Effective Theories of Flavor & the Non-Universal MSSM
Planck 2016 Michael Jay Pérez
IFIC CSIC-University of Valencia 5/25/2016
In collaboration with M. López-Ibáñez, D. Das, O. Vives
The Flavor Puzzle
2
A Theory of Flavor?
• Large hierarchies
• Small mixing
A Theory of Flavor?
• Large hierarchies
• Small mixing
4
Froggatt-Nielsen Mechanism
• Nice way to explain hierarchy in Yukawa matrices
• Spontaneously broken flavor symmetry generates Yukawas
• Small Expansion parameter :
• Unfortunately, many possible choices for Flavor Symmetry!
• Abelian U(1), SU(3), Non-Abelian Discrete…
The Real Problem…
• Large Redundancies in Yukawa Sector!
• Only masses + CKM and MNSP Matrices are observable
• 3 mixing angles + 1 Dirac phase each
• Expansion parameter is dimensionless
• Flavor scale can be arbitrarily heavy!
6
Flavor Opportunities
• New Couplings needed!
• What is the structure of the right-handed mixing?
• Small? (CKM) or Large? (MNSP)
• New flavor couplings a generic feature of many NP models
• “Flavor Puzzle” can become “Flavor Opportunities!”
SUSY as a Lab for Flavor
• Perfect example of calculable NP models with new flavor couplings
• New flavor structures in SUSY soft-breaking terms : Trilinear interactions (A terms) and
sfermion soft masses
• If there is a Flavor symmetry, it applies at the level of the super-fields
• Ex : Controls the form of the super potential…
• Soft terms
8
Two possibilities…
• Soft terms already present below the
SUSY Breaking scale
• Soft terms must respect the flavor symmetry
• Corrections generated as
functions of epsilon
• Ex : Gravity Mediation
• Soft terms
generated after flavor breaking
• Only
renormalizable remnant below Flavor breaking
scale are Yukawas
• Ex : Gauge Mediation
Two possibilities…
• Soft terms already present below the
SUSY Breaking scale
• Soft terms must respect the flavor symmetry
• Corrections generated as
functions of epsilon
• Ex : Gravity Mediation
• Soft terms
generated after flavor breaking
• Only
renormalizable remnant below Flavor breaking
scale are Yukawas
• Ex : Gauge Mediation
MSSM & Flavor
• Superpotential fixed by Yukawas
• SUSY Breaking contains unknown flavor parameters (100+!)
• SUSY Breaking communicated to “visible
sector” through non-renormalizable interactions
• Modify W and Kähler potential K
• Assume a single source of universal SUSY breaking
Froggatt Nielsen Effective MSSM
• Two contributions to W and K
• Effective operators from FN
• SUSY Breaking contributions ~ F
• Easiest way to organize is in terms of Supergraphs!
12
Yukawa Sector
A Terms
• Same type of Supergraph generates the A term, but multiple possibilities!
14
Kähler Function
Kähler Flavon contributions
16
Example : Toy U(1) Model
Toy U(1) Model
18
Further Work
• Non-Abelian symmetries
• Lepton sector
• Phenomenological studies
• Realistic Models
SU(3) Model
20
