Lafaye, R.

Plehn, T.

Zerwas, D.

HAL-IN2P3

SFITTER: A tool to determine supersymmetricparametersR. Lafaye, T. Plehn, D. ZerwasTo cite this version:R. Lafaye, T. Plehn, D. Zerwas. SFITTER: A tool to determine supersymmetric parameters.Belanger G., Boudjema F., Guilllet J.Ph., Pilon E. Les Houches Workshop: Physics at TeVColliders 3, May 2003, Les Houches, France. Non Mentionne, pp.194-198, 2003. <in2p3-00021633>HAL Id: in2p3-00021633http://hal.in2p3.fr/in2p3-00021633Submitted on 8 Apr 2004HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.LAPP-EXP 2003-27 December 2003        SFITTER : a tool to determine supersymmetric parameters    R. Lafaye   LAPP-IN2P3-CNRS, BP. 110, F-74941 Annecy-le-Vieux Cedex  T. Plehn  CERN, CH-1211 Geneva 23  D. Zerwas  LAL-IN2P3-CNRS, BP. 34, F-91898 Orsay Cedex      Abstract    SFITTER is a new tool to determine supersymmetric model parameters from collider measurements. It allows to perform a grid search for the minimal χ2 and/or a fit of a given model. Currently, the model parameters in the general MSSM or in a gravity mediated SUSY breaking model can be tested using a given set of mass, branching ratio and cross section measurements.  SFITTER: A Tool to Determine Supersymmetric ParametersR. Lafaye, T. Plehn, D. ZerwasLAPP-Annecy, France, CERN, Switzerland, LAL-Orsay, FranceAbstractSFITTER is a new tool to determine supersymmetric model parameters fromcollider measurements. It allows to perform a grid search for the minimal χ2and/or a fit of a given model. Currently, the model parameters in the generalMSSM or in a gravity mediated SUSY breaking model can be tested using agiven set of mass, branching ratio and cross section measurements.1. IntroductionThe most important task for the LHC as well as for any future Linear Collider is to study in detail themechanism which leads to electroweak symmetry breaking. While the Standard Model describes allavailable high energy physics experiments, it still has to be regarded as an effective theory, valid at theweak scale. New physics are expected to appear at the TeV energy scale. The minimal supersymmetricextension of the Standard Model (MSSM) can provide a description of physics up to the unification scale.If supersymmetry or any other high-scale extension of the Standard Model is discovered, it will becrucial to determine its fundamental high-scale parameters from weak-scale measurements [1, 2]. TheLHC and a future Linear Collider will provide a wealth of measurements [3], which due to their com-plexity require a proper treatment to unravel the corresponding high-scale physics. Even in the generalweak-scale MSSM without any unification or SUSY breaking assumptions the measurements of massesand couplings are not likely to be independend measurements; moreover, linking supersymmetric parti-cle masses to weak-scale SUSY parameters involves non-trivial mixing to mass eigenstates in essentiallyevery sector of the theory. On top of that, for example in gravity mediated SUSY breaking scenarios(mSUGRA/cMSSM) a given weak-scale SUSY parameter will always be sensitive to several high-scaleparameters which contribute through renormalization group running. Therefore, a fit of the model pa-rameters using all experimental information available will lead to the best sensitivity and make the mostefficient use of the information available.If the starting point of the fit is not known and many parameters are involved, the allowed pa-rameter space might not be sampled completely in the fit approach. To avoid boundaries imposed bynon-physical parameter points, which can confine the fit to a ‘wrong’ parameter region, combining the fitwith an initial evaluation of a multi-dimensional grid is the optimal approach. In the general MSSM theweak-scale parameters can vastly outnumber the collider measurements, so that a complete parameterfit is not possible and one has to limit oneselve to a subset of parameters. In SFITTER both grid andfit are realised and can be combined, including a general correlation matrix and the option to excludeparameters of the model from the fit/grid by fixing them to a value.2. SFITTER — Program StructureCurrently, SFITTER uses the predictions for the supersymmetric masses provided by SUSPECT [4], butthe conventions of the SUSY Les Houches accord [5] could be helpful, if provided as a common block/C-structure, to ease interfacing other programs. The branching ratios and e+e− production cross sectionsare provided by MSMlib [6], which has been used extensively at LEP and cross checked with Ref. [7].The next-to-leading order hadron collider cross sections are computed using PROSPINO [8, 9, 10]. Thefitting program uses the MINUIT package [11]. The determination of χ2 includes a general correlationmatrix between measurements. For unphysical points in supersymmetric parameter space, χ2 is set to1030.2.1 Initialization and SteeringThe program SFITTER is driven by two files: the first one sets up the measurements and the correspond-ing errors. For each measurement one specifies if it is to be used in the grid (G) or in the MINUIT fit (M)or in both.//set all errors to 0.5% of their central valueDATA_ERR = 0.005//randomize the measurements around their nominal valueRANDOMIZE = 1//Higgs mass and error to be used in the Fit onlym_h = 112.6 +/- 0.1 [-/M]//Neutralino1 mass to be used in Grid and Fitm_chi0_1 = 180.2 +/- 5.1 [G/M]//Correlation between two chargino mass measurementsCORR(m_chi+_1,m_chi+_2) = 0.03The second file initializes everything related to the weak-scale or high-scale MSSM model parameters.First the model (mSUGRA, pMSSM etc) is specified, then the starting values of all MSSM parameters,boundaries, stepsize and the number of points in the grid are specified. Moreover, the user defines if acertain MSSM model parameter is included in the grid and in the fit:MODEL=MSUGRA // use MSUGRA// use the GRID (or not)GRID=1// M0 used in grid and fit, grid of 10+1 steps between 0 and 1000.M0=500. [M/G] STEP=200. LOW=0. HIGH=1000. GRID=10// A0 used only in fitA0=0. [M/-] STEP=200. LOW=-1000. HIGH=1000.2.2 mSUGRA/cMSSM Parameter DeterminationAssuming that SUSY breaking is mediated by gravitational interactions (mSUGRA/cMSSM) we fit fouruniversal high-scale parameters to a toy set of collider measurements: the universal scalar and gauginomasses, m0, m1/2, the trilinear coupling A0 and the ratio of the Higgs vacuum expectation values, tanβ.The sign of the Higgsino mass parameter µ is a discrete parameter and therefore fixed. The assumeddata set is the set of all supersymmetric particle masses for the SUSY parameter point SPS1a [12, 13],as computed by SUSPECT. The errors on the toy mass measurements are uniformly set to 0.5%. Thestarting points for the mSUGRA parameters are fixed to the mean of the lower and upper limit in the fit,i.e. they are not necessarily even close to the true SPS1a values. The result of the fit is shown in Tab. 1.With SFITTER the true parameter values were reconstructed well within the quoted errors, in spite ofstarting values relatively far away from the true ones. The measurement of m0 and m1/2 is very precise,while the sensitivity of the masses on tanβ and A0 is significantly weaker.The correlations between the different high-scale SUSY parameters are also given in Tab. 1. Onecan understand the correlation matrix step by step [14]: first, the universal gaugino mass m1/2 can beextracted very precisely from the physical gaugino masses. The determination of the universal scalarmass m0 is dominated by the weak-scale scalar particle spectrum, but in particular the squark masses arealso strongly dependent on the universal gaugino mass, because of mixing effects in the renormalizationgroup running. Hence, a strong correlation between the m0 and m1/2 occurs. The universal trilinearcoupling A0 can be measured through the third generation weak-scale mass parameters Ab,t,τ . However,the Ab,t,τ which appear for example in the off-diagonal elements of the scalar mass matrices, also dependon m0 and m1/2, so that A0 is strongly correlated with m0 and m1/2.In the SPS1a scenario, the pseudoscalar Higgs is heavy and the Higgs masses do not show astrong dependence on tanβ. Because of the large mass difference between gauginos and Higgsinos theyTrue FitStart FitResultm0 100 500 100.01±0.58m1/2 250 500 249.99±0.31tanβ 10 50 10.03±0.37A0 -100 0 -100.1±5.26m0 m1/2 tanβ A0m0 1 -0.47 0.41 0.26m1/2 1 -0.07 -0.30tanβ 1 0.35A0 1Table 1: Left: summary of mSUGRA fit in SPS1a: true values, starting values, fit values. As in SPS1a we fix µ > 0. All massvalues are given in GeV. Right: the (symmetric) correlation matrix of all SUSY parameters in the mSUGRA fit.essentially decouple, and the neutralino/chargino sector will not yield a good determination of tanβ. Thestop mixing is governed by At, and not by µ/ tanβ, while the sbottom mixing is small altogether. Onlythe stau mixing is large and driven by µ tanβ in the off-diagonal element of the stau mass matrix. Thestau mass parameters are dominated by m0, in particular the smaller right handed stau mass. Therefore,one expects tanβ to be strongly correlated with m0 and less with m1/2. The result from SFITTER asshown in Tab. 1 is in agreement with this prediction. Thus, the results obtained with SFITTER can beunderstood from the particular features of the SPS1a spectrum.2.3 MSSM Parameter DeterminationIn total 24 parameters describe the unconstrained weak-scale MSSM. They are listed in Tab. 2: tanβjust like in mSUGRA, plus three soft SUSY breaking gaugino masses Mi, the Higgsino mass parameterµ, the pseudoscalar Higgs mass mA, the soft SUSY breaking masses for the right sfermions, Mf˜R , thecorresponding masses for the left doublet sfermions, Mf˜L and finally the trilinear couplings of the thirdgeneration sfermions At,b,τ .In any MSSM spectrum, in first approximation, the parameters M1, M2, µ and tanβ determinethe neutralino and chargino masses and couplings. We exploit this feature to illustrate the option to use agrid before the start the complete MINUIT fit. For testing purposes, the error on all mass measurementsis again set 0.5%. The starting values of the parameters are set to their nominal values, this study is thusless general than the one of mSUGRA. Then we minimize χ2 on a grid. For this grid minimization thesix chargino and neutralino masses are used as measurements to determine the four SUSY parametersM1, M2, µ and tanβ only. The step size of the grid is 10 for tanβ and 100 GeV for the three massparameters. After the minimization, these four parameters obtained from the minimum χ2 on the gridare fixed and all remaining parameters are fitted. Only in a final run all SUSY parameters are releasedand fitted, to give the final results quoted in Tab. 2.In Tab. 2 the intermediate (after the grid evaluation) results, the final results and the nominalvalues are shown. The final fit values indeed converges to the correct central values within its error. Thecentral values of the fit are in good agreement with generated values, except for the trilinear couplingAb. As already mentioned in the discussion of the mSUGRA fit, the mixing between the two sbottommass states is very small, so the assumed precision of the 0.5% is insufficient to determine the parameterfrom the mass measurements alone. As At enters in the calculation of the lightest Higgs, additionalsensitivity for this parameter comes from the mass measurement of the lightest Higgs boson. The useof branching ratios and cross section measurements should significantly increase the precision in futurestudies, especially for Aτ and Ab.3. ConclusionsSFITTER is a new program to determine suspersymmetric parameters from experimental measurements.The parameters can be extracted either using a fit, a multi-dimensional grid minimisation, or a combi-nation of the two. Correlations between measurements can be specified and are taken into account inthe calculation of the χ2. SUSPECT, MSMlib and PROSPINO are used to calculate the predictions forAfterGrid AfterFit SPS1a AfterGrid AfterFit SPS1atanβ 10 10.62±2.5 10 Mu˜R 528.03 528.06±2.8 532.1M1 100 102.05±0.61 102.2 Md˜R 525.12 525.14±2.8 529.3M2 200 191.65±1.4 191.8 Mc˜R 528.03 528.06±2.8 532.1M3 579.37 579.33±4.8 589.4 Ms˜R 525.12 525.15±2.8 529.3µ 300 344.04±1.2 344.3 Mt˜R 417.36 415.44±5.7 420.2mA 399.38 399.14±1.2 399.1 Mb˜R 524.59 523.99±2.9 525.6Me˜R 138.24 138.23±0.76 138.2 Mq˜1L 549.58 549.61±2.1 553.7Mµ˜R 138.24 138.23±0.76 138.2 Mq˜2L 549.58 549.61±2.1 553.7Mτ˜R 135.58 135.51±2.1 135.5 Mq˜3L 493.59 494.38±2.7 501.3Me˜L 198.74 198.75±0.68 198.7 Aτ˜ -724.25 -286.78±549 -253.5Mµ˜L 198.74 198.75±0.68 198.7 At˜ -502.19 -495.19±15 -504.9Mτ˜L 197.79 197.81±0.89 197.8 Ab˜ 975.12 999.78±49 -799.4Table 2: Result for the general MSSM parameter determination in SPS1a. Shown are the nominal parameter values, the resultafter the grid and the final result. The deviation in the squark sector of 1% is an artefact of differences between MSSM andmSUGRA part of the renomalization group code [4]. All masses are given in GeV.the masses, branching ratios and production cross sections. A more realistic set of the measurements forexample assuming the SPS1a mass spectrum for the LHC and and a future Linear Collider will be stud-ied as a next step. The impact of correlations between measurements on the estimated errors of MSSMparameters will be studied in detail. In the future public version of the program we will include differentgenerators for the calculation of masses and branching ratios.AcknowledgementsThe authors would like to thank the organizers of the Les Houches workshop and the convenors of theSUSY-group for the constructive atmosphere in which SFITTER was born. TP would in particular liketo thank Michael Spira for allowing him to participate in the Higgs and the BSM sessions at the LesHouches workshop.References[1] G. A. Blair, W. Porod, and P. M. Zerwas. Reconstructing supersymmetric theories at high energyscales. Phys. Rev., D63:017703, 2001.[2] G. A. Blair, W. Porod, and P. M. Zerwas. The reconstruction of supersymmetric theories at highenergy scales. ((u)). Eur. Phys. J., C27:263–281, 2003.[3] K. Desch, J. Kalinowski, G. Moortgat-Pick, M. M. Nojiri, and G. Polesello. Susy parameter deter-mination in combined analyses at lhc/lc. 2003.[4] Abdelhak Djouadi, Jean-Loic Kneur, and Gilbert Moultaka. Suspect: A fortran code for the super-symmetric and higgs particle spectrum in the mssm. 2002.[5] P. Skands et al. Susy les houches accord: Interfacing susy spectrum calculators, decay packages,and event generators. 2003.[6] G. Ganis. Msmlib (unpublished).[7] Vernon D. Barger et al. Cp-violating phases in susy, electric dipole moments, and linear colliders.Phys. Rev., D64:056007, 2001.[8] W. Beenakker, R. Hopker, M. Spira, and P. M. Zerwas. Squark and gluino production at hadroncolliders. Nucl. Phys., B492:51–103, 1997.[9] W. Beenakker, M. Kramer, T. Plehn, M. Spira, and P. M. Zerwas. Stop production at hadroncolliders. Nucl. Phys., B515:3–14, 1998.[10] W. Beenakker et al. The production of charginos/neutralinos and sleptons at hadron colliders. Phys.Rev. Lett., 83:3780–3783, 1999.[11] F. James and M. Roos. ’minuit’ a system for function minimization and analysis of the parametererrors and correlations. Comput. Phys. Commun., 10:343–367, 1975.[12] B. C. Allanach et al. The snowmass points and slopes: Benchmarks for susy searches. Eur. Phys.J., C25:113–123, 2002.[13] Nabil Ghodbane and Hans-Ulrich Martyn. Compilation of susy particle spectra from snowmass2001 benchmark models. 2002.[14] Manuel Drees and Stephen P. Martin. Implications of susy model building. 1995.

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