added function ca(beta)

constants/juobs_const.jl

@@ -99,4 +99,39 @@ zv(beta::Float64)         = Zv[b_values .== beta][1]
 zs_over_zp(beta::Float64) = ZS_over_ZP[b_values .== beta][1]
 rm(beta::Float64)         = RM[b_values .== beta][1]
 ba_bp(beta::Float64)      = BA_BP[b_values .== beta][1]
-Z(beta::Float64)          = ZZ[b_values .== beta][1]
\ No newline at end of file
+Z(beta::Float64)          = ZZ[b_values .== beta][1]
+
+
+@doc raw""" 
+  ca(beta:Float64; verbose::Bool = true, acceptance:Float64=10^-2)
+
+it compute the ca coefficient of the axial vector current improvement
+As of now, check whether g_0^2 < 1.8+acceptance and if true give ca according to arXiv:1502.04999
+otherwise it gives 0
+The default value of acceptance has no real justification at the moment
+If verbose = true, it prints a warning if the g_0^2 is > 1.8  
+
+"""
+
+function ca(beta::Float64; verbose::Bool = true, acceptance::Float64 = 10^-2)
+  g02 = 6/beta; 
+  if (1.8-g02)>-acceptance # for g_0^2 about 1.8 and below it work. I decided on a 10^-2 acceptance range
+    p0 = 9.2056
+    p1 = -13.9847
+    e= exp(p0+p1/g02)
+    return -0.006033*g02*(1+e)
+  end
+  if verbose
+    @warn raw"""
+    no valid expression for g_0^2>1.8
+    your g_0^2 = $(g02)
+    return value set to 0. 
+    If you want to use this formula, then modify the acceptance value by calling
+    ```@example
+    ca(beta, acceptance=<your value>) 
+    ``` 
+    """
+  end
+  return 0.0
+end
+