10.2 \(a_{\mu}^{W}\) cov

10.2.1 quadratic

The continuum fit is done with the function \[ \begin{cases} a_{\mu}^{W}(eq,\ell)+\frac{10}{9}\Delta_{GS}=P[0]+a^2P[1]- \frac{10}{9}\Delta_{GS}(P[3]a^2)+ P[5](M_{\pi}-M_{\pi}^{phys})\\ a_{\mu}^{W}(op,\ell)+\frac{10}{9}\Delta_{GS}=P[0]+a^2P[2]-\frac{10}{9}\Delta_{GS}(P[4]a^2)+ P[5](M_{\pi}-M_{\pi}^{phys}) \end{cases} \]

\[\begin{gather} \chi^2/d.o.f.=0.00614783 \\ P[0]=2.10501e-08\pm (4e-10) \\ P[1]=-2.71802e-07\pm (1.7e-07) \\ P[2]=-1.87139e-07\pm (1.7e-07) \\ P[3]=-186.451\pm (59) \\ P[4]=123.097\pm (88) \\ P[5]=1.87816e-05\pm (1.7e-05) \\ P[6]=2.44009e-05\pm (1.7e-05) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.99& -0.99& -0.0343& -0.0932& 0.979& 0.977\\ -0.99& 1& 0.99& 0.114& 0.142& -0.982& -0.997\\ -0.99& 0.99& 1& 0.0671& 0.181& -0.997& -0.98\\ -0.0343& 0.114& 0.0671& 1& 0.223& -0.0715& -0.136\\ -0.0932& 0.142& 0.181& 0.223& 1& -0.191& -0.162\\ 0.979& -0.982& -0.997& -0.0715& -0.191& 1& 0.975\\ 0.977& -0.997& -0.98& -0.136& -0.162& 0.975& 1\\ \end{pmatrix} \\det=0\\ \end{gather}\]}

we plot \(a_\mu^W(eq(op))+\frac{10}{9}\Delta_{GS}+\frac{10}{9}\Delta_{GS} P[3(4)]a^2\)

title<- paste("amu_W_l_RF__w1_a4_eq_op_common__cov")
file=sprintf("./shiny/fit_plots/fit_all/%s_fit_P.dat",title)
df<-read_fit_P_file(file)
cat("$\\chi^2_{dof}=$",df$chi2,"\n\n")

\(\chi^2_{dof}=\) 1.23569

for(i in seq_along(df$P[,1]) )
  cat("$P[",i-1,"]=$",mean_print(df$P[i,2],df$P[i,3] ),"\n\n")

\(P[ 0 ]=\) 2.108(40)e-8

\(P[ 1 ]=\) -2.7(1.7)e-7

\(P[ 2 ]=\) -2.2(1.7)e-7

\(P[ 3 ]=\) -163(57)

\(P[ 4 ]=\) 88(88)

\(P[ 5 ]=\) 2.4(1.6)e-5

file=sprintf("./shiny/fit_plots/fit_all/%s_fit_out_ysub_afm.txt",title)
if(!file.exists(file)){
  file=sprintf("./fit_all/%s_fit_data.txt",title)
}
df<- read.table(file, header=FALSE, fill=TRUE)


gg<- myggplot()
idy<-9
gg<-gg+  geom_point(data=df, mapping=aes(x=df[,1] , y=df[,idy],
                          color=as.factor(df[,idy+2]), shape=as.factor(df[,idy+2])) 
                    ,width=1e-4)  +labs(color = "", shape="")
gg<-gg + geom_errorbar(data=df, mapping=aes(x=df[,1] , ymin=df[,idy]-df[,idy+1],
               ymax=df[,idy]+df[,idy+1],color=as.factor(df[,idy+2]),shape=as.factor(df[,idy+2]) ) 
               ,width=1e-4)


df[,7]<-plyr::laply(df[,7],eq_op)
datalist = list()
for (n in c(1:2)){
  
file=sprintf("/home/garofalo/analysis/g-2/fit_all/%s_fit_out_n%d_afm.txt",title,n-1)
datalist[[n]]<- read.table(file, header=FALSE, fill=TRUE,   
                 col.names=c(paste0("x",n),paste0("fit",n),paste0("fiterr",n)))

gg<-gg + geom_ribbon(data=datalist[[n]], mapping=aes_string(x=datalist[[n]][,1] , ymin=datalist[[n]][,2]-datalist[[n]][,3], ymax=datalist[[n]][,2]+datalist[[n]][,3]),alpha=0.5, fill="red")
gg<-gg + geom_line(data=datalist[[n]], mapping=aes_string(x=datalist[[n]][,1] , y=datalist[[n]][,2]  ),color="red" )

}

fig<- myplotly(gg,"","$a^2(\\mbox{fm})$", "$a_{\\mu}^{W}(\\ell)$", to_print = TRUE)

title<- paste("amu_W_l_RF__w1_a4_eq_op__cov")
file=sprintf("./shiny/fit_plots/fit_all/%s_fit_P.dat",title)
df<-read_fit_P_file(file)
cat("$\\chi^2_{dof}=$",df$chi2,"\n\n")

\(\chi^2_{dof}=\) 0.00614783

for(i in seq_along(df$P[,1]) )
  cat("$P[",i-1,"]=$",mean_print(df$P[i,2],df$P[i,3] ),"\n\n")

\(P[ 0 ]=\) 2.105(40)e-8

\(P[ 1 ]=\) -2.7(1.7)e-7

\(P[ 2 ]=\) -1.9(1.7)e-7

\(P[ 3 ]=\) -186(59)

\(P[ 4 ]=\) 123(88)

\(P[ 5 ]=\) 1.9(1.7)e-5

\(P[ 6 ]=\) 2.4(1.7)e-5

file=sprintf("./shiny/fit_plots/fit_all/%s_fit_out_ysub_afm.txt",title)
if(!file.exists(file)){
  file=sprintf("./fit_all/%s_fit_data.txt",title)
}
df<- read.table(file, header=FALSE, fill=TRUE)


gg<- myggplot()
idy<-9
gg<-gg+  geom_point(data=df, mapping=aes(x=df[,1] , y=df[,idy],
                          color=as.factor(df[,idy+2]), shape=as.factor(df[,idy+2])) 
                    ,width=1e-4)  +labs(color = "", shape="")
gg<-gg + geom_errorbar(data=df, mapping=aes(x=df[,1] , ymin=df[,idy]-df[,idy+1],
               ymax=df[,idy]+df[,idy+1],color=as.factor(df[,idy+2]),shape=as.factor(df[,idy+2]) ) 
               ,width=1e-4)


df[,7]<-plyr::laply(df[,7],eq_op)
datalist = list()
for (n in c(1:2)){
  
file=sprintf("/home/garofalo/analysis/g-2/fit_all/%s_fit_out_n%d_afm.txt",title,n-1)
datalist[[n]]<- read.table(file, header=FALSE, fill=TRUE,   
                 col.names=c(paste0("x",n),paste0("fit",n),paste0("fiterr",n)))

gg<-gg + geom_ribbon(data=datalist[[n]], mapping=aes_string(x=datalist[[n]][,1] , ymin=datalist[[n]][,2]-datalist[[n]][,3], ymax=datalist[[n]][,2]+datalist[[n]][,3]),alpha=0.5, fill="red")
gg<-gg + geom_line(data=datalist[[n]], mapping=aes_string(x=datalist[[n]][,1] , y=datalist[[n]][,2]  ),color="red" )

}

fig<- myplotly(gg,"","$a^2(\\mbox{fm})$", "$a_{\\mu}^{W}(\\ell)$", to_print = TRUE)