Prospects for compact hexaquarks under the limitation imposed by quark confinement

The limitation of flavor constituents for compact multiquarks is crucial for understanding the strong interaction at the low energy scale. Utilizing the MIT bag model that incorporates perturbative interactions and confinement energy <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>E</a:mi> <a:mrow> <a:mi>CON</a:mi> </a:mrow> </a:msub> </a:math> , we derive a critical bag radius <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>R</c:mi> <c:mi>c</c:mi> </c:msub> <c:mo>=</c:mo> <c:mn>5.61</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:msup> <c:mrow> <c:mi>GeV</c:mi> </c:mrow> <c:mrow> <c:mo>−</c:mo> <c:mn>1</c:mn> </c:mrow> </c:msup> </c:math> from the condition <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>E</e:mi> <e:mrow> <e:mi>CON</e:mi> </e:mrow> </e:msub> <e:mo>&lt;</e:mo> <e:mn>0</e:mn> </e:math> at zero temperature and zero baryon density, which aligns with the string-breaking distance of 1.2–1.4 fm. Applying this framework to 6-, 7-, and 8-quark systems, we find the bag radii <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>R</g:mi> <g:mn>0</g:mn> </g:msub> </g:math> to be highly sensitive to relativistic effects from light quarks, leading to the exclusion of most heavy-light flavor configurations (e.g., <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>n</i:mi> <i:mn>3</i:mn> </i:msup> <i:msup> <i:mover accent="true"> <i:mi>c</i:mi> <i:mo stretchy="false">¯</i:mo> </i:mover> <i:mn>3</i:mn> </i:msup> </i:math> , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>n</m:mi> <m:mn>3</m:mn> </m:msup> <m:mover accent="true"> <m:mi>n</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:msup> <m:mover accent="true"> <m:mi>c</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mn>2</m:mn> </m:msup> </m:math> ) due to positive <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>E</s:mi> <s:mrow> <s:mi>CON</s:mi> </s:mrow> </s:msub> </s:math> and radii exceeding the critical radius. Color-spin wave functions are constructed using Young tableaux to evaluate interaction matrices and Okubo-Zweig-Iizuka-superallowed decays. Broad decay widths in fully heavy systems for Okubo-Zweig-Iizuka-superallowed modes could arise from wave function overlaps due to heavy flavor symmetry, suggesting possible narrow widths for <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>n</u:mi> <u:mi>n</u:mi> <u:mi>b</u:mi> <u:mover accent="true"> <u:mi>b</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> <u:mover accent="true"> <u:mi>b</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> <u:mover accent="true"> <u:mi>b</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> </u:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>n</cb:mi> <cb:mi>n</cb:mi> <cb:mi>n</cb:mi> <cb:mover accent="true"> <cb:mi>b</cb:mi> <cb:mo stretchy="false">¯</cb:mo> </cb:mover> <cb:mover accent="true"> <cb:mi>b</cb:mi> <cb:mo stretchy="false">¯</cb:mo> </cb:mover> <cb:mover accent="true"> <cb:mi>b</cb:mi> <cb:mo stretchy="false">¯</cb:mo> </cb:mover> </cb:math> hexaquarks. This phenomenological approach provides insights into the limitations on multiquarks imposed by confinement. It recommends experimental searches at LHCb for these states.