This is a repository for the leptoquark model explored in arXiv:1803.05962 by A.Monteux and A.Rajaraman. Please cite the paper if you use this UFO or find this useful.

The UFO file was generated with FeynRules.

Examples on how to generate events with Madgraph are provided below.

In this model we introduce composite scalar leptoquarks $S_1$ and $\tilde{S}_1$ (in the notation of Buchmüller, Ruckl, Wyler), as well as a scalar singlet $N$ and composite scalar color-sextets and octets. The standard leptoquark interaction Lagrangian is

to which we add interactions involving the neutral scalar (here and below, all the G's have dimensions of mass^-1)

and interactions of the sextet and octet

Finally, the singlet has an effective coupling to quarks and leptons

Download the UFO file here, and untar it in your mg5_aMC/models directory.

The BSM fields and the Lagrangian are defined in the FeynRules input composite_LQ.fr.

We have translated the lagrangians in FeynRules to generate a UFO file, keeping the names and symbols of parameters as close as possible to the nomenclature above (parameters with a ~ have a t in front of their names, e.g. $\tilde{S}_1$->tS1, $\tilde G$->tG).

field
quantum numbers	(3,1,-1/3)	(3,1,-4/3)	(1,1,0)	(6,1,-2/3)	(3,1,-8/3)	(8,1,0)
mg5 name	S1b	tS1b	nn	six	tsix	oct
PID	9000010	9000011	9000050	9000060	9000061	9000080

By default the leptoquarks are at 600 GeV, the sextet and octet at 1500 GeV, and the singlet scalar at 100 GeV.

Most couplings in the Lagrangian above are set to zero, apart from the entries that allow decays with c,tau or b,mu (which were the final states we were interested in the paper). For simplicity the defaults have all LH couplings set to zero and only turned on the RH couplings.

In particular, the only non-zero entries are the 23 components of the g,G matrices, the 32 components of tg,tGs, as well as gNu₂ and gNd₃. Defaults are 1 for all non-zero dimensionless couplings, and 10³ GeV (or 10^-3 GeV^-1) for non-zero dimensionful couplings.

We considered QCD pair-production of the scalars above, followed by multiple decay steps. One can either write the whole process in Madgraph, or only produce the leptoquarks and let Pythia handle the decays (the latter is considerably faster, especially with the many final states present). For Pythia to know how to decay the new particles, we use compute_widths in Madgraph to calculate the branching ratios.
NB There is a bug/feature in compute_widths where it does not write partial widths of a colored particle if the width is less than the QCD scale, which can happen for some of the default parameters used.

See below for correcting this behavior in Madgraph

All processes used in our paper are present in composite_LQ_test.mg5 and can be generated at once by running

bin/mg5_amc  composite_LQ_test.mg5

For completeness, we also list each process below.

import model composite_LQ_UFO
generate p p > s1b s1b~
output lqlq_ccctau
launch
 set nevents 100
 set g1r2x3 0
 set gnnd3 0
 set gnnu2 1
 compute_widths s1b
 compute_widths nn
 done

import model composite_LQ_UFO
generate p p > ts1b ts1b~
output lqlq_bbbmu
launch
 set nevents 100
 set gt1r3x2 0
 set gnnu2 0
 set gnnd3 1
 compute_widths ts1b
 compute_widths nn
 done

import model composite_LQ_UFO
generate p p > six six~
output lq_sixsix_ccctau
launch
 set nevents 100
 set g1r2x3 0
 set gnnd3 0
 set gnnu2 1
 compute_widths six
 compute_widths s1b
 compute_widths nn
 done

import model composite_LQ_UFO
generate p p > tsix tsix~
output lq_sixsix_bbbmu
launch
 set nevents 100
 set gt1r3x2 0
 set gnnu2 0
 set gnnd3 1
 compute_widths tsix
 compute_widths ts1b
 compute_widths nn
 done

import model composite_LQ_UFO
generate p p > oct  oct
output lq_octoct
launch
 set nevents 100
 set GtS8r3x2 0
 set GS8r2x3 0.001
 set g1r2x3 0
 set gnnd3 0
 set gnnu2 1
 compute_widths 9000080
 compute_widths s1b
 compute_widths nn
 done

launch lq_octoct
 set nevents 100
 set GS8r2x3 0
 set GtS8r3x2 0.001
 set gt1r3x2 0
 set gnnu2 0
 set gnnd3 1
 compute_widths 9000080
 compute_widths ts1b
 compute_widths nn
 done

That's it!

When Madgraph (in versions MG5_aMC 2.2--2.6+) calculates the width of a colored particle and finds it is smaller than the QCD scale, it automatically discard that decay mode (with a warning: "width of colored particle lower than QCD scale". While it is true that the correct decay should be computed between hadronized states, the decay chain is correctly captured by the undressed process, and one expects only O(1) deviations for the numerical value of the width (see e.g. this launchpad post).

Remembering that we are computing the widths only to fill the decay table so that pythia can use them (and we do not even care about the numerical values), we discard this warning.

One should therefore comment out three blocks in MG5_aMC_v2_XX/madgraph/interface/madgraph_interface.py, in the function do_compute_widths where the warning appears (the only three blocks where "QCD scale" appears). For MG5_AMC 2.6.1, the blocks to be commented out are copied below

## line 8027 of madgraph_interface.py ##
                    elif 0 < value < 0.1 and particle['color'] !=1:
                        logger.warning("partial width of particle %s lower than QCD scale:%s. Set it to zero. (%s)" \
                                   % (particle.get('name'), value, decay_to))
                        value = 0

## line 8097 of madgraph_interface.py ##
            if particle['color'] !=1 and 0 < width.real < 0.1:
                logger.warning("width of colored particle \"%s(%s)\" lower than QCD scale: %s. Set width to zero "
                               % (particle.get('name'), pid, width.real))
                width = 0

## line 8110 of madgraph_interface.py ##
                if 0 < BR.value * width <0.1 and particle['color'] !=1:
                    logger.warning("partial width of particle %s lower than QCD scale:%s. Set it to zero. (%s)" \
                                   % (particle.get('name'), BR.value * width, BR.lhacode[1:]))
                                     
                    continue