Changes between Initial Version and Version 1 of TwoHiggsDoublet


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Timestamp:
03/20/12 16:15:33 (7 years ago)
Author:
trac
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  • TwoHiggsDoublet

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     3== The 2HDM implementation ==
     4
     5The two-Higgs-doublet model (2HDM) has been extensively studied for
     6more than twenty years, even though it has often been only
     7considered as the scalar sector of larger models like the MSSM
     8\citeGunion:1989we} or Little Higgs models
     9\cite{Arkani-Hamed:2002qx}. The generic 2HDM considered here may
     10display by itself an interesting phenomenology justifying its
     11study. As a non exhaustive list, let us mention new sources of %$CP$%
     12violation in scalar-scalars interactions \cite{Branco:1999fs},
     13tree-level flavor changing neutral currents (FCNCs) due to non
     14diagonal Yukawa interactions, dark matter candidates
     15\cite{Barbieri:2006dq} or Higgs bosons lighter than the LEP bound
     16\cite{Gerard:2007kn}.
     17
     18In the ``full'' version of the model (2hdm_full), no particular
     19restrictions are imposed on the interactions allowed by gauge
     20invariance, except electric charge conservation. Many diagrams
     21involving tree-level FCNCs and violating the %$CP$% symmetry are thus
     22present. The user who is not interested in these phenomena should use
     23the ``simplified'' version of the model (2hdm), where the number
     24of generated diagrams is in general much smaller.
     25
     26The following naming convention is used: h+ and h- stand
     27for the positively and negatively charged Higgs bosons and h1,
     28h2 and h3 stand for the neutral ones. Since the %$CP$%
     29invariance of the potential is not assumed, the neutral bosons are not
     30necessarily $CP$ eigenstates and the standard naming convention in
     31this case (ie, h1 being the lightest one and h3 the
     32heaviest one) is used.
     33
     34TwoHiggsCalc is the calculator associated with the model. It has been
     35written in C and is accessible from a web interface. It has been
     36designed to compute input values for the 2HDM extension of
     37MadGraph/MadEvent but it can also be used as an independent
     38tool. Starting from various parameters of the Lagrangian, such as the
     39vacuum expectation values (vevs) or the Yukawa couplings, the program
     40computes useful secondary physical quantities at leading order such as
     41the scalar mass spectrum, the mixing matrix, the total decay widths
     42and the branching ratios.
     43
     44TwoHiggsCalc reads input and writes out results in a specific format
     45close to the ``SUSY Les Houches Accord 1.0" convention for SUSY
     46parameters \cite{Skands:2003cj}. This format can later be read by
     47MadEvent to perform numerical calculations for 2HDM processes. A
     48README file describing this modified version of the LHA format used
     49as input convention is available. To ease the use of TwoHiggsCalc, a
     50web form has been designed to automatize the parameter card writing
     51process. Numerical values for the parameters (units being fixed when
     52needed) can be entered on this form. Some simple algebraic expressions
     53can also be used. The +,-,*,/ operators and the
     54reserved keyword  PI, eg, PI/2+3*PI/2, are correctly interpreted.
     55
     56
     57In the general 2HDM, one has the freedom to choose a specific basis
     58for entering parameters. All the possible choices are physically
     59equivalent (see eg \cite{Davidson:2005cw} for a
     60discussion). TwoHiggsCalc and the 2HDM model both assume that the
     61parameters are given in a particular basis, called the ``Higgs basis''
     62where only one Higgs doublet gets a vacuum expectation value. An
     63independent program , Gen2HB, has been written to convert parameters
     64given in an arbitrary basis (where both Higgs doublets get vevs),
     65called ``generic'', to parameters in the Higgs basis. See
     66\cite{Branco:1999fs} for more information on basis invariance and on
     67the notation used.
     68
     69The scalar potential in the Higgs basis reads
     70
     71%$
     72V &=& \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)\\
     73  & & \lambda_1 \left(H_1^\dag H_1\right)^2+ \lambda_2 \left(H_2^\dag
     74  H_2\right)^2\\ & & + \lambda_3 \left(H_1^\dag
     75  H_1\right)\left(H_2^\dag H_2\right)+ \lambda_4 \left(H_1^\dag
     76  H_2\right)\left(H_2^\dag H_1\right)\\ & & +\left[\left( \lambda_5
     77  H_1^\dag H_2 + \lambda_6 H_1^\dag H_1+ \lambda_7 H_2^\dag
     78  H_2\right)\left(H_1^\dag H_2\right)+\mathrm{h.c.}\right]\,.
     79$%
     80
     81All parameters in front of quartic terms and the charged Higgs mass
     82are input parameters, while %$\mu_1$%, %$\mu_2$% and %$\mu_3$% are fixed by
     83minimization constraints and by the vev extracted from the observed SM
     84parameters. %$\lambda_1$% to %$\lambda_4$% are real while %$\lambda_5$% in
     85general is complex. However, since only the phase differences between
     86%$\lambda_5$%, %$\lambda_6$%, %$\lambda_7$% and %$\mu_3$% matter, the phase of
     87%$\lambda_5$% can always be rotated out. It is thus considered as a real
     88parameter while %$\lambda_6$% and %$\lambda_7$% are a priori complex.
     89
     90In the same basis, the Yukawa interactions read
     91
     92%$
     93\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]\\
     94& &+\frac{\overline{E_L}\sqrt{2}}{v}\left[(M_e H_1 +   Y_e   H_2)e_R\right]\,.
     95$%
     96
     97Yukawa couplings are expected to be given in the physical basis for
     98fermions, ie, in the basis where the mass matrix is diagonal. Since
     99in the Higgs basis only the first Higgs doublet gets a non zero vev,
     100the %$M$% matrices are completely fixed by the physical fermion masses
     101and CKM mixing matrix (restricted to Cabibbo angle) while the %$Y$%
     102matrices (giving the couplings of the second Higgs doublet) are a
     103priori free. For these matrices, the first index refers to doublet
     104generation while the second refers to the singlet generation. For
     105example, Y2B stands for the complex Yukawa couplings of the
     106second Higgs doublet to the second generation quark left doublet and
     107to the bottom singlet.
     108
     109In the generic basis, similar expressions are assumed. For the scalar
     110potential all parameters in front of quartic terms are inputs as well
     111as %$\tan(\beta)$%, the norm of %$\mu_3$% and the phase of %$v_2$%.  The
     112overall vev is again extracted from SM parameters while mass terms
     113parameters, like %$\mu_1$%, %$\mu_2$% and the phase of %$\mu_3$%, are fixed
     114by the minimization constraints. %$\lambda_1$% to %$\lambda_4$% are real
     115parameters, %$\lambda_5$%, %$\lambda_6$% and %$\lambda_7$% are a priori
     116complex. Like in the Higgs basis, the Yukawa couplings must be given
     117in the physical basis for fermions. Since the mass matrices are fixed,
     118only the Yukawa coupling matrices of the second Higgs doublet
     119(%$\Gamma$%), is required. The other one is going to be automatically
     120evaluated to match observed fermion masses and CKM mixing matrix
     121(restricted to Cabibbo angle). For the %$\Gamma$% matrix, the first
     122index refers to doublet generation while the second one refer to the
     123singlet generation.  For example, G2B stands for the complex
     124Yukawa couplings of the second Higgs doublet to the second generation
     125quark left doublet and to the bottom singlet.
     126
     127Given the above parameters and some SM parameters, TwoHiggsCalc
     128computes the following quantities
     129
     130   * Scalar particles mass spectrum
     131   * Normalized mixing matrix of neutral scalars (called $T$ in \cite{Branco:1999fs})
     132   * Decay widths for all scalars as well as for $W$ and $Z$ bosons
     133      and the top quark. All widths are evaluated at tree-level using
     134      the same couplings as in MadEvent. Below threshold formulas
     135      are included for the scalar decays into two vector bosons and
     136      the one loop driven scalar decay into two gluons is also
     137      computed.
     138
     139The LHA blocks and parameters used by MadEvent are given in
     140Table below. All blocks in the table are provided by
     141TwoHiggsCalc. Note that if parton density functions (PDFs) are used in
     142the MadEvent run, the value for %$\alpha_s$% at %$M_Z$% and the order of
     143its running is given by the PDF. Otherwise %$\alpha_s(M_Z)$% is given by
     144block SMINPUTS, parameter 3, and the order of running is taken
     145to be 2-loop. The scale where %$\alpha_s$% is evaluated can be fixed or
     146evaluated on an event-by-event basis like in the SM.
     147
     148||Block||Comment||
     149||SMINPUTS||From 1 to 4, SM parameters, see the SM section for more details||
     150||MGSMPARAM||Extra block with %$\sin\theta_W$% and %$M_W$%, see the SM section for more details||
     151||MGYUKAWA}||``Yukawa'' masses used in the Yukawa couplings evaluation||
     152||MGCKM ||The full CKM matrix||
     153||BASIS||Basis choice, must be 1 (Higgs basis) for MadEvent !||
     154||MINPAR||Scalar potential parameters in the Higgs basis||
     155||YUKAWA2||Yukawa couplings of the second Higgs doublet||
     156||MASS|| All SM particles masses, plus the five new Higgs boson masses||
     157||TMIX|| The scalar mixing matrix||
     158||DECAY|| For all the Higgs bosons, top, %$W^\pm$% and %$Z$%||
     159
     160-- Main.MichelHerquet - 09 Apr 2007
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