\subsection{QCD studies}
\label{sec:QCD}

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 $\sintw$, 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}.
