## 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)

### 12.1.6 logarithm with exponent 1

this fit does not work

$a_{\mu}^{W-OS}(l)-a_{\mu}^{W-TM}(l)=P[0]\frac{a^2}{\log (w_0/2/a)^1}-P[1] \frac{10 }{ 9} \Delta_{GS}a^2$

$$\chi^2_{dof}=$$ 15.0696

$$P[ 0 ]=$$ -3.70(31)e-8

$$P[ 1 ]=$$ -22(65)

### 12.1.7 logarithm with exponent -0.2

this fit does not work

$a_{\mu}^{W-OS}(l)-a_{\mu}^{W-TM}(l)=P[0]\frac{a^2}{\log (w_0/2/a)^{-0.2}}-P[1] \frac{10 }{ 9} \Delta_{GS}a^2$

$$\chi^2_{dof}=$$ 2.74557

$$P[ 0 ]=$$ -4.96(38)e-8

$$P[ 1 ]=$$ -209(73)