Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge I.} Bottomonia

Abstract

In the framework of the spectral integral equation, we consider the $b\bar{b}$ states and their radiative transitions. We reconstruct the $b\bar{b}$ interaction on the basis of data for the levels of the bottomonium states with $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, $1^{++}$, $2^{++}$ as well as the data for the radiative transitions ${\rm Y}(3S)\to \gamma {\chi }_{bJ}(2P)$ and ${\rm Y}(2S)\to \gamma {\chi }_{bJ}(1P)$ with $J=0,1,2$. We calculate bottomonium levels with the radial quantum numbers $n\le 6$, their wave functions and corresponding radiative transitions. The ratios $Br[{\chi }_{bJ}(2P)\to \gamma {\rm Y}(2S)]/Br[{\chi }_{bJ}(2P)\to \gamma {\rm Y}(1S)]$ for $J=0,1,2$ are found in the agreement with data. We determine the $b\bar{b}$ component of the photon wave function using the data for the $e^{+}{e}^{-}$ annihilation, $e^{+}{e}^{-}\to {\rm Y}(9460)$, ${\rm Y}(10023)$, ${\rm Y}(10036)$, ${\rm Y}(10580)$, ${\rm Y}(10865)$, ${\rm Y}(11019)$, and predict partial widths of the two-photon decays $η_{b0}\to\ggam$, $χ_{b0}\to\ggam$, $χ_{b2}\to\ggam$ for the radial excitation states below $B\bar{B}$ threshold ($n\le 3$).

43 pages, 13 figures

References in corpus (34)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Observation of the Narrow State $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ in $\bar{p}p$ Collisions at $\sqrt{s}=1.96 \TeV$
• Properties of heavy quarkonia and B_c mesons in the relativistic quark model
• Short Range Structure in the X(3872)
• The D*0 D0bar threshold resonance
• Charmonium Options for the X(3872)
• Charmonium levels near threshold and the narrow state $X(3872) \to π^{+}π^{-}\jpsi$
• Systematics of q anti-q states in the (n,M^2) and (J,M^2) planes
• Interference and binding effects in decays of possible molecular component of X(3872)
• Molecular States of Heavy Quark Mesons
• The light baryon spectrum in a relativistic quark model with instanton-induced quark forces II. The strange baryon spectrum
• Two-Photon Decays of Mesons in a Relativistic Quark Model
• Gluon Propagator in the Infrared Region
• Meson--photon transition form factors and resonance cross-sections in e^+ e^- collisions
• Photon--meson transition form factors $\gamma {\pi }^0$, $\gamma \eta$ and $\gamma {\eta }^{\prime }$ at low and moderately high $Q^2$
• Radiative decays of basic scalar, vector and tensor mesons and the determination of the P-wave q\bar q multiplet
• The Meson Spectrum in a Covariant Quark Model
• Relativistic two-photon and two-gluon decay rates of heavy quarkonia
• Quark structure of the pion and pion form factor
• Study of the Process $e^{+}{e}^{-}\to K_L^0{K}_S^0$ in the C.M.Energy Range 1.05-1.38 GeV with CMD-2
• Pion-photon and photon-pion transition form factors in light-cone formalism
• Moment-operator expansion for the two-meson, two-photon and fermion-antifermion states
• On the mass, width and coupling constants of the f0(980)
• Electromagnetic Annihilation Rates of ${\chi }_{c0}$ and ${\chi }_{c2}$ with Both Relativistic and QCD Radiative Corrections
• The upper limit of the e+e- partial width of X(3872)
• Heavy Quarkonia in the Instantaneous Bethe-Salpeter Model
• Radiative Scalar Meson Decays in the Light-Front Quark Model
• The X(3872) and the 3941 MeV peak in omega+J/Psi
• Sector of the $2^{++}$ mesons: observation of the tensor glueball
• Charmonium in the instantaneous approximation
• Radiative decays of quarkonium states, momentum operator expansion and nilpotent operators
• Evidence for a 4th state related to the three JPC = 2++, pi- p -> phi phi n states explainable by 2++ Glueball production

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• Bottomonium Spectrum with Screened Potential
• Magnetic properties of ground-state mesons
• Production of ${\chi }_b$-mesons at LHC
• Canonical interpretation of the ${\eta }_2(1870)$
• Production of ${\chi }_c$- and ${\chi }_b$-mesons in high energy hadronic collisions
• Decay rates of quarkonia with NRQCD formalism using spectroscopic parameters of potential models
• Constructing new pseudoscalar meson nonets with the observed $X(2100)$, $X(2500)$, and $\eta (2225)$
• Production of ${\eta }_Q$ meson at LHC
• Decay rates and electromagnetic transitions of heavy quarkonia
• ${\eta }_Q$ meson photoproduction in ultrarelativistic heavy ion collisions