Production of the ΞN dibaryon as a weakly bound system in pp collisions

The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Ξ</a:mi><a:mi>N</a:mi></a:math> interaction plays an important role in understanding the long-anticipated <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>H</d:mi></d:math> dibaryon. Recent lattice QCD calculations verified the attractive nature of the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="normal">Ξ</f:mi><f:mi>N</f:mi></f:math> interaction. On the other hand, whether it is strong enough to generate a bound state remains inconclusive. In this work, assuming it can generate a weakly bound state, we study the yields of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="normal">Ξ</i:mi><i:mi>N</i:mi></i:math> dibaryon for different binding energies in <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>p</l:mi><l:mi>p</l:mi></l:math> collisions at 7 TeV using the coalescence model and the transport model PACIAE. The yields are estimated first numerically and then analytically, adopting a Yukawa-type wave function. In particular, we find that in the weak binding limit, there exists a universal relation between the yield and the binding energy, valid for <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>p</n:mi><n:mi>p</n:mi></n:math> collisions.