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[CERN-TH.6824/93]{}\
[ACT-3/93]{}\
[CTP-TAMU-12/93]{}\
[SHEP 92/93-14]{}

[**PERTURBATIVE QCD DATA ARE CONSISTENT WITH LIGHT GLUINOS**]{}\
\
\
[*CH - 1211 Geneva 23*]{}\
\
[*Center for Theoretical Physics, Department of Physics, Texas A&M University*]{}\
[*College Station, TX 77843-4242, USA*]{} and [*Astroparticle Physics Group, Houston Advanced Research Center (HARC)*]{}\
[*The Woodlands, TX 77382, USA*]{}\
and\
\
[*Physics Department, University of Southampton*]{}\
[*Highfield, Southampton SO9 5NH, England*]{}\
\

We discuss systematically the consistency of light gluinos with data on perturbative QCD from deep inelastic scattering, quarkonia, jets at LEP, and the total hadronic cross-section in ${e^+ e^-}$ annihilation on the $Z$ peak and elsewhere. We demonstrate that, in addition to the well-known increase in the value of $\alpha_s(m_Z)$ inferred from lower-energy data due to the slower running of $\alpha_s$ in the presence of light gluinos, the value of $\alpha_s(m_Z)$ extracted from the LEP data must also be $increased$, as a result of including the effects of virtual light gluinos. The effect of these increases in other estimates of $\alpha_s(m_Z)$ is to make them more consistent with the value extracted from the total $e^+ e^-$ cross-section, which would otherwise appear distinctly higher. We discuss the possibility of looking for light gluinos in four-jet events at LEP, and their possible implications for scaling violations at HERA.

CERN-TH.6824/93\
[ACT-3/93]{}\
[CTP-TAMU-12/93]{}\
[SHEP 92/93-14]{}\
March 1993

[**Table 1**]{}\
Extraction of $\alpha_s(M_Z)$ from low energy data

  ------------------------------------------------------ ----------------- ---------------------- ---------------------- ----------------------
                                                                                                                         

                         Process                                                                                         

                                                         Without gluinos   $m_{gluino}=3 \ GeV$   $m_{gluino}=4 \ GeV$   $m_{gluino}=5 \ GeV$

                                                                                                                         

         $\frac{\Gamma(\Upsilon \rightarrow ggg)}        $0.121\pm .005$   $0.140\pm .006$        $0.137\pm              $0.136\pm .006$
    {\Gamma(\Upsilon \rightarrow \mu^+\mu^-)}_{(LEP)}$                                             0.006$                

                                                                                                                         

         $\frac{\Gamma(\Upsilon \rightarrow ggg)}        $0.118\pm .005$   $0.136\pm .006$        $0.134                 $0.132\pm .006$
   {\Gamma(\Upsilon \rightarrow \mu^+\mu^-)}_{(World)}$                                            \pm 0.006$            

                                                                                                                         

                                                                                                                         

               $J/\Psi, \  \Upsilon$ decays              $0.113\pm .005$   $ 0.129\pm .006$       $0.127\pm .006$        $0.126\pm .006$

                                                                                                                         

                                                                                                                         

                          D.I.S.                         $0.112\pm .004$   $0.129 \pm .005$       $0.127                 $ 0.125\pm
                                                                                                   \pm .005 $            .005 $

                                                                                                                         
  ------------------------------------------------------ ----------------- ---------------------- ---------------------- ----------------------

[**Table 2**]{}\
Extraction of $\alpha_s(M_Z)$ from jets data at LEP\

  ---------------------- ------------------ ------------------
                                            
   Event Shape Variable                     
                         Without gluinos    With gluinos
                         0.120 ($\aleph$)   0.129-0.134
            C            0.124 (Delphi)     0.134-0.139
                         0.127 (Opal)       0.137-0.142
                         0.126 ($\aleph$)   0.134-0.139
            T            0.123 (Delphi)     0.131-0.135
                         0.118 (L3)         0.126-0.130
                         0.127 (Opal)       0.135-0.140
                         0.126 ($\aleph$)   0.143-0.152
           EEC           0.129 (Delphi)     0.147-0.156
                         0.128 (Opal)       0.152-0.162
                         0.132 ($\aleph$)   0.141-0.145
          $M_H$          0.125 (Delphi)     0.133-0.137
                         0.128 (Opal)       0.136-0.141
                         0.141 ($\aleph$)   0.150-0.155
          $M_D$          0.122 (Delphi)     0.130-0.134
                         0.118 (Opal)       0.126-0.130
                         0.113 ($\aleph$)   0.122-0.127
            O            0.122 (Delphi)     0.132-0.137
                         0.121 (Opal)       0.130-0.136
                         0.110 ($\aleph$)   0.114-0.115
           AEEC          0.114 (Delphi)     0.118-0.120
                         0.116 (Opal)       0.120-0.122
                                            
     Weighted Average    0.120$\pm .006$    0.132$\pm .007$
                                            
                                            
      After $\pi^2$                         
      Exponentiation     0.113 $\pm$ .006   0.124 $\pm$ .007
                                            
  ---------------------- ------------------ ------------------

[99]{} G. Farrar and P. Fayet, Phys. Lett. [**76B**]{} (1978) 575.\
UA1 Collaboration, C. Albajar et al., Phys. Lett. [**B198**]{} (1987) 261 and references therein.\
HELIOS Collaboration, T. Akesson et al., Zeit. f. Phys. [**C52**]{} (1991) 219.\
NA3 Collaboration, J.P. Dishaw et al., Phys. Lett. [**85B**]{} (1979) 142.\
I. Antoniadis, J. Ellis, and D.V. Nanopoulos, Phys. Lett. [**B262**]{} (1991) 109;\
L. Clavelli, Phys. Rev. [**D45**]{} (1992) 3276 and [**D46**]{} (1992) 2112;\
L. Clavelli, P.W. Coulter and K. Yuan, Univ. of Alabama preprint UAHEP 924 (1992);\
L. Clavelli, P.H. Cox and K. Yuan, Univ. of Alabama preprint UAHEP 9211 (1992).\
M. Jezabek and J.H. Kuhn, Phys. Lett. [**B301**]{} (1993) 121.\
R.K. Ellis, D.A. Ross and A.E. Terrano, Nucl. Phys. [**B178**]{} (1981) 421.\
B.A. Campbell, J. Ellis and S. Rudaz, Nucl. Phys. [**B198**]{} (1982) 1.\
S. Bethke,   Proceedings of XXVI International Conference on High Energy Physics, Dallas, Texas, August 1992.\
J. Ellis, G.G. Ross and M.K. Gaillard, Nucl. Phys. [**B111**]{} (1976) 253.\
J. Ellis, D.V. Nanopoulos, and D.A. Ross, Phys. Lett. [**B267**]{} (1991) 132;\
M. Dine and J. Sapirstein, Phys. Rev. Lett. [**43**]{} (1979) 668;\
K.G. Chetyrkin, A.L. Kataev, and F.V. Tkachov, Phys. Lett. [**B85**]{} (1979) 227;\
Delphi Collaboration, P. Abreu et al., Phys. Lett. [**B255**]{} (1991) 466,\
CERN preprint PPE/93-29 (1993).\
Aleph Collaboration, D. Decamp et al., Phys. Lett. [**B284**]{} (1992) 151.\
J. Ellis, S. Kelley and D.V. Nanopoulos, Phys. Lett. [**B249**]{} (1990) 441;\
Phys. Lett. [**B287**]{} (1992) 95.\

[**Figure Caption**]{}

Histograms of the $C$ and thrust distributions for the three-jet region, showing the lowest-order differential cross-section (dotted line) and the higher-order differential cross section without gluinos (thin solid line) and with gluinos (thick solid line). The thickness of the solid line is a measure of the theoretical uncertainty in the gluino effect.
