0000000000432211
AUTHOR
M. Albaladejo
Form factors of the isovector scalar current and the $\eta\pi$ scattering phase shifts
A model for S-wave $\eta\pi$ 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 $\eta\pi\to\eta\pi$, $\eta\pi\to K\bar{K}$ 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-Omn\`es problem, thus allowing to compute the $\eta\pi$ and $K\bar{K}$ form factor matrix elements of the $I=1$ scalar current from …
Form factors of the isovector scalar current and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta \pi $$\end{document}ηπ scattering phase shifts
A model for S-wave \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta \pi $$\end{document}ηπ scattering is proposed which could be realistic in an energy range from threshold up to above 1 GeV, where inelasticity is dominated by the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K{\bar{K}}$$\end{document}KK¯ channel. The T-matrix,…
Signature of an $h_1$ state in the $J/\psi \to \eta h_1 \to \eta K^{*0}\bar{K}^{*0}$ decay
The BES data on the $J/\psi \to \eta K^{*0}\bar{K}^{*0}$ reaction show a clear enhancement in the $K^{*0}\bar{K}^{*0}$ mass distribution close to the threshold of this channel. Such an enhancement is usually a signature of a L=0 resonance around threshold, which in this case would correspond to an $h_1$ state with quantum numbers $I^G(J^{PC})=0^-(1^{+-})$. A state around $1800\ \text{MeV}$ results from the interaction of the $K^* \bar{K}^*$ using the local hidden gauge approach. We show that the peak observed in $J/\psi \to \eta K^{*0}\bar{K}^{*0}$ naturally comes from the creation of this $h_1$ state with mass and width around $1830\ \text{MeV}$ and $110\ \text{MeV}$, respectively. A secon…
Shedding light on the $ X(3930) $ and $ X(3960) $ states with the $B^- \to K^- J/\psi \omega $ reaction
We have studied the contribution of the state $X(3930)$, coming from the interaction of the $D \overline{D}$ and $D^{+}_s D^{-}_s$ channels, to the $B^- \to K^- J/\psi \omega $ decay. The purpose of this work is to offer a complementary tool to see if the $X(3930)$ state observed in the $D^+ D^-$ channel is the same or not as the $X(3960)$ resonance claimed by the LHCb collaboration from a peak in the $D^{+}_s D^{-}_s$ mass distribution around threshold. We present results for what we expect in the $J/\psi \omega $ mass distribution in the $B^- \to K^- J/\psi \omega $ decay and conclude that a clear signal should be seen around $3930\,\rm MeV$. At the same time, finding no extra resonance s…
Finite volume treatment of ππ scattering and limits to phase shifts extraction from lattice QCD
We study theoretically the effects of finite volume for pipi scattering in order to extract physical observables for infinite volume from lattice QCD. We compare three different approaches for pipi scattering (lowest order Bethe-Salpeter approach, N/D and inverse amplitude methods) with the aim to study the effects of the finite size of the box in the potential of the different theories, specially the left-hand cut contribution through loops in the crossed t,u-channels. We quantify the error made by neglecting these effects in usual extractions of physical observables from lattice QCD spectra. We conclude that for pipi phase-shifts in the scalar-isoscalar channel up to 800 MeV this effect i…
$D\bar{D}^*$ scattering and $\chi_{c1}(3872)$ in nuclear matter
We study the behaviour of the $\chi_{c1}(3872)$, also known as $X(3872)$, in dense nuclear matter. We begin from a picture in vacuum of the $X(3872)$ as a purely molecular $(D \bar D^*-c.c.)$ state, generated as a bound state from a heavy-quark symmetry leading-order interaction between the charmed mesons, and analyze the $D \bar D^*$ scattering $T-$matrix ($T_{D \bar D^*}$) inside of the medium. Next, we consider also mixed-molecular scenarios and, in all cases, we determine the corresponding $X(3872)$ spectral function and the $D \bar D^*$ amplitude, with the mesons embedded in the dense environment. We find important nuclear corrections for $T_{D \bar D^*}$ and the pole position of the r…
Femtoscopic correlation function for the $T_{cc}(3875)^+$ state
We have conducted a study of the femtoscopic correlation functions for the $D^0D^{*+}$ and $D^+D^{*0}$ channels that build the $T_{cc}$ state. We develop a formalism that allows us to factorize the scattering amplitudes outside the integrals in the formulas, and the integrals involve the range of the strong interaction explicitly. For a source of size of 1 fm, we find values for the correlation functions of the $D^0 D^{*+}$ and $D^+D^{*0}$ channels at the origin around 30 and 2.5, respectively, and we see these observables converging to unity already for relative momenta of the order of 200 MeV. We conduct tests to see the relevance of the different contributions to the correlation function…
$a_0-f_0$ mixing in the Khuri-Treiman equations for $\eta\to 3\pi$
A reliable determination of the isospin breaking double quark mass ratio from precise experimental data on $\eta\to 3\pi$ 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 $\eta\to 3\pi$ amplitudes. Matrix generalisations of the equations describing elastic $\pi\pi$ rescattering with $I=0,\,2$ are introduced which accomodate both $\pi\pi/K\bar{K}$ and $\eta\pi/K\bar{K}$ coupled-channel rescattering. Isospin violation induced by the physical …
Searching for a hidden charm $h_1$ state in the $X(4660) \to \eta h_1$ and $X(4660) \to \eta D^* \bar D^*$ decays
We explore the possibility of experimentally detecting a predicted $h_1 ~[I^G(J^{PC})=0^-(1^{+-})]$ state of hidden charm made out from the $D^* \bar D^*$ interaction. The method consists in measuring the decay of X(4660) into $\eta D^* \bar D^*$, determining the binding energy with respect to the $D^* \bar D^*$ threshold from the shape of the $D^* \bar D^*$ invariant mass distribution. A complementary method consists in looking at the inclusive $X(4660) \to \eta X$ decay, searching for a peak in the $X$ invariant mass distribution given by the missing X(4660), $\eta$ mass. We make calculations to determine the partial decay width of $X(4660) \to \eta h_1$ from the measured $X(4660) \to \et…