Model for BSM physics studies in ttbar production (​arxiv:0712.2355) Version 1.3

The {{{ topBSM }}} is a model implemented to study BSM effects in the ttbar invariant mass spectrum. This model includes the following possible resonances in the ttbar spectrum:

• spin-0, color singlet
• spin-0, color octet
• spin-1, color singlet
• spin-1, color octet
• spin-2, ADD model
• spin-2, RS model

Note that this {{{ topBSM }}} model can only be used for ttbar production. Any other final state might lead to inconsistencies in the evaluation of the diagrams. This model uses a special {{{ param_card.dat }}} and {{{ run_card.dat }}} that can be found here​ and here​.

spin-0, color singlet

(proc_card.dat​: topBSM spin-0 color singlet proc_card.dat)

The spin-0, color singlet particle, in the {{{ topBSM }}} called {{{ s0 }}} (PDG code: 6000045), is a Higgs-like particle that couples only to top quarks. The production of the spin-0 is only through a top quark loop by gluon fusion. And its decay is directly to two top quarks with a branching ratio $\textrm{BR}(s0\to t\bar{t})=1$.

It's coupling strength to the top quark is by default equal to the SM Higgs coupling to top quarks, i.e., %$im_t/v$%, but this can be changed in the {{{ param_card.dat }}}. In the {{{ param_card.dat }}} there are the following two lines:

         1.     1.00000000e+00   # s0scalarf  ,spin-0 scalar mult.fac.
         2.     0.00000000e+00   # s0axialf   ,spin-0 pseudo-scalar mult.fac.

These two values correspond to multiplication factors for the coupling strength, i.e., %$g_{s0tt}=$% {{{ s0scalarf }}} %$i\frac{m_t}{v}+$% {{{ s0axialf }}} $\frac{m_t}{v}\gamma_5$. Hence, the spin-0 can be a scalar or a pseudo-scalar or a mixed CP state by playing around with these two factors.

Due to the loop in the production mechanism the coupling strength between the gluons and the {{{ s0 }}} depends on its momentum. Therefore it is important to set the flag {{{ fixed_couplings }}} to false in the {{{ run_card.dat }}}. (See above for a sample {{{ run_card.dat }}})

The width is calculated automatically and is not read from the {{{ param_card.dat }}} (this takes into account the values for {{{ s0scalarf }}} and {{{ s0axialf }}}).

spin-0, color octet

(proc_card_o0.dat​: topBSM spin-0 color octet proc_card.dat)

The spin-0, color octet particle, in the {{{ topBSM }}} called {{{ o0 }}} (PDG code: 6000046), is a scalar, colored particle that couples only to top quarks. The production of the spin-0 is only through a top quark loop by gluon fusion. And its decay is directly to two top quarks with a branching ratio $\textrm{BR}(s0\to t\bar{t})=1$.

It's coupling strength to the top quark is by default equal to the SM Higgs coupling to top quarks, i.e., %$im_t/v$%, but this can be changed in the {{{ param_card.dat }}}. In the {{{ param_card.dat }}} there are the following two lines:

         3.     1.00000000e+00   # o0scalarf  ,spin-0 scalar mult.fac.
         4.     0.00000000e+00   # o0axialf   ,spin-0 pseudo-scalar mult.fac.

These two values correspond to multiplication factors for the coupling strength, i.e., %$g_{o0tt}=$% {{{ o0scalarf }}} %$i\frac{m_t}{v}+$% {{{ o0axialf }}} $\frac{m_t}{v}\gamma_5$. Hence, the spin-0 can be a scalar or a pseudo-scalar or a mixed CP state by playing around with these two factors.

Due to the loop in the production mechanism the coupling strength between the gluons and the {{{ o0 }}} depends on its momentum. Therefore it is important to set the flag {{{ fixed_couplings }}} to false in the {{{ run_card.dat }}}. (See above for a sample {{{ run_card.dat }}})

The width is calculated automatically and is not read from the {{{ param_card.dat }}} (this takes into account the values for {{{ o0scalarf }}} and {{{ o0axialf }}}).

spin-1, color singlet

(proc_card_S1.dat​: topBSM spin-1 color singlet proc_card.dat)

The spin-1, color singlet particle in the {{{ topBSM }}} is called {{{ s1 }}} (PDG code: 6000047). This spin-1 particle is a similar to the SM Z boson. Its mass and width have to be set in the {{{ param_card.dat }}}. By default it has the same couplings as the SM Z boson (only couplings to fermions are implemented). By changing the multiplication factors in the {{{ BLOCK MGUSER }}} in the {{{ param_card.dat }}} the coupling strengths can be altered.

spin-1, color octet

(proc_card_O1.dat​: topBSM spin-1 color octet proc_card.dat)

The spin-1, color octet particle in the {{{ topBSM }}} is called {{{ o1 }}} (PDG code: 6000048). This spin-1 particle is a similar to a heavy gluon. Its mass and width have to be set in the {{{ param_card.dat }}}. By default it has the same couplings as the gluon (only couplings to quarks are implemented). By changing the multiplication factors in the {{{ BLOCK MGUSER }}} in the {{{ param_card.dat }}} the coupling strengths can be altered.

spin-2, ADD model

(proc_card_ADD.dat​: topBSM spin-2 ADD proc_card.dat)

The spin-2 graviton particle of the large extra dimensions model (ADD) is called {{{ s2 }}} in the {{{ topBSM }}} (PDG code: 6000049). Due to the large extra dimensions, the KK gravitons are almost degenerate in mass. Therefore in this model there is not a single resonance, but a very large number that contribute only together significantly. Effectively the denominator of the graviton propagator is calcelled by the sum over all the KK states.

There is a cut-off scale {{{ mstring }}} that you have to specify in the {{{ param_card.dat }}}, as well as the number of extra dimensions (so far only implemented for 3 extra dimensions). The mass of the {{{ s2 }}} should be set equal to the cut-off scale, while the width is not used at all. Note that this cut-off scale is parameter in the model, this is not a cut on the ttbar invariant mass, and there will be ​essay writing events produced above this cut-off scale.

For this model it is important that the couplings are calculated on an event-by-event basis, hence one should set the flag {{{ fixed_couplings }}} in the {{{ run_card.dat }}} to false. (For an example {{{ run_card.dat }}} see above.)

spin-2, RS model

(proc_card_RS.dat​: topBSM spin-2 RS proc_card.dat)

In the RS model there are a number of KK resonances with their mass ratio's given by the zeros of the BesselJ function. The mass of the first resonance has to be given in the {{{ param_card }}}, the others are calculated by the MadGraph code. Also the widths are calculated internally. Furthermore the ratio of %$\kappa/\bar{M}_{\textrm{planck}}$% also has to be specified in the {{{ BLOCK MGUSER }}} to specify the size of the coupling. Note that the RS gravitons are implemented to couple only to quarks and gluons, but in the calculation of the widths, couplings to all SM particles are taken into account.

Only the first 10 resonances are implemented, called {{{ g1 }}}, {{{ g2 }}},..., {{{ g0 }}} (PDG codes: 6000050...6000059) so setting the mass of the first resonance small and using a large value for the coupling strength should be used with care, because effects from higher resonances start getting more important in this part of the parameter space.

-- Main.RikkertFrederix - 09 Dec 2008