Phenomenology of multiple parton radiation in semi-inclusive deep-inelastic scattering

TL;DR

In semi-inclusive DIS, fixed-order perturbative QCD struggles in the current fragmentation region due to abundant soft and collinear radiation, producing large logarithms in $q_T$. The authors apply a Collins-Soper-Sterman–type resummation in $b$-space, combining a perturbative Sudakov $S^P(b,Q,...)$ with a nonperturbative $S^{NP}(b,Q,x,z)$ to compute cross sections and the $z$-flow, and they validate the approach by comparison to HERA measurements of energy flow and charged-particle multiplicities. They obtain updated nonperturbative Sudakov parametrizations (e.g., $S^{NP}_z(b,Q,x)$ and a $z$-dependent $S^{NP}$ for multiplicities) that yield better data-theory agreement across observables, while noting the need for higher-order corrections at large $q_T$. The study reveals a strong dynamical role for small-$x$ and small-$z$ soft radiation in sDIS and provides a framework to analyze additional observables, with implications for how resummation and nonperturbative effects are modeled in current fragmentation.

Abstract

In the current region of semi-inclusive deep-inelastic scattering, most events are accompanied by intensive radiation of soft and collinear partons which cannot be reliably described at any fixed order of perturbative QCD. In this paper, a resummation formalism that describes such multiple parton radiation is compared to the HERA data on semi-inclusive DIS, including the distributions of energy flow and charged particle multiplicity. We show that the resummation of multiple parton radiation improves the agreement between the theory and the data. We make some suggestions on further experimental study of multiple parton radiation at HERA.

Figures (5)

• Figure 1: Comparison of the resummed $z$-flow in the current region of the hCM frame with the data in the low-$Q^2$ bins from Refs. H1z2 (filled circles) and H1z1 (empty circles). The parametrization of the nonperturbative Sudakov factor in (\ref{['SNPz']}) is used. For the bin with $\langle Q^2\rangle=33.2 \hbox{GeV}^2$ and $\langle x \rangle = 0.0047$, the ${\cal O}(\alpha_s)$ contribution for $\mu_F=Q$ is shown as a dashed curve.
• Figure 2: Comparison of the resummed $z$-flow in the current region of the hCM frame with the data in the high-$Q^2$ bins from Ref. H1z2. The parametrization of the nonperturbative Sudakov factor in (\ref{['SNPz']}) is used. For the bin with $\langle Q^2\rangle=617 \hbox{GeV}^2$ and $\langle x \rangle = 0.026$, the ${\cal O}(\alpha_s)$ contribution for $\mu_F=Q$ is shown as a dashed curve.
• Figure 3: The distributions (a) $\langle p_T^2 \rangle$ vs. $x_F$ and (b) $\langle q_T^2 \rangle$ vs. $x_F$ for the charged particle multiplicity at $\langle W \rangle = 120 \hbox{GeV}, \ \langle Q^2 \rangle = 28 \hbox{GeV}^2$. The experimental points for the distribution $\langle p_T^2 \rangle$ vs. $x_F$ are from Fig. 3c of Ref. ZEUSchgd96. The "experimental" points for the distribution $\langle q_T^2 \rangle$ vs. $x_F$ are derived using Eq. (\ref{['pT2toqT2']}). The solid and dashed curves correspond to the resummed and the next-to-leading order ($\mu_F = Q$) multiplicity, respectively.
• Figure 4: The dependence of the charged particle multiplicity on the transverse momentum $p_T$ of the observed particles in the hCM frame. The data points are from ZEUSchgd96. The solid and dashed curves correspond to the resummed and NLO multiplicities, respectively.
• Figure 5: The dependence of the charged particle multiplicity on the Feynman variable $x_F$ in the hCM frame. The solid curve corresponds to the resummed multiplicity. The dashed, lower dotted and upper dotted curves correspond to the NLO multiplicity calculated for $\mu_F = Q,\ 0.5 Q$ and $2 Q$, respectively.