# Exploring new physics through contact interactions in lepton pair production at a linear collider Page: 3 of 6

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3

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

channels.

III. ANALYSIS

The theoretical formulas (2) (7) have been implemented in PANDORA [10] 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-

--VV KK+

1.02 1.02 TeV SR

1.01 1.01

1 1

0.99 0.99

0.98 ee 0.98

0.97 ' '''0.97

-1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1

cosO cosO

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.

IV. RESULTS

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.