Improved determination of Heavy Quarkonium magnetic dipole transitions in pNRQCD

Abstract

We compute the magnetic dipole transitions between low lying Heavy Quarkonium states in a model independent way. We use the weak-coupling version of the effective field theory named potential NRQCD with the static potential exactly incorporated in the leading order Hamiltonian. The precision we reach is $k_{\gamma }^3/m^2\times \mathcal{O}({\alpha }_s^2,v^2)$ and $k_{\gamma }^3/m^2\times \mathcal{O}(v^4)$ for the allowed and forbidden transitions respectively. We also resum the large logarithms associated to the heavy quark mass scale. The specific transitions considered in this paper are the following: ${\rm Y}(1S)\to {\eta }_b(1S)\gamma$, $J/\psi (1S)\to {\eta }_c(1S)\gamma$, $h_b(1P)\to {\chi }_{b0,1}(1P)\gamma$, ${\chi }_{b2}(1P)\to h_b(1P)\gamma$, ${\rm Y}(2S)\to {\eta }_b(2S)\gamma$, ${\rm Y}(2S)\to {\eta }_b(1S)\gamma$ and ${\eta }_b(2S)\to {\rm Y}(1S)\gamma$. The effect of the new power counting is found to be large and the exact treatment of the soft logarithms of the static potential makes the factorization scale dependence much smaller. The convergence for the $b\bar{b}$ ground state is quite good, and also quite reasonable for the $c\bar{c}$ ground state and the $b\bar{b}$ 1P state. For all of them we give solid predictions. For the 2S decays the situation is less conclusive, yet our results are perfectly consistent with existing data, as the previous disagreement with experiment for the ${\rm Y}(2S)\to {\eta }_b(1S)\gamma$ decay fades away. We also profit to compute some expectation values like the electromagnetic radius, r^2, or p^2. We find r^2 to be nicely convergent in all cases, whereas the convergence of p^2 is typically worse.

42 pages, 15 figures. Numbering of references on figure 9 has been corrected

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• Quarkonia and their transitions
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• Three-Loop Chromomagnetic Interaction in HQET
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• Charmonium Spectroscopy in Strong Magnetic Fields by QCD Sum Rules: S-Wave Ground States
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
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• Charmonium and Charmoniumlike States at the BESIII Experiment
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• Measurement of $J/\psi \to \gamma {\eta }_{\mathrm{c}}$ decay rate and ${\eta }_{\mathrm{c}}$ parameters at KEDR
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• Hindered M1 Radiative Decay of ${\rm Y}(2S)$ from Lattice NRQCD
• Electric dipole transitions of $1P$ bottomonia
• The Glueball content of ${\eta }_c$
• Heavy meson thresholds in Born-Oppenheimer Effective field theory
• Study of the electromagnetic Dalitz decays $\psi ({\rm Y})\to {\eta }_c({\eta }_b)l^{+}{l}^{-}$
• Self-consistent $M1$ radiative transitions of excited $B_c$ and heavy quarkonia with different polarizations in the light-front quark model
• Frame dependence of transition form factors in light-front dynamics
• Quarkonium radiative decays from the hadronic Paschen-Back effect
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• $E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation
• Study of the radiative decay $J/\psi \to {\eta }_c+\gamma$ in light cone sum rules
• Hindered magnetic dipole transitions between P-wave bottomonia and coupled-channel effects
• Observation of ${\rm Y}(2S)\to \gamma {\eta }_b(1S)$ decay
• Relativistic two-body calculation of $b\bar{b}$-mesons radiative decays
• Experimental review of the ${\rm Y}(1S,2S,3S)$ physics at $e^{+}{e}^{-}$ colliders and the LHC
• pNRQCD determination of E1 radiative transitions
• Line shape and the experimental determination of the $J/\psi \to \gamma {\eta }_c$ branching fraction
• Radiative transitions of charmonium states in a constituent quark model
• Study of the Magnetic Dipole Transition of $J/\psi \to \gamma {\eta }_c$ via ${\eta }_c\to p\bar{p}$
• Radiative transitions of charmonium states in the covariant confined quark model
• Radiative and Dalitz decays of ${\rm Y}(1S)$ in the light of the ATOMKI X17 anomaly
• Line shape of the $J\psi \to \gamma {\eta }_c$ decay
• Non-Markovian dynamics of bottomonia in the QGP