1. Two-Loop Decoupling Coefficients 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

2. 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

3. RGE program of the SPA Project L eff 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  s within MSSM http://spa.desy.de/spa/ 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

4. Bottom-up Approach Running: M=91.18 GeV M SUSY =? M GUT = 10 16 GeV Allow two mass scales for the intermediate states: M SUSY1 =400GeV, MSUSY2=1000GeV more flexible approach full SUSY-QCD (full) RUN GUT n-loop [M GUT ] [M SUSY1 ] DEC, (n-1)-loop g,6 SUSY-QCD (g,6) RUN n-loop [M SUSY2 ] DEC, (n-1)-loop 5 QCD (5) RUN [M Z ] n-loop

5. 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:  G  p  ),  c  p  ) -one-loop - two-loop

6. - 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]

7. Phenomenological Results Input parameters: m top = 174.3 GeV,  s (M Z ) =0.1187 ± 0.002 m SUSY = 400 GeV, M SUSY = 1000 GeV For used QCD relation [Z. Bern et al ’02] at M Z   s  GUT  with three-loop accuracy : three-loop running [I. Jack et al ‘96] + two-loop matching  s  GUT  as a function of the matching scales and the loop orders Scenario A

8.  s  GUT  as a function of  th1 and  th2 :

9.  s  (  ) as a function of  bands due to exp. and theor. errors on

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

12. Conclusions Two-loop decoupling  g + known three-loop running  2 Three-loop accuracy for  s  running 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