Scale Invariance
and
Neutrino Mass
By Kristian McDonald
of the TRIUMF theory group
R. Foot, A. Kobakhidze, KM, R.Volkas, PRD 76, 075014 (2007); PRD 77,35006 (2008).
Outline
- Scale invariance and the hierarchy problem
- A toy model
- The Standard Model and neutrino mass
Scale invariance and the hierarchy problem
- SM is almost scale invariant
- Broken explicitly by scalar mass
- hierarchy problem
- SUSY or Technicolor
- QCD also breaks scale invariance
Broken scale invariance in QCD
- Classical QCD has no scale
- Quantum effects generate a scale
- Scale is stable; why?
Can we learn anything .......
Anomalous Ward Identities
Bardeen (‘95), Hill (05), FKMV (07), Meissner and Nicolai (07).
- Quadratic divergences are not a manifestation of the
anomaly
- Cutoff breaks scale invariance explicitly
- Should we regularize to preserve the symmetry?
No ---- if scale invariance is not a classical symmetry.
But if it is .........
Regularizing to preserve scale invariance
- Dimensional regularization is ideal
- Breaks scale invariance weakly
as does the trace anomaly
- Hard cutoff is fine
- Same thing occurs in SUSY
Features of a model
- Classically scale invariant
- Must generate:
Planck scale
Weak scale & SM
Neutrino mass
- No Landau poles (at least below the Planck scale)
A Two Scalar Toy Model
- Scale invariant potential
- Couple to Ricci scalar
- Identify:
- Dimensional transmutation
A Two Scalar Toy Model
- Weak scale vanishes in decoupling limit
- Hierarchy is technically natural
- Similar to SUSY GUT
- At tree level
- At one loop
A Two Scalar Toy Model: Features
- No Landau pole gives Higgs mass bound
- Scalar masses related
- Light scalar modifies Newtonian potential
Gildener-Weinberg Method
- Requires
- We had
- Need natural parameters, as defined by ‘t Hooft
Applied to the SM
- Add singlet S to the SM
- Forbid tree level violation of scale invariance
- Scalar H identified as SM Higgs
- Light scalar mass
- Symmetry breaking not stable!
Neutrino Mass
Can we generate Nu mass and stabilize the vacuum?
- Try adding right-chiral neutrino N
- Doesn’t help
Small mass: t still dominates
Large mass: N dominates loops
- Need a heavy boson
Neutrino Mass
Tree level mass
Radiative mass
Both cases similar
Neutrino Mass
- Label scalar as B
- Potential has the form:
- Same vacuum pattern
Neutrino Mass: Loop Effects
- Loops correct vacuum structure
- Large hierarchy: can be sensitive
- Two ways to preserve the hierarchy:
Tune it or use ‘t Hooft natural parameters
- Gives mass bound
The PGB
- No tree level mass
- Loops induce a mass
- Bound on B mass gives:
- Modified short distance gravity
Conclusions
- Mass as a quantum effect?
- Hierarchy problem doesn’t arise
- Toy model has main features
- Hypothesis: Nu mass mechanism stabilizes vacuum
- Requires:
B < 100 TeV
Modified gravity:
H < 190 GeV
h < 1 eV