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4  Pion B64

4.1 Pion only sea corrections

M_{PS} = 0.056583(49) χ2/dof= 1.4645

M_{PS}+mul_correction = 0.056562(48) χ2/dof= 1.5369

M_{PS}+mus_correction = 0.056579(69) χ2/dof= 1.0714

M_{PS}+muc_correction = 0.05636(41) χ2/dof= 0.56652

010203040506000.10.20.30.40.50.60.7
\verb|M_{PS}|\verb|M_{PS}+mul_correction|\verb|M_{PS}+mus_correction|\verb|M_{PS}+muc_correction|\verb|M_{PS}_rewlTM|\verb|M_{PS}_rewsOS|\verb|M_{PS}_rewcOS|\verb|M_{PS}_rew_scndgTM|\verb|M_{PS}_rewcOS_0.25|\verb|M_{PS}_rewcOS_0.02|\verb|M_{PS}_rew_charm0.1_strange0_ndgTM|$t/a$$m_{eff}(t)$

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4.2 fπ

f_{PS} = 0.052556(66) , χ2/dof= 0.086138

f_{PS}+mul_correction = 0.052677(62) , χ2/dof= 0.11058

f_{PS}+mus_correction = 0.05245(10) , χ2/dof= 0.02969

f_{PS}+muc_correction = 0.05273(63) , χ2/dof= 0.012943

df_{PS}/dmuc_correction = 0.06(21) χ2/dof= 0

f_{PS}+muc_correction = 0.05273(63) χ2/dof= 0.012943

f_{PS}_rewlTM = 0.052421(79) , χ2/dof= 0.064406

df_{PS}/drewlTM = 2.55(52) χ2/dof= 0

f_{PS}_rewsOS = 0.052544(86) , χ2/dof= 0.069855

f_{PS}_rewcOS = 0.05164(27) , χ2/dof= 0.91234

f_{PS}_rew_scndgTM = χ2/dof= -nan

f_{PS}_rewcOS_0.25 = 0.05232(17) , χ2/dof= 0.0143

df_{PS}/drewcOS_0.25 = -0.34(21) χ2/dof= 0

f_{PS}(mciso)_rewcOS_0.25 = 0.05161(63) χ2/dof= 0

f_{PS}_rewcOS_0.02 = 0.052555(66) , χ2/dof= 0.085302

df_{PS}/drewcOS_0.02 = -0.01(11) χ2/dof= 0

f_{PS}(mciso)_rewcOS_0.02 = 0.05251(31) χ2/dof= 0

df_{PS}/drewcOS_0.1 = -0.09(13) χ2/dof= 0

f_{PS}(mciso)_rewcOS_0.1 = 0.05231(38) χ2/dof= 0

[1] “same statistic of gm2 LMA” df_{PS}/drewcOS_0.1 = -0.20(11) χ2/dof= 0

f_{PS}(mciso)_rewcOS_0.1 = 0.05204(31) χ2/dof= 0

[1] “—” df_{PS}/drew_charm0.1_strange0_ndgTM = 0.04(17) χ2/dof= 0

f_{PS}(mciso)_rew_charm0.1_strange0_ndgTM = 0.05265(47) χ2/dof= 0

01020304050600.010.0120.0140.0160.018
\verb|f_{PS}|\verb|f_{PS}+mul_correction|\verb|f_{PS}+mus_correction|\verb|f_{PS}+muc_correction|\verb|f_{PS}_rewlTM|\verb|f_{PS}_rewsOS|\verb|f_{PS}_rewcOS|\verb|f_{PS}_rew_scndgTM|\verb|f_{PS}_rewcOS_0.25|\verb|f_{PS}_rewcOS_0.02|$t/a$$af_{PS}(t)$

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4.3 Analytic derivative

Delta_mul_f_{PS} = -2.26(36) , χ2/dof= 0.016969

0102030405060−2.5−2−1.5−1
\verb|Delta_mul_f_{PS}|$t/a$$af_{PS}(t)$

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4.4 derivative

dM_{PS}/dmul_correction dM_{PS}/dmus_correction dM_{PS}/dmuc_correction dM_{PS}/drewlTM dM_{PS}/drewsOS dM_{PS}/drew_charm0.1_strange0_ndgTM dM_{PS}/drewcOS_0.02 dM_{PS}/drewcOS_0.25−0.200.2
$dM/d\mu$

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0200400600800100012001400−1−0.500.511.5
(df_{PS}/dmuc_correction,loop)(df_{PS}/dmul_correction,loop)(df_{PS}/dmus_correction,loop)(df_{PS}/drew_0.01_to_0.01027408_OS,rew)(df_{PS}/drew_0.03125_to_0.03152408_OS,rew)(df_{PS}/drew_0.1232229005_to_0.1234969805_OS,rew)(df_{PS}/drew_charm0.1_strange0_ndgTM,rew)(df_{PS}/drewcOS_0.02,rew)(df_{PS}/drewcOS_0.1,rew)(df_{PS}/drewcOS_0.25,rew)(df_{PS}/drewlTM,rew)(df_{PS}/drewsOS,rew)$1/am$$df_{PS}/d\mu$
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00.050.10.150.2−1−0.500.511.5
(df_{PS}/dmuc_correction,loop)(df_{PS}/dmul_correction,loop)(df_{PS}/dmus_correction,loop)(df_{PS}/drew_0.01_to_0.01027408_OS,rew)(df_{PS}/drew_0.03125_to_0.03152408_OS,rew)(df_{PS}/drew_0.1232229005_to_0.1234969805_OS,rew)(df_{PS}/drew_charm0.1_strange0_ndgTM,rew)(df_{PS}/drewcOS_0.02,rew)(df_{PS}/drewcOS_0.1,rew)(df_{PS}/drewcOS_0.25,rew)(df_{PS}/drewlTM,rew)(df_{PS}/drewsOS,rew)$am$$df_{PS}/d\mu$

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02004006008001000120014001600−2−1.5−1−0.500.511.5
looprew$1/am$$f_{PS}d(M_{PS}/f_{PS})/d\mu$

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Warning: The shape palette can deal with a maximum of 6 discrete values because more
than 6 becomes difficult to discriminate
ℹ you have requested 7 values. Consider specifying shapes manually if you need
  that many of them.
0200400600800100012001400−2−1.5−1−0.500.511.5
f_{PS}d(M_{PS}/f_{PS})/dmuc_correctionf_{PS}d(M_{PS}/f_{PS})/dmul_correctionf_{PS}d(M_{PS}/f_{PS})/dmus_correctionf_{PS}d(M_{PS}/f_{PS})/drewcOS_0.02f_{PS}d(M_{PS}/f_{PS})/drewcOS_0.25f_{PS}d(M_{PS}/f_{PS})/drewlTMf_{PS}d(M_{PS}/f_{PS})/drewsOS$1/am$$f_{PS}d(M_{PS}/f_{PS})/d\mu$

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4.5 der correlator

dC(t=20)/drewlTM dC(t=20)/drewsOS dC(t=20)/drewcOS_0.25−0.500.511.52
dC(t=20)/drewlTM dC(t=20)/drewsOS dC(t=20)/drewcOS_0.25$dC(t=20)/d\mu$

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4.6 mpcac sea corrections

mpcac = 1.82(83)e-5 χ2/dof= 0.86109

mpcac+mul_correction = 1.5(1.3)e-6 χ2/dof= 2.795

mpcac+mus_correction = 1.5(1.3)e-6 χ2/dof= 2.795

mpcac+muc_correction = 1.5(1.3)e-6 χ2/dof= 2.795

010203040506000.010.020.030.040.050.060.07
\verb|mpcac|\verb|mpcac+mul_correction|\verb|mpcac+mus_correction|\verb|mpcac+muc_correction|\verb|mpcac_rewlTM|\verb|mpcac_rewsOS|\verb|mpcac_rewcOS|$t/a$$m_{pcac}(t)$

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5 sources scaling

01020304050600.10.20.30.40.50.6
\verb|M_{PS}_rewlTM_100s|\verb|M_{PS}_rewlTM_50s|\verb|M_{PS}_rewlTM_25s|\verb|M_{PS}_rewlTM_1s|$t/a$$m_{eff}(t)$

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01020304050600.10.20.30.40.50.6
\verb|M_{PS}_rewcOS_0.1_h20|\verb|M_{PS}_rewcOS_0.1_h10|\verb|M_{PS}_rewcOS_0.1_h5|$t/a$$m_{eff}(t)$

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5.1 rew history

the step in strange is dmu=-5.942533e-4 while in all the other is set to 0.1 the step for the charm dmu=2.35147398e-4

20040060080010001200012345
c h20c h10c h5s 0.01-0.01027 conf$e^{w(U)-<w>}$

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10020030040050060070001e+72e+73e+74e+75e+76e+7
charm_0.25charmconf$e^{w(U)-<w>}$

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5.2 histogram jackknife distribution

The error is the width of the distribution multiplied by √N−1

5.3 histogram loop

5.4 histogram rew