== Two Universal Extra Dimensions ==

=== Author ===

Peter Manning Jr[[BR]]
University of California Santa Cruz[[BR]]
pmmannin at ucsc dot edu[[BR]]

=== Description of the model and references ===

In the Two Universal Extra Dimensions (2UED) model, all of the Standard Model fields are permitted to propagate in the six dimensional space-time. This model is similar to its predecessor, the Universal Extra Dimensions (MUED) model in that the extra dimensions are compactified on some manifold. There are several schema for compactifying two extra dimensions (reference), but in the case of this model, the two extra dimensions are compactified on a chiral square. The topology of the chiral square is that of a sphere with two conical singularities. This scheme allows for the existence of chiral fermions, as there are in the Standard Model. There are several very phenomenologically attractive features of this model. These include the existence of a heavy, weakly interacting, stable particle (dark matter candidate), allowance of only integer multiples of 3 fermion generations, as well as the production of a completely new set of heavy scalar particles. 

The particle spectra of 2UED includes all of the Standard Model particles as well as their Kaluza-Klein excitations in either one or both of the compactified extra dimensions. Upon compactification one recovers the four dimensional gauge fields, but are left with 2 extra components. One of these components, the spinless adjoint to the gauge field, is invariant under 6D gauge transformations. The other, orthogonal excitation, shifts under such a transformation and corresponds to the Nambu-Goldstone boson eaten by the massive vector gauge field level by level. The 6D fermions have four components corresponding to the + or - 6D chiralities and the familiar L and R 4D chiralities. In order to insure 6D anomaly cancellation and fermion mass generation, the chiralities of the weak-doublet quarks (leptons) are forced to be opposite those of the weak-singlet quarks (leptons). That is, for each generation of quarks, there are the following fields: Q+ = (U+,D+), U-, D-, as well as the analogous fields for the leptons. Each of these 6D chiralities is composed of a combination of L and R handed components. Below is a table summarizing the 2UED particle content for the (0,0), (1,0) and (1,1) levels of excitation, where (0,0) are the standard model fields, (1,0) are fields with excitations in 1 extra dimension and (1,1) are fields with excitations in both extra dimensions. 

||''' ''Standard Model Fields'' '''||||||||||||
||'''Particle Name'''||'''Mode'''||'''Description'''||'''FeynRules Name'''||'''MG Name'''||'''CH Name'''||
||u||(0,0)||Standard Model up quark||u ||u|| ||
||d||(0,0)||Standard Model down quark||d ||d || ||
||c||(0,0)||Standard Model charm quark||c||c || ||
||s||(0,0)||Standard Model strange quark||s||s || ||
||t||(0,0)||Standard Model top quark||t||t || ||
||b||(0,0)||Standard Model bottom quark||b||b || ||
||e||(0,0)||Standard Model electron||e||e || ||
||ve||(0,0)||Standard Model electron neutrino||ve||ve || ||
||mu||(0,0)||Standard Model muon||m||m|| ||
||vmu||(0,0)||Standard Model muon neutrino||vm||vm || ||
||tau||(0,0)||Standard Model tau ||tt||tt|| ||
||vtau||(0,0)||Standard Model tau neutrino||vt||vt || ||
||A||(0,0)||Standard Model photon ||A||a || ||
||Z||(0,0)||Standard Model Z-boson ||Z||z || ||
||W||(0,0)||Standard Model W-boson ||W||w || ||
||g||(0,0)||Standard Model gluon ||G||g || ||

||''' ''(1,0) Fields'' '''||||||||||||
||'''Particle Name'''||'''Mode'''||'''Description'''||'''FeynRules Name'''||'''MG Name'''||'''CH Name'''||
||E10+||(1,0)||chirality + electron||e1p||e1p-||||
||VE10+||(1,0)||chirality + electron-neutrino||ve1p||ve1p-||||
||Mu10+||(1,0)||chirality + muon||m1p||m1p-||||
||VMu10+||(1,0)||chirality + muon-neutrino||vm1p||vm1p-||||
||Tau10+||(1,0)||chirality + tau||tt1p||tt1p-||||
||VTau10+||(1,0)||chirality + tau-neutrino||vt1p||vt1p-||||