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mitchell porter
Gold Member
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- TL;DR
- Complexified gauge theory and larger chiral symmetries
I thought of posting this under Particle Physics, but it does go slightly beyond standard model, and in a way that could point to some larger theories, so I post it here.
"A path to confine gluons and fermions through complex gauge theory" (Amaral et al 2020)
"New picture on the mesons mass relations" (Amaral et al 2025)
I'll try to summarize. There is a conventional explanation for the masses of the pions, kaons, and eta mesons. Eight of them are Goldstone bosons of the broken chiral symmetry [SU(3)L x SU(3)R] / SU(3)V. This implies "GMOR relations" in which the hierarchy of light quark masses (m_s > m_u, m_d) implies the relationships among most of the meson masses. The exception is the eta0 meson. In this case there is another meson, eta0-prime, which is a singlet of the chiral symmetry, and which is made heavy by interactions with instantons in the QCD vacuum. eta0 and eta0-prime mix, and give us the heavy phenomenological eta and eta-prime mesons.
An extra technical detail is that the GMOR mass perturbation arising from the quark masses can be represented group-theoretically by a "spurion field" corresponding to the λ_8 element of SU(3). This is not normally regarded as very meaningful, it's just how the quark mass pattern would be encoded.
What the Brazilians do is work with a larger chiral symmetry, U(3)L x U(3)R, which means that they are bringing that ninth meson, eta-prime, into play. When you look at the pattern of masses this time, the spurion is now "T0 - sqrt(2) T8", an element of U(3). But this element already appeared in their 2020 paper, in which they proposed a model of confinement in which the gauge group of QCD is SL(3,C), the complexification of SU(3). In that paper they also had nine fields, the usual eight gluons plus a current made of two new fundamental scalar fields.
They suggest that something similar might therefore be happening in the flavor sector. To be explicit in a way that they aren't: the implication is that the light quark masses are being determined by a process analogous to their model of confinement in complexified color.
All this could just be the group-theory analogue of the kind of numerological coincidence that can send a person astray when they investigate the unexplained parameters of the standard model. I suspect a majority of particle physicists would be happy to dismiss it as a coincidence. But some of us here have had reason to investigate the possibility of deep relationships between color and flavor, or between the strong and the electroweak sectors. So maybe this idea from Brazil warrants a little consideration.
The details are a bit messy. On the meson side, the ninth element is simply the eta0-prime meson. But on the gluon side, the ninth element is two new scalar fields, coupled in a nonstandard way (normally you would just combine them into a single complex scalar field, but that won't work here). Also, they complexify the gauge group of the strong force! Complex gauge groups are generally fatal for a Yang-Mills field, though there are a handful of contexts in which they work out.
On the other hand, in some of the heterodox unified theories (like some of the ones mentioned in the recent gravi-GUT thread), you want a complexified gauge group to work. People who work on those, might want to take an interest here.
Regarding the exact mechanism of complexification on the flavor side, it seems to me you could either suppose that there is a whole new Yang-Mills field corresponding to the gauging of flavor, and that it is complexified too (which would make sense if all the Yang-Mills forces are fundamentally complexified). Or, you might suppose that the gauging of flavor is more tightly unified with the gauging of color. You already have an emergent gauging of flavor in standard QCD via the rho meson... You'd also still need to make contact with the Higgs yukawa couplings, whether through flavon VEVs or modular symmetries or in some other way, in order that the group-theoretic pattern can show up there.
Apriori, the odds are probably against this working out, as they are for anything this far outside standard theory. But the details are concrete enough that, if you already have an interest in complexified gauge theory or color/flavor crossovers, it's probably worth spending a little time investigating these ideas.
"A path to confine gluons and fermions through complex gauge theory" (Amaral et al 2020)
"New picture on the mesons mass relations" (Amaral et al 2025)
I'll try to summarize. There is a conventional explanation for the masses of the pions, kaons, and eta mesons. Eight of them are Goldstone bosons of the broken chiral symmetry [SU(3)L x SU(3)R] / SU(3)V. This implies "GMOR relations" in which the hierarchy of light quark masses (m_s > m_u, m_d) implies the relationships among most of the meson masses. The exception is the eta0 meson. In this case there is another meson, eta0-prime, which is a singlet of the chiral symmetry, and which is made heavy by interactions with instantons in the QCD vacuum. eta0 and eta0-prime mix, and give us the heavy phenomenological eta and eta-prime mesons.
An extra technical detail is that the GMOR mass perturbation arising from the quark masses can be represented group-theoretically by a "spurion field" corresponding to the λ_8 element of SU(3). This is not normally regarded as very meaningful, it's just how the quark mass pattern would be encoded.
What the Brazilians do is work with a larger chiral symmetry, U(3)L x U(3)R, which means that they are bringing that ninth meson, eta-prime, into play. When you look at the pattern of masses this time, the spurion is now "T0 - sqrt(2) T8", an element of U(3). But this element already appeared in their 2020 paper, in which they proposed a model of confinement in which the gauge group of QCD is SL(3,C), the complexification of SU(3). In that paper they also had nine fields, the usual eight gluons plus a current made of two new fundamental scalar fields.
They suggest that something similar might therefore be happening in the flavor sector. To be explicit in a way that they aren't: the implication is that the light quark masses are being determined by a process analogous to their model of confinement in complexified color.
All this could just be the group-theory analogue of the kind of numerological coincidence that can send a person astray when they investigate the unexplained parameters of the standard model. I suspect a majority of particle physicists would be happy to dismiss it as a coincidence. But some of us here have had reason to investigate the possibility of deep relationships between color and flavor, or between the strong and the electroweak sectors. So maybe this idea from Brazil warrants a little consideration.
The details are a bit messy. On the meson side, the ninth element is simply the eta0-prime meson. But on the gluon side, the ninth element is two new scalar fields, coupled in a nonstandard way (normally you would just combine them into a single complex scalar field, but that won't work here). Also, they complexify the gauge group of the strong force! Complex gauge groups are generally fatal for a Yang-Mills field, though there are a handful of contexts in which they work out.
On the other hand, in some of the heterodox unified theories (like some of the ones mentioned in the recent gravi-GUT thread), you want a complexified gauge group to work. People who work on those, might want to take an interest here.
Regarding the exact mechanism of complexification on the flavor side, it seems to me you could either suppose that there is a whole new Yang-Mills field corresponding to the gauging of flavor, and that it is complexified too (which would make sense if all the Yang-Mills forces are fundamentally complexified). Or, you might suppose that the gauging of flavor is more tightly unified with the gauging of color. You already have an emergent gauging of flavor in standard QCD via the rho meson... You'd also still need to make contact with the Higgs yukawa couplings, whether through flavon VEVs or modular symmetries or in some other way, in order that the group-theoretic pattern can show up there.
Apriori, the odds are probably against this working out, as they are for anything this far outside standard theory. But the details are concrete enough that, if you already have an interest in complexified gauge theory or color/flavor crossovers, it's probably worth spending a little time investigating these ideas.