1. Hints for Low Supersymmetry Scale from Analysis of Running Couplings
Dimitri Bourilkov
University of Florida
DPF06, October 31, 2006, Waikiki, HI, USA

2. Introduction What happens at (much) higher scales?
3 separate couplings at the Z peak …
D.Bourilkov
DPF06

3. Motivation I
If SUSY is discovered, phenomena arising from the quantum structure of space-time can be studied experimentally
By 1991 the weak coupling was measured with much higher precision than the strong one at LEP
In a famous paper U.Amaldi et al. (PL B260 (1991) 447) showed that in contrast to the SM the MSSM leads to a single unification scale
MSUSY = 103.0±1.0 GeV
MGUT = ±0.3 GeV
1/GUT = 25.7 ± 1.7
so for the SUSY scale: 11 < MSUSY < GeV
At the time the relative error in (MZ), sin2MS and s(MZ) was 0.24 %, 0.77 % and 4.6 %
D.Bourilkov
DPF06

4. Motivation II
From RPP 2004/6 the relative error in (MZ), sin2MS and s(MZ) is %, 0.065% and 1.0%, so we have improved by more than an order of magnitude except for the strong coupling (less than 5 times)
So new analyses are in order (here we expand the analysis from hep-ph/ , hep-ph/ )
Some recent analyses:
W. de Boer, C.Sander,
hep-ph/
B.Allanach et al., hep-ph/
N.Arkani-Hamed, S.Dimopoulos,
hep-th/
Example of a fit with MSUSY = MTOP
D.Bourilkov
DPF06

5. Side Remark
It is amazing that we are trying to extrapolate from 102 to 1016 GeV
From experiments we now that even interpolation or modest extrapolations can be non-trivial
We measure the “offsets” around the Z peak and rely on theory to give us the “slopes” of the running couplings – without errors – up to the GUT scale
This may be an illusion e.g. extra dimensions could modify the running already at TeV scales, so the “unification” point could be imaginary
D.Bourilkov
DPF06

6. Experimental Inputs From Review of Particle Properties 2004
1/(MZ) = ± 0.018
sin2MS = ±
s(MZ) is a different story (larger statistical errors and theory uncertainties); will use the latest results from RPP 2006
s(MZ) = ± from Lattice QCD
s(MZ) = ± World Average
s(MZ) = ± World Average sans Lattice QCD
s(MZ) = ± RPP2004 QCD section
D.Bourilkov
DPF06

7. Analysis technique 2 minimization with 3 parameters: fit with MINUIT
MSUSY , MGUT , 1/GUT
Strong correlation (> 0.999) between MGUT and 1/GUT : problem can be re-factored with 2 parameters, taking 1/GUT as the weighted average of the 3 couplings at any given scale (results are numerically the same except the error on the GUT coupling)
Even so the correlation MSUSY – MGUT is > 0.96
Threshold corrections around the GUT scale (– 4%) for 2-loop-RG running fits
D.Bourilkov
DPF06

8. Running Couplings
1-loop Renormalization Group (RG) running – can solve analytically
1/() = 1/() - (bi/2) . ln(/)
The coefficients for the 3 couplings are independent and given by the SM or MSSM
2-loop-RG running: additional terms so the 3 couplings depend on each other – solved numerically; the errors depend on the scale (for typical GUT scales they grow by 4, 12 and 6 % for the 3 couplings)
D.Bourilkov
DPF06

9. Example of SUSY Fit
D.Bourilkov
DPF06

10. Fit Results s(MZ) from MSUSY [GeV] MGUT 1/GUT
Lattice QCD threshold correction (-4%)
± 0.25
± 0.07
22.8 ± 0.4
Lattice QCD threshold correction (-3%)
± 0.18
± 0.05
23.8 ± 0.3
Lattice QCD threshold correction (-5%)
± 0.23
± 0.07
21.9 ± 0.4
World Average
± 0.38
± 0.12
22.6 ± 0.7
World Average sans Lattice
± 0.37
± 0.12
22.3 ± 0.7
D.Bourilkov
DPF06

11. New Analyses - Add More Data
LEP2 has measured the qq cross section above Z with combined precision ~ 1% and theoretical uncertainty < 0.3 % (and provides correlations between points)
Fit the data with SM or SUSY running couplings (SUSY scale as parameter)
1/(1,2,3) change in SM by -0.9, 1.3, 11.3% from Z -> 201 GeV
1/(1,2,3) will change by , 0.4, 7.5% e.g. for SUSY scale ~ 130 GeV
Slight excess ~ 2  is “filled” nicely by SUSY running
MSUSY = GeV
no correlations: MSUSY = GeV
D.Bourilkov
DPF06

12. Fit Measurements of s @ LEP2
Measurements are difficult / dominated by systematic uncertainties at LEP2 (we use the L3 final result and LEP combined preliminary – QCD WG)
SUSY Fit to L3 data:
MSUSY = 137 ± 38 GeV
SUSY Fit to LEP data:
MSUSY = 172 ± 18 GeV
D.Bourilkov
DPF06

13. Fit Measurements of s @ CDF
Measurements are difficult / dominated by systematic uncertainties at CDF (energy scale and resolution; interplay with the gluon PDF uncertainty at high X values).
SUSY Fit to CDF data:
MSUSY = 153 ± 49 GeV
D.Bourilkov
DPF06

14. Conclusions
The MSSM still provides coupling unification at a GUT scale well below the Planck scale for the newest set of measurements
The strong coupling is a key for interpreting the results: “high” values require uncomfortably low SUSY scales ~ 10 GeV – excluded
The “low” s(MZ) values favor SUSY scales just around the corner: MSUSY < 197 (148) GeV for World Average ‘06 (Lattice QCD) at one-sided 95 % CL  or reversing the argument an attractive “low” SUSY scale favors s(MZ) ~ – 0.119
New analyses above the Z peak (sensitive to the actual running of the couplings) produce a remarkably coherent picture:
qq LEP2: MSUSY = GeV
s LEP2: L3: MSUSY = 137 ± 38 GeV LEP: MSUSY = 172 ± 18 GeV
s CDF: MSUSY = 153 ± 49 GeV
A word of caution: most results are preliminary; there are strong correlations in the s measurements which are not published / not taken into account in the fits
The SUSY scales emerging from this analysis are well in the LHC (TEVATRON?) direct discovery range: stay tuned!
D.Bourilkov
DPF06