Changes between Initial Version and Version 1 of TwoHiggsDoublet

Timestamp:

Mar 20, 2012, 4:15:33 PM (12 years ago)

Author:

trac

Comment:

--

TwoHiggsDoublet

@@ +1 @@
+
+
+== The 2HDM implementation ==
+
+The two-Higgs-doublet model (2HDM) has been extensively studied for
+more than twenty years, even though it has often been only
+considered as the scalar sector of larger models like the MSSM
+\citeGunion:1989we} or Little Higgs models
+\cite{Arkani-Hamed:2002qx}. The generic 2HDM considered here may
+display by itself an interesting phenomenology justifying its
+study. As a non exhaustive list, let us mention new sources of %$CP$%
+violation in scalar-scalars interactions \cite{Branco:1999fs},
+tree-level flavor changing neutral currents (FCNCs) due to non
+diagonal Yukawa interactions, dark matter candidates
+\cite{Barbieri:2006dq} or Higgs bosons lighter than the LEP bound
+\cite{Gerard:2007kn}.
+
+In the ``full'' version of the model (2hdm_full), no particular
+restrictions are imposed on the interactions allowed by gauge
+invariance, except electric charge conservation. Many diagrams
+involving tree-level FCNCs and violating the %$CP$% symmetry are thus
+present. The user who is not interested in these phenomena should use
+the ``simplified'' version of the model (2hdm), where the number
+of generated diagrams is in general much smaller.
+
+The following naming convention is used: h+ and h- stand
+for the positively and negatively charged Higgs bosons and h1,
+h2 and h3 stand for the neutral ones. Since the %$CP$%
+invariance of the potential is not assumed, the neutral bosons are not
+necessarily $CP$ eigenstates and the standard naming convention in
+this case (ie, h1 being the lightest one and h3 the
+heaviest one) is used.
+
+TwoHiggsCalc is the calculator associated with the model. It has been
+written in C and is accessible from a web interface. It has been
+designed to compute input values for the 2HDM extension of
+MadGraph/MadEvent but it can also be used as an independent
+tool. Starting from various parameters of the Lagrangian, such as the
+vacuum expectation values (vevs) or the Yukawa couplings, the program
+computes useful secondary physical quantities at leading order such as
+the scalar mass spectrum, the mixing matrix, the total decay widths
+and the branching ratios.
+
+TwoHiggsCalc reads input and writes out results in a specific format
+close to the ``SUSY Les Houches Accord 1.0" convention for SUSY
+parameters \cite{Skands:2003cj}. This format can later be read by
+MadEvent to perform numerical calculations for 2HDM processes. A 
+README file describing this modified version of the LHA format used
+as input convention is available. To ease the use of TwoHiggsCalc, a
+web form has been designed to automatize the parameter card writing
+process. Numerical values for the parameters (units being fixed when
+needed) can be entered on this form. Some simple algebraic expressions
+can also be used. The +,-,*,/ operators and the
+reserved keyword  PI, eg, PI/2+3*PI/2, are correctly interpreted.
+
+
+In the general 2HDM, one has the freedom to choose a specific basis
+for entering parameters. All the possible choices are physically
+equivalent (see eg \cite{Davidson:2005cw} for a
+discussion). TwoHiggsCalc and the 2HDM model both assume that the
+parameters are given in a particular basis, called the ``Higgs basis''
+where only one Higgs doublet gets a vacuum expectation value. An
+independent program , Gen2HB, has been written to convert parameters
+given in an arbitrary basis (where both Higgs doublets get vevs),
+called ``generic'', to parameters in the Higgs basis. See
+\cite{Branco:1999fs} for more information on basis invariance and on
+the notation used.
+
+The scalar potential in the Higgs basis reads 
+
+%$
+V &=& \mu_1 H_1^\dag H_1 +\mu_2 H_2^\dag H_2-\left(\mu_3 H_1^\dag H_2+\mathrm{h.c.}\right)\\
+  & & \lambda_1 \left(H_1^\dag H_1\right)^2+ \lambda_2 \left(H_2^\dag
+  H_2\right)^2\\ & & + \lambda_3 \left(H_1^\dag
+  H_1\right)\left(H_2^\dag H_2\right)+ \lambda_4 \left(H_1^\dag
+  H_2\right)\left(H_2^\dag H_1\right)\\ & & +\left[\left( \lambda_5
+  H_1^\dag H_2 + \lambda_6 H_1^\dag H_1+ \lambda_7 H_2^\dag
+  H_2\right)\left(H_1^\dag H_2\right)+\mathrm{h.c.}\right]\,.
+$%
+
+All parameters in front of quartic terms and the charged Higgs mass
+are input parameters, while %$\mu_1$%, %$\mu_2$% and %$\mu_3$% are fixed by
+minimization constraints and by the vev extracted from the observed SM
+parameters. %$\lambda_1$% to %$\lambda_4$% are real while %$\lambda_5$% in
+general is complex. However, since only the phase differences between
+%$\lambda_5$%, %$\lambda_6$%, %$\lambda_7$% and %$\mu_3$% matter, the phase of
+%$\lambda_5$% can always be rotated out. It is thus considered as a real
+parameter while %$\lambda_6$% and %$\lambda_7$% are a priori complex.
+
+In the same basis, the Yukawa interactions read
+
+%$
+\mathcal{L}''Y&=&\frac{\overline{Q''L}\sqrt{2}}{v}\left[(M_d H_1 +   Y_d   H_2)d_R+(M_u \tilde{H}''1 +   Y''u   \tilde{H}''2)u''R\right]\\
+& &+\frac{\overline{E_L}\sqrt{2}}{v}\left[(M_e H_1 +   Y_e   H_2)e_R\right]\,.
+$%
+
+Yukawa couplings are expected to be given in the physical basis for
+fermions, ie, in the basis where the mass matrix is diagonal. Since
+in the Higgs basis only the first Higgs doublet gets a non zero vev,
+the %$M$% matrices are completely fixed by the physical fermion masses
+and CKM mixing matrix (restricted to Cabibbo angle) while the %$Y$%
+matrices (giving the couplings of the second Higgs doublet) are a
+priori free. For these matrices, the first index refers to doublet
+generation while the second refers to the singlet generation. For
+example, Y2B stands for the complex Yukawa couplings of the
+second Higgs doublet to the second generation quark left doublet and
+to the bottom singlet.
+
+In the generic basis, similar expressions are assumed. For the scalar
+potential all parameters in front of quartic terms are inputs as well
+as %$\tan(\beta)$%, the norm of %$\mu_3$% and the phase of %$v_2$%.  The
+overall vev is again extracted from SM parameters while mass terms
+parameters, like %$\mu_1$%, %$\mu_2$% and the phase of %$\mu_3$%, are fixed
+by the minimization constraints. %$\lambda_1$% to %$\lambda_4$% are real
+parameters, %$\lambda_5$%, %$\lambda_6$% and %$\lambda_7$% are a priori
+complex. Like in the Higgs basis, the Yukawa couplings must be given
+in the physical basis for fermions. Since the mass matrices are fixed,
+only the Yukawa coupling matrices of the second Higgs doublet
+(%$\Gamma$%), is required. The other one is going to be automatically
+evaluated to match observed fermion masses and CKM mixing matrix
+(restricted to Cabibbo angle). For the %$\Gamma$% matrix, the first
+index refers to doublet generation while the second one refer to the
+singlet generation.  For example, G2B stands for the complex
+Yukawa couplings of the second Higgs doublet to the second generation
+quark left doublet and to the bottom singlet.
+
+Given the above parameters and some SM parameters, TwoHiggsCalc
+computes the following quantities
+
+   * Scalar particles mass spectrum
+   * Normalized mixing matrix of neutral scalars (called $T$ in \cite{Branco:1999fs})
+   * Decay widths for all scalars as well as for $W$ and $Z$ bosons
+      and the top quark. All widths are evaluated at tree-level using
+      the same couplings as in MadEvent. Below threshold formulas
+      are included for the scalar decays into two vector bosons and
+      the one loop driven scalar decay into two gluons is also
+      computed.
+
+The LHA blocks and parameters used by MadEvent are given in
+Table below. All blocks in the table are provided by
+TwoHiggsCalc. Note that if parton density functions (PDFs) are used in
+the MadEvent run, the value for %$\alpha_s$% at %$M_Z$% and the order of
+its running is given by the PDF. Otherwise %$\alpha_s(M_Z)$% is given by
+block SMINPUTS, parameter 3, and the order of running is taken
+to be 2-loop. The scale where %$\alpha_s$% is evaluated can be fixed or
+evaluated on an event-by-event basis like in the SM.
+
+||Block||Comment||
+||SMINPUTS||From 1 to 4, SM parameters, see the SM section for more details||
+||MGSMPARAM||Extra block with %$\sin\theta_W$% and %$M_W$%, see the SM section for more details|| 
+||MGYUKAWA}||``Yukawa'' masses used in the Yukawa couplings evaluation||
+||MGCKM ||The full CKM matrix|| 
+||BASIS||Basis choice, must be 1 (Higgs basis) for MadEvent !||
+||MINPAR||Scalar potential parameters in the Higgs basis||
+||YUKAWA2||Yukawa couplings of the second Higgs doublet||
+||MASS|| All SM particles masses, plus the five new Higgs boson masses||
+||TMIX|| The scalar mixing matrix||
+||DECAY|| For all the Higgs bosons, top, %$W^\pm$% and %$Z$%||
+
+-- Main.MichelHerquet - 09 Apr 2007
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