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Register a new userA Triangle Singularity as the Origin of the $a_1(1420)$
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The COMPASS experiment recently discovered a new isovector resonance-like signal with axial-vector quantum numbers, the $a_1(1420)$, decaying to $f_0(980)pi$. With a mass too close to and a width smaller than the axial-vector ground state $a_1(1260)$, it was immediately interpreted as a new light exotic meson, similar to the $X$, $Y$, $Z$ states in the hidden-charm sector. We show that a resonance-like signal fully matching the experimental data is produced by the decay of the $a_1(1260)$ ground state into $K^ast(Kpi)bar{K}$ and subsequent rescattering through a triangle singularity into the coupled $f_0(980)pi$ channel. The amplitude for this process is calculated using a novel method based on partial-wave projections. For the first time, the triangle singularity model is fitted to the partial-wave data of the COMPASS experiment. Despite having less parameters, this fit shows a slightly better quality than the one using a resonance hypothesis and thus eliminates the need for an additional resonance in order to describe the data. We thereby demonstrate for the first time that a resonance-like structure in the experimental data can be described by rescattering through a triangle singularity, providing evidence for a genuine three-body effect.
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The LHCb collaboration reported the observation of a narrow peak in the $D^- K^+$ invariant mass distributions from the $B^+to D^+ D^- K^+$ decay. The peak is parameterized in terms of two resonances $X_0(2900)$ and $X_1(2900)$ with the quark contents $bar{c}bar{s}ud$, and their spin-parity quantum numbers are $0^+$ and $1^-$, respectively. We investigate the rescattering processes which may contribute to the $B^+to D^+ D^- K^+$ decays. It is shown that the $D^{*-}K^{*+}$ rescattering via the $chi_{c1}K^{*+}D^{*-}$ loop or the $bar{D}_{1}^{0}K^{0}$ rescattering via the $D_{sJ}^{+}bar{D}_{1}^{0}K^{0}$ loop simulate the $X_0(2900)$ and $X_1(2900)$ structures. Such phenomena are due to the analytical property of the scattering amplitudes with the triangle singularities located to the vicinity of the physical boundary.
We compare contributions from the triangle diagram and the $Dbar D^*$ bubble chain to the processes of $e^{+}e^{-}rightarrow J/psipi^{+}pi^{-}$ and $e^{+}e^{-}rightarrow (Dbar D^*)^mppi^{pm}$. By fitting the $J/psipi$ maximum spectrum and the $Dbar D^*$ spectrum, we find that the triangle diagram cannot explain the new data from BESIII Collaboration at center of mass at 4.23GeV and 4.26GeV, simultaneously. On the contrary, the molecular assignment of $Z_c(3900)$ gives a much better description.
The COMPASS collaboration at CERN has measured diffractive dissociation of 190 GeV/$c$ pions into the $pi^-pi^-pi^+$ final state using a stationary hydrogen target. A partial-wave analysis (PWA) was performed in bins of $3pi$ mass and four-momentum transfer using the isobar model and the so far largest PWA model consisting of 88 waves. A narrow $J^{PC} = 1^{++}$ signal is observed in the $f_0(980),pi$ channel. We present a resonance-model study of a subset of the spin-density matrix selecting $3pi$ states with $J^{PC} = 2^{++}$ and $4^{++}$ decaying into $rho(770),pi$ and with $J^{PC} = 1^{++}$ decaying into $f_0(980),pi$. We identify a new $a_1$ meson with mass $(1414^{+15}_{-13})$ MeV/$c^2$ and width $(153^{+8}_{-23})$ MeV/$c^2$. Within the final states investigated in our analysis, we observe the new $a_1(1420)$ decaying only into $f_0(980),pi$, suggesting its exotic nature.
We study the $bar K p to Y Kbar K pi$ reactions with $bar K = bar K^0, K^-$ and $Y=Sigma^0, Sigma^+, Lambda$, in the region of $Kbar K pi$ invariant masses of $1200-1550$ MeV. The strong coupling of the $f_1(1285)$ resonance to $K^* bar K$ makes the mechanism based on $K^*$ exchange very efficient to produce this resonance observed in the $Kbar K pi$ invariant mass distribution. In addition, in all the reactions one observes an associated peak at $1420$ MeV which comes from the $K^* bar K$ decay mode of the $f_1(1285)$ when the $K^*$ is placed off shell at higher invariant masses. We claim this to be the reason for the peak of the $K^* bar K$ distribution seen in the experiments which has been associated to the $f_1(1420)$ resonance.
A resonance-like structure as narrow as 10 MeV is observed in the $K^-p$ invariant mass distributions in $Lambda_c^+to p K^- pi^+$ at Belle. Based on the large data sample of about 1.5 million events and the small bin width of just 1 MeV for the $K^-p$ invariant mass spectrum, the narrow peak is found precisely lying at the $Lambdaeta$ threshold. While lacking evidence for a quark model state with such a narrow width at this mass region, we find that this narrow structure can be naturally identified as a threshold cusp but enhanced by the nearby triangle singularity via the $Lambda$-$a_0(980)^+$ or $eta$-$Sigma(1660)^+$ rescatterings.
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