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. D.BourilkovDPF06 + JPS062 Introduction 3 separate couplings at the Z peak …What happens at (much) higher scales?

3. D.BourilkovDPF06 + JPS063 Motivation I If SUSY is discovered, phenomena arising from the quantum structure of space-time can be studied experimentallyIf 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 LEPBy 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 scaleIn 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 M SUSY = 10 3.0±1.0 GeV M SUSY = 10 3.0±1.0 GeV M GUT = 10 16.0±0.3 GeV M GUT = 10 16.0±0.3 GeV 1/  GUT = 25.7 ± 1.7 1/  GUT = 25.7 ± 1.7 so for the SUSY scale: 11 < M SUSY < 91200 GeV so for the SUSY scale: 11 < M SUSY < 91200 GeV At the time the relative error in  (M Z ), sin 2  MS and  s (M Z ) was 0.24 %, 0.77 % and 4.6 %At the time the relative error in  (M Z ), sin 2  MS and  s (M Z ) was 0.24 %, 0.77 % and 4.6 %

4. D.BourilkovDPF06 + JPS064 Motivation II From RPP 2004/6 the relative error in  (M Z ), sin 2  MS and  s (M Z ) 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)From RPP 2004/6 the relative error in  (M Z ), sin 2  MS and  s (M Z ) 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)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 M SUSY = M TOP

5. D.BourilkovDPF06 + JPS065 Side Remark It is amazing that we are trying to extrapolate from 10 2 to 10 16 GeVIt is amazing that we are trying to extrapolate from 10 2 to 10 16 GeV From experiments we now that even interpolation or modest extrapolations can be non-trivialFrom 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 scaleWe 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 imaginaryThis may be an illusion e.g. extra dimensions could modify the running already at TeV scales, so the “unification” point could be imaginary

6. D.BourilkovDPF06 + JPS066 Experimental Inputs From Review of Particle Properties 2004From Review of Particle Properties 2004 –1/  (M Z ) = 127.918 ± 0.018 –sin 2  MS = 0.23120 ± 0.00015  s (M Z ) is a different story (larger statistical errors and theory uncertainties); will use the latest results from RPP 2006  s (M Z ) is a different story (larger statistical errors and theory uncertainties); will use the latest results from RPP 2006 –  s (M Z ) = 0.1170 ± 0.0012 from Lattice QCD –  s (M Z ) = 0.1176 ± 0.002 World Average –  s (M Z ) = 0.1185 ± 0.002 World Average sans Lattice QCD –  s (M Z ) = 0.1187 ± 0.002 RPP2004 QCD section

7. D.BourilkovDPF06 + JPS067 Analysis technique  2 minimization with 3 parameters: fit with MINUIT  2 minimization with 3 parameters: fit with MINUIT M SUSY, M GUT, 1/  GUT Strong correlation (> 0.999) between M GUT 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 )Strong correlation (> 0.999) between M GUT 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 M SUSY – M GUT is > 0.96Even so the correlation M SUSY – M GUT is > 0.96 Threshold corrections around the GUT scale (– 4%) for 2-loop-RG running fitsThreshold corrections around the GUT scale (– 4%) for 2-loop-RG running fits

8. D.BourilkovDPF06 + JPS068 Running Couplings 1-loop Renormalization Group (RG) running – can solve analytically 1/  ( ) = 1/  (  ) - (b i /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)

9. D.BourilkovDPF06 + JPS069 Example of SUSY Fit

10. D.BourilkovDPF06 + JPS0610 Fit Results  s (M Z ) from  s (M Z ) from M SUSY M SUSY [GeV] [GeV] M GUT M GUT [GeV] [GeV] 1/  GUT 1/  GUT Lattice QCD threshold correction (-4%) 10 1.76 ± 0.25 10 16.57 ± 0.07 22.8 ± 0.4 Lattice QCD threshold correction (-3%) 10 2.32 ± 0.18 10 16.39 ± 0.05 23.8 ± 0.3 Lattice QCD threshold correction (-5%) 10 1.26 ± 0.23 10 16.74 ± 0.07 21.9 ± 0.4 World Average World Average 10 1.67 ± 0.38 10 16.61 ± 0.12 22.6 ± 0.7 World Average sans Lattice 10 1.52 ± 0.37 10 16.65 ± 0.12 22.3 ± 0.7

11. D.BourilkovDPF06 + JPS0611 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)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)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 GeV1/  (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 GeV1/  (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 M SUSY = 129 +27 -23 GeV no correlations: M SUSY = 129 +16 -16 GeV

12. D.BourilkovDPF06 + JPS0612 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: M SUSY = 137 ± 38 GeV SUSY Fit to LEP data: M SUSY = 172 ± 18 GeV

13. D.BourilkovDPF06 + JPS0613 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: M SUSY = 153 ± 49 GeV

14. D.BourilkovDPF06 + JPS0614 Conclusions The MSSM still provides coupling unification at a GUT scale well below the Planck scale for the newest set of measurementsThe 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 – excludedThe strong coupling is a key for interpreting the results: “high” values require uncomfortably low SUSY scales ~ 10 GeV – excluded The “low”  s (M Z ) values favor SUSY scales just around the corner: M SUSY < 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 (M Z ) ~ 0.117 – 0.119The “low”  s (M Z ) values favor SUSY scales just around the corner: M SUSY < 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 (M Z ) ~ 0.117 – 0.119 New analyses above the Z peak (sensitive to the actual running of the couplings) produce a remarkably coherent picture:New analyses above the Z peak (sensitive to the actual running of the couplings) produce a remarkably coherent picture: –qq data @ LEP2: M SUSY = 129 +27 -23 GeV –  s data @ LEP2: L3: M SUSY = 137 ± 38 GeV LEP: M SUSY = 172 ± 18 GeV –  s data @ CDF: M SUSY = 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 fitsA 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!The SUSY scales emerging from this analysis are well in the LHC (TEVATRON?) direct discovery range: stay tuned!