<- data.frame(
df "en" = c("B64", "C80"),
"kappa" = c(0.139426500000, 0.138752850000),
"mul_sim" = c(0.00072, 0.0006),
"musig_sim" = c(0.1246864, 0.106585999855),
"mudel_sim" = c(0.1315052, 0.107146000965),
"ms_sim" = c(0,0),
"mc_sim" = c(0,0),
"Zp_Zs" = c(0.79018, 0.82308),
"mul" = c(0.0006669, 0.0005864),
"musig" = c(0,0),
"mudel" = c(0,0),
"ms" = c(0.018267, 0.016053),
"mc" = c(0.23134, 0.19849)
)
9 ndg params
A matching between the ndg parameter and the OS can be defined as
This matching scheme has the problem that needs to be know very precise to estimate well the cancellation in the .
An alternative scheme used in the gm2 strange and charm paper is where is some value close enough to such higer order in the expansion are negligible. The derivative is splitted in sea and valence contribution the derivative with respect to the valence is computed as finite difference and the derivative with respect to the sea is computed with the scalar insertions.
library(dplyr)
Attaching package: 'dplyr'
The following objects are masked from 'package:stats':
filter, lag
The following objects are masked from 'package:base':
intersect, setdiff, setequal, union
library(knitr)
# df$ms_sim<- df$musig_sim- df$
<- mutate(df,
df ms_sim = musig_sim - Zp_Zs * mudel_sim,
mc_sim = musig_sim + Zp_Zs * mudel_sim
)
<- mutate(df,
df musig = (ms + mc) / 2,
mudel = (mc - ms) / Zp_Zs / 2
)print(df$mc_sim,digits = 12)
[1] 0.228599178936 0.194775730329
kable(df[, c(1:7)], digits = 20)
en | kappa | mul_sim | musig_sim | mudel_sim | ms_sim | mc_sim |
---|---|---|---|---|---|---|
B64 | 0.1394265 | 0.00072 | 0.1246864 | 0.1315052 | 0.02077362 | 0.2285992 |
C80 | 0.1387529 | 0.00060 | 0.1065860 | 0.1071460 | 0.01839627 | 0.1947757 |
kable(df[, c(8:13)], digits = 20)
Zp_Zs | mul | musig | mudel | ms | mc |
---|---|---|---|---|---|
0.79018 | 0.0006669 | 0.1248035 | 0.1348256 | 0.018267 | 0.23134 |
0.82308 | 0.0005864 | 0.1072715 | 0.1108258 | 0.016053 | 0.19849 |
now we cange only the charm keeping the strange at the simulation point
library(dplyr)
library(knitr)
<- mutate(df,
df1 musig = (ms_sim + mc) / 2,
mudel = (mc - ms_sim) / Zp_Zs / 2
)# musigma = 0.1260567
# mudelta = 0.1332397
# 2Kappamubar = 0.0351512889651
# 2KappaEpsBar = 0.0371542900641
# kappa = 0.1394265
#
# #epsbar = 0.1394265
# 2Kappamubar2 = 0.034769065158
# 2KappaEpsBar2 = 0.036670563765
# kappa2 = 0.1394265
kable(df1[, c(1, 2, 3, 4, 9, 10)], digits = 13)
en | kappa | mul_sim | musig_sim | mul | musig |
---|---|---|---|---|---|
B64 | 0.1394265 | 0.00072 | 0.1246864 | 0.0006669 | 0.1260568 |
C80 | 0.1387529 | 0.00060 | 0.1065860 | 0.0005864 | 0.1084431 |
library(dplyr)
library(knitr)
# keeping ms fixed and change mc form
# mc_sim =0.2285992
=0.22887328 # 0.1 of the iso-sim step
mc_targ <- mutate(df,
df1 musig = (ms_sim + mc_targ) / 2,
mudel = (mc_targ - ms_sim) / Zp_Zs / 2
)kable(df1[, c(1, 2, 3, 4, 10,11)], digits = 16)
en | kappa | mul_sim | musig_sim | musig | mudel |
---|---|---|---|---|---|
B64 | 0.1394265 | 0.00072 | 0.1246864 | 0.1248235 | 0.1316786 |
C80 | 0.1387529 | 0.00060 | 0.1065860 | 0.1236348 | 0.1278594 |
options(digits=16)
cat("2*kap*mub = ", df1$kappa*2*df1$musig,"\n")
2*kap*mub = 0.0348073936511998 0.03430935469479172
cat("2*kap*epsb = ", df1$kappa*2*df1$mudel,"\n")
2*kap*epsb = 0.03671898440436382 0.0354817090476069
cat("denominator\n")
denominator
cat("2*kap*mub = ", df1$kappa*2*df1$musig_sim,"\n")
2*kap*mub = 0.0347691766992 0.02957822249996168
cat("2*kap*epsb = ", df1$kappa*2*df1$mudel_sim,"\n")
2*kap*epsb = 0.0366706195356 0.029733625999993