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A. X. El-Khadra

Publications and source records attributed to A. X. El-Khadra.

At least 19 recordsLinked to original sources
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.

hep-ph↗
arXiv2022

Semileptonic form factors for $B \to D^\ast\ellν$ at nonzero recoil from 2 + 1-flavor lattice QCD

We present the first unquenched lattice-QCD calculation of the form factors for the decay $B\rightarrow D^\ast\ellν$ at nonzero recoil. Our analysis includes 15 MILC ensembles with $N_f=2+1$ flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from $a\approx 0.15$ fm down to $0.045$ fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valence $b$ and $c$ quarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element $|V_{cb}|$. We obtain $\left|V_{cb}\right| = (38.40 \pm 0.68_{\textrm{th}} \pm 0.34_{\textrm{exp}} \pm 0.18_{\textrm{EM}})\times 10^{-3}$. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall $χ^2\text{/dof} = 126/84$, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict $R(D^\ast) = 0.265 \pm 0.013$, which confirms the current tension between theory and experiment.

hep-lat↗
arXiv2022

Snowmass Theory Frontier Report

This report summarizes the recent progress and promising future directions in theoretical high-energy physics (HEP) identified within the Theory Frontier of the 2021 Snowmass Process.

hep-ph↗
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

Data-driven evaluations of Euclidean windows to scrutinize hadronic vacuum polarization

In this paper, we discuss how windows in Euclidean time can be used to isolate the origin of potential conflicts between evaluations of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon in lattice QCD and from $e^+e^-\to\text{hadrons}$ cross-section data. We provide phenomenological comparison numbers evaluated from $e^+e^-\to\text{hadrons}$ data for the window quantities most commonly studied in lattice QCD, complete with the correlations among them. We discuss and evaluate modifications of window parameters that could be useful in dissecting the energy dependence of tensions in the HVP integral and emphasize that further optimizations require a precise knowledge of the full covariance matrix in lattice-QCD calculations as well.

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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

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

Hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment from four-flavor lattice QCD

We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from {the} connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from $a \approx 0.06$ to~0.15~fm. The up- and down-quark masses in our simulations have equal masses $m_l$. We obtain, in this world where all pions have the mass of the $π^0$, $10^{10} a_μ^{ll}({\rm conn.}) = 637.8\,(8.8)$, in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. Our final result for the total $\mathcal{O}(α^2)$ hadronic vacuum polarization to the muon's anomalous magnetic moment is~$10^{10}a_μ^{\rm HVP,LO} = 699(15)_{u,d}(1)_{s,c,b}$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both {\it ab-initio} lattice-QCD calculations and phenomenological determinations from experimental $e^+e^-$-scattering data. It is $1.3σ$ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of $a_μ$ with theoretical calculations of the other contributions.

hep-lat↗
arXiv2019

$B$-meson semileptonic form factors on (2+1+1)-flavor HISQ ensembles

We report updates to an ongoing lattice-QCD calculation of the form factors for the semileptonic decays $B \to π\ell ν$, $B_s \to K \ell ν$, $B \to π\ell^+ \ell^-$, and $B \to K \ell^+ \ell^-$. The tree-level decays $B_{(s)} \to π(K) \ell ν$ enable precise determinations of the CKM matrix element $|V_{ub}|$, while the flavor-changing neutral-current interactions $B \to π(K) \ell^+ \ell^-$ are sensitive to contributions from new physics. This work uses MILC's (2+1+1)-flavor HISQ ensembles at approximate lattice spacings between $0.057$ and $0.15$ fm, with physical sea-quark masses on four out of the seven ensembles. The valence sector is comprised of a clover $b$ quark (in the Fermilab interpretation) and HISQ light and $s$ quarks. We present preliminary results for the form factors $f_0$, $f_+$, and $f_T$, including studies of systematic errors.

hep-lat↗
arXiv2019

The hadronic vacuum polarization of the muon from four-flavor lattice QCD

We present an update on the ongoing calculations by the Fermilab Lattice, HPQCD, and MILC Collaboration of the leading-order (in electromagnetism) hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. Our project employs ensembles with four flavors of highly improved staggered fermions, physical light-quark masses, and four lattice spacings ranging from $a \approx 0.06$ to 0.15 fm for most of the results thus far.

hep-lat↗
arXiv2019

$B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD

We calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to $a\approx 0.03$~fm and several values of the light-quark mass down to the physical value $\frac{1}{2}(m_u+m_d)$. We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the $B$-meson decay constants with the HISQ action for the first time directly at the physical $b$-quark mass. We obtain the most precise determinations to-date of the $D$- and $B$-meson decay constants and their ratios, $f_{D^+} = 212.7(0.6)$~MeV, $f_{D_s} = 249.9(0.4)$~MeV, $f_{D_s}/f_{D^+} = 1.1749(16)$, $f_{B^+} = 189.4 (1.4)$~MeV, $f_{B_s} = 230.7(1.3)$~MeV, $f_{B_s}/f_{B^+} = 1.2180(47)$, where the errors include statistical and all systematic uncertainties. Our results for the $B$-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the Standard-Model predictions for the rare leptonic decays $\overline{\mathcal{B}}(B_s \to μ^+μ^-) = 3.64(11) \times 10^{-9}$, $\overline{\mathcal{B}}(B^0 \to μ^+μ^-) = 1.00(3) \times 10^{-10}$, and $\overline{\mathcal{B}}(B^0 \to μ^+μ^-)/\overline{\mathcal{B}}(B_s \to μ^+μ^-) = 0.0273(9)$ to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities $f_{p4s}$, $M_{p4s}$, and $R_{p4s}$. We obtain the most precise lattice-QCD determination to date of the ratio $f_{K^+}/f_{π^+} = 1.1950(^{+16}_{-23})$~MeV.

hep-lat↗
arXiv2019

$|V_{us}|$ from $K_{\ell 3}$ decay and four-flavor lattice QCD

Using HISQ $N_f=2+1+1$ MILC ensembles with five different values of the lattice spacing, including four ensembles with physical quark masses, we have performed the most precise computation to date of the $K\toπ\ellν$ vector form factor at zero momentum transfer, $f_+^{K^0π^-}(0)=0.9696(15)_\text{stat}(12)_\text{syst}$. This is the first calculation that includes the dominant finite-volume effects, as calculated in chiral perturbation theory at next-to-leading order. Our result for the form factor provides a direct determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|=0.22333(44)_{f_+(0)}(42)_\text{exp}$, with a theory error that is, for the first time, at the same level as the experimental error. The uncertainty of the semileptonic determination is now similar to that from leptonic decays and the ratio $f_{K^+}/f_{π^+}$, which uses $|V_{ud}|$ as input. Our value of $|V_{us}|$ is in tension at the 2--$2.6σ$ level both with the determinations from leptonic decays and with the unitarity of the CKM matrix. In the test of CKM unitarity in the first row, the current limiting factor is the error in $|V_{ud}|$, although a recent determination of the nucleus-independent radiative corrections to superallowed nuclear $β$ decays could reduce the $|V_{ud}|^2$ uncertainty nearly to that of $|V_{us}|^2$. Alternative unitarity tests using only kaon decays, for which improvements in the theory and experimental inputs are likely in the next few years, reveal similar tensions. As part of our analysis, we calculated the correction to $f_+^{Kπ}(0)$ due to nonequilibrated topological charge at leading order in chiral perturbation theory, for both the full-QCD and the partially-quenched cases. We also obtain the combination of low-energy constants in the chiral effective Lagrangian $[C_{12}^r+C_{34}^r-(L_5^r)^2](M_ρ)=(2.92\pm0.31)\cdot10^{-6}$.

hep-lat↗
arXiv2019

$B\to D^\ast\ellν$ at non-zero recoil

The current status of the lattice-QCD calculations of the form factors of the $B\to D^\ast\ellν$ semileptonic decay is reviewed. Particular emphasis is given to the most mature calculation at non-zero recoil coming from the Fermilab Lattice and MILC collaborations. Blinded, preliminary results for the form factors are shown, including a preliminary, but detailed error budget. The lattice results seem to favor a large slope at small recoil, in contrast to the latest untagged results coming from the Belle collaboration. A comprehensive comparison between the latest BGL $z$ expansions of Belle, Babar, the lattice and a joint BGL fit including lattice and Belle data is presented, and a roadmap to improve the current calculation is discussed. The current implications for $V_{cb}$ and $R(D^\ast)$ are discussed.

hep-lat↗
arXiv2019

$D$ meson Semileptonic Decay Form Factors at $q^2 = 0$

We discuss preliminary results for the vector form factors $f_+^{\{π,K\}}$ at zero-momentum transfer for the decays $D\toπ\ellν$ and $D\to K \ellν$ using MILC's $N_f = 2+1+1$ HISQ ensembles at four lattice spacings, $a \approx 0.042, 0.06, 0.09$, and 0.12 fm, and various HISQ quark masses down to the (degenerate) physical light quark mass. We use the kinematic constraint $f_+(q^2)= f_0(q^2)$ at $q^2 = 0$ to determine the vector form factor from our study of the scalar current, which yields $f_0(0)$. Results are extrapolated to the continuum physical point in the framework of hard pion/kaon SU(3) heavy-meson-staggered $χ$PT and Symanzik effective theory. Our calculation improves upon the precision achieved in existing lattice-QCD calculations of the vector form factors at $q^2=0$. We show the values of the CKM matrix elements $|V_{cs}|$ and $|V_{cd}|$ that we would obtain using our preliminary results for the form factors together with recent experimental results, and discuss the implications of these values for the second row CKM unitarity.

hep-lat↗
arXiv2019

$B_s\to K\ellν$ decay from lattice QCD

We use lattice QCD to calculate the form factors $f_+(q^2)$ and $f_0(q^2)$ for the semileptonic decay $B_s\to K\ellν$. Our calculation uses six MILC asqtad 2+1 flavor gauge-field ensembles with three lattice spacings. At the smallest and largest lattice spacing the light-quark sea mass is set to 1/10 the strange-quark mass. At the intermediate lattice spacing, we use four values for the light-quark sea mass ranging from 1/5 to 1/20 of the strange-quark mass. We use the asqtad improved staggered action for the light valence quarks, and the clover action with the Fermilab interpolation for the heavy valence bottom quark. We use SU(2) hard-kaon heavy-meson rooted staggered chiral perturbation theory to take the chiral-continuum limit. A functional $z$ expansion is used to extend the form factors to the full kinematic range. We present predictions for the differential decay rate for both $B_s\to Kμν$ and $B_s\to Kτν$. We also present results for the forward-backward asymmetry, the lepton polarization asymmetry, ratios of the scalar and vector form factors for the decays $B_s\to K\ellν$ and $B_s\to D_s \ellν$. Our results, together with future experimental measurements, can be used to determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$.

hep-lat↗
arXiv2018

Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD

We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from $a\approx0.15$~fm to $0.03$~fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $\overline{\text{MS}}$-renormalized masses are $m_u(2~\text{GeV}) = 2.130(41)$~MeV, $m_d(2~\text{GeV}) = 4.675(56)$~MeV, $m_s(2~\text{GeV}) = 92.47(69)$~MeV, $m_c(3~\text{GeV}) = 983.7(5.6)$~MeV, and $m_c(m_c) = 1273(10)$~MeV, with four active flavors; and $m_b(m_b) = 4195(14)$~MeV with five active flavors. We also obtain ratios of quark masses $m_c/m_s = 11.783(25)$, $m_b/m_s = 53.94(12)$, and $m_b/m_c = 4.578(8)$. The result for $m_c$ matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of $α_s^4$. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: $\overlineΛ_\text{MRS}=555(31)$~MeV in the minimal renormalon-subtracted (MRS) scheme, $μ_π^2 = 0.05(22)~\text{GeV}^2$, and $μ_G^2(m_b)=0.38(2)~\text{GeV}^2$. The MRS scheme [Phys. Rev. D97, 034503 (2018), arXiv:1712.04983 [hep-ph]] is the key new aspect of our method.

hep-lat↗
arXiv2018

B- and D-meson leptonic decay constants and quark masses from four-flavor lattice QCD

We describe a recent lattice-QCD calculation of the leptonic decay constants of heavy-light pseudoscalar mesons containing charm and bottom quarks and of the masses of the up, down, strange, charm, and bottom quarks. Results for these quantities are of the highest precision to date. Calculations use 24 isospin-symmetric ensembles of gauge-field configurations with six different lattice spacings as small as approximately 0.03 fm and several values of the light quark masses down to physical values of the average up- and down-sea-quark masses. We use the highly-improved staggered quark (HISQ) formulation for valence and sea quarks, including the bottom quark. The analysis employs heavy-quark effective theory (HQET). A novel HQET method is used in the determination of the quark masses.

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