Non-perturbative effects in the energy-energy correlation

We discuss $1/Q$ corrections to hard processes in QCD where $Q$ is a large mass parameter like the total energy in $e^+e^-$ annihilation. The main problem we address ourselves to is whether these corrections to different processes (concentrating for definiteness on the Thrust and the Drell-Yan cross section) can be related to each other in a reliable way so that the phenomenology of the $1/Q$ corrections can be developed. We derive first the relation valid to lowest order usi...

In this article we study, via analytical methods, $1/Q$ non-perturbative power corrections to event shape mean values, addressing in particular the question of their interplay with soft perturbative emissions. Specifically we point out that energy-ordered soft perturbative emissions that precede a non-perturbative emission, give rise to terms of the form $\frac{1}{Q} \left (\alpha_s \ln \frac{Q}{\Lambda} \right)^n$. While such terms are formally higher order in the strong cou...

We consider heavy quark mass ($m$) effects in the Energy-Energy Correlation function in $e^+e^- \to hadrons$ at high energy $Q$, in the back-to-back (two-jet) region. In the ultra-relativistic limit, $Q \gg m$, the QCD Sudakov form factor $S(b)$ in impact parameter ($b$-)space reads: \begin{eqnarray} \log S(b) &=& - \int_{m^2}^{Q^2} \frac{dk^2}{k^2} \left\{ \log\left(\frac{Q^2}{k^2}\right) A[\alpha_S(k^2)] + B[\alpha_S(k^2)]\right\} [1-J_0(b k)] \nonumber\\ && - \int_0^{m^2} ...

There is ample evidence, dating as far back as Low's theorem, that the universality of soft emissions extends beyond leading power in the soft energy. This universality can, in principle, be exploited to generalise the formalism of threshold resummations beyond leading power in the threshold variable. In the past years, several phenomenological approaches have been partially successful in performing such a resummation. Here, we briefly review some recent developments which pa...

The energy-energy correlator (EEC) is an event shape observable which probes the angular correlations of energy depositions in detectors at high energy collider facilities. It has been investigated extensively in the context of precision QCD. In this work, we introduce a novel definition of EEC adapted to the Breit frame in deep-inelastic scattering (DIS). In the back-to-back limit, the observable we propose is sensitive to the universal transverse momentum dependent (TMD) pa...

We present results obtained from a study of the structure of hadronic events recorded by the L3 detector at various centre-of-mass energies. The distributions of event shape variables and the energy dependence of their mean values are measured from 30GeV to 189GeV and compared with various QCD models. The energy dependence of the moments of event shape variables is used to test a power law ansatz for the non-perturbative component. We obtain a universal value of the non-pertu...

The size of non-perturbative corrections to event shape observables is predicted to fall like powers of the inverse centre of mass energy. These power corrections are investigated for different observables from $e^+e^-$-annihilation measured at LEP as well as previous experiments. The obtained corrections are compared to other approaches and theoretical predictions. Measurements of $\alpha_s$ using power corrections are compared to conventional methods.

We estimate the effects of non-perturbative physics on the differential distributions of infrared- and collinear-safe $e^+e^-$ event shape variables, by extending the notion of an infrared-regular effective strong coupling, which accounts for the non-perturbative corrections to the mean values of several shape variables, to their distributions. This leads to $1/Q$ power corrections over a range of values of the shape variables considered, where $Q$ is the centre-of-mass energ...

We introduce the azimuthal correlation for the deep inelastic scattering process. We present the QCD prediction to the level of next-to-leading log resummation, matching to the fixed order prediction. We also estimate the leading non-perturbative power correction. The observable is compared with the energy-energy correlation in e+e- annihilation, on which it is modelled. The effects of the resummation and of the leading power correction are both quite large. It would therefor...

A few comments are made on the role of nonperturbative and perturbative power corrections. This is followed by a description of energy flow observables and correlations that may provide a flexible approach to rapidity distributions in hadronic scattering.