one-loop inert and pseudo-inert minima pedro ferreira isel and cftc, ul, portugal toyama, 14/02/2015...
DESCRIPTION
The Two-Higgs Doublet potential m 2 12, λ 5, λ 6 and λ 7 complex - seemingly 14 independent real parameters Most general SU(2) × U(1) scalar potential: Most frequently studied model: model with a Z 2 symmetry, Φ 2 → -Φ 2, meaning m 12, λ 6, λ 7 = 0. It avoids potentially large flavour-changing neutral currents.TRANSCRIPT
One-loop inert and pseudo-inert minima
Pedro Ferreira
ISEL and CFTC, UL, PortugalToyama, 14/02/2015
Preliminary results, with Bogumila Swiezewska, Univerity of Warsaw
The Two-Higgs Doublet potential
m212, λ5, λ6 and λ7 complex - seemingly 14 independent real parameters
Most general SU(2) × U(1) scalar potential:
Most frequently studied model: model with a Z2 symmetry,
Φ2 → -Φ2, meaning m12, λ6, λ7 = 0.
It avoids potentially large flavour-changing neutral currents.
Z2-symmetric model
Coupling to fermions
MODEL I: Only Φ2 couples to fermions.
MODEL II: Φ2 couples to up-quarks, Φ1 to down quarks and leptons.. . .
• SEVEN real independent parameters.
• The symmetry must be extended to the whole lagrangian, otherwise the model would not be renormalizable.
Inert: Only Φ1 couples to fermions.
Inert vacua – preserve Z2 symmetry
• The INERT minimum,
• Since only Φ1 has Yukawa couplings, fermions are massive – “OUR” minimum.
00
and 0
21 2
11 v
• The PSEUDO-INERT minimum,
• Since only Φ1 has Yukawa couplings, fermions are massless.
221
02
1 and 00
v
WHY BOTHER?
In the inert minimum, the second doublet originates perfect Dark Matter candidates!
Inert neutral scalars do not couple to fermions or have triple vertices with gauge bosons.
Tree-level vacuum solutions
INERT:
PSEUDO-INERT:
E. Ma, Phys. Rev. D73 077301 (2006); R. Barbieri, L.J. Hall and V.S. Rychkov Phys. Rev. D74:015007 (2006); L. Lopez Honorez, E. Nezri, J. F. Oliver and M. H. G. Tytgat, JCAP 0702, 028(2007); L. Lopez Honorez and C. E. Yaguna, JHEP 1009, 046(2010); L. Lopez Honorez and C. E. Yaguna, JCAP 1101, 002 (2011)
These minima can coexist in the potential, which raises a troubling possibility...
Local minimum -INERT
Global minimum – PSEUDO-INERT
MeVmGeVmGeVmGeVv
e
t
W
511.017380
246
!0!080
246
e
t
W
mm
GeVmGeVv
Tree-level relations between the depth of the potential at minima
Let v be the VEV at the INERT minimum, and v’ the PSEUDO-INERT VEV. Then:
QUESTIONS:
•HOW DO THESE RELATIONS CHANGE WITH LOOP CORRECTIONS?
•CAN THERE BE AN “INVERSION” OF INERT AND •PSEUDO-INERT MINIMA DEPTHS AT ONE-LOOP?
The one-loop inert minima were studied by Gil, Chankowski and Krawczyck in Phys. Lett. B717 (2012) 396, but the emphasis here is in comparing the relations between depths of tree-level and one-loop potentials.
One-loop effective potential
• Field-dependent mass eigenvalues - PAIN.
• TOY MODEL – only scalar sector (so far), global SU(2)×U(1).
• Scalar masses calculated using (so far) the effective potential approximation (second derivatives of the potential).
• Compute one-loop effective potential.
• Minimize it, requiring SIMULTANEOUS EXISTENCE of inert and pseudo-inert vacua.
• Compute ALL SQUARED MASSES at both vacua and demand they are all positive – COEXISTING MINIMA.
• Demand that, at the inert vacuum, v = 246 GeV, mh = 125 GeV.
• Compare depths of potentials at both minima.
As of 14/02/2015... Do one-loop corrections “invert” the depths of the potential?
: Tree-level expected relative depths
: One-loop computed relative depths
Inversion of minima for 3% of scanned parameter space
Now here’s something interesting...
: Tree-level expected relative depths
: One-loop computed relative depths
Inversion of minima for 0.5% of scanned parameter space!
Tree-level obtained formula seems almost exact...
Now here’s something EVEN MORE interesting...
IMPOSSIBLE TO HAVE SIMULTANEOUS MINIMA IN THIS REGION AT TREE-LEVEL!
NO CONCLUSIONS – ONLY FUTURE HARD WORK!
- Recover from jet-lag...