<- data.frame(
df "en" = c("B64", "C80","96"),
"kappa" = c(0.139426500000, 0.138752850000, 0.137972174000),
"mul_sim" = c(0.00072, 0.0006, 0.00054),
"musig_sim" = c(0.1315052, 0.107146000965, 0.087911000000),#0.077706999882
"mudel_sim" = c(0.1246864, 0.106585999855, 0.086224000000),#0.074646999976
"ms_sim" = c(0,0,0),
"mc_sim" = c(0,0,0),
"Zp_Zs" = c(0.79018, 0.82308, 0.85095),
"mul" = c(0.0006669, 0.0005864, 0.0004934),
"musig" = c(0,0,0),
"mudel" = c(0,0,0),
"ms_iso" = c(0.018267, 0.016053, 0.013559),
"mc_iso" = c(0.23134, 0.19849, 0.16474)
)
12 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_iso + mc_iso) / 2,
mudel = (mc_iso - ms_iso) / Zp_Zs / 2
)print(df$mc_sim,digits = 12)
[1] 0.230029899552 0.194874805726 0.161283312800
kable(df[, c(1:7)], digits = 20)
en | kappa | mul_sim | musig_sim | mudel_sim | ms_sim | mc_sim |
---|---|---|---|---|---|---|
B64 | 0.1394265 | 0.00072 | 0.1315052 | 0.1246864 | 0.03298050 | 0.2300299 |
C80 | 0.1387529 | 0.00060 | 0.1071460 | 0.1065860 | 0.01941720 | 0.1948748 |
96 | 0.1379722 | 0.00054 | 0.0879110 | 0.0862240 | 0.01453869 | 0.1612833 |
kable(df[, c(8:13)], digits = 20)
Zp_Zs | mul | musig | mudel | ms_iso | mc_iso |
---|---|---|---|---|---|
0.79018 | 0.0006669 | 0.1248035 | 0.13482561 | 0.018267 | 0.23134 |
0.82308 | 0.0005864 | 0.1072715 | 0.11082580 | 0.016053 | 0.19849 |
0.85095 | 0.0004934 | 0.0891495 | 0.08883072 | 0.013559 | 0.16474 |
now we cange only the charm keeping the strange at the simulation point
library(dplyr)
library(knitr)
<- mutate(df,
df1 musig = (ms_sim + mc_iso) / 2,
mudel = (mc_iso - 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 | 0.1315052 | 0.0006669 | 0.13216025 |
C80 | 0.1387529 | 0.00060 | 0.1071460 | 0.0005864 | 0.10895360 |
96 | 0.1379722 | 0.00054 | 0.0879110 | 0.0004934 | 0.08963934 |
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 | 0.1315052 | 0.1309269 | 0.1239545 |
C80 | 0.1387529 | 0.00060 | 0.1071460 | 0.1241452 | 0.1272392 |
96 | 0.1379722 | 0.00054 | 0.0879110 | 0.1217060 | 0.1259384 |
options(digits=16)
cat("2*kap*mub = ", df1$kappa*2*df1$musig,"\n")
2*kap*mub = 0.03650935611963307 0.03445101120121027 0.0335840782922007
cat("2*kap*epsb = ", df1$kappa*2*df1$mudel,"\n")
2*kap*epsb = 0.03456509229315717 0.03530960365515591 0.03475199451439068
cat("denominator\n")
denominator
cat("2*kap*mub = ", df1$kappa*2*df1$musig_sim,"\n")
2*kap*mub = 0.0366706195356 0.029733625999993 0.024258543577028
cat("2*kap*epsb = ", df1$kappa*2*df1$mudel_sim,"\n")
2*kap*epsb = 0.0347691766992 0.02957822249996168 0.023793025461952