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B. Moussallam

Publications and source records attributed to B. Moussallam.

At least 19 recordsLinked to original sources
arXiv2021

Deriving experimental constraints on the scalar form factor in the second-class $\tau \to\eta \pi \nu$ mode

The rare second-class decay mode of the $\tau$ into $\eta\pi\nu$ could be observed for the first time at Belle II. It is important to try to derive a reliable evaluation of the branching fraction and of the energy distribution of this mode within the standard-model. Many predictions exist already in the literature which can differ by one to two orders of magnitude. Here, an approach based on a systematic use of the property of analyticity of form factors and scattering amplitudes in QCD is discussed. In particular, we will show that the scalar form factor in the $\tau$ decay can be related to photon-photon scattering and radiative $\phi$ decay amplitudes for which precise experimental measurements have been performed by the Belle and KLOE collaborations.

hep-ph↗
arXiv2021

Revisiting $γ^*\toγπ^0η$ near the $ϕ(1020)$ using analyticity and the left-cut structure

Amplitudes of the form $γ^*(q^2)\to γP_1P_2$ appear as sub-processes in the computation of the muon $g-2$. We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at $q^2=m^2_ϕ$. Starting from an exact parameter-free dispersive representation for the $S$-wave satisfying QCD asymptotic constraints and Low's soft photon theorem we derive, in an effective theory spirit, a two-channel Omnès integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of $P_1P_2=πη$, we show that a very good fit of the KLOE data can be achieved with two real parameters, using a $T$-matrix previously determined from $γγ$ scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the $T$-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the $I=1$ scalar form factors and to the $a_0(980)$ resonance complex pole are presented.

hep-ph↗
arXiv2020

The $πη$ interaction and $a_0$ resonances in photon-photon scattering

We revisit the information on the two lightest $a_0$ resonances and $S$-wave $πη$ scattering that can be extracted from photon-photon scattering experiments. For this purpose we construct a model for the $S$-wave photon-photon amplitudes which satisfies analyticity properties, two-channel unitarity and obeys the soft photon as well as the soft pion constraints. The underlying I=1 hadronic $T$-matrix involves six phenomenological parameters and is able to account for two resonances below 1.5 GeV.We perform a combined fit of the $γγ\to πη$ and $γγ\to K_SK_S$ high statistics experimental data from the Belle collaboration. Minimisation of the $χ^2$ is found to have two distinct solutions with approximately equal $χ^2$. One of these exhibits a light and narrow excited $a_0$ resonance analogous to the one found in the Belle analysis. This however requires a peculiar coincidence between the $J=0$ and $J=2$ resonance effects which is likely to be unphysical. In both solutions the $a_0(980)$ resonance appears as a pole on the second Riemann sheet. The location of this pole in the physical solution is determined to be $m-iΓ/2=1000.7^{+12.9}_{-0.7} -i\,36.6^{+12.7}_{-2.6}$ MeV. The solutions are also compared to experimental data in the kinematical region of the decay $η\toπ^0γγ$. In this region an isospin violating contribution associated with $π^+π^-$ rescattering must be added for which we provide a dispersive evaluation.

hep-ph↗
arXiv2019

The Belle II Physics Book

We present the physics program of the Belle II experiment, located on the intensity frontier SuperKEKB $e^+e^-$ collider. Belle II collected its first collisions in 2018, and is expected to operate for the next decade. It is anticipated to collect 50/ab of collision data over its lifetime. This book is the outcome of a joint effort of Belle II collaborators and theorists through the Belle II theory interface platform (B2TiP), an effort that commenced in 2014. The aim of B2TiP was to elucidate the potential impacts of the Belle II program, which includes a wide scope of physics topics: B physics, charm, tau, quarkonium, electroweak precision measurements and dark sector searches. It is composed of nine working groups (WGs), which are coordinated by teams of theorist and experimentalists conveners: Semileptonic and leptonic B decays, Radiative and Electroweak penguins, phi_1 and phi_2 (time-dependent CP violation) measurements, phi_3 measurements, Charmless hadronic B decay, Charm, Quarkonium(like), tau and low-multiplicity processes, new physics and global fit analyses. This book highlights "golden- and silver-channels", i.e. those that would have the highest potential impact in the field. Theorists scrutinised the role of those measurements and estimated the respective theoretical uncertainties, achievable now as well as prospects for the future. Experimentalists investigated the expected improvements with the large dataset expected from Belle II, taking into account improved performance from the upgraded detector.

hep-ex↗
arXiv2018

Workshop on Pion-Kaon Interactions (PKI2018) Mini-Proceedings. Editors: M. Amaryan, Ulf-G. Meißner, C. Meyer, J. Ritman, and I. Strakovsky

This volume is a short summary of talks given at the PKI2018 Workshop organized to discuss current status and future prospects of pi-K interactions. The precise data on pi-K interaction will have a strong impact on strange meson spectroscopy and form factors that are important ingredients in the Dalitz plot analysis of a decays of heavy mesons as well as precision measurement of Vus matrix element and therefore on a test of unitarity in the first raw of the CKM matrix. The workshop has combined the efforts of experimentalists, Lattice QCD, and phenomenology communities. Experimental data relevant to the topic of the workshop were presented from the broad range of different collaborations like CLAS, GlueX, COMPASS, BaBar, BELLE, BESIII, VEPP-2000, and LHCb. One of the main goals of this workshop was to outline a need for a new high intensity and high precision secondary KL beam facility at JLab produced with the 12 GeV electron beam of CEBAF accelerator. This workshop is a successor of the workshops Physics with Neutral Kaon Beam at JLab [1] held at JLab, February, 2016; Excited Hyperons in QCD Thermodynamics at Freeze-Out [2] held at JLab, November, 2016; New Opportunities with High-Intensity Photon Sources [3] held at CUA, February, 2017. Further details about the PKI2018 Workshop can be found on the web page of the conference: http://www.jlab.org/conferences/pki2018/ .

hep-ph↗
arXiv2017

Extended chiral Khuri-Treiman formalism for $η\to 3π$ and the role of the $a_0(980)$, $f_0(980)$ resonances

Recent experiments on $η\to 3π$ decays have provided an extremely precise knowledge of the amplitudes across the Dalitz region which represent stringent constraints on theoretical descriptions. We reconsider an approach in which the low-energy chiral expansion is assumed to be optimally convergent in an unphysical region surrounding the Adler zero, and the amplitude in the physical region is uniquely deduced by an analyticity-based extrapolation using the Khuri-Treiman dispersive formalism. We present an extension of the usual formalism which implements the leading inelastic effects from the $K\bar{K}$ channel in the final-state $ππ$ interaction as well as in the initial-state $ηπ$ interaction. The constructed amplitude has an enlarged region of validity and accounts in a realistic way for the influence of the two light scalar resonances $f_0(980)$ and $a_0(980)$ in the dispersive integrals. It is shown that the effect of these resonances in the low energy region of the $η\to 3π$ decay is not negligible, in particular for the $3π^0$ mode, and improves the description of the energy variation across the Dalitz plot. Some remarks are made on the scale dependence and the value of the double quark mass ratio $Q$.

hep-ph↗
arXiv2017

How to employ $\bar{B}^0_d \to J/ψ(πη,\bar{K}K)$ decays to extract information on $πη$ scattering

We demonstrate that dispersion theory allows one to deduce crucial information on $πη$ scattering from the final-state interactions of the light mesons visible in the spectral distributions of the decays $\bar{B}^0_d \to J/ψ(π^0η,K^+K^-,K^0\bar{K}^0)$. Thus high-quality measurements of these differential observables are highly desired. The corresponding rates are predicted to be of the same order of magnitude as those for $\bar{B}^0_d \to J/ψπ^+π^-$ measured recently at LHCb, letting the corresponding measurement appear feasible.

hep-ph↗
arXiv2015

Form factors of the isovector scalar current and the $ηπ$ scattering phase shifts

A model for S-wave $ηπ$ scattering is proposed which could be realistic in an energy range from threshold up to above one GeV, where inelasticity is dominated by the $K\bar{K}$ channel. The $T$-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order $p^4$ exactly for the $ηπ\toηπ$, $ηπ\to K\bar{K}$ amplitudes and approximately for $K\bar{K}\to K\bar{K}$. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omnès problem, thus allowing to compute the $ηπ$ and $K\bar{K}$ form factor matrix elements of the $I=1$ scalar current from the $T$-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the $a_0(980)$, $a_0(1450)$ resonances, as well as the chiral results of the $ηπ$ and $K\bar{K}$ scalar radii which are predicted to be remarkably small at $O(p^4)$. This $T$-matrix model could be used for a unified treatment of the $ηπ$ final-state interaction problem in processes such as $η'\to ηππ$, $ϕ\toηπγ$, or the $ηπ$ initial-state interaction in $η\to3π$.

hep-ph↗
arXiv2015

$a_0-f_0$ mixing in the Khuri-Treiman equations for $η\to 3π$

A reliable determination of the isospin breaking double quark mass ratio from precise experimental data on $η\to 3π$ decays should be based on the chiral expansion of the amplitude supplemented with a Khuri-Treiman type dispersive treatment of the final-state interactions. We discuss an extension of this formalism which allows to estimate the effects of the $a_0(980)$ and $f_0(980)$ resonances and their mixing on the $η\to 3π$ amplitudes. Matrix generalisations of the equations describing elastic $ππ$ rescattering with $I=0,\,2$ are introduced which accomodate both $ππ/K\bar{K}$ and $ηπ/K\bar{K}$ coupled-channel rescattering. Isospin violation induced by the physical $K^+-K^0$ mass difference and by direct $u-d$ mass difference effects are both accounted for in the dispersive integrals. Numerical solutions are constructed which illustrate how the large resonance effects at 1 GeV propagate down to low energies. They remain small in the physical region of the decay, due to the matching constraints with the NLO chiral amplitude, but they are not negligible and go in the sense of further improving the agreement with experiment for the Dalitz plot parameters.

hep-ph↗
arXiv2014

Analyticity of $ηπ$ isospin-violating form factors and the $τ\toηπν$ second-class decay

We consider the evaluation of the $ηπ$ isospin-violating vector and scalar form factors relying on a systematic application of analyticity and unitarity, combined with chiral expansion results. It is argued that the usual analyticity properties do hold (i.e. no anomalous thresholds are present) in spite of the instability of the $η$ meson in QCD. Unitarity relates the vector form factor to the $ηπ\to ππ$ amplitude: we exploit progress in formulating and solving the Khuri-Treiman equations for $η\to 3π$ and in experimental measurements of the Dalitz plot parameters to evaluate the shape of the $ρ$-meson peak. Observing this peak in the energy distribution of the $τ\to ηπν$ decay would be a background-free signature of a second-class amplitude. The scalar form factor is also estimated from a phase dispersive representation using a plausible model for the $ηπ$ elastic scattering $S$-wave phase shift and a sum rule constraint in the inelastic region. We indicate how a possibly exotic nature of the $a_0(980)$ scalar meson manifests itself in a dispersive approach. A remark is finally made on a second-class amplitude in the $τ\toππν$ decay.

hep-ph↗
arXiv2014

Light Meson Dynamics Workshop. Mini proceedings

The mini-proceedings of the Light Meson Dynamics Workshop held in Mainz from February 10th to 12th, 2014, are presented. The web page of the conference, which contains all talks, can be found at https://indico.cern.ch/event/287442/overview .

hep-ph↗
arXiv2013

Unified dispersive approach to $γ^*\toγππ$ and $γγ\toππ$

A representation of the amplitude $γ^*(q^2)\toγππ$ is proposed which combines large $N_c$ chiral resonance Lagrangian modelling with general unitarity and analyticity properties. The amplitude is constrained from $γγ$ scattering results and $e^+ e^- \toγπ^0π^0$ measurements by the CMD-2 and SND collaborations. As an application, the contribution of the $ππ+γ$ states in the HVP contribution to the muon $g-2$ are reconsidered, taking into account the effect of the strong $S$-wave $ππ$ rescattering in a model independent way.

hep-ph↗
arXiv2013

MesonNet 2013 International Workshop. Mini-proceedings

The mini-proceedings of the MesonNet 2013 International Workshop held in Prague from June 17th to 19th, 2013, are presented. MesonNet is a research network within EU HadronPhysics3 project (1/2012 -- 12/2014). The web page of the conference, which contains all talks, can be found at http://ipnp.mff.cuni.cz/mesonnet13

hep-ph↗
arXiv2013

Unified dispersive approach to real and virtual photon-photon scattering at low energy

Previous representations of pion pair production amplitudes by two real photons at low energy, which combine dispersion theoretical constraints with elastic unitariy, chiral symmetry and soft photon constraints are generalized to the case where one photon is virtual. The constructed amplitudes display explicitly the dependence on the $ππ$ phase-shifts, on pion form factors and on pion polarizabilities. They apply both for space-like and time-like virtualities despite the apparent overlap of the left and right-hand cuts, by implementing a definition of resonance exchange amplitudes complying with analyticity and consistent limiting prescriptions for the energy variables. Applications are made to the pion generalized polarizabilies, to vector meson radiative decays, and to the $σγ$ electromagnetic form factor. Finally, and evaluation of the contribution of $γππ$ states in the hadronic vacuum polarization to the muon $g-2$ is given, which should be less model dependent than previous estimates.

hep-ph↗
arXiv2013

Dispersive evaluation of the second-class amplitude $τ\toηπν_τ$ in the standard model

We reevaluate the two form factors relevant for the $ηπ$ second-class $τ$ decay mode, making systematic use of analyticity, unitarity, combined with updated inputs to the NLO chiral constraints. We focus, in particular, on the shape of the $ρ$ resonance peak which is a background-free signature of a second-class current. Its dispersive construction requires the $ηπ\toππ$ scattering amplitude which we derive from a family of Khuri-Treiman equations solutions constrained with accurate recent results on the $η\to3π$ Dalitz plot.

hep-ph↗
arXiv2011

Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $σ(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $α_s G^2$ and to two photons. The Roy dispersive representation for the $ππ$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the $K\Kbar$ threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omnès dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $σ$, $κ$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $α_s G^2$ we find a significant coupling to both the $σ$ and the $f_0(980)$.

hep-ph↗
arXiv2010

MO analysis of the high statistics Belle results on $γγ\to π^+π^-,π^0π^0$ with chiral constraints

We reconsider Muskhelishvili-Omnès (MO) dispersive representations of photon-photon scattering to two pions, motivated by the very high statistics results recently released by the Belle collaboration for charged as well as neutral pion pairs and also by recent progress in the determination of the low-energy $ππ$ scattering amplitude. Applicability of this formalism is extended beyond 1 GeV by taking into account inelasticity due to $K\bar{K}$ . A modified MO representation is derived which has the advantage that all polynomial ambiguities are collected into the subtraction constants and have simple relations to pion polarizabilities. It is obtained by treating differently the exactly known QED Born term and the other components of the left-hand cut. These components are approximated by a sum over resonances. All resonances up to spin two and masses up to $\simeq1.3$ GeV are included. The tensor contributions to the left-hand cut are found to be numerically important. We perform fits to the data imposing chiral constraints, in particular, using a model independent sum rule result on the $p^6$ chiral coupling $c_{34}$. Such theoretical constraints are necessary because the experimental errors are dominantly systematic. Results on further $p^6$ couplings and pion dipole and quadrupole polarizabilities are then derived from the fit. The relevance of the new data for distinguishing between two possible scenarios of isospin breaking in the $f_0(980)$ region is discussed.

hep-ph↗