arXiv subjects

S. Simula

Publications and source records attributed to S. Simula.

At least 19 recordsLinked to original sources

arXiv2026

The hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment in isospin-symmetric lattice QCD with twisted-mass fermions

We present a lattice-QCD calculation of the leading-order hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon in isospin-symmetric QCD. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks at four lattice spacings and at values of the quark-mass parameters matching the definition of isospin-symmetric QCD given in the FLAG review 2024 and in the 2025 edition of the Muon $g-2$ Theory Initiative White Paper (WP25). After retuning the simulation parameters to precisely match these two definitions of isospin-symmetric QCD, and after carrying out an extrapolation to the continuum limit based on the data at lattice spacings $a \simeq 0.049, 0.057, 0.068$ and $0.079$~fm, and spatial lattice sizes up to $L \simeq 7.7$~fm, we obtain $a_μ^{\rm HVP, FLAG}(\rm{iso}) = (720.0 \pm 6.9) \times 10^{-10}$ and $a_μ^{\rm HVP, WP25}(\rm{iso}) = (714.8 \pm 7.4) \times 10^{-10}$. Our results, which have a relative uncertainty of about $1 \%$, agree well with the corresponding determinations by other lattice groups. After adding to our determination of $a_μ^{\rm HVP, WP25}(\rm{iso})$ the leading isospin-breaking corrections provided in the WP25, namely $a_μ^{\rm HVP, WP25}({\rm IB}) = 0.1(3.4)\times 10^{-10}$, we obtain for the full HVP the value $a_μ^{\rm HVP}= (714.9 \pm 8.1)\times 10^{-10}$. This result translates into a Standard Model prediction for the muon anomalous magnetic moment that is fully consistent with the latest result by the Fermilab Muon $g-2$ experiment and strengthens the tension between lattice QCD and data-driven (pre-CMD3) dispersive determinations.

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arXiv2026

The Semileptonic B Frontier: LHC, B-factories, Lattice QCD & the Hunt for Precision

This review document summarizes the main outcomes and key theoretical and experimental developments discussed at the workshop ``The Semileptonic $B$ Frontier: LHC, $B$-Factories, Lattice QCD & the Hunt for Precision'', held at Laboratori Nazionali di Frascati on 16--18 February, https://agenda.infn.it/event/49469/. Bringing together experimentalists and theorists, the meeting addressed recent advances and outstanding challenges in both charged-current ($b \to c/u\,\ellν$) and neutral-current ($b \to s\,\ell^+\ell^-$) semileptonic $b$-hadron decays. We synthesize current experimental measurements from Belle, Belle~II, and LHCb with state-of-the-art theoretical inputs---including Lattice QCD determinations, Heavy Quark Expansion (HQE) frameworks, and QED radiative corrections. In addition to reviewing the status of CKM matrix elements, hadronic form factor extractions, and Lepton Flavor Universality (LFU) tests, this report highlights novel observables and fitting techniques designed to maximize the sensitivity of future analyses and guide upcoming data-taking campaigns.

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arXiv2026

Rare kaon decays $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$: Standard Model predictions from lattice QCD

Weak decays of charged kaons with an additional lepton-antilepton pair, $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$ ($K_{\ell2\ell'}$), are suppressed at order $O(G_{F}^{2}α_{\rm em}^{2})$ in the Standard Model (SM) and provide sensitive probes of its flavour structure, as well as independent determinations of the Cabibbo angle $|V_{us}|$. In this Letter we present the SM predictions for all four channels with $\ell,\ell' =e,μ$, based on the first complete lattice QCD calculation of the structure-dependent form factors reported in a companion paper [1]. Using the PDG value [2] $|V_{us}|^{\rm PDG}=0.22431(85)$, we obtain branching fractions with controlled uncertainties and precisions ranging from $2\%$ to $7\%$, depending on the channel. For the three modes with published measurements, our results agree with experiment. For the $K_{\mu2μ}$ mode, for which no published experimental result is available, we compare our prediction with the preliminary NA62 result, finding agreement at the $1.4σ$ level. Conversely, the measured decay rates can be used together with our results to extract $|V_{us}|$ from these modes. A weighted average over the two most precise channels, $K_{\mu2e}$ and $K_{\mu2μ}$, yields $|V_{us}|=0.2283(42)$, corresponding to a $1.8\%$ determination. These results pave the way for using $K_{\ell2\ell'}$ decays as precision probes of the SM.

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arXiv2026

Complete lattice QCD calculation of $K^{-}\to \ell^{-}\barν_{\ell}\ell^{'+}\ell^{'-}$ form factors

We present the first complete lattice QCD calculation of the four structure-dependent form factors governing the rare charged kaon decay $K^- \to \ell^- \barν_\ell \ell'^+ \ell'^-$, with fully controlled statistical and systematic uncertainties. Our calculation is based on gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ flavors of Wilson-clover twisted-mass fermions. Simulations are performed directly at the physical values of the light and strange quark masses, and include an estimate of the quark-disconnected contributions in which the virtual photon couples to sea quarks. All four form factors are determined across the kinematical region probed by experiments. The Spectral Function Reconstruction (SFR) method of Ref. [1] is employed to overcome the analytic continuation problem for dilepton invariant masses above the two-pion threshold. Finite-volume effects are investigated using ensembles with spatial extents $L\simeq [3.8,7.6]~\mathrm{fm}$, while the continuum limit is obtained from three lattice spacings in the range $a\in[0.057, 0.08]~\mathrm{fm}$. Our results for the form factors enable the evaluation of decay rates and differential observables for all four channels, $K^- \to e^- \barν_e e^+ e^-$, $K^- \to e^- \barν_e μ^+ μ^-$, $K^- \to μ^- \barν_μe^+ e^-$, and $K^- \to μ^- \barν_μμ^+ μ^-$, thereby providing first-principles Standard Model predictions against which existing and upcoming measurements can be directly compared. A detailed phenomenological analysis of the decay rates and associated observables is presented in a companion paper [2].

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arXiv2026

Theoretical framework for lattice QCD computations of $B\to K \ell^+ \ell^-$ and $\bar{B}_s\to \ell^+\ell^- γ$ decays rates, including contributions from charming penguin diagrams

We develop a strategy for computing the $B\to K\ell^+\ell^-$ and $\bar{B}_s\toγ\ell^+\ell^-$ decay amplitudes using lattice QCD (where $\ell^\pm$ are charged leptons). We focus on those terms which contain complex contributions to the amplitude, due to on-shell intermediate states propagating between the weak operator and electromagnetic current(s). Such terms, which are generally estimated using model calculations and represent significant uncertainties in the phenomenological predictions for these decays, cannot be computed using standard lattice QCD techniques. It has recently been shown that such contributions can be computed using spectral-density methods and our proposed strategy, which we discuss in detail, is built on this approach. The complex contributions include the ``charming penguins" (matrix elements of the current-current operators $O_1^{(c)}$ and $O_2^{(c)}$ defined in Eq. (6) below), in which the charm-quark loop can propagate long distances, particularly close to the region of charmonium resonances. They also include the contributions from the chromomagnetic operator ($O_8$ in standard notation, defined in Eq. (8) below). We discuss the renormalization of the ultra-violet divergences, and in particular those which arise due to ``contact" terms, and explain how those which appear as inverse powers of the lattice spacing can be subtracted non-perturbatively. We apply the spectral density methods in an instructive exploratory computation of the charming penguin diagram in $B\to K\ell^+\ell^-$ decays in which the virtual photon is emitted from the charm-quark loop (the diagram in Fig. 1(a) below) and discuss the prospects and strategies for the reliable determination of the amplitudes in future dedicated computations; computations which are however, beyond the scope of the present paper.

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arXiv2025

Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point

We present a lattice QCD calculation of the radiative leptonic decay rates of the kaon, improving upon our previous work, arXiv:2006.05358. Our analysis uses gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with $N_{f} = 2 + 1 + 1$ flavors of Wilson-clover twisted mass fermions. For the first time, we go beyond the electroquenched approximation by including quark-disconnected contributions. Several key improvements have been implemented: (i) the simulations are now performed directly at physical light- and strange-quark masses, (ii) finite-size effects are carefully investigated using lattices with spatial extents ranging from $L \simeq 3.8\,\mathrm{fm}$ to $L \simeq 7.7\,\mathrm{fm}$, and (iii) the continuum extrapolation is based on three lattice spacings in the range $a \in [0.08, 0.058]\,\mathrm{fm}$. As a result of the high-precision determination of the relevant correlation functions, we reduce the uncertainties on both the axial and vector form factors by nearly a factor of two compared to our previous analysis. When compared to experimental measurements in the electron channel ($K^- \to e^- \barν_e γ$), our results show a tension -- at the level of $2.6$ standard deviations -- with respect to KLOE data. On the other hand, they are compatible with measurements from the E36 Collaboration at J-PARC. In the muonic decay channel ($K^- \to μ^- \barν_μγ$), we confirm the tensions, already observed in our previous study, between lattice QCD predictions and ISTRA+ and OKA data, which are both primarily sensitive to the value of the negative-helicity form factor $F^{-}$.

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arXiv2025

Semileptonic $B \to D^*$ decays from light to $τ$ leptons: the extraction of the form factor $F_2$ from data

We extend the Standard Model (SM) analysis of Ref. [1], which was limited to light leptons in the final state, to the semileptonic $B \to D^* τν_τ$ decay. By using quantities that can be analised without the knowledge of $\vert V_{cb}\vert$, we derive important information about the helicity amplitudes and the hadronic form factors that can be compared with the predictions of lattice QCD calculations. In particular, there is a difficulty in reproducing simultaneously the experimental values of $R(D^*)$ and of other quantities relevant for the semitauonic decays within the SM. As a byproduct of our analysis, we also present a determination of $\vert V_{cb}\vert$ from the total decay rate.

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arXiv2025

What we can learn from the angular differential rates (only) in semileptonic $B \to D^* \ell ν_\ell$ decays

We present a simple approach to the study of semileptonic $B \to D^* \ell ν_\ell$ decays based on the angular distributions of the final state particles only. Our approach is model independent and never requires the knowledge of $\vert V_{cb} \vert$. By studying such distributions in the case of light leptons, a comparison between results from different data sets from the Belle and BelleII Collaborations and between data and Standard Model calculations is also given for several interesting quantities. A good consistency is observed between some of the experimental results and the theoretical predictions.

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arXiv2024

Strange and charm quark contributions to the muon anomalous magnetic moment in lattice QCD with twisted-mass fermions

We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon in isospin symmetric QCD. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks at five lattice spacings and at values of the quark mass parameters that are close and/or include the isospin symmetric QCD point of interest. After computing the small corrections necessary to precisely match this point, and carrying out an extrapolation to the continuum limit based on the data at lattice spacings $a \simeq 0.049, 0.057, 0.068, 0.080$~fm and spatial lattice sizes up to $L \simeq 7.6$~fm, we obtain $a_μ^{\rm HVP}(s) = (53.57 \pm 0.63) \times 10^{-10}$ and $a_μ^{\rm HVP}(c) = (14.56 \pm 0.13) \times 10^{-10}$, for the quark-connected strange and charm contributions, respectively. Our findings agree well with the corresponding results by other lattice groups.

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arXiv2024

Inclusive hadronic decay rate of the $τ$ lepton from lattice QCD: the $\bar u s$ flavour channel and the Cabibbo angle

We present a lattice determination of the inclusive decay rate of the process $τ\mapsto X_{us} ν_τ$ in which the $τ$ lepton decays into a generic hadronic state $X_{us}$ with $\bar u s$ flavour quantum numbers. Our results have been obtained in $n_f=2+1+1$ iso-symmetric QCD with full non-perturbative accuracy, without any OPE approximation and, except for the presently missing long-distance isospin-breaking corrections, include a solid estimate of all sources of theoretical uncertainties. This has been possible by using the Hansen-Lupo-Tantalo method [1] that we have already successfully applied in [2] to compute the inclusive decay rate of the process $τ\mapsto X_{ud} ν_τ$ in the $\bar u d$ flavour channel. By combining our first-principles theoretical results with the presently-available experimental data we extract the CKM matrix element $\vert V_{us}\vert$, the Cabibbo angle, with a $0.9$\% accuracy, dominated by the experimental error.

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arXiv2024

Updates on the determination of $\vert V_{cb} \vert$, $R(D^{*})$ and $\vert V_{ub} \vert/\vert V_{cb} \vert$

We present an updated determination of the values of $\vert V_{cb} \vert$, $R(D^*)$ and $\vert V_{ub} \vert/\vert V_{cb} \vert$ based on the new data on semileptonic $B \to D^* \ell ν_\ell$ decays by the Belle and Belle-II Collaborations and on the recent theoretical progress in the calculation of the form factors relevant for semileptonic $B \to D^* \ell ν_\ell$ and $B_s \to K \ell ν_\ell$ decays. In particular we present results derived by applying either the Dispersive Matrix (DM) method of Refs. [1-6] or the more standard Boyd-Grinstein-Lebed (BGL) [7] approach to the most recent values of the form factors determined in lattice QCD. Using all the available lattice results for the form factors from the DM method we get the theoretical value $R^{\rm th}(D^*) = 0.262 \pm 0.009$ and we extract from a bin-per-bin analysis of the experimental data the value $\vert V_{cb} \vert = (39.92 \pm 0.64) \cdot10^{-3}$. Our result for $R(D^*)$ is consistent with the latest experimental world average $R^{\rm exp}(D^*) = 0.284 \pm 0.012$ [8]} at the $\simeq 1.5\,σ$ level. Our value for $\vert V_{cb} \vert$ is compatible with the latest inclusive determinations $\vert V_{cb} \vert^{\rm incl} = (41.97 \pm 0.48) \cdot 10^{-3}$ [9] and $\vert V_{cb} \vert^{\rm incl} = (41.69\pm 0.63) \cdot 10^{-3}$ [10] within $\simeq 2.6$ and $\simeq 2.0$ standard deviations, respectively. From a reappraisal of the calculations of $\vert V_{ub} \vert / \vert V_{cb} \vert$, we also obtain $\vert V_{ub} \vert / \vert V_{cb} \vert = 0.087\pm 0.009$ in good agreement with the result $\vert V_{ub} \vert / \vert V_{cb} \vert = 0.0844\pm 0.0056$ from the latest FLAG review [11].

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arXiv2024

The $B_{s}\to μ^{+}μ^{-}γ$ decay rate at large $q^{2}$ from lattice QCD

We determine, by means of lattice QCD calculations, the local form factors describing the $B_{s}\to μ^{+}μ^{-}γ$ decay. For this analysis we make use of the gauge configurations produced by the ETM Collaboration with $N_{f}=2+1+1$ flavour of Wilson-Clover twisted-mass fermions at maximal twist. To obtain the $B_{s}$ meson form-factors, we perform simulations for several heavy-strange meson masses $m_{H_{s}}$ in the range $m_{H_{s}} \in [ m_{D_{s}}, 2 m_{D_{s}} ]$, and extrapolate to the physical $B_{s}$ meson point $m_{B_{s}}\simeq 5.367~{\rm GeV}$ making use of the HQET scaling laws. We cover the region of large di-muon invariant masses $\sqrt{q^{2}} > 4.16\,{\rm GeV}$, and use our results to determine the branching fraction for $B_{s}\to μ^{+}μ^{-}γ$, which has been recently measured by LHCb in the region $\sqrt{q^{2}} > 4.9\,{\rm GeV}$. The largest contribution to the uncertainty in the partial branching fractions at values of $\sqrt{q^{2}} < 4.8\,{\rm GeV}$ is now due to resonance and other long-distance effects, including those from "charming penguins", which we estimate by summing over the contributions from the $J_P=1^-$ charmonium resonances.

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arXiv2023

Dispersive analysis of the experimental data on the electromagnetic form factor of charged pions at spacelike momenta

The experimental data on the electromagnetic form factor of charged pions available at spacelike momenta are analyzed using the Dispersive Matrix (DM) approach, which describes the momentum dependence of hadronic form factors without introducing any explicit parameterization and includes properly the constraints coming from unitarity and analyticity. The unitary bound is evaluated nonperturbatively making use of the results of lattice QCD simulations of suitable two-point correlation functions contributing to the HVP term of the muon. Thanks to the DM method we determine the pion charge radius from existing spacelike data in a completely model-independent way and consistently with the unitary bound, obtaining $< r_π>_{DM} = 0.703 \pm 0.027$ fm. This finding differs by $\simeq 1.6$ standard deviations from the latest PDG value $< r_π>_{PDG} = 0.659 \pm 0.004$ fm, which is dominated by the very precise results of dispersive analyses of timelike data coming from measurements of the cross section of the $e^+ e^- \to π^+ π^-$ process. We have analyzed the spacelike data using also traditional $z$-expansions, like the Boyd-Grinstein-Lebed (BGL) or Bourrely-Caprini-Lellouch (BCL) fitting functions and adopting a simple procedure that incorporates ab initio the non-perturbative unitary bound in the fitting process. We get $< r_π>_{BGL} = 0.711 \pm 0.039$ fm and $< r_π>_{BCL} = 0.709 \pm 0.028$ fm in nice agreement with the DM result. We have addressed also the issue of the onset of perturbative QCD by performing a sensitivity study of the pion form factor at large spacelike momenta, based only on experimental spacelike data and unitarity. Hence, although the leading pQCD behaviour is found to set in only at very large momenta, our DM bands may provide information about the pre-asymptotic effects related to the scale dependence of the pion distribution amplitude.

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arXiv2023

Spectral-function determination of complex electroweak amplitudes with lattice QCD

We present a novel method to determine on the lattice both the real and imaginary parts of complex electroweak amplitudes involving two external currents and a single hadron or the QCD vacuum in the external states. The method is based on the spectral representation of the relevant time-dependent correlation functions and, by extending the range of applicability of other recent proposals built on the same techniques, overcomes the difficulties related to the analytic continuation from Minkowskian to Euclidean time, arising when intermediate states with energies smaller than the external states contribute to the amplitude. In its simplest form, the method relies on the standard $i \varepsilon$ prescription to regularize the Feynman integrals and at finite $\varepsilon$ it requires to verify the condition $1/L \ll \varepsilon \ll Δ(E)$, where $L$ is the spatial extent of the lattice and, for any given energy $E$, $Δ(E)$ represents the typical size of the interval around $E$ in which the hadronic amplitude is significantly varying. In order to illustrate the effectiveness of this approach in a realistic case, we apply the method to evaluate non-perturbatively the hadronic amplitude contributing to the radiative leptonic decay $D_s \to\ellν_\ell\,γ^*$, working for simplicity with a single lattice ensemble at fixed volume and lattice spacing.

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arXiv2023

Lattice calculation of the $D_{s}$ meson radiative form factors over the full kinematical range

We compute the structure-dependent axial and vector form factors for the radiative leptonic decays $D_s\to \ellν_\ellγ$, where $\ell$ is a charged lepton, as functions of the energy of the photon in the rest frame of the $D_s$ meson. The computation is performed using gauge-field configurations with 2+1+1 sea-quark flavours generated by the European Twisted Mass Collaboration and the results have been extrapolated to the continuum limit. For the vector form factor we observe a very significant partial cancellation between the contributions from the emission of the photon from the strange quark and that from the charm quark. The results for the form factors are used to test the reliability of various Anzätze based on single-pole dominance and its extensions, and we present a simple parametrization of the form factors which fits our data very well and which can be used in future phenomenological analyses. Using the form factors we compute the differential decay rate and the branching ratio for the process $D_s\to eν_eγ$ as a function of the lower cut-off on the photon energy. With a cut-off of 10 MeV for example, we find a branching ratio of Br$(E_γ>10\,\mathrm{MeV})=4.4(3)\times 10^{-6}$ which, unlike some model calculations, is consistent with the upper bound from the BESIII experiment Br$(E_γ>10\,\mathrm{MeV})<1.3\times 10^{-4}$ at 90% confidence level. Even for photon energies as low as 10 MeV, the decay $D_s\to eν_eγ$ is dominated by the structure-dependent contribution to the amplitude (unlike the decays with $\ell=μ$ or $τ$), confirming its value in searches for hypothetical new physics as well as in determining the Cabibbo-Kobayashi-Maskawa (CKM) parameters at $O(α_\mathrm{em})$, where $α_{\mathrm{em}}$ is the fine-structure constant.

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arXiv2022

Time windows of the muon HVP from twisted-mass lattice QCD

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arXiv2022

Exclusive determinations of $\vert V_{cb} \vert$ and $R(D^{*})$ through unitarity

In this work we apply the Dispersive Matrix (DM) method of Refs. [1,2] to the lattice computations of the Form Factors (FFs) entering the semileptonic $B \to D^* \ell ν_\ell$ decays, recently produced by the FNAL/MILC Collaborations [3] at small, but non-vanishing values of the recoil variable ($w-1$). Thanks to the DM method we obtain the FFs in the whole kinematical range accessible to the decay in a completely model-independent and non-perturbative way, implementing exactly both unitarity and kinematical constraints. Using our theoretical bands of the FFs we extract $\vert V_{cb} \vert$ from the experimental data and compute the theoretical value of $R(D^*)$. Our final result for $\vert V_{cb} \vert$ reads $\vert V_{cb} \vert = (41.3 \pm 1.7) \cdot 10^{-3}$, compatible with the most recent inclusive estimate at the $0.5σ$ level. Moreover, we obtain the pure theoretical value $R(D^*) = 0.275 \pm 0.008$, which is compatible with the experimental world average at the $\sim 1.3 σ$ level.

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arXiv2022

Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_μ^{\rm HVP}$, in the so-called short and intermediate time-distance windows, $a_μ^{\rm SD}$ and $a_μ^{\rm W}$, defined by the RBC/UKQCD Collaboration [1]. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavors tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\simeq 0.057, 0.068$ and $0.080$ fm with spatial lattice sizes up to $L \simeq 7.6$~fm. For the short distance window we obtain $a_μ^{\rm SD}({\rm ETMC}) = 69.27\,(34) \cdot 10^{-10}$, which is consistent with the recent dispersive value of $a_μ^{\rm SD}(e^+ e^-) = 68.4\,(5) \cdot 10^{-10}$ [2]. In the case of the intermediate window we get the value $a_μ^{\rm W}({\rm ETMC}) = 236.3\,(1.3) \cdot 10^{-10}$, which is consistent with the result $a_μ^{\rm W}({\rm BMW}) = 236.7\,(1.4) \cdot 10^{-10}$ [3] by the BMW collaboration as well as with the recent determination by the CLS/Mainz group of $a_μ^{\rm W}({\rm CLS}) = 237.30\,(1.46) \cdot 10^{-10}$ [4]. However, it is larger than the dispersive result of $a_μ^{\rm W}(e^+ e^-) = 229.4\,(1.4) \cdot 10^{-10}$ [2] by approximately $3.6$ standard deviations. The tension increases to approximately $4.5$ standard deviations if we average our ETMC result with those by BMW and CLS/Mainz. Our accurate lattice results in the short and intermediate windows point to a possible deviation of the $e^+ e^-$ cross section data with respect to Standard Model predictions in the low and intermediate energy regions, but not in the high energy region.

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