1 M_\pi
Mpi-cA.12.48 = 0.08029(15) , \chi^2/dof= 0.92164
0.08028579 0.0001535833
Mpi-cB.72.64 = 0.056566(43) , \chi^2/dof= 0.0099863
0.05656583 4.271331e-05
Mpi-cB.72.96 = 0.056534(15) , \chi^2/dof= 0.01935
0.05653413 1.460993e-05
Mpi-cC.06.80 = 0.047227(34) , \chi^2/dof= 0.12123
0.04722655 3.352617e-05
Mpi-cD.54.96 = 0.040621(30) , \chi^2/dof= 0.055095
0.04062079 2.978815e-05
Mpi-cE.44.11 = 0.033830(29) , \chi^2/dof= 0.39457
0.0338297 2.881185e-05
Mpi-cC.20.48 = 0.08551(12) , \chi^2/dof= 1.0171
<r >
1.1 Mpi fit (only as test)
to determine a\mu_\ell we fit \frac{M_\pi^2}{f_\pi^2}= 2 \left(\frac{aB}{a^2f_\pi^2}\right) a\mu_\ell \left[1+5\xi\log \xi +P\xi \right] where left hand site is a function of the variable a\mu_\ell and \left(\frac{aB}{a^2f_\pi^2}\right) is a fit parameter for each lattice spacing and P a global parameter for all lattices. We define \xi=2\left(\frac{aB}{a^2f_\pi^2}\right) a\mu_\ell. After the fit we solve for a\mu_\ell imposing the physical value of the ratio \frac{M_\pi^2}{f_\pi^2}\bigg|_{phys}
\chi^2/dof= 2.16335
| P | value |
|---|---|
| P[0] | 892.1(1.5) |
| P[1] | 1018.4(2.3) |
| P[2] | 1203.4(3.5) |
| P[3] | 1384.7(4.9) |
| P[4] | 1.210(81) |
<r >
| Ens. | a\mu_\ell |
|---|---|
| B | 0.0006675(23) |
| C | 0.0005847(23) |
| D | 0.0004948(22) |
| E | 0.0004301(21) |
1.2 Mpi fit only physical point (test)
\chi^2/dof= 0.472663
| P | value |
|---|---|
| P[0] | 940(19) |
| P[1] | 1067(21) |
| P[2] | 1267(24) |
| P[3] | 1453(26) |
| P[4] | 6.0(1.8) |
<r >
| Ens. | a\mu_\ell | a\mu_\ell(phys point only) |
|---|---|---|
| B | 0.0006675(23) | 0.0006650(26) |
| C | 0.0005847(23) | 0.0005860(25) |
| D | 0.0004948(22) | 0.0004936(22) |
| E | 0.0004301(21) | 0.0004303(22) |
1.2.1 adding A ensemble (only as test)
\chi^2/dof= 4.64378
| P | value |
|---|---|
| P[0] | 812.1(6.2) |
| P[1] | 889.0(1.4) |
| P[2] | 1015.9(2.2) |
| P[3] | 1200.7(3.4) |
| P[4] | 1381.6(4.9) |
| P[5] | 1.448(70) |
<r >
| Ens. | a\mu_\ell |
|---|---|
| A | 0.0007317(57) |
| B | 0.0006684(23) |
| C | 0.0005849(23) |
| D | 0.0004949(22) |
| E | 0.0004301(21) |
1.3 a2 term C20.48 no A12.48
adding an extra parameter \frac{M_\pi^2}{f_\pi^2}= 2 \left(\frac{aB}{a^2f_\pi^2}\right) a\mu_\ell \left[1+5\xi\log \xi +P\xi +P_1 a^2 \right]
\chi^2/dof= 0.753925
| P | value |
|---|---|
| P[0] | 713(30) |
| P[1] | 830(25) |
| P[2] | 976(21) |
| P[3] | 1183(18) |
| P[4] | 1382(15) |
| P[5] | 6.55(38) |
| P[6] | 15.0(4.5) |
<r >
| Ens. | a\mu_\ell | a\mu_\ell-no-max-tw |
|---|---|---|
| A | 0.0007483(59) | 0.0007499(60) |
| B | 0.0006667(23) | 0.0006667(23) |
| C | 0.0005860(25) | 0.0005842(23) |
| D | 0.0004940(23) | 0.0004944(23) |
| E | 0.0004305(22) | 0.0004298(22) |
1.4 A12.48 no C20.48
\chi^2/dof= 0.869561
| P | value |
|---|---|
| P[0] | 714(30) |
| P[1] | 826(27) |
| P[2] | 968(23) |
| P[3] | 1180(19) |
| P[4] | 1377(16) |
| P[5] | 6.46(44) |
| P[6] | 15.8(4.9) |
<r >
1.5 A12.48 no C20.48 + strange misstuning
\chi^2/dof= 10728.9
| P | value |
|---|---|
| P[0] | 683.2(5.5) |
| P[1] | 801.9(4.1) |
| P[2] | 946.7(6.0) |
| P[3] | 1163.7(4.4) |
| P[4] | 1363.8(5.7) |
| P[5] | 6.00(25) |
| P[6] | 20.68(98) |
<r >
1.6 A12.48 no C20.48 + strange misstuning, unitary (used for a\mu_\ell determination)
\chi^2/dof= 0.407355
| P | value |
|---|---|
| P[0] | 686.2(7.7) |
| P[1] | 801.1(5.7) |
| P[2] | 947.3(6.1) |
| P[3] | 1165.3(4.5) |
| P[4] | 1363.1(8.1) |
| P[5] | 6.06(28) |
| P[6] | 20.5(1.3) |
<r >
| Ens. | a\mu_\ell |
|---|---|
| A | 0.0007479(99) |
| B | 0.0006670(27) |
| C | 0.0005862(42) |
| D | 0.0004931(28) |
| E | 0.0004305(31) |
1.6.1 reweighting
\chi^2/dof= 0.0950052
| P | value |
|---|---|
| P[0] | 0.174(58) |
| P[1] | 0.085(26) |
| P[2] | 0.101(15) |
| P[3] | 0.156(20) |
| P[4] | 2600(105) |
| P[5] | -1.98(29)e+5 |
<r >
| Ens. | a\mu_\ell |
|---|---|
| A | 0.0007461(58) |
| B | 0.0006666(23) |
| C | 0.0005862(25) |
| D | 0.0004940(23) |
| E | 0.0004305(22) |