Exploring new physics through contact interactions in lepton pair production at a linear collider Page: 3 of 6
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Analogous formulas can be obtained for p+ - and T+T- final states. Since phenomenology of string models
with multiple generations has not been studied in detail, we will not consider the effects of Regge states in these
The theoretical formulas (2) (7) have been implemented in PANDORA  to scan the scale parameters of
our models (referred to as VV, AA, SR, KK+, KK- and TeV in the following). At each scan point the angular
distribution of the produced leptons is studied calculating the expected number of events in 10 bins of cos 0,
with a cut of Icos 01 <0.9 imposed on the outgoing electron polar angle in the case of Bhabha scattering. The
ratio of the predicted new physics cross-section to the SM cross-section for electron and muon pair production
is shown in Figure 1 for all the models considered at a 500 GeV LC.
1.04 . I . . . . I I1.04 . . . . . . I
1.03 (a) 103 (b) AA KK-
1.02 1.02 TeV SR
0.98 ee 0.98
0.97 ' '''0.97
-1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
FIG. 1: Ratio of the predicted new physics cross-section to the SM cross-section for (a) electron and (b) muon pair
production as a function of the lepton polar angle for the models AA (A=71 TeV), VV (A=85 TeV), TeV (M,=14 TeV),
KK+ (MH=3.4 TeV), KK- (MH=3.4 TeV) and SR (MS=1.7 TeV) at a 500 GeV LC. The scale parameters have been
chosen to be at the sensitivity reach with 100 fb-I1 integrated luminosity.
For each considered model and parameter value 100-1000 Monte Carlo (MC) experiments are generated
using Poisson statistics. These are in turn compared to all theoretical models (including SM) by calculating
the X2 of the MC and the predicted theoretical distributions, accounting for a fully correlated systematic error
of 2% as well. (We will use the term true model for the model which is assumed to be true, ie. which was
used to generate the MC experiments.) We define the confidence level (CL) at which a model with a given
parameter can be excluded by the ratio of its X2 probability to the highest X2 probability for any model with
any parameter considered:
1 - CL P(X2)/ max(P(X2)) (9)
The expected CL is computed as the median value for all the MC experiments generated with the same model
and parameter value.
For each new physics model considered, we have calculated the maximum value of the scale parameter for
which the Standard Model hypothesis is expected to be excluded at the 95% CL. We list these limits, for
three sample values of the LC energy and luminosity, in Table I. The corresponding limits for the exclusion
of all models but the true one are inevitably somewhat lower, as shown in the Table II. This effect is more
pronounced when only one channel is analysed, as is necessarily the case for the SR model where at present
theoretical calculations only exist for Bhabha scattering. In most cases, however, combining all the channels
allows one to distinguish between the theoretical models almost up to the SM sensitivity reach of Table I, with
the model selection sensitivity reach of Table II being only about 5-15% lower. In Figure 2 we plot 1 - CL
corresponding to the best fit for each tested model in the electron pair final state as a function of the scale
parameter of the true model for the case of a 500 GeV LC with 100 fb-1 luminosity.
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Perelstein, Maxim & Pasztor, Gabriella. Exploring new physics through contact interactions in lepton pair production at a linear collider, article, December 4, 2001; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc784665/m1/3/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.