Search

In the context of the anomalous magnetic moment of the muon, the hadronic contribution plays a crucial role, especially given its large contribution to the final error. Currently, lattice QCD simulations are in disagreement with dispersive calculations based on $e^+e^-$ hadronic cross sections. The new MUonE experiment intends to shed light on this situation extracting the hadronic contribution to the running of the electromagnetic coupling in the space-like region, $\Delta \alpha_{\rm had}(t)$, from elastic $e\mu$ scattering. Still, due to the limited kinematic range that can be covered by the experiment, a powerful method must be devised to accurately extract the desired hadronic contribution from a new experiment of this type. In this work, we show how Pad\'e and D-Log Pad\'e approximants profiting from the analyticity of the correlator governing the hadronic contribution can be a powerful tool in reaching the required precision., Comment: Contribution to the QNP2024 - The 10th International Conference on Quarks and Nuclear Physics. arXiv admin note: text overlap with arXiv:2405.13638

We computed for the first time the $\tau$ data-driven Euclidean windows for the hadronic vacuum polarization contribution to the muon g-2. We showed that $\tau$-based results agree with the available lattice window evaluations and with the full result. On the intermediate window, where all lattice evaluations are rather precise and agree, $\tau$-based results are compatible with them. This is particularly interesting, given that the disagreement of the $e^+e^-$ data-driven result with the lattice values in this window is the main cause for their discrepancy, affecting the interpretation of the $a_\mu$ measurement in terms of possible new physics., Comment: 6 pages, 3 figures. Contribution to the proceedings of QNP2024 - The 10th International Conference on Quarks and Nuclear Physics, to be published in PoS

Through a holographic model of QCD, we present a phenomenological approach to study the running of the strong coupling constant $\alpha_s$ in both non-perturbative and perturbative regimes. The renormalization of the metric tensor, driven by the Ricci Flow, and the breaking of conformal and chiral symmetries -- thanks to introducing a double dilaton model and large-$N_c$ corrections -- allow us to relate the existence of an infrared fixed point in the coupling constant with a smooth matching to pQCD well above 2 GeV. The proposed dilaton model yields linear Regge trajectories and vector decay constants similar to their experimental counterparts., Comment: 9 pages, 3 figures

We review the tau data-driven computation of Euclidean windows for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (a_mu), which agree with the lattice results, making the difference of the $e^+e^-$ data-driven methods with them more intriguing. This conundrum needs to be solved by next year, when the final FNAL a_mu measurement will be published, in order to extract firm conclusions on possible new physics effects., Comment: Contribution to the proceedings of the 17th International Workshop on Tau Lepton Physics, Louisville, USA, 4-8 December 2023

The MUonE experiment is designed to extract the hadronic contribution to the electromagnetic coupling in the space-like region, $\Delta \alpha_{\rm had}(t)$, from elastic $e\mu$ scattering. The leading order hadronic vacuum polarization contribution to the muon $g-2$, $a_\mu^{\mathrm{HVP, \,LO}}$, can then be obtained from a weighted integral over $\Delta \alpha_{\rm had}(t)$. This, however, requires knowledge of $\Delta \alpha_{\rm had}(t)$ in the whole domain of integration, which cannot be achieved by experiment. In this work, we propose to use Pad\'e and D-Log Pad\'e approximants as a systematic and model-independent method to fit and reliably extrapolate the future MUonE experimental data, extracting $a_\mu^{\mathrm{HVP,\,LO}}$ with a conservative but competitive uncertainty, using no, or very limited, external information. The method relies on fundamental analytic properties of the two-point correlator underlying $a_\mu^{\mathrm{HVP,\,LO}}$ and provides lower and upper bounds for the result for $a_\mu^{\mathrm{HVP,\,LO}}$. We demonstrate the reliability of the method using toy data sets generated from a model for $\Delta \alpha_{\rm had}(t)$ reflecting the expected statistics of the MUonE experiment., Comment: 32 pages, 8 figures. App. B removed. Results unchanged. Matches published version

We review recent progress on the numerical determination of the Hadronic Light-by-Light contribution to the anomalous magnetic moment of the muon. We advocate for a slight increase of the White Paper number for its Standard Model prediction, to $(102\pm17)\times10^{-11}$, accounting for a revised contribution from axial-vector mesons and short-distance constraints. This $\sim10\%$ larger result seems to be supported by the most recent lattice QCD evaluations., Comment: 5 pages + references. Accepted for publication in the proceedings of the HADRON 2023 Conference, Genova, Italy, 5-9 June 2023

Windows in Euclidean time have become a standard tool for comparing lattice QCD and data-driven computations of the hadronic vacuum polarization (HVP) contribution to the muon $g-2$. Here we review our results, obtained using isospin-rotated $\tau^-\to\pi^-\pi^0\nu_\tau$ data instead of $e^+e^-\to\pi^+\pi^-$ measurements, and compare them to other approaches. Consistency of the tau-based and lattice results hints to underestimated uncertainties in the $e^+e^-$ data. If that is the case, the theory prediction of the muon $g-2$ would only lie at $\sim 2\sigma$ from its measured value., Comment: Contribution to the proceedings of 26th International Conference in Quantum Chromodynamics (QCD23), 10-14 july 2023, Montpellier - FR; 6 pages, 5 figures, 1 table

We compute for the first time the $\tau$ data-driven Euclidean windows for the hadronic vacuum polarization contribution to the muon $g-2$. We show that $\tau$-based results agree with the available lattice window evaluations and with the full result. On the intermediate window, where all lattice evaluations are rather precise and agree, $\tau$-based results are compatible with them. This is particularly interesting, given that the disagreement of the $e^+e^-$ data-driven result with the lattice values in this window is the main cause for their discrepancy, affecting the interpretation of the $a_\mu$ measurement in terms of possible new physics., Comment: 15 pages, 4 figures, 4 tables. Accepted for publication in PLB

We determine the bottom quark mass $\hat{m}_b$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD to ${\cal O} (\hat\alpha_s^3)$. Our approach is based on the mutual consistency across a set of moments where experimental data are required for the resonance contributions only. Additional experimental information from the continuum region can then be used for stability tests and to assess the theoretical uncertainty. We find $\hat{m}_b(\hat{m}_b) = (4180.2 \pm 7.9)$ MeV for $\hat\alpha_s(M_Z) = 0.1182$., Comment: 20 pages, 7 figures

We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to $\Gamma(H\to b \bar b)$, to be $c_5=-6900\pm 1400$. With this result, the perturbative series becomes almost insensitive to renormalization scale variations and the intrinsic QCD truncation uncertainty is tiny. This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in $\Gamma(H\to b \bar b)$ will remain largely dominated by the Standard Model parameters., Comment: 21 pages, 3 figures. Significantly shorter than v1. Results unchanged. Changes in presentation and discussions. Accepted by JHEP

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

We study perturbative unitarity constraints on generic Yukawa interactions where the involved fields have arbitrary quantum numbers under an $\prod_i SU(N_i) \otimes U(1)$ group. We derive compact expressions for the bounds on the Yukawa couplings for the cases where the fields transform under the trivial, fundamental or adjoint representation of the various $SU(N)$ factors. We apply our results to specific models formulated to explain the anomalous measurements of $(g-2)_\mu$ and of the charged- and neutral-current decays of the $B$ mesons. We show that, while these models can generally still explain the observed experimental values, the required Yukawa couplings are pushed at the edge of the perturbative regime., Comment: 50 pages, 10 figures; typos fixed, references added, matches published version

In this paper we present a detailed study of the four-body decay $B^0\to K^{+}\pi^{-}\ell^{+}\ell^{-}$, where tensions with the Standard Model predictions have been observed. Our analysis of the decay with P- and S-wave contributions to the $K^{+}\pi^{-}$ system develops a complete understanding of the symmetries of the distribution, in the case of massless and massive leptons. In both cases, the symmetries determine relations between the observables in the $B^0\to K^{+}\pi^{-}\ell^{+}\ell^{-}$ decay distribution. This enables us to define the complete set of observables accessible to experiments, including several that have not previously been identified. The new observables arise when the decay rate is written differentially with respect to $m_{K\pi}$. We demonstrate that experiments will be able to fit this full decay distribution with currently available data sets and investigate the sensitivity to new physics scenarios given the experimental precision that is expected in the future. The symmetry relations provide a unique handle to explore the behaviour of S-wave observables by expressing them in terms of P-wave observables, therefore minimising the dependence on poorly-known S-wave form factors. Using this approach, we construct two theoretically clean S-wave observables and explore their sensitivity to new physics. By further exploiting the symmetry relations, we obtain the first bounds on the S-wave observables using two different methods and highlight how these relations may be used as cross-checks of the experimental methodology. We identify a zero-crossing point that would be at a common dilepton invariant mass for a subset of P- and S-wave observables, and explore the information on new physics and hadronic effects that this zero point can provide., Comment: 49 pages, 25 figures

We revisit well-known short-distance constraints relating the hadronic light-by light Green's function to the $\langle VVA \rangle$ one, that have been a subject of debate over the past years in the context of the muon $(g-2)$. Specifically, we identify a relation among the longitudinal and transverse degrees of freedom that is enforced by the axial anomaly that, by contrast, has not received attention in the past. Such relation allows, among other things, to overcome the problem of basis ambiguities when describing axial-vector mesons transition form factors, but further applications are discussed as well, with special focus on the role of axial-vector mesons in the HLbL contribution to the muon $(g-2)$. Our results should also contribute to a better understanding of the, so far, controversial interplay among short-distance constraints with longitudinal and transverse degrees of freedom, such as axial-vector mesons. This is key to confront the theoretical and experimental result for the muon $(g-2)$ that, currently, exhibits a $4.2\sigma$ tension., Comment: 11 pages+references; major revision including a new model; version accepted for publication in Journal of Physics G

In this article we investigate in detail the possibility of accounting for the $b\to s\ell^+\ell^-$ and $(g-2)_\mu$ anomalies via loop contributions involving with new scalars and fermions. For this purpose, we first write down the most general Lagrangian which can generate the desired effects and then calculate the generic expressions for all relevant $b\to s$ Wilson coefficients. Here we extend previous analysis by allowing that the new particles can also couple to right-handed Standard Model (SM) fermions as preferred by recent $b\to s\ell^+\ell^-$ data and the anomalous magnetic moment of the muon. In the second part of this article we illustrate this generic approach for a UV complete model in which we supplement the Standard Model by a $4^{\rm th}$ generation of vector-like fermions and a real scalar field. This model allows one to coherently address the observed anomalies in $b\to s\ell^+\ell^-$ transitions and in $a_\mu$ without violating the bounds from other observables (in particular $B_s -\bar B_s$ mixing) or LHC searches. In fact, we find that our global fit to this model, after the recent experimental updates, is very good and prefers couplings to right-handed SM fermions, showing the importance of our generic setup and calculation performed in the first part of the article., Comment: 44 pages, 10 figures, 7 tables

We perform a model-independent global fit to $b\to s\ell^+\ell^-$ observables to confirm existing New Physics (NP) patterns (or scenarios) and to identify new ones emerging from the inclusion of the updated LHCb and Belle measurements of $R_K$ and $R_{K^*}$, respectively. Our analysis, updating Refs. [1,2] and including these new data, suggests the presence of right-handed couplings encoded in the Wilson coefficients ${\cal C}_{9'\mu}$ and ${\cal C}_{10'\mu}$. It also strengthens our earlier observation that a lepton flavour universality violating (LFUV) left-handed lepton coupling (${\cal C}_{9\mu}^{\rm V}=-{\cal C}_{10\mu}^{\rm V}$), often preferred from the model building point of view, accommodates the data better if lepton-flavour universal (LFU) NP is allowed, in particular in ${\cal C}_{9}^{\rm U}$. Furthermore, this scenario with LFU NP provides a simple and model-independent connection to the $b\to c\tau \nu$ anomalies, showing a preference of $\approx 7\,\sigma$ with respect to the SM. It may also explain why fits to the whole set of $b\to s\ell^+\ell^-$ data or to the subset of LFUV data exhibit stronger preferences for different NP scenarios. Finally, motivated by $Z^\prime$ models with vector-like quarks, we propose four new scenarios with LFU and LFUV NP contributions that give a very good fit to data. We provide also an addendum collecting our updated results after including the data for the $B\to K^*\mu\mu$ angular distribution released in 2020 by the LHCb collaboration., Comment: 18 pages, 36 figures. Includes Addendum in an appendix with updated fit results and discussion taking into account the LHCb results on $B\to K^{*}\mu\mu$ angular observables of March, 2020. Colours of plots uniformized all over the paper. Version published at EPJC

The deviations with respect to the Standard Model that are currently observed in $b \to s \ell\ell$ transitions, or $B$ anomalies, can be interpreted in terms of different New Physics (NP) scenarios within a model-independent effective approach. We identify a set of internal tensions of the fit that require further attention and whose theoretical or experimental nature could be determined with more data. In this landscape of NP, we discuss possible ways to discriminate among favoured NP hypotheses in the short term thanks to current and forthcoming observables. While an update of $R_K$ should help to disentangle the type of NP we may be observing (Lepton-Flavour Universality Violating and/or Lepton Flavour Universal), additional observables, in particular $Q_5$, turn out to be central to determine which NP hypothesis should be preferred. We also analyse the preferences shown by the current global fit concerning various NP hypotheses, using two different tools: the behaviour of the pulls of individual observables under NP scenarios and the directions favoured by approximate quadratic parametrisations of the observables in terms of Wilson coefficients., Comment: 37 pages, 16 figures

We compute the generic one-loop contribution involving scalar leptoquarks (LQ) to the $W$ and $Z$ leptonic decay widths. In our computation we include for the first time the finite terms and the corrections due to the external momenta of the electroweak bosons, which is a step beyond the leading-logarithmic approximation considered in the literature so far. We show that the terms we include can be numerically quite significant. They amount to about $20\%$ for scalar LQ masses below $1.5$~TeV, as currently allowed by the direct searches at the LHC. To further illustrate the relevance of our results we revisit a model with two light scalar LQs, proposed to accommodate the $B$-physics anomalies. We show that the finite terms we computed can reduce the tension with the $Z$-pole data., Comment: Minor typos amended

This document collects the proceedings of the PHOTON 2017 conference ("International Conference on the Structure and the Interactions of the Photon", including the 22th "International Workshop on Photon-Photon Collisions", and the "International Workshop on High Energy Photon Colliders") held at CERN (Geneva) in May 2017. The latest experimental and theoretical developments on the topics of the PHOTON conference series are covered: (i) $\gamma\,\gamma$ processes in e$^+$e$^-$, proton-proton (pp) and nucleus-nucleus (AA) collisions at current and future colliders, (ii) $\gamma$-hadron interactions in e$^\pm$p, pp, and AA collisions, (iii) final-state photon production (including Standard Model studies and searches beyond it) in pp and AA collisions, and (iv) high-energy $\gamma$-ray astrophysics. These proceedings are dedicated to the memory of Maria Krawczyk., Comment: 296 pages. CERN-Proceedings-2018-001 (CERN, Geneva, 2018), to appear. arXiv admin note: substantial text overlap with arXiv:1804.05614, arXiv:1708.06683, arXiv:1709.09044, arXiv:1708.00912, arXiv:1708.07173, arXiv:1709.02985, arXiv:1709.00176, arXiv:1709.05167, arXiv:1708.05756, arXiv:1708.09759, arXiv:1708.07531, arXiv:1703.08450, arXiv:1711.02551, arXiv:1511.07794, arXiv:1712.10104, arXiv:1708.05776, arXiv:1712.10202, arXiv:1709.07110, arXiv:1702.08730, arXiv:1709.02648, arXiv:1411.6397

The deviations with respect to the Standard Model (SM) that are currently observed in $b \to s \ell\ell$ transitions (the so-called flavour anomalies) can be interpreted in terms of different New Physics (NP) scenarios within a model-independent effective approach. We reconsider the determination of NP in global fits from a different perspective by removing one implicit hypothesis of current analyses, namely that NP is only Lepton-Flavour Universality Violating (LFUV). We examine the roles played by LFUV NP and Lepton-Flavour Universal (LFU) NP altogether, providing new directions to identify the possible theory beyond the SM responsible for the anomalies observed. New patterns of NP emerge due to the possibility of allowing at the same time large LFUV and LFU NP contributions to $C_{10\mu}$, which provides a different mechanism to obey the constraint from the $B_s \to\mu^+\mu^-$ branching ratio. In this landscape of NP, we discuss how to discriminate among these scenarios in the short term thanks to current and forthcoming observables. While the update of $R_K$ will be a major milestone to confirm the NP origin of the flavour anomalies, additional observables, in particular the LFUV angular observable $Q_5$, turn out to be central to assess the precise NP scenario responsible for the observed anomalies., Comment: 9 pages. v2 matches the published version

Perturbative QCD corrections to hadronic $\tau$ decays and $e^+e^-$ annihilation into hadrons below charm are obtained from the Adler function, which at present is known in the chiral limit to five-loop accuracy. Extractions of the strong coupling, $\alpha_s$, from these processes suffer from an ambiguity related to the treatment of unknown higher orders in the perturbative series. In this work, we exploit the method of Pad\'e approximants and its convergence theorems to extract information about higher-order corrections to the Adler function in a systematic way. First, the method is tested in the large-$\beta_0$ limit of QCD, where the perturbative series is known to all orders. We devise strategies to accelerate the convergence of the method employing renormalization scheme variations and the so-called D-log Pad\'e approximants. The success of these strategies can be understood in terms of the analytic structure of the series in the Borel plane. We then apply the method to full QCD and obtain reliable model-independent predictions for the higher-order coefficients of the Adler function. For the six-, seven-, and eight-loop coefficients we find $c_{5,1} = 277\pm 51$, $c_{6,1}=3460\pm 690$, and $c_{7,1}=(2.02\pm0.72)\times 10^4$, respectively, with errors to be understood as lower and upper bounds. Our model-independent reconstruction of the perturbative QCD corrections to the $\tau$ hadronic width strongly favours the use of fixed-order perturbation theory (FOPT) for the renormalization-scale setting., Comment: 40 pages, 8 figures. Five references added. Minor changes. To appear in Journal of High Energy Physics

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

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 determine the charm quark mass ${\hat m}_c({\hat m}_c)$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD. Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules, including the one for the zeroth moment. Existing data from the continuum region can then be used to bound the theoretical error. Our result is ${\hat m}_c({\hat m}_c) = 1272 \pm 8$ MeV for $\hat\alpha_s(M_Z) = 0.1182$. Special attention is given to the question how to quantify and justify the uncertainty., Comment: 6 pages, 4 figures, talk presented at the 2017 European Physical Society conference on High Energy Physics (EPS-HEP 2017), July 5-12, 2017, Venice, Italy

The parton model relations in conjunction with quark-hadron duality in deep inelastic scattering suggests an asymptotic dominance of quark-diquark type of baryonic excited states with a radial Regge uniformly distributed mass squared spectrum $M_{n}^2 = \mu^2 n + M_0^2$. We argue that this points to a lineary quark-diquark confining potential. We analyze the radial ($n$) and angular-momentum ($J$) Regge trajectories for all light-quark states with baryon number one listed in the 2016 edition of the Particle Data Tables. The parameters of the mass squared trajectories are obtained by linear regression assuming $\Delta M_n^2 \sim M_n \Gamma_n $ weighted with the width $\Gamma_n$ of the resonance and the error analysis is carried out accordingly., Comment: 6 pages, 3 figures

We computed the leading order Wilson coefficients relevant to all the exclusive $b\to s\ell^+\ell^-$ decays in the framework of Two Higgs Doublet Model (2HDM) with a softly broken $\mathbb{Z}_2$ symmetry by including the $\mathcal{O}(m_b)$ corrections. We elucidate the issue of appropriate matching between the full and the effective theory when dealing with the (pseudo-)scalar operators for which keeping the external momenta different from zero is necessary. We then make a phenomenological analysis by using the measured $\mathcal{B}(B_s\to \mu^+\mu^-)$ and $\mathcal{B}(B\to K \mu^+\mu^-)_{\mathrm{high}-q^2}$, for which the hadronic uncertainties are well controlled, and discussed their impact on various types of 2HDM. A brief discussion of the decays with $\tau$-leptons in the final state is also made., Comment: 37 pages, 9 figures, version published in EPJC

We employ a mathematical framework based on rational approximants in order to calculate the pseudoscalar-pole piece of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, $a_{\mu}^{\textrm{HLbL};P}$. The method is systematic and data based, profiting from over 13 different collaborations, and able to ascribe, for the first time, a systematic uncertainty which provides for the model independence. As a result, we obtain $a_{\mu}^{\textrm{HLbL};P}=94.3(5.3) \times10^{-11}$, which uncertainty is well below the one foreseen at future experiments measuring the $(g_{\mu}-2)$., Comment: 19 pages, 7 figures

In this paper, we present preliminary results of the determination of the charm quark mass $\hat{m}_c$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at ${\cal O} (\hat \alpha_s^3)$. Self-consistency between two different sum rules allow to determine the continuum contribution to the moments without requiring experimental input, except for the charm resonances below the continuum threshold. The existing experimental data from the continuum region is used, then, to confront the theoretical determination and reassess the theoretic uncertainty., Comment: 13 pages, 4 figures. Matches the published version in Modern Physics Letters A. arXiv admin note: text overlap with arXiv:1610.08531

We determine the charm quark mass $\hat{m}_c$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at ${\cal O} (\hat\alpha_s^3)$. Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules. Existing data from the continuum region can then be used to bound the theoretic uncertainty. Our result is $\hat{m}_c(\hat{m}_c) = 1272 \pm 8$~MeV for $\hat\alpha_s(M_Z) = 0.1182$., Comment: 28 pages, 6 figures

Recent measurements of $b\to s\mu^+\mu^-$ processes at LHCb and BELLE have revealed tensions at the $2-3\,\sigma$ level between the Standard Model (SM) prediction and the experimental results in the channels $B\to K^*\mu^+\mu^-$ and $B_s\to\phi\mu^+\mu^-$, as well as in the lepton-flavor universality violating observable $R_K={\rm Br}(B\to K\mu^+\mu^-)/{\rm Br}(B\to Ke^+e^-$). Combined global fits to the available $b\to s\mu^+\mu^-$ data suggest that these tensions might have their common origin in New Physics (NP) beyond the SM because some NP scenarios turn out to be preferred over the SM by $4-5\,\sigma$. The fact that all these anomalies are related to muons further suggests a connection (and a common NP explanation) with the long-standing anomaly in the anomalous magnetic moment of the muon, $a_\mu$. In this article, we study the impact of a generic class of NP models featuring new heavy scalars and fermions that couple to the SM fermions via Yukawa-like interactions. We consider two different scenarios, introducing either one additional fermion and two scalars or two additional fermions and one scalar, and examine all possible representations of the new particles under the SM gauge group with dimension up to the adjoint one. The models induce one-loop contributions to $b\to s\mu^+\mu^-$ and $a_\mu$ which are capable of solving the respective anomalies at the $2\sigma$ level, albeit a relatively large coupling of the new particles to muons is required. In the case of $b\to s\mu^+\mu^-$, stringent constraints from $B_s-\overline{B}_s$ mixing arise which can be relaxed if the new fermion is a Majorana particle., Comment: 24 pages, 7 figures, discussion of D-meson mixing and Z --> mu^+ mu^- added, conclusions unchanged, journal version

In this work, we present our recent results on a new and alternative data-driven determination for the hadronic light-by-light pseudoscalar-pole contribution to the muon $(g-2)$. Our approach is based on Canterbury approximants, a rational approach to describe the required transition form factors, which provides a systematic and model-independent framework beyond traditional large-$N_c$ approaches. As a result, we obtain a competitive determination with errors according to future $(g-2)$ experiments including, for the first time, a well-defined systematic uncertainty., Comment: 13 pages, 3 figures, contributions to Determination of the Fundamental Parameters in QCD; matches the published proceedings version

We discuss the determination of the $f_0(500)$ (or $\sigma$) resonance by analytic continuation through Pad\'e approximants of the $\pi\pi$-scattering amplitude from the physical region to the pole in the complex energy plane. The aim is to analyze the uncertainties of the method, having in view the fact that analytic continuation is an ill-posed problem in the sense of Hadamard. Using as input a class of admissible parameterizations of the scalar-isoscalar $\pi\pi$ partial wave, which satisfy with great accuracy the same set of dispersive constraints, we find that the Roy-type integral representations lead to almost identical pole positions for all of them, while the predictions of the Pad\'e approximants have a larger spread, being sensitive to features of the input parameterization that are not controlled by the dispersive constraints. Our conservative conclusion is that the $\sigma$-pole determination by Pad\'e approximants is consistent with the prediction of Roy-type equations, but has an uncertainty almost a factor two larger., Comment: 11 pages, 13 figures

In this work, we calculate the branching ratios for the $\eta(\eta')\rightarrow\bar{\ell}\ell$ decays, where $\ell = e,\mu$. These processes have tiny rates in the standard model due to spin flip, loop, and electromagnetic suppression, for what they could be sensitive to New Physics effects. In order to provide a reliable input for the Standard Model, we exploit the general analytical properties of the amplitude. For that purpose, we invoke the machinery of Canterbury approximants, which provides a systematic description of the underlying hadronic physics in a data-driven fashion. Given the current experimental discrepancies, we discuss in detail the role of the resonant region and comment on the reliability of $\chi$PT calculations. Finally, we discuss the kind of new physics which we think would be relevant to account for them., Comment: 35 pages, 18 figures. V2 matches the published version

We present our model-independent and data-driven method to describe pseudoscalar meson transition form factors in the space- and (low-energy) time-like regions. The method is general and conforms a toolkit applicable to any other form factor, of one and two variables, with the potential to include both high- and low-energy QCD constraints altogether. The method makes use of analyticity and unitary properties of form factors, it is simple, systematic and can be improved upon by including new data. In the present discussion, the method is used to show the impact of experimental data for precision calculations in the low-energy sector of the Standard Model. In particular, due to its relevance for New Physics searches, we have considered the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon (the pseudoscalar exchange contribution), the pseudoscalar decays into lepton pairs, and the determination of the mixing parameters of the $\eta$ and $\eta'$ system. For all of them we provide the most updated results in a data-driven manner., Comment: 10 pages, 9 figures. Invited talk by P.M. at the FCCP2015 - Workshop on "Flavour changing and conserving processes," 10-12 September 2015,Anacapri, Capri Island, Italy

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

A systematic study of the $\eta$-$\eta'$ mixing in Large-$N_c$ chiral perturbation theory is presented with special emphasis on the role of the next-to-next-to-leading-order contributions in the combined momentum, quark-mass, and $1/N_c$ expansions. At this order, loop corrections as well as OZI-rule-violating pieces need to be included. Mixing angles as well as pseudoscalar decay constants are discussed within this framework. The results are compared with recent phenomenological approaches., Comment: 10 pages, 3 figures, talk presented by P. Masjuan at the 8th International Workshop on Chiral Dynamics, 29 June 2015 - 3 July 2015, Pisa, Italy

The pseudoscalar decays into lepton pairs $P\rightarrow\overline{\ell}\ell$ are analyzed with the machinery of Canterbury approximants, an extension of Pad\'e approximants to bivariate functions. This framework provides an ideal model-independent approach to implement all our knowledge of the pseudoscalar transition form factors driving these decays, can be used for data analysis, and allows to include experimental data and theoretical constraints in an easy way, and determine a systematic error. We find that previous theoretical estimates for these branching ratios have underestimated their theoretical uncertainties. From our updated results, the existing experimental discrepancies for $\pi^0\rightarrow e^+e^-$ and $\eta\rightarrow \mu^+\mu^-$ channels cannot be explained unless the doubly-virtual transition form factors behavior -not yet measured- are out of theoretical expectations, which is an interesting result both for anomalous magnetic moments of leptons, and for physics beyond the standard model., Comment: 9 pages, 3 figures. Proceedings to Chiral Dynamics 2015 conference in Pisa

We present our recent results on the hadronic light-by-light pseudoscalar-exchange contribution to the anomalous magnetic moment of the muon using rational approximants. Our work provides a generalization of Pad\'e approximants to the bivariate case to describe the most general doubly-virtual transition form factor, which is required in the calculation. This method provides a powerful tool to systematically implement the known experimental data on transition form factors in the space-like region and low energies in a model-independent way. Given the lack of experimental data on the doubly-virtual transition form factor, we make use of the pseduoscalar decays into lepton pairs. We find an interesting and puzzling situation which calls for new experimental measurements to clarify the present state., Comment: 10 pages, 4 figures. Proceedings to PHOTON 2015 conference in Novosibirsk

A diboson excess has been observed ---albeit with very limited statistical significance--- in $WW$, $WZ$ and $ZZ$ final states at the LHC experiments using the accumulated 8 TeV data. Assuming that these signals are due to resonances resulting from an extended symmetry breaking sector in the standard model and exact custodial symmetry we determine using unitarization methods the values of the relevant low-energy constants in the corresponding effective Lagrangian. Unitarity arguments also predict the widths of these resonances. We introduce unitarized form factors to allow for a proper treatment of the resonances in Monte Carlo generators and a more precise comparison with experiment., Comment: 17 pages, 7 figures. The new version contains an updated and revised list of references as well as a slightly extended conclusion section

The current 3$\sigma$ discrepancy between experiment and Standard Model predictions for $\pi^0 \to e^+e^-$ is reconsidered using the Pad\'e Theory for bivariate functions, the Canterbury approximants. This method provides a model-independent data-driven approximation to the decay as soon as experimental data for the doubly virtual $\pi^0$ transition form factor are available. It also implements the correct QCD constraints of the form factor both at low- and high-energies. We reassess the Standard Model result including, for the first time, a systematic error. Our result, BR$(\pi^0 \to e^+e^-)=6.23(5)\times 10^{-8}$, still represents a discrepancy larger than $2\sigma$, unsurmountable with our present knowledge of the Standard Model, and would claim New Physics if the experimental result is confirmed by a new measurement. Our method also provides the adequate tool to extract the doubly virtual form factor from experimental data in a straightforward manner. This measurement would further shrink our error and establish once and for all the New Physics nature of the discrepancy. In addition, we remark the challenge this discrepancy poses in the evaluation of the hadronic light-by-light scattering contribution to the $(g-2)_{\mu}$, specially confronted with the foreseen accuracy of the forthcoming $(g-2)_{\mu}$ experiments., Comment: v2: 7 pages, 5 figures. Improved approximation, reduced final errors, conclusions unchanged

This talk, dedicated to Eef van Beveren on the occasion of his birthday, reviews some of our results concerning the hadron spectroscopy, Regge trajectories, and the large-Nc meson-dominance of hadronic form factors., Comment: 6 pages, 7 figures, talk presented by WB at EEF70, Workshop on Unquenched Hadron Spectroscopy: Non-Perturbative Models and Methods of QCD vs. Experiment, Coimbra, Portugal, 1-5 September 2014

In this talk I review the recent progress on the numerical evaluation of the Hadronic Light-by-Light contribution to the anomalous magnetic moment of the muon and I discuss the role of experimental data on the accuracy of its determination., Comment: 4 pages, Invited talk at the 13th International Workshop on Tau Lepton Physics, Aachen, Germany, 15-19 September, 2014. References added

We employ a systematic and model-independent method to extract, from space- and time-like data, the $\eta$ and $\eta'$ transition form factors (TFFs) obtaining the most precise determination for their low-energy parameters and discuss the $\Gamma_{\eta\rightarrow\gamma\gamma}$ impact on them. Using TFF data alone, we also extract the $\eta-\eta'$ mixing parameters, which are compatible to those obtained from more sophisticated and input-demanding procedures., Comment: 4 pages, 2 figures, presented at the 13th International Workshop on Meson Production, Properties and Interaction (MESON 2014); added references

In this work, we present a precise and model--independent method to extract resonance pole parameters from phase-shift scattering data. These parameters are defined from the associated poles in the second Riemann sheet, unfolded by the analytic continuation to the complex pole using Pad\'e approximants. Precise theoretical parameterizations of pion-pion scattering phase shifts based on once-- and twice-- subtracted dispersion relations are used as input, whose functional form allows us to show the benefit and accuracy of the method. In particular, we extract from these parametrization the pole positions of the $f_0(500)$ at $\sqrt{s}=(453\pm 15) - i(297 \pm 15)$ MeV, the $\rho(770)$ at $\sqrt{s}=(761.4\pm 1.2)-i(71.8 \pm 1.0)$ MeV, and the pole of the $f_2(1270)$, located at $\sqrt{s}=(1267.3\pm 1.7)-i(95.0\pm 2.3)$ MeV. The couplings of the resonances to two pions are also determined with high precision, obtaining respectively, $3.8\pm 0.4$ GeV, $5.92\pm 0.15$ and $4.41\pm 0.23$ GeV$^{-1}$. Special attention is dedicated to the systematic treatment of the theoretical and statistical uncertainties, together with their comparison with previous determinations., Comment: 5 pages, 3 figures

We present the mini-proceedings of the workshops Hadronic contributions to the muon anomalous magnetic moment: strategies for improvements of the accuracy of the theoretical prediction and $(g-2)_{\mu}$: Quo vadis?, both held in Mainz from April 1$^{\rm rst}$ to 5$^{\rm th}$ and from April 7$^{\rm th}$ to 10$^{\rm th}$, 2014, respectively., Comment: 84 pages, 23+18 contributions. Editors: Tom Blum, Pere Masjuan, and Marc Vanderhaeghen

The $\pi^0$, $\eta$, and $\eta^\prime$ transition form factors in the space-like region are analyzed at low and intermediate energies in a model-independent way through the use of rational approximants. Slope and curvature parameters as well as their values at infinity are extracted from experimental data. These results are suited for constraining hadronic models such as the ones used for the hadronic light-by-light scattering piece of the anomalous magnetic moment of the muon, and for the mixing parameters of the $\eta - \eta^\prime$ system., Comment: Contribution to the 13th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2013), Rome, Italy, 30 September - October 4, 2013. 4 pages, 3 figures. v2: Reference added

The half width rule provides a way to consider 1/Nc corrections to hadronic models containing resonances. Consequences of such ideas for hadron form factors and Regge trajectories are explored, with special emphasis on the possibility to describe the spectrum of light and heavy unflavored vector mesons in a universal way., Comment: Contribution by P.M to the 13th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2013), Rome, Italy, 30 September - October 4, 2013. 4 pages, 4 figures

In his Comment, D. Bugg argues against our usage of the PDG collection of light non-strange states together with the half-width rule to analyze the linearity of radial and angular-moment Regge trajectories in the large-N_c limit. After taking into account his observations on our choice of data, the radial Regge trajectories are again analyzed. We still find that our conclusion on the lack of universality between radial- and angular-momentum Regge trajectories is valid., Comment: 3 pages, 2 figures. Version to appear in Phys.Rev. D

Using the new non-analytic reconstruction method obtained from Mellin-Barnes properties, one can extract the value $m_c(\bar{\text{MS}}) = 1.12 \pm 0.08 \;\; \text{GeV}$ from experimental data of the radiation-corrected measured hadronic cross section to the calculated lowest-order cross section for muon pair production in the heavy-quark approximation., Comment: Proceeding of the Xth Quark Confinement and the Hadron Spectrum, October 8-12, 2012

Using the momentum dependence of the dressed quark mass and the well-known formulae for the mass dependent quark-loop contribution to the light-by-light scattering insertions, we compute the hadronic light-by-light contribution to the muon anomalous magnetic moment. The relevant momentum running in the quark loop is calculated from the $\pi^0$ exchange contribution to the light- by-light scattering. Special emphasis on the reconstruction of the pseudoscalar transition form factor is made, and the $\pi^0$ contribution to the hadronic light-by-light is, as well, updated., Comment: 9 pages, 5 figures