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