== 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, as well as phenomenologically interesting 2UED including the existence of a heavy, weakly interacting, stable particle (dark matter candidate), allowancing only integer multiples of 3 fermion generations, and the production of a completely new set of heavy scalar particles. 

The particle spectra of 2UED includes all of the Standard Model particles, their Kaluza-Klein excitations in either one or both of the compactified extra dimensions, as well as scalar spinless adjoints to the excited vector gauge fields. Upon compactification one recovers the four dimensional gauge fields, but are left with two extra components. One of these components, the aforementioned scalar 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, including a - chirality neutrino field. 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. 

Particles produced in this model must conserve Kaluza-Klein parity in their decays. That is, a (1,0) particle must decay to another (1,0) particle and a standard model particle. Conversely, standard model particles can only pair produce KK particles. There is an exception to this rule. If the interaction is localized on either of the conical singularities, KK number may be violated, while still preserving KK parity. For example, the process gg -> Gmu11 conserves the KK even parity, (2 (0,0) particles to 1 (1,1) particle), but does not preserve KK number. These KK number violating operators are what allows for Gmu11, GH11, as well as the other level (1,1) KK excitations of the gauge fields and their spinless adjoints to decay to top quark pairs. 


||''' ''Standard Model Fermion Fields'' '''||||||||||||
||'''Particle Name'''||'''Mode'''||'''Description'''||'''FeynRules Name'''||'''MG Name'''||'''CH Name'''||
||u, c, t||(0,0)||Standard Model up, charm, top quarks||u, c, t ||u, c, t|| ||
||d, s, b||(0,0)||Standard Model down, strange, bottom quarks||d, s, b ||d, s, b|| ||
||e,mu,tau||(0,0)||Standard Model electron, muon, tau||e||e-,m-,tt- || ||
||ve, vmu, vtau ||(0,0)||Standard Model electron, mu, tau neutrino||ve, vmu, vtau||ve, vmu, vtau || ||
||''' ''Standard Model Gauge Fields'' '''||||||||||||
||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 || ||

||''' ''KK (1,0) Fermion Fields'' '''||||||||||||
||'''Particle Name'''||'''Mode'''||'''Description'''||'''FeynRules Name'''||'''MG Name'''||'''CH Name'''||
||UQ10+, CQ10+, TQ10+ ||(1,0)||Chirality + KK up,charm,top quark||u1p, c1p, t1p ||u1p, c1p, t1p|| ||
||DQ10+, SQ10+, BQ10+ ||(1,0)||Chirality + KK down,strange,bottom quark||d1p, s1p ,b1p ||d1p, s1p, b1p|| ||
||E10+, Mu10+, Tau10+||(1,0)||Chirality + KK electron, muon, tau||e1p, m1p, tt1p||e1p-, m1p-, tt1p-||||
||VE10+, VMu10+, VTau10+||(1,0)||Chirality + KK electron, muon, tau-neutrino||ve1p, vm1p, vt1p||ve1p, vm1p, vt1p||||
||UQ10-, CQ10-, TQ10- ||(1,0)||Chirality - KK up,charm,top quark||u1m, c1m, t1m ||u1m, c1m, t1m|| ||
||DQ10-, SQ10-, BQ10- ||(1,0)||Chirality - KK down,strange,bottom quark||d1m, s1m ,b1m ||d1m, s1m, b1m|| ||
||E10-, Mu10-, Tau10-||(1,0)||Chirality - KK electron, muon, tau||e1m, m1m, tt1m||e1m-, m1m-, tt1m-||||
||VE10-, VMu10-, VTau10-||(1,0)||Chirality - KK electron, muon, tau-neutrino||ve1m, vm1m, vt1m||ve1m, vm1m, vt1m||||
||''' ''KK (1,0) Gauge Fields'' '''||||||||||||
||B10, W10, Z10, G10||(1,0)||Vector KK photon, W, Z and Gluon ||B10, W10, Z10, G10 ||B10,W10,Z10,G10||||
||BH10, WH10, ZH10, GH10||(1,0)||Scalar KK photon, W, Z and Gluon ||BH10, WH10, ZH10, GH10 ||BH10,WH10,ZH10,GH10||||

||''' ''KK (1,1) Fermion Fields'' '''||||||||||||
||'''Particle Name'''||'''Mode'''||'''Description'''||'''FeynRules Name'''||'''MG Name'''||'''CH Name'''||
||UQ11+, CQ11+, TQ11+ ||(1,1)||Chirality + KK up,charm,top quark||u2p, c2p, t2p ||u2p, c2p, t2p|| ||
||DQ11+, SQ11+, BQ11+ ||(1,1)||Chirality + KK down,strange,bottom quark||d2p, s2p ,b2p ||d2p, s2p, b2p|| ||
||E11+, Mu11+, Tau11+||(1,1)||Chirality + KK electron, muon, tau||e2p, m2p, tt2p||e2p-, m2p-, tt2p-||||
||VE11+, VMu11+, VTau11+||(1,1)||Chirality + KK electron, muon, tau-neutrino||ve2p, vm2p, vt2p||ve2p, vm2p, vt2p||||
||UQ11-, CQ11-, TQ11- ||(1,1)||Chirality - KK up,charm,top quark||u2m, c2m, t2m ||u2m, c2m, t2m|| ||
||DQ11-, SQ11-, BQ11- ||(1,1)||Chirality - KK down,strange,bottom quark||d2m, s2m ,b2m ||d2m, s2m, b2m|| ||
||E11-, Mu11-, Tau11-||(1,1)||Chirality - KK electron, muon, tau||e2m, m2m, tt2m||e2m-, m2m-, tt2m-||||
||VE11-, VMu11-, VTau11-||(1,1)||Chirality - KK electron, muon, tau-neutrino||ve2m, vm2m, vt2m||ve2m, vm2m, vt2m||||
||''' ''KK (1,1) Gauge Fields'' '''||||||||||||
||B11, W11, Z11, G11||(1,1)||Vector KK photon, W, Z and Gluon ||B11, W11, Z11, G11 ||B11,W11,Z11,G11||||
||BH11, WH11, ZH11, GH11||(1,1)||Scalar KK photon, W, Z and Gluon ||BH11, WH11, ZH11, GH11 ||BH11,WH11,ZH11,GH11||||