arXiv subjects

L. R. Dai

Publications and source records attributed to L. R. Dai.

At least 19 recordsLinked to original sources

arXiv2026

Study of the $J/ψ\to Λ\barΣ^0η$ reaction

We study the isospin violating $J/ψ\to Λ\bar Σ^0 η$ reaction, recently measured by the BESIII collaboration, by looking at the dominant terms with $\bar Σ^0$ and a pair of pseudoscalar-baryon particles that form together an SU(3) singlet and can thus couple to the $J/ψ$. Next we allow these pairs to undergo final state interaction to produce the final $ηΛ$. We find that the relevant original channels are $\bar K N$ and $K Ξ$, and the non cancelation of terms involving charged and neutral particles, because of their different masses, is responsible for the reaction. With that mechanism we find a good agreement with the three experimental mass distributions.

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arXiv2024

Photoproduction of the $ Λ(1800) $

We have carried out a study of the $γ~ p \rightarrow p K^{+} K^{*-} (K^{*-} \rightarrow K^{-} π^{0}) $, $ γ~p \rightarrow p K^{+} K^{*-} ( K^{*-} \rightarrow \bar{K}^{0} π^{-} )$ and $ γ~p \rightarrow K^{+} K^{-}p$ reactions, producing the $K^+ Λ(1800)$ final state, from the perspective that the $Λ(1800)$ resonance is dynamically generated from the interaction of $\bar{K}^* N$ with its coupled vector-baryon channels, in complete analogy to the $Λ(1405)$ generated from the interaction of $\bar{K} N$ and its coupled pseudoscalar-baryon channels. The two reactions are complementary and their mass distributions are tied to the particular nature of this resonance in that framework. We provide much information on the shapes and strength of the invariant mass distributions of these reactions, and the energy dependence of the cross sections, that when contrasted with future experiments should shed valuable light on the nature of this resonance and its analogy to the $Λ(1405)$.

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arXiv2024

Triangle singularity in the $J/ψ\to ϕπ^+ a_0^-(π^- η),\; ϕπ^- a_0^+(π^+ η)$ decays

We study the $J/ψ\to ϕπ^+ a_0(980)^- (a_0^- \to π^- η)$ decay, evaluating the double mass distribution in terms of the $π^- η$ and $π^+ a^-_0$ invariant masses. We show that the $π^- η$ mass distribution exhibits the typical cusp structure of the $a_0(980)$ seen in recent high statistics experiments, and the $π^+ a^-_0$ spectrum shows clearly a peak around $M_{\rm inv}(π^+ a^-_0)=1420 \,{\rm MeV}$, corresponding to a triangle singularity. When integrating over the two invariant masses we find a branching ratio for this decay of the order of $10^{-5}$, which is easily accessible in present laboratories. We also call attention to the fact that the signal obtained is compatible with a bump experimentally observed in the $ηπ^+π^-$ mass distribution in the $J/ψ\to ϕηπ^+π^-$ decay and encourage further analysis to extract from there the $ϕπ^+ a_0^-$ and $ϕπ^- a_0^+$ decay modes.

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arXiv2023

Correlation function for the $T_{bb}$ state: Determination of the binding, scattering lengths, effective ranges and molecular probabilities

We perform a study of the $B^{*+}B^0,B^{*0}B^+$ correlation functions using an extension of the local hidden gauge approach which provides the interaction from the exchange of light vector mesons and gives rise to a bound state of these components in $I=0$ with a binding energy of about $21$~MeV. After that, we face the inverse problem of determining the low energy observables, scattering length and effective range for each channel, the possible existence of a bound state, and, if found, the couplings of such a state to each $B^{*+}B^0,B^{*0}B^+$ component as well as the molecular probabilities of each of the channels. We use the bootstrap method to determine these magnitudes and find that, with errors in the correlation function typical of present experiments, we can determine all these magnitudes with acceptable precision. In addition, the size of the source function of the experiment from where the correlation functions are measured can be also determined with a high precision.

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arXiv2023

The isospin and compositeness of the $T_{cc}(3875)$ state

We perform a fit to the LHCb data on the $T_{cc}(3875)$ state in order to determine its nature. We use a general framework that allows to have the $D^0 D^{*+}$, $D^+ D^{*0}$ components forming a molecular state, as well as a possible nonmolecular state or contributions from missing coupled channels. From the fits to the data we conclude that the state observed is clearly of molecular nature from the $D^0 D^{*+}$, $D^+ D^{*0}$ components and the possible contribution of a nonmolecular state or missing channels is smaller than 3\%, compatible with zero. We also determine that the state has isospin $I=0$ with a minor isospin breaking from the different masses of the channels involved, and the probabilities of the $D^0 D^{*+}$, $D^+ D^{*0}$ channels are of the order of 69\% and 29\% with uncertainties of 1\%. The differences between these probabilities should not be interpreted as a measure of the isospin violation. Due to the short range of the strong interaction where the isospin is manifested, the isospin nature is provided by the couplings of the state found to the $D^0 D^{*+}$, $D^+ D^{*0}$ components, and our results for these couplings indicate that we have an $I=0$ state with a very small isospin breaking. We also find that the potential obtained provides a repulsive interaction in $I=1$, preventing the formation of an $I=1$ state, in agreement with what is observed in the experiment.

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arXiv2023

Evolution of genuine states to molecular ones: The $T_{cc}(3875)$ case

We address the issue of the compositeness of hadronic states and demonstrate that starting with a genuine state of nonmolecular nature, but which couples to some meson-meson component to be observable in that channel, if that state is blamed for a bound state appearing below the meson-meson threshold it gets dressed with a meson cloud and it becomes pure molecular in the limit case of zero binding. We discuss the issue of the scales, and see that if the genuine state has a mass very close to threshold, the theorem holds, but the molecular probability goes to unity in a very narrow range of energies close to threshold. The conclusion is that the value of the binding does not determine the compositeness of a state. However, in such extreme cases we see that the scattering length gets progressively smaller and the effective range grows indefinitely. In other words, the binding energy does not determine the compositeness of a state, but the additional information of the scattering length and effective range can provide an answer. We also show that the consideration of a direct attractive interaction between the mesons in addition to having a genuine component, increases the compositeness of the state. Explicit calculations are done for the $T_{cc}(3875)$ state, but are easily generalized to any hadronic system.

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arXiv2023

Evolution of compact states to molecular ones with coupled channels: The case of the $X(3872)$

We study the molecular probability of the $X(3872)$ in the $D^0 \bar D^{*0}$ and $D^+ D^{*-}$ channels in several scenarios. One of them assumes that the state is purely due to a genuine nonmolecular component. However, it gets unavoidably dressed by the meson components to the point that in the limit of zero binding of the $D^0 \bar D^{*0}$ component becomes purely molecular. Yet, the small but finite binding allows for a nonmolecular state when the bare mass of the genuine state approaches the $D^0 \bar D^{*0}$ threshold, but, in this case the system develops a small scattering length and a huge effective range for this channel in flagrant disagreement with present values of these magnitudes. Next we discuss the possibility to have hybrid states stemming from the combined effect of a genuine state and a reasonable direct interaction between the meson components, where we find cases in which the scattering length and effective range are still compatible with data, but even then the molecular probability is as big as $95 \%$. Finally, we perform the calculations when the binding stems purely from the direct interaction between the meson-meson components. In summary we conclude, that while present data definitely rule out the possibility of a dominant nonmolecular component, the precise value of the molecular probability requires a more precise determination of the scattering length and effective range of the $D^0 \bar D^{*0}$ channel, as well as the measurement of these magnitudes for the $D^+ D^{*-}$ channel which have not been determined experimentally so far.

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arXiv2023

The $D^+_s \to K^+ π^+ π^-$ reaction and the scalar $f_0(500)$, $f_0(980)$ and $K^*_0 (700)$ resonances

We develop a model to reproduce the mass distributions of pairs of mesons in the Cabibbo-suppressed $D^+_s \to K^+ π^+ π^-$ decay. The largest contributions to the process comes from the $D^+_s \to K^+ ρ^0$ and $D^+_s \to K^{*0} π^+$ decay modes, but the $D^+_s \to K^*_0(1430) π^+$ and $D^+_s \to K^+ f_0(1370)$ modes also play a moderate role and all of them are introduced empirically. Instead, the contribution of the $f_0(500)$, $f_0(980)$ and $K^*_0(700)$ resonances is introduced dynamically by looking at the decay modes at the quark level, hadronizing $q \bar{q}$ pairs to give two mesons, and allowing these mesons to interact to finally produce the $K^+ π^+ π^-$ final state. These last three modes are correlated by means of only one parameter. We obtain a fair reproduction of the experimental data for the three mass distributions as well as the relative weight of the three light scalar mesons, which we see as further support for the nature of these states as dynamically generated from the interaction of pseudoscalar mesons.

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arXiv2023

Repercussion of the $a_0(1710)$ [$a_0(1817)$] resonance and future developments

In this paper, we discuss the significance and prospect for the newly discovered a0(1710)[a0(1817)] resonance state at BESIII experiment, in which they reported the observation of a scalar meson of spin-parity $J^P=0^+$ with isospin $I=1$, branded as $a_0(1817)$. This state may be the same particle as the $a_0(1710)$ observed by the BaBar experiment earlier. As early as 2008, we found that f0(1710) can be regarded as a $K^* \bar{K}^*$ molecular state based on the chiral unitary theory, and there is a partner state $a_0(1710)$ with an isospin $I=1$. Our theoretical prediction based on this picture is in good agreement with the latest BESIII data, which further supports the molecular state picture of $a_0(1710)[a_0(1817)]$. If it is indeed the isospin partner state of $f_0(1710)$, this would rule out $f_0(1710)$ as a glueball candidate. This paper briefly reviews the relevant theoretical studies and suggests new experiments to further examine the nature of $a_0(1710)[a_0(1817)]$.

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arXiv2022

How much is the compositeness of a bound state constrained by $a$ and $r_0$? The role of the interaction range

We present an approach that allows one to obtain information on the compositeness of molecular states from combined information of the scattering length of the hadronic components, the effective range, and the binding energy. We consider explicitly the range of the interaction in the formalism and show it to be extremely important to improve on the formula of Weinberg obtained in the limit of very small binding and zero range interaction. The method allows obtaining good information also in cases where the binding is not small. We explicitly apply it to the case of the deuteron and the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ states and determine simultaneously the value of the compositeness within a certain range, as well as get qualitative information on the range of the interaction.

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arXiv2022

The $\bar{B}^0 \to D^{+} \bar{D}^{0} K^- $ reaction to detect the $I=0, J^P=1^+$ partner of the $X_0(2866)$

We have chosen the $\bar{B}^0 \to D^{*+} \bar{D}^{*0} K^-$ reaction in order to observe the $I=0, J^P=1^+$ ($R_1$) partner state of the $X_0(2866)$ stemming from the $D^*\bar{K}^*$ molecular picture. The reaction proceeds via external emission in the most favored Cabibbo decay mode and one observes the $R_1$ state as a very strong peak versus the background in the $D^{*+} K^-$ spectrum. The branching ratio for $R_1$ production in this reaction is estimated of the order of $4\times 10^{-3}$. The method used, applied to the $B^+ \to D^- D^+ K^+$ reaction, produces a ratio of signal to background in the $D^- K^+$ spectrum in very good agreement with the LHCb experiment that observed the $X_0(2866)$.

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arXiv2022

Looking for the exotic $X_0(2866)$ and its $J^P=1^+$ partner in the $\bar{B}^0 \to D^{()+} K^- K^{()0} $ reactions

We propose two reactions, $\bar{B}^0 \to K^0 D^{+} K^-$ and $\bar{B}^0 \to K^{*0} D^{*+} K^-$, already measured at Belle, to look into the $J^P=0^+$, $X_0(2866)$ state and a $1^+$ partner of molecular $D^*\bar{K}^*$ nature, by looking at the $D^+ K^-$ and $D^{*+} K^-$ invariant mass distributions, respectively. Very clear peaks over the background are predicted and the branching ratios for the production of these states are evaluated to facilitate the task of determining the needed statistics for their observation. The fact that the $K^{*0} K^-$ mass distribution from accumulation of events of different reactions is already available, indicates that one is not far away from having the needed statistics to see peaks in the $D^{(*)+} K^-$ mass distributions, so far not yet analyzed.

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arXiv2022

Masses and widths of the exotic molecular $B_{(s)}^{()} B_{(s)}^{()}$ states

We study the interaction of the doubly bottom systems $BB$, $B^* B$, $B_s B$, $B_s^* B$, $B^* B^*$, $B^* B_s$, $B^*B_s^*$, $B_s B_s$, $B_s B_s^*$, $B_s^* B_s^*$ by means of vector meson exchange with Lagrangians from an extension of the local hidden gauge approach. The full s-wave scattering matrix is obtained implementing unitarity in coupled channels by means of the Bethe-Salpeter equation. We find poles below the channel thresholds for the attractively interacting channels $B^* B$ in $I=0$, $B^*_s B-B^*B_s$ in $I=\frac{1}{2}$, $B^* B^*$ in $I=0$, and $B^*_s B^*$ in $I=\frac{1}{2}$, all of them with $J^P=1^+$. For these cases the widths are evaluated identifyng the dominant source of imaginary part. We find binding energies of the order of $10-20$ MeV, and the widths vary much from one system to the other: of the order of 10-100 eV for the $B^* B$ system and $B^*_s B-B^*B_s$, about $6$ MeV for the $B^* B^*$ system and of the order of $0.5$ MeV for the $B^*_s B^*$ system.

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arXiv2021

The $D_s^+ \to π^+ K_s^0 K_s^0 $ reaction \\and the $I=1$ partner of the $f_0(1710)$ state

We have identified the decay modes of the $D_s^+ \to π^+ K^+ K^- , π^+ K_s^0 K_s^0$ reactions producing two vector mesons and one pseudoscalar. The posterior vector-vector interaction generates two resonances that we associate to the $f_0(1710)$ and the $a_0(1710)$ recently claimed. We find two acceptable scenarios that give results for the ratio of the branching ratios of these two reactions in agreement with experiment. With these two scenarios we make predictions for the branching ratios of the $D_s^+ \to π^0 K^+ K_s^0$ reaction, finding values within the range of $(2.0 \pm 0.7)\times 10^{-3}$. Comparison of these predictions with coming experimental results on that latter reaction will be very most useful to deepen our understanding on the nature of these two resonances.

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arXiv2021

Prediction of new $T_{cc}$ states of $D^{} D^{}$ and $D^{}_s D^{}$ molecular nature

We extend the theoretical framework used of describe the $T_{cc}$ state as a molecular state of $D^* D$ and make predictions for the $D^*D^*$ and $D^*_s D^*$ systems, finding that they lead to bound states only in the $J^P=1^+$ channel. Using input needed to describe the $T_{cc}$ state, basically one parameter to regularize the loops of the Bethe-Salpeter equation, we find bound states with bindings of the order of the MeV and similar widths for $D^*D^*$ system, while the $D^{*}_s D^{*}$ system develops a strong cusp around threshold.

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arXiv2020

Tau decay into $ν_τ$ and $a_1(1260)$, $b_1(1235)$, and two $K_1(1270)$

We study the $τ\to ν_τA$ decay, with $A$ an axial-vector meson. We produce the $a_1(1260)$ and $b_1(1235)$ resonances in the Cabibbo favored mode and two $K_1(1270)$ states in the Cabibbo suppressed mode. We take advantage of previous chiral unitary approach results where these resonances appear dynamically from the vector and pseudoscalar meson interaction in s-wave. Actually two different poles were obtained associated to the $K_1(1270)$ quantum numbers. We find that the unmeasured rates for $b_1(1235)$ production are similar to those of the $a_1(1260)$ and for the two $K_1$ states we suggest to separate the present information on the $\bar K ππ$ invariant masses into $\bar K^* π$ and $ρK$ modes, the channels to which these two resonances couple most strongly, predicting that these modes peak at different energies and have different widths. These measurements should shed light on the existence of these two $K_1$ states.

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arXiv2019

$J/ψ$ decay into $ϕ(ω)$ and vector-vector molecular states

Based on the picture that the $ f_0(1370), f_0(1710), f_2(1270), f'_2(1525), \bar{K}^{*0}_2(1430)$ resonances are dynamically generated from the vector-vector interaction, we study the decays $J/ψ\to ϕ(ω) f_0(1370) [f_0(1710)]$, $J/ψ\to ϕ(ω) f_2(1270) [f'_2(1525)]$, and $J/ψ\to K^{*0} \bar{K}^{*0}_2(1430)$ and make predictions for seven independent ratios that can be done among them. The starting mechanism is that the $J/ψ$ decays into three vectors, followed by the final state interaction of a pair of them. The weights of the different three vector primary channels are obtained from the basic assumption that the $J/ψ$ ($c \bar c$) is an SU(3) singlet. By means of only one free parameter we predict four ratios in good agreement with experiment, make two extra predictions for rates yet unmeasured, and disagree on one data for which only upper bounds are reported. Further measurements are most welcome to complete the information required for these ratios that are testing the nature of these resonances as dynamically generated.

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arXiv2019

Helicity amplitudes in the $\bar{B} \to D^{*} \barν_ττ$ decay with $V-A$ breaking in the quark sector

In view of the recent measurement of the $F_L^{D^*}$ magnitude in the $\bar{B} \to D^{*} \barν_ττ$ reaction we evaluate this magnitude within the standard model and for a family of models with the $γ^μ-αγ^μγ_5$ current structure for the quarks for different values of $α$. At the same time we evaluate also the transverse contributions, $M=-1$, $M=+1$, and find that the difference between the $M=-1$ and $M=+1$ contributions is far more sensitive to changes in $α$ than the longitudinal component.

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