arXiv subjects

F. Sanfilippo

Publications and source records attributed to F. Sanfilippo.

At least 37 records · Page 2Linked to original sources

arXiv2022

Virtual Photon Emission in Leptonic Decays of Charged Pseudoscalar Mesons

We study the radiative leptonic decays $P\to\ellν_\ell\,\ell^{\prime\,+}\ell^{\prime\,-}$, where $P$ is a pseudoscalar meson and $\ell$ and $\ell^\prime$ are charged leptons. In such decays the emitted photon is off-shell and, in addition to the "point-like" contribution in which the virtual photon is emitted either from the lepton or the meson treated as a point-like particle, four structure-dependent (SD) form factors contribute to the amplitude. We present a strategy for the extraction of the SD form factors and implement it in an exploratory lattice computation of the decay rates for the four channels of kaon decays ($\ell,\ell^\prime=e,μ$). It is the SD form factors which describe the interaction between the virtual photon and the internal hadronic structure of the decaying meson, and in our procedure we separate the SD and point-like contributions to the amplitudes. We demonstrate that the form factors can be extracted with good precision and, in spite of the unphysical quark masses used in our simulation ($m_π\simeq 320\,$MeV and $m_K\simeq 530\,$MeV), the results for the decay rates are in reasonable semiquantitative agreement with experimental data (for the channels where these exist). Following this preparatory work, the emphasis of our future work will be on obtaining results at physical quark masses and on the control of the systematic uncertainties associated with discretisation and finite-volume errors.

hep-lat↗

arXiv2022

Virtual Photon Emission in Leptonic Decays of Pseudoscalar Mesons

We present a preliminary non-perturbative lattice calculation of the form factors entering the processes $K\to \ell\,ν_\ell\,\ell'^+\,\ell'^-$ and of the corresponding branching ratios. These form factors describe the interaction between the mediating virtual photon and the internal hadronic structure of the meson. By separating them from the point-like contribution to the matrix element we are able to isolate and reconstruct the structure-dependent contribution to the decay width. Our numerical analysis employs only one gauge ensemble and so it is affected by systematic uncertainties due to the missing continuum and physical point extrapolation. Despite this, we already find a reasonable agreement with the experimental data and with the next to leading order Chiral Perturbation Theory predictions. The method is general and can be applied to any pseudoscalar meson, though for heavier mesons the possibility of internal lighter states becomes problematic and still needs a proper study. A non-perturbative, model-independent lattice evaluation of these processes would allow further progress in the theoretical predictions of SM hadronic quantities and in the search of New Physics.

hep-lat↗

arXiv2021

Lattice determination of the pion mass difference $M_{π^{+}} - M_{π^{0}}$ at order $\mathcal{O}(α_{em})$ and $\mathcal{O}( (m_{d}-m_{u})^{2})$ including disconnected diagrams

We present our preliminary results concerning the charged/neutral pion mass difference $M_{π^{+}} - M_{π^{0}}$ at order $\mathcal{O}(α_{em})$ in the QED interactions, and for $M_{π^{+}} - M_{π^{0}}$ at order $\mathcal{O}\left( (m_{d}-m_{u})^{2}\right)$ in the strong isospin-breaking term. The latter contribution provides a determination of the $\rm{SU}(2)$ chiral perturbation theory low-energy constant $\ell_{7}$, whose present estimate is affected by a rather large uncertainty. The disconnected contributions appearing in the diagrammatic expansion of $M_{π^{+}} - M_{π^{0}}$, being very noisy, are notoriously difficult to evaluate and have been neglected in our previous calculations. By making use of twisted mass Lattice QCD simulations and adopting the RM123 method, we will show that taking profit from our recently proposed rotated twisted-mass (RTM) scheme, tailored to improve the signal on these kinds of observables, it is possible to evaluate the disconnected diagrams with good precision. For the QED induced pion mass difference, we obtain, after performing the extrapolation towards the continuum and thermodynamic limit and at the physical point, the preliminary value $M_{π^{+}}-M_{π^{0}} = 4.622~(95)~{\rm MeV}$, that is in good agreement with the experimental result. For the determination of the low-energy constant $\ell_{7}$, our result $\ell_{7} = 2.5~(1.4)\times 10^{-3}$, which is limited so far to a single lattice spacing, is in agreement and improves phenomenological estimates.

hep-lat↗

arXiv2021

Electromagnetic conductivity of quark-gluon plasma at non-zero baryon density

In this preprint we present our results on the study of the electromagnetic conductivity in dense quark-gluon plasma obtained within lattice simulations with $N_f = 2 + 1$ dynamical quarks. We employ stout improved rooted staggered quarks at the physical point and the tree-level Symanzik improved gauge action. The simulations are performed at imaginary baryon chemical potential, and the Tikhonov regularisation method is used to extract the conductivity from current-current correlators. Our results indicate an increase of QGP electromagnetic conductivity with real baryon density, and this dependence is quite strong.

hep-lat↗

arXiv2021

Quark masses using twisted mass fermion gauge ensembles

We present a calculation of the up, down, strange and charm quark masses performed within the lattice QCD framework. We use the twisted mass fermion action and carry out simulations that include in the sea two light mass-degenerate quarks, as well as the strange and charm quarks. In the analysis we use gauge ensembles simulated at three values of the lattice spacing and with light quarks that correspond to pion masses in the range from 350 MeV to the physical value, while the strange and charm quark masses are tuned approximately to their physical values. We use several quantities to set the scale in order to check for finite lattice spacing effects and in the continuum limit we get compatible results. The quark mass renormalization is carried out non-perturbatively using the RI'-MOM method converted into the $\overline{\rm MS}$ scheme. For the determination of the quark masses we use physical observables from both the meson and the baryon sectors, obtaining $m_{ud} = 3.636(66)(^{+60}_{-57})$~MeV and $m_s = 98.7(2.4)(^{+4.0}_{-3.2})$~MeV in the $\overline{\rm MS}(2\,{\rm GeV})$ scheme and $m_c = 1036(17)(^{+15}_{-8})$~MeV in the $\overline{\rm MS}(3\,{\rm GeV})$ scheme, where the first errors are statistical and the second ones are combinations of systematic errors. For the quark mass ratios we get $m_s / m_{ud} = 27.17(32)(^{+56}_{-38})$ and $m_c / m_s = 11.48(12)(^{+25}_{-19})$.

hep-lat↗

arXiv2021

Determination of the light, strange and charm quark masses using twisted mass fermions

We present results for the light, strange and charm quark masses using $N_f=2+1+1$ twisted mass fermion ensembles at three values of the lattice spacing, including two ensembles simulated with the physical value of the pion mass. The analysis is done both in the meson and baryon sectors. The difference in the mean values found in the two sectors is included as part of the systematic error. The presentation is based on the work of Ref. [1], where more details can be found.

hep-lat↗

arXiv2021

Ratio of kaon and pion leptonic decay constants with $N_f = 2 + 1 + 1$ Wilson-clover twisted-mass fermions

We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (isoQCD), $f_K / f_π$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from $\sim 0.068$ to $\sim 0.092$ fm with linear lattice size up to $L \sim 5.5$~fm. The scale is set by the PDG value of the pion decay constant, $f_π^{isoQCD} = 130.4~(2)$ MeV, at the isoQCD pion point, $M_π^{isoQCD} = 135.0~(2)$ MeV, obtaining for the gradient-flow (GF) scales the values $w_0 = 0.17383~(63)$ fm, $\sqrt{t_0} = 0.14436~(61)$ fm and $t_0 / w_0 = 0.11969~(62)$ fm. The data are analyzed within the framework of SU(2) Chiral Perturbation Theory (ChPT) without resorting to the use of renormalized quark masses. At the isoQCD kaon point $M_K^{isoQCD} = 494.2~(4)$ MeV we get $(f_K / f_π)^{isoQCD} = 1.1995~(44)$, where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{us}|$ and for the first-row CKM unitarity are discussed.

hep-lat↗

arXiv2021

Rotated twisted-mass: a convenient regularization scheme for isospin breaking QCD and QED lattice calculations

We propose a scheme of lattice twisted-mass fermion regularization which is particularly convenient for application to isospin breaking (IB) QCD and QED calculations, based in particular on the so called RM123 approach, in which the IB terms of the action are treated as a perturbation. The main, practical advantage of this scheme is that it allows the calculation of IB effects on some mesonic observables, like e.g. the pi+ - pi0 mass splitting, using lattice correlation functions in which the quark and antiquark fields in the meson are regularized with opposite values of the Wilson parameter r. These correlation functions are found to be affected by much smaller statistical fluctuations, with respect to the analogous functions in which quark and antiquark fields are regularized with the same value of r. Two numerical application of this scheme, that we call "rotated twisted-mass", within pure QCD and QCD+QED respectively, are also provided for illustration.

hep-lat↗

arXiv2021

Electromagnetic corrections to leptonic decay rates of charged pseudoscalar mesons: finite-volume effects

In Carrasco et al. we have recently proposed a method to calculate $O(e^2)$ electromagnetic corrections to leptonic decay widths of pseudoscalar mesons. The method is based on the observation that the infrared divergent contributions (that appear at intermediate stages of the calculation and that cancel in physical quantities thanks to the Bloch-Nordsieck mechanism) are universal, i.e. depend on the charge and the mass of the meson but not on its internal structure. In this talk we perform a detailed analysis of the finite-volume effects associated with our method. In particular we show that also the leading $1/L$ finite-volume effects are universal and perform an analytical calculation of the finite-volume leptonic decay rate for a point-like meson.

hep-lat↗

arXiv2021

Unitarity Bounds for Semileptonic Decays in Lattice QCD

In this work we discuss in detail the non-perturbative determination of the momentum dependence of the form factors entering in semileptonic decays using unitarity and analyticity constraints. The method contains several new elements with respect to previous proposals and allows to extract, using suitable two-point functions computed non-perturbatively, the form factors at low momentum transfer $q^2$ from those computed explicitly on the lattice at large $q^2$, without any assumption about their $q^2$-dependence. The approach will be very useful for exclusive semileptonic $B$-meson decays, where the direct calculation of the form factors at low $q^2$ is particularly difficult due to large statistical fluctuations and discretisation effects. As a testing ground we apply our approach to the semileptonic $D \to K \ell ν_\ell$ decay, where we can compare the results of the unitarity approach to the explicit direct lattice calculation of the form factors in the full $q^2$-range. We show that the method is very effective and that it allows to compute the form factors with rather good precision.

hep-lat↗

arXiv2021

First direct lattice calculation of the chiral perturbation theory low-energy constant $\ell_7$

We evaluate by means of lattice QCD calculations the low-energy constant $\ell_{7}$ which parametrizes strong isospin effects at NLO in $\rm{SU}(2)$ chiral perturbation theory. Among all low-energy constants at NLO, $\ell_{7}$ is the one known less precisely, and its uncertainty is currently larger than $50\%$. Our strategy is based on the RM123 approach in which the lattice path-integral is expanded in powers of the isospin breaking parameter $Δm= (m_{d}-m_{u})/2$. In order to evaluate the relevant lattice correlators we make use of the recently proposed rotated twisted-mass (RTM) scheme. Within the RM123 approach, it is possible to cleanly extract the value of $\ell_{7}$ from either the pion mass splitting $M_{π^{+}}-M_{π^{0}}$ induced by strong isospin breaking at order $\mathcal{O}\left((Δm)^{2}\right)$ (mass method), or from the coupling of the neutral pion $π^{0}$ to the isoscalar operator $\left(\bar{u}γ_{5}u + \bar{d}γ_{5} d\right)/\sqrt{2}$ at order $\mathcal{O}(Δm)$ (matrix element method). In this pilot study we limit the analysis to a single ensemble generated by the Extended Twisted Mass Collaboration (ETMC) with $N_{f}=2+1+1$ dynamical quark flavours, which corresponds to a lattice spacing $a\simeq 0.095~{\rm fm}$ and to a pion mass $M_π\simeq 260~{\rm MeV}$. We find that the matrix element method outperforms the mass method in terms of resulting statistical accuracy. Our determination, $\ell_{7} = 2.5(1.4)\times 10^{-3}$, is in agreement and improves previous calculations.

hep-lat↗

arXiv2021

Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data

We present a comparison of existing experimental data for the radiative leptonic decays $P\to\ellν_\ellγ$, where $P=K$ or $π$ and $\ell=e$ or $μ$, from the KLOE, PIBETA, E787, ISTRA+ and OKA collaborations with theoretical predictions based on the recent non-perturbative determinations of the structure-dependent vector and axial-vector form factors, $F_V$ and $F_A$ respectively. These were obtained using lattice QCD+QED simulations at order $O(α_{\mathrm{em}})$ in the electromagnetic coupling. We find good agreement with the KLOE data on $K\to eν_eγ$ decays from which the form factor $F^+=F_V+F_A$ can be determined. For $K\toμν_μγ$ decays we observe differences of up to 3\,-\,4 standard deviations at large photon energies between the theoretical predictions and the data from the E787, ISTRA+ and OKA experiments and similar discrepancies in some kinematical regions with the PIBETA experiment on radiative pion decays. A global study of all the kaon-decay data within the Standard Model results in a poor fit, largely because at large photon energies the KLOE and E787 data cannot be reproduced simultaneously in terms of the same form factor $F^+$. The discrepancy between the theoretical and experimental values of the form factor $F^-=F_V-F_A$ is even more pronounced. These observations motivate future improvements of both the theoretical and experimental determinations of the structure-dependent form factors $F^+$ and $F^-$, as well as further theoretical investigations of models of "new physics" which might for example, include possible flavor changing interactions beyond $V - A$ and/or non-universal corrections to the lepton couplings.

hep-ph↗

arXiv2020

Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM

We consider a set of half-BPS operators in $\mathcal{N}=4$ super Yang-Mills theory which are appropriate for describing single-particle states of superstring theory on AdS${}_5 \times S^5$. These single-particle operators are defined to have vanishing two-point functions with all multi-trace operators and therefore correspond to admixtures of single- and multi-traces. We find explicit formulae for all single-particle operators and for their two-point function normalisation. We show that single-particle $U(N)$ operators belong to the $SU(N)$ subspace, thus for length greater than one they are simply the $SU(N)$ single-particle operators. Then, we point out that at large $N$, as the length of the operator increases, the single-particle operator naturally interpolates between the single-trace and the $S^3$ giant graviton. At finite $N$, the multi-particle basis, obtained by taking products of the single-particle operators, gives a new basis for all half-BPS states, and this new basis naturally cuts off when the length of any of the single-particle operators exceeds the number of colours. From the two-point function orthogonality we prove a multipoint orthogonality theorem which implies vanishing of all near-extremal correlators. We then compute all maximally and next-to-maximally extremal free correlators, and we discuss features of the correlators when the extremality is lowered. Finally, we describe a half-BPS projection of the operator product expansion on the multi-particle basis which provides an alternative construction of four- and higher-point functions in the free theory.

hep-th↗

arXiv2020

First lattice calculation of radiative leptonic decay rates of pseudoscalar mesons

We present a non-perturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell \bar ν_\ell γ$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. Together with the non-perturbative determination of the corrections to the processes $P\to \ell \bar ν_\ell$ due to the exchange of a virtual photon, this allows accurate predictions at $O(α_{em})$ to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $D_s$ meson. We are able to separate unambiguously and non-pertubatively the point-like contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully non-perturbative $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements also at $O(α_{em})$. Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data.

hep-lat↗

arXiv2019

Non-perturbative renormalization in QCD+QED and its application to weak decays

We present a novel strategy to renormalize lattice operators in QCD+QED, including first order QED corrections to the non-perturbative evaluation of QCD renormalization constants. Our procedure takes systematically into account the mixed non-factorizable QCD+QED effects which were neglected in previous calculations, thus significantly reducing the systematic uncertainty on renormalization corrections. The procedure is presented here in the RI'-MOM scheme, but it can be applied to other schemes (e.g. RI-SMOM) with appropriate changes. We discuss the application of this strategy to the calculation of the leading isospin breaking corrections to the leptonic decay rates $Γ(π_{μ2})$ and $Γ(K_{μ2})$, evaluated for the first time on the lattice. The precision in the matching to the $W$-regularization scheme is improved to $\mathcal{O}(α_{em}α_s(M_W))$ with respect to previous calculations. Finally, we show the updated precise result obtained for the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|$.

hep-lat↗

arXiv2019

Light-meson leptonic decay rates in lattice QCD+QED

The leading electromagnetic (e.m.) and strong isospin-breaking corrections to the $π^+ \to μ^+ ν[γ]$ and $K^+ \to μ^+ ν[γ]$ leptonic decay rates are evaluated for the first time on the lattice. The results are obtained using gauge ensembles produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks. The relative leading-order e.m.~and strong isospin-breaking corrections to the decay rates are 1.53(19)\% for $π_{μ2}$ decays and 0.24(10)\% for $K_{μ2}$ decays. Using the experimental values of the $π_{μ2}$ and $K_{μ2}$ decay rates and updated lattice QCD results for the pion and kaon decay constants in isosymmetric QCD, we find that the Cabibbo-Kobayashi-Maskawa matrix element $ | V_{us}| = 0.22538(46)$, reducing by a factor of about $1.8$ the corresponding uncertainty in the Particle Data Group review. Our calculation of $|V_{us}|$ allows also an accurate determination of the first-row CKM unitarity relation $| V_{ud}|^2 + | V_{us}|^2 + | V_{ub}|^2 = 0.99988(46)$. Theoretical developments in this paper include a detailed discussion of how QCD can be defined in the full QCD+QED theory and an improved renormalisation procedure in which the bare lattice operators are renormalised non-perturbatively into the (modified) Regularization Independent Momentum subtraction scheme and subsequently matched perturbatively at $O(α_{em}α_s(M_W))$ into the W-regularisation scheme appropriate for these calculations.

hep-lat↗

arXiv2019

Radiative corrections to semileptonic decay rates

We discuss the theoretical framework required for the computation of radiative corrections to semileptonic decay rates in lattice simulations, and in particular to those for $K_{\ell3}$ decays. This is an extension of the framework we have developed and successfully implemented for leptonic decays. New issues which arise for semileptonic decays, include the presence of unphysical terms which grow exponentially with the time separation between the insertion of the weak Hamiltonian and the sink for the final-state meson-lepton pair. Such terms must be identified and subtracted. We discuss the cancellation of infrared divergences and show that, with the QED$_\mathrm{\,L}$ treatment of the zero mode in the photon propagator, the $O(1/L)$ finite-volume corrections are "universal". These corrections however, depend not only on the semileptonic form factors $f^\pm(q^2)$ but also on their derivatives $df^\pm/dq^2$. (Here $q$ is the momentum transfer between the initial and final state mesons.) We explain the perturbative calculation which would need to be performed to subtract the $O(1/L)$ finite-volume effects.

hep-lat↗

arXiv2019

Real photon emissions in leptonic decays

We present a non-perturbative calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell \bar ν_\ell γ$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. Together with the non-perturbative determination of the virtual photon corrections to the processes $P\to \ell \bar ν_\ell$, this will allow accurate predictions to be made at $O(α_{em})$ for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $B$ meson. We are able to separate unambiguously the point-like contribution, the square of which leads to the infrared divergence in the decay rate, from the structure dependent, infrared-safe, terms in the amplitude. The fully non-perturbative, $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to significantly improved precision in the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. Precise predictions for the emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data.

hep-lat↗