Hadron spectrum, quark masses, and decay constants from light overlap fermions on large lattices

We present results from a simulation of quenched overlap fermions with Lüscher-Weisz gauge field action on lattices up to ${24}^{3}48$ and for pion masses down to $\approx 250\mathrm{MeV}$. Among the quantities we study are the pion, rho, and nucleon masses; the light and strange quark masses; and the pion decay constant. The renormalization of the scalar and axial vector currents is done nonperturbatively in the RI-MOM scheme. The simulations are performed at two different lattice spacings, $a\approx 0.1\mathrm{fm}$ and $\approx 0.15\mathrm{fm}$, and on two different physical volumes, to test the scaling properties of our action and to study finite volume effects. We compare our results with the predictions of chiral perturbation theory and compute several of its low-energy constants. The pion mass is computed in sectors of fixed topology as well.

Figure 1

The effective range $F(r)$ as a function of $r/a$ on the ${16}^{3}32$ lattice at $\beta =8.45$ for $\rho =1.4$, together with an exponential fit. The fit gave $\mu =1.11(1)$.

Figure 2

Condition number and $\mu$ on the ${16}^{3}32$ lattice at $\beta =8.45$ for $\rho =1.2$, 1.3, 1.4, 1.5, and 1.6, from left to right.

Figure 3

The effective pseudoscalar mass from the correlation function of the axial vector current $A_4$ on the ${24}^{3}48$ lattice at $\beta =8.45$, using smeared sources and local sinks.

Figure 4

The effective rho mass on the ${24}^{3}48$ lattice at $\beta =8.45$, using smeared sources and local sinks. The horizontal lines indicate the fit interval as well as the value and error of the mass.

Figure 5

The effective nucleon mass on the ${24}^{3}48$ lattice at $\beta =8.45$, using smeared sources and local sinks. The horizontal lines indicate the fit interval as well as the value and error of the mass. The data points at the lowest three quark masses have been computed with low-mode averaging.

Figure 6

The same as the previous figure, but for the lowest three quark masses without using low-mode averaging.

Figure 7

APE plot on the ${24}^{3}48$ lattice at $\beta =8.45$ (○) and on the ${16}^{3}32$ lattices at $\beta =8.0$ ($\square$) and $\beta =8.45$ ($▵$), together with the experimental value ($*$).

Figure 8

Chiral extrapolation of the pseudoscalar decay constant on the ${24}^{3}48$ lattice at $\beta =8.45$ (○) and on the ${16}^{3}32$ lattice at $\beta =8.0$ ($\square$).

Figure 9

Chiral extrapolation of the pseudoscalar mass on the ${24}^{3}48$ lattice at $\beta =8.45$ (○) and on the ${16}^{3}32$ lattice at $\beta =8.0$ ($\square$). The curves show the fits for ${\alpha }_{\Phi }^q=0$.

Figure 10

The parameter ${\delta }_{\mathrm{eff}}$ on the ${16}^{3}32$ lattice at $\beta =8.0$ together with a linear fit (top panel) and on the ${24}^{3}48$ lattice at $\beta =8.45$ (bottom panel), as a function of the average quark mass ${\overline{m}}_q=(m_q+m_q^{\prime })/2$.

Figure 11

The pseudoscalar mass on the ${16}^{3}32$ lattice at $\beta =8.0$ for $|Q|=0,\dots ,9$, from left to right. The data have been displaced horizontally. The true quark masses are indicated by the arrow at the bottom rim of the figure. The curve is from Fig. 9.

Figure 12

Chiral extrapolation of the vector meson mass on the ${24}^{3}48$ lattice at $\beta =8.45$ (○) and on the ${16}^{3}32$ lattice at $\beta =8.0$ ($\square$), together with the experimental value ($*$). The solid curves show the fits. The dashed curve in the top left corner shows the energy of the state of two pseudoscalar mesons.

Figure 13

Chiral extrapolation of the nucleon mass on the ${24}^{3}48$ lattice at $\beta =8.45$ (○) and on the ${16}^{3}32$ lattice at $\beta =8.0$ ($\square$), together with the experimental value ($*$). The curves show the fits.

Figure 14

The renormalization constant $Z_A$ on the ${24}^{3}48$ lattice at $\beta =8.45$.

Figure 15

Chiral extrapolation of $Z_A$ on the ${24}^{3}48$ lattice at $\beta =8.45$, together with its value in the chiral limit ($●$).

Figure 16

Chiral extrapolation of ${\Lambda }_S$ (top panel), ${\Lambda }_P$ (middle panel), and ${\Lambda }_A$ (bottom panel) on the ${16}^{3}32$ lattice at $\beta =8.45$ for some representative momenta $p=(n_1,n_2,n_3,n_4)$ in units of $2\pi /aL$ ($n_1,n_2,n_3$) and $\pi /aL$ ($n_4$).

Figure 17

The ratio ${\Lambda }_S(\mu )/{\Lambda }_P(\mu )$ as a function of $\mu$ on the ${16}^{3}32$ lattice at $\beta =8.45$.

Figure 18

The scale invariant renormalization constant $Z_S^{\mathrm{RGI}}$ on the ${16}^{3}32$ lattice at $\beta =8.0$ (○) and $\beta =8.45$ ($\square$).