Theoretical expectations for high mass photon pairs inl+l−

Abstract

Recently, the L3 collaboration has reported the observation of four events in the reactions e + e − → ll + γγ, l = e, µ, τ , with the invariant photon pair mass near 60 GeV in a data sample collected in the L3 detector corresponding to 950,000 produced Z 0 's. More recently, more data from the other LEP collaborations have become available. In this paper, we use the Monte Carlo genrator YFS3 and our recent exact results on e + e − → ll + γγ to assess the QED expectations for such L3-type high mass photon pair events in e + e − → ll + γγ + n(γ) near the Z 0 resonance.Recently, the L3 collaboration reported [1] the observation of high-mass γγ pairs in the reactions e + e − → ll+γγ in the Z 0 resonance region; in particular, four such events were reported with the invariant γγ mass near 60 GeV from a data sample corresponding to 950,000 produced Z 0 's in the LEP e + e − colliding beam device. More recently, related data from the ALEPH, DELPHI, and OPAL Collaborations [2] have become available, and hence, an immediate issue which needs to be addressed is that of the theoretical expectations from the basic QED processes themselves for such high-mass photon pairs. It is this issue which we shall address in what follows.More specifically, we want to use the YFS Monte Carlo approach [3] to higher-order SU 2L ×U 1 processes introduced by two of us (S.J.and B.F.L.W.) and the recent exact results [4] by the three of us on the processes e + e − → ll+γγ, l = e, µ, τ , in the Z 0 resonance region to assess the probability that the observations in Refs. [1,2] are consistent with higher-order QED processes. This means that the over-all normalization of our calculations in the L3 acceptance must be known even in the presence of the strong initial state radiative effects associated with the Z 0 resonance line shape. Accordingly, we will employ our YFS Monte Carlo event generator [3], which treats e + e − → f f +n(γ), in the Z 0 resonance region with the n(γ) multiple photon radiation for both the initial and final fermion. Here, f is a fundamental SU 2L × U 1 fermion. We should stress that, strictly speaking, f = e is implicit in YFS3. However, in the L3 acceptance for the high mass γγ pairs, kinematical cuts eliminate any large effect from the exchanges in e + e − → e + e − + n(γ) which are not the s-channel Z 0 exchange, so that we can use YFS3 for our analysis at the currently required level of precision. Our recent results in Ref.[4] of course do not have any such qualification in their applicability to the L3-type events for e + e − γγ final states: the full matrix element is available from Ref.[4], and indeed, it will be used to check the validity of our YFS3 s-channel exchange approach to the high γγ mass L3-type e + e − γγ final states, for example.What we will do in this paper then is to set the QED higher order expectations for the L3-type high γγ invariant mass events. We hope that sufficient data will be taken so that the statistical errors on the experimental results analyzed in this paper will cease to be the over-r...

Bhabha process at LEP — theoretical calculations

“…The improved calculation with a new smaller error tag for the Z exchange was done during the workshop and published in Ref. [17]. The corresponding improvement of the matrix element for the Z exchange is implemented in BHLUMI [7].…”

“…Gradual improvements concern mainly the matrix element. More and more cross-checks are built up in order to better determine its technical precision, see [1,8].…”

Higher-order radiative corrections to low-angle Bhabha scattering: the YFS Monte Carlo approach

“…The error was found at the beginning of the LEP2 workshop { results in the workshop and workshop proceedings [2] from the BHLUMI program correspond to version 4.03 (or 2.02a) in which the error is already corrected. It is worth stressing that the error was found not by c hance, but during the routine round of tests on the matrix element in BH-LUMI which lead to a precise estimate of the missing third-order leading-log contribution in BHLUMI 1 .…”

“…The error showed up for the rst time in the second round of tests [3], in which the example of calorimetric event selection was used. Strictly speaking, the additional term +( p ) 1 4 ln(1 ~1 is not an error but an adjustment of the non-exponentiated matrix element such that the di erence between the exponentiated and non-exponentiated cross sections does include only O( 3 ) contributions and none of O( 2 ). This improvement is necessary to make the discussion of the sub-leading O( 2 ) contributions easier and cleaner, see [2].…”

“…The replacement o f 1 2 ln(1 ~1 ~1 + l n ( 1 1 1 ) with 3 4 ln(1 ~1 ) 1 4 ln(1 ~1) corrects for a genuine second-order leading-log error. This error was not noticed earlier because for a non-calorimetric event selection like the \academic trigger" in [1] or the BARE1 of [2] its e ect cancels exactly between initial and nal state emission { only for the calorimetric kind of event selection it does a ect the total cross section. The rst round of comparisons of the Monte Carlo with semi-analytical calculations [4] was done for a non-calorimetric event selection, for which the error is numerically invisible.…”