SHERPA: Multi-Domain Research Systems

• SHERPA is a versatile family of research systems spanning high-energy physics, accelerator physics, machine learning, astronomy, and federated learning.
• It automates complex workflows such as NLO QCD matching, hyperparameter optimization, and forward modeling using integrated algorithms and modular components.
• Its implementations enable precise collider-event generation, efficient beam extraction, robust privacy-preserving protocols, and adaptive panorama synthesis.

SHERPA is a name used for several research systems across high-energy physics, accelerator physics, machine learning, astronomy, federated learning, and generative modeling. In particle physics, Sherpa is a general-purpose Monte Carlo event generator for collider-event simulation, combining hard-scattering matrix elements, QCD and electroweak corrections, parton showers, hadronisation, and decays in a single framework (Schumann, 2017). In other domains, SHERPA denotes a bent-crystal positron-extraction project at DAΦNE, a Python hyperparameter-optimization library, an astronomical fitting environment, a privacy-preserving multi-party entity-alignment protocol, a model-driven framework for LLM execution, and a seam-aware adaptation method for open-domain $360^\circ$ panorama generation (Garattini et al., 2021, Hertel et al., 2020, Siemiginowska et al., 2024, Jimenez-Gutierrez et al., 21 Apr 2026, Chen et al., 29 Aug 2025, Kang et al., 10 Jun 2026).

1. Sherpa as a collider-event generator

Sherpa, in high-energy collider physics, is a multi-purpose event generator intended to cover the full chain from hard production to particle-level final states. Its core components include internal tree-level matrix-element generators such as AMEGIC and COMIX, automated Catani–Seymour subtraction for NLO QCD, interfaces to one-loop providers such as OpenLoops and Recola, dipole-based parton showers, hadronisation, underlying event, and decay machinery (Schumann, 2017, Pellen, 2017, Bothmann et al., 2024). In this role it occupies the same broad category as Pythia and Herwig, while being particularly associated with matrix-element-plus-shower workflows, native matching and multijet merging, and a close coupling between subtraction, shower kinematics, and matrix-element generation (Schumann, 2017).

A standard NLO structure implemented within Sherpa is

$$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$

with $\mathrm{d}\sigma^{\text{B}}$ the Born term, $\mathrm{d}\sigma^{\text{V}}$ the virtual correction, $\mathrm{d}\sigma^{\text{R}}$ the real-emission contribution, $\mathrm{d}\sigma^{\text{D}}$ the Catani–Seymour subtraction term, and $\mathrm{d}\sigma^{\text{I}}$ the integrated subtraction counterterm (Schumann, 2017). Sherpa automates the construction of Born, real, dipole, and integrated-dipole pieces, while external one-loop providers supply the virtual amplitudes. This automation was extended early to an automated POWHEG implementation in Sherpa for processes with a simple colour structure, where the hardest emission is generated first from an NLO-weighted Born distribution $\bar B$, and subsequent softer radiation is delegated to the shower (Hoeche et al., 2010).

Matching and merging are central to Sherpa’s identity. The framework employs S-MC@NLO-style matching to combine NLO matrix elements with its dipole shower, and it supports multi-jet merging schemes such as MEPS@LO and MEPS@NLO, with shower vetoes and Sudakov reweighting to avoid double counting between matrix-element and shower domains (Schumann, 2017). In deeply inelastic scattering, Sherpa was extended to handle hadronic final states with multiple hard scales through merging of higher-order tree-level matrix elements with truncated parton showers, using a DIS-specific sliding merging scale,

$$Q_{\rm cut} = \bar{Q}_{\rm cut} \left[1 + \frac{\bar{Q}_{\rm cut}^2}{S_{\rm DIS}^2\, Q^2}\right]^{-1/2},$$

so that both high-$Q^2$ and low-$$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$0, high-$$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$1 events are placed in the matrix-element domain (Carli et al., 2010).

Sherpa also serves as a framework for beyond-the-Standard-Model calculations at tree level through automated import of UFO model information into COMIX, including automatically generated C++ implementations of Lorentz structures, decay widths and branching ratios computed from the same building blocks, and spin-correlated decay cascades embedded in shower and hadronisation workflows (Höche et al., 2014). This established Sherpa not only as a Standard-Model event generator but also as a general platform for automated amplitude generation and full hadron-level simulation.

2. Precision perturbation theory, showers, and event-generation workflows

Sherpa’s development has been closely tied to precision collider phenomenology, especially automated NLO QCD calculations, realistic top-quark simulations, and uncertainty propagation through matched and merged event samples (Schumann, 2017). The framework provides on-the-fly event reweighting for scale and PDF variations, allowing systematic uncertainty estimates without regenerating events. Applications discussed in the literature include $$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$2 jets, single-top production in four- and five-flavour schemes, $$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$3, and $$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$4, with the characteristic pattern that NLO QCD substantially reduces scale-variation bands relative to LO (Schumann, 2017, 1711.02568).

Single-top production offers a concrete illustration of Sherpa’s role as a full NLO+PS framework. For $$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$5-, $$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$6-, and $$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$7-channel production at $$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$8 TeV, Sherpa was used to generate NLO QCD predictions matched to the dipole shower, followed by hadronisation, decays, and underlying event, yielding results in very good agreement with measured values and quantifying theory uncertainties (1711.02568). In that study, uncertainties associated with the choice between the four- and five-flavour schemes were found to be typically of the order of $$\sigma^{\text{NLO}} = \int_n \Big( \mathrm{d}\sigma^{\text{B}} + \mathrm{d}\sigma^{\text{V}} + \mathrm{d}\sigma^{\text{I}} \Big) + \int_{n+1} \Big( \mathrm{d}\sigma^{\text{R}} - \mathrm{d}\sigma^{\text{D}} \Big),$$9–$\mathrm{d}\sigma^{\text{B}}$0 over large regions of phase space, while larger differences could occur in specific corners such as high-$\mathrm{d}\sigma^{\text{B}}$1 observables (1711.02568).

Sherpa 3, as described in the 2024 overview, consolidates these ingredients into a broader event-generation ecosystem spanning pp, ep, $\mathrm{d}\sigma^{\text{B}}$2, $\mathrm{d}\sigma^{\text{B}}$3, $\mathrm{d}\sigma^{\text{B}}$4, and diffractive collisions, while adding higher-order electroweak approximations, hard diffraction at NLO QCD, heavy-flavour matching in NLO multijet merging, polarised cross-section calculations, and a new colour-reconnection model (Bothmann et al., 2024). This suggests a continuing movement from process-by-process implementation toward a single configurable framework in which perturbative accuracy, beam structure, QED effects, spin information, and non-perturbative modeling are handled as interoperable modules.

3. Electroweak corrections, Sudakov logarithms, polarisation, and diffraction

A major line of Sherpa development concerns electroweak corrections. At high energies, one-loop EW corrections are dominated by Sudakov logarithms of the form

$\mathrm{d}\sigma^{\text{B}}$5

arising from soft-collinear exchange between external legs and from soft or collinear emission together with wave-function and parameter renormalization (Thompson, 2016). Sherpa implements these corrections as a multiplicative per-phase-space-point $\mathrm{d}\sigma^{\text{B}}$6-factor applied to hard matrix elements, following Denner–Pozzorini’s process-independent formalism. At one loop,

$\mathrm{d}\sigma^{\text{B}}$7

with the correction assembled from sums over relevant pairs of external legs and electroweak boson exchanges (Thompson, 2016). The 2020 automation paper generalised this to arbitrary Standard-Model processes and exposed separate leading and subleading logarithmic contributions as named event weights, with an exponentiated option

$\mathrm{d}\sigma^{\text{B}}$8

for resummed next-to-leading logarithmic predictions (Bothmann et al., 2020).

Phenomenologically, these EW effects can be large. In the 2016 implementation paper, for $\mathrm{d}\sigma^{\text{B}}$9jet production at a $\mathrm{d}\sigma^{\text{V}}$0 TeV LHC, the Sudakov correction to the leading-jet transverse momentum becomes increasingly negative with $\mathrm{d}\sigma^{\text{V}}$1 and reaches almost $\mathrm{d}\sigma^{\text{V}}$2 at $\mathrm{d}\sigma^{\text{V}}$3 TeV, with similar behaviour for on-shell and off-shell $\mathrm{d}\sigma^{\text{V}}$4 production (Thompson, 2016). The 2020 automation paper found similarly large suppressions in on-shell $\mathrm{d}\sigma^{\text{V}}$5 production and electroweak-induced dijets, and provided the first estimate of electroweak corrections at the multiplicity $\mathrm{d}\sigma^{\text{V}}$6 jets in the Sudakov approximation (Bothmann et al., 2020).

Full NLO EW automation in Sherpa relies on interfaces to OpenLoops and Recola, combined with Sherpa’s own subtraction machinery for QED-like singularities (Pellen, 2017, Schumann, 2017). For multi-jet merged simulations, an $\mathrm{d}\sigma^{\text{V}}$7 approximation—virtual EW one-loop corrections without explicit real weak-boson emission—can be applied as an event-wise $\mathrm{d}\sigma^{\text{V}}$8-factor on top of merged QCD samples (Schumann, 2017). Sherpa 3 then places this together with EW Sudakov corrections into a broader precision hierarchy for event generation (Bothmann et al., 2024).

A separate but related extension concerns polarised cross sections for vector boson production. Within a narrow-width treatment of intermediate $\mathrm{d}\sigma^{\text{V}}$9 and $\mathrm{d}\sigma^{\text{R}}$0 bosons, Sherpa was extended to compute all polarisation combinations in a single simulation run and to provide direct predictions for interference between different intermediate polarisation states (Hoppe et al., 2023). The implementation constructs production tensors and decay matrices and can transform them to different polarisation bases and frames, so that longitudinal, transverse, and interference components are available as event weights at LO, LO+PS, in multijet-merged calculations, and in approximate NLO QCD matched simulations (Hoppe et al., 2023).

Hard diffraction constitutes another major Sherpa 3 extension. The 2024 diffraction paper presents the first complete simulation framework for diffractive jet production at NLO QCD matched to the parton shower, both in diffractive DIS and in diffractive photoproduction, using diffractive PDFs and fluxes together with SHERPA’s standard NLO+PS machinery (Krauss et al., 2024). In DIS, the implementation validates Collins-factorisation-based predictions against H1 data. In photoproduction, however, the framework highlights factorisation breaking and argues that at NLO the direct component must also be suppressed, not only the resolved component, when fitting H1 and ZEUS data (Krauss et al., 2024).

4. The SHERPA project at DAΦNE

In accelerator physics, SHERPA refers to “Slow High-efficiency Extraction from Ring Positron Accelerator,” a project at the DAΦNE complex aimed at slowly extracting a high-quality positron beam from a storage ring using bent crystals (Garattini et al., 2021). The central idea is a non-resonant alternative to conventional slow extraction: instead of driving the beam toward a tune resonance, SHERPA uses coherent channeling in a bent silicon crystal to provide a small angular kick, which lattice optics then amplify into a displacement at an extraction septum.

The basic optics relation is

$\mathrm{d}\sigma^{\text{R}}$1

where $\mathrm{d}\sigma^{\text{R}}$2 is the crystal-induced kick, $\mathrm{d}\sigma^{\text{R}}$3 and $\mathrm{d}\sigma^{\text{R}}$4 are the Twiss $\mathrm{d}\sigma^{\text{R}}$5-functions at the crystal and septum, and $\mathrm{d}\sigma^{\text{R}}$6 is the phase advance between them (Garattini et al., 2021). For DAΦNE energies of about $\mathrm{d}\sigma^{\text{R}}$7 MeV positrons, the project focuses on ultra-thin silicon crystals of about $\mathrm{d}\sigma^{\text{R}}$8–$\mathrm{d}\sigma^{\text{R}}$9, with a benchmark bend angle of about $\mathrm{d}\sigma^{\text{D}}$0 mrad. Based on sub-GeV electron channeling data, a $\mathrm{d}\sigma^{\text{D}}$1 silicon crystal can yield a deflection angle of about $\mathrm{d}\sigma^{\text{D}}$2 mrad and a channeling efficiency of about $\mathrm{d}\sigma^{\text{D}}$3 for electrons, with theory predicting higher efficiency for positrons (Garattini et al., 2021).

The stated goal is to provide positron spills of $\mathrm{d}\sigma^{\text{D}}$4 length with excellent energy spread and emittance, primarily for PADME-type fixed-target experiments. Preliminary studies described in the project paper indicate extended spill structures over $\mathrm{d}\sigma^{\text{D}}$5 turns, corresponding to $\mathrm{d}\sigma^{\text{D}}$6, with the expectation that RF control can stretch this further toward the millisecond range (Garattini et al., 2021). The project is also framed as a demonstrator of crystal-assisted extraction for sub-GeV leptons, distinct from earlier crystal-extraction work at high-energy hadron machines.

5. SHERPA in machine learning, federated learning, LLM control, and panorama generation

In machine learning, Sherpa is an open-source Python library for hyperparameter optimization designed for computationally expensive, iterative training procedures such as deep neural networks (Hertel et al., 2020). Its abstractions include parameters, trials, algorithms, and a study object, and it supports random search, grid search, Bayesian optimization through GPyOpt, asynchronous successive halving, population-based training, local search, and repeated trials for noisy objectives (Hertel et al., 2020). It also includes parallel and cluster execution via schedulers and MongoDB-backed coordination, together with an interactive dashboard for monitoring learning curves and comparing trials (Hertel et al., 2020).

A distinct 2025 system named SHERPA introduces a model-driven framework for LLM execution based on hierarchical state machines (Chen et al., 29 Aug 2025). There the execution model of an LLM-driven agent is formalised as

$\mathrm{d}\sigma^{\text{D}}$7

with states, event triggers, actions, guard conditions, entry and exit actions, a transition function, an initial state, and final states (Chen et al., 29 Aug 2025). The purpose is to encode domain-specific best practices as explicit behavioural models rather than as free-form prompting strategies, so that transition policies—rule-based, LLM-based, or hybrid—can control multi-step workflows for tasks such as code generation, class-name generation, and question answering (Chen et al., 29 Aug 2025).

In vertical federated learning, Sherpa.ai denotes a privacy-preserving multi-party entity-alignment protocol based on private set union rather than private set intersection (Jimenez-Gutierrez et al., 21 Apr 2026). The objective is to construct a universal index over identifiers without disclosing which samples are shared. The protocol uses commutative exponentiation over $\mathrm{d}\sigma^{\text{D}}$8, with a basic single-component encryption

$\mathrm{d}\sigma^{\text{D}}$9

and extends this to exact order-preserving alignment and unordered, typo-tolerant alignment using $\mathrm{d}\sigma^{\text{I}}$0-gram tokenisation and thresholded comparison (Jimenez-Gutierrez et al., 21 Apr 2026). The paper formalises a local-to-global index mapping $\mathrm{d}\sigma^{\text{I}}$1 for each party, so that VFL training can proceed over the union of identifiers while hiding intersection membership (Jimenez-Gutierrez et al., 21 Apr 2026).

In generative vision, SHERPA is a lightweight adaptation framework for turning a planar text-to-image model into an open-domain $\mathrm{d}\sigma^{\text{I}}$2 panorama generator in equirectangular projection (Kang et al., 10 Jun 2026). It combines frequency-selective Circular RoPE, circular latent encoding and decoding, image-side FFN adapters, and a dual-path training scheme that separates geometry supervision from unpaired stylized prompting (Kang et al., 10 Jun 2026). Circular RoPE replaces the seam-sensitive high-frequency horizontal rotary band by integer-periodic harmonics,

$\mathrm{d}\sigma^{\text{I}}$3

so that horizontal positional phases are periodic over panorama width $\mathrm{d}\sigma^{\text{I}}$4, while a yaw-consistency loss regularises stylistic generation under cyclic horizontal rolls (Kang et al., 10 Jun 2026).

6. Sherpa as an astronomical fitting environment

Sherpa is also an open-source Python fitting package developed primarily by the Chandra X-ray Center for forward modeling and fitting of one-dimensional and two-dimensional data, especially in the Poisson regime relevant to X-ray astronomy (Siemiginowska et al., 2024). It provides a high-level interactive user interface and a lower-level Python object layer, with core modules for data containers, model construction, instrument responses, statistics, optimization methods, error estimation, simulation, and Bayesian analysis (Siemiginowska et al., 2024).

The package supports generic data types such as Data1D, Data1DInt, and Data2D, as well as astronomy-specific structures such as DataPHA, DataARF, and DataRMF, allowing forward folding of source models through calibration responses (Siemiginowska et al., 2024). A typical spectral prediction takes the form

$\mathrm{d}\sigma^{\text{I}}$5

with $\mathrm{d}\sigma^{\text{I}}$6 the redistribution matrix element, $\mathrm{d}\sigma^{\text{I}}$7 the effective area, and $\mathrm{d}\sigma^{\text{I}}$8 the source model (Siemiginowska et al., 2024). Sherpa includes Gaussian and Poisson fit statistics, optimizers such as Levenberg–Marquardt, Nelder–Mead, and differential evolution, and Bayesian tools for low-count Poisson data and calibration uncertainties (Siemiginowska et al., 2024).

Its applications span optical spectroscopy, X-ray spectroscopy, imaging, time-series analysis, and multiwavelength studies, and the package is explicitly designed to be extensible with user-defined models, statistics, and optimizers (Siemiginowska et al., 2024). In this usage, Sherpa is not a Monte Carlo event generator but a general scientific modeling and fitting environment, with a different software lineage and a distinct user community.

Across these usages, SHERPA denotes not a single technology but a family of research systems whose common feature is explicit control over complex workflows: event generation in collider phenomenology, beam extraction in accelerator physics, optimization in machine learning, parametric fitting in astronomy, privacy-preserving alignment in federated learning, hierarchical control of LLM execution, and topology-aware adaptation in panoramic image synthesis.