( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> )-dimensional scalar field model analysis of beam spin asymmetry in the electropr

We explore exclusive scalar meson electroproduction off a scalar target in the ( <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>1</a:mn> </a:mrow> </a:math> )-dimensional scalar field model. This model analysis is a straightforward extension of the previous ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>1</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> )-dimensional model analysis presented in Choi []. In contrast to the ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mn>1</e:mn> <e:mo>+</e:mo> <e:mn>1</e:mn> </e:mrow> </e:math> )-dimensional model, the ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mn>3</g:mn> <g:mo>+</g:mo> <g:mn>1</g:mn> </g:mrow> </g:math> )-dimensional model allows us to compute the beam spin asymmetry (BSA), which is proportional to the imaginary part of the product of the two Compton form factors (CFFs) that appear in the hadronic current of the present scalar meson electroproduction process. We compute both real and imaginary parts of the CFFs and note that the BSA is detectable for <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:mo>−</i:mo> <i:mi>t</i:mi> <i:mo>/</i:mo> <i:msup> <i:mrow> <i:mi>Q</i:mi> </i:mrow> <i:mrow> <i:mn>2</i:mn> </i:mrow> </i:msup> <i:mo>≳</i:mo> <i:mn>0.1</i:mn> </i:mrow> </i:math> , although it gets quite small in the kinematic region <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mo>−</k:mo> <k:mi>t</k:mi> <k:mo>/</k:mo> <k:msup> <k:mi>Q</k:mi> <k:mn>2</k:mn> </k:msup> <k:mo>≪</k:mo> <k:mn>0.1</k:mn> </k:math> , where the factorization of the generalized parton distribution (GPD) is attainable. We find the analytic forms of the leading-twist GPD for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Efremov-Radyushkin-Brodsky-Lepage (ERBL) regions in the ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mn>3</m:mn> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> )-dimensional scalar field model, confirming its uniqueness independent of the hadronic current component. While we verify that the GPD sum rule for the total result of summing the DGLAP and ERBL regions holds for all components of the hadronic current, we note that the respective correspondence of the DGLAP and ERBL regions to the valence and nonvalence parts of the electromagnetic form factor holds only for the light-front plus component of the hadronic current but not for any other components of the hadronic current. We discuss the polynomiality of the GPD up to the second moments and remark on accessible ranges of kinematics to measure the BSA and CFFs with respect to the future experimental efforts of extracting the leading-twist GPDs.