arXiv subjects

V. R. Debastiani

Publications and source records attributed to V. R. Debastiani.

At least 19 recordsLinked to original sources

arXiv2019

A non-relativistic model for the $[cc][\bar{c}\bar{c}]$ tetraquark

We use a non-relativistic model to study the spectroscopy of a tetraquark composed of $[cc][\bar{c}\bar{c}]$ in a diquark-antidiquark configuration. By numerically solving the Schrödinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the $c\bar{c}$ spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained. We find that the spin-dependent interaction is sizable in the diquark-antidiquark system, despite the heavy diquark mass, and also that the diquark has a finite size if treated in the same way as the $c\bar{c}$ systems. We find that the lowest $S$-wave $T_{4c}$ tetraquarks might be below their thresholds of spontaneous dissociation into low-lying charmonium pairs, while orbital and radial excitations would be mostly above the corresponding charmonium pair thresholds. Finally, we repeat the calculations without the confining part of the potential and obtain bound diquarks and bound tetraquarks. This might be relevant to the study of exotic charmonium in the quark-gluon plasma. The $T_{4c}$ states could be investigated in the forthcoming experiments at the LHC and Belle II.

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arXiv2018

Description of the $Ξ_c$ and $Ξ_b$ states as molecular states

In this work we study several $Ξ_c$ and $Ξ_b$ states dynamically generated from the meson-baryon interaction in coupled channels, using an extension of the local hidden gauge approach in the Bethe-Salpeter equation. These molecular states appear as poles of the scattering amplitudes, and several of them can be identified with the experimentally observed $Ξ_c$ states, including the $Ξ_c(2790)$, $Ξ_c(2930)$, $Ξ_c(2970)$, $Ξ_c(3055)$ and $Ξ_c(3080)$. Also, for the recently reported $Ξ_b(6227)$ state, we find two poles with masses and widths remarkably close to the experimental data, for both the $J^P=1/2^-$ and $J^P=3/2^-$ sectors.

hep-ph↗

arXiv2018

Considerations on the Schmid theorem for triangle singularities

We investigate the Schmid theorem, which states that if one has a tree level mechanism with a particle decaying to two particles and one of them decaying posteriorly to two other particles, the possible triangle singularity developed by the mechanism of elastic rescattering of two of the three decay particles does not change the cross section provided by the tree level. We investigate the process in terms of the width of the unstable particle produced in the first decay and determine the limits of validity and violation of the theorem. One of the conclusions is that the theorem holds in the strict limit of zero width of that resonance, in which case the strength of the triangle diagram becomes negligible compared to the tree level. Another conclusion, on the practical side, is that for realistic values of the width, the triangle singularity can provide a strength comparable or even bigger than the tree level, which indicates that invoking the Schmid theorem to neglect the triangle diagram stemming from elastic rescattering of the tree level should not be done. Even then, we observe that the realistic case keeps some memory of the Schmid theorem, which is visible in a peculiar interference pattern with the tree level.

hep-ph↗

arXiv2018

Dynamical Hadrons

In this talk I briefly review the theory of resonances dynamically generated from hadron-hadron scattering, sometimes referred to as "molecules"S. I give some classical examples of meson-meson and meson-baryon systems, as well as a few examples of different approaches to describe the interaction between hadrons. To conclude, I comment on a few recent works that suggest that some of the five new narrow $Ω_c$ states, recently discovered by the LHCb collaboration, can be interpreted as meson-baryon molecules.

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arXiv2018

Doubly charmed $Ξ_{cc}$ molecular states from meson-baryon interaction

Stimulated by the new experimental LHCb findings associated with the $Ω_c$ states, some of which we have described in a previous work as being dynamically generated through meson-baryon interaction, we have extended this approach to make predictions for new $Ξ_{cc}$ molecular states in the $C=2$, $S=0$ and $I=1/2$ sector. These states manifest themselves as poles in the solution of the Bethe-Salpeter equation in coupled channels. The kernels of this equation were obtained using the Lagrangians coming from the hidden local gauge symmetry, where the interactions are dominated by the exchange of light vector mesons. The extension of this approach to the heavy sector stems from the realization that the dominant interaction corresponds to having the heavy quarks as spectators, which implies the preservation of the heavy quark symmetry. As a result, we get several states: two states from the pseudoscalar meson-baryon interaction with $J^P=1/2^-$, and masses around $4080$ and $4090$ MeV, and one at $4150$ MeV for $J^P=3/2^-$. Furthermore, from the vector meson-baryon interaction we get three states degenerate with $J^P=1/2^-$ and $3/2^-$ from $4220$ MeV to $4330$ MeV, and two more states around $4280$ MeV and $4410$ MeV, degenerate with $J^P=1/2^-,\, 3/2^-$ and $5/2^-$.

hep-ph↗

arXiv2018

Molecular $Ω_b$ states

Motivated by the recent finding of five $Ω_c$ states by the LHCb collaboration, and the successful reproduction of three of them in a recent approach searching for molecular states of meson-baryon with the quantum numbers of $Ω_c$, we extend these ideas and make predictions for the interaction of meson-baryon in the beauty sector, searching for poles in the scattering matrix that correspond to physical states. We find several $Ω_b$ states: two states with masses 6405~MeV and 6465~MeV for $J^P= \frac{1}{2}^-$; two more states with masses 6427~MeV and 6665~MeV for $\frac{3}{2}^-$; and three states between 6500 and 6820~MeV, degenerate with $J^P=\frac{1}{2}^-,\,\frac{3}{2}^-$, stemming from the interaction of vector-baryon in the beauty sector.

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arXiv2018

$\boldsymbol{Ω_b^- \to (Ξ_c^+ \, K^-) \, π^-}$ and the $\boldsymbol{Ω_c}$ states

We study the weak decay $Ω_b^- \to (Ξ_c^+ \, K^-) \, π^-$, in view of the narrow $Ω_c$ states recently measured by the LHCb collaboration and later confirmed by the Belle collaboration. The $Ω_c(3050)$ and $Ω_c(3090)$ are described as meson-baryon molecular states, using an extension of the local hidden gauge approach in coupled channels. We investigate the $ΞD$, $Ξ_c \bar K$ and $Ξ_c^\prime \bar K$ invariant mass distributions making predictions that could be confronted with future experiments, providing useful information that could help determine the quantum numbers and nature of these states.

hep-ph↗

arXiv2018

Molecular $Ω_c$ states generated from coupled meson-baryon channels

We have investigated $Ω_c$ states that are dynamically generated from the meson-baryon interaction. We use an extension of the local hidden gauge to obtain the interaction from the exchange of vector mesons. We show that the dominant terms come from the exchange of light vectors, where the heavy quarks are spectators. This has as a consequence that heavy quark symmetry is preserved for the dominant terms in the $(1/m_Q)$ counting, and also that the interaction in this case can be obtained from the $\textrm{SU(3)}$ chiral Lagrangians. We show that for a standard value for the cutoff regulating the loop, we obtain two states with $J^{P}={1/2}^{-}$ and two more with $J^{P}={3/2}^{-}$, three of them in remarkable agreement with three experimental states in mass and width. We also make predictions at higher energies for states of vector-baryon nature.

hep-ph↗

arXiv2018

Production and mixing of scalar mesons in $η_c$ and $χ_{c1}$ decays

We briefly discuss how the chiral unitary approach in coupled channels and $SU(3)$ symmetry can be used to describe the production of $f_0(500)$, $f_0(980)$ and $a_0(980)$ in the $χ_{c1} \to ηπ^+ π^-$ reaction, recently measured by the BESIII collaboration. In this reaction a very strong peak for the $a_0(980)$ can be seen in the $ηπ$ invariant mass, while clear signals for the $f_0(500)$ and $f_0(980)$ appear in the one of $π^+π^-$. Next, we show the predictions made with the same model for the analogous decay $η_c \to ηπ^+ π^-$, which could also be measured experimentally. We discuss the differences of these two reactions which are interesting to test the picture where these scalar mesons are dynamically generated from the interaction of pairs of pseudoscalars. Furthermore, we comment on a new recent work where the same model was used to study the $a_0(980) - f_0(980)$ mixing in the $χ_{c1} \to π^0 π^0 η$ and $χ_{c1} \to π^0 π^+ π^-$ reactions, showing that quantitative agreement with the experimental measurement of this mixing, also performed by BESIII, can be obtained, revealing interesting aspects of the dynamics of this process and the importance of coupled channels.

hep-ph↗

arXiv2018

Study of the $DK K$ and $DK \bar{K}$ systems

Using the Fixed Center Approximation to Faddeev equations we have investigated the $DKK$ and $DK\bar{K}$ three-body systems, considering that the $D^*_{s0}(2317)$ acts as the heavy cluster in both cases, generated from the $DK$ interaction in isospin 0. For the $DK\bar{K}$ system we have found evidence of a state with $I(J^P)=1/2(0^-)$ and mass about $2833 - 2858$ MeV, above the threshold of $D^*_{s0}(2317)\bar{K}$. Our results indicate that this state is dominated by a $Df_0(980)$ component, then it could be searched for in the $ππD$ invariant mass. On the other hand, no clear evidence related to a state from the $DKK$ interaction is found.

hep-ph↗

arXiv2017

Spectroscopy of the All-Charm Tetraquark

We use a non-relativistic model to study the mass spectroscopy of a tetraquark composed by $c \, \bar{c} \, c \, \bar{c}$ quarks in the diquark-antidiquark picture. By numerically solving the Schrödinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the $c\bar{c}$ spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained. We find that the spin-dependent interaction is sizable in the diquark-antidiquark system, despite of the heavy diquark mass, and that the diquark has a finite size if treated in analogy to the $c\bar{c}$ systems. We find that the lowest $S$-wave $T_{4c}$ tetraquarks might be below their thresholds of spontaneous dissociation into low-lying charmonium pairs, while orbital and radial excitations would be mostly above the corresponding charmonium pair threshold. These states could be investigated in the forthcoming experiments at LHCb and Belle II.

hep-ph↗

arXiv2017

The radiative decay $D^0 \to \bar{K}^{*0} γ$ with vector meson dominance

Motivated by the experimental measurements of $D^0$ radiative decay modes we have proposed a model to study the $D^0\to \bar{K}^{*0}γ$ decay, by establishing a link with $D^0\to \bar{K}^{*0}V$ $(V=ρ^0,\, ω)$ decays through the vector meson dominance hypothesis. In order to do this properly, we have used the Lagrangians from the local hidden gauge symmetry approach to account for $Vγ$ conversion. As a result, we have found the branching ratio $\mathcal{B}[D^0\to \bar{K}^{*0}γ] =(1.55 - 3.44)\times 10^{-4}$, which is in fair agreement with the experimental values reported by Belle and Babar collaborations.

hep-ph↗

arXiv2017

$a_0(980) - f_0(980)$ mixing in $χ_{c1} \to π^0 f_0(980) \to π^0 π^+ π^-$ and $χ_{c1} \to π^0 a_0(980) \to π^0 π^0 η$

We study the isospin breaking in the reactions $χ_{c1} \to π^0 π^+ π^-$ and $χ_{c1} \to π^0 π^0 η$ and its relation to the $a_0(980) - f_0(980)$ mixing, which was measured by the BESIII Collaboration. We show that the same theoretical model previously developed to study the $χ_{c1} \to ηπ^+ π^-$ reaction (also measured by BESIII), and further explored in the predictions to the $η_{c} \to ηπ^+ π^-$, can be successfully employed in the present study. We assume that the $χ_{c1}$ behaves as an $SU(3)$ singlet to find the weight in which trios of pseudoscalars are created, followed by the final state interaction of pairs of mesons to describe how the $a_0(980)$ and $f_0(980)$ are dynamically generated, using the chiral unitary approach in coupled channels. The isospin violation is introduced through the use of different masses for the charged and neutral kaons, either in the propagators of the pairs of mesons created in the $χ_{c1}$ decay, or in the propagators inside the $T$ matrix, constructed through the unitarization of the scattering and transition amplitudes of pairs of pseudoscalar mesons. We find that violating isospin inside the $T$ matrix makes the $π^0η\to π^+π^-$ amplitude nonzero, which gives an important contribution and also enhances the effect of the $K\bar{K}$ term. Also, we find that in the total amplitude the most important effect is the isospin breaking inside the $T$ matrix, due to the constructive sum of $π^0η\to π^+π^-$ and $K\bar{K} \to π^+ π^-$, which is essential to get a good agreement with the experimental measurement of the mixing.

hep-ph↗

arXiv2017

On the binding of the $BD\bar{D}$ and $BDD$ systems

We study theoretically the $BD\bar{D}$ and $BDD$ systems to see if they allow for possible bound or resonant states. The three-body interaction is evaluated implementing the Fixed Center Approximation to the Faddeev equations which considers the interaction of a $D$ or $\bar{D}$ particle with the components of a $BD$ cluster, previously proved to form a bound state. We find an $I(J^P)=1/2(0^-)$ bound state for the $BD\bar{D}$ system at an energy around $8925-8985$ MeV within uncertainties, which would correspond to a bottom--hidden-charm meson. In contrast, the $BDD$ system, which would be bottom--double-charm and hence manifestly exotic, we have found hints of a bound state in the energy region $8935-8985$ MeV, but the results are not stable under the uncertainties of the model, and we cannot assure, neither rule out, the possibility of a $BDD$ three-body state.

hep-ph↗

arXiv2017

Production of $f_0(500)$, $f_0(980)$ and $a_0(980)$ in the $χ_{c1} \to ηπ^+ π^-$ and $η_c \to ηπ^+ π^-$ decays

Using the chiral unitary approach in coupled channels and $SU(3)$ symmetry we describe the production of $f_0(500)$, $f_0(980)$ and $a_0(980)$ in the $χ_{c1} \to ηπ^+ π^-$ reaction, recently performed by the BESIII collaboration. A very strong peak for the $a_0(980)$ can be seen in the $ηπ$ invariant mass, while clear signals for the $f_0(500)$ and $f_0(980)$ appear in the one of $π^+π^-$. Next, we make predictions for the analogous decay $η_c \to ηπ^+ π^-$, which could also be measured experimentally. We discuss the differences of these reactions which are interesting to test the picture where these scalar mesons are dynamically generated from the interaction of pairs of pseudoscalars.

hep-ph↗

arXiv2017

Study of the $DKK$ and $DK\bar{K}$ systems

Using the Fixed Center Approximation to Faddeev equations we have investigated the $DKK$ and $DK\bar{K}$ three-body systems, considering that the $DK$ dynamically generates, through its $I=0$ component, the $D^*_{s0}(2317)$ molecule. According to our findings, for $DK\bar{K}$ interaction we have found an evidence of a state $I(J^P)=1/2(0^-)$ just above the $D^*_{s0}(2317)\bar{K}$ threshold and around the $Df_0(980)$ thresholds, with mass about $2833 - 2858$ MeV, made mostly of $Df_0(980)$. On the other hand, no evidence related to a state from the $DKK$ interaction is found. The state found could be seen in the $ππD$ invariant mass.

hep-ph↗

arXiv2017

Role of a triangle singularity in the $πN(1535)$ contribution to $γp \to p π^0 η$

We have studied the $γp \to p π^0 η$ reaction paying attention to the two main mechanisms at low energies, the $γp \to Δ(1700) \to ηΔ(1232)$ and the $γp \to Δ(1700) \to πN(1535)$. Both of them are driven by the photoexcitation of the $Δ(1700)$ and the second one involves a mechanism that leads to a triangle singularity. We are able to evaluate quantitatively the cross section for this process and show that it agrees with the experimental determination. Yet, there are some differences with the standard partial wave analysis which does not include explicitly the triangle singularity. The exercise also shows the convenience to explore possible triangle singularities in other reactions and how a standard partial analysis can be extended to accommodate them.

hep-ph↗

arXiv2016

Predictions for $η_c \to ηπ^+ π^-$ producing $f_0(500)$, $f_0(980)$ and $a_0(980)$

We perform calculations for the $η_c \to ηπ^+ π^-$ decay using elements of SU(3) symmetry to see the weight of different trios of pseudoscalars produced in this decay, prior to the final state interaction of the mesons. After that, the interaction of pairs of mesons, leading finally to $ηπ^+ π^-$, is done using the chiral unitary approach. We evaluate the $π^+ π^-$ and $πη$ mass distributions and find large and clear signals for $f_0(500)$, $f_0(980)$ and $a_0(980)$ excitation. The reaction is similar to the $χ_{c1} \to ηπ^+ π^-$, which has been recently measured at BESIII and its implementation and comparison with these predictions will be very valuable to shed light on the nature of the low mass scalar mesons.

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