Transversity generalized parton distributions of the Δ with the diquark spectator model

We show quark transversity generalized parton distributions (GPDs) of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi mathvariant="normal">Δ</a:mi> <a:mo>+</a:mo> </a:msup> </a:math> isobar by using the diquark spectator model for the first time. First, this model is tested by electric charge, magnetic-dipole, and axial charge form factors, and it is used for calculating the transversity GPDs <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msubsup> <d:mi>H</d:mi> <d:mrow> <d:mn>1</d:mn> <d:mo>,</d:mo> <d:mn>3</d:mn> <d:mo>,</d:mo> <d:mn>5</d:mn> <d:mo>,</d:mo> <d:mn>7</d:mn> </d:mrow> <d:mrow> <d:mi>q</d:mi> <d:mi>T</d:mi> </d:mrow> </d:msubsup> </d:math> of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msup> <f:mi mathvariant="normal">Δ</f:mi> <f:mo>+</f:mo> </f:msup> </f:math> . The quark transversity distribution <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>h</i:mi> <i:mn>1</i:mn> </i:msub> </i:math> is then obtained from the transversity GPDs in the forward limit. Then, helicity-flip amplitudes are shown numerically by using relations between the helicity amplitudes and the GPDs. Finally, by taking first moments of the GPDs, tensor form factors are obtained and we predict the tensor charge. Experimentally, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi>N</k:mi> <k:mtext>−</k:mtext> <k:mi mathvariant="normal">Δ</k:mi> </k:mrow> </k:math> transition GPDs are investigated in deeply virtual Compton scattering and virtual meson-production processes, and generalized distribution amplitudes, which correspond to the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>s</n:mi> </n:math> -channel GPDs, could be investigated by the two-photon processes <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msup> <p:mi>γ</p:mi> <p:mo>*</p:mo> </p:msup> <p:mi>γ</p:mi> <p:mo stretchy="false">→</p:mo> <p:mi mathvariant="normal">Δ</p:mi> <p:mover accent="true"> <p:mi mathvariant="normal">Δ</p:mi> <p:mo stretchy="false">¯</p:mo> </p:mover> </p:math> at the electron-positron colliders. Therefore, the spin- <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:mn>3</w:mn> <w:mo>/</w:mo> <w:mn>2</w:mn> </w:mrow> </w:math> <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi mathvariant="normal">Δ</y:mi> </y:math> GPDs could become interesting quantities experimentally in the future.