Theoretical investigation into spectrum of <inline-formula><tex-math id="M232">\begin{document}${{{\bf{A}}}}^{{\boldsymbol{2}}}{{\boldsymbol{\Pi}} }_{{\boldsymbol{1/2}}}{\boldsymbol{\leftarrow}} {{{\bf{X}}}}^{{\boldsymbol{2}}}{{\boldsymbol{\Sigma}} }_{{\boldsymbol{1/2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M232.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210522_M232.png"/></alternatives></inline-formula> transition for CaH molecule toward laser cooling