13 w_0 scale setting
The fit antsaz: \left(\frac{w_0}{a}\right)_{lat}=\frac{w_0^{iso}}{a}\left[1+P[5](\xi-\xi^{iso})\right] with \xi=\frac{M_\pi^2}{(4\pi f_\pi)^2}, and the chiral LO from (Bär and Golterman 2014, eq (4.8)).
volume effects:
C.06.112 is higher than C.06.80
B.072.96 is higher than B.072.64 althought compatible within errors
the on on M_\pi and f_\pi in the x-axis are included
misstuning corrections:
m_0
m_{\ell,s,c}
13.1 iter 0
\chi^2/dof= 3.61635
| par | a_from_w0 | a_from_fpi |
|---|---|---|
| a(A) | 0.094475(93) | 0.09022(64) |
| a(B) | 0.080892(26) | 0.079507(47) |
| a(C) | 0.068757(38) | 0.068187(66) |
| a(D) | 0.057125(34) | 0.056858(76) |
| a(E) | 0.049148(38) | 0.048919(65) |
| P[5] | 0.574(24) | 0 |
<r >
13.2 with corrections
\chi^2/dof= 1.58581
| par | a_from_w0 | a_from_fpi |
|---|---|---|
| a(A) | 0.09420(12) | 0.09022(64) |
| a(B) | 0.08117(10) | 0.079614(53) |
| a(C) | 0.06890(10) | 0.068143(67) |
| a(D) | 0.05751(13) | 0.056936(78) |
| a(E) | 0.049078(61) | 0.048930(64) |
| P[5] | 0.663(31) | 0 |
adding a2*xi
\chi^2/dof= 0.253175
| par | a_from_w0 | a_from_fpi |
|---|---|---|
| a(A) | 0.09390(18) | 0.09022(64) |
| a(B) | 0.08129(11) | 0.079614(53) |
| a(C) | 0.06891(10) | 0.068143(67) |
| a(D) | 0.05754(13) | 0.056936(78) |
| a(E) | 0.049086(62) | 0.048930(64) |
| P[5] | -0.20(24) | 0 |
| P[6] | -217(64) | 0 |
<r >
14 comparing w0 before and after corrections
<r >
14.1 w0 using a from fpi (corrections included)
P[0] represent w_0 at the physical point. BMW value shoul be 0.17236
\chi^2/dof= 3.10512
| P | value |
|---|---|
| P[0] | 0.1696(20) |
| P[1] | 0.659(35) |
| P[2] | 8.0(6.4) |
| P[3] | -1371(720) |
<r >
14.2 fit the difference (corrections included)
\chi^2/dof= 2.30467
| P | value |
|---|---|
| P[0] | -0.045(45) |
| P[1] | 47.7(8.0) |
<r >
15 ratio a_w0 / a_fpi
\chi^2/dof= 1.16564
| P | value |
|---|---|
| P[0] | 0.9942(24) |
| P[1] | 3.93(53) |
BAIC average ratio of a: 0.9960(55)
w0 from fpi FLAG: 0.17306(95)
fpi from w0 WP25: 131.03(72)
<r >