The running of the strong coupling constant, $R_{e^+e^-},R_Z$ and $R_\tau$ is
studied on the three-loop level. Based on experimental data of $R_{e^+e^-},R_Z$
and $R_\tau$ and the LEP multijet analysis, the light gluino scenario is
excluded to 99.97% CL (window I) and 99.89% CL (window III).Comment: 7 pages, 6 figures, talk at HEP97, Jerusale

Csikor, Ferenc

Fodor, Zoltan

English

arXiv

Csikor, F

Fodor, Z

ELTE Digital Institutional Repository (EDIT)

arXiv:hep-ph/9712269v1  4 Dec 1997Closing the light gluino windowF. Csikor † (csikor@hal9000.elte.hu)Z. Fodor †† ⋆ (fodor@theory4.kek.jp)† Inst. Theor. Phys., Eötvös University, Budapest, Hungary†† KEK, Theory Group, 1–1 Oho, Tsukuba 305, JapanITP-Budapest 538KEK-TH-551Abstract. The running of the strong coupling constant, Re+e− , RZ and Rτ isstudied on the three-loop level. Based on experimental data of Re+e− , RZ and Rτand the LEP multijet analysis, the light gluino scenario is excluded to 99.97% CL(window I) and 99.89% CL (window III).1 Introduction and motivationAsymptotic freedom is one of the most interesting predictions of QCD. Onecan study this by measuring the running coupling constant at different en-ergies and comparing the results. Fig. 1 shows αs running as obtained fromdifferent experiments together with QCD predictions. Of course QCD is invery good shape. Nevertheless one may quantify this statement. This is notthe subject of the present talk, for details see [1]. One may also speculateon slower running than required by QCD. A popular possibility is the lightgluino extension of QCD. In this paper we discuss that this scenario can beexcluded using three-loop perturbative results and the existing experimentaldata [1].The experimentally excluded regions of light gluinos (1996 status) – massv. lifetime – are shown in Fig. 2. The moral is that window I., i.e. lighter than1.5 GeV and window III. i.e. masses between 3 GeV and 5 GeV are allowedby these results.Last year has brought important technical development of the subject,namely 3-loop results have been calculated [2]–[4]. It has been emphasizedthat light gluinos are obtained naturally from gauge mediated SUSY breaking[5, 6]. Also some new papers both experimental [7]–[9] and theoretical [10, 11]presenting results on light gluino exclusion have appeared. [12]–[14] critisizesthe exclusion results.⋆ On leave from Inst. Theor. Phys., Eötvös University1 Presented by F. Csikor at the International Europhysics Conference on High EnergyPhysics, Jerusalem, August 19–26 1997.2 F. Csikor Z. FodorQCD350 MeV150 MeV 250 MeV100 MeVΛ MS(5) α  (Μ  )s Z0.1280.1210.1120.1060.10.20.30.40.5αs (Q)1 10 100Q [GeV]Heavy QuarkoniaHadron Collisionse+e-  AnnihilationDeep Inelastic ScatteringNLO NNLOTheoryData LatticeFig. 1. αs running and QCD predictions2 Theoretical and experimental inputsDescribing Re+e− , RZ and Rτ in the light gluino scenario qualitative dif-ferences compared to ordinary QCD appear. Since the effective number offermions is larger, running of αs(Q) becomes slower. Including the new de-grees of freedom in cross section calculations and taking into account thelarger phase-space one finds that a smaller αs describes the data at anygiven energy.The basic idea of the present paper is the following. We suppose thatstrong interaction is described by a gauge theory based on a simple Lie-group,thus hadronic cross-sections, widths, β-function are given by CF , CA, TF andthe active number of fermions. Then by looking for CF , CA, TF , ng̃ to describedata accurately, we can determine the CL a given gauge theory is excludedor supported by data. Since the energy range from Mτ to MZ is rather large,it is nontrivial for a hypothetical theory to reproduce both the cross sectionvalues and the running of αs(Q).The theoretical inputs of our analyses areO(α3s) calculations ofRe+e− , RZand Rτ for arbitrary group theoretical coefficients. The experimental inputsof the analysis are Rτ given by ALEPH and CLEO Rτ = 3.616(20)), RZgiven by the LEP groups (RZ = 20.778(29)) and hadronic cross sections atenergies 5 GeV–MZ (all existing published data (and some unpublished)).The total number of data points included is 182.1104: Excluding light gluinos 32 410CUSB10-6UA1Bernsteinm [GeV]ARGUS-12-1010-8τ[s]10ARGUSFig. 2. Light gluino exclusion limits3 Treatment of different sources of errorsBesides the data the errors are also very important for a fit. Being too op-tomistic destroys reliability of the results. When realized that data implygluino exclusion, we have choosen to use very conservative error estimates.We treat uncertainties in a unified manner, add the systematic errors lin-early and total systematic and statistical errors quadratically. The accuracyof Re+e− and RZ is limited by experiments, while for Rτ theoretical uncer-tainty dominates. For higher order perturbative corrections we suppose thatthe error is the last computed term (asymptotic series). For Rτ this givessignificantly larger error than usually assumed. For Rτ mass and nonpertur-bative corrections are taken into account following [15].Since experimental errors are correlated, we minimizeχ2 = ∆TV −1∆ . (1)∆ is an n-vector of the residuals of Ri −Rfit, n is the number of individualresults, V is n× n error matrix.4 Light gluino results from running of αs(Q)First we present results from fiting Re+e− , RZ , Rτ , i.e. αs running. An ex-ample of a two parameter (x = CA/CF , y = Tf/CF ) fit is shown in Fig. 3for the case of window III. More quantitatively: we exclude window III lightgluinos with a small mass dependence to 93(91)% CL for mg̃=3(5) GeV. Forwindow I we do not use Rτ in the fit and get only 71 % exclusion CL.4 F. Csikor Z. FodorFig. 3. Exclusion from αs running for mg̃=3 GeV (window III)Following [10] we fixed the underlying group to SU(3) and determinedthe number of gluinos. This corresponds to a one parameter fit for ng̃. Forwindow III we get ng̃=0.0078±0.52, 88% CL exclusion and for window Ing̃=-0.070±0.7, 80% CL exclusion (without Rτ ).Farrar [12] claims that increasing our Rτ error estimate by a factor 2leads to 68% exlusion for window III case. Performing the calculation we get87(85)% and 81% for window III 2 and 1 parameter fits, respectively.5 Combination with jet analysis at LEPLEP groups have determined the group theoretical factors x,y comparingexperimental results with leading order 4 jet and higher order 2,3 jet predic-tions. A summary of the earlier results was given in [16] and shown in Fig.4. To illustrate what happens when our analysis based on αs running is com-bined with a LEP jet analysis, Fig. 5 shows the 1σ excluded regions for theOPAL jet analysis alone [17] (which actually does not exclude light gluinos)and ours (copied from Fig. 3). Note that the overlap of the two regions israther small, resulting in stronger exclusion than any of the uncombined anal-yses. It is also clear that increasing the jet analysis ellipsis or shifting it doesnot change the overlap region too much, i.e. the exclusion changes only verylittle.In the actual calculation we have included the older LEP jet analyses andthe new ALEPH result [8]. To take into account higher order corrections of4 jet QCD predictions we have increased the axes of the error ellipse by 12%of the theoretical x and y values (relative correction of O(αs)). This change1104: Excluding light gluinos 5Fig. 4. LEP 4 jet analyses exclusion resultsFig. 5. Comparison of excluded regions from αs running and OPAL 4 jet analysiswould destroy the predictive power of the (uncombined) multi-jet analysisfor old data.An example of the 2 parameter fits is shown in Fig. 6. More quantitatively,for window III light gluino (mg̃ =3(5) GeV) the exclusion is 99.99(99.89)%CL. For window I light gluino it is: 99.97% CL.We also performed 1 parameter fits. For window III: ng̃=-0.156±0.27 (-0.197±0.32) with mg̃ =3(5) GeV i.e. 99.96(99.76)%CL exclusion. For windowI: ng̃=-0.35±0.33 i.e. we have 99.96% CL exclusion.6 F. Csikor Z. FodorFig. 6. Exclusion from combined method, 2 parameter fitFarrar [12] claims that increasing the ALEPH errors by a factor 3 wouldlead to 68% gluino exclusion. Performing the actual calculation we get atleast 95% exclusion for all cases of the combined analysis.6 Summary, conclusionWe have obtained light gluino exclusion from fits of Re+e− , RZ and Rτ , i.e.essentally from αs running. We have combined this analysis with the LEP jetanalysis. Our combined analysis results in much more stringent light gluinoexclusion than LEP jet analysis alone or αs running alone. The best CL’s are99.97% for window I and 99.89% for window III light gluino exclusion. Ourresults are independent of light gluino lifetime.This work was partially supported by Hung. Sci. grants OTKA-T16248,T22929.References[1] F.Csikor, Z.Fodor, Phys. Rev. Letters 78 (1997) 4335 and to be published[2] K.G. Chetyrkin, Phys. Lett. B391 (1997) 402[3] L.J. Clavelli, L.R. Surguladze, Phys. Rev. Lett. 78 (1997) 1632[4] L.J. Clavelli, P.W. Coulter, L.R. Surguladze, Phys. Rev. D55 (1997) 4268[5] S. Raby, Phys. Rev. D56 (1997) 2852 and this proceedings[6] R. N. Mohapatra, S. Nandi, Phys. Rev. Letters 79 (1997) 181[7] F. Abe et al. (CDF), Phys. Rev. D56 (1997) 1357[8] R. Barate et al., Zeit. Phys. C76 (1997) 1911104: Excluding light gluinos 7[9] J. Adams et al. (KTeV), hep-ex/9709028[10] A. de Gouvêa, H. Murayama, Phys. Lett. B400 (1997) 117[11] Z. Nagy, Z. Trócsányi, hep-ph/9708343[12] G. Farrar, hep-ph/9707467[13] G. Farrar, hep-ph/9710277[14] G. Farrar, hep-ph/9710395[15] G. Altarelli, P. Nason, G. Ridolfi, Z. Phys. C68 (1995) 257[16] M. Schmelling, , in Proc. of 15th Int. Conf. Physics in Collision, Ed.Frontieres, Gif-Sur-Yvette, p. 287 (1995)[17] R. Akers et al. (OPAL), Z. Physik C65 (1995) 367

Closing the light gluino window

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Closing the light gluino window

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