Observation of String Breaking in QCD

TL;DR

String breaking in QCD is resolved for nf=2 at zero temperature by treating the system as a two-state mixing problem between a static QQ string and a BB pair, analyzed through a 2×2 correlation matrix that captures both explicit and implicit mixing. The study combines advanced variance-reduction techniques (TEA, SET, HPA) with optimized smearing and a fat-link static action to achieve high-precision results, locating a string-breaking distance of $r_c \\approx 15a \\approx 1.25$ fm and a minimal gap $\\Delta E_c \\approx 0.022 a^{-1} \\approx 51$ MeV, with a mixing angle $\\theta(r_c) \\approx \pi/4$. The transition rate $g(r)$ peaks in the mixing region, reaching about $\\,320$ MeV, and becomes $\\approx\\Delta E_c/2$ at rc, reflecting the underlying strong-coupling dynamics. The findings connect to quarkonium physics through a Born-Oppenheimer/pNRQCD perspective and enable controlled extrapolations toward nf=2+1 with lighter sea quarks, highlighting the relevance for hadronic decays near open-flavor thresholds.

Abstract

We numerically investigate the transition of the static quark-antiquark string into a static-light meson-antimeson system. Improving noise reduction techniques, we are able to resolve the signature of string breaking dynamics for n_f=2 lattice QCD at zero temperature. This result can be related to properties of quarkonium systems. We also study short-distance interactions between two static-light mesons.

Figures (22)

• Figure 1: Comparison of effective masses of static-light correlation functions, obtained employing static actions with and without fat temporal links. The wave function has been optimized to yield best ground state overlap for the fat link static action. SET and HPA have been applied in both cases.
• Figure 2: Comparison of the $\overline{Q}Q$ potential in lattice schemes with and without fat temporal links, in both cases for $t_{\min}/a=5$. String breaking is expected to take place around $\overline{r}=r_c\approx 15\,a$ but this is not visible from the Wilson loop data alone. The curve represents a funnel fit to the fat link data and the error band is this parametrization shifted upwards by the amount $2\delta m$, where $a\delta m=0.174(7)$.
• Figure 3: Effective static-light masses, obtained with SET alone, with HPA SET and with all three methods combined.
• Figure 4: The errors of effective static-light masses, obtained with SET alone, with HPA SET and with all three methods combined.
• Figure 5: The relative magnitude of the TEA contribution within the static-light correlation function, with and without HPA.