arXiv subjects

Renwick J. Hudspith

Publications and source records attributed to Renwick J. Hudspith.

At least 19 recordsLinked to original sources

arXiv2026

$F_K/F_π$ as a precision test of a new four flavor Domain Wall Fermion action

We present a new set of lattice QCD ensembles with four flavors of smeared Möbius Domain Wall Fermions with good chiral symmetry and small fifth-dimensional extent. A modest amount of computing resources was sufficient to generate 30 publicly-available ensembles spanning five lattice spacings and a broad range of pion masses down to physical. To scrutinize our action we determine $F_{K^{\pm}}/F_{π^{\pm}} = 1.1962(34)$, a key quantity for precision CKM unitarity tests, heralding a future of inexpensive high-precision calculations of hadronic observables with chiral fermions.

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arXiv2025

Probing how bright the quark-gluon plasma glows in lattice QCD

Determining the spectrum of photons emitted by the quark-gluon plasma non-perturbatively remains an open computational challenge. In this letter we calculate two moments of that spectrum at a temperature $T\approx 254\,$MeV, employing lattice QCD with two flavors of $\mathrm{O}(a)$-improved Wilson fermions, without facing an inverse problem. Our central value for the difference of these two moments, which is sensitive to photon energies $ω\gtrsim πT$, is lower than, but compatible with that obtained by integrating the leading-order weak-coupling photon spectrum. This study informs the $\textit{direct photon puzzle}$ in heavy-ion collision phenomenology, where it has proved difficult to simultaneously explain the yield and azimuthal anisotropy of photons not originating from final-state hadronic decays.

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arXiv2024

QCD in the chiral SU(3) limit from baryon masses on Lattice QCD ensembles

The baryon masses on CLS ensembles are used to determine the LEC that characterize QCD in the flavor-SU(3) limit with vanishing up, down, and strange quark masses. Here we reevaluate some of the baryon masses on flavor-symmetric ensembles with much-improved statistical precision, in particular for the decuplet states. These additional results then lead to a more significant chiral extrapolation of the Lattice data set to its chiral SU(3) limit. Our results are based on the chiral Lagrangian with baryon octet and decuplet fields considered at the one-loop level. Finite-box and discretization effects of the Lattice data are considered systematically. While in our global fit of the data we insist on large-Nc sum rules for the LEC that enter at N3LO, all other LEC are unconstrained. In particular, we obtain values for the chiral limit of the pion decay constant and the isospin-limit of the quark-mass ratio compatible with the FLAG report.

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arXiv2024

Hot QCD matter around the chiral crossover: a lattice study with $O(a)$-improved Wilson fermions

Using lattice QCD simulations with $O(a)$-improved Wilson quarks and physical up, down and strange quark masses, we investigate the properties of thermal QCD matter at the temperatures $T=\{128,154,192\}\mathrm{MeV}$ with a fixed lattice spacing $a=0.064\mathrm{fm}$ and volume $V=(6.1\text{fm})^3$. We find that the pion quasiparticle, defined as the low-energy pole in the two-point function of the axial charge, becomes lighter as the temperature increases and give an argument based on hydrodynamics as to why the pole becomes purely diffusive above the chiral crossover. We study the thermal modification of the isovector vector spectral function using the Backus-Gilbert method, finding an enhancement at low energies and a depletion at energies around $1\mathrm{GeV}$.The analogous study of the axial-vector channel reveals a larger enhancement at energies below $1\mathrm{GeV}$, and we show that these findings are consistent with rigorous spectral sum rules. The difference between vector and axial-vector correlators, an order parameter for chiral symmetry, turns out to be overall suppressed by more than an order of magnitude at the crossover.

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arXiv2024

Precise Omega baryons from lattice QCD

In this paper we determine the masses of $I(J^P)=0\left(3/2^+\right)$ and $0\left(3/2^-\right)$ $Ω$-baryon ground states using lattice QCD. We utilise Wilson-clover ensembles with $2+1$ dynamical quark flavours generated by the CLS consortium along a trajectory with a constant trace of the quark-mass matrix. We show that N$^3$LO $\text{SU}(3)_f$ chiral perturbation theory expressions describe the ground-state masses with positive-parity well, and we use them to set the lattice scale. Methodologically, our combination of gauge-fixed wall sources and the generalized Pencil of Functions allows for high-precision determinations of the lattice spacing at a relative error of around $0.3\%$ with controlled excited-state contamination. The fit we perform allows for the continuum value of $t_0$ to vary, thereby determining this quantity with a comparable level of precision to that of the lattice scale. Using the resulting scales our measurement of the negative-parity $Ω^{3/2^{-}}$ state is found to be consistent with the recently-discovered $Ω(2012)^-$, which can therefore be assigned the quantum numbers $I(J^P)=0\left(3/2^-\right)$.

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arXiv2024

The thermal photon emissivity at the QCD chiral crossover from imaginary momentum correlators

The thermal photon emissivity at the QCD chiral crossover is investigated using imaginary momentum correlators. These have been measured on a newly generated $20 \times 96^3$ lattice-QCD ensemble with $\mathcal{O}(a)$-improved Wilson quarks and physical up, down and strange quark masses at a temperature $T=154$\,MeV near the pseudo-critical temperature. In order to realize the photon on-shell condition, the spatially transverse Euclidean correlators have to be evaluated at imaginary spatial momenta. Employing a bounding method, we present a preliminary result on the quantity $H_E(ω_1)$, which corresponds to an energy-moment of the photon spectral function $σ(ω)/ω$ defined by the weight function $1/(ω^2+ω_n^2)$, the $ω_n$ being integer multiples of $2πT$.

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arXiv2023

Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel

Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor $g$ of the muon to deviate from the value of two predicted by Dirac's theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon $(g-2)$. Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at https://github.com/RJHudspith/KQED.

hep-lat↗

arXiv2023

Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD

Euclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon $g-2$ serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations. In this paper, we present results for the intermediate time window observable computed using O($a$) improved Wilson fermions at six values of the lattice spacings below 0.1\,fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-Lüscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of QCD+QED around the isosymmetric theory. Our result at the physical point is $a_μ^{\mathrm{win}}=(237.30\pm0.79_{\rm stat}\pm1.22_{\rm syst})\times10^{-10}$, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of 3.9$σ$ with a recent evaluation of $a_μ^{\mathrm{win}}$ based on the data-driven method.

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arXiv2022

Intermediate window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from O$(a)$ improved Wilson quarks

Following the publication of the new measurement of the anomalous magnetic moment of the muon, the discrepancy between experiment and the theory prediction from the $g-2$ theory initiative has increased to $4.2\,σ$. Recent lattice QCD calculations predict values for the hadronic vacuum polarization contribution that are larger than the data-driven estimates, bringing the Standard Model prediction closer to the experimental measurement. Euclidean time windows in the time-momentum representation of the hadronic vacuum polarization contribution to the muon $g-2$ can help clarify the discrepancy between the phenomenological and lattice predictions. We present our calculation of the intermediate distance window contribution using $N_\mathrm{f}=2+1$ flavors of O$(a)$ improved Wilson quarks. We employ ensembles at six lattice spacings below $0.1\,$fm and pion masses down to the physical value. We present a detailed study of the continuum limit, using two discretizations of the vector current and two independent sets of improvement coefficients. Our result at the physical point displays a tension of $3.9\,σ$ with a recent evaluation of the intermediate window based on the data-driven method.

hep-lat↗

arXiv2022

The charm-quark contribution to light-by-light scattering in the muon $(g-2)$ from lattice QCD

We compute the hadronic light-by-light scattering contribution to the muon $g-2$ from the charm quark using lattice QCD. The calculation is performed on ensembles generated with dynamical $(u,d,s)$ quarks at the SU(3)$_{\rm f}$ symmetric point with degenerate pion and kaon masses of around 415 MeV. It includes the connected charm contribution, as well as the leading disconnected Wick contraction, involving the correlation between a charm and a light-quark loop. Cutoff effects turn out to be sizeable, which leads us to use lighter-than-physical charm masses, to employ a broad range of lattice spacings reaching down to 0.039 fm and to perform a combined charm-mass and continuum extrapolation. We use the $η_c$ meson to define the physical charm-mass point and obtain a final value of $a_μ^{\rm HLbL,c} = (2.8\pm 0.5) \times 10^{-11}$, whose uncertainty is dominated by the systematics of the extrapolation. Our result is consistent with the estimate based on a simple charm-quark loop, whilst being free of any perturbative scheme dependence on the charm mass. The mixed charm-light disconnected contraction contributes a small negative amount to the final value.

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arXiv2021

Isospin-breaking Effects in Octet and Decuplet Baryon Masses

We present work designed to compute baryon masses on $N_f = 2 + 1$ CLS ensembles including isospin-breaking effects due to non-degenerate light quark masses and electromagnetic interactions. These effects are determined at leading order via a perturbative expansion around the iso-symmetric theory. We furthermore apply a group-theoretical operator construction for the various interpolators describing the different members of the baryon octet and decuplet based on a classification by spin, parity, and flavor content.

hep-lat↗

arXiv2021

Hadronic light-by-light contribution to $(g-2)_μ$ from lattice QCD: a complete calculation

We compute the hadronic light-by-light scattering contribution to the muon $g-2$ from the up, down, and strange-quark sector directly using lattice QCD. Our calculation features evaluations of all possible Wick-contractions of the relevant hadronic four-point function and incorporates several different pion masses, volumes, and lattice-spacings. We obtain a value of $a_μ^{\text{Hlbl}} = 106.8(14.7) \times 10^{-11}$ (adding statistical and systematic errors in quadrature), which is consistent with current phenomenological estimates and a previous lattice determination. It now appears conclusive that the hadronic light-by-light contribution cannot explain the current tension between theory and experiment for the muon $g-2$.

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arXiv2020

Hadronic light-by-light contribution to $(g-2)_μ$ from lattice QCD with SU(3) flavor symmetry

We perform a lattice QCD calculation of the hadronic light-by-light contribution to $(g-2)_μ$ at the SU(3) flavor-symmetric point $m_π=m_K\simeq 420\,$MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain $a_μ^{\rm hlbl} = (65.4\pm 4.9 \pm 6.6)\times 10^{-11}$, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.

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arXiv2019

Developments in the position-space approach to the HLbL contribution to the muon $g-2$ on the lattice

The measurement of the anomalous magnetic moment of the muon and its prediction allow for a high-precision test of the Standard Model (SM). In this proceedings article we present ongoing work combining lattice QCD and continuum QED in order to determine an important SM contribution to the magnetic moment, the hadronic light-by-light contribution. We compute the quark-connected contribution in the Mainz position-space approach and investigate the long-distance part of our data using calculations of the $π^0$-pole and charged pion loop contributions.

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arXiv2018

Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD

We continue our study of heavy-light four-quark states and find evidence from lattice QCD for the existence of a strong-interaction-stable $I(J^P)=0(1^+)$ $ud\bar{c}\bar{b}$ tetraquark with mass in the range of 15 to 61 MeV below $\bar{D}B^*$ threshold. Since this range includes the electromagnetic $\bar{D}Bγ$ decay threshold, current uncertainties do not allow us to determine whether such a state would decay electromagnetically, or only weakly. We also perform a study at fixed pion mass, with NRQCD for the heavy quarks, simulating $qq^\prime \bar{b}^\prime \bar{b}$ and $q q^\prime \bar{b}^\prime\bar{b}^\prime$ tetraquarks with $q,\, q^\prime =ud$ or $\ell s$ and variable, unphysical $m_{b^\prime}$ in order to investigate the heavy mass-dependence of such tetraquark states. We find that the dependence of the binding energy follows a phenomenologically-expected form and that, though NRQCD breaks down before $m_{b^\prime}=m_c$ is reached, the results at higher $m_{b^\prime}$ clearly identify the $ud\bar{b}^\prime \bar{b}$ channel as the most likely to support a strong-interaction-stable tetraquark state at $m_{b^\prime}=m_c$. This observation serves to motivate the direct $ud\bar{c}\bar{b}$ simulation. Throughout we use dynamical $n_f=2+1$ ensembles with pion masses $m_π=$415, 299, and 164 MeV reaching down almost to the physical point, a relativistic heavy quark prescription for the charm quark, and NRQCD for the bottom quark(s).

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arXiv2018

Dark Matter from Strong Dynamics: The Minimal Theory of Dark Baryons

As a simple model for dark matter, we propose a QCD-like theory based on $\rm{SU}(2)$ gauge theory with one flavor of dark quark. The model is confining at low energy and we use lattice simulations to investigate the properties of the lowest-lying hadrons. Compared to QCD, the theory has several peculiar differences: there are no Goldstone bosons or chiral symmetry restoration when the dark quark becomes massless; the usual global baryon number symmetry is enlarged to $\rm{SU}(2)_B$, resembling isospin; and baryons and mesons are unified together in $\rm{SU}(2)_B$ iso-multiplets. We argue that the lightest baryon, a vector boson, is a stable dark matter candidate and is a composite realization of the hidden vector dark matter scenario. The model naturally includes a lighter state, the analog of the $η^\prime$ in QCD, for dark matter to annihilate into to set the relic density via thermal freeze-out. Dark matter baryons may also be asymmetric, strongly self-interacting, or have their relic density set via $3 \to 2$ cannibalizing transitions. We discuss some experimental implications of coupling dark baryons to the Higgs portal.

hep-ph↗

arXiv2018

$α_s$ from the Lattice Hadronic Vacuum Polarisation

We present a determination of the QCD coupling constant, $α_s$, obtained by fitting lattice results for the flavour $ud$ hadronic vacuum polarisation function to continuum perturbation theory. We use $n_f=2+1$ flavours of Domain Wall fermions generated by the RBC/UKQCD collaboration and three lattice spacings $a^{-1}=1.79,\, 2.38$ and $3.15\ \text{GeV}$. Several sources of potential systematic error are identified and dealt with. After fitting and removing expected leading cut-off effects, we find for the five-flavour $\overline{\text{MS}}$ coupling the value $α_s(M_Z)=0.1181(27)^{+8}_{-22}$, where the first error is statistical and the second systematic.

hep-lat↗

arXiv2018

A resolution of the inclusive flavor-breaking $τ$ $|V_{us}|$ puzzle

We revisit the puzzle of $|V_{us}|$ values obtained from the conventional implementation of hadronic-$τ$-decay-based flavor-breaking finite-energy sum rules lying $>3 σ$ below the expectations of three-family unitarity. Significant unphysical dependences of $|V_{us}|$ on the choice of weight, w, and upper limit, $s_0$, of the experimental spectral integrals entering the analysis are confirmed, and a breakdown of assumptions made in estimating higher dimension, $D>4$, OPE contributions is identified as the main source of these problems. A combination of continuum and lattice results is shown to suggest a new implementation of the flavor-breaking sum rule approach in which not only $|V_{us}|$, but also $D>4$ effective condensates, are fit to data. Lattice results are also used to clarify how to reliably treat the slowly converging D=2 OPE series. The new sum rule implementation is shown to cure the problems of the unphysical w- and $s_0$-dependence of $|V_{us}|$ and to produce results $\sim 0.0020$ higher than those of the conventional implementation. With B-factory input, and using, in addition, dispersively constrained results for the $Kπ$ branching fractions, we find $\vert V_{us}\vert =0.2231(27)_{exp}(4)_{th}$, in excellent agreement with the result from $K_{\ell 3}$, and compatible within errors with the expectations of three-family unitarity, thus resolving the long-standing inclusive $τ$ $|V_{us}|$ puzzle.

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