Hadronic final states in deep-inelastic scattering with Sherpa

TL;DR

DIS final states involve multiple hard scales, presenting a challenge for standard MC approaches. The authors extend SHERPA with a merging framework that combines multi-parton tree-level matrix elements and parton showers, including a low-$Q^2$ extension designed to fill the full real-emission phase space. Their predictions are validated against a wide set of HERA measurements, showing good agreement across jet rates, multi-jet observables, jet shapes, energy flows, and identified hadron spectra, while systematically assessing theoretical uncertainties. The work demonstrates the viability of DIS data to tune hadronisation models and validates the merging approach in a genuinely multi-scale environment, with implications for LHC phenomenology in similar kinematic regimes.

Abstract

We extend the multi-purpose Monte-Carlo event generator Sherpa to include processes in deeply inelastic lepton-nucleon scattering. Hadronic final states in this kinematical setting are characterised by the presence of multiple kinematical scales, which were up to now accounted for only by specific resummations in individual kinematical regions. Using an extension of the recently introduced method for merging truncated parton showers with higher-order tree-level matrix elements, it is possible to obtain predictions which are reliable in all kinematical limits. Different hadronic final states, defined by jets or individual hadrons, in deep-inelastic scattering are analysed and the corresponding results are compared to HERA data. The various sources of theoretical uncertainties of the approach are discussed and quantified. The extension to deeply inelastic processes provides the opportunity to validate the merging of matrix elements and parton showers in multi-scale kinematics inaccessible in other collider environments. It also allows to use HERA data on hadronic final states in the tuning of hadronisation models.

Figures (22)

• Figure 1: Schematic view of the scattering kinematics in the Breit frame for leading-order $e^\pm q\to e^\pm q$ scattering and 2-jet production processes in DIS. The lightly shaded blob denotes the incoming proton. For 2-jet events with large jet transverse energy, $E_{T,B}^2\gtrsim Q^2$, the $2\to 2$ process depicted by the dark shaded blob in Fig. \ref{['sub@fig:diskin_two']} sets the hard scale.
• Figure 2: Differential 2-jet rates defined by the exclusive $k_T$-jet algorithm in the Breit frame for deep-inelastic scattering events with $Q^2>4\,{\rm GeV}^2$. Part \ref{['sub@fig:recoil']} compares the influence of different recoil strategies, while parts \ref{['sub@fig:mecorr_new']} and \ref{['sub@fig:mecorr_old']} show the effect of matrix element corrections. Monte Carlo samples were generated using the parton shower model of Schumann:2007mg. Scheme 1 stands for the recoil strategy in Platzer:2009jqHoeche:2009xy, while scheme 2 labels the original strategy employed in Schumann:2007mg.
• Figure 3: Schematic view of three possible core process choices in DIS three-jet production. Part \ref{['sub@fig:multicore_one']} corresponds to the most probable core process being the virtual photon exchange, while additional hard partons are interpreted as parton shower emissions. Parts \ref{['sub@fig:multicore_two']} and \ref{['sub@fig:multicore_three']} depict configurations, where the most probable core process is the interaction of the virtual photon with a parton and a pure QCD $2\to 2$ process, respectively.
• Figure 4: The differential 2- and 3-jet rates in merged event samples of varying $\bar{Q}_{\rm cut}$\ref{['sub@fig:merging_qbarcut']}, varying $S_{\,\rm DIS}$\ref{['sub@fig:merging_sdis']} and varying shower recoil strategy \ref{['sub@fig:merging_recoil']}. See also Fig. \ref{['fig:shower']} for notation. Coloured lines display the contributions of different final state multiplicity matrix elements. The central parameter value is chosen as $\bar{Q}_{\rm cut}=5$ GeV and $S_{\,\rm DIS}=0.6$. The maximum parton multiplicity in hard matrix elements is $N_{\rm max}=3$.
• Figure 5: Schematic view of the splittings of an initial-state parton with a final-state spectator and the splitting of a final-state parton with an initial-state spectator. The blob denotes the hard matrix element. Incoming and outgoing lines label initial- and final-state partons, respectively.