== Minimal Universal Extra Dimensions (MUED) ==
=== Author ===
Priscila de Aquino
* Katholieke Universiteit Leuven & Universite Catholique de Louvain - CP3
* priscila@itf.fys.kuleuven.be
=== 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:
* [http://prola.aps.org/abstract/PRD/v66/i5/e056006 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'':
* [http://home.fnal.gov/~kckong/mued/mued.ps 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:
* [http://prola.aps.org/abstract/PRD/v66/i3/e036005 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): [attachment:MUED.tar.gz 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: [attachment:MUED.nb 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