S. M. Barr’s research while affiliated with University of Delaware and other places

... The extended models for radiative fermion masses can mainly be categorized into two classes based on the nature of new particle(s) propagating in the fermion self-energy loops 1 (a) spin-0 (see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] for example) and (b) spin-1 [24][25][26][27][28][29]. In the case of the latter, SM gauge symmetry needs to be extended to include a gauged flavour symmetry group G F and the radiative correction can be determined in terms of the gauge couplings and masses of the new gauge bosons. ...

Reference:

Gauged SU(3)F and loop induced quark and lepton masses

... The flavor structure was later relaxed in refs. [8][9][10][11][12], since one could have distinguished threegenerational SM quarks/leptons as long as there are three distinctive 10 F 's according to the flavor identifications. This was recently re-stated in ref. [12] that an SU(8) theory with 156 chiral fermions is the minimal framework where three-generational SM quarks/leptons can transform differently, when one embeds them into distinctive chiral irreducible anomaly-free fermion sets (IRAFFSs) in the UV theory. ...

Reference:

The Standard Model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an SU(8) theory

... It was pointed out and discussed in Refs. [3][4][5][6][7] that multiple fermion generations, such as n g = 3 for the SM case, can be embedded non-trivially in GUT groups of SU(7) and beyond. 1 Therefore, it is natural to conjecture that the SM fermion mass hierarchies may originate from the intermediate symmetry breaking scale of some non-minimal GUT with SU(N ≥ 7) [4,5]. Historically, the embedding of the SM generations as well as fermion mass hierarchies were studied in the context of technicolor and extended technicolor models [8][9][10][11][12], where the symmetry breakings are due to the fermion bi-linear condensates. ...

Reference:

Bottom quark and tau lepton masses in a toy $$\textrm{SU}(6)$$ model