arXiv subjects

R. J. Hudspith

Publications and source records attributed to R. J. Hudspith.

At least 19 recordsLinked to original sources

arXiv2026

Exotic $B_s$ mesons in the continuum from a nonperturbatively-tuned heavy quark action

In this work we predict the masses and binding energies of two $B_s$ exotic-meson candidates using Lattice QCD, namely the $B_{s0}^*$ and $B_{s1}$. We use a relativistic heavy-quark action for the valence b-quark in our simulations, tuned fully non-perturbatively by a neural network. This allows us to take the continuum limit and eliminates the largest systematic we attributed to our previous determination of these states using Lattice-NRQCD. This is the first Lattice QCD study to show that these states remain deeply bound in the continuum limit. We thoroughly benchmark our heavy-quark approach by reproducing the experimental values of the 1S hyperfine splittings of $B$ and $B_s$ mesons, as well as the mass splitting between the $B$ and $B_s$ mesons. Our final results yield binding energies with respect to the $BK$ and $B^*K$ thresholds of $-65.9(6.0)(3.0)_\text{Iso}$ MeV and $-60.6(6.6)(3.0)_\text{Iso}(1.0)_\text{GEVP}$ MeV for the $B_{s0}^*$ and $B_{s1}$ respectively.

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arXiv2025

The anomalous magnetic moment of the muon in the Standard Model: an update

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_μ$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the $e^+e^-\toπ^+π^-$ cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a_μ^\text{SM} = 116\,592\,033(62)\times 10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-6 of E989 at Fermilab, one finds $a_μ^\text{exp} - a_μ^\text{SM} =38(63)\times 10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

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arXiv2024

Improved analysis of strong-interaction-stable doubly-bottom tetraquarks on the lattice

We update earlier lattice results for the binding energies of the flavor antitriplet of strong-interaction-stable doubly bottom, $J^P=1^+$ tetraquarks, employing an extended sink construction which produces significantly improved ground-state effective-mass plateaus, as well as new, larger-volume ensembles which reduce possible finite-volume effects at lighter pion masses. The updated bindings are $115(17)$ MeV for the $I=0$ member of the antitriplet and $47(8)$ MeV for its $I=1/2$ partner. We also provide an update of our earlier study of the variable heavy mass dependence of binding in the $1^+$ channel and new results on this dependence for binding in the $0^+$ channel, accessible when the two heavy quarks have unequal masses. Implications of these results of potential relevance to experimental searches for signals of the production of doubly bottom tetraquarks and/or a possible bottom-charm partner of the $T_{cc}$ are also discussed.

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arXiv2024

Quark mass dependence of doubly heavy tetraquark binding

The existence of bound doubly heavy tetraquark states was confirmed by the recent LHCb discovery of the doubly charmed $T_{cc}$, less than 1 MeV below the meson pair threshold. Others states with two heavy (bottom or charm) quarks could also be bound, perhaps more deeply. Here we discuss our previous work, and the improvements in our current, updated analysis of various heavy-heavy-light-light tetraquark candidates, including the light and heavy quark mass dependence of the binding.

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arXiv2023

Exotic Tetraquark states with two $\bar{b}$-quarks and $J^P=0^+$ and $1^+$ $B_s$ states in a nonperturbatively-tuned Lattice NRQCD setup

We use $n_f=2+1$ Wilson-clover gauge-field ensembles from the CLS consortium in a Lattice NRQCD setup to predict the binding energy of a $I(J^P)=0(1^+)$ $ud\bar{b}\bar{b}$ tetraquark and a $\frac{1}{2}(1^+)$ $\ell s\bar{b}\bar{b}$ tetraquark. We determine the binding energies with respect to the relevant $BB^*$ and $B_sB^*$ thresholds respectively to be $112.0(13.2)$ MeV for the $ud\bar{b}\bar{b}$, and $46.4(12.3)$ MeV for the $\ell s\bar{b}\bar{b}$. We also determine the ground-state $J^P=0^+$ $B_{s0}^*$ and $1^+$ $B_{s1}$ mesons to lie $75.4(14.0)$ and $78.7(13.9)$ MeV below the $BK$ and $B^*K$ thresholds respectively. Our errors are entirely dominated by systematics due to discretisation effects. To achieve these measurements, we performed a neural network based nonperturbative tuning of the Lattice NRQCD Hamiltonian's parameters against the basic bottomonium spectrum. For all lattice spacings considered we can reproduce the continuum splittings of low-lying bottomonia. It is worth remarking that our nonperturbative tuning parameters deviate from 1 by significant amounts, particularly the term $c_2$.

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arXiv2021

A fully non-perturbative charm-quark tuning using machine learning

We present a relativistic heavy-quark action tuning for the charm sector on ensembles generated by the CLS consortium. We tune a particular 5-parameter action in an entirely non-perturbative and -- up to the chosen experimental input -- model-independent way using machine learning and the continuum experimental charmonium ground-state masses with various quantum numbers. In the end we are reasonably successful; obtaining a set of simulation parameters that we then verify produces the expected spectrum. In the future, we will use this action for finite-volume calculations of hadron-hadron scattering.

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arXiv2020

The anomalous magnetic moment of the muon in the Standard Model

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $α$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(α^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_μ/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(α^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(α^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_μ^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$σ$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

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arXiv2020

A lattice investigation of exotic tetraquark channels

We perform an $n_f=2+1$ lattice study of a number of channels where past claims exist in the literature for the existence of strong-interaction-stable light-heavy tetraquarks. We find no evidence for any such deeply-bound states, beyond the $J^P=1^+$, $I=0$ $ud\bar{b}\bar{b}$ and $I=1/2$ $ls\bar{b}\bar{b}$ states already identified in earlier lattice studies. We also describe a number of systematic improvements to our previous lattice studies, including working with larger $m_πL$ to better suppress possible finite volume effects, employing extended sinks to better control excited-state contamination, and expanding the number of operators used in the GEVP analyses. Our results also allow us to rule out several phenomenological models which predict significant tetraquark binding in channels where no such binding is found.

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arXiv2017

Neutral kaon mixing beyond the Standard Model with nf=2+1 chiral fermions part II: Non Perturbative Renormalisation of the $ΔF=2$ four-quark operators

We compute the renormalisation factors (Z-matrices) of the $ΔF=2$ four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf=2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to MS, the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.

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arXiv2016

Domain wall QCD with physical quark masses

We present results for several light hadronic quantities ($f_π$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit' with a number of other ensembles with heavier pion masses. We use the physical values of $m_π$, $m_K$ and $m_Ω$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_π$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $\bar {\rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11).

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arXiv2016

Lattice calculation of the leading strange quark-connected contribution to the muon $g-2$

We present results for the leading hadronic contribution to the muon anomalous magnetic moment due to strange quark-connected vacuum polarisation effects. Simulations were performed using RBC--UKQCD's $N_f=2+1$ domain wall fermion ensembles with physical light sea quark masses at two lattice spacings. We consider a large number of analysis scenarios in order to obtain solid estimates for residual systematic effects. Our final result in the continuum limit is $a_μ^{(2)\,{\rm had},\,s}=53.1(9)\left(^{+1}_{-3}\right)\times10^{-10}$.

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arXiv2015

Neutral Kaon mixing beyond the Standard Model

We compute the hadronic matrix elements of the four-quark operators needed for the study of $K^0-{\bar K^0}$ mixing beyond the Standard Model. We have used $n_f=2+1$ flavours of domain wall fermion (DWF) at two values of the lattice spacing ($a\approx0.08$ and $a\approx0.11\text{fm}$) and with lightest unitary pion mass of $\approx300\,\text{MeV}$. Renormalisation is performed non-perturbatively and the impact of different intermediate momentum schemes is investigated.

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arXiv2015

A resolution of the puzzle of low V_us values from inclusive flavor-breaking sum rule analyses of hadronic tau decay

Continuum and lattice methods are used to investigate systematic issues in the sum rule determination of $V_{us}$ using inclusive hadronic $τ$ decay data. Results for $V_{us}$ employing assumptions for $D>4$ OPE contributions used in previous conventional implementations of this approach are shown to display unphysical dependence on the sum rule weight, $w$, and choice of upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest a new implementation of the sum rule approach with not just $\vert V_{us}\vert$, but also $D>4$ effective condensates, fit to data. Lattice results are also shown to provide a quantitative assessment of truncation uncertainties for the slowly converging $D=2$ OPE series. The new sum rule implementation yields $\vert V_{us}\vert$ results free of unphysical $s_0$- and $w$-dependences and $\sim 0.0020$ higher than that obtained using the conventional implementation. With preliminary new experimental results for the $Kπ$ branching fraction, the resulting $\vert V_{us}\vert$ is in excellent agreement with that based on $K_{\ell 3}$, and compatible within errors with expectations from three-family unitarity.

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arXiv2015

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

A combination of continuum and lattice methods is used to investigate systematic issues in the finite-energy-sum-rule determination of $V_{us}$ based on flavor-breaking combinations of hadronic $τ$ decay data. Results for $V_{us}$ obtained using assumptions for $D>4$ OPE contributions employed in previous conventional implementations of this approach are shown to display significant unphysical dependences on the choice of sum rule weight, $w$, and upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest the necessity of a new implementation of the flavor-breaking sum rule approach, in which not only $\vert V_{us}\vert$, but also $D>4$ effective condensates are fit to data. Lattice results also provide a means of quantifying the truncation error for the slowly converging $D=2$ OPE series. The new implementation is shown to produce $\vert V_{us}\vert$ results free of unphysical $s_0$- and $w$-dependences and typically $\sim 0.0020$ higher than the (unstable) results found using the conventional implementation. With preliminary new experimental results for the $Kπ$ branching fraction, the resulting $\vert V_{us}\vert$ is in excellent agreement with that obtained from $K_{\ell 3}$, and compatible within errors with expectations from three-family unitarity.

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arXiv2014

Conjugate Directions in Lattice Landau and Coulomb Gauge Fixing

We provide details expanding on our implementation of a non-linear conjugate gradient method with Fourier acceleration for lattice Landau and Coulomb gauge fixing. We find clear improvement over the Fourier accelerated steepest descent method, with the average time taken for the algorithm to converge to a fixed, high accuracy, being reduced by a factor of 2 to 4. We show such improvement for the logarithmic definition of the gauge fields here, having already shown this to be the case for a more common definition. We also discuss the implementation of an optimal Fourier accelerated steepest descent method.

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arXiv2014

Fourier Accelerated Conjugate Gradient Lattice Gauge Fixing

We provide details of the first implementation of a non-linear conjugate gradient method for Landau and Coulomb gauge fixing with Fourier acceleration. We find clear improvement over the Fourier accelerated steepest descent method, with the average time taken for the algorithm to converge to a fixed, high accuracy, being reduced by a factor of 2 to 4.

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arXiv2014

A Combined NNLO Lattice-Continuum Determination of $L_{10}^r$

The renormalized next-to-leading-order (NLO) chiral low-energy constant, $L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor $ud$ $V-A$ correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for $L_{10}^r$. Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with current versions of the strange hadronic $τ$ branching fractions as input, we find $L_{10}^r(m_ρ)\, =\, -0.00346(32)$. This result represents the first NNLO determination of $L_{10}^r$ having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.

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arXiv2014

Domain Wall QCD with Near-Physical Pions

We present physical results for a variety of light hadronic quantities obtained via a combined analysis of three 2+1 flavour domain wall fermion ensemble sets. For two of our ensemble sets we used the Iwasaki gauge action with beta=2.13 (a^-1=1.75(4) GeV) and beta=2.25 (a^-1=2.31(4) GeV) and lattice sizes of 24^3 x 64 and 32^3 x 64 respectively, with unitary pion masses in the range 293(5)-417(10) MeV. The extent L_s for the 5^th dimension of the domain wall fermion formulation is L_s=16 in these ensembles. In this analysis we include a third ensemble set that makes use of the novel Iwasaki+DSDR (Dislocation Suppressing Determinant Ratio) gauge action at beta = 1.75 (a^-1=1.37(1) GeV) with a lattice size of 32^3 x 64 and L_s=32 to reach down to partially-quenched pion masses as low as 143(1) MeV and a unitary pion mass of 171(1) MeV, while retaining good chiral symmetry and topological tunneling. We demonstrate a significant improvement in our control over the chiral extrapolation, resulting in much improved continuum predictions for the above quantities. The main results of this analysis include the pion and kaon decay constants, f_π=127(3)_{stat}(3)_{sys} MeV and f_K = 152(3)_{stat}(2)_{sys} MeV respectively (f_K/f_π= 1.199(12)_{stat}(14)_{sys}); the average up/down quark mass and the strange-quark mass in the MSbar-scheme at 3 GeV, m_{ud}(MSbar, 3 GeV) = 3.05(8)_{stat}(6)_{sys} MeV and m_s(MSbar, 3 GeV) = 83.5(1.7)_{stat}(1.1)_{sys}; the neutral kaon mixing parameter in the MSbar-scheme at 3 GeV, B_K(MSbar,3 GeV) = 0.535(8)_{stat}(13)_{sys}, and in the RGI scheme, \hat B_K = 0.758(11)_{stat}(19)_{sys}; and the Sommer scales r_1 = 0.323(8)_{stat}(4)_{sys} fm and r_0 = 0.480(10)_{stat}(4)_{sys} (r_1/r_0 = 0.673(11)_{stat}(3)_{sys}). We also obtain values for the SU(2) ChPT effective couplings, \bar{l_3} = 2.91(23)_{stat}(7)_{sys}$ and \bar{l_4} = 3.99(16)_{stat}(9)_{sys}.

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