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 #ifndef PDF_Main_PDF_Electron_H
 #define PDF_Main_PDF_Electron_H
 
 #include "PDF/Main/PDF_Base.H"
 
 namespace PDF {
   class PDF_Electron : public PDF_Base {
     double m_mass;
     double m_alpha,m_beta;
     double m_xpdf;
     int    m_izetta,m_order,m_init;
   public:
     PDF_Electron(const ATOOLS::Flavour,const int,const int);
     ~PDF_Electron() {}
     PDF_Base * GetCopy();
 
     void   CalculateSpec(const double&,const double&);
     double GetXPDF(const ATOOLS::Flavour&);
     double GetXPDF(const kf_code&, bool);
 
     bool EWOn() { return true; }
 
   };
   /*!
     \class PDF_Electron
     \brief This is a pure QED structure function for an electron or, more general, for a lepton. 
 
     This class houses the QED structure function for an electron, or, more general, charged
     leptons in the parametrization of 
     <A HREF=""></A>. 
     It is based on the leading log
     approximation leading to exponentiation including further higher order terms up to
     \f${\cal O}(\alpha^3)\f$ in the electromagnetic coupling constant. Furthermore, different
     exponentiation schemes are available, see also 
     <A HREF=""></A>.
   */
   /*!
     \var double PDF_Electron::m_alpha
     The electromagnetic coupling constant, taken at the scale at which the structure 
     function is to be evaluated.
   */
   /*!
     \var double PDF_Electron::m_beta
     The characteristic exponent of the lepton PDF. It is given by
     \f[
     \beta = \alpha(m_l^2)/\pi (\log(E^2/m_l^2)-1)
     \f]
   */
   /*!
     \var double PDF_Electron::m_mass
     The mass of the lepton.
   */
   /*!
     \var int PDF_Electron::m_order
     The order in alpha for the caluclation of the structure function.
   */
   /*!
     \var int PDF_Electron::m_izetta
     The \f$\zeta\f$-scheme for the definition of how the logarithms enter the exponentiation.
   */
   /*!
     \fn PDF_Electron::PDF_Electron(const ATOOLS::Flavour,const int,const int)
     The constructor, initializes all constant parameters for evaluation in Calculate.
   */
   /*!
     \fn PDF_Base * PDF_Electron::GetCopy()
     A method to initialize another electron PDF as exact copy of the current one.
     This is needed for the initial state shower of APACIC.
   */
   /*!
     \fn void PDF_Electron::CalculateSpec(const double&, const double&);
     Here, the following expression is evaluated:
     \f[
     \begin{array}{l}
     f(x,Q^2) = \\ \\ \\ \\ \\
     \end{array}
     \begin{array}{l}
     (1-x)^{\frac{\beta}{2}-1}\cdot
     \frac{\beta\exp\left(\frac12\Gamma_E*\beta+\frac38\beta_S\right)}{2\gamma}\\
     - \frac{\beta_H}{4}(1+x)
     - \frac{\beta_H^2}{32}
     \left[\frac{1+3x^2}{1-x}\log(x) + 4(1+x)\log(1-x)+5+x\right]\\
     - \frac{\beta_H^3}{384}
       \left[\vphantom{\frac32}
             (1+x)\left(6\mbox{\rm Li}_2(x)+12\log^2(1-x)-3\pi^2\right) \right.\\
       \;\;\;\;\;\;\;\; 
             + \frac{1}{1-1x}\left(\frac{3(1+8x+3x^2)}{2}\log(x)
                             + 6(x+5)(1-x)\log(1-x)
           +12(1+x^2)\log(x)\log(1-x) \right.\\
        \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left.\left.              
           +12(1+x^2)\log(x)\log(1-x)
           -\frac{1+7x^2}{2}\log^2(x)
           +\frac{39-24x-15x^2}{4}\right)\right]\,,
     \end{array}
     \f]
     where a number of choices are possible for the various \f$\beta\f$.
     Defining 
     \f[
     L = 2\log\frac{Q}{m_e}\;,\;\;
     \beta_e = \frac{2\alpha (L-1)}{\pi}\;,\;\; 
     \eta = \frac{2\alpha L}{\pi} 
     \f]
     for various values of \f$\zeta\f$ (m_izetta) the \f$\beta\f$ are given by:
     \f[
     \zeta = \left\{
             \begin{array}{l} 0 \\ 1 \\ \mbox{\rm else}\end{array}
             \begin{array}{l}  \beta = \beta_e\,,\;\; \beta_H = \beta_S = \eta\,,\\
                         \beta = \beta_S = \beta_e\,,\;\; \beta_H = \eta\,,\\
                         \beta = \beta_S = \beta_H = \beta_e\,.
       \end{array}\right.
     \f]
     The above expression for \f$f(x,Q^2)\f$ is valid for
     \f[ 
     x\in [0,0.9999]\,,
     \f]
     and the pdf weight yields
     \f[
     {\cal W}(x,Q^2) = x f(x,Q^2)\,.
     \f]
     For
     \f[ 
     x\in [0.9999,0.999999]
     \f]
     the pdf is replaced by
     \f[
     {\cal W}(x,Q^2) = x f(x,Q^2)\cdot \frac{100^{\beta/2}}{100^{\beta/2}-1}\,.
     \f]
     For higher $x$ values a zero is returned. Hence, the modification for the high \f$x\f$
     range basically amounts to moving a good portion of the contributions from the potentially 
     numerically instable region close to 1 to a lower range.
   */
 } 
 #endif // PDF_Electron_H

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