

Logarithmic corrections to $\mathbf{a^2}$ scaling in lattice QCD with Wilson and Ginsparg-Wilson quarks

We analyse the leading logarithmic corrections to the $a^2$ scaling of lattice artefacts in QCD, following the seminal work of Balog, Niedermayer and Weisz in the O(n) non-linear sigma model. Limiting the discussion to contributions from the action, the leading logarithmic corrections can be determined by the anomalous dimensions of mass-dimension 6 operators. These operators form a minimal on-shell basis of the Symanzik Effective Theory. We present results for non-perturbatively O($a$) improved Wilson and Ginsparg-Wilson quarks.

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arXiv2019

Asymptotic behavior of cutoff effects in Yang-Mills theory and in Wilson's lattice QCD

Discretization effects of lattice QCD are described by Symanzik's effective theory when the lattice spacing, $a$, is small. Asymptotic freedom predicts that the leading asymptotic behavior is $\sim a^n [\bar g^2(a^{-1})]^{\hatγ_1} \sim a^n \left[\frac{1}{-\log(aΛ)}\right]^{\hatγ_1}$. For spectral quantities, $n=d$ is given in terms of the (lowest) canonical dimension, $d+4$, of the operators in the local effective Lagrangian and $\hatγ_1$ is proportional to the leading eigenvalue of their one-loop anomalous dimension matrix $γ^{(0)}$. We determine $γ^{(0)}$ for Yang-Mills theory ($n=2$) and discuss consequences in general and for perturbatively improved short distance observables. With the help of results from the literature, we also discuss the $n=1$ case of Wilson fermions with perturbative O$(a)$ improvement and the discretization effects specific to the flavor currents. In all cases known so far, the discretization effects are found to disappear faster than the naive $\sim a^n$ and the log-corrections are a rather weak modification -- in contrast to the two-dimensional O(3) sigma model.

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arXiv2019

Logarithmic corrections to $\mathbf{a^2}$ scaling in lattice Yang Mills theory

We analyse the leading logarithmic corrections to the $a^2$ scaling of lattice artefacts in QCD, following the seminal work of Balog, Niedermayer and Weisz in the O(n) non-linear sigma model. Restricting our attention to contributions from the action, the leading logarithmic corrections can be determined by the anomalous dimensions of a minimal on-shell basis of mass-dimension 6 operators. We present results for the SU(N) pure gauge theory. In this theory the logarithmic corrections reduce the cutoff effects. These computations are the first step towards a study of full lattice QCD at O($a^2$), which is in progress.

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arXiv2017

SU(3) Yang Mills theory at small distances and fine lattices

We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to $a=0.015$ fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behaviour of the action density $E(t)$ close to the boundaries, the feasibility of the small flow-time expansion and the extraction of the $Λ$-parameter from the static force at small distances. For the latter, significant deviations from the 4-loop perturbative $β$-function are visible at $α\approx 0.2\,$. We still can extrapolate to extract $r_0Λ$.

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