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

sGUT as a function of th1 and th2 :

s( ) as a function of bands due to exp. and theor. errors on

• Comparison with the s running by Allanach et al ’04 (two-loop)

Conclusions

• Two-loop decoupling g + known three-loop running 2

Three-loop accuracy for srunning within MSSM

• Very good stability of the HO perturbative expansion w.r.t.

matching scales (source of theoretical uncertainties)

• Large uncertainties due to SUSY mass pattern