[Paper Review] Combining Pati-Salam and Flavour Symmetries

Thorsten Feldmann, Florian Hartmann+2 more|arXiv (Cornell University)|Jun 2, 2015

Particle physics theoretical and experimental studies35 references4 citations

TL;DR

This paper proposes a Pati-Salam grand unified theory (GUT) extended with gauged flavour symmetries, where heavy fermionic partners and flavon fields mediate spontaneous flavour symmetry breaking via renormalizable couplings. The model generates realistic Yukawa matrices for quarks and leptons through VEVs of singlet and triplet flavons, leading to observable deviations in third-generation flavour and electroweak precision observables while satisfying constraints from light-flavour physics.

ABSTRACT

We construct an extension of the Standard Model (SM) which is based on grand unification with Pati-Salam symmetry. The setup is supplemented with the idea of spontaneous flavour symmetry breaking which is mediated through flavon fields with renormalizable couplings to new heavy fermions. While we argue that the new gauge bosons in this approach can be sufficiently heavy to be irrelevant at low energies, the fermionic partners of the SM quarks, in particular those for the third generation, can be relatively light and provide new sources of flavour violation. The size of the effects is constrained by the observed values of the SM Yukawa matrices, but in a way that is different from the standard minimal-flavour violation approach. We determine characteristic deviations from the SM that could eventually be observed in future precision measurements.

Motivation & Objective

• To construct a renormalizable Pati-Salam GUT model that incorporates spontaneous flavour symmetry breaking via flavon fields.
• To explain the hierarchical structure of SM Yukawa matrices without relying on minimal-flavour violation assumptions.
• To identify measurable deviations from the SM in electroweak and flavour observables, particularly involving the third-generation quarks.
• To ensure consistency with indirect flavour constraints from $K$-$\overline{K}$ mixing and rare kaon decays.
• To extend the framework to include realistic charged lepton and neutrino masses through additional flavon structures.

Proposed method

• Introduce heavy vector-like fermion partners for each SM quark generation, transforming under the Pati-Salam gauge group and the flavour symmetry.
• Implement a $Z_2$ symmetry relating the two $SU(2)$ factors to ensure left-right symmetry in the model.
• Introduce matrix-valued flavon fields transforming as singlets and triplets under the $SU(2) \times SU(2)'$ factors to break flavour symmetry.
• Use VEVs of flavon fields to generate effective Yukawa couplings: $Y_{u,d} \sim \text{inverse of flavon VEVs}$, with $Y_u \neq Y_d$ due to different flavon contributions.
• Apply a sequence of basis transformations to diagonalize the fermion mass matrices, leading to effective $\mathcal{K}$-matrices for gauge currents.
• Derive approximate mass basis expressions for the gauge interactions, including corrections up to $\mathcal{O}(\epsilon^3)$, to compute flavour-violating effects.

Experimental results

Research questions

• RQ1 How can Pati-Salam GUTs be extended with gauged flavour symmetries to generate realistic Yukawa textures?
• RQ2 What role do flavon VEVs—specifically singlet and triplet representations—play in distinguishing up- and down-type quark Yukawa matrices?
• RQ3 Can the model produce observable flavour-violating effects in the third generation while remaining consistent with constraints from first- and second-generation flavour observables?
• RQ4 How do the gauge interactions of the heavy fermion partners modify the $\mathcal{K}$-matrices of the $W$ and $Z$ bosons in the approximate mass basis?
• RQ5 Can the framework be extended to include realistic charged lepton and neutrino masses through additional flavon fields?

Key findings

• The model generates $Y_u \neq Y_d$ through separate VEVs of $SU(2)$ singlet and triplet flavons, enabling realistic quark masses and mixing angles.
• The top quark partner $t'$ is predicted to be relatively light, with significant mixing to the SM top quark, making it potentially accessible at the LHC.
• Flavour-violating effects are strongly enhanced in the third generation, leading to measurable deviations in electroweak precision observables.
• Indirect constraints from $K$-$\overline{K}$ mixing and rare kaon decays are naturally satisfied due to the structure of the flavour symmetry breaking.
• The effective $\mathcal{K}$-matrices for $W$ and $Z$ bosons in the approximate mass basis include $\mathcal{O}(\epsilon^3)$ corrections, which encode the dominant flavour-violating contributions.
• The framework can be systematically extended to include charged lepton and neutrino masses via additional flavon fields with appropriate quantum numbers.