Pentaquarks made of light quarks and their admixture to baryons

This paper is a continuation of our studies of multiquark hadrons. The antisymmetrization of their wave functions required by Fermi statistics is nontrivial, as it mixes orbital, color, spin, and flavor structures. In our previous papers we developed a method to find them based on the representations of the permutation group, and derived the explicit wave functions for baryons excited to the first and second shells ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>L</a:mi> <a:mo>=</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> , 2), tetraquarks <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>q</c:mi> <c:mi>q</c:mi> <c:mover accent="true"> <c:mi>q</c:mi> <c:mo stretchy="false">¯</c:mo> </c:mover> <c:mover accent="true"> <c:mi>q</c:mi> <c:mo stretchy="false">¯</c:mo> </c:mover> </c:math> and hexaquarks ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mn>6</i:mn> <i:mi>q</i:mi> </i:math> ). Now we apply it to light pentaquarks ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>q</k:mi> <k:mi>q</k:mi> <k:mi>q</k:mi> <k:mi>q</k:mi> <k:mover accent="true"> <k:mi>q</k:mi> <k:mo stretchy="false">¯</k:mo> </k:mover> </k:math> ), in the S- and P-shells ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>L</o:mi> <o:mo>=</o:mo> <o:mn>0</o:mn> </o:math> , 1). Using Jacobi coordinates, one can use the hyperdistance approximation in 12-dimensional space. We further address the issue of “unquenching” of baryons, by considering their mixing with pentaquarks, via two channels, through the addition of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>σ</q:mi> </q:math> -like or <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>π</s:mi> </s:math> -like <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mover accent="true"> <u:mi>q</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> <u:mi>q</u:mi> </u:math> pairs. This mixing is central for understanding of the observed flavor asymmetry of the antiquark sea, the amount of orbital motion issue as well as other nucleon properties.