Processing math: 100%

kappa 0.140064

This is a unitary setup κsea=κvalence

Correlators

P5P5 = 0.2358(36) χ2/dof= 883.81

V0P5 = 0.01329(25) χ2/dof= 8479.2

A0P5 = -0.00475(12) χ2/dof= 10.826

V0P5_insP = -0.313(22) χ2/dof= 5.3516

020406080100−0.4−0.3−0.2−0.100.10.20.30.4
labelP5P5V0P5A0P5V0P5_insPmeffy

MPS

MPS= 167.3(2.1) MeV

M_{PS} = 0.07698(95) χ2/dof= 0.43318

ΔM

Here we compute the variation of MPS respect to the bare mass m

DeltaM = -2.09(14) χ2/dof= 0.37252

DeltaMt = 18(41) χ2/dof= 0.33376

010203040−2e+4−1e+401e+42e+4
labelDeltaMDeltaMtmeffty

mpcac

mpcac = -0.001079(78) χ2/dof= 0.79115

deltam = 0.0120(14) χ2/dof= 2.1906

deltam_sub = 0.00713(29) χ2/dof= 0.38428

01020304000.0050.010.0150.020.025
labeldeltamdeltam_submeffty

new estimate of κcr

Expanding in taylor series in m the correlator and observing that mO=OP5 (there is a factor two in the correlator that in the code is called V0P5P5 since insertion of P5 is done in only one quark line)

V0P5(mcr)=V0P5(m)+iδmV0P5P5(m) since V0P5(mcr)=0 then

δm=V0P5iV0P5P5 using the fact that the numerator is purely immaginary and the denominator real we have δm=Im(V0P5)Re(V0P5P5)

form the relation κ=1/(2m+8) we have

κcr=κ(1+2δmκ). Since the correlator V0P5P5 is not flat in time but linear when we are far from maximal twist, we can subtract the linear part V0P5=B(eMteM(Tt))mV0P5=iV0P5P5=(mB)(eMteM(Tt))(mM)B(teMt(Tt)eM(Tt)) with mM computed in the section before

## Current $kappa=0.140064$
## $kappa_{cr}$= 0.139595(54)
## $kappa_{cr,sub}$= 0.139785(11)

kappa 0.139779

This is not a unitary setup κsea=0.140064

MPS

MPS= 143.3(1.6) MeV

M_{PS} = 0.06596(72) χ2/dof= 0.25425

ΔM

DeltaM = 1.07(13) χ2/dof= 0.23577

DeltaMt = 39(20) χ2/dof= 0.031808

010203040−4000−3000−2000−100001000200030004000
labelDeltaMDeltaMtmeffty

mpcac

mpcac = 0.000431(44) χ2/dof= 0.90198

deltam = -0.00225(18) χ2/dof= 0.55268

deltam_sub = -0.00212(15) χ2/dof= 0.47876

010203040−0.025−0.02−0.015−0.01−0.0050
labeldeltamdeltam_submeffty

new estimate of κcr

## Current $kappa=0.139779$
## $kappa_{cr}$= 0.1398671(71)
## $kappa_{cr,sub}$= 0.1398617(58)

kappa 0.1398563

This is not a unitary setup κsea=0.140064

MPS

M_{PS} = 0.06428(68) χ2/dof= 0.41313

MPS= 139.7(1.5) MeV

ΔM

DeltaM = 0.05(11) χ2/dof= 0.25218

DeltaMt = 1.4(4.9) χ2/dof= 2.2876

010203040−3000−2000−1000010002000
labelDeltaMDeltaMtmeffty

mpcac

mpcac = 2.7(53.4)e-6 χ2/dof= 0.74192

deltam = -0.00024(17) χ2/dof= 0.36804

deltam_sub = -0.00024(17) χ2/dof= 0.36914

010203040−0.01−0.008−0.006−0.004−0.0020
labeldeltamdeltam_submeffty

new estimate of κcr

## Current $kappa=0.1398563$
## $kappa_{cr}$= 0.1398656(65)
## $kappa_{cr,sub}$= 0.1398656(65)