A Heavy Quark-Antiquark Annihilations

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Does Charm-Anticharm (in relative S-wave with spin-1) annihilates to a single photon? How does this vertex look like in QCD?
 
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That would violate total 4-momentum conservation.
 
It can, however, got to a "virtual photon", i.e., a "dilepton" which is an ##e^+ e^-## or ##\mu^+ \mu^-## pair. This lead to the discovery of the ##J/\psi## ("The November Revolution") and thus the discovery of charm (expected from the GIM mechanism in electroweak theory):

https://en.wikipedia.org/wiki/J/psi_meson
 

Thread 'Toponium Discovered'

Toponium is a hadron which is the bound state of a valance top quark and a valance antitop quark. Oversimplified presentations often state that top quarks don't form hadrons, because they decay to bottom quarks extremely rapidly after they are created, leaving no time to form a hadron. And, the vast majority of the time, this is true. But, the lifetime of a top quark is only an average lifetime. Sometimes it decays faster and sometimes it decays slower. In the highly improbable case that...
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Thread 'Dirac-Delta from Normalization of Continuous Eigenfunctions'

I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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