14 | | 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. |
| 14 | 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, 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. |
37 | | ||uq10+||(0,0)||Chirality + up quark||u1p ||u1p|| || |
38 | | ||dq10+||(0,0)||Chirality + down quark||d1p ||d1p || || |
39 | | ||cq10+||(0,0)||Chirality + charm quark||c1p||c1p || || |
40 | | ||sq10+||(0,0)||Chirality + strange quark||s1p||s1p || || |
41 | | ||tq10+||(0,0)||Chirality + top quark||t1p||t1p || || |
42 | | ||bq10+||(0,0)||Chirality + bottom quark||b1p||b1p || || |
43 | | ||E10+||(1,0)||chirality + electron||e1p||e1p-|||| |
44 | | ||VE10+||(1,0)||chirality + electron-neutrino||ve1p||ve1p-|||| |
45 | | ||Mu10+||(1,0)||chirality + muon||m1p||m1p-|||| |
46 | | ||VMu10+||(1,0)||chirality + muon-neutrino||vm1p||vm1p-|||| |
47 | | ||Tau10+||(1,0)||chirality + tau||tt1p||tt1p-|||| |
48 | | ||VTau10+||(1,0)||chirality + tau-neutrino||vt1p||vt1p-|||| |
49 | | |
50 | | | |
51 | | |
| 37 | ||Uq10+||(1,0)||Chirality + up quark||u1p ||u1p|| || |
| 38 | ||Dq10+||(1,0)||Chirality + down quark||d1p ||d1p || || |
| 39 | ||Cq10+||(1,0)||Chirality + charm quark||c1p||c1p || || |
| 40 | ||Sq10+||(1,0)||Chirality + strange quark||s1p||s1p || || |
| 41 | ||Tq10+||(1,0)||Chirality + top quark||t1p||t1p || || |
| 42 | ||Bq10+||(1,0)||Chirality + bottom quark||b1p||b1p || || |
| 43 | ||E10+||(1,0)||Chirality + electron||e1p||e1p-|||| |
| 44 | ||VE10+||(1,0)||Chirality + electron-neutrino||ve1p||ve1p-|||| |
| 45 | ||Mu10+||(1,0)||Chirality + muon||m1p||m1p-|||| |
| 46 | ||VMu10+||(1,0)||Chirality + muon-neutrino||vm1p||vm1p-|||| |
| 47 | ||Tau10+||(1,0)||Chirality + tau||tt1p||tt1p-|||| |
| 48 | ||VTau10+||(1,0)||Chirality + tau-neutrino||vt1p||vt1p-|||| |
| 49 | ||Uq10-||(1,0)||Chirality - up quark||u1m ||u1m|| || |
| 50 | ||Dq10-||(1,0)||Chirality - down quark||d1m ||d1m || || |
| 51 | ||Cq10-||(1,0)||Chirality - charm quark||c1m||c1m || || |
| 52 | ||Sq10-||(1,0)||Chirality - strange quark||s1m||s1m || || |
| 53 | ||Tq10-||(1,0)||Chirality - top quark||t1m||t1m || || |
| 54 | ||Bq10-||(1,0)||Chirality - bottom quark||b1m||b1m || || |
| 55 | ||E10-||(1,0)||Chirality - electron||e1m||e1m-|||| |
| 56 | ||VE10-||(1,0)||Chirality - electron-neutrino||ve1m||ve1m-|||| |
| 57 | ||Mu10-||(1,0)||Chirality - muon||m1m||m1m-|||| |
| 58 | ||VMu10-||(1,0)||Chirality - muon-neutrino||vm1m||vm1m-|||| |
| 59 | ||Tau10-||(1,0)||Chirality - tau||tt1m||tt1m-|||| |
| 60 | ||VTau10-||(1,0)||Chirality - tau-neutrino||vt1m||vt1m-|||| |
| 61 | ||B10||(1,0)||Chirality + tau-neutrino||vt1m||vt1m-|||| |