hints for low supersymmetry scale from analysis of running couplings

Hints for Low Supersymmetry Hints for Low Supersymmetry Scale from Analysis of Running Scale from Analysis of Running

CouplingsCouplings

Dimitri BourilkovDimitri BourilkovUniversity of Florida

DPF06 + JPS06, October 31, 2006, Waikiki, HI, USA

D.Bourilkov DPF06 + JPS06 2

IntroductionIntroduction

3 separate couplings at the Z peak …What happens at (much) higher scales?


Motivation IMotivation I

• If SUSY is discovered, phenomena arising from the quantum If SUSY is discovered, phenomena arising from the quantum structure of space-time can be studied experimentallystructure of space-time can be studied experimentally

• By 1991 the By 1991 the weak coupling was measured with much higher weak coupling was measured with much higher precision than the strongprecision than the strong one at LEP one at LEP

• In a famous paper U.Amaldi et al. (In a famous paper U.Amaldi et al. (PL PL B260B260 (1991) 447 (1991) 447) showed ) showed that in contrast to the SM the MSSM leads to a single that in contrast to the SM the MSSM leads to a single unification scaleunification scale

MMSUSY SUSY = 10= 103.03.0±1.0±1.0 GeV GeV

MMGUTGUT = 10 = 1016.0±0.316.0±0.3 GeV GeV

1/1/GUTGUT = 25.7 ± 1.7 = 25.7 ± 1.7

so for the SUSY scale: 11 < Mso for the SUSY scale: 11 < MSUSYSUSY < 91200 GeV < 91200 GeV

• At the time the relative error in At the time the relative error in (M(MZZ), sin), sin22MSMS and and ss(M(MZZ) )

was 0.24 %, 0.77 % and 4.6 %was 0.24 %, 0.77 % and 4.6 %


Motivation IIMotivation II

• From RPP 2004/6 From RPP 2004/6 the relative the relative error in error in (M(MZZ), sin), sin22MSMS and and

ss(M(MZZ) is 0.014%, 0.065% ) is 0.014%, 0.065%

and 1.0%, so we have and 1.0%, so we have improved by improved by moremore than an than an order of magnitude order of magnitude except for except for the strong coupling (less than the strong coupling (less than 5 times)5 times)

• So new analyses are in order So new analyses are in order (here we expand the analysis (here we expand the analysis from from hep-ph/0410350 , hep-ph/0410350 , hep-ph/0602168hep-ph/0602168))

Some recent analyses:Some recent analyses:W. de Boer, C.Sander,W. de Boer, C.Sander,

hep-ph/0307049hep-ph/0307049

B.Allanach et al., hep-ph/0407067B.Allanach et al., hep-ph/0407067

N.Arkani-Hamed, S.Dimopoulos,N.Arkani-Hamed, S.Dimopoulos,

hep-th/0405159hep-th/0405159

Example of a fit with Example of a fit with MMSUSYSUSY = M = MTOPTOP


Side RemarkSide Remark

• It is amazing that we are trying to extrapolate It is amazing that we are trying to extrapolate from 10from 1022 to 10 to 101616 GeV GeV

• From experiments we now that even From experiments we now that even interpolationinterpolation or modest extrapolationsor modest extrapolations can be non-trivialcan be non-trivial

• We measure the “offsets” around the Z peak and We measure the “offsets” around the Z peak and rely on theory to give us the “slopes” of the rely on theory to give us the “slopes” of the running couplings – running couplings – without errorswithout errors – up to the – up to the GUT scaleGUT scale

• This may be an illusion e.g. extra dimensions This may be an illusion e.g. extra dimensions could modify the running already at TeV scales, could modify the running already at TeV scales, so the “unification” point could be imaginaryso the “unification” point could be imaginary


Experimental InputsExperimental Inputs

• From Review of Particle Properties 2004From Review of Particle Properties 2004– 1/1/(M(MZZ) = 127.918 ± 0.018) = 127.918 ± 0.018

– sinsin22MS MS = 0.23120 ± 0.00015= 0.23120 ± 0.00015

ss(M(MZZ) is a different story (larger statistical errors ) is a different story (larger statistical errors

and theory uncertainties); will use the latest results and theory uncertainties); will use the latest results from RPP 2006from RPP 2006 ss(M(MZZ) = 0.1170 ± 0.0012 from Lattice QCD) = 0.1170 ± 0.0012 from Lattice QCD

ss(M(MZZ) = 0.1176 ± 0.002 World Average) = 0.1176 ± 0.002 World Average

ss(M(MZZ) = 0.1185 ± 0.002 World Average sans Lattice QCD) = 0.1185 ± 0.002 World Average sans Lattice QCD

ss(M(MZZ) = 0.1187 ± 0.002 RPP2004 QCD section) = 0.1187 ± 0.002 RPP2004 QCD section


Analysis techniqueAnalysis technique

22 minimization with 3 parameters: minimization with 3 parameters: fit with MINUITfit with MINUIT

MMSUSY SUSY , , MMGUTGUT , 1/ , 1/GUTGUT

• Strong correlation (> 0.999) between MStrong correlation (> 0.999) between MGUTGUT and and

1/1/GUT GUT : problem can be re-factored with 2 : problem can be re-factored with 2

parameters, taking 1/parameters, taking 1/GUT GUT as the weighted average of as the weighted average of

the 3 couplings at any given scale (the 3 couplings at any given scale (results are results are

numerically the same except the error on the GUT couplingnumerically the same except the error on the GUT coupling))

• Even so the correlation Even so the correlation MMSUSY SUSY – – MMGUT GUT is > 0.96is > 0.96

• Threshold corrections around the GUT scale (– 4%) Threshold corrections around the GUT scale (– 4%) for 2-loop-RG running fitsfor 2-loop-RG running fits


Running CouplingsRunning Couplings

1-loop Renormalization Group (RG) running1-loop Renormalization Group (RG) running – – can solve analytically can solve analytically 1/1/(() = 1/) = 1/(() - (b) - (bii/2/2) . ln() . ln(//))

The coefficients for the 3 couplings are The coefficients for the 3 couplings are independentindependent and given by the SM or MSSMand given by the SM or MSSM

2-loop-RG running2-loop-RG running: additional terms so the 3 : additional terms so the 3 couplings couplings depend on each otherdepend on each other – solved – solved numerically; the errors depend on the numerically; the errors depend on the scalescale (for (for typical GUT scales they grow by 4, 12 and 6 % typical GUT scales they grow by 4, 12 and 6 % for the 3 couplings)for the 3 couplings)


Example of SUSY FitExample of SUSY Fit


Fit ResultsFit Results

ss(M(MZZ) from) from

MMSUSY SUSY

[GeV][GeV]

MMGUTGUT

[GeV][GeV] 1/1/GUTGUT

Lattice QCD Lattice QCD threshold correction (-4%)threshold correction (-4%)

10101.76 1.76 ± 0.25± 0.25 101016.57 ± 0.0716.57 ± 0.07 22.8 ± 0.422.8 ± 0.4


10102.32 2.32 ± 0.18± 0.18 101016.39 ± 0.0516.39 ± 0.05 23.8 ± 0.323.8 ± 0.3


10101.26 1.26 ± 0.23± 0.23 101016.74 ± 0.0716.74 ± 0.07 21.9 ± 0.421.9 ± 0.4

World AverageWorld Average 10101.67 1.67 ± 0.38± 0.38 101016.61 ± 0.1216.61 ± 0.12 22.6 ± 0.722.6 ± 0.7

World Average World Average sans Latticesans Lattice 10101.52 1.52 ± 0.37± 0.37 101016.65 ± 0.1216.65 ± 0.12 22.3 ± 0.722.3 ± 0.7


New Analyses - Add More DataNew Analyses - Add More Data

• LEP2 has measured the qq LEP2 has measured the qq cross section above Z with cross section above Z with combined precision ~ 1% combined precision ~ 1% and theoretical uncertainty and theoretical uncertainty < 0.3 % (and provides < 0.3 % (and provides correlations between points)correlations between points)

• Fit the data with SM or Fit the data with SM or SUSY running couplings SUSY running couplings (SUSY scale as parameter)(SUSY scale as parameter)

• 1/1/(1,2,3) change in SM by (1,2,3) change in SM by -0.9, 1.3, 11.3% from Z -> -0.9, 1.3, 11.3% from Z -> 201 GeV201 GeV

• 1/1/(1,2,3) will change by (1,2,3) will change by -1.2, 0.4, 7.5% e.g. for SUSY -1.2, 0.4, 7.5% e.g. for SUSY scale ~ 130 GeVscale ~ 130 GeV

Slight excess ~ 2 Slight excess ~ 2 is “filled” is “filled” nicely by SUSY runningnicely by SUSY running

MMSUSY SUSY = 129 = 129 +27+27-23-23 GeV GeV

no correlations: no correlations: MMSUSY SUSY = 129 = 129 +16+16-16-16 GeV GeV


Fit Measurements of Fit Measurements of s s @ LEP2@ 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:SUSY Fit to L3 data:

MMSUSY SUSY = 137 = 137 ±± 38 GeV 38 GeV

SUSY Fit to LEP data:SUSY Fit to LEP data:



Fit Measurements of Fit Measurements of s s @ @ CDFCDF

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:SUSY Fit to CDF data:



ConclusionsConclusions• The MSSM still provides coupling unification at a GUT scale well below the The MSSM still provides coupling unification at a GUT scale well below the

Planck scale for the newest set of measurementsPlanck scale for the newest set of measurements • The strong coupling is a key for interpreting the results: The strong coupling is a key for interpreting the results: “high” values require “high” values require

uncomfortably low SUSY scales ~ 10 GeV – excludeduncomfortably low SUSY scales ~ 10 GeV – excluded• The “low” The “low” ss(M(MZZ)) values favor SUSY scales just around the corner: values favor SUSY scales just around the corner:

MMSUSY SUSY < < 197197 ( (148148) GeV for ) GeV for World Average ‘06World Average ‘06 ( (Lattice QCDLattice QCD) ) at at one-sided 95 % CL one-sided 95 % CL or reversing the argument an attractive “low” SUSY or reversing the argument an attractive “low” SUSY scale favors scale favors ss(M(MZZ) ~ 0.117 – 0.119) ~ 0.117 – 0.119

• New analyses above the Z peak (sensitive to the actual New analyses above the Z peak (sensitive to the actual running of the couplings) produce a remarkably running of the couplings) produce a remarkably coherent picture:coherent picture:– qq data @ LEP2: Mqq data @ LEP2: MSUSY SUSY = 129 = 129 +27+27

-23-23 GeV GeV s s data @ LEP2data @ LEP2: : L3: ML3: MSUSY SUSY = 137 = 137 ±± 38 GeV LEP: M 38 GeV LEP: MSUSY SUSY = 172 = 172 ±± 18 GeV 18 GeV s s data @ CDFdata @ CDF:: M MSUSY SUSY = 153 = 153 ±± 49 GeV 49 GeV

• A word of caution: most results are preliminary; there are strong correlations in the A word of caution: most results are preliminary; there are strong correlations in the s s measurements which are not published / not taken into account in the fitsmeasurements which are not published / not taken into account in the fits

• The SUSY scales emerging from this analysis are well in the The SUSY scales emerging from this analysis are well in the LHC (TEVATRON?) direct discovery range: stay tuned!LHC (TEVATRON?) direct discovery range: stay tuned!

hints for low supersymmetry scale from analysis of running couplings

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