[Paper Review] Evidence for a charged charmonium-like $Z_c^+$ from QCD

Saša Prelovšek, C. B. Lang+2 more|arXiv (Cornell University)|May 29, 2014

Quantum Chromodynamics and Particle Interactions28 references17 citations

TL;DR

This study presents the first ab-initio lattice QCD calculation confirming the existence of a charged charmonium-like $Z_c^+$ state with quantum numbers $I^G(J^{PC})=1^+(1^{+-})$ at a mass of $4.16 \pm 0.03 \pm 0.16~\text{GeV}$, supporting its emergence only when diquark-antidiquark creation operators are included, and suggesting a possible link to the experimentally observed $Z_c^+(4020)/Z_c^+(4025)$ or $Z_c^+(4200)$ states.

ABSTRACT

Recently experimentalists have discovered a new state of matter in form of charged charmonium-like hadrons $Z_c^+$. Unlike conventional hadrons, these contain at least two valence quarks and two antiquarks ($\bar cc\bar d u$). We address the question whether the existence of such a new form of hadrons is supported by QCD via a first-principle calculation using Lattice QCD. We find a candidate for the charged charmonium-like state $Z_c^{+}$ with quantum numbers $I^G(J^{PC})=1^+(1^{+-})$. This is the first ab-initio QCD calculation establishing such a hadron. The state is found at mass $m=4.16\pm 0.03\pm 0.16\pm {\cal O}(\Gamma_{Z_c})~$GeV and could be related to the recently discovered $Z_c^+(4020)/Z_c^+(4025)$ or $Z_c^+(4200)$. The $Z_c^+$ candidate emerges only when diquark-antidiquark creation operators are included in the simulation. The resulting overlap of the established $Z_c^+$ to our basis of creation operators ${\cal O}_j$ may shed light on its nature.

Motivation & Objective

• To investigate whether the existence of charged charmonium-like hadrons such as $Z_c^+$ is supported by quantum chromodynamics (QCD) through first-principle calculations.
• To determine if such exotic states with four-quark content ($\bar{c}c\bar{d}u$) can emerge from QCD dynamics without phenomenological assumptions.
• To identify the quantum numbers and mass of a candidate $Z_c^+$ state using lattice QCD simulations.
• To examine the role of diquark-antidiquark creation operators in the formation of the $Z_c^+$ state.

Proposed method

• Employing lattice QCD simulations with a non-perturbative approach to compute the spectrum of hadronic states with four-quark Fock components.
• Using a basis of creation operators including diquark-antidiquark interpolating fields to effectively couple to the $Z_c^+$ state.
• Performing variational analysis on correlation matrices to extract the lowest-lying energy states and their quantum numbers.
• Applying the L"uscher method and energy splitting analysis to determine the quantum numbers $I^G(J^{PC})=1^+(1^{+-})$ of the state.
• Including systematic uncertainties from statistical errors, finite volume effects, and the $\mathcal{O}(\Gamma_{Z_c})$ width correction.
• Analyzing the overlap of the extracted state with the creation operator basis to infer its internal structure and dynamics.

Experimental results

Research questions

• RQ1 Does QCD, via first-principle lattice calculations, support the existence of a charged charmonium-like state $Z_c^+$ with $I^G(J^{PC})=1^+(1^{+-})$?
• RQ2 What is the mass of the $Z_c^+$ state as predicted by ab-initio QCD simulations?
• RQ3 Is the $Z_c^+$ state only generated when diquark-antidiquark creation operators are included in the simulation?
• RQ4 How does the overlap of the $Z_c^+$ state with the creation operator basis inform its internal structure?
• RQ5 Can the lattice QCD prediction for the $Z_c^+$ state be linked to the experimentally observed $Z_c^+(4020)/Z_c^+(4025)$ or $Z_c^+(4200)$ states?

Key findings

• The lattice QCD calculation identifies a candidate state with quantum numbers $I^G(J^{PC})=1^+(1^{+-})$, consistent with the $Z_c^+$ state.
• The state is found at a mass of $4.16 \pm 0.03 \pm 0.16~\text{GeV}$, with systematic uncertainties including $\mathcal{O}(\Gamma_{Z_c})$ effects.
• The $Z_c^+$ state emerges only when diquark-antidiquark creation operators are included in the simulation, indicating their essential role in forming the state.
• The overlap of the $Z_c^+$ state with the creation operator basis provides insight into its internal structure and dynamics.
• The calculated mass and quantum numbers are consistent with the experimentally observed $Z_c^+(4020)/Z_c^+(4025)$ or $Z_c^+(4200)$ states.
• This is the first ab-initio QCD calculation establishing the existence of a charged charmonium-like $Z_c^+$ state, providing strong theoretical support for its reality in QCD.