Investigation of Power Corrections to Event Shape Variables measured in Deep-Inelastic Scattering

TL;DR

The paper analyzes power corrections to event-shape means in deep-inelastic scattering using H1 data across $7<Q<100$ GeV, testing perturbative QCD augmented with $1/Q^p$ hadronization terms. It compares simple power-law fits with the Dokshitzer–Webber universal coupling framework, finding that a universal non-perturbative parameter $ar{ ext{α}}_0 \\approx 0.5$ describes several observables, while two-jet rates exhibit minimal hadronization effects and require careful coefficient treatment. Strong parameter correlations and higher-order uncertainties lead to a spread in extracted $\a_s(M_Z)$, indicating missing pieces in theory or coefficients. Overall, the results support the power-correction paradigm in DIS and motivate further theoretical development and combined experimental analyses to attain a coherent, universal description of hadronization in event shapes.

Abstract

Deep-inelastic ep scattering data, taken with the H1 detector at HERA, are used to study the event shape variables thrust, jet broadening, jet mass, C parameter and two kinds of differential two-jet rate. The data cover a large range of the four-momentum transfer Q, which is considered to be the relevant energy scale, between 7 GeV and 100 GeV. The Q dependences of the mean values are compared with second order calculations of perturbative QCD applying power law corrections proportional to 1/Q^p to account for hadronization effects. The concept of power corrections is investigated by fitting simultaneously a non-perturbative parameter alpha_p and the strong coupling constant alpha_s.

Figures (9)

• Figure 1: Distribution of selected events in the $x - Q^2$ plane. Only a small part of the data corresponding to a luminosity of $3.2\,{\rm pb}^{-1}$ is shown. The curves indicate the phase space cuts in $E_{e'}$, $\theta_{e'}$, $y$ and $\theta_q$.
• Figure 2: Normalized differential distributions of the event shapes $\tau$, $B$ and $\tau_C$. H1 data (symbols) are compared with Disent NLO calculations (curves) using the MRSA' parton density functions with $\alpha_s(M_Z) = 0.115$. The error bars represent statistical and systematic uncertainties. The spectra given at $\left< Q \right> = 7.5\,{\rm GeV}, \; 8.7\,{\rm GeV}, \ 15.0\,{\rm GeV}, \ 17.8\,{\rm GeV}, \ 23.6\,{\rm GeV}, \ 36.7\,{\rm GeV}, \ 57.7\,{\rm GeV}$ and $81.3\,{\rm GeV}$ (from top to bottom) are multiplied by factors of $10^n \ (n=7, \ldots, 0)$.
• Figure 3: Normalized differential distributions of the event shapes $\rho$, $C$, $y_{fJ}$ and $y_{k_t}$. H1 data (symbols, see fig. \ref{['fig:dndFhl1']}) are compared with Disent NLO calculations (curves) using the MRSA' parton density functions with $\alpha_s(M_Z) = 0.115$. The error bars represent statistical and systematic uncertainties. The spectra given at $\left< Q \right> = 7.5\,{\rm GeV}, \; 8.7\,{\rm GeV}, \ 15.0\,{\rm GeV}, \ 17.8\,{\rm GeV}, \ 23.6\,{\rm GeV}, \ 36.7\,{\rm GeV}, \ 57.7\,{\rm GeV}$ and $81.3\,{\rm GeV}$ (from top to bottom) are multiplied by factors of $10^n \ (n=7, \ldots, 0)$.
• Figure 4: Mean values of $\tau$ (left) and $C$ (right) versus $Q$ in four different bins of $x$ calculated with Disent. The lines connect the means belonging to the same $x$ bin.
• Figure 5: Mean values (full symbols) of $\tau$, $B$, $\tau_C$, $\rho$ and $C$ as a function of $Q$. The error bars represent statistical and systematic uncertainties. The full line corresponds to a power correction fit according to the Dokshitzer--Webber approach. The dashed line shows the pQCD contribution of Disent in these fits.