Discriminating SUSY models at LHC using MCMCs

1. Discriminating SUSY models at LHC using MCMCs Sylvain Fichet LPSC Grenoble with Sabine Kraml (LPSC) To appear in the BSM report of the Les Houches PhysTeV 2009 Workshop

2. Introduction Approach 2 • Let’s assume that TeV-scale SUSY exists… • …and the LHC measured a part of the mass spectrum. • Would this set of information be sufficient to partially determine high scale parameters • of the model describing SUSY breaking ? • Sufficient to exclude models ? To discriminate between different models ? • And if not, what additional information could help ?

3. Introduction Approach 2 • Let’s assume that TeV-scale SUSY exists… • …and the LHC measured a part of the mass spectrum. • Would this set of information be sufficient to partially determine high scale parameters • of the model describing SUSY breaking ? • Sufficient to exclude models ? To discriminate between different models ? • And if not, what additional information could help ? • We did a study considering a spectrum from Supersymmetric Gauge • Higgs Unification (SGHU) [0906.2957], trying to discriminate it against mSUGRA. • We used Monte Carlo Markov Chains (MCMCs) to sample the likelihood • function associated to the assumed data.

4. Introduction MCMCS for model discrimination 3 • Basic algorithm to sample the likelihood function : • Given a point in the parameter space with associated likelihood , • choose randomly an other point with associated likelihood . • If , keep the new point and re-do the loop. • If , keep the new point with probability , • else keep the older , and re-do the loop. • The distribution of points will reproduce the function . • Post-processing : • Supress first points (burn-in) • Check convergence • Interest : • Find maxima of the likelihood. • Any integral is done using sums and histograms.

5. Introduction MCMCS for model discrimination 1 1 4 • Two interpretations for the likelihood function : • If model overconstrained by measurements : • the maximum likelihood gives the best fit point. • (frequentist analysis) • If model underconstrained by measurements : • continuous set(s) in the parameter space reaches the maximum… • (Bayesian analysis) • More credible value ? Bayesian inference : • Relative credibility of 2 models ? Bayes factor :

6. Setup SGHU vs mSUGRA Bulk 2 Higgs doublets 3rd gen Gauge-Higgs 1,2nd gen Branes (4D) 5 • An aside on SGHU : • Class of model of orbifold SUSY GUT with Gauge-Higgs unification : • Complete 5D model with SU(6) GHU [hep-ph/0210257] : • Confinement of matter fields controls mass hierarchies • (yukawas couplings) and soft scalar parameters : • the 3rd generation is large and non universal, • others are vanishing. • 4 free continous parameters : (at high scale)

7. Setup SGHU vs mSUGRA 6 • Differences between the 2 models : • In the Higgs sector : • mSUGRA : and , fixed by EWSB • SGHU : and , fixed by EWSB • (needs a different algorithm to be computed) • In the scalar sector : • mSUGRA : full universality • All scalar masses equal to , all A-terms equal to • SGHU : hierarchy and non universality • Implies SFOS dilepton generically :

8. Setup Experimental assumptions if if 7 • Let’s assume a realistic measurement of a SUSY spectrum… • We use the benchmark point D of SGHU : • with • Sparticles masses extracted from invariant-mass distributions with 3% uncertainty, thanks to the decay • Average mass of squarks of 1st and 2nd generation : • Slepton masses : and if • ( ) • 2 hypothesis for the heavy Higgs sector, depending if one of the masses is measured (H1) or not (H0). • Uncertainty of on the light Higgs mass and the top mass.

9. Setup Models parameters and ranges 8 • Model parameters • mSUGRA : • SGHU : • CPU limitations • As SGHU points are long to compute, we use a version with free non-universal 3rd • generation, which is faster to compute, but has much more parameters : • Ranges • mSUGRA : • , no bounds on others • SGHU (modified) : • , • , , • These bounds enclose the parameter space of the full SGHU model. • Parameters are also limited by theoretical bounds : CCB and tachyons.

10. Results Likelihoods in parameter space, H0 case 9 • Max and mean likelihoods : • mSUGRA has • model underconstrained. • Bayes factor • no Baeysian preference.

11. Results Likelihoods in parameter space, H0 case 9 • 1D and 2D marginalized likelihoods • mSUGRA : constrained • SGHU : constrained • Max and mean likelihoods : • mSUGRA has • model underconstrained. • Bayes factor • no Baeysian preference. SGHU SUGRA

12. Results Likelihoods in parameter space, H1 case 10 • 1D and 2D marginalized likelihoods • mSUGRA : constrained • SGHU : constrained • Max and mean likelihoods : • mSUGRA has • model ~ overconstrained. • Bayes factor • not sufficient to assess • weak preference. SGHU SUGRA

13. Results Indirect observables likelihoods 11 How to improve discrimination ? H0 case H1 case • Including the relic density in the analysis will improve the discrimination in H0 case. • Including the 2 low energy observables in the analysis will strongly improve the discrimination in H1 case.

14. Results Masses likelihoods 12 How to improve discrimination ? H0 case H1 case H1 case • , , permit discrimination through the scalar sector • permits discrimination through the Higgsino sector • Non-observation of can give additional information on scalar non-universality. LC : LHC :

15. Conclusion 13 • Summary : • In our case study, the sparticle masses taken alone are not sufficient to discriminate the 2 models. However… • If the heavy Higgs sector is measured, the low energy observables have • a strong discriminating power. • If the heavy Higgs sector is unknown, taking into account the relic density • is necessary. • A refinement on observables can also improve the discrimination. • A LC would permit to measure the spectrum without ambiguity and do the discrimination easily. • Outlook : • The relation (Higgs masses universality) appears in other classes of models. It needs further investigation to understand its consequences, independently from the other parameters.

16. Thanks for your attention !

17. EXTRAS

18. Fixed point vs dichotomy f(x) f(x) x x f(x)-x 2 3 1 x

19. Algorithm Choice of SuSy breaking model : high-scale boundary conditions GUT scale Phys. masses/couplings Check : EWSB EWSB scale Sparticles mass matrices diagonalization Check : Spectrum minization, compute or Mz scale SuSy finite corrections to τ, b, t & sparticles masses Low scale values modified iteration Exp. data & guess of

20. A mSUGRA example : Higgs Gauginos Sparticles Gluino dominated squark running Radiative EWSB

21. Higgs sector Higgs potential (after some gauge rotations) : -potentiel bounded from below : -non-trivial minimum : Minimization : with

22. Higgs sector • The bilinear parameter µ • The bilinear parameter B (susy breaking) • Higgs masses (susy breaking) with

23. Interesting features of other RGES • Superpotential parameter corrections are proportional to the parameters themselves : • All susy-breaking parameters depend on gaugino masses . • Squark masses receive large negative corrections from the gluino mass : • mass receives large positive corrections from the top yukawa : with

24. Couplings and sparticles masses • Yukawas • Trilinear couplings (susy breaking) • Sparticle masses (susy breaking)