We evaluate the contribution to the $X(3872)$ width from a triangle mechanism in which the $X$ decays into $D^{*0}\bar{D}^0 -cc$, then the $D^{*0} (\bar{D}^{*0})$ decays into $D^0 π^0$ ($\bar{D}^0 π^0$) and the $D^0 \bar{D}^0$ fuse to produce $π^+ π^-$. This mechanism produces an asymmetric peak from a triangle singularity in the $π^+ π^-$ invariant mass with a shape very sensitive to the $X$ mass. We evaluate the branching ratios for a reaction where this effect can be seen in the $B^- \to K^- π^0 π^+ π^-$ reaction and show that the determination of the peak in the invariant mass distribution of $π^+ π^-$ is all that is needed to determine the $X$ mass. Given the present uncertainties in the $X$ mass, which do not allow to know whether the $D^{*0} \bar{D}^0$ state is bound or not, measurements like the one suggested here should be most welcome to clarify this issue.
In this article, a possible interpretation of the pentaquark candidates recently observed at LHCb is given. We show that the reaction dynamics and the peculare kinematics situation can produce the peak in the spectrum and the sharp phase motion. The mechanism called triangle singularity likely causes the appearance of the new pentaquarks candidates.
In this work, we propose that there exists a moving triangle singularity in the $ψ(2S) \to π^+ π^- K^+ K^-$ process, whose position can vary from 1.158 to 1.181 GeV in the invariant mass spectrum of $K^+K^-$. After a precise analysis on this process, it turns out that after doing some cuts on $m_{π^+π^-}$, experiments do have the opportunity to observe this triangle singularity. In addition, when changing the cuts on $m_{π^+π^-}$, the movement of the predicted triangle singularity can also be observed. Thus, we suggest future experiments, especially Super Tau-Charm Facility (STCF), to do an an…
If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced in $e^+ e^-$ annihilation by the creation of $D^{*0} \bar D^{*0}$ from a virtual photon followed by the rescattering of the charm-meson pair into $X$ and a photon. A triangle singularity produces a narrow peak in the cross section for $e^+ e^- \to X γ$ about 2.2 MeV above the $D^{*0} \bar{D}^{*0}$ threshold. We predict the normalized cross section in the region near the peak. The peak from the triangle singularity may be observable by the BESIII detector.
We perform calculations showing that a source producing $K^* \bar{K}^*$ in $J = 2$ and $L=0$ gives rise to a triangle singularity at $1810$ MeV with a width of about $200$ MeV from the mechanism $K^* \to πK$ and then $K\bar{K}^*$ merging into the $a_1(1260)$ resonance. We suggest that this is the origin of the present $f_2(1810)$ resonance and propose to look at the $πa_1(1260)$ mode in several reactions to clarify the issue.
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 exercis…
We present a model for the $J/ψΛ$ spectrum in $B^-\to J/ψΛ\bar{p}$ decays, including the $P_{ψs}^Λ(4338)$ baryon recently observed by the LHCb collaboration. We assume production via triangle diagrams which couple to the final state via non-perturbative interactions which are constrained by heavy-quark and $SU_3$-flavor symmetry. The bulk of the distribution is described by a triangle diagram with a color-favored electroweak vertex, while the sharp $P_{ψs}^Λ(4338)$ enhancement is due to the triangle singularity in another diagram featuring a $1/2^-$ baryon consistent with $Σ_c(2800)$. We predi…
We show that loop-induced processes involving new physics particles can readily satisfy Landau Equation and trigger triangular singularities at high energy colliders, leading to fully visible Standard Model final states. Four-particle vertices in new physics allow triangular singularity diagrams to evade large virtuality suppression. In addition, a $t$-channel triangular singularity can also occur in particle scattering processes that may extend to low momentum exchange. We discuss several typical scenarios in supersymmetric and extended Higgs models, then identify the singular component in th…
First Evidence for an Unambiguous Triangle Singularity from $ψ(2S) \to p\bar{p}η$
Nanjing Normal University（南京师范大学）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）
We show that the $τ^-$ decay into $f_1(1285)π^-ν_τ$ is dominated by a triangle loop mechanism with $K^*$, $\bar K^*$ and $K$ (or $\bar K$) as internal lines, which manifests a strong enhancement reminiscent of a nearby singularity present in the narrow $K^*$ limit. The $f_1(1285)$ is then produced by its coupling to the $K^*\bar K$ and $\bar K^*K$ which is obtained from a previous model where this resonance was dynamically generated as a molecular $K^*\bar K$ (or $\bar K^*K$) state using the techniques of the chiral unitary approach. We make predictions for the $f_1 π$ mass distribution which …
We calculate the cross section for $e^+ e^-$ annihilation into $D^{*0} \bar D^0 +γ$ at center-of-mass energies near the $D^{*0} \bar D^{*0}$ threshold under the assumption that $X(3872)$ is a weakly bound charm meson molecule. The Dalitz plot has a $\bar D^{*0}$ resonance band in the squared invariant mass $t$ of $\bar D^0 γ$. In the limit as the decay width of the $D^{*0}$ goes to 0, the Dalitz plot also has a narrow band in the squared invariant mass $u$ of $D^{*0} \bar D^0$ from a charm-meson triangle singularity. At the physical value of the $D^{*0}$ width, the narrow band reduces to a sho…
The light axial vector mesons can couple to $K^*\bar{K}+c.c.$ in an $S$ wave at the tree level. Due to the near-threshold $S$-wave interactions the couplings can be affected by the final state interactions. It is of peculiar interest that the pion exchange between $K^*\bar{K}+c.c.$ can go through a triangle diagram which is within the kinematics of the triangle singularity (TS). This mechanism will introduce energy dependence and a $D$-wave amplitude to the vertex couplings. Hence, it should be necessary to investigate the role played by the $K^*\bar{K}+c.c.$ threshold in order to have a bette…
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…
We show the effects of a triangle singularity mechanism for the $γp \to K^+Λ(1405)$ reaction. The mechanism has a $N^*$ resonance around 2030 MeV, which decays into $K^* Σ$. The $K^*$ decays to $K^+ π$, and the $πΣ$ merge to form the $Λ(1405)$. This mechanism produces a peak around $\sqrt{s} = 2110$ MeV, and has its largest contribution around cos$θ=0$. The addition of this mechanism to other conventional ones, leads to a good reproduction of ${\rm d}σ/{\rm dcos}θ$ and the integrated cross section around this energy, providing a solution to a problem encountered in previous theoretical models.
The double-charm tetraquark meson $T_{cc}^+(3875)$ can be produced in high-energy proton-proton collisions by the creation of the charm mesons $D^{*+} D^0$ at short distances followed by their binding into $T_{cc}^+$. The $T_{cc}^+$ can also be produced by the creation of $D^{*+} D^{*+}$ at short distances followed by their rescattering into $T_{cc}^+ π^+$. A charm-meson triangle singularity produces a narrow peak in the $T_{cc}^+ π^+$ invariant mass distribution 6.1 MeV above the threshold with a width of about 1 MeV. Well beyond the peak, the differential cross section decreases with the inv…
We have done a study of the $B^- \to K^- π^0 X(3872)$ reaction by means of a triangle mechanism via the chain of reactions: $B^- \to K^- D^{*0}\bar D^{*0}$; $D^{*0} \to π^0 D^0$; $D^0\bar D^{*0}\to X(3872)$. We show that this mechanism generates a triangle singularity in the $π^0 X(3872)$ invariant mass for a very narrow window of the $X(3872)$ mass, around the present measured values, and show that the peak positions and the shape of the mass distributions are sensitive to the $X(3872)$ mass, such that a measurement of the reaction can serve to improve on the present values of this mass. In p…
We have investigated the cross section for the $π^-p\rightarrow K^0πΣ$ and $pp\rightarrow pK^+πΣ$ reactions paying attention to a mechanism that develops a triangle singularity. The triangle diagram is realized by the decay of a $N^*$ to $K^*Σ$ and the $K^*$ decay into $πK$, and the $πΣ$ finally merges into $Λ(1405)$. The mechanism is expected to produce a peak around $2140$ MeV in the $KΛ(1405)$ invariant mass. We found that a clear peak appears around $2100$ MeV in the $KΛ(1405)$ invariant mass which is about $40$ MeV lower than the expectation, and that is due to the resonance peak of a $N^…
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 th…
The role of triangle singularity in isospin breaking process $J/ψ\to Λ\barΛ π$ and the possible evidence of $Σ^*(\frac{1}{2}^-)$ states
School of Physics and Technology, Nanjing Normal University（南京师范大学物理科学与技术学院）；University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）
We show the important role played by the $πΔ(1232)$ channel in the build up of the $N(1700)(3/2^-)$ resonance due to the non-trivial enhancement produced by a singularity of a triangular loop. The $N(1700)$ is one of the dynamically generated resonances produced by the coupled channel vector-baryon interaction. The $πΔ$ channel was neglected in previous works but we show that it has to be incorporated into the coupled channel formalism due to an enhancement produced by a singularity in the triangular loop with $ρ$, nucleon and $π$ as internal loop lines and $π$ and $Δ$ as external ones. The en…
We compare contributions from the triangle diagram and the $D\bar D^*$ bubble chain to the processes of $e^{+}e^{-}\rightarrow J/ψπ^{+}π^{-}$ and $e^{+}e^{-}\rightarrow (D\bar D^*)^\mpπ^{\pm}$. By fitting the $J/ψπ$ maximum spectrum and the $D\bar D^*$ 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.
In this work, we study the spin density matrix element $ρ_{00}$ of the $ϕ$ in the decay $J/ψ\rightarrow ηπϕ$. In previous studies, a band around 1.4 GeV on the $π^0ϕ$ distribution in Dalitz plot was reported by the BESIII Collaboration. This structure may be caused by the production of a resonance or the triangle singularity mechanism. We find that the predictions of the spin density matrix elements of the final $ϕ$ based on these mechanisms show distinct features. Thus the measurement of the spin density matrix elements of the $ϕ$ in this reaction may offer an alternative way to study the tri…
We study the $J/ψ\rightarrow K^+ K^- f_0(980)(a_0(980))$ reaction and find that the mechanism to produce this decay develops a triangle singularity around $M_{\rm inv}(K^- f_0/K^- a_0) \approx 1515$~MeV. The differential width $dΓ/ dM_{\rm inv}(K^- f_0/K^- a_0)$ shows a rapid growth around the invariant mass being 1515~MeV as a consequence of the triangle singularity of this mechanism, which is directly tied to the nature of the $f_0(980)$ and $a_0(980)$ as dynamically generated resonances from the interaction of pseudoscalar mesons. The branching ratios obtained for the $J/ψ\rightarrow K^+ K^…
We develop a model for the $pp \to π^+ d$ reaction based on the $pp \to Δ(1232) N$ transition followed by $Δ(1232) \to πN'$ decay and posterior fusion of $N N'$ to give the deuteron. We show that the triangle diagram depicting this process develops a triangle singularity leading to a large cross section of this reaction compared to ordinary fusion reactions. The results of the calculation also show that the process is largely dominated by the $pp$ system in $L=2, S=0$, which transfers $J=2$ to the final $π^+ d$ system. This feature is shown to be well suited to provide $L=2,S=1$, $J^\mathrm{to…
Triangle mechanisms for $B^0\to (J/ψπ^+π^-) K^+π^-$ are studied. Experimentally, an $X(3872)$ peak has been observed in this process. When the final $(J/ψπ^+π^-)π$ invariant mass is around the $D^*\bar D^*$ threshold, one of the triangle mechanisms causes a triangle singularity and generates a sharp $X(3872)$-like peak in the $J/ψπ^+π^-$ invariant mass distribution. The Breit-Wigner mass and width fitted to the spectrum are 3871.68 MeV (a few keV above the $D^{*0}\bar{D}^0$ threshold) and $\sim$0.4 MeV, respectively.These Breit-Wigner parameters hardly depends on a choice of the model paramete…
We consider a triangle diagram for $B^0\to (J/ψπ^+π^-) K^+π^-$ where an $X(3872)$ peak has been observed experimentally. We demonstrate that a triangle singularity inherent in the triangle diagram creates a sharp peak in the $J/ψπ^+π^-$ invariant mass distribution when the final $(J/ψπ^+π^-)π$ invariant mass is at and around the $D^*\bar D^*$ threshold. The position and width of the peak is 3871.68 MeV (a few keV above the $D^{*0}\bar{D}^0$ threshold) and $\sim$0.4 MeV, respectively, in perfect agreement with the precisely measured $X(3872)$ mass and width: $3871.69\pm 0.17$ MeV and $< 1.2$ Me…
We investigate the $B^0\to π^- K^+ X(3872)$ decay via the $D_{s1}(2536)\bar{D} D^*$ rescattering diagram. The line shape of the $K^+X(3872)$ distribution curve around $D_{s1}(2536)\bar{D}$ threshold is very sensitive to the $X(3872)$ mass because the triangle singularity (TS) can be generated from the loop. By means of this characteristic, we can determine whether the $X(3872)$ mass is below or above the $D^{\ast 0}\bar{D}^0$ threshold with high precision. The narrowness of $D_{s1}(2536)$ in the loop is one of the key reasons why the TS mechanism of measuring the $X(3872)$ mass may work. The $…
We discuss the possibility that production of final states with bottomonium and light mesons at the peak $Υ(6S)$ in the $e^+e^-$ annihilation at approximately 11.00 GeV is in fact due to a triangular singularity at the threshold of the heavy meson pair production $B_1(5721) \bar B + c.c.$ through the process $e^+e^- \to B_1(5721) \bar B \to Z_b(10610) \, π$. The presence of the hidden-bottom resonance $Z_b(10610)$ then explains the observed enhanced production of the final channels with both ortho- and para- bottomonium states, $Υ(nS) ππ$ and $h_b(kP) ππ$. The discussed mechanism also predicts…
``Three-mass triangles'' are a class of integral functions appearing in one-loop gauge theory amplitudes. We discuss how the complex analytic properties and singularity structures of these amplitudes can be combined with generalised unitarity techniques to produce compact expressions for three-mass triangle coefficients. We present formulae for the N=1 contributions to the n-point NMHV amplitude.
A resonance-like structure as narrow as 10 MeV is observed in the $K^-p$ invariant mass distributions in $Λ_c^+\to p K^- π^+$ 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 $Λη$ 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 $Λ$-$a_0(980)^+$ or $η$-$Σ(1660…
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 st…
In this work, the triangle singularity mechanism is investigated in the $ψ(2S) \to p \bar{p} η/ p \bar{p} π^0$ process. The triangle loop composed by $J/ψ$, $η$ and $p$ has a singularity in the physical kinematic range for the $ψ(2S) \to p \bar{p} η/ p \bar{p} π^0$ process, and it would generate a very narrow peak in the invariant mass spectrum of $pη(π)$ around $1.56387$ GeV, which is far away from both the threshold and relative resonances. In these processes, all the involved vertices are constrained by the experimental data. Thus, we can make a precise model independent prediction here. It…
In this article, the analyticity of triangle loop integral with complex masses of internal particles is discussed in a new perspective, base on which we obtain the explicit width dependence of the absorptive part of the triangle amplitude. We reanalyze the decay pattern of $η(1405/1475)$ with the width effects included in the triangle singularity (TS) mechanism. Based on the present experimental information, we provide a self-consistent description of the $K\bar{K}π$, $ηππ$, and $3π$ decay channels for $η(1405/1475)$. Our results confirm the claim that the TS mechanism plays a decisive role in…
It was proposed that the narrow $P_c(4450)$ structure observed by the LHCb Collaboration in the reaction $Λ_b\to J/ψp K$ might be due to a triangle singularity around the $χ_{c1}$--proton threshold at 4.45~GeV. We discuss the occurrence of a similar triangle singularity in the $J/ψp$ invariant mass distribution for the decay $Λ_b\to J/ψp π$, which could explain the bump around 4.45~GeV in the data. More precise measurements of this process would provide valuable information towards an understanding of the $P_c$ structures.
A $Σ^*$ resonance with spin-parity $J^P = 1/2^-$ and mass in the vicinity of the $\bar{K}N$ threshold has been predicted in the unitary chiral approach and inferred from the analysis of CLAS data on the $γp \to K^+ π^0 Σ^0$ reaction. In this work, based on the dominant Cabibbo favored weak decay mechanism, we perform a study of $Λ_c^+ \to π^+ π^0 Σ^*$ with the possible $Σ^*$ state decaying into $π^- Σ^+$ through a triangle diagram. 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 $Σ^*$ through a triangle loop co…
We present a systematic study of the productions and decays of light axial vector mesons with $J^{PC}=1^{+\pm}$ in charmonium decays. In the quark model scenario, the two axial vector nonets are connected with each other by the Gell-Mann-Okubo mass relation through the mixing between two $K_1$ states (i.e. $K_1(1270)$ and $K_1(1400)$) with configurations of $^3P_1$ and $^1P_1$. The mixing angles between $f_1$ and $f_1'$ (i.e. $f_1(1285)$ and $f_1(1420)$), and between $h_1$ and $h_1'$ (i.e. $h_1(1170)$ and $h_1(1415)$) can be reliably constrained. We then introduce the intermediate $K^*\bar{K}+…
We perform calculations for the $\bar B_s^0 \to J/ψπ^0 f_0(980)$ and $\bar B_s^0 \to J/ψπ^0 a_0(980)$ reactions, showing that the first one is isospin-suppressed while the second one is isospin-allowed. The reaction proceeds via a triangle mechanism, with $\bar B_s^0 \to J/ψK^* \bar K +c.c.$, followed by the decay $K^* \to Kπ$ and a further fusion of $K\bar K$ into the $f_0(980)$ or $a_0(980)$. We show that the mechanism develops a singularity around the $π^0 f_0(980)$ or $π^0 a_0(980)$ invariant mass of 1420 MeV where the $π^0 f_0$ and $π^0 a_0$ decay modes are magnified and also the ratio of…
Triangle and other kinematic singularities are very sensitive to the precise masses and widths of the intervening particles. Therefore, the effect that the heavy-ion collision medium can have on those masses and widths, as captured by finite-temperature field theory and reported in the literature, may erase the singularity from the spectrum if the effect is large enough and the loop completes before the hot gas freezes out. A very timely example is provided by the $Z_{cs}(3985)$ structure recently reported by BES-III in a $(D_s^-D^{*0}+D_s^{*-}D^0)$ spectrum recoiling against a $K^+$. If a new…
We predict that triangle singularities of hadron spectroscopy can be strongly affected in heavy ion collisions. To do it we examine various effects on the singularity-inducing triangle loop of finite temperature in the terminal hadron phase. It appears that peaks seen in central heavy ion collisions are more likely to be hadrons than rescattering effects under two conditions. First, the flight-time of the intermediate hadron state must be comparable to the lifetime of the equilibrated fireball (else, the reaction mostly happens in vacuo after freeze out). Second, the medium effect over the tri…
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 $χ_{c1}K^{*+}D^{*-}$ loop or the $\bar{D}_{1}^{0}K^{0}$ rescattering via the $D_{sJ}^{+}\bar{D}_{1…
We investigate in detail the "triangle singularity" regions of meson loops where the corresponding intermediate mesons are nearly-on-shell and have relatively small momenta, and the two heavy mesons strongly interact with each other in an $S$ wave. This $S$-wave interaction will make such kind of meson loops always enhanced and can explain experimental observations of threshold enhancements. We show that the production of the $Y(4260)$ and the recently observed $Z_c(3900)$ can be related to each other by this mechanism which will allow for a possible understanding of the nature of these thresh…
The possible role of the triangle mechanism in the $B^-$ decay into $D^{*0}π^-π^0η$ and $D^{*0}π^-π^+π^-$ is investigated. In this process, the triangle singularity appears from the decay of $B^-$ into $D^{*0}K^-K^{*0}$ followed by the decay of $K^{*0}$ into $π^-K^+$ and the fusion of the $K^+K^-$ which forms the $a_0(980)$ or $f_0(980)$ which finally decay into $π^0η$ or $π^+π^-$ respectively. The triangle mechanism from the $\bar{K}^*K\bar{K}$ loop generates a peak around 1420 MeV in the invariant mass of $π^-a_0$ or $π^-f_0$, and gives sizable branching fractions $Br(B^-\rightarrow D^{*0}π^…
The role of triangle mechanism in the decay process $J/ψ\to K^- K^+ a_1(1260)$ is probed. In this mechanism, a close-up resonance with mass $1823$ MeV and width $122$ MeV decays into $K^* ϕ, K^* \to K π$ and then $K^* \bar{K}$ fuses into the $a_1(1260)$ resonance. We find that this mechanism leads to a triangle singularity around $M_{\rm inv}(K^- a_1(1260))\approx 1920$ MeV, where the axial-vector meson $a_1(1260)$ is considered as a dynamically generated resonance. With the help of the triangle mechanism we find sizable branching ratios $\text{Br}(J/ψ\to K^- K^+ a_1(1260),a_1 \to πρ)=1.210 \t…
$Z_1(4050)$ and $Z_2(4250)$ observed in $\bar{B}^0\toχ_{c1}K^-π^+$ by the Belle Collaboration are candidates of charged charmonium-like states that minimally includes two quarks and two antiquarks. While $Z_1(4050)$ and $Z_2(4250)$ have been interpreted as tetraquark states previously, we propose a completely different scenario based on a kinematical effect called the triangle singularity. We demonstrate that the triangle singularities cause in the $χ_{c1}π^+$ invariant mass distribution resonance-like bumps that fit very well the Belle data. If these bumps are simulated by the $Z_1(4050)$ and…
We demonstrate that triangle singularity (TS) and box singularity (BS) mechanisms can produce unique narrow enhancements at the $Λ_c\bar{D}$ and $Λ_c\bar{D}^*$ thresholds in the invariant mass spectra of $J/ψp$ and $J/ψpπ$, respectively. Taking into account that such mechanisms only depend on the initial $Σ_c^{(*)}\bar{D}^{(*)}$ interactions near threshold within the TS or BS kinematic regimes, the $Λ_c\bar{D}$ and $Λ_c\bar{D}^*$ threshold enhancements can be regarded as a feed-down phenomenon originated from both the heavier pentaquark decays and the $Σ_c^{(*)}\bar{D}^{(*)}$ scatterings from …
We propose novel triangle relations, not the well-known triangle singularity, for better understanding of the exotic XYZ states. Nine XYZ resonances, X(3872), Y(4230), Zc(3900), X(4012), Y(4360/4390), Zc(4020), X(4274), Y(4660), and Zcs(3985) have been classified into triples to construct three triangles based on the assumption that they are all tetra-quark states. We also suggest some channels deserving search for with high priority based on this hypothesis, as well as predictions of a few production/decay rates of these channels. We hope further experimental studies of the XYZ states will be…
We investigate the anomalous triangle singularity (ATS) and its possible manifestations in various processes. We show that the ATS should have important impact on our understanding of the nature of some newly observed threshold states. Discussions on how to distinguish the ATS phenomena from genuine dynamic pole structures are presented.
If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced in $e^+ e^-$ annihilation by the creation of $D^{*0} \bar D^{*0}$ from a virtual photon followed by the rescattering of the P-wave charm-meson pair into the $X$ and a photon. A triangle singularity produces a narrow peak in the cross section for $e^+ e^- \to X γ$ 2.2 MeV above the $D^{*0} \bar{D}^{*0}$ threshold. We predict the normalized cross section in the region of the peak. We show that the absorptive contribution to the cross section for $e^+ e^- \to D^{*0} \bar D^{*0} \to X γ$, which was calculated previously by…
The unitarity triangle on the first quadrant in the $ρ-η$ plane is discussed in the framework of the quark mass matrices in the NNI basis. If the quark mass matrices of the up-type is the Fritzsch one and the down-type is the one proposed by Branco et al., respectively, one gets the unitarity triangle with the vertex on the first quadrant. This simple model may be a candidate of the quark mass matrix ansatze, if the allowed region of the vertex of the unitarity triangle is restricted in the first quadrant by future experiments.
We examine the unitarity triangle of the KM matrix by using the general quark mass matrices on the NNI basis. The Fritzsch anzätz is modified by introducing four additional parameters. The KM matrix elements are expressed in terms of quark mass ratios, two phases and four additional parameters. It is found that the vertex of the unitarity triangle is predicted to be almost in the second quadrant on the $ρ-η$ plane as far as $V_{us}\simeq -{\displaystyle \sqrt{\frac{m_d}{m_s}}e^{ip}+ \sqrt{\frac{m_u}{m_c}}e^{iq}}$ is held.
