Two-Loop DecouplingCoefficients for s within MSSM
Outline
• Motivation
• Two-Loop Decoupling Coefficients within MSSM
• Phenomenological Results
Luminita Mihaila*
Universität Karlsruhe
22 July 2005
* in collaboration with R. Harlander and M. Steinhauser
Motivation
• Reconstruction of super symmetric (SUSY) theory at high energies:
extrapolation of coupling constants using RGE to GUT-scale U. Amaldi, W. de Boehr, H. Fürstenau ‘91, …, A. Blair, W.Porod, P. Zerwas ’03, Allanach et al ‘04
largest uncertainties from s)
- need of precise running of s (higher order RGE)
- check stability of s at GUT scale w.r.t. HO perturbative corrections
• RGE program of the SPA Project
Leff fixed by high-precision low-energy measurements RGE (Bottom-up Approach)
Fundamental Theory fixed by high-energy constraints: GUT, mSUGRA, GMSB, AMSB
- required three-loop accuracy for swithin MSSM http://spa.desy.de/spa/
• Mass-independent renormalization schemes ( ) used for HO calculations
- decoupling theorem (T. Appelquist and J. Carazzone ´75) does not hold
- decoupling of heavy particles by hand
- known only at one-loop order within MSSM
Bottom-up Approach
• Running: M=91.18 GeV MSUSY=? MGUT= 1016 GeV
• Allow two mass scales for the intermediate states: MSUSY1 =400GeV, MSUSY2=1000GeV more flexible approach
SUSY-QCD(fullfull) RUN GUT
n-loop [MGUT] [MSUSY1] DEC, (n-1)-loop
SUSY-QCD(g,6g,6) RUN
n-loop [MSUSY2] DEC, (n-1)-loop
QCD(55) RUN
[MZ] n-loop
• Definition of s matching coefficients
g within EFT:
• Computation of g : Green’s functions in effective and full theory
- decoupling coeff. independent of momentum
- for p = 0 vacuum diagrams
- scaleless integrals = 0 contributions only from the “hard parts”
• Two-point functions for g and c: Gp), cp)
-one-loop
- two-loop
- three-point func. Gcc(p,k): only two-loop contributions
• Technicalities
- Regularization Scheme: Dim. Reduction
- Renormalization Scheme: s within
: on-shell
• Results:
- one-loop:
- two-loop: available for specific mass hierarchies [ R. Harlander et al ‘05]
Phenomenological Results
• Input parameters: mtop = 174.3 GeV, s (MZ) =0.1187 ± 0.002
mSUSY = 400 GeV, MSUSY = 1000 GeV
• For used QCD relation [Z. Bern et al ’02] at MZ
sGUT with three-loop accuracy : three-loop running [I. Jack et al ‘96] +
two-loop matching
sGUT as a function of the
matching scales and the loop orders
Scenario A