Transversity generalized parton distributions in spin- 3/2 particles

The definitions of the quark and gluon transversity generalized parton distributions (GPDs) in spin-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>3</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:mrow></a:math> particles are obtained in the light-cone gauge. It is found that they contain 16 independent components for each parton. Their even or odd property is found in terms of a skewness variable, and the odd transversity GPDs vanish in the forward limit. There are 16 amplitudes with helicity flip of quark or gluon. We conclude that all the amplitudes, unpolarized, polarized, and transversity amplitudes, have a common factor <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>F</c:mi><c:mo stretchy="false">(</c:mo><c:mi>ζ</c:mi><c:mo stretchy="false">)</c:mo></c:math> carrying all the complex parts. Here, the variable <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>ζ</g:mi></g:math> is the helicity difference <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>ζ</i:mi><i:mo>=</i:mo><i:mo stretchy="false">(</i:mo><i:msup><i:mrow><i:mi>λ</i:mi></i:mrow><i:mrow><i:mo>′</i:mo></i:mrow></i:msup><i:mo>−</i:mo><i:mi>λ</i:mi><i:mo stretchy="false">)</i:mo><i:mo>−</i:mo><i:mo stretchy="false">(</i:mo><i:msup><i:mrow><i:mi>μ</i:mi></i:mrow><i:mrow><i:mo>′</i:mo></i:mrow></i:msup><i:mo>−</i:mo><i:mi>μ</i:mi><i:mo stretchy="false">)</i:mo></i:mrow></i:math> for the amplitude <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:msub><o:mrow><o:mi mathvariant="script">A</o:mi></o:mrow><o:mrow><o:msup><o:mrow><o:mi>λ</o:mi></o:mrow><o:mrow><o:mo>′</o:mo></o:mrow></o:msup><o:msup><o:mrow><o:mi>μ</o:mi></o:mrow><o:mrow><o:mo>′</o:mo></o:mrow></o:msup><o:mo>,</o:mo><o:mi>λ</o:mi><o:mi>μ</o:mi></o:mrow></o:msub></o:mrow></o:math>. This kinematical factor is associated with the transfer of the orbital angular momentum in the quark- and gluon-spin-<r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mn>3</r:mn><r:mo>/</r:mo><r:mn>2</r:mn></r:mrow></r:math> particle scattering amplitudes. We also derive another main physical quantity, transversity distribution, from the transversity GPDs in the forward limit for the spin-<t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mrow><t:mn>3</t:mn><t:mo>/</t:mo><t:mn>2</t:mn></t:mrow></t:math> particles. Published by the American Physical Society 2024