Search

We study current experimental bounds on charged lepton flavor violating (CLFV) $\mu$-$e$ interactions in the model-independent framework of the Standard Model Effective Field Theory (SMEFT). Assuming a generic flavor structure in the quark sector, we consider the contributions of CLFV operators to low-energy observables, including $\mu\to e\gamma$ and $\mu\to e$ conversion for quark-flavor conserving operators and CLFV meson decays for quark-flavor violating operators. At high energy, we consider limits on CLFV decays of the Higgs and Z bosons and of the top quark, and obtain bounds on operators with light quarks by recasting searches for production of $e\mu$ pairs in $pp$ collisions at the Large Hadron Collider (LHC). We connect observables at low- and high-energy by taking into account renormalization group running and matching between CLFV operators. We also discuss the sensitivity of the future Electron-Ion Collider, where the prospective bounds are derived by imposing simple cuts on final state particles. We find that, in a single operator scenario, bounds on purely leptonic operators are dominated by $\mu \rightarrow e \gamma$ and $\mu \rightarrow e$ conversion. Semileptonic operators with down-type quarks are also dominantly constrained by low-energy observables, while LHC searches lead the bounds on up-type quark-flavor violating operators. Taking simplified multiple-coupling scenarios, we show that it is easy to evade the strongest low-energy bounds from spin-independent $\mu \rightarrow e$ conversion, and that collider searches are competitive and complementary to constraints from spin-dependent $\mu \rightarrow e$ conversion and other low-energy probes., Comment: 43 pages, 7 figures

Working with Resonance Chiral Theory, within the two resonance multiplets saturation scheme, we satisfy leading (and some subleading) chiral and asymptotic QCD constraints and accurately fit simultaneously the $\pi^{0},\eta,\eta^{\prime}$ transition form factors, for single and double virtuality. In the latter case, we supplement the few available measurements with lattice data to ensure a faithful description. Mainly due to the new results for the doubly virtual case, we improve over existing descriptions for the $\eta$ and $\eta^\prime$. Our evaluation of the corresponding pole contributions to the hadronic light-by-light piece of the muon $g-2$ read: $a_\mu^{\pi^{0}\text{-}\rm{pole}}=\left(61.9\pm0.6^{+2.4}_{-1.5}\right)\times10^{-11}$, $a_\mu^{\eta\text{-}\rm{pole}}=\left(15.2\pm0.5^{+1.1}_{-0.8}\right)\times10^{-11}$ and $a_\mu^{\eta^\prime\text{-}\rm{pole}}=\left(14.2\pm0.7^{+1.4}_{-0.9}\right)\times10^{-11}$, for a total of $a_\mu^{\pi^0+\eta+\eta^{\prime}\text{-}\rm{pole}}=\left(91.3\pm1.0^{+3.0}_{-1.9}\right)\times10^{-11}$, where the first and second errors are the statistical and systematic uncertainties, respectively., Comment: 49 pages, 8 figures. The correlations between the pseudo-data points from Lattice QCD were considered and the Global Analysis was changed accordingly in this version. Furthermore, the high energy behavior was analyzed in the whole spectrum of asymmetries between the single virtual and the double virtual case

It has been long-understood that final state rescattering effects provide $\mathcal{O}(1)$ corrections to hadronic meson decays rates, such as $\eta\to\pi\pi\pi$ and $\eta^{\prime}\to\eta\pi\pi$. Hence, one would expect that such effects would be just as important in axio-hadronic $\eta$ and $\eta^{\prime}$ decays, such as $\eta^{(\prime)}\to\pi\pi a$, where $a$ is an axion or axion-like particle (ALP). And indeed they are, as we show in this paper by using the treatment of dispersion relations to include the effects of strong final state interactions in several axio-hadronic processes, namely, $\eta^{(\prime)}\to\pi^0\pi^0 a$, $\eta^{(\prime)}\to\pi^+\pi^- a$, and $\eta^{\prime}\to\eta\pi^0 a$. We also compute the perturbative, leading order decay rates for multiple ALP emission, such as in $\eta^{(\prime)}\to\pi^{0}aa$, $\eta^{\prime}\to\eta aa$ and $\eta^{(\prime)}\to aaa$, and briefly discuss the expected corrections from strong interactions and the processes that must be considered for an accurate rate estimation of these multi-ALP decay channels., Comment: 29 pages, 9 figures

This document presents the initial scientific case for upgrading the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) to 22 GeV. It is the result of a community effort, incorporating insights from a series of workshops conducted between March 2022 and April 2023. With a track record of over 25 years in delivering the world's most intense and precise multi-GeV electron beams, CEBAF's potential for a higher energy upgrade presents a unique opportunity for an innovative nuclear physics program, which seamlessly integrates a rich historical background with a promising future. The proposed physics program encompass a diverse range of investigations centered around the nonperturbative dynamics inherent in hadron structure and the exploration of strongly interacting systems. It builds upon the exceptional capabilities of CEBAF in high-luminosity operations, the availability of existing or planned Hall equipment, and recent advancements in accelerator technology. The proposed program cover various scientific topics, including Hadron Spectroscopy, Partonic Structure and Spin, Hadronization and Transverse Momentum, Spatial Structure, Mechanical Properties, Form Factors and Emergent Hadron Mass, Hadron-Quark Transition, and Nuclear Dynamics at Extreme Conditions, as well as QCD Confinement and Fundamental Symmetries. Each topic highlights the key measurements achievable at a 22 GeV CEBAF accelerator. Furthermore, this document outlines the significant physics outcomes and unique aspects of these programs that distinguish them from other existing or planned facilities. In summary, this document provides an exciting rationale for the energy upgrade of CEBAF to 22 GeV, outlining the transformative scientific potential that lies within reach, and the remarkable opportunities it offers for advancing our understanding of hadron physics and related fundamental phenomena., Comment: Updates to the list of authors; Preprint number changed from theory to experiment; Updates to sections 4 and 6, including additional figures

We study the decay $J/\psi\to\pi^{+}\pi^{-}\pi^{0}$ within the framework of the Khuri-Treiman equations. We find that the BESIII experimental di-pion mass distribution in the $\rho(770)$-region is well reproduced with a once-subtracted $P$-wave amplitude. Furthermore, we show that $F$-wave contributions to the amplitude improve the description of the data in the $\pi\pi$ mass region around 1.5 GeV. We also present predictions for the $J/\psi\to\pi^{0}\gamma^{*}$ transition form factor., Comment: 20 pages, 9 figures

The sensitivity of the rare decays $\eta^{(\prime)}\to\pi^{0}\gamma\gamma$ and $\eta^{\prime}\to\eta\gamma\gamma$ to signatures of a leptophobic $B$ boson in the MeV-GeV mass range is analyzed in this work. By adding an explicit $B$-boson resonance exchange, $\eta\to B\gamma\to\pi^{0}\gamma\gamma$, to the Standard Model contributions from vector and scalar meson exchanges, and employing experimental data for the associated branching ratios, it allows us to improve the current constraints on the $B$-boson mass $m_{B}$ and coupling to Standard Model particles $\alpha_{B}$. From these constraints and the analysis of the available experimental $\gamma\gamma$ invariant mass distribution, we show that a $B$-boson signature in the resonant mass range $m_{\pi^{0}}\lesssim m_{B}\lesssim m_{\eta}$ is strongly suppressed and would be very difficult to experimentally identify, assuming that the leptophobic $B$ boson only decays to Standard Model particles. In contrast, the limits outside this mass window are less stringent and the corresponding $t$- and $u$-channel signatures may still be observable in the data, as it occurs with the nonresonant Standard Model $\rho$, $\omega$ and $\phi$ meson exchanges. In addition, we make use of experimental data from the $\eta^{\prime}\to\pi^{0}\gamma\gamma$ and $\eta^{\prime}\to\eta\gamma\gamma$ decays to explore larger $B$-boson masses. Our results are relevant for the $B$-boson search programs at existing and forthcoming light-meson facilities, such as KLOE(-II) and Jefferson Lab Eta Factory experiments., Comment: 15 pages, 12 figures, 1 table; v2 includes a discussion of the uncertainty of the Standard Model estimate and an improvement in the overall presentation

We highlight the need for the development of comprehensive amplitude analysis methods to further our understanding of hadron spectroscopy. Reaction amplitudes constrained by first principles of $S$-matrix theory and by QCD phenomenology are needed to extract robust interpretations of the data from experiments and from lattice calculations., Comment: 15 pages, 9 figures. Contribution to Snowmass 2021

The last two decades have witnessed the discovery of a myriad of new and unexpected hadrons. The future holds more surprises for us, thanks to new-generation experiments. Understanding the signals and determining the properties of the states requires a parallel theoretical effort. To make full use of available and forthcoming data, a careful amplitude modeling is required, together with a sound treatment of the statistical uncertainties, and a systematic survey of the model dependencies. We review the contributions made by the Joint Physics Analysis Center to the field of hadron spectroscopy., Comment: 98 pages, 58 figures. To appear in Progress in Particle and Nuclear Physics

In light of the first observation of the semileptonic decay $B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$ by the LHCb collaboration, we revisit the determination of the CKM parameter $|V_{ub}|$ from exclusive semileptonic $B$-meson decays. A controlled theoretical input on the Standard Model $B\to\pi$ and $B_{s}\to K$ vector and scalar form factors from Lattice QCD in the large $q^{2}$ region, in combination with experimental measurements of the differential $B\to\pi\ell\nu_{\ell}$ and $B^{0}_{s}\to K^{-}\mu^{+}\nu_{\mu}$ branching ratio distributions, has allowed us determine $|V_{ub}|=3.86(11)\times10^{-3}$ and $|V_{ub}|=3.58(9)\times10^{-3}$ from the analyses of the individual decay channels, respectively, and $|V_{ub}|=3.68(5)\times10^{-3}$ from a simultaneous analysis of both decays, which is only a $1.4\%$ error and differs by $1.8\sigma$ with respect to the value from inclusive determinations $|V_{ub}|=4.25(12)^{+15}_{-14}(23)\times10^{-3}$. Our results are based on the use of Pad\'{e} approximants to the participating form factors, highlight the importance of the decay $B_{s}\to K\mu\nu_{\mu}$ in complementing the traditional $B\to\pi\ell\nu_{\ell}$ one in the exclusive determination of $|V_{ub}|$, and allow obtain, to the best of our knowledge, the first correlated results for the $B\to\pi$ and $B_{s}\to K$ vector and scalar form factors. We hope that our study strengthens the case for precise measurements of the differential $B_{s}\to K\ell\nu_{\ell}$ decay rate with a finer resolution of the $q^{2}$ bins, as it would definitely allow achieving more conclusive results for $|V_{ub}|$., Comment: 16 pages, 10 figures

In light of recent experimental results, we revisit the dispersive analysis of the $\omega \to 3\pi$ decay amplitude and of the $\omega\pi^0$ transition form factor. Within the framework of the Khuri-Treiman equations, we show that the $\omega \to 3\pi$ Dalitz-plot parameters obtained with a once-subtracted amplitude are in agreement with the latest experimental determination by BESIII. Furthermore, we show that at low energies the $\omega\pi^0$ transition form factor obtained from our determination of the $\omega \to 3\pi$ amplitude is consistent with the data from MAMI and NA60 experiments.

We perform a global analysis of exclusive hadronic tau decays into one and two mesons using the low-energy limit of the Standard Model Effective Field Theory up to dimension six, assuming left-handed neutrinos. A controlled theoretical input on the Standard Model hadronic form factors, based on chiral symmetry, dispersion relations, data and asymptotic QCD properties, has allowed us to set bounds on the New Physics effective couplings using the present experimental data. Our results highlight the importance of semileptonic $\tau$ decays in complementing the traditional low-energy probes, such nuclear $\beta$ decays or semileptonic pion and kaon decays, and the high-energy measurements at LHC scales. This makes yet another reason for considering hadronic tau decays as golden modes at Belle-II., Comment: 9 pages, 2 figures. arXiv admin note: text overlap with arXiv:1911.08341

We analyze the decays $\tau^-\to K^-(\eta^{(\prime)},K^0) \nu_\tau$ within an effective field theory that includes the most general interactions between Standard Model fields up to dimension six, assuming left-handed neutrinos. In particular, we examine different interesting phenomenological observables i.e. decay spectra and branching ratio, Dalitz plot distributions and the forward-backward asymmetry, to explore the sensitivity of the corresponding decays to the effects of non-standard interactions. A controlled theoretical input on the Standard Model hadronic form factors, based on chiral symmetry, dispersion relations, data and asymptotic QCD properties, has allowed us to set bounds on the New Physics scalar and tensor effective couplings using the measured branching ratios. These are found to be in line with the findings of our series of previous analyses of two-meson tau decays and less precise than the constraints obtained from semileptonic kaon decays. In order to set stringent limits on these couplings, we will use all available experimental data of all possible di-meson tau decays. This is our next step plan, that we hope to be of interest for future experimental analyses of these decays., Comment: 16 pages, 15 figures

We review the state-of-the-art theoretical analyses of tau decays into a pair of mesons and a neutrino. The participant vector and scalar form factors, $f_{+}(s)$ and $f_{0}(s)$, are described in the frame of Chiral Perturbation Theory with resonances supplemented by dispersion relations, and the physical parameters of the intermediate resonances produced in the decay are extracted through the pole position of $f_{+,0}(s)$ in the complex plane. As a side result, we also determine the low-energy observables associated to the form factors. We hope our study to be of interest for present and future experimental analyses of these decays., Comment: 6 pages, 4 figures. Contribution to the Proceedings of the International Workshop "e+e- Collisions From Phi to Psi 2019", held in Novosibirsk, Russia, from February 25 to March 1, 2019. To be published in EPJ Web Of Conferences

We explore the potential of a combined analysis of the decays $\tau^{-}\to\pi^{-}\pi^{0}\nu_{\tau}$ and $\tau^{-}\to K^{-}K_{S}\nu_{\tau}$ in the determination of the $\rho(1450)$ and $\rho(1700)$ resonance properties in the frame of resonance Chiral Theory supplemented by dispersion relations. On the one hand, we take advantage of the very precise data on the modulus squared of the pion vector form factor $|F_{V}^{\pi}|^{2}$ obtained by Belle to carry out a very dedicated analysis of the region where these resonances come up into play. Our study provides an improved treatment of the systematic theoretical errors and, as a most important result, we conclude that they dominate over the fit uncertainties in the determination of the $\rho(1450)$ and $\rho(1700)$ pole parameters and tend to be larger than in other determinations quoted in the literature where these errors were ignored or underestimated. The results of our analysis are summarized in numerical tables for the form factor modulus and phase, including both statistical and systematic errors, that can be found as ancillary material of this paper. As a byproduct, we also determine the low-energy observables of the pion vector form factor and the $\rho$-pole position. On the other hand, we benefit from the recent experimental data for the transition $\tau^{-}\to K^{-}K_{S}\nu_{\tau}$ released by BaBar to perform a first analysis of its decay spectrum and discuss the role of these resonances in this decay. We point out that higher-quality data on the $K^{-}K_{S}$ decay channel will allow compete with the $|F_{V}^{\pi}|^{2}$ ones and improve the determination of the $\rho(1450)$ and $\rho(1700)$ resonance parameters as a result of a combined analysis. We hope our study to be of interest for present and future experimental analysis of these decays., Comment: 35 pages, 8 figures, 2 ancillary files

The scalar and vector meson exchange contributions to the doubly radiative decays $\eta^{(\prime)}\to\pi^0\gamma\gamma$ and $\eta^\prime\to\eta\gamma\gamma$ are analysed within the Linear Sigma Model and Vector Meson Dominance frameworks, respectively. Predictions for the diphoton invariant mass spectra and the associated integrated branching ratios are given and compared with current available experimental data. Whilst a satisfactory description of the shape of the $\eta\to\pi^{0}\gamma\gamma$ and $\eta^\prime\to\pi^{0}\gamma\gamma$ decay spectra is obtained, thus supporting the validity of the approach, the corresponding branching ratios cannot be reproduced simultaneously. A first theoretical prediction for the recently measured $\eta^\prime\to\eta\gamma\gamma$ by the BESIII collaboration is also presented., Comment: 16 pages, 4 figures, 2 tables; v2: includes experimental measurement for the $\eta^\prime\to\eta\gamma\gamma$, a better treatment for the $\sigma$ propagator and a new discussion on the values of the $VP\gamma$ couplings

We study the hadronic $\eta^{\prime}\to\eta\pi\pi$ decays within the framework of $U(3)_{L}\otimes U(3)_{R}$ Chiral Perturbation Theory including resonance states and the complete one-loop corrections. The amplitude is projected in partial waves and unitarized by means of the $N/D$ method resumming both the important $S$-and $D$-wave $\pi\pi$ and the subleading $S$-wave $\pi\eta$ final-state interactions. The participating scalar multiplet mass and coupling strengths are determined from fits to the Dalitz plot experimental data recently released by the A2 collaboration. As a byproduct of our analysis, the associated Dalitz-plot slope parameters are found to be $a=-0.072(7)_{\rm{stat}}(8)_{\rm{syst}}\,, b=-0.052(1)_{\rm{stat}}(2)_{\rm{syst}}\,, d=-0.051(8)_{\rm{stat}}(6)_{\rm{syst}}$, which lie in the ballpark of the current experimental and theoretical determinations., Comment: 45 pages, 12 figures

We reassess the $B\to\pi\ell\nu_{\ell}$ differential branching ratio distribution experimental data released by the BaBar and Belle Collaborations supplemented with all lattice calculations of the $B\to\pi$ form factor shape available up to date obtained by the HPQCD, FNAL/MILC and RBC/UKQCD Collaborations. Our study is based on the method of Pad\'{e} approximants, and includes a detailed scrutiny of each individual data set that allow us to obtain $|V_{ub}|=3.53(8)_{\rm{stat}}(6)_{\rm{syst}}\times10^{-3}$. The semileptonic $B^{+}\to\eta^{(\prime)}\ell^{+}\nu_{\ell}$ decays are also addressed and the $\eta$-$\eta^{\prime}$ mixing discussed., Comment: 29 pages, 7 figures. Comments are welcome

The discovery of $\Xi_{cc}^{++}$ by the LHCb Collaboration triggers predictions of more doubly charmed baryons. By taking into account both the $P$-wave excitations between the two charm quarks and the scattering of light pseudoscalar mesons off the ground state doubly charmed baryons, a set of negative-parity spin-1/2 doubly charmed baryons are predicted already from a unitarized version of leading order chiral perturbation theory. Moreover, employing heavy antiquark-diquark symmetry the relevant low-energy constants in the next-to-leading order are connected with those describing light pseudoscalar mesons scattering off charmed mesons, which have been well determined from lattice calculations and experimental data. Our calculations result in a spectrum richer than that of heavy mesons. We find two very narrow $J^P=1/2^-$ $\Omega_{cc}^P$, which very likely decay into $\Omega_{cc}\pi^0$ breaking isospin symmetry. In the isospin-1/2 $\Xi_{cc}^P$ sector, three states are predicted to exist below 4.2~GeV with the lowest one being narrow and the other two rather broad. We suggest to search for the $\Xi_{cc}^{P}$ states in the $\Xi_{cc}^{++}\pi^-$ mode. Searching for them and their analogues are helpful to establish the hadron spectrum., Comment: 6 pages, 3 figures; accepted for publication as a Rapid Communication in Physical Review D

We employ a mathematical framework based on rational approximants in order to calculate meson form factors. The method profits from unitary, is systematic and data based, and is able to ascribe a systematic uncertainty which provides for the desired model independence. Two examples are discussed: the transition form factor entering the pseudoscalar-pole piece of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, and the $B \to \pi$ form factor participating the $B\to\pi\ell\nu_{\ell}$ differential branching ratios which allows to determine the $|V_{ub}|$ CKM parameter., Comment: Talk given by P.M at the XVII International Conference on Hadron Spectroscopy and Structure - Hadron2017 held in Salamanca, Spain, 25-29 September, 2017

We analyze the second-class current decays $\tau^{-}\to\pi^{-}\eta^{(\prime)}\nu_{\tau}$ in the framework of Chiral Perturbation Theory with resonances. Taking into account $\pi^{0}$-$\eta$-$\eta^{\prime}$ mixing, the $\pi^{-}\eta^{(\prime)}$ vector form factor is extracted, in a model-independent way, using existing data on the $\pi^{-}\pi^{0}$ one. For the participant scalar form factor, we have considered different parameterizations ordered according to their increasing fulfillment of analyticity and unitarity constraints. We start with a Breit-Wigner parameterization dominated by the $a_{0}(980)$ scalar resonance and after we include its excited state, the $a_{0}(1450)$. We follow by an elastic dispersion relation representation through the Omn\`{e}s integral. Then, we illustrate a method to derive a closed-form expression for the $\pi^{-}\eta$, $\pi^{-}\eta^{\prime}$ (and $K^{-}K^{0}$) scalar form factors in a coupled-channels treatment. Finally, predictions for the branching ratios and spectra are discussed emphasizing the error analysis. An interesting result of this study is that both $\tau^{-}\to\pi^{-}\eta^{(\prime)}\nu_{\tau}$ decay channels are promising for the soon discovery of second-class currents at Belle-II. We also predict the relevant observables for the partner $\eta^{(\prime)}_{\ell 3}$ decays, which are extremely suppressed in the Standard Model., Comment: 32 pages, 17 figures. This version contains substantial changes and improvements as compared to the first one

The $\eta^\prime$ transition form factor is reanalyzed in view of the recent BESIII first observation of the Dalitz decay $\eta^\prime\to\gamma e^+e^-$ in both space- and time-like regions at low and intermediate energies using the Pad\'e approximants method. The present analysis provides a suitable parameterization for reproducing the measured form factor in the whole energy region and allows to extract the corresponding low-energy parameters together with a prediction of its values at the origin, related to $\Gamma_{\eta^\prime\to\gamma\gamma}$, and the asymptotic limit. The $\eta$-$\eta^\prime$ mixing is reassessed within a mixing scheme compatible with the large-$N_c$ chiral perturbation theory at next-to-leading order, with particular attention to the OZI-rule--violating parameters. The $J/\psi$, $Z\to\eta^{(\prime)}\gamma$ decays are also considered and predictions reported., Comment: 12 pages, 15 figures. v2 matches the published version

The dilepton invariant mass spectra and integrated branching ratios of the single and double Dalitz decays $\mathcal{P}\to\ell^{+}\ell^{-}\gamma$ and $\mathcal{P}\to\ell^{+}\ell^{-}\ell^{+}\ell^{-}$ ($\mathcal{P}=\pi^{0}, \eta, \eta^{\prime}$; $\ell=e$ or $\mu$) are predicted by means of a data-driven approach based on the use of rational approximants applied to $\pi^{0}, \eta$ and $\eta^{\prime}$ transition form factor experimental data in the space-like region., Comment: 18 pages, 11 figures. This version matches the published version

The potential of performing a combined analysis of the strangeness-changing decays $\tau^{-}\to K_{S}\pi^{-}\nu_{\tau}$ and $\tau^{-}\to K^{-}\eta\nu_{\tau}$ for unveiling the $K^{*}(1410)$ resonance pole parameters is illustrated. Our study is carried out within the framework of Chiral Perturbation Theory, including resonances as explicit degrees of freedom. Resummation of final state interactions are considered through a dispersive parameterization of the required form factors. A considerable improvement in the determination of the pole position with mass $M_{K^{*}(1410)}=1304\pm17$ MeV and width $\Gamma_{K^{*}(1410)}=171\pm62$ MeV is obtained., Comment: Talk given at XIth Quark Confinement and Hadron Spectrum, 8-12th September (2014), Saint Petersburg (Russia)

The MesonNet International Workshop was held in the Laboratori Nazionali di Frascati from September the 29th to October the 1st, 2014, being the concluding meeting of the MesonNet research network within EU HadronPhysics3 project. MesonNet is a research network focused on light meson physics gathering experimentalist and theoreticians from Europe and abroad. An overview of the research projects related to the scope of the network is presented in these mini-proceedings., Comment: 93 pages, 12 figures, MesonNet 2014 International Workshop, 29/9 - 1/10 Frascati LNF INFN

In a combined study of the decay spectra of $\tau^-\to K_S\pi^-\nu_\tau$ and $\tau^-\to K^-\eta\nu_\tau$ decays within a dispersive representation of the required form factors, we illustrate how the $K^*(1410)$ resonance parameters, defined through the pole position in the complex plane, can be extracted with improved precision as compared to previous studies. While we obtain a substantial improvement in the mass, the uncertainty in the width is only slightly reduced, with the findings $M_{K^{*\prime}}=1304 \pm 17\,$MeV and $\Gamma_{K^{*\prime}} = 171 \pm 62\,$MeV. Further constraints on the width could result from updated analyses of the $K\pi$ and/or $K\eta$ spectra using the full Belle-I data sample. Prospects for Belle-II are also discussed. As the $K^-\pi^0$ vector form factor enters the description of the decay $\tau^-\to K^-\eta\nu_\tau$, we are in a position to investigate isospin violations in its parameters like the form factor slopes. In this respect also making available the spectrum of the transition $\tau^-\to K^-\pi^0\nu_\tau$ would be extremely useful, as it would allow to study those isospin violations with much higher precision., Comment: 20 pages, 1figure

We have studied the $\tau^-\to K^-\eta^{(\prime)}\nu_\tau$ decays within Chiral Perturbation Theory including resonances as explicit degrees of freedom. We have considered three different form factors according to treatment of final-state interactions. In increasing degree of soundness: Breit-Wigner, exponential resummation and dispersive representation. We find that although the first one fails in accounting for the data on the $K\eta$ mode, the other two approaches provide good fits to them which are sensitive to the $K^\star(1410)$ pole parameters, that are determined to be $M_{K^{\star\prime}}\,=\,(1330^{+27}_{-41})$ MeV and $\Gamma_{K^{\star\prime}}\,=\,(217^{+68}_{-122})$ MeV. These values are competitive with the standard determination from $\tau^-\to(K\pi)^-\nu_\tau$ decays. The corresponding predictions for the $\tau^-\to K^-\eta^{\prime}\nu_\tau$ channel respect the current upper bound and hint to the discovery of this decay mode in the near future., Comment: 26 pages, 6 tables, 4 figures. Minor changes to match published version. Journal reference and DOI added