MODEL/Main/Running_AlphaQED.H

0001 #ifndef MODEL_Main_Running_AlphaQED_H
0002 #define MODEL_Main_Running_AlphaQED_H
0003
0004 #include "ATOOLS/Phys/Flavour.H"
0005 #include "ATOOLS/Math/Function_Base.H"
0006
0007 namespace MODEL {
0008   class Running_AlphaQED : public ATOOLS::Function_Base {
0009     const static double m_A[4],m_B[4],m_C[4];
0010     double m_alpha0;
0011
0012     double  PiGamma(const ATOOLS::Flavour &, double);
0013   public:
0014     Running_AlphaQED(const double);
0015
0016     double operator()(double);
0017     double AqedThomson()  { return m_alpha0; }
0018
0019     void PrintSummary();
0020   };
0021
0022   extern Running_AlphaQED * aqed;
0023
0024   /*!
0025     \class Running_AlphaQED
0026     \brief The class for the (running) electromagnetic coupling constant.
0027
0028     This is an implementation of the
0029     <A HREF="http://131.169.91.193/cgi-bin/spiface/find/hep/www?key=2184940">
0030     electromagnetic coupling constant </A> by R. Kleiss et al. with the
0031     <A HREF="http://131.169.91.193/cgi-bin/spiface/find/hep/www?key=2076233">
0032     hadronic component</A> by H. Burkhardt et al..
0033   */
0034   /*!
0035     \var const static double Running_AlphaQED::m_A[4]
0036     The \f$A_i\f$ parameters needed to calculate the hadronic component of \f$\alpha_{QED}\f$
0037     \f[A_0 = 0.0,\; A_1 = 0.0,\; A_2 = 0.00165,\; A_3 = 0.00221\,.\f]
0038   */
0039   /*!
0040     \var const static double Running_AlphaQED::m_B[4]
0041     The \f$A_i\f$ parameters needed to calculate the hadronic component of \f$\alpha_{QED}\f$
0042     \f[B_0 = 0.00835,\; B_1 = 0.00238,\; B_2 = 0.00299,\; B_3 = 0.00293\,.\f]
0043   */
0044   /*!
0045     \var const static double Running_AlphaQED::m_C[4]
0046     The \f$A_i\f$ parameters needed to calculate the hadronic component of \f$\alpha_{QED}\f$
0047     \f[C_0 = 1.0,\; C_1 = 3.927,\; C_2 = 1.0,\; C_3 = 1.0\f]
0048   */
0049   /*!
0050     \var double Running_AlphaQED::m_alpha0
0051     \f$\alpha_{QED}\f$ in the Thomson limit,
0052     \f[\alpha^{(0)}_{QED} = 1/137.03599976\,.\f]
0053   */
0054   /*!
0055     \fn double Running_AlphaQED::PiGamma(const ATOOLS::Flavour &, double)
0056     With the mass of the particle and the scale the vacuum polarization is given by
0057     \f[\Pi_\gamma(m^2,s)] = \left\{ \begin{array}{lcl}
0058                     -5/3-\log(m^2/s)\;& \;\mbox{\rm if}\;& \; 4m^2/s<10^{-3}\\
0059                     1/3-(1+2m^2/s)
0060                     \left[2+\sqrt{1-4m^2/s}\cdot
0061               \log\frac{1-\sqrt{1-4m^2/s}}{1+\sqrt{1-4m^2/s}}\right]
0062                     \;&\;\mbox{\rm if}\;&\; 4m^2/s<1\\
0063                     0\;& \;\mbox{\rm if}\;& \; 4m^2/s\ge 1
0064         \end{array} \right.\f]
0065   */
0066   /*!
0067     \fn Running_AlphaQED::Running_AlphaQED(const double);
0068     Initialises \f$\alpha_{QED}\f$ with the value at scale t=0
0069   */
0070   /*!
0071     \fn double Running_AlphaQED::operator()(double);
0072     Returns the value for running \f$\alpha_{QED}\f$.
0073     \f[\alpha_{QED}(Q^2) = \frac{\alpha^{(0)}_{QED}}{1-\sigma}\,,\f]
0074     where
0075     \f[\sigma = \sigma_{\rm lepton} + \sigma_{\rm hadron} + \sigma_{\rm top}\f]
0076     The leptonic component is given by
0077     \f[\sigma_{\rm lepton}(Q^2) = \sum\limits_{l=e^-,\mu^-,\tau^-}
0078       \frac{\alpha^{(0)}_{QED}}{3\pi}\cdot\Pi_\gamma(l,Q^2)\,.\f]
0079     \f[\sigma_{\rm hadron}(Q^2) = A[i] + B[i] \log\left(1+C[i]\cdot Q^2\right)\,.\f]
0080     \f[\sigma_{\rm top}(Q^2) = \frac{\alpha^{(0)}_{QED}}{3\pi}\cdot\Pi_\gamma(t,Q^2)\,.\f]
0081   */
0082   /*!
0083     \fn double Running_AlphaQED::AqedThomson()
0084     Returns \f$\alpha_{QED}\f$ in the Thomson limit.
0085   */
0086 }
0087 #endif