Charmonium-onium: A fully charmed tetraquark

Paper Title: Observation of structure in the $J/\psi$ -pair mass spectrum

Authors: LHCb Collaboration

Reference: https://arxiv.org/pdf/2006.16957.pdf

My (artistic) rendition of a tetraquark. The blue and orange balls represent charm and anticharm quarks with gluons connecting all of them.

The Announcement

The LHCb collaboration reports a 5-sigma resonance at 6.9 GeV, consistent with predictions of a fully-charmed tetraquark state.

The Background

One of the ways quarks interact with each other is the strong nuclear force. This force is unlike the electroweak or gravitational forces in that the interaction strength increases with the separation between quarks, until it sharply falls off at roughly $10^{-15}$ m. We say that the strong force is “confined” due to this sharp drop off. It is also dissimilar to the other forces in that the Strong force is non-perturbative. For perturbation theory to work well, the more complex a Feynman diagram becomes, the less it should contribute to the process. In the strong interaction though, each successive diagram contributes more than the previous one. Despite these challenges, physicists have still made sense organizing the zoo of quarks and bound states that come from particle collisions.

The quark ( $q$ ) model [1,2] classifies hadrons into Mesons ( $q \bar{q}$ ) and Baryons ( $qqq$ or $\bar{q}\bar{q}\bar{q}$ ). It also allows for the existence of exotic hadrons like the tetraquark ( $qq\bar{q}\bar{q}$ ) or pentaquark ( $qqq\bar{q}\bar{q}\bar{q}$ ). The first evidence for an exotic hardon of this nature came in 2003 from the Belle Collaboration [1]. According to the LHCb collaboration, “all hadrons observed to date, including those of exotic nature, contain at most two heavy charm ( $c$ ) or bottom ( $b$ ) quarks, whereas many QCD-motivated phenomenological models also predict the existence of states consisting of four heavy quarks.” In this paper, the LHCb reports evidence of a $cc\bar{c}\bar{c}$ state, the first fully charmed tetraquark state.

The Method

Perhaps the simplest way to form a fully charmed tetraquark state, $T_{ cc \bar{c}\bar{c}}$ from now on, is to form two charmonium states ( $J/\psi$ ) which then themselves form a bound state. This search focuses on pairs of charmonium that are produced from two separate interactions, as opposed to resonant production through a single interaction. This is advantageous because “the distribution of any di- $J/\psi$ observable can be constructed using the kinematics from single $J/\psi$ production.” In other words, independent $J/\psi$ production reduces the amount of work it takes to construct observables.

Once $J/\psi$ is formed, the most useful decay it undergoes is into pairs of muons with about a 6% branching ratio [2]. To form $J/\psi$ candidates, the di-muon invariant mass must be between $3.0 - 3.2$ GeV. To form a di- $J/\psi$ candidate, the $T_{ cc \bar{c}\bar{c}}$ , all four muons are required to have originated from the same proton-proton collision point. This eliminates the possibility of associating two $J/\psi$ s from two different proton collisions.

The Findings

When the dust settles, the LHCb finds a $5-\sigma$ resonance at $m_{\text{di}- J/\psi} = 6905 \pm 11 \pm 7$ MeV with a width of $\Gamma = 80 \pm 19 \pm 33$ MeV. This resonance is just above twice the $J/\psi$ mass.