arXiv subjects

M. Albaladejo

Publications and source records attributed to M. Albaladejo.

At least 55 records · Page 3Linked to original sources

arXiv2017

What is the right formalism to search for resonances?

Hadron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B -> psi pi K and B -> Dbar pi pi decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.

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↗

arXiv2016

$Z_c(3900)$: Confronting theory and lattice simulations

We consider a recent $T$-matrix analysis by Albaladejo {\it et al.}, [Phys.\ Lett.\ B {\bf 755}, 337 (2016)] which accounts for the $J/ψπ$ and $D^\ast\bar{D}$ coupled--channels dynamics, and that successfully describes the experimental information concerning the recently discovered $Z_c(3900)^\pm$. Within such scheme, the data can be similarly well described in two different scenarios, where the $Z_c(3900)$ is either a resonance or a virtual state. To shed light into the nature of this state, we apply this formalism in a finite box with the aim of comparing with recent Lattice QCD (LQCD) simulations. We see that the energy levels obtained for both scenarios agree well with those obtained in the single-volume LQCD simulation reported in Prelovsek {\it et al.} [Phys.\ Rev.\ D {\bf 91}, 014504 (2015)], making thus difficult to disentangle between both possibilities. We also study the volume dependence of the energy levels obtained with our formalism, and suggest that LQCD simulations performed at several volumes could help in discerning the actual nature of the intriguing $Z_c(3900)$ state.

hep-ph↗

arXiv2015

Decay widths of the spin-2 partners of the X(3872)

We consider the $X(3872)$ resonance as a $J^{PC}=1^{++}$ $D\bar D^*$ hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers $2^{++}$, $X_{2}$, which would be a $D^*\bar D^*$ loosely bound state. The $X_{2}$ is expected to decay dominantly into $D\bar D$, $D\bar D^*$ and $\bar D D^*$ in $d$-wave. In this work, we calculate the decay widths of the $X_{2}$ resonance into the above channels, as well as those of its bottom partner, $X_{b2}$, the mass of which comes from assuming heavy flavor symmetry for the contact terms. We find partial widths of the $X_{2}$ and $X_{b2}$ of the order of a few MeV. Finally, we also study the radiative $X_2\to D\bar D^{*}γ$ and $X_{b2} \to \bar B B^{*}γ$ decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the $D\bar D^{*}$ or $B\bar B^{*}$ final state interaction.

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

Signature of an $h_1$ state from $J/ψ\to ηK^{0}\bar{K}^{0}$ and theoretical description of the $Z_c(3900)$ and $Z_c(4020)$ as $D \bar D^$ and $D^ \bar D^*$ molecular states

In this talk we address two topics: The first one is an empirical explanation in terms of a new state $h_1$ of the peak in the $K^{*0}\bar{K}^{*0}$ invariant mass distribution close to threshold of this channel in the $J/ψ\to ηK^{*0}\bar{K}^{*0}$ decay. The second one is a theoretical description of the isospin $I=1$ $Z_c(3900)$ and $Z_c(4020)$ states in terms of molecular states of $D \bar D^*+ cc$ and $D^* \bar D^*$.

hep-ph↗

arXiv2013

Hidden charm molecules in a Finite Volume

In the present paper we address the interaction of charmed mesons in hidden charm channels in a finite box. We use the interaction from a recent model based on heavy quark spin symmetry that predicts molecules of hidden charm in the infinite volume. The energy levels in the box are generated within this model, and several methods for the analysis of these levels ("inverse problem") are investigated.

hep-lat↗

arXiv2013

Recent Developments on Hadron Interaction and Dynamically Generated Resonances

In this talk I report on the recent developments in the subject of dynamically generated resonances. In particular I discuss the $γp \to K^0 Σ^+$ and $γn \to K^0 Σ^0$ reactions, with a peculiar behavior around the $K^{*0} Λ$ threshold, due to a $1/2^-$ resonance around 2035 MeV. Similarly, I discuss a BES experiment, $J/ψ\to ηK^{*0} \bar K^{*0}$ decay, which provides evidence for a new $h_1$ resonance around 1830 MeV that was predicted from the vector-vector interaction. A short discussion is then made about recent advances in the charm and beauty sectors.

hep-ph↗

arXiv2013

Finite volume treatment of $ππ$ scattering in the $ρ$ channel

We make a theoretical study of $ππ$ scattering with quantum numbers $J^{PC}=1^{--}$ in a finite box. To calculate physical observables for infinite volume from lattice QCD, the finite box dependence of the potentials is not usually considered. We quantify such effects by means of two different approaches for vector-isovector $ππ$ scattering based on Unitarized Chiral Perturbation Theory results: the Inverse Amplitude Method and another one based on the $N/D$ method. We take into account finite box effects stemming from higher orders through loops in the crossed $t,u-$channels as well as from the renormalization of the coupling constants. The main conclusion is that for $ππ$ phase shifts in the isovector channel one can safely apply Lüscher based methods for finite box sizes of $L$ greater than $2 m_π^{-1}$.

hep-lat↗

arXiv2013

Searching for a hidden charm $h_1$ state in the $X(4660) \to ηh_1$ and $X(4660) \to ηD^* \bar D^*$ 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 $ηD^* \bar D^*$, 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 $X(4660) \to ηX$ decay, searching for a peak in the $X$ invariant mass distribution given by the missing X(4660), $η$ mass. We make calculations to determine the partial decay width of $X(4660) \to ηh_1$ from the measured $X(4660) \to ηD^* \bar D^*$ distribution. This estimation should serve in an experiment to foresee the possibility of detecting the $h_1$ state on top of the background of inclusive events.

hep-ph↗

arXiv2013

Signature of an $h_1$ state in the $J/ψ\to ηh_1 \to ηK^{0}\bar{K}^{0}$ decay

The BES data on the $J/ψ\to ηK^{*0}\bar{K}^{*0}$ 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 $J/ψ\to ηK^{*0}\bar{K}^{*0}$ naturally comes from the creation of this $h_1$ state with mass and width around $1830\ \text{MeV}$ and $110\ \text{MeV}$, respectively. A second analysis, model independent, corroborates the first result, confirming the relationship of the enhancement in the invariant mass spectrum with the $h_1$ resonance.

hep-ph↗

arXiv2012

Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves

We consider nucleon-nucleon interactions from chiral effective field theory applying the N/D method. The case of coupled partial waves is now treated, extending Ref. [1] where the uncoupled case was studied. As a result three N/D elastic-like equations have to be solved for every set of three independent partial waves coupled. As in the previous reference the input for this method is the discontinuity along the left-hand cut of the nucleon-nucleon partial wave amplitudes. It can be calculated perturbatively in chiral perturbation theory because it involves only irreducible two-nucleon intermediate states. We apply here our method to the leading order result consisting of one-pion exchange as the source for the discontinuity along the left-hand cut. The linear integral equations for the N/D method must be solved in the presence of L - 1 constraints, with L the orbital angular momentum, in order to satisfy the proper threshold behavior for L>= 2. We dedicate special attention to satisfy the requirements of unitarity in coupled channels. We also focus on the specific issue of the deuteron pole position in the 3S1-3D1 scattering. Our final amplitudes are based on dispersion relations and chiral effective field theory, being independent of any explicit regulator. They are amenable to a systematic improvement order by order in the chiral expansion.

nucl-th↗

arXiv2012

On the size of the sigma meson and its nature

In this work the nature of the σor f_0(600) resonance is discussed by evaluating its quadratic scalar radius, \la r^2\ra_s^σ. This allows one to have a quantitative estimate for the size of this resonance. We obtain that the σresonance is a compact object with $\la r^2\ra_s^σ=(0.19\pm0.02)-i(0.06\pm0.02)$ fm^2. Within our approach, employing unitary chiral perturbation theory, the σis a dynamically generated resonance that stems from the pion-pion interactions. Given its small size we conclude that the two pions inside the resonance are merged. A four-quark picture is then more appropriate. However, when the pion mass increases, for pion masses somewhat above 400 MeV, the picture of a two-pion molecule is the appropriate one. The σis then a spread ππbound state. These results are connected with other recent works that support a non standard nature of the σas well, while fulfilling strong QCD constraints, as well as with lattice QCD. We offer a detailed study of the low-energy S-wave ππscattering data from where we extract our values for the threshold parameters of S-wave ππphase shifts, the {\cal O}(p^4) chiral perturbation theory low energy constants as well as the σpole position. From the comparison with other accurate determinations in the literature we obtain the average values for the isospin 0 S-wave ππthreshold parameters, $a_0^0=0.220\pm0.003$, $b_0^0=0.279\pm 0.003 M_π^{-2}$, and for the real and imaginary parts of the σpole position in \sqrt{s}, $458\pm14-i(261\pm17)$ MeV. The quark mass dependence of the size of the σ, its mass and width are considered too. The latter agree accurately with a previous lattice QCD calculation. The fact that the mass of this resonance tends to follow the threshold of two pions is a clear indication that the σis a dynamically generated meson-meson resonance.

hep-ph↗

arXiv2012

Finite volume treatment of pi pi 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 is negligible for box sizes bigger than 2.5m_pi^-1 and of the order of 5% at around 1.5-2m_pi^-1. For isospin 2 the finite size effects can reach up to 10% for that energy. We also quantify the error made when using the standard Luscher method to extract physical observables from lattice QCD, which is widely used in the literature but is an approximation of the one used in the present work.

hep-lat↗

arXiv2011

Nucleon-nucleon interactions from dispersion relations: Elastic partial waves

We consider nucleon-nucleon (NN) interactions from chiral effective field theory. In this work we restrict ourselves to the elastic NN scattering. We apply the N/D method to calculate the NN partial waves taking as input the one-pion exchange discontinuity along the left-hand cut. This discontinuity is amenable to a chiral power counting as discussed by Lacour, Oller and Meissner [Ann. Phys. (NY) 326, 241 (2011)], with one-pion exchange as its leading order contribution. The resulting linear integral equation for a partial wave with orbital angular momentum L>=2 is solved in the presence of L-1 constraints, so as to guarantee the right behavior of the D and higher partial waves near threshold. The calculated NN partial waves are based on dispersion relations and are independent of regulator. This method can also be applied to higher orders in the calculation of the discontinuity along the left-hand cut and extended to triplet coupled partial waves.

nucl-th↗

arXiv2010

Scalar-Pseudoscalar scattering and pseudoscalar resonances

The interactions between the f_0(980) and a_0(980) scalar resonances and the lightest pseudoscalar mesons are studied. We first obtain the interacting kernels, without including any ad hoc free parameter, because the lightest scalar resonances are dynamically generated. These kernels are unitarized, giving the final amplitudes, which generate pseudoscalar resonances, associated with the K(1460), π(1300), π(1800), η(1475) and X(1835). We also consider the exotic channels with I=3/2 and I^G=1^+ quantum numbers. The former could be also resonant in agreement with a previous prediction.

hep-ph↗