12.1 \(a_{\mu}^{W-OS}(l)-a_{\mu}^{W-TM}(l)\)
12.1.1 plot of the difference:
\[ a_{\mu}^{W-OS}(l)-a_{\mu}^{W-TM}(l)=P[0]a^2-P[1] \frac{10 }{ 9} \Delta_{GS}a^2 \]
\(\chi^2_{dof}=\) 4.65289
\(P[ 0 ]=\) -4.75(37)e-8
\(P[ 1 ]=\) -174(71)
12.1.2 adding \(M_\pi\) dependence:
\[ a_{\mu}^{W-OS}(l)-a_{\mu}^{W-TM}(l)=P[0]a^2-P[1] \frac{10 }{ 9} \Delta_{GS}a^2+P[2](M_\pi-M_\pi^{phys}) \] the units of \(P[2]\) are \(MeV^{-1}\), in the plot the point are shifted to \(M_\pi^{phys}\)
\(\chi^2_{dof}=\) 7.20142
\(P[ 0 ]=\) -3.95(60)e-8
\(P[ 1 ]=\) -179(73)
\(P[ 2 ]=\) -9.8(6.3)e-12
12.1.3 logarithm:
this fit does not work
\[ a_{\mu}^{W-OS}(l)-a_{\mu}^{W-TM}(l)=P[0]\frac{a^2}{\log (w_0/a)^3}-P[1] \frac{10 }{ 9} \Delta_{GS}a^2 \]
\(\chi^2_{dof}=\) 21.8474
\(P[ 0 ]=\) -1.49(13)e-7
\(P[ 1 ]=\) 64(62)
12.1.4 \(a^4\)
\[ a_{\mu}^{W-OS}(l)-a_{\mu}^{W-TM}(l)=P[0]a^2-P[1] \frac{10 }{ 9} \Delta_{GS}a^2+P[2]a^4 \]
\(\chi^2_{dof}=\) 0.0130655
\(P[ 0 ]=\) -9.9(1.8)e-8
\(P[ 1 ]=\) -295(80)
\(P[ 2 ]=\) 8.0(2.7)e-6
12.1.5 logarithm with exponent 2
this fit does not work
\[ a_{\mu}^{W-OS}(l)-a_{\mu}^{W-TM}(l)=P[0]\frac{a^2}{\log (w_0/2/a)^2}-P[1] \frac{10 }{ 9} \Delta_{GS}a^2 \]
\(\chi^2_{dof}=\) 22.8574
\(P[ 0 ]=\) -2.91(26)e-8
\(P[ 1 ]=\) 77(61)