Global Analysis of Bhabha Scattering at LEP2 and Limits on Low Scale Gravity Models

A global analysis of the data on Bhabha scattering from the four LEP experiments ALEPH, DELPHI, L3 and OPAL is performed to search for effects of virtual graviton exchange in models with low scale gravity. No statistically significant deviations from the Standard Model expectations are observed and lower limits on the scale of models with large extra dimensions of ΛT = 1.077 TeV for λ = −1 and ΛT = 1.412 TeV for λ = +1 at 95 % confidence level are derived. ∗ e-mail: [email protected] Introduction The Standard Model (SM) has been tremendously successful when confronting the theory with data coming from the highest energy accelerators. Still, we believe that it is not complete, and one of the first questions in all searches for new physics is what is the relevant scale, where new phenomena will become accessible to experiments. Recently, a radical proposal has been put forward by Arkani-Hamed, Dimopoulos and Dvali [1] for the solution of the hierarchy problem, which brings close the electroweak scale mEW ∼ 1 TeV and the Planck scale MPl = 1 √ GN ∼ 10 TeV. In this framework the effective 4 dimensional MPl is connected to a new MPl(4+n) scale in a (4+n) dimensional theory: MPl ∼ M 2+n Pl(4+n)R n (1) where there are n extra compact spatial dimensions of radius ∼ R. Putting MPl(4+n) ∼ mEW, for n = 1 we get R ∼ 10 cm, which is excluded experimentally, but already for n = 2 the result is R ∼ 0.1 − 1 mm, which is below the current experimental limits from gravitational experiments. In this work we will adopt the notation from [2] and call the gravitational mass scale MD. This scale is relevant in direct searches for graviton production. In the case of virtual graviton exchange, which is the subject of our analysis, the corresponding scale is the ultraviolet cutoff energy, denoted ΛT in [2] and Ms in [3, 4], with the relation Ms = (2/π) ΛT. The two scales are expected to be close to each other. This paper is organized as follows. In section 2, we describe the effects of virtual graviton exchange in Bhabha scattering, which turns out to be the single most sensitive channel at LEP2 energies. In the following section the experimental data used in this analysis is presented. In section 4 the results of the global fit are shown and limits on low scale gravity models are derived. Virtual Graviton Exchange in Bhabha Scattering The differential cross section for fermion-pair production in e+e− collisions can be decomposed in the usual way as: dσ dΩ = SM(s, t) + ε · CInt(s, t) + ε 2 · CGraviton(s, t) (2) where SM(s, t) is the Standard Model contribution, CGraviton(s, t) comes from the virtual graviton exchange and CInt(s, t) is the interference between the SM and the low scale gravity terms. The exact form of these functions is given in [2] for all final states, in [3] for final states other than electrons and in [4] for Bhabha scattering. Here we will use the results from the calculations by Rizzo. The independent theoretical calculations in [2] give numerically values which are very close and produce the same final results. In the formula above ε = λ Ms . (3) The coefficient λ is of O(1) and can not be calculated explicitly without knowledge of the full quantum gravity theory. In the following analysis we will assume that λ = ±1 in order to study both the cases of positive and negative interference. It should be noted that the exchange of a spin 2 particle leads to terms ∼ cos θ and ∼ cos θ, which makes the differential cross sections a unique signature for this type of physics.