Instantons at HERA

Perturbative QCD successfully describes hard scattering processes. Beyond these, nonperturbative processes are predicted by QCD as well, e.g. processes mediated via instanton configurations in the path integral [52]. Of particular interest in ep collisions are instanton processes which simultaneously produce n_f light $\overline{q_L}q_R$ pairs and hence violate chirality by $\Delta Q_5=2n_f$ units. Ordinarily these processes are exponentially suppressed, by a factor ${\rm exp}[-4\pi/\alpha_S]$. In conjunction with multiple gluon emission, however, this suppression is ameliorated by a factor ${\rm exp}[-4\pi F(x')/\alpha_S(\mu)]$, where the so-called ``holy-grail function'' F(x') equals unity at x'=1. F(x') is known to decrease with decreasing x', to about 1/2 at $x'\simeq 0.2$ but is not reliably calculable for small values of x' [52].

The expected fraction, f^(I), of instanton induced events, compared to generic DIS events at the same x and Q², depends critically on the shape of the holy-grail function at small x'. Expectations range between 10^-6<f^(I)<10^-3 if F(x') approaches a constant below $x'_{min}=0.2\dots 0.3$ [52]. Because several $q\bar q$ pairs and gluons are produced isotropically, the striking signature of instanton-induced events would be very high particle multiplicity and high average transverse energy deposition over a large region of the available phase space.

H1 reported on a search for such events [53]. The best limits are obtained from the non-observation of events with large charged particle multiplicities. For 80 <W< 220 GeV, limits of $f^{(I)}\nostrocostrutto < \over \sim0.5\%$ have been set [53]. These limits are still about one order of magnitude larger than expectations from instanton calculations [52], but they begin to probe the interesting parameter range.