Standard Model interactions

The Standard Model of particles and interactions, based on the %$SU(3)c \times SU(2)L \times U(1)_Y$ gauge symmetry has been available since the first versions of both MadGraph and more recently of MadEvent. There is, however, one important differences w.r.t. the previous version of the package, regarding how the couplings of the models are handled. As was already mentioned in the previous section, the task of computing from the parameters in the Lagrangian (primary parameters) all the secondary parameters (masses, widths and dependent parameters) needed by MadGraph is left to an external program, the SM Calculator. The output of the SM Calculator is a parameter card, param_card.dat, which contains the numerical values of the main couplings (primary and secondary) of a specific model. The parameter card has a format compliant with the SUSY Les Houches Accord.

A simple example is given by the EW parameters that characterize the gauge $SU(2)L \times U(1)Y$ interactions and its breaking: in the Standard Model there are five relevant parameters, %$\alpha_{em}, G_F, \sin \theta W, mZ,m_W$ of which only three are independent at tree level. Various schemes differing by the choice of the parameters considered independent are used in the literature. In the SM Calculator, the default is to take %$G_F,m_Z,m_W$ as inputs and derive $\alpha_{em}, \sin \theta_W$, but other choices are available. As a result a consistent and unique set of values of the couplings appearing in the Feynman rules is derived and used for the computation of the amplitudes.

Another sometimes important feature of our SM implementation, is the possibility of distinguishing between the kinematic mass (pole mass) for the quarks and that entering in the Yukawa coupling definition ($\overline{MS}$ mass). For the latter, the user can choose to evolve the mass to the scale corresponding to the Higgs mass, which leads to an improvement of the perturbative expansion.

Finally, we mention that various versions of the Standard Model are actually available for specific studies. For example, in the minimal SM (sm) the CKM matrix is diagonal while in the smckm model a mixing between the first and second generation is allowed (Cabibbo angle). Another example is the sm_nohiggs model where the Higgs has been eliminated and the EWSB sector behaves as a non-linear sigma-model.

-- Main.MichelHerquet - 09 Apr 2007