Observation of string breaking in QCD

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.

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 $\overline{r}=r_c\approx 15a$ 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.

Figure 6

The effect of HPA on SET for the example of $C_{QB}$ at $t=4a$, as a function of the distance $\overline{r}$. The normalization is arbitrary and we have employed local sources and sinks.

Figure 7

The ratio $-C_{BB}^{\mathrm{con}}/C_{BB}$ as a function of $t$ for various $r=Ra$. The splines are drawn to guide the eye.

Figure 8

The ratio $-C_{QB}^2/(C_{QQ}{C}_{BB})$ as a function of $t$ for various $r=Ra$. The splines are drawn to guide the eye.

Figure 9

The ratio $C_{BB}^{\mathrm{dis}}/C_B^2$ as a function of $t$ for small $r=Ra$.

Figure 10

Expected spectrum in the absence of mixing effects. The ground state at small $r$ has no overlap with the $|B⟩$ sector but is only contained within $C_{QQ}$. At $r>r_c$ the ground state is only visible in $C_{BB}$.

Figure 11

Effective masses. The solid symbols are from $C_{BB}(t)$, the open symbols from the Wilson loop $C_{QQ}(t)$. The horizontal line corresponds to twice the mass of a static-light meson.

Figure 12

Effective masses from the Wilson loop $C_{QQ}$. The lowest horizontal line is $2m_B$. The other two horizontal lines denote the central values of the respective excited state expectations from a global linear plus Coulomb fit to the potential from $2<R\le 13$ Wilson loop data. The open pentagons, from $C_{BB}^{\mathrm{dis}}$, demonstrate the plateau quality within the $C_{BB}$ sector.

Figure 13

The two energy levels, as a function of $\overline{r}$, normalized with respect to $2m_B$ (horizontal line). The curve corresponds to the three-parameter fit to $E_1(\overline{r})$, Eqs. (80, 81, 82), for $0.2\mathrm{fm}\le \overline{r}\le 0.9\mathrm{fm}<r_c$.

Figure 14

The same as Fig. 13, for the string breaking region.

Figure 15

The mixing angle $\theta$, as a function of $\overline{r}$. The curve corresponds to the parametrization Eqs. (85, 86, 87, 88).

Figure 16

The same as Fig. 15, for the string breaking region.

Figure 17

The energy gap $\Delta E=E_2-E_1$ with (circles) and without (squares) mixing.

Figure 18

The transition rate $g$ between $|B⟩$ and $|Q⟩$ states, as a function of $\overline{r}$.

Figure 19

The modified Michael ratio Eq. (96) for different $r=Ra$ values, as a function of $t$. The horizontal error bands correspond to the fitted transition rates.

Figure 20

The first two energy levels within the $I=0$ and $I=1$ sectors, at short distances.

Figure 21

The $I=0$ and $I=1$ excited state energies, relative to $2m_B$, at short distances, $\overline{r}<r_0\approx 6a$.

Figure 22

The energy levels in physical units for $n_f=2$ at a quark mass of slightly less than the strange quark mass (data points). The bands represent our $n_f=2+1$ speculation.