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L. R. Dai

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

At least 37 records · Page 2Linked to original sources
arXiv2018

$τ$ decay into a pseudoscalar and an axial-vector meson

We study theoretically the decay $τ^- \to ν_τP^- A$, with $P^-$ a $π^-$ or $K^-$ and $A$ an axial-vector resonance $b_1(1235)$, $h_1(1170)$, $h_1(1380)$, $a_1(1260)$, $f_1(1285)$ or any of the two poles of the $K_1(1270)$. The process proceeds through a triangle mechanism where a vector meson pair is first produced from the weak current and then one of the vectors produces two pseudoscalars, one of which reinteracts with the other vector to produce the axial resonance. For the initial weak hadronic production we use a recent formalism to account for the hadronization after the initial quark-antiquark pair produced from the weak current, which explicitly filters G-parity states and obtain easy analytic formulas after working out the angular momentum algebra. The model also takes advantage of the chiral unitary theories to evaluate the vector-pseudoscalar amplitudes, where the axial-vector resonances were obtained as dynamically generated from the VP interaction. We make predictions for invariant mass distribution and branching ratios for the channels considered.

hep-ph↗
arXiv2018

Polarization amplitudes in $τ^- \to ν_τ V P$ decay beyond the standard model

We use a recent formalism of the weak hadronic reactions $τ^- \to ν_τ M_1 M_2$ to study the helicity amplitudes in $τ^- \to ν_τ V P$ decay. This recent formalism maps the transition matrix elements at the quark level into hadronic matrix elements, and finally writes the weak matrix elements in terms of easy analytical formulas evaluated by means of an elaborate angular momentum algebra. The formalism provides directly the amplitudes for the different spin third components of the vector mesons involved. We extend the formalism to a general case, with the operator $γ^μ-αγ^μγ_5$, that can account for different models beyond the standard model and study in detail the $τ^- \to ν_τ K^{*0} K^{-} $ reaction for the different helicities of the $K^{*0}$. The results are shown in terms of the $α$ parameter that differs for each model. We find that $\frac{d Γ}{d M_{\rm inv}^{(K^{*0} K^{-} )}}$ is very different for the different components $M=\pm 1, 0$ and in particular the magnitude $\frac{d Γ}{d M_{\rm inv}^{(K^{*0} K^{-} )}}|_{M=+1} -\frac{d Γ}{d M_{\rm inv}^{(K^{*0} K^{-} )}}|_{M=-1} $ is very sensitive to the $α$ parameter, which makes the investigation of this magnitude a most welcome initiative to test different models beyond the standard model.

hep-ph↗
arXiv2018

Helicity amplitudes in $B \to D^{*} \barν l$ decay

We use a recent formalism of the weak hadronic reactions that maps the transition matrix elements at the quark level into hadronic matrix elements, evaluated with an elaborate angular momentum algebra that allows finally to write the weak matrix elements in terms of easy analytical formulas. In particular they appear explicitly for the different spin third components of the vector mesons involved. We extend the formalism to a general case, with the operator $γ^μ-αγ^μγ_5$, that can accommodate different models beyond the standard model and study in detail the $B \to D^{*} \barν l$ reaction for the different helicities of the $D^*$. The results are shown for each amplitude in terms of the $α$ parameter that is different for each model. We show that $\frac{d Γ}{d M_{\rm inv}^{(νl)}}$ is very different for the different components $M=\pm 1, 0$ and in particular the magnitude $\frac{d Γ}{d M_{\rm inv}^{(νl)}}|_{M=-1} -\frac{d Γ}{d M_{\rm inv}^{(νl)}}|_{M=+1} $ is very sensitive to the $α$ parameter, which suggest to use this magnitude to test different models beyond the standard model. We also compare our results with the standard model and find very similar results, and practically identical at the end point of $M_{\rm inv}^{(νl)}= m_B- m_{D^*}$.

hep-ph↗
arXiv2018

Triangle singularity in $τ^- \to ν_τπ^- f_0(980)$ ($a_0(980)$) decays

We study the triangle mechanism for the decay $τ^- \to ν_τπ^- f_0(980)$, with the $f_0(980)$ decaying into $π^+ π^- $. This process is initiated by $τ^- \to ν_τK^{*0} K^-$ followed by the $K^{*0}$ decay into $π^- K^+$, then the $K^- K^+$ produce the $f_0(980)$ through a triangle loop containing $ K^* K^+ K^-$ which develops a singularity around $1420$~MeV in the $πf_0(980)$ invariant mass. We find a narrow peak in the $π^+ π^-$ invariant mass distribution, which originates from the $f_0(980)$ amplitude. Similarly, we also study the triangle mechanism for the decay $τ\to νπ^- a_0(980)$, with the $a_0(980)$ decaying into $π^0 η$. The final branching ratios for $π^- f_0(980)$ and $π^- a_0(980)$ are of the order of $4 \times 10^{-4}$ and $7 \times 10^{-5}$, respectively, which are within present measurable range. Experimental verification of these predictions will shed light on the nature of the scalar mesons and on the origin for the "$a_1(1420)$" peak observed in other reactions.

hep-ph↗
arXiv2018

The $B^+ \to J/ψωK^+ $ reaction and $D^*\bar{D}^*$ molecular states

We study the $B^+ \to J/ψωK^+ $ reaction, measured by the LHCb collaboration, and show that it is driven by the presence of two resonances, the $X(3940)$ and $X(3930)$, that are of molecular nature and couple most strongly to $D^* \bar{D}^*$, but also to $J/ψω$. Because of that, in the $J/ψω$ mass distribution we find a peak related to the excitation of the resonances and a cusp with large strength at the $D^* \bar{D}^*$ threshold.

hep-ph↗
arXiv2018

Semileptonic decays of $B^{(*)}$, $D^{(*)}$ into $ν l$ and pseudoscalar or vector mesons

We perform a study of the $B^{(*)}$, $D^{(*)}$ semileptonic decays, using a different method than in conventional approaches, where the matrix elements of the weak operators are evaluated and a detailed spin-angular momentum algebra is performed to obtain very simple expressions at the end for the different decay modes. Using only one experimental decay rate in the $B$ or $D$ sectors, the rates for the rest of decay modes are predicted and they are in good agreement with experiment. Some discrepancies are observed in the $τ$ decay mode for which we find an explanation. We perform evaluations for $B^*$ and $D^*$ decay rates that can be used in future measurements, now possible in the LHCb collaboration.

hep-ph↗
arXiv2018

$τ^- \to ν_τ M_1 M_2$, with $M_1, M_2$ pseudoscalar or vector mesons

We perform a calculation of the $τ^- \to ν_τ M_1 M_2$, with $M_1, M_2$ either pseudoscalar or vector mesons using the basic weak interaction and angular momentum algebra to relate the different processes. The formalism also leads to a different interpretation of the role played by $G$-parity in these decays. We also observe that, while $p$-wave $M_1 M_2$ production is compatible with chiral perturbation theory and experiment, $VP$ and $VV$ $p$-wave production is clearly incompatible with experiment and we develop the formalism also in this case. We compare our results with experiment and make predictions for unmeasured decays, and we show the value of these reactions, particularly if the $M_1 M_2$ mass distribution is measured, as a tool to learn about the meson-meson interaction and the nature of some resonances, coupling to two mesons, which are produced in such decays.

hep-ph↗
arXiv2018

Anomalous enhancement of the isospin-violating $Λ(1405)$ production by a triangle singularity in $Λ_c\rightarrowπ^+π^0π^0Σ^0$

The decay of $Λ_c^+$ into $π^+π^0Λ(1405)$ with the $Λ(1405)$ decay into $π^0Σ^0$ through a triangle diagram is studied. This process is initiated by $ Λ_c^+ \to π^+ \bar{K}^*N $, then the $\bar{K}^*$ decays into $\bar{K} π$ and $\bar{K} N$ produce the $Λ(1405)$ through a triangle loop containing $\bar{K}^*N\bar{K}$ which develops a singularity around $1890$ MeV. This process is prohibited by the isospin symmetry, but the decay into this channel is enhanced by the contribution of the triangle diagram, which is sensitive to the mass of the internal particles. We find a narrow peak in the $π^0Σ^0$ invariant mass distribution, which originates from the $Λ(1405)$ amplitude, but is tied to the mass differences between the charged and neutral $\bar{K}$ or $N$ states. The observation of the unavoidable peak of the triangle singularity in the isospin-violating $Λ(1405)$ production would provide further support for hadronic molecular picture of the $Λ(1405)$ and further information on the $\bar{K} N $ interaction.

hep-ph↗
arXiv2018

Disclosing $D^*\bar{D}^*$ molecular states in the $B_c^- \to π^- J/ψω$ decay

We study the $B_c^- \to π^- J/ψω$ and $B_c^- \to π^- D^* \bar{D}^*$ reactions and show that they are related by the presence of two resonances, the $X(3940)$ and $X(3930)$, that are of molecular nature and couple most strongly to $D^* \bar{D}^*$, but also to $J/ψω$. Because of that, in the $J/ψω$ mass distribution we find a cusp with large strength at the $D^* \bar{D}^*$ threshold and predict the ratio of strengths between the peak of the cusp and the maximum of the $D^* \bar{D}^*$ distribution close to $D^* \bar{D}^*$ threshold, which are distinct features of the molecular nature of these two resonances.

hep-ph↗
arXiv2016

The "$a_1(1420)$" peak as the $πf_0(980)$ decay mode of the $a_1(1260)$

We study the decay mode of the $a_1(1260)$ into a $π^+$ in p-wave and the $f_0(980)$ that decays into $π^+ π^-$ in s-wave. The mechanisms proceeds via a triangular mechanism where the $a_1(1260)$ decays into $K^* \bar K$, the $K^*$ decays to an external $π^+$ and an internal $K$ that fuses with the $\bar K$ to produce the $f_0(980)$ resonance. The mechanism develops a singularity at a mass of the $a_1(1260)$ around 1420 MeV, producing a peak in the cross section of the $πp$ reaction, used to generate the mesonic final state, which provides a natural explanation of all the features observed in the COMPASS experiment, where a peak observed at this energy is tentatively associated to a new resonance called $a_1(1420)$. On the other hand, the triangular singularity studied here gives rise to a remarkable feature, where a peak is seen for a certain decay channel of a resonance at an energy about 200 MeV higher than its nominal mass.

hep-ph↗
arXiv2015

$B^0 \to D^0 \bar D^0 K^0$, $B^+ \to D^0 \bar D^0 K^+$ and the scalar $D \bar D$ bound state

We study the $B^0$ decay to $D^0 \bar D^0 K^0$ based on the chiral unitary model that generates the X(3720) resonance, and make predictions for the $D^0 \bar D^0$ invariant mass distribution. From the shape of the distribution, the existence of the resonance below threshold could be induced. We also predict the rate of production of the X(3720) resonance to the $D^0 \bar D^0$ mass distribution with no free parameters.

hep-ph↗
arXiv2014

The low lying scalar resonances in the $D^0$ decays into $K^0_s$ and $f_0(500)$, $f_0(980)$, $a_0(980)$

The $D^0$ decay into $K^0_s$ and a scalar resonance, $f_0(500)$, $f_0(980)$, $a_0(980)$, is studied obtaining the scalar resonances from final state interaction of a pair of mesons produced in a first step in the $D^0$ decay into $K^0_s$ and the pair of pseudoscalar mesons. This weak decay is very appropriate for this kind of study because it allows to produce the three resonances in the same decay in a process that is Cabibbo allowed, hence the rates obtained are large compared to those of $\bar{B}^0$ decays into $J/ψ$ and a scalar meson that have at least one Cabibbo suppressed vertex. Concretely the $a_0(980)$ production is Cabibbo allowed here, while it cannot be seen in the $\bar{B}^0_s$ decay into $J/ψa_0(980)$ and is doubly Cabibbo suppressed in the $\bar{B}^0$ decay into $J/ψa_0(980)$ and has not been identified there. The fact that the three resonances can be seen in the same reaction, because there is no isospin conservation in the weak decays, offers a unique opportunity to test the ideas of the chiral unitary approach where these resonances are produced from the interaction of pairs of pseudoscalar mesons.

hep-ph↗
arXiv2014

Meson baryon components in the states of the baryon decuplet

We apply an extension of the Weinberg compositeness condition on partial waves of $L=1$ and resonant states to determine the weight of meson-baryon component in the $Δ(1232)$ resonance and the other members of the $J^P= \frac{3}{2}^+$ baryon decuplet. We obtain an appreciable weight of $πN$ in the $Δ(1232)$ wave function, of the order of 60 \%, which looks more natural when one recalls that experiments on deep inelastic and Drell Yan give a fraction of $πN$ component of 34 \% for the nucleon. We also show that, as we go to higher energies in the members of the decuplet, the weights of meson-baryon component decrease and they already show a dominant part for a genuine, non meson-baryon, component in the wave function. We write a section to interpret the meaning of the Weinberg sum-rule when it is extended to complex energies and another one for the case of an energy dependent potential.

hep-ph↗
arXiv2012

The $KD$, $ηD_s$ interaction in finite volume and the nature of the $D_{s^* 0}(2317)$ resonance

An SU(4) extrapolation of the chiral unitary theory in coupled channels done to study the scalar mesons in the charm sector is extended to produce results in finite volume. The theory in the infinite volume produces dynamically the $D_{s^*0}(2317)$ resonance by means of the coupled channels $KD$, $ηD_s$. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the bound states and phase shifts in the infinite volume from the lattice data is addressed. We observe that it is possible to obtain accurate $KD$ phase shifts and the position of the $D_{s^*0}(2317)$ state, but it requires the explicit consideration of the two coupled channels in the analysis if one goes close to the $ηD_s$ threshold. We also show that the finite volume spectra look rather different in case the $D_{s^*0}(2317)$ is a composite state of the two mesons, or if it corresponds to a non molecular state with a small overlap with the two meson system. We then show that a careful analysis of the finite volume data can shed some light on the nature of the $D_{s^*0}(2317)$ resonance as a $KD$ molecule or otherwise.

hep-lat↗
arXiv2011

Limits to the Fixed Center Approximation to Faddeev equations: the case of the $ϕ(2170)$

The Fixed Center Approximation to the Faddeev equations (FCA) has been used lately with success in the study of bound systems of three hadrons. It is also important to set the limits of the approach in those problems to prevent proliferation of inaccurate predictions. In this paper we study the case of the $ϕ(2170)$, which has been described by means of Faddeev equations as a resonant state of $ϕ$ and $K \bar{K}$, and show the problems derived from the use of the FCA in its study. At the same time we also expose the limitations of an alternative approach recently proposed.

hep-ph↗
arXiv2010

The $f_0(1370)$, $f_0(1710)$, $f_2(1270)$, $f_2'(1525)$, and $K_2^*(1430)$ as dynamically generated states from vector meson - vector meson interaction

We report on some recent developments in understanding the nature of the low-lying mesonic resonances $f_0(1370)$, $f_0(1710)$, $f_2(1270)$, $f_2'(1525)$, and $K_2^*(1430)$. In particular we show that these five resonances can be dynamically generated from vector meson--vector meson interaction in a coupled-channel unitary approach, which utilizes the phenomenologically very successful hidden-gauge Lagrangians to produce the interaction kernel between two vector mesons, which is then unitarized by the Bethe-Salpeter-equation method. The data on the strong decay branching ratios, total decay widths, and radiative decay widths of these five states, and on related $J/ψ$ decay processes can all be well described by such an approach. We also make predictions, compare them with the results of earlier studies, and highlight observables that if measured can be used to distinguish different pictures of these resonances.

hep-ph↗
arXiv2010

Study of the $J/ψ\to ϕ(ω) f_2(1270)$, $J/ψ\to ϕ(ω) f'_2(1525)$ and $J/ψ\to K^{*0}(892) \bar{K}^{* 0}_2(1430)$ decays

We present an approach to study the decay modes of the $J/ψ$ into a vector meson and a tensor meson, taking into account the nature of the $f_2(1270)$, $f'_2(1525)$, $\bar{K}^{* 0}_2(1430)$ resonances as dynamically generated states from the vector meson-vector meson interaction. We evaluate four ratios of partial decay widths in terms of a flavor dependent OZI breaking parameter and the results obtained compare favorably with experiment. The fit to the data is possible due to the particular strength and sign of the couplings of the resonances to pairs of vector mesons given by the theory, thus providing a nontrivial test for the idea of these tensor states as dynamically generated from the vector-vector interaction.

nucl-th↗