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Hints for Low Supersymmetry Scale from Analysis of Running Couplings

Hints for Low Supersymmetry Scale from Analysis of Running Couplings. Dimitri Bourilkov University of Florida DPF06 + JPS06, October 31, 2006, Waikiki, HI, USA. Introduction. What happens at (much) higher scales?. 3 separate couplings at the Z peak …. Motivation I.

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Hints for Low Supersymmetry Scale from Analysis of Running Couplings

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  1. Hints for Low Supersymmetry Scale from Analysis of Running Couplings Dimitri Bourilkov University of Florida DPF06 + JPS06, October 31, 2006, Waikiki, HI, USA

  2. Introduction What happens at (much) higher scales? 3 separate couplings at the Z peak … DPF06 + JPS06

  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 = 1016.0±0.3 GeV 1/GUT = 25.7 ± 1.7 so for the SUSY scale: 11 < MSUSY < 91200 GeV • At the time the relative error in (MZ), sin2MS and s(MZ) was 0.24 %, 0.77 % and 4.6 % DPF06 + JPS06

  4. From RPP 2004/6 the relative error in (MZ), sin2MS and s(MZ) is 0.014%, 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/0410350 , hep-ph/0602168) Some recent analyses: W. de Boer, C.Sander, hep-ph/0307049 B.Allanach et al., hep-ph/0407067 N.Arkani-Hamed, S.Dimopoulos, hep-th/0405159 Example of a fit with MSUSY = MTOP Motivation II DPF06 + JPS06

  5. Side Remark • It is amazing that we are trying to extrapolate from 102 to 1016 GeV • From experiments we now that even interpolationor modest extrapolationscan 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 DPF06 + JPS06

  6. Experimental Inputs • From Review of Particle Properties 2004 • 1/(MZ) = 127.918 ± 0.018 • sin2MS = 0.23120 ± 0.00015 • s(MZ) is a different story (larger statistical errors and theory uncertainties); will use the latest results from RPP 2006 • s(MZ) = 0.1170 ± 0.0012 from Lattice QCD • s(MZ) = 0.1176 ± 0.002 World Average • s(MZ) = 0.1185 ± 0.002 World Average sans Lattice QCD • s(MZ) = 0.1187 ± 0.002 RPP2004 QCD section DPF06 + JPS06

  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 DPF06 + JPS06

  8. Running Couplings 1-loop Renormalization Group (RG) running – can solve analytically 1/() = 1/() - (bi/2) . ln(/) The coefficients for the 3 couplings are independentand 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) DPF06 + JPS06

  9. Example of SUSY Fit DPF06 + JPS06

  10. Fit Results DPF06 + JPS06

  11. 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 -1.2, 0.4, 7.5% e.g. for SUSY scale ~ 130 GeV Slight excess ~ 2  is “filled” nicely by SUSY running MSUSY = 129 +27-23 GeV no correlations: MSUSY = 129 +16-16 GeV New Analyses - Add More Data DPF06 + JPS06

  12. 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 Fit Measurements of s @ LEP2 DPF06 + JPS06

  13. 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 Fit Measurements of s @ CDF DPF06 + JPS06

  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) ~ 0.117 – 0.119 • New analyses above the Z peak (sensitive to the actual running of the couplings) produce a remarkably coherent picture: • qq data @ LEP2: MSUSY = 129 +27-23 GeV • s data @ LEP2: L3: MSUSY = 137 ± 38 GeV LEP: MSUSY = 172 ± 18 GeV • s data @ 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! DPF06 + JPS06

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