arXiv subjects

C. T. H. Davies

Publications and source records attributed to C. T. H. Davies.

At least 19 recordsLinked to original sources

arXiv2025

Utility of a hybrid approach to the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment

An accurate calculation of the leading-order hadronic vacuum polarisation (LOHVP) contribution to the anomalous magnetic moment of the muon ($a_μ$) is key to determining whether a discrepancy, suggesting new physics, exists between the Standard Model and experimental results. This calculation can be expressed as an integral over Euclidean time of a current-current correlator $G(t)$, where $G(t)$ can be calculated using lattice QCD or, with dispersion relations, from experimental data for $e^+e^-\to\mbox{hadrons}$. The BMW/DMZ collaboration recently presented a hybrid approach in which $G(t)$ is calculated using lattice QCD for most of the contributing $t$ range, but using experimental data for the largest $t$ (lowest energy) region. Here we study the advantages of varying the position $t=t_1$ separating lattice QCD from data-driven contributions. The total LOHVP contribution should be independent of $t_1$, providing both a test of the experimental input and the robustness of the hybrid approach. We use this criterion and a correlated fit to show that Fermilab/HPQCD/MILC lattice QCD results from 2019 strongly favour the CMD-3 cross-section data for $e^+e^-\toπ^+π^-$ over a combination of earlier experimental results for this channel. Further, the resulting total LOHVP contribution obtained is consistent with the result obtained by BMW/DMZ, and supports the scenario in which there is no significant discrepancy between the experimental value for $a_μ$ and that expected in the Standard Model. We then discuss how improved lattice results in this hybrid approach could provide a more accurate total LOHVP across a wider range of $t_1$ values with an uncertainty that is smaller than that from either lattice QCD or data-driven approaches on their own.

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arXiv2023

Standard Model predictions for $B\to K\ell^+\ell^-$, $B\to K\ell_1^- \ell_2^+$ and $B\to Kν\barν$ using form factors from $N_f=2+1+1$ lattice QCD

We use HPQCD's recent lattice QCD determination of $B \to K$ scalar, vector and tensor form factors to determine Standard Model differential branching fractions for $B \to K \ell^+\ell^-$, $B\to K \ell_1^+\ell_2^-$ and $B \to Kν\overlineν$. These form factors are calculated across the full $q^2$ range of the decay and have smaller uncertainties than previous work, particularly at low $q^2$. For $B \to K \ell^+ \ell^-$ we find the Standard Model branching fraction in the $q^2$ region below the squared $J/ψ$ mass to exceed the LHCb results, with tensions as high as $4.2σ$ for $B^+\to K^+μ^+μ^-$. For the high $q^2$ region we see $2.7σ$ tensions. The tensions are much reduced by applying shifts to Wilson coefficients $C_9$ and $C_{10}$ in the effective weak Hamiltonian, moving them away from their Standard Model values consistent with those indicated by other $B$ phenomenology. We also update results for lepton-flavour ratios $R^μ_e$ and $R^τ_μ$ and the `flat term', $F_H^{\ell}$ in the differential branching fraction for $\ell\in\{e,μ,τ\}$. Our results for the form-factor-dependent contributions needed for searches for lepton-flavour-violating decays $B\to K\ell^-_1\ell^+_2$ achieve uncertainties of 7%. We also compute the branching fraction $\mathcal{B}(B\to Kν\barν)$ with an uncertainty below 10%, for comparison with future experimental results.

hep-ph↗

arXiv2023

Nonperturbative comparison of clover and HISQ quarks in lattice QCD and the properties of the phi meson

We compare correlators for pseudoscalar and vector mesons made from valence strange quarks using the clover quark and highly improved staggered quark (HISQ) formalisms in full lattice QCD. We use fully nonperturbative methods to normalise vector and axial vector current operators made from HISQ quarks, clover quarks and from combining HISQ and clover fields. This allows us to test expectations for the renormalisation factors based on perturbative QCD, with implications for the error budget of lattice QCD calculations of the matrix elements of clover-staggered $b$-light weak currents, as well as further HISQ calculations of the hadronic vacuum polarisation. We also compare the approach to the (same) continuum limit in clover and HISQ formalisms for the mass and decay constant of the $ϕ$ meson. Our final results for these parameters, using single-meson correlators and neglecting quark-line disconnected diagrams are: $m_ϕ =$ 1.023(6) GeV and $f_ϕ = $ 0.238(3) GeV in good agreement with experiment. The results come from calculations in the HISQ formalism using gluon fields that include the effect of $u$, $d$, $s$ and $c$ quarks in the sea with three lattice spacing values and $m_{u/d}$ values going down to the physical point.

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arXiv2023

$B\to K$ and $D\to K$ form factors from fully relativistic lattice QCD

We present the result of lattice QCD calculation of the scalar, vector and tensor form factors for the $B\to K\ell^+\ell^-$ decay, across the full physical range of momentum transfer. We use the highly improved staggered quark (HISQ) formalism for all valence quarks on eight ensembles of gluon field configurations generated by the MILC collaboration. These include four flavours of HISQ quarks in the sea, with three ensembles having the light $u/d$ quarks at physical masses. In the first fully relativistic calculation of these form factors, we use the heavy-HISQ method. This allows us to determine the form factors as a function of heavy quark mass from the $c$ to the $b$, and so we also obtain new results for the $D\to K$ tensor form factor. The advantage of the relativistic formalism is that we can match the lattice weak currents to their continuum counterparts much more accurately than in previous calculations; our scalar and vector currents are renormalised fully nonperturbatively and we use a well-matched intermediate momentum-subtraction scheme for our tensor current. Our scalar and vector $B\to K$ form factors have uncertainties of less than 4% across the entire physical $q^2$ range and the uncertainty in our tensor form factor is less than 7%. Our heavy-HISQ method allows us to map out the dependence on heavy-quark mass of the form factors and we can also see the impact of changing spectator quark mass by comparing to earlier HPQCD results for the same quark weak transition but for heavier mesons.

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arXiv2022

Windows on the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment

An accurate determination of the leading-order hadronic vacuum polarisation (HVP) contribution to the anomalous magnetic moment of the muon is critical to understanding the size and significance of any discrepancy between the Standard Model prediction and experimental results being obtained by the Muon g-2 experiment at Fermilab. The Standard Model prediction is currently based on a data-driven approach to the HVP using experimental results for $σ(e^+e^-\rightarrow\,\mathrm{hadrons})$. Lattice QCD aims to provide a result with similar uncertainty from calculated vector-vector correlation functions, but the growth of statistical and systematic errors in the $u/d$ quark correlation functions at large Euclidean time has made this difficult to achieve. We show that restricting the lattice contributions to a one-sided window $0<t<t_1$ can greatly improve lattice results while still capturing a large fraction of the total HVP. We illustrate this by comparing windowed lattice results based on the 2019 Fermilab Lattice/HPQCD/MILC HVP analysis with corresponding results obtained from the KNT19 analysis of $R_{e^+e^-}$ data. For $t_1=1.5$ fm, 70% of the total HVP is contained within the window and our lattice result has an error of~0.7%, only about twice as big as the error from the $e^+e^-$~analysis. We see a tension of 2.7$σ$ between the two results. With increased statistics in the lattice data the one-sided windows will allow stringent tests of lattice and $R_{e^+e^-}$ results that include a large fraction of the total HVP contribution.

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arXiv2022

The search for new physics in $B \to K \ell^+\ell^-$ and $B \to K ν\barν$ using precise lattice QCD form factors

We present HPQCD's improved scalar, vector and tensor form factors for $B \to K$ semileptonic decays, using the heavy-HISQ formalism for more accurate normalisation of the weak currents. Working with masses close to the physical $b$ on the finest ensemble and including three ensembles with physical light quarks, we cover the full physical $q^2$ range with good precision. Our uncertainties at $q^2=0$ are a factor of three better than earlier work. We compare Standard Model observables using our form factors to experimental measurements for the rare flavour changing neutral current processes $B \to K \ell^+\ell^-$ and $B \to K ν\barν$ and discuss the significance of the tensions that arise.

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arXiv2022

Properties of low-lying charmonia and bottomonia from lattice QCD + QED

The precision of lattice QCD calculations has been steadily improving for some time and is now approaching, or has surpassed, the 1% level for multiple quantities. At this level QED effects, i.e. the fact that quarks carry electric as well as color charge, come into play. In this report we will summarise results from the first lattice QCD+QED computations of the properties of ground-state charmonium and bottomonium mesons by the HPQCD Collaboration.

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arXiv2021

Precision bottomonium properties and b quark mass from lattice QCD

As tests of QCD in the bottomonium system, we give the most accurate results to date for the ground-state hyperfine splitting and the $Υ$ leptonic width from full lattice QCD. These quantities are both accurately known from experiment, so can provide a good test of $b$ physics, but previous lattice results have been rather imprecise. We also test the impact on these quantities of the $b$ quark's electric charge. Our results are: $M_Υ-M_{η_b} = $ 57.5(2.3)(1.0) MeV (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{η_b} =$ 724(12) MeV and $f_Υ =$ 677.2(9.7) MeV, giving $Γ(Υ\rightarrow e^+e^-) =$ 1.292(37)(3) keV. We also give a new determination of the ratio of the masses for $b$ and $c$ quarks that is completely nonperturbative in lattice QCD and includes the calculation of QED effects for the first time. This gives a result for the $b$ quark mass of $\overline{m}_b(\overline{m}_b,n_f=5) =$ 4.202(21) GeV.

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arXiv2021

$V_{cs}$ determination from $D \to{}K \ell ν$

Semileptonic $D \to{}K \ell ν$ decays provide one angle of attack to get at the CKM matrix element $V_{cs}$, complementary to the study of leptonic $D_s$ decays. Here, HPQCD present the results of a recently published, improved determination of $V_{cs}$. We discuss a new, precise determination of $D\to K$ scalar and vector form factors from a lattice calculation on eight different $N_f=2+1+1$ MILC gluon field ensembles using the HISQ action, including three with physical light quark masses. When combined with experimental results, we are able to extract $|V_{cs}|=0.9663(80)$ to a sub percent level of precision for the first time. This is achieved using three different methods, which each combine our form factors with different sets of experimental results in different ways, with the results in very good agreement. Our primary method is to use $q^2$-binned data for the differential decay rate, but we also calculate $V_{cs}$ from the total branching fraction and from the value $|V_{cs}|f_+(0)$, which is also quoted by some experiments.

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arXiv2021

Improved $V_{cs}$ determination using precise lattice QCD form factors for $D \rightarrow K \ell ν$

We provide a 0.8\%-accurate determination of $V_{cs}$ from combining experimental results for the differential rate of $D \rightarrow K$ semileptonic decays with precise form factors that we determine from lattice QCD. This is the first time that $V_{cs}$ has been determined with an accuracy that allows its difference from 1 to be seen. Our lattice QCD calculation uses the Highly Improved Staggered Quark (HISQ) action for all valence quarks on gluon field configurations generated by the MILC collaboration that include the effect of $u$, $d$, $s$ and $c$ HISQ quarks in the sea. We use eight gluon field ensembles with five values of the lattice spacing ranging from 0.15 fm to 0.045 fm and include results with physical $u/d$ quarks for the first time. Our calculated form factors cover the full $q^2$ range of the physical decay process and enable a Standard Model test of the shape of the differential decay rate as well as the determination of $V_{cs}$ from a correlated weighted average over $q^2$ bins. We obtain $|V_{cs}|= 0.9663(53)_{\text{latt}}(39)_{\text{exp}}(19)_{η_{EW}}(40)_{\text{EM}}$, where the uncertainties come from lattice QCD, experiment, short-distance electroweak and electromagnetic corrections, respectively. This last uncertainty, neglected for $D \rightarrow K \ell ν$ hitherto, now needs attention if the uncertainty on $V_{cs}$ is to be reduced further. We also determine $V_{cs}$ values in good agreement using the measured total branching fraction and the rates extrapolated to $q^2=0$. Our form factors enable tests of lepton flavour universality violation. We find the ratio of branching fractions for $D^0 \rightarrow K^-$ with $μ$ and $e$ in the final state to be $R_{μ/e}=0.9779(2)_{\text{latt}}(50)_{\mathrm{EM}}$ in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections.

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arXiv2021

Determination of $\overline{m}_b/\overline{m}_c$ and $\overline{m}_b$ from $n_f=4$ lattice QCD$+$QED

We extend HPQCD's earlier $n_f=4$ lattice-QCD analysis of the ratio of $\overline{\mathrm{MSB}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find that $\overline{m}_b(μ)/\overline{m}_c(μ)=4.586(12)$ at renormalization scale $μ=3$\,GeV. This result is nonperturbative. Combining it with HPQCD's recent lattice QCD$+$QED determination of $\overline{m}_c(3\mathrm{GeV})$ gives a new value for the $b$-quark mass: $\overline{m}_b(3\mathrm{GeV}) = 4.513(26)$GeV. The $b$-mass corresponds to $\overline{m}_b(\overline{m}_b, n_f=5) = 4.202(21)$GeV. These results are the first based on simulations that include QED.

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arXiv2021

Toward accurate form factors for $B$-to-light meson decay from lattice QCD

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical $B_s\toη_s$ decay, over the full physical range of $q^2$. This is a useful testing ground both for lattice QCD and for our wider understanding of the behaviour of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on $N_f = 2 + 1 + 1$ gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalisation of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD $b$ quarks and with reduced errors at low $q^2$, supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavour symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ($b\to c$) to the numerically more challenging heavy-to-light decays.

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arXiv2021

Bottomonium precision tests from full lattice QCD: hyperfine splitting, $Υ$ leptonic width and $b$ quark contribution to $e^+e^- \rightarrow$ hadrons

We calculate the mass difference between the $Υ$ and $η_b$ and the $Υ$ leptonic width from lattice QCD using the Highly Improved Staggered Quark formalism for the $b$ quark and including $u$, $d$, $s$ and $c$ quarks in the sea. We have results for lattices with lattice spacing as low as 0.03 fm and multiple heavy quark masses, enabling us to map out the heavy quark mass dependence and determine values at the $b$ quark mass. Our results are: $M_Υ -M_{η_b} = 57.5(2.3)(1.0) \,\mathrm{MeV}$ (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{η_b}=724(12)$ MeV and $f_Υ =677.2(9.7)$ MeV, giving $Γ(Υ\rightarrow e^+e^-) = 1.292(37)(3) \,\mathrm{keV}$. The hyperfine splitting and leptonic width are both in good agreement with experiment, and provide the most accurate lattice QCD results to date for these quantities by some margin. At the same time results for the time moments of the vector-vector correlation function can be compared to values for the $b$ quark contribution to $σ(e^+e^- \rightarrow \mathrm{hadrons})$ determined from experiment. Moments 4--10 provide a 2\% test of QCD and yield a $b$ quark contribution to the anomalous magnetic moment of the muon of 0.300(15)$\times 10^{-10}$. Our results, covering a range of heavy quark masses, may also be useful to constrain QCD-like composite theories for beyond the Standard Model physics.

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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.

hep-ph↗

arXiv2020

Renormalisation of the tensor current in lattice QCD and the $J/ψ$ tensor decay constant

Lattice QCD calculations of form factors for rare Standard Model processes such as $B \to K \ell^+ \ell^-$ use tensor currents that require renormalisation. These renormalisation factors, $Z_T$, have typically been calculated within perturbation theory and the estimated uncertainties from missing higher order terms are significant. Here we study tensor current renormalisation using lattice implementations of momentum-subtraction schemes. Such schemes are potentially more accurate but have systematic errors from nonperturbative artefacts. To determine and remove these condensate contributions we calculate the ground-state charmonium tensor decay constant, $f_{J/ψ}^T$, which is also of interest in beyond the Standard Model studies. We obtain $f_{J/ψ}^T(\bar{\text{MS}}, 2\ \mathrm{GeV})=0.3927(27)$ GeV, with ratio to the vector decay constant of 0.9569(52), significantly below 1. We also give $Z_T$ factors, converted to the $\bar{\mathrm{MS}}$ scheme, corrected for condensate contamination. This contamination reaches 1.5\% at a renormalisation scale of 2 GeV (in the preferred RI-SMOM scheme) and so must be removed for accurate results.

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arXiv2020

Challenges in Semileptonic B Decays

Two of the elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix, $|V_{ub}|$ and $|V_{cb}|$, are extracted from semileptonic B decays. The results of the B factories, analysed in the light of the most recent theoretical calculations, remain puzzling, because for both $|V_{ub}|$ and $|V_{cb}|$ the exclusive and inclusive determinations are in clear tension. Further, measurements in the $τ$ channels at Belle, Babar, and LHCb show discrepancies with the Standard Model predictions, pointing to a possible violation of lepton flavor universality. LHCb and Belle II have the potential to resolve these issues in the next few years. This article summarizes the discussions and results obtained at the MITP workshop held on April 9--13, 2018, in Mainz, Germany, with the goal to develop a medium-term strategy of analyses and calculations aimed at solving the puzzles. Lattice and continuum theorists working together with experimentalists have discussed how to reshape the semileptonic analyses in view of the much higher luminosity expected at Belle II, searching for ways to systematically validate the theoretical predictions in both exclusive and inclusive B decays, and to exploit the rich possibilities at LHCb.

hep-ph↗

arXiv2020

QED interaction effects on heavy meson masses from lattice QCD+QED

Hadron masses are subject to few MeV corrections arising from QED interactions, almost entirely arising from the electric charge of the valence quarks. The QED effects include both self-energy contributions and interactions between the valence quarks/anti-quarks. By combining results from different signs of the valence quark electric charge we are able to isolate the interaction term which is dominated by the Coulomb piece, $\langle α_{\mathrm{QED}}e_{q_1}e_{\overline{q}_2}/r \rangle$, in the nonrelativistic limit. We study this for $D_s$, $η_c$ and $J/ψ$ mesons, working in lattice QCD plus quenched QED. We use gluon field configurations that include up, down, strange and charm quarks in the sea at multiple values of the lattice spacing. Our results, including also values for mesons with quarks heavier than charm, can be used to improve phenomenological models for the QED contributions. The QED interaction term carries information about meson structure; we derive effective sizes $\langle 1/r_{\mathrm{eff}} \rangle^{-1}$ for $η_c$, $J/ψ$ and $D_s$ of 0.206(8) fm, 0.321(14) fm and 0.307(31) fm respectively.

hep-lat↗

arXiv2020

Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/ψ$ leptonic width, charm quark mass and $a_μ^c$

We have performed the first $n_f = 2+1+1$ lattice QCD computations of the properties (masses and decay constants) of ground-state charmonium mesons. Our calculation uses the HISQ action to generate quark-line connected two-point correlation functions on MILC gluon field configurations that include $u/d$ quark masses going down to the physical point, tuning the $c$ quark mass from $M_{J/ψ}$ and including the effect of the $c$ quark's electric charge through quenched QED. We obtain $M_{J/ψ}-M_{η_c}$ (connected) = 120.3(1.1) MeV and interpret the difference with experiment as the impact on $M_{η_c}$ of its decay to gluons, missing from the lattice calculation. This allows us to determine $ΔM_{η_c}^{\mathrm{annihiln}}$ =+7.3(1.2) MeV, giving its value for the first time. Our result of $f_{J/ψ}=$ 0.4104(17) GeV, gives $Γ(J/ψ\rightarrow e^+e^-)$=5.637(49) keV, in agreement with, but now more accurate than experiment. At the same time we have improved the determination of the $c$ quark mass, including the impact of quenched QED to give $\overline{m}_c(3\,\mathrm{GeV})$ = 0.9841(51) GeV. We have also used the time-moments of the vector charmonium current-current correlators to improve the lattice QCD result for the $c$ quark HVP contribution to the anomalous magnetic moment of the muon. We obtain $a_μ^c = 14.638(47) \times 10^{-10}$, which is 2.5$σ$ higher than the value derived using moments extracted from some sets of experimental data on $R(e^+e^- \rightarrow \mathrm{hadrons})$. This value for $a_μ^c$ includes our determination of the effect of QED on this quantity, $δa_μ^c = 0.0313(28) \times 10^{-10}$.

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