First determination of fragmentation functions in an exotic-hadron candidate

Abstract

In recent years, there are experimental reports on exotic-hadron candidates, which have different quark configurations from ordinary $q\bar q$ and $qqq$ constituents. However, it is not easy to confirm their exotic nature from global observables such as masses, spins, parities, and decay widths. At high energies, internal quark and gluon configurations could become more apparent because hadrons should be described by fundamental degrees of freedom of quarks and gluons in quantum chromodynamics. One of such possibilities is to use the fragmentation functions (FFs). In this work, accurate FFs of an exotic hadron candidate $f_0$(980) are determined for the first time by an global analysis of experimental data on $e^+ + e^- \to f_0 (980)+X$ with recent precise measurements of the Belle collaboration. From the global analysis, we found that their second moments have a relation $M_u = M_d \ll M_s \sim M_g $ for up-quark, down-quark, strange-quark, and gluon FFs. Furthermore, the function $D_s^{f_0}(z)$ is distributed in the larger-$z$ region in comparison with the functions $D_{u}^{f_0}(z)$, $D_{d}^{f_0}(z)$, and $D_g^{f_0}(z)$. These facts support that the $f_0 (980)$ has the $s\bar s$ configuration at high energies. This is a new finding that $f_0 (980)$ should be considered mainly as the $s\bar s$ state, which is different from our usual understanding as a tetraquark (or $K\bar K$) hadron from low-energy studies. Our results could indicate the transition of the internal configuration picture that $f_0 (980)$ looks like a $q\bar q$ state at high energies although it is described by tetra-quark or $K\bar K$ molecule state at low energies. It sheds light on a new direction in exotic hadron physics.