PhD project: Infrared fixed-point interpretation of QCD-like theories
Project description
The idea that the strong interaction may be governed by an infrared fixed point predates the discovery of QCD. The underlying picture is that spontaneous chiral-symmetry breaking also breaks scale symmetry and, in doing so, generates hadron masses. The associated Nambu–Goldstone mode of the broken scale symmetry, the dilaton, restores the conformal Ward identity in the deep infrared. In QCD, the natural dilaton candidate is the $\sigma$-meson ($f_0(500)$), a state that has puzzled particle physicists for decades. In the physical world this particle (or resonance) decays rapidly into two pions, but little is known about its behaviour when the explicit scale-symmetry breaking due to the up, down, and strange quark masses is removed.
Recent developments, both formal and empirical, suggest that this scenario may indeed be realised in gauge theories such as QCD. On the formal side, scaling exponents extracted under the fixed-point assumption and matched to dilaton effective theory yield a coherent and empirically consistent picture. On the empirical side, lattice studies are finding unexpectedly light scalar states, and fits to gravitational form factors are again consistent with the dilaton interpretation.
Beyond its intrinsic theoretical appeal, this scenario could provide fresh insight for researchers studying confinement and chiral symmetry breaking in QCD. There is additional motivation from model building: if the order parameters for spontaneous chiral symmetry breaking ($F_\pi$) and scale symmetry breaking ($F_\sigma$) are equal, then one can construct an effective theory in which the Higgs sector is replaced by a new gauge theory that is indistinguishable from the Standard Model at leading order. Although empirical indications suggest that $F_\pi/F_\sigma \approx 1$, there is currently no clear understanding of why this ratio should hold.
Projects include:
Extending chiral perturbation theory to incorporate the $\sigma$-meson, with the goal of achieving a full NLO classification and comparing the results with experimental data -especially in channels where a dilaton could play a significant role (notably in $SU_F(3)$ chiral perturbation theory).
The study of gravitational form factorsÂ
Studying hadron scattering as a function of the $\sigma$-meson mass using methods based on unitarity and analyticity, akin to modern bootstrap techniques.
Some references:
https://arxiv.org/pdf/2312.13761 (wider scenario)
https://arxiv.org/pdf/2508.18537 (gravitational form factors)
Project supervisor
- Professor Roman Zwicky (School of Physics & Astronomy, University of Edinburgh)
The project supervisor welcomes informal enquiries about this project.
Find out more about this research area
The links below summarise our research in the area(s) relevant to this project:
- Find out more about Fundamental Theory.
- Find out more about Particle Physics Theory.
- Find out more about the Institute for Particle and Nuclear Physics.
What next?
- Find out how to apply for our PhD degrees.
- Find out about fees and funding and studentship opportunities.
- View and complete the application form (on the main University website).
- Find out how to contact us for more information.