Analysis of the $$\psi (4040)$$ and $$\psi (4160)$$ decay into $$D^{(*)} {{\bar{D}}}^{(*)}$$, $$D_s^{(*)}{{\bar{D}}}_s^{(*)}$$

In this work, we calculate the amplitudes of the processes $$c{{\bar{c}}}({^3P_J}) \rightarrow DD,DD^*, D^*D^* \rightarrow c\bar{c}({^3P_J})$$ c c ¯ ( 3 P J ) → D D , D D ∗ , D ∗ D ∗ → c c ¯ ( 3 P J ) in the leading order of the nonrelativistic expansion. The imaginary parts of the amplitudes are corresponding to the branch decay widths of the charmonium $$c{{\bar{c}}}({^3P_J}) \rightarrow DD,DD^*, D^*D^*$$ c c ¯ ( 3 P J ) → D D , D D ∗ , D ∗ D ∗ and the real parts are corresponding to the mass shifts of the charmonium $$c{{\bar{c}}}({^3P_J})$$ c c ¯ ( 3 P J ) due to these decay channels. After absorbing the polynomial contributions which are pure real, the ratios between the branch decay widths and the corresponding mass shifts are only dependent on the center-of-mass energy. We find the decay widths and the mass shifts of the $$^3P_2$$ 3 P 2 states are exact zero in the leading order. The ratios between the branch decay widths and the mass shifts for the $$^3P_0, {^3P_1}$$ 3 P 0 , 3 P 1 states are larger than 5 when the center-of-mass energy is above the $$DD,DD^*, D^*D^*$$ D D , D D ∗ , D ∗ D ∗ threshold. The dependence of the mass shifts on the center-of-mass energy is nontrivial especially when the center-of-mass energy is below the threshold. The analytic results can be extended to the b quark sector directly.

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“…Furthermore, the similar discussion can be extended to the S wave states and compared with the similar studies in Ref. [63,64].…”

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confidence: 66%

Decay widths of $$^3 P_J$$ charmonium to $$DD,DD^,D^D^*$$ and corresponding mass shifts of $$^3 P_J$$ charmonium

Cao¹,

Zhou

2020

Eur. Phys. J. C

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“…In an analysis of the production of charmed mesons and charmed strange mesons in the region of ψ(4040) and ψ(4160) resonances in e + e − collisions in Ref. [71], the couplings of ψ(4040) and ψ(4160) to two charmed mesons and charmed strange mesons are factorized. The couplings are assumed to be proportional to a coefficient (denoted as g Ri in the reference), the values of which are listed in Table 1 of the reference.…”

Section: Numerical Cross Sections and Discussionmentioning

confidence: 99%

Cross sections for 2-to-1 meson–meson scattering

Weber

2021

Eur. Phys. J. C

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We study the processes $$K{\bar{K}} \rightarrow \phi $$ K K ¯ → ϕ , $$\pi D \rightarrow D^*$$ π D → D ∗ , $$\pi {\bar{D}} \rightarrow {\bar{D}}^*$$ π D ¯ → D ¯ ∗ , and the production of $$\psi (3770)$$ ψ ( 3770 ) , $$\psi (4040)$$ ψ ( 4040 ) , $$\psi (4160)$$ ψ ( 4160 ) , and $$\psi (4415)$$ ψ ( 4415 ) mesons in collisions of charmed mesons or charmed strange mesons. The process of 2-to-1 meson–meson scattering involves a quark and an antiquark from the two initial mesons annihilating into a gluon and subsequently the gluon being absorbed by the spectator quark or antiquark. Transition amplitudes for the scattering process derive from the transition potential in conjunction with mesonic quark–antiquark wave functions and the relative-motion wave function of the two initial mesons. We derive these transition amplitudes in the partial wave expansion of the relative-motion wave function of the two initial mesons so that parity and total-angular-momentum conservation are maintained. We calculate flavor and spin matrix elements in accordance with the transition potential and unpolarized cross sections for the reactions using the transition amplitudes. Cross sections for the production of $$\psi (4040)$$ ψ ( 4040 ) , $$\psi (4160)$$ ψ ( 4160 ) , and $$\psi (4415)$$ ψ ( 4415 ) relate to nodes in their radial wave functions. We suggest the production of $$\psi (4040)$$ ψ ( 4040 ) , $$\psi (4160)$$ ψ ( 4160 ) , and $$\psi (4415)$$ ψ ( 4415 ) as probes of hadronic matter that results from the quark–gluon plasma created in ultrarelativistic heavy-ion collisions.

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“…The three charmonia have also been studied in the B + → K + µ + µ − decay and the B + → D + D − K + decay by the LHCb Collaboration [8]. In meson degrees of freedom an electron-positron collision produces one photon, and the photon then converts into ψ(4040), ψ(4160), or ψ(4415) [9,10]. In quark degrees of freedom the photon produced in the electron-positron annihilation splits into a charm quark and a charm antiquark which evolve nonperturbatively into ψ(4040), ψ(4160), or ψ(4415) with certain probabilities.…”

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confidence: 99%

Production of $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$ mesons in hadronic matter

Li,

Xu,

Weber

2022

Preprint

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Analysis of the $$\psi (4040)$$ and $$\psi (4160)$$ decay into $$D^{()} {{\bar{D}}}^{()}$$, $$D_s^{()}{{\bar{D}}}_s^{()}$$

Cited by 5 publications

References 17 publications

Decay widths of $$^3 P_J$$ charmonium to $$DD,DD^,D^D^*$$ and corresponding mass shifts of $$^3 P_J$$ charmonium

Decay widths of $$^3 P_J$$ charmonium to $$DD,DD^,D^D^*$$ and corresponding mass shifts of $$^3 P_J$$ charmonium

Cross sections for 2-to-1 meson–meson scattering

Production of $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$ mesons in hadronic matter

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Analysis of the $$\psi (4040)$$ and $$\psi (4160)$$ decay into $$D^{(*)} {{\bar{D}}}^{(*)}$$, $$D_s^{(*)}{{\bar{D}}}_s^{(*)}$$

Cited by 5 publications

References 17 publications

Decay widths of $$^3 P_J$$ charmonium to $$DD,DD^*,D^*D^*$$ and corresponding mass shifts of $$^3 P_J$$ charmonium

Decay widths of $$^3 P_J$$ charmonium to $$DD,DD^*,D^*D^*$$ and corresponding mass shifts of $$^3 P_J$$ charmonium

Cross sections for 2-to-1 meson–meson scattering

Production of $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$ mesons in hadronic matter

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Analysis of the $$\psi (4040)$$ and $$\psi (4160)$$ decay into $$D^{()} {{\bar{D}}}^{()}$$, $$D_s^{()}{{\bar{D}}}_s^{()}$$

Decay widths of $$^3 P_J$$ charmonium to $$DD,DD^,D^D^*$$ and corresponding mass shifts of $$^3 P_J$$ charmonium

Decay widths of $$^3 P_J$$ charmonium to $$DD,DD^,D^D^*$$ and corresponding mass shifts of $$^3 P_J$$ charmonium