add function for computing GL FSE correction factors

R/gl_fse_corr.R

@@ -0,0 +1,32 @@
+#' apply parameter-free Gasser-Leutwyler FSE corrections
+#' @details Apply FSE correction of a meson mass and decay constant
+#' based on eqs. 8 and 9 of Colangeo, Duerr, Haefeli [Nucl.Phys.B 721 (2005)]
+#' going back to Gasser and Leutwyler. Note that we employ the normalisation
+#' in which f_pi = 130.4.
+#' Note that \code{xi} and \code{lambda} below can be either of length one
+#' or of the same length as the vectors \code{Mps_V} and \code{fps_V}. When
+#' applying the correction to bootstrap samples, it might make sense
+#' to pass the original data values for \code{xi} and \code{lambda}.
+#' @param Mps_V Numeric vector, meson masses in any type of units. 
+#' @param fps_V Numeric vector, meson decay constants in the same units as
+#' \code{Mps_V}.
+#' @param xi Numeric vector, the ratio \eqn{M_{ps}^2 / (4 \pi f_\pi)^2}. Either of length
+#' one, in which case it is used for all \code{Mps_V} and \code{fps_V} or of the same
+#' length as \code{Mps_V} and \code{fps_V}. 
+#' @param lambda Numeric, the dimensionless product \eqn{M_{ps} \cdot L}. 
+#' @return Data frame with two columns containing the correction factors \code{K_mps}
+#' and \code{K_fps} for which we have:
+#' \deqn{ M_{ps}(L) = M_{ps}(\infty) \cdot K_{M_{ps} + \mathcal{O}(M_{ps} \xi^2) }
+#' \deqn{ f_{ps}(L) = f_{ps}(\infty) \cdot K_{f_{ps} + \mathcal{O}(f_{ps} \xi^2) }
+#' @export
+gl_fse_corr <- function(Mps_V, fps_V, xi, lambda){
+  stopifnot( length(xi) == length(lambda) )
+  stopifnot( length(Mps_V) == length(fps_V) )
+  if( length(xi) > 1 ){
+    stopifnot( length(xi) == length(Mps_V) )
+  }
+
+  g1_tilde <- g1(lambda)
+  return(data.frame(K_Mps = (1+0.5*xi*g1_tilde), K_fps = (1-2*xi*g1_tilde)))
+}
+