Chapter 3 Correlator fit
3.0.1 different tentatives of fitting the l-l correlator
Here we try to interpolate the correlator at \(t_0=0.2 fm\), we use the following function to interpolate:
C_{l}^{eq}_2exp: \(N (P[0]e^{P[1](t)}+P[2]e^{P[3](t)})\)C_{l}^{eq}_1exp: \(N (P[0]e^{P[1](t)})\)C_{l}^{eq}_poly2: \(P[0]+P[1](t-t_0)+P[2](t-t_0)^2\)C_{l}^{eq}_poly3: \(P[0]+P[1](t-t_0)+P[2](t-t_0)^2+P[3](t-t_0)^3\)
\(N\) is not a fit parameter but a normalization to ensure that the correlator at
\(t_0\) is \(c(t_0)=P[0]\), for istance in C_{l}^{eq}_1exp \(N=e^{-P[1]t_0}\)
The most promising one is the C_{l}^{eq}_2exp using 4 points. Below result
and plot for each of the fits.
Notice we are plotting in log10 scale and the polynomial get distorted
C_{l}^{eq}_2exp = -3.58(21)e+5 3.401(71) 1.728(24)e+8 -19.420(95) \(\chi^2/dof=\) inf
C_{l}^{eq}_1exp = 9.48(23)e+6 -17.00(12) \(\chi^2/dof=\) 20936
C_{l}^{eq}_poly2 = 1.297(35)e+7 -2.417(16)e+8 1.064(16)e+9 \(\chi^2/dof=\) 6.9873e+05
C_{l}^{eq}_poly3 = 8.32(25)e+6 -1.734(46)e+8 2.0222(31)e+9 -7.47(17)e+9 \(\chi^2/dof=\) inf
C_{l}^{eq}_poly2_3pt = 7.23(33)e+6 -2.274(55)e+8 2.435(36)e+9 \(\chi^2/dof=\) inf