12.1 aW−OSμ(l)−aW−TMμ(l)

12.1.1 plot of the difference:

aW−OSμ(l)−aW−TMμ(l)=P[0]a2−P[1]109ΔGSa2

χ2dof= 4.65289

P[0]= -4.75(37)e-8

P[1]= -174(71)

00.0020.0040.0060.008−4e−10−3.5e−10−3e−10−2.5e−10−2e−10−1.5e−10−1e−10−0.5e−100
amu_W_l_diff__w1___cov$a^2(\mbox{fm})$$a_{\mu}^{W,OS}(\ell)-a_{\mu}^{W,TM}(\ell)$

12.1.2 adding Mπ dependence:

aW−OSμ(l)−aW−TMμ(l)=P[0]a2−P[1]109ΔGSa2+P[2](Mπ−Mphysπ) the units of P[2] are MeV−1, in the plot the point are shifted to Mphysπ

χ2dof= 7.20142

P[0]= -3.95(60)e-8

P[1]= -179(73)

P[2]= -9.8(6.3)e-12

00.0020.0040.0060.008−3.5e−10−3e−10−2.5e−10−2e−10−1.5e−10−1e−10−0.5e−100
amu_W_l_diff__w1__Mpi_cov$a^2(\mbox{fm})$$a_{\mu}^{W,OS}(\ell)-a_{\mu}^{W,TM}(\ell)$

12.1.3 logarithm:

this fit does not work

aW−OSμ(l)−aW−TMμ(l)=P[0]a2log(w0/a)3−P[1]109ΔGSa2

χ2dof= 21.8474

P[0]= -1.49(13)e-7

P[1]= 64(62)

00.0010.0020.0030.0040.0050.0060.0070.008−5e−10−4e−10−3e−10−2e−10−1e−100
amu_W_l_diff_log_3_w1___cov$a^2(\mbox{fm})$$a_{\mu}^{W,OS}(\ell)-a_{\mu}^{W,TM}(\ell)$

12.1.4 a4

aW−OSμ(l)−aW−TMμ(l)=P[0]a2−P[1]109ΔGSa2+P[2]a4

χ2dof= 0.0130655

P[0]= -9.9(1.8)e-8

P[1]= -295(80)

P[2]= 8.0(2.7)e-6

00.0020.0040.0060.008−3.5e−10−3e−10−2.5e−10−2e−10−1.5e−10−1e−10−0.5e−100
amu_W_l_diff__w1_a4__cov$a^2(\mbox{fm})$$a_{\mu}^{W,OS}(\ell)-a_{\mu}^{W,TM}(\ell)$

12.1.5 logarithm with exponent 2

this fit does not work

aW−OSμ(l)−aW−TMμ(l)=P[0]a2log(w0/2/a)2−P[1]109ΔGSa2

χ2dof= 22.8574

P[0]= -2.91(26)e-8

P[1]= 77(61)

00.0010.0020.0030.0040.0050.0060.0070.008−6e−10−5e−10−4e−10−3e−10−2e−10−1e−100
amu_W_l_diff_log_2_w2___cov$a^2(\mbox{fm})$$a_{\mu}^{W,OS}(\ell)-a_{\mu}^{W,TM}(\ell)$

12.1.6 logarithm with exponent 1

this fit does not work

aW−OSμ(l)−aW−TMμ(l)=P[0]a2log(w0/2/a)1−P[1]109ΔGSa2

χ2dof= 15.0696

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

P[1]= -22(65)

00.0010.0020.0030.0040.0050.0060.0070.008−5e−10−4e−10−3e−10−2e−10−1e−100
amu_W_l_diff_log_1_w2___cov$a^2(\mbox{fm})$$a_{\mu}^{W,OS}(\ell)-a_{\mu}^{W,TM}(\ell)$

12.1.7 logarithm with exponent -0.2

this fit does not work

aW−OSμ(l)−aW−TMμ(l)=P[0]a2log(w0/2/a)−0.2−P[1]109ΔGSa2

χ2dof= 2.74557

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

P[1]= -209(73)

00.0020.0040.0060.008−4e−10−3.5e−10−3e−10−2.5e−10−2e−10−1.5e−10−1e−10−0.5e−10
amu_W_l_diff_log_-0.2_w2___cov$a^2(\mbox{fm})$$a_{\mu}^{W,OS}(\ell)-a_{\mu}^{W,TM}(\ell)$