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the precise measurement of the z total decay width at lep and its agreement with its standard model prediction  @xcite ( with @xmath5@xmath6 ) @xmath7 are often exploited to constrain the cross section of new physics processes  @xcite .
indeed , under the assumption that new physics contributions to the z width are exclusively positive ( as is the case for processes kinematically allowed at @xmath8 ) , this agreement allows a 95% confidence level ( c.l . ) limit of @xmath9 to be set on any exotic contribution to @xmath10 .
however , extensions of the standard model , such as supersymmetry or technicolor , generate a whole set of new particles , which may or may not be produced in @xmath11  collisions at @xmath8 .
the particles that are too heavy to be produced in z decays may still contribute to the z width through vacuum polarization diagrams with a generally undetermined sign .
it may therefore well occur that negative contributions be sizeable and invalidate the widely used aforementioned limit on @xmath12 .
it is the purpose of this letter to derive model - independent limits on additional contributions to z decays , and to use these limits to unambiguously constrain the light gluino mass window .
it is indeed controversial if a light gluino @xmath3  of mass below 5@xmath6  is phenomenologically viable  @xcite
. a review of existing limits and of the related weak points can be found in ref .
in particular , a study of the qcd colour factors from four - jet angular correlations and the differential two - jet rate in z decays , performed by aleph , allowed a 95%c.l .
lower limit of 6.3@xmath6  to be set on @xmath13  @xcite .
however , it was argued by the light gluino defenders  @xcite that this limit was to be weakened because _ ( i ) _ the theory uncertainties were too aggressive ; and _ ( ii ) _ no next - to - leading - order mass corrections were available for the four - jet angular correlations .
this letter is organized as follows . in section  [ sec :
vacuum ] , the reader is reminded of the model - independent parametrization of the weak loop corrections to the electroweak observables according to the @xmath0 formalism  @xcite .
this formalism is extended in section  [ sec : hadronic ] to the corrections caused by any new physics production process , in either the hadronic , the leptonic or the invisible final state .
the result is applied to the @xmath14 process in section  [ sec : gluino ] and a model - independent lower limit on the gluino mass is obtained .
virtual contributions to the `` electroweak observables '' have been parametrized in a model - independent way by several authors . here , the choice was made to parametrize the basic electroweak observables , _
i.e. _ , those sensitive to the weak loop corrections , with the ( linearized ) @xmath0 formalism , according to  @xcite    @xmath15    where @xmath16 are the born approximations of the corresponding observables , _
i.e. , _ without any weak loop corrections , and where the pure qcd- and qed - corrections were parametrized as @xmath17    in the standard model , or in any theory that does not predict new open processes in @xmath11  collisions at @xmath8 , the three @xmath0 s can then be fit to the precise measurements of lep and slc  @xcite , summarized in table  [ tab : data ] .
.precise lep and slc measurements of the z lineshape parameters ( @xmath18 , @xmath19 , @xmath20 ) , of @xmath21 and of @xmath22 , together with their correlation matrix .
the last two measurements have been taken here as uncorrelated with the first three  @xcite .
[ tab : data ] [ cols="<,<,>,>,>,>,>",options="header " , ]     because the existence of new particles could also modify the evolution of the electromagnetic coupling constant from 0 to @xmath23 , it was checked whether these limits could be affected by a variation of @xmath24 . this check is illustrated in fig .
[ fig : alpha]a , where it appears that the standard model value of @xmath25 yields the largest upper limits on the three partial widths . the limits of table  [ tab :
limit ] are therefore conservative in this respect .
new light hadronic flavours would also modify the evolution of the strong coupling constant .
although , as already mentioned , @xmath26 is constrained by measurements performed directly at the z mass scale , it is also determined with at least as accurate low energy measurements extrapolated at @xmath23 . a different scaling law for the latter would modify the world average of @xmath26 . however , a contribution from new coloured scalars or fermions would always slow down the running from low energy to @xmath23  so as to increase the value of @xmath27  @xcite . as shown in fig .
[ fig : alpha]b , such an increase of @xmath26 would render more constraining the limits on the hadronic and invisible partial widths . the limit on the leptonic width
would be slightly weakened , but would anyway remain the strongest of the three constraints .
the conservative choice of ignoring this effect was made throughout .
finally , it may be argued that a new hadronic contribution to z decays would decrease the value of @xmath26 fitted from the z lineshape .
however , the @xmath26 world average and its uncertainty ( saturated by common theory errors ) , and therefore the result of the present fit , do not change noticeably when the @xmath26 measurement from the z lineshape in taken out .
( 160,80 ) ( 71,70)(a ) ( 150,70)(b ) ( 0,-2 ) ( 80,-2 )    the fit of @xmath28  can be repeated in any other configuration of hadronic , leptonic and invisible contributions to the z decays from the new physics process .
let @xmath29 , @xmath30  and @xmath31  be the fractions of hadronic , leptonic and invisible final states produced by the new physics process under consideration . by definition , a final state which is neither hadronic nor leptonic is called invisible , therefore @xmath32 .
the z lineshape parameters of eqs .
( 3 ) to  ( 5 ) are modified according to @xmath33 , \\
r_\ell & \longrightarrow & r_\ell\ , \left[1+{\ensuremath{\varepsilon_{\rm np}}}\left ( 1.43{\ensuremath{x_{\rm had}}}-9.89{\ensuremath{x_\ell}}\right)\right ] , \\
\sigma_{\rm had } & \longrightarrow & \sigma_{\rm had}\ ,   \left[1 + { \ensuremath{\varepsilon_{\rm np}}}\left(-2.00 + 1.43{\ensuremath{x_{\rm had}}}+9.89{\ensuremath{x_\ell}})\right ) \right].\end{aligned}\ ] ] the ( @xmath29 , @xmath31 ) plane was scanned and the fit performed at each point , yielding a limit on @xmath28  everywhere in this plane . the corresponding 95%c.l .
limit on @xmath34 , the new physics contribution to the z total width , is displayed in fig .
[ fig : plane]a .
similarly , the limit on @xmath34 under the hypothesis that the new particle production contributes to hadronic and invisible final states , and to only one lepton flavour ( @xmath35 or @xmath36 ) , is shown in fig .
[ fig : plane]b .
( 160,80 ) ( 0,-2 ) ( 71,70)(a ) ( 150,70)(b ) ( 80,-2 )    very constraining limits on @xmath34 are set all over the plane , but no absolute limit can be obtained when the new particle production leads to fractions in the hadronic , invisible and leptonic ( three flavours ) final states identical to the z branching fractions . in this case , only @xmath18 depends on @xmath28 .
equations  ( 4 ) to  ( 7 ) no longer yield an independent determination of @xmath37  and @xmath38  with meaningful accuracy , because they all depend on the same linear combination of the two quantities . as a result
, the new particle contribution to the z width can always be cancelled by the @xmath39 virtual contribution , if a sufficient amount of fine tuning takes place .
whether or not this amount of fine tuning is acceptable would need different measurements and/or more theory to decide .
the results obtained in section  [ sec : hadronic ] can be applied to a variety of new processes . in this letter , they are used to constrain the cross section of the gluino production at @xmath8 in the process @xmath40 displayed in fig .
[ fig : gunion ] as a function of the gluino mass  @xcite .
because this cross section is the product of the @xmath41 cross section and a term that describes the gluon splitting into a gluino pair , the uncertainties related to the weak loop corrections to @xmath14 were alleviated by using the measured  cross section in the prediction .
when the gluino is light , the final state arising from this process is purely hadronic irrespective of the gluino decay and hadronization , and therefore contributes solely to the z hadronic decay width in all quark flavours .
upper limit on the production cross section at @xmath8 can then be set at 67pb ( table  [ tab : limit ] ) .
the corresponding lower limit on the gluino mass can be read off from the curve in fig .
[ fig : gunion ] , and is ( including a 2% systematic uncertainty on @xmath27 ) @xmath42    ( 160,95 ) ( 25,-2 )    1.6 mm    this limit confirms the one obtained by aleph  @xcite with an independent study of the qcd colour factors , which makes no use of the absolute z decay rates , and that derived from the running of the strong coupling constant  @xcite , which checks in addition the compatibility of the @xmath26 measurements at all energy scales . because it would add fully independent information and because it would avoid the conservative choices of section  [ sec : hadronic ] to be made ,
a combination of these results would further consolidate the light gluino exclusion .
for instance , a combination of the present limit and that of ref .
@xcite yields lower limits on @xmath13  of 6.8@xmath6  and 5.7@xmath6  at 95% and 99.63%c.l .
, respectively .
the present limit is not affected by the criticisms put forward to invalidate the previous results .
it is only if three different fine tuning processes took place , _
i.e. , _    1 .
if other new particles were produced in association with the gluino with a cross section of the order of or larger than that of the gluino production , but still were not directly detected at lep ; 2 .   if these processes led to final states such that the overall fractions of hadronic , invisible and leptonic new decays be similar to those of the z decays , for all lepton and quark flavours ; 3 .   and
if additional new physics yielded large negative virtual contributions to the z total decay width ( from the @xmath43 combination ) to exactly compensate this multiple new particle production ;    that the limit derived with the method presented in this letter would not hold .
i leave it to the champions of the light gluino scenario to find a theory in which this devilish conspiracy could take place .
a method to derive model - independent limits on new physics contributions to z decays has been presented . no general upper limit on the total z decay width
could be obtained , but very stringent constraints apply when the final states produced by the new physics process of interest are known . in particular , conservative upper limits have been put on @xmath18 of 0.55 , 1.3 and 3.9 mev in the case of purely leptonic ( @xmath35 or @xmath36 ) , invisible and hadronic final states .
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+ h.baer , k.cheung and j.f.gunion , ; + and modified to include initial - state radiation and generate events in + p.verdier , _ `` recherche des squarks et des gluinos dans lexprience delphi au lep '' _ , phd thesis , unpublished ; + the photon initial - state radiation correction was determined with the remt1 code described in + f.a.berends and r.kleiss , ; + the resummed qcd next - to - leading - order correction to gluon splitting in a gluino pair ( as well as a cross check of the leading order ) was computed according to + h.seymour , ; + with proper susy - qcd colour factors and @xmath26 running with one light gluino  @xcite .
the precise measurements of the `` electroweak observables '' performed at lep and slc are well consistent with the standard model predictions . 
 deviations from the standard model arising from vacuum polarization diagrams ( also called `` weak loop corrections '' ) have been constrained in a model - independent manner with the @xmath0 formalism . within the same formalism , additional deviations from new physics production processes can also be constrained , still in a model - independent way . 
 for instance , a 95%c.l . 
 limit of @xmath1 is set on the partial width of any purely hadronic exotic contribution to z decays . when applied to the @xmath2  @xmath3@xmath3  process , it allows an absolute lower limit to be set on the gluino mass , @xmath4 which definitely closes the so - called light gluino mass window .