Fixing bug in the massive NLO CC coefficient functions

vbertone · May 26, 2020 · 1e057d4 · 1e057d4
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Showing 14 changed files with 23 additions and 35 deletions.
diff --git a/doc/pdfs/CC_observables_def.pdf b/doc/pdfs/CC_observables_def.pdf
diff --git a/doc/pdfs/Complex_DGLAP.pdf b/doc/pdfs/Complex_DGLAP.pdf
diff --git a/doc/pdfs/DIS.pdf b/doc/pdfs/DIS.pdf
diff --git a/doc/pdfs/Evolution_code.pdf b/doc/pdfs/Evolution_code.pdf
diff --git a/doc/pdfs/Lagrange_derivative.pdf b/doc/pdfs/Lagrange_derivative.pdf
diff --git a/doc/pdfs/Luminosities.pdf b/doc/pdfs/Luminosities.pdf
diff --git a/doc/pdfs/QCD_QED_common_basis.pdf b/doc/pdfs/QCD_QED_common_basis.pdf
diff --git a/doc/pdfs/TruncatedSolution.pdf b/doc/pdfs/TruncatedSolution.pdf
diff --git a/doc/pdfs/intrinsic_charm.pdf b/doc/pdfs/intrinsic_charm.pdf
diff --git a/doc/pdfs/manual.pdf b/doc/pdfs/manual.pdf
diff --git a/doc/pdfs/matching_conditions.pdf b/doc/pdfs/matching_conditions.pdf
diff --git a/doc/pdfs/running_mass.pdf b/doc/pdfs/running_mass.pdf
diff --git a/doc/sources/DIS.tex b/doc/sources/DIS.tex
@@ -492,7 +492,7 @@ \subsubsection{Charged Current Coefficient Functions}
                    z)}{1-z}\right]_++
                    2\left(-1+\ln\frac{K_F^2}{\lambda}\right)\left[\frac{1}{1-z}\right]_+\\
   \\ &+& \displaystyle
-         \frac{\lambda-1}{\lambda^2}\left[\frac{1}{1-\lambda z}\right]_+
+         \frac{\lambda-1}{\lambda^2}\left[\frac{1}{1-\lambda z}\right]
          +\frac{1}{2}\left[\frac{1-z}{(1-\lambda z)^2}\right]_+\bigg\}
 \end{array}\,,
 \end{equation}
@@ -509,7 +509,7 @@ \subsubsection{Charged Current Coefficient Functions}
                                                                                                                 2\left(-1+\ln\frac{K_F^2}{\lambda}\right)\left[\frac{1}{1-z}\right]_+\\
   \\ &+& \displaystyle
          \frac{2\lambda^2-\lambda-1}{\lambda}\left[\frac{1}{1-\lambda
-         z}\right]_+ +\frac{1}{2}\left[\frac{1-z}{(1-\lambda
+         z}\right] +\frac{1}{2}\left[\frac{1-z}{(1-\lambda
          z)^2}\right]_+\bigg\}
 \end{array}\,,
 \end{equation}
@@ -525,7 +525,7 @@ \subsubsection{Charged Current Coefficient Functions}
                                                                                                                 \left[\frac{2\ln(1-z)-\ln(1-\lambda z)}{1-z}\right]_++
                                                                                                                 2\left(-1+\ln\frac{K_F^2}{\lambda}\right)\left[\frac{1}{1-z}\right]_+\\
   \\ &+& \displaystyle \frac{\lambda-1}{\lambda}\left[\frac{1}{1-\lambda
-         z}\right]_+ +\frac{1}{2}\left[\frac{1-z}{(1-\lambda
+         z}\right] +\frac{1}{2}\left[\frac{1-z}{(1-\lambda
          z)^2}\right]_+\bigg\}
 \end{array}\,,
 \end{equation}
@@ -541,7 +541,7 @@ \subsubsection{Charged Current Coefficient Functions}
                                                                        z)\right)(1+z)+3\\ \\ &+&\displaystyle 2
                                                                                                  \left[\frac{2\ln(1-z)-\ln(1-\lambda z)}{1-z}\right]_++ 2
                                                                                                  \left(-1+\ln\frac{K_F^2}{\lambda}\right)\left[\frac{1}{1-z}\right]_+\\
-  \\ &-& \displaystyle 2\left[\frac{1}{1-\lambda z}\right]_+
+  \\ &-& \displaystyle 2\left[\frac{1}{1-\lambda z}\right]
          +\frac{1}{2}\left[\frac{1-z}{(1-\lambda z)^2}\right]_+\bigg\} + 2C_F
          \left[\lambda K_A \delta(1-z) + (1+\lambda)z\right]
 \end{array}\,.
@@ -574,10 +574,6 @@ \subsubsection{Charged Current Coefficient Functions}
   -\int_0^xdz\frac{\ln(1-z)}{1-z} = \frac12
   \ln^2(1-x)\,,
 \end{equation}
-\begin{equation}
-  -\int_0^x\frac{dz}{1-\lambda z} =
-  \frac{1}{\lambda}\ln(1-\lambda x)\,,
-\end{equation}
 \begin{equation}
   -\int_0^xdz\frac{1-z}{(1-\lambda z)^2} =
   \frac{1}{\lambda^2}\ln(1-\lambda
@@ -598,8 +594,7 @@ \subsubsection{Charged Current Coefficient Functions}
   C^{(1)}_{1,q}&\rightarrow& \displaystyle
                              C^{(1)}_{1,q} +
                              2C_F\bigg[2\ln^2(1-x)-2R(x)+2\left(-1+\ln\frac{K_F^2}{\lambda}\right)\ln(1-x)\\
-  \\ &&\displaystyle +\frac{\lambda-1}{\lambda^3}\ln(1-\lambda
-        x)+\frac{1}{2\lambda^2}\ln(1-\lambda
+  \\ &&\displaystyle +\frac{1}{2\lambda^2}\ln(1-\lambda
         x)+\frac{1-\lambda}{2\lambda}\frac{x}{1-\lambda x}\bigg]\delta(1-z)
 \end{array}\,,
 \end{equation}
@@ -609,8 +604,7 @@ \subsubsection{Charged Current Coefficient Functions}
                              C^{(1)}_{2,q} +
                              2C_F\bigg[2\ln^2(1-x)-2R(x)+2\left(-1+\ln\frac{K_F^2}{\lambda}\right)\ln(1-x)\\
   \\ &&\displaystyle
-        +\frac{2\lambda^2-\lambda-1}{\lambda^2}\ln(1-\lambda
-        x)+\frac{1}{2\lambda^2}\ln(1-\lambda
+        +\frac{1}{2\lambda^2}\ln(1-\lambda
         x)+\frac{1-\lambda}{2\lambda}\frac{x}{1-\lambda x}\bigg]\delta(1-z)
 \end{array}\,,
 \end{equation}
@@ -619,8 +613,7 @@ \subsubsection{Charged Current Coefficient Functions}
   C^{(1)}_{3,q}&\rightarrow& \displaystyle
                              C^{(1)}_{3,q} +
                              2C_F\bigg[2\ln^2(1-x)-2R(x)+2\left(-1+\ln\frac{K_F^2}{\lambda}\right)\ln(1-x)\\
-  \\ &&\displaystyle +\frac{\lambda-1}{\lambda^2}\ln(1-\lambda
-        x)+\frac{1}{2\lambda^2}\ln(1-\lambda
+  \\ &&\displaystyle +\frac{1}{2\lambda^2}\ln(1-\lambda
         x)+\frac{1-\lambda}{2\lambda}\frac{x}{1-\lambda x}\bigg]\delta(1-z)
 \end{array}\,,
 \end{equation}
@@ -629,8 +622,7 @@ \subsubsection{Charged Current Coefficient Functions}
   C^{(1)}_{L,q}&\rightarrow& \displaystyle
                              C^{(1)}_{L,q} +
                              2C_F(1-\lambda)\bigg[2\ln^2(1-x)-2R(x)+2\left(-1+\ln\frac{K_F^2}{\lambda}\right)\ln(1-x)\\
-  \\ &&\displaystyle -\frac{2}{\lambda}\ln(1-\lambda
-        x)+\frac{1}{2\lambda^2}\ln(1-\lambda
+  \\ &&\displaystyle +\frac{1}{2\lambda^2}\ln(1-\lambda
         x)+\frac{1-\lambda}{2\lambda}\frac{x}{1-\lambda x}\bigg]\delta(1-z)
 \end{array}\,.
 \end{equation}

diff --git a/src/DIS/MassiveCoefficientFunctions.f b/src/DIS/MassiveCoefficientFunctions.f
@@ -469,7 +469,9 @@ function c2ns1cca(xi,z)
       c2ns1cca = 2d0 * CF * ( - ( 1d0 + z**2 ) * dlog(z) / ( 1d0 - z )
      1         + ( 2d0 - dlog( kQF2 / lambda ) 
      2         -  2d0 * dlog( 1d0 - z ) + dlog( 1d0 - lambda * z ) ) 
-     3         * ( 1d0 + z ) + 1d0 / lambda )
+     3         * ( 1d0 + z ) + 1d0 / lambda
+     4         + ( 2d0 * lambda**2 - lambda - 1d0 ) / lambda 
+     4         / ( 1d0 - lambda * z ) )
 *
       return
       end
@@ -501,9 +503,7 @@ function c2ns1ccb(xi,z)
       c2ns1ccb = 2d0 * CF * ( 2d0 * ( 2d0 * dlog( 1d0 - z ) 
      1         - dlog( 1d0 - lambda * z ) ) / ( 1d0 - z ) 
      2         + 2d0 * ( - 1d0 + dlog( kQF2 / lambda ) ) / ( 1d0 - z )
-     3         + ( 2d0 * lambda**2 - lambda - 1d0 ) / lambda 
-     4         / ( 1d0 - lambda * z ) + ( 1d0 - z ) 
-     5         / ( 1d0 - lambda * z )**2 / 2d0 )
+     3         + ( 1d0 - z ) / ( 1d0 - lambda * z )**2 / 2d0 )
 *
       return
       end
@@ -542,9 +542,8 @@ function c2ns1ccc(Rf,xi,z)
      2         + 3d0 * dlog( kQF2 / lambda ) / 2d0
      3         + 2d0 * ln1mz**2 - 2d0 * Rf 
      4         + 2d0 * ( - 1d0 + dlog( kQF2 / lambda ) ) * ln1mz
-     5         + ( 2d0 * lambda**2 - lambda - 1d0 / 2d0 ) 
-     6         * ln1mlz / lambda**2 + ( 1d0 - lambda ) * z 
-     7         / 2d0 / lambda / ( 1d0 - lambda * z ) )
+     5         + ln1mlz / 2d0 / lambda**2 + ( 1d0 - lambda ) * z 
+     6         / 2d0 / lambda / ( 1d0 - lambda * z ) )
 *
       return
       end
@@ -611,8 +610,8 @@ function clns1cca(xi,z)
       clns1cca = 2d0 * CF * ( ( - ( 1d0 + z**2 ) * dlog(z) 
      1         / ( 1d0 - z ) + ( - dlog( kQF2 / lambda ) 
      2         -  2d0 * dlog( 1d0 - z ) + dlog( 1d0 - lambda * z ) ) 
-     3         * ( 1d0 + z ) + 3d0 ) * ( 1d0 - lambda ) 
-     4         + ( 1d0 + lambda ) * z )
+     3         * ( 1d0 + z ) + 3d0 - 2d0 / ( 1d0 - lambda * z ) )
+     4         * ( 1d0 - lambda ) + ( 1d0 + lambda ) * z )
 *
       return
       end
@@ -644,8 +643,8 @@ function clns1ccb(xi,z)
       clns1ccb = 2d0 * CF * ( 2d0 * ( 2d0 * dlog( 1d0 - z ) 
      1         - dlog( 1d0 - lambda * z ) ) / ( 1d0 - z )
      2         + 2d0 * ( - 1d0 + dlog( kQF2 / lambda ) ) / ( 1d0 - z ) 
-     3         - 2d0 / ( 1d0 - lambda * z ) + ( 1d0 - z ) 
-     4         / ( 1d0 - lambda * z )**2 / 2d0 ) * ( 1d0 - lambda )
+     3         + ( 1d0 - z ) / ( 1d0 - lambda * z )**2 / 2d0 )
+     4         * ( 1d0 - lambda )
 *
       return
       end
@@ -684,8 +683,7 @@ function clns1ccc(Rf,xi,z)
      2         + 3d0 * dlog( kQF2 / lambda ) / 2d0
      3         + 2d0 * ln1mz**2 - 2d0 * Rf 
      4         + 2d0 * ( - 1d0 + dlog( kQF2 / lambda ) ) * ln1mz
-     5         + ( - 2d0 * lambda + 1d0 / 2d0 ) 
-     6         * ln1mlz / lambda**2 + ( 1d0 - lambda ) * z 
+     5         + ln1mlz / 2d0 / lambda**2 + ( 1d0 - lambda ) * z 
      7         / 2d0 / lambda / ( 1d0 - lambda * z ) )
      8         * ( 1d0 - lambda ) + lambda * KA )
 *
@@ -756,7 +754,8 @@ function c3ns1cca(xi,z)
       c3ns1cca = 2d0 * CF * ( - ( 1d0 + z**2 ) * dlog(z) / ( 1d0 - z ) 
      1         + ( 1d0 - dlog( kQF2 / lambda ) 
      2         -  2d0 * dlog( 1d0 - z ) + dlog( 1d0 - lambda * z ) ) 
-     3         * ( 1d0 + z ) + 1d0 / lambda )
+     3         * ( 1d0 + z ) + 1d0 / lambda + ( lambda - 1d0 ) / lambda 
+     4         / ( 1d0 - lambda * z ) )
 *
       return
       end
@@ -788,9 +787,7 @@ function c3ns1ccb(xi,z)
       c3ns1ccb = 2d0 * CF * ( 2d0 * ( 2d0 * dlog( 1d0 - z ) 
      1         - dlog( 1d0 - lambda * z ) ) / ( 1d0 - z )
      2         + 2d0 * ( - 1d0 + dlog( kQF2 / lambda ) ) / ( 1d0 - z ) 
-     3         + ( lambda - 1d0 ) / lambda 
-     4         / ( 1d0 - lambda * z ) + ( 1d0 - z ) 
-     5         / ( 1d0 - lambda * z )**2 / 2d0 )
+     3         + ( 1d0 - z ) / ( 1d0 - lambda * z )**2 / 2d0 )
 *
       return
       end
@@ -829,8 +826,7 @@ function c3ns1ccc(Rf,xi,z)
      2         + 3d0 * dlog( kQF2 / lambda ) / 2d0 
      3         + 2d0 * ln1mz**2 - 2d0 * Rf 
      4         + 2d0 * ( - 1d0 + dlog( kQF2 / lambda ) ) * ln1mz
-     5         + ( lambda - 1d0 / 2d0 ) 
-     6         * ln1mlz / lambda**2 + ( 1d0 - lambda ) * z 
+     5         + ln1mlz / 2d0 / lambda**2 + ( 1d0 - lambda ) * z 
      7         / 2d0 / lambda / ( 1d0 - lambda * z ) )
 *
       return