The double thresholds distort the lineshapes of the $P_{\psi s}^{\Lambda }(4338{)}^0$ resonance

Abstract

Very recently, the LHCb Collaboration reported the first observation of the hidden charm pentaquark with strangeness, $P_{\psi s}^{\Lambda }(4338{)}^0$. Considering this state is very close to the ${\Xi }_c^0{\bar{D}}^0$ and ${\Xi }_c^{+}{D}^{-}$ thresholds, we explore the possible bias of the Breit-Wigner parameterization, with emphasis on the effect of its coupling to the double thresholds ${\Xi }_c^0{\bar{D}}^0$ and ${\Xi }_c^{+}{D}^{-}$. We first use a qualitative picture based on the ``uniformization" of the Riemann surface of the two-channel system to understand the positions of the enhancement. Then we use the Lippmann-Schwinger equation (LSE) formalism (equivalent to the $K$-matrix parameterization) with two models, the zero-range model and Flatté model to investigate the $J/\psi \Lambda$ lineshapes. Our results show that the nominal peak of the $P_{\psi s}^{\Lambda }(4338{)}^0$ could arise either from the pole well above the ${\Xi }_c^{+}{D}^{-}$ threshold on the $(-,+)$ sheet or from the pole well below the ${\Xi }_c^0{\bar{D}}^0$ threshold on the $(-,-)$ sheet in the two-channel system. Using the Breit-Wigner distribution to depict the above two lineshapes could be misleading. We also find a novel type of lineshapes with the enhancement constrained by the threshold difference. We urge the LHCb collaboration to perform the refined experimental analysis considering the unitarity and analyticity, e.g. using the K-matrix parameterization. As a by-product, we obtain that the ratio of the isospin violating decay ${\Gamma }_{P_{\psi s}^{\Lambda }\to J/\psi \Sigma }/{\Gamma }_{P_{\psi s}^{\Lambda }\to J/\psi \Lambda }$ could be up to $10\%$.

15 pages,16 figures. Accepted version by Physical Review D. Adopting the uniformization of the two-channel Riemann surface

References in corpus (31)

• Pentaquark and Tetraquark states
• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• Prediction of narrow $N^{\ast }$ and ${\Lambda }^{\ast }$ resonances with hidden charm above 4 GeV
• Evidence of a $J/\psi \Lambda$ structure and observation of excited ${\Xi }^{-}$ states in the ${\Xi }_b^{-}\to J/\psi \Lambda K^{-}$ decay
• Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state
• Isospin breaking effects in the X(3872) resonance
• Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum
• Isospin breaking decays as a diagnosis of the hadronic molecular structure of the $P_c(4457)$
• Establishing the first hidden-charm pentaquark with strangeness
• Spectrum of the strange hidden charm molecular pentaquarks in chiral effective field theory
• Probing the long-range structure of the $T_{cc}^{+}$ with the strong and electromagnetic decays
• Isospin breaking, coupled-channel effects, and X(3872)
• Systematics of the heavy flavor hadronic molecules
• Scattering Models for Ultracold Atoms
• The $P_{cs}(4459)$ pentaquark from a combined effective field theory and phenomenological perspective
• $Z_{cs}(3985{)}^{-}$ as the $U$-spin partner of $Z_c(3900{)}^{-}$ and implication of other states in the ${\text{SU(3)}}_F$ symmetry and heavy quark symmetry
• Magnetic dipole moments of the hidden-charm pentaquark states: $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$
• Magnetic moments and transition magnetic moments of $P_c$ and $P_{cs}$ states
• Magnetic moments of the hidden-charm strange pentaquark states
• A Phenomenological analysis on isospin-violating decay of $X(3872)$
• Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{\psi s}^{\Lambda }(4338)$ and $P_{cs}(4459)$
• New strange pentaquarks
• Investigation of hidden-charm pentaquarks with strangeness $S=-1$
• Revisit the isospin violating decays of $X(3872)$
• Implications of the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ as two different states
• Predicting the ${\bar{D}}_s^{(\ast )}{D}_s^{(\ast )}$ bound states as the partners of $X(3872)$
• Analysis of the $P_{cs}(4338)$ and related pentaquark molecular states via the QCD sum rules
• A New Method to Extract Information of Near-Threshold Resonances: Uniformized Pole-Sum Representation of Green's Function and T-matrix
• Near-threshold Spectrum from Uniformized Mittag-Leffler Expansion -Pole Structure of $Z(3900)$-
• Application of the Uniformized Mittag-Leffler Expansion to $\Lambda (1405)$
• Analytic Map of Three-Channel S Matrix -Generalized Uniformization and Mittag-Leffler Expansion-

Cited by in corpus (24)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Pole determination of $P_{\psi s}^{\Lambda }(4338)$ and possible $P_{\psi s}^{\Lambda }(4255)$ in $B^{-}\to J/\psi \Lambda \bar{p}$
• Exploring the electromagnetic properties of the ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}_s^{\ast }$ and ${\Omega }_c^{(\ast )}{\bar{D}}_s^{\ast }$ molecular states
• Spectrum of the molecular pentaquarks
• $P_{\psi s}^{\Lambda }(4459)$ and $P_{\psi s}^{\Lambda }(4338)$ as molecular states in $J/\psi \Lambda$ invariant mass spectra
• Surveying the mass spectra and the electromagnetic properties of the ${\Xi }_c^{(\prime ,\ast )}{D}^{(\ast )}$ molecular pentaquarks
• Spectrum of the molecular tetraquarks: Unraveling the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$
• Higher molecular $P_{\psi s}^{\Lambda /\Sigma }$ pentaquarks arising from the ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}_1/{\Xi }_c^{(\prime ,\ast )}{\bar{D}}_2^{\ast }$ interactions
• Unveiling the Structure of Hidden-Bottom Strange Pentaquarks via Magnetic Moments
• On the possibility of testing the two-peak structure of the LHCb hidden-charm strange pentaquark $P_{cs}(4459{)}^0$ in near-threshold antikaon-induced charmonium production on protons and nuclei
• Molecular states in $D_s^{(\ast )+}{\Xi }_c^{{(}^{\prime },\ast )}$ systems
• Molecular $P_{\psi }$ pentaquarks from light-meson exchange saturation
• Classification of Coupled-Channel Near-Threshold Structures
• Towards modeling the short-range interactions of hidden/open charm pentaquark molecular states
• Role of the short-range dynamics in the formation of $D^{(\ast )}{\bar{D}}^{(\ast )}/B^{(\ast )}{\bar{B}}^{(\ast )}$ hadronic molecules
• Possible molecules of triple-heavy pentaquarks within the extended local hidden gauge formalism
• Electromagnetic characteristics as probes into the inner structures of the predicted ${\Xi }_c^{{(}^{\prime },\ast )}{D}_s^{(\ast )}$ molecular states
• Strong decays of the $P_{cs}(4338)$ and its high isospin cousin via the QCD sum rules
• Hidden charm ${\mathcal{P}}_{cs}(4338{)}^0$ production in baryonic $B^{-}\to J/\psi \Lambda \bar{p}$ decay
• Five-flavor molecular pentaquarks in the ${\Xi }_b^{(\prime ,\ast )}{\bar{D}}^{(\ast )}$ and ${\Xi }_c^{(\prime ,\ast )}{B}^{(\ast )}$ systems
• Analysis of the hidden-charm pentaquark candidates in the $J/\psi \Lambda$ mass spectrum via the QCD sum rules
• Searching for a $P_{cs}(4200)$ state in the ${\Lambda }_b\to \varphi {\eta }_c\Lambda$ reaction
• Role of the short-range dynamics in simultaneous interpretation of $P_{cs}$ pentaqurks via ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}^{(\ast )}$ molecules
• Exotic hadrons associated with $b$-quark