Study of the timelike electromagnetic form factors of the Λc

In this paper, the reaction of electron-positron annihilation into <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msubsup><a:mrow><a:mi mathvariant="normal">Λ</a:mi></a:mrow><a:mrow><a:mi>c</a:mi></a:mrow><a:mrow><a:mo>+</a:mo></a:mrow></a:msubsup><a:msubsup><a:mrow><a:mover accent="true"><a:mrow><a:mi mathvariant="normal">Λ</a:mi></a:mrow><a:mrow><a:mo stretchy="false">¯</a:mo></a:mrow></a:mover></a:mrow><a:mrow><a:mi>c</a:mi></a:mrow><a:mrow><a:mo>−</a:mo></a:mrow></a:msubsup></a:mrow></a:math> is investigated. The <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi mathvariant="normal">Λ</g:mi><g:mi>c</g:mi><g:mo>+</g:mo></g:msubsup><g:msubsup><g:mover accent="true"><g:mi mathvariant="normal">Λ</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mi>c</g:mi><g:mo>−</g:mo></g:msubsup></g:math> scattering amplitudes are obtained by solving the Lippmann-Schwinger equation. The contact, annihilation, and two pseudoscalar-exchange potentials are taken into account in the spirit of the chiral effective field theory. The amplitudes of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>e</m:mi><m:mo>+</m:mo></m:msup><m:msup><m:mi>e</m:mi><m:mo>−</m:mo></m:msup><m:mo stretchy="false">→</m:mo><m:msubsup><m:mi mathvariant="normal">Λ</m:mi><m:mi>c</m:mi><m:mo>+</m:mo></m:msubsup><m:msubsup><m:mover accent="true"><m:mi mathvariant="normal">Λ</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mi>c</m:mi><m:mo>−</m:mo></m:msubsup></m:math> are constructed by the distorted wave Born approximation method, with the final state interactions of the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msubsup><t:mi mathvariant="normal">Λ</t:mi><t:mi>c</t:mi><t:mo>+</t:mo></t:msubsup><t:msubsup><t:mover accent="true"><t:mi mathvariant="normal">Λ</t:mi><t:mo stretchy="false">¯</t:mo></t:mover><t:mi>c</t:mi><t:mo>−</t:mo></t:msubsup></t:math> rescattering implemented. By fitting to the experimental data, the unknown couplings are fixed, and high-quality solutions are obtained. With these amplitudes, the individual electromagnetic form factors in the timelike region, <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msubsup><z:mi>G</z:mi><z:mi>E</z:mi><z:msub><z:mi mathvariant="normal">Λ</z:mi><z:mi>c</z:mi></z:msub></z:msubsup></z:math>, <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msubsup><cb:mi>G</cb:mi><cb:mi>M</cb:mi><cb:msub><cb:mi mathvariant="normal">Λ</cb:mi><cb:mi>c</cb:mi></cb:msub></cb:msubsup></cb:math>, and their ratio, <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msubsup><fb:mi>G</fb:mi><fb:mi>E</fb:mi><fb:msub><fb:mi mathvariant="normal">Λ</fb:mi><fb:mi>c</fb:mi></fb:msub></fb:msubsup><fb:mo>/</fb:mo><fb:msubsup><fb:mi>G</fb:mi><fb:mi>M</fb:mi><fb:msub><fb:mi mathvariant="normal">Λ</fb:mi><fb:mi>c</fb:mi></fb:msub></fb:msubsup></fb:math>, are extracted. Both modulus and phases are predicted. These individual electromagnetic form factors reveal new insights into the properties of the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msub><jb:mi mathvariant="normal">Λ</jb:mi><jb:mi>c</jb:mi></jb:msub></jb:math>. The separated contributions of the Born term, contact, annihilation, as well as the two pseudoscalar-exchange potentials to the electromagnetic form factors are isolated. It is found that the Born term dominates the whole energy region. The contact term plays a crucial role in the enhancement near the threshold, and the annihilation term is essential in generating the fluctuation of the electromagnetic form factors.