As another example of the importance of precision measurements, the LEP determination of \(\alpha_{\rm s}(m_{\rm Z})\) was already able, in association with \(\sin^{2}\theta_{\rm W}^{\rm eff}\), to distinguish between supersymmetric and non-supersymmetric models of grand unification \cite{Ellis:1990,Amaldi:1991,Langacker:1991,Giunti:1991}. The prospective TLEP accuracies on these quantities would take this confrontation between theory and experiments to a completely new level.

The exceptionally large event samples collected at TLEP will also allow the determination of the fragmentation functions of different hadrons in a much wider \(x\) range than currently available, improving the understanding of the heavy quark fragmentation process and of the fragmentation of photons. The QCD parton showers and the non-perturbative physics of fragmentation and hadronization will also be studied in detail, providing stringent constraints on Monte Carlo generators \cite{0710.3820,0811.4622,0803.0883} and triggering new developments in the theoretical framework, such as multi-leg matching to parton showers. The \(\gamma\gamma\) and \(e\gamma\) interactions will also be studied with great precision at TLEP, probing BFKL and nonperturbative QCD dynamics \cite{Aurenche}.

Quarkonium production measurements at TLEP would also help testing the universality of the long-distance-matrix elements describing the evolution from the point-like \({\rm Q\bar{Q}}\) state to the observed hadron, a hypothesis underlying the nonrelativistic QCD factorization framework. Besides such precision studies of QCD, a well-understood production of heavy-quark bound states at TLEP can be crucial for the discovery of, e.g., stoponium, gluino-onium and other (nonrelativistic) bound states at the VHE-LHC \cite{1307.7425}.