Weak interaction axial form factors of the octet baryons in nuclear medium

We study the axial-vector and the induced pseudoscalar form factors associated with the weak transitions between the octet baryon members in nuclear medium, using a covariant constituent quark model. We extend previous calculations of the axial transition form factors from the vacuum (free space) to the nuclear medium (symmetric nuclear matter). The extension of the model to the nuclear medium takes into account the modifications of the properties of hadrons in the medium (masses and coupling constants), as determined by the quark-meson coupling model. The axial-vector (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>G</a:mi><a:mi>A</a:mi></a:msub></a:math>) and the induced pseudoscalar (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>G</c:mi></c:mrow><c:mrow><c:mi>P</c:mi></c:mrow></c:msub></c:mrow></c:math>) form factors are evaluated for different values of the nuclear density <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ρ</e:mi></e:math> in terms of the square transfer momentum <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>q</g:mi><g:mn>2</g:mn></g:msup><g:mo>=</g:mo><g:mo>−</g:mo><g:msup><g:mi>Q</g:mi><g:mn>2</g:mn></g:msup></g:math>. We conclude that, in general, the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>G</i:mi><i:mi>A</i:mi></i:msub></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>G</k:mi><k:mi>P</k:mi></k:msub></k:math> form factors are reduced in the nuclear medium. The reduction is stronger for light baryons and high densities. The medium modifications are milder for the heavier octet baryons, particularly at large <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>Q</m:mi><m:mn>2</m:mn></m:msup></m:math>. The calculations presented here can be used to estimate the cross sections of neutrino and antineutrino scattering with nucleus, and neutrino and antineutrino scattering with hyperons bound to a nucleus, as well as those in the cores of compact stars.