Hard-scattering approach to strongly hindered electric dipole transitions between heavy quarkonia

The conventional wisdom in dealing with electromagnetic transition between heavy quarkonia is the multipole expansion, when the emitted photon has a typical energy of order quarkonium binding energy. Nevertheless, in the case when the energy carried by the photon is of order typical heavy quark momentum, the multipole expansion doctrine is expected to break down. In this work, we apply the “hard-scattering” approach originally developed to tackle the strongly hindered magnetic dipole (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>M</a:mi><a:mn>1</a:mn></a:math>) transition [Y. Jia , ] to the strongly hindered electric dipole (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>E</c:mi><c:mn>1</c:mn></c:math>) transition between heavy quarkonia. We derive the factorization formula for the strongly hindered <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>E</e:mi><e:mn>1</e:mn></e:math> transition rates at the lowest order in velocity and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>α</g:mi><g:mi>s</g:mi></g:msub></g:math> in the context of the nonrelativistic QCD, and conduct a detailed numerical comparison with the standard predictions for various bottomonia and charmonia <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>E</i:mi><i:mn>1</i:mn></i:math> transition processes. Published by the American Physical Society 2024