Minimal Universal Extra Dimensions (MUED)

Author

Priscila de Aquino

• Katholieke Universiteit Leuven & Universite Catholique de Louvain - CP3
• priscila@…

Description of the model & references

One popular aproach to solve the Hierarchy Problem of the Standard Model is to extend space-time to higher dimensions. In this framework, the usual four-dimensional space-time is contained in a four-dimensional brane embedded in a large structure with N additional dimensions, the bulk.

Here, we shall focus on the Universal Extra Dimensional theory, in which the usual Standard Model particles are free to propagate in the bulk. As a consequence, these particles will be seem on the effective theory as a tower of N 4-dimensional particles with the same quantum numbers, but with increasing masses. This is called the Kaluza-Klein tower. Momentum conservation in the 5-dimensional space-time generates a conserved Kaluza-Klein number, which implies that different Kaluza-Klein modes can not mix with eachother.

In this implementation, a theory with five dimensions is considered, in which the fifth dimension is spatial and compactified on a S1/Z2 orbifold of radius R. We start from the most general five-dimensional Lagrangian. FeynRules derives the four-dimensional lagrangian automatically by imposing dimensional reduction and integratig out the extra-coordinate y.

The minimal Universal extra dimensional model is given in:

• ​Physical Review D 66 (2002) 056006: H-C. Cheng, K.T. Matchev, M. Schmaltz, Bosonic Supersymmetry? Getting fooled at the LHC.

This implementation was based in another existing implementation in CalcHEP:

• ​mued.ps: A. Datta, K. Kong, K. T. Matchev, Minimal Universal Extra Dimensions in CalcHEP /CompHEP.

The masses of Kaluza-Klein particles are computed via 1 loop:

• ​Physical Review D 66 (2002) 036005: H.-C. Cheng, K. T. Matchev, M. Schmaltz, Radiative Corrections to Kaluza-Klein Masses.

Model files & extensions

The MUED implementation:

• Main FeynRules files (as a tar-ball): ​MUED.tar.gz.
• Run mued.fr. This is the main file. All the other files are called by this main file.
• Example of a Mathematica® notebook loading the model and the parameters: ​MUED.nb.

Instructions

The MUED is implemented in unitary gauge.

• The switch FeynmanGauge (future devlopments) must thus be set to False,
• To run it in CalcHEP the switch FeynmanGauge must be set to True when asking the !CalcHEP output, and then to False before any run.
• In MadGraph, the maximal number of particles must be increased to run the model:
  • Increase the value of max_particles in params.inc in the MadGraphII directory from 2**7-1 to 2**8-1
  • Remove all excecutables in the MadGraphII directory (rm -rf *.o).
  • recompile MadGraph by typing make in the MadGraph main directory.

Validation

In order to validate our implementation, we have checked 118 processes using a center-of-mass energy of 1400 GeV. It was done the following way:

• Comparison of the built-in Madgraph Standard-Model and FeynRules generated Madgraph MUED for Standard Model processes. This comparison was done using squared matrix element at given phase-space points.
• Comparison of the existing CalcHEP MUED (CH-ST) with the FeynRules generated ones in CalcHEP *,* Madgraph and Sherpa: CH-FR, MG-FR and SH-FR, through the calculation of several 2-to-2 cross-sections. All the checks performed were conclusive.

• Validation Table - SM + Fermions (Cross sections given in pb): ValidationMUED.jpg

• Validation Table - Gauge (Cross sections given in pb): ValidationGauge.jpg