Relativistic effects in M1 radiative decays of heavy-light mesons

We discuss the M1 radiative transitions <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>D</a:mi><a:mo>*</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:mi>D</a:mi><a:mi>γ</a:mi></a:math>, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msubsup><d:mi>D</d:mi><d:mi>s</d:mi><d:mo>*</d:mo></d:msubsup><d:mo stretchy="false">→</d:mo><d:msub><d:mi>D</d:mi><d:mi>s</d:mi></d:msub><d:mi>γ</d:mi></d:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>B</g:mi><g:mo>*</g:mo></g:msup><g:mo stretchy="false">→</g:mo><g:mi>B</g:mi><g:mi>γ</g:mi></g:math>, and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msubsup><j:mi>B</j:mi><j:mi>s</j:mi><j:mo>*</j:mo></j:msubsup><j:mo stretchy="false">→</j:mo><j:msub><j:mi>B</j:mi><j:mi>s</j:mi></j:msub><j:mi>γ</j:mi></j:math>. A relativistic potential model is proposed. The corresponding Hamiltonian, when expanded to terms of the order of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>v</m:mi><m:mn>2</m:mn></m:msup><m:mo>/</m:mo><m:msup><m:mi>c</m:mi><m:mn>2</m:mn></m:msup></m:math>, where <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>v</o:mi></o:math> are the quark velocities, coincides with the Breit Hamiltonian. This model allows making predictions for the widths of radiative transitions of mesons with one light quark. Taking into account relativistic effects is especially important for the transitions <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msubsup><q:mi>D</q:mi><q:mi>s</q:mi><q:mrow><q:mo>*</q:mo><q:mo>+</q:mo></q:mrow></q:msubsup><q:mo stretchy="false">→</q:mo><q:msubsup><q:mi>D</q:mi><q:mi>s</q:mi><q:mo>+</q:mo></q:msubsup><q:mi>γ</q:mi></q:math> and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mrow><t:msup><t:mrow><t:mi>D</t:mi></t:mrow><t:mrow><t:mo>*</t:mo><t:mo>+</t:mo></t:mrow></t:msup><t:mo stretchy="false">→</t:mo><t:msup><t:mrow><t:mi>D</t:mi></t:mrow><t:mrow><t:mo>+</t:mo></t:mrow></t:msup><t:mi>γ</t:mi></t:mrow></t:math>, where there is a large compensation in the magnitude of the magnetic moment of these mesons. Our results are consistent with known experimental data.