Abstract:The discovery by the ATLAS and CMS experiments of a new boson with mass around 125 GeV and with measured properties compatible with those of a Standard-Model Higgs boson, coupled with the absence of discoveries of phenomena beyond the Standard Model at the TeV scale, has triggered interest in ideas for future Higgs factories. A new circular e + e − collider hosted in a 80 to 100 km tunnel, TLEP, is among the most attractive solutions proposed so far. It has a clean experimental environment, produces high luminosity for top-quark, Higgs boson, W and Z studies, accommodates multiple detectors, and can reach energies up to the tt threshold and beyond. It will enable measurements of the Higgs boson properties and of Electroweak Symmetry-Breaking (EWSB) parameters with unequalled precision, offering exploration of physics beyond the Standard Model in the multi-TeV range. Moreover, being the natural precursor of the VHE-LHC, a 100 TeV hadron machine in the same tunnel, it builds up a long-term vision for particle physics. Altogether, the combination of TLEP and the VHE-LHC offers, for a great cost effectiveness, the best precision and the best search reach of all options presently on the market. This paper presents a first appraisal of the salient features of the TLEP physics potential, to serve as a baseline for a more extensive design study.

Dimensional arguments lead to say that N excitons in a sample of volume V behave as bosons for λ N a 3 x /V ≪ 1, ax being the exciton radius and λ a dimensionless factor. The Mott criterion, which is based on the disappearance of all exciton bound states because of screening, gives λ ≃ 1. Since excitons feel each other through both Coulomb interaction and Pauli exclusion between their electrons and holes, criteria based on the underlying fermionic character of the exciton should be even more relevant. When the density of electron-hole (e-h) pairs in semiconductors is very large, the carriers form an e-h plasma. Although the plasma's Coulomb energy is large, it remains small compared to its kinetic energy so that, in this regime, the Coulomb interaction can be treated as a perturbation (with possible high-order processes, such as RPA or "bubble" diagrams, in order to avoid spurious divergences [1]). The situation is quite different in the low-density regime, where one electron basically interacts with only one hole, giving birth to a hydrogenoid "atom" called exciton. Since bound states only appear if the Coulomb interaction between electron and hole is treated exactly, i.e., to all orders in perturbation, an exciton may be viewed as the result of a repeated interaction between electron and hole through "ladder" diagrams [2].From dimensional arguments, we expect the cross-over between the two regimes to appear when the distance between two excitons is of the order of their size, i.e., when λ N a 3 x /V ≃ 1, a x being the exciton Bohr radius, N the number of excitons in the sample volume V , and λ a dimensionless factor.The high-density regime in which the Coulomb energy is dominated by the kinetic energy is valid when the parameter r s , defined by N 4 3 π(r s a x ) 3 /V = 1, is small compared to 1. This leads to λ = 4 π/3 ≃ 4. The prefactor λ can also be obtained by evaluating the carrier density for which, due to Coulomb screening, no excitonic bound state survives. The accepted result [3] for this Mott density leads to λ ≃ 1.According to the spin-statistics theorem, excitons, which are composite particles made of two fermions, should behave as bosons. While the above λ's have been deduced from considerations in which the Coulomb interaction plays a crucial role, criteria based on the underlying fermionic character of the excitons should be even more relevant. Indeed, excitons are not perfect bosons because they "feel" each other not only through Coulomb interaction but also through Pauli exclusion between their electrons and holes [4,5].In this Letter, we address the question: Up to what density can excitons be treated as bosons? We show that the criteria based on the fermionic character of excitons generate prefactors λ larger than 1 by two orders of magnitude. This casts new light upon the possible observation of the challenging Bose condensation of excitons.For the sake of simplicity, we will restrict here to excitons with zero total momentum. In terms of the free electron (a † k ) and hole (b † −k ) creati...

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