Bayesian inference requires determining the posterior distribution, a task that becomes particularly challenging when the dimension of the parameter space is large and unknown. This limitation arises in many physics problems, such as mixture models (MM) with an unknown number of components or the inference of overlapping signals in noisy data, as in the laser interferometer space antenna (LISA) global fit problem. Traditional approaches, such as product-space methods or reversible-jump Markov chain Monte Carlo (RJMCMC), often face efficiency and convergence limitations. This paper presents , a continuous-time Markov chain Monte Carlo (CTMCMC) framework that models parameter evolution through Poisson-driven birth, death, and mutation processes. is designed to sample models of unknown dimensionality. By requiring detailed balance through adaptive rate definitions, CTMCMC achieves automatic acceptance of trans-dimensional moves and high sampling efficiency. The code features waiting time weighted estimators, optimized memory storage, and a modular design for easy customization. We validate on three benchmark problems: an analytic trans-dimensional distribution, joint inference of sine waves and Lorentzians in time series, and a Gaussian MM with an unknown number of components. In all cases, the code shows excellent agreement with analytical and nested sampling results. All these features push as a powerful alternative to RJMCMC for large- and variable-dimensional Bayesian inference problems.

Italy

Gabriele Astorino

Lorenzo Dall’Armi

United Kingdom

Riccardo Buscicchio

Joachim Pomper

Angelo Ricciardone

Walter Pozzo

samsara: a continuous-time Markov chain Monte Carlo sampler for trans-dimensional Bayesian analysis

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msup><mi>χ</mi><mn>2</mn></msup></math> value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

P. Risse

N. Derakhshanian

T. Ježo

K. Kovařík

A. Kusina

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We study entropy production in deep inelastic scattering using Monte Carlo simulations. We show that the dominant contribution to entropy is due to soft gluons. This contribution is usually neglected in standard Monte Carlo approaches, since it does not affect hadronic spectra. However, it is relevant for entropy and multiplicity distributions, as we demonstrate with explicit calculations. We further show that as one includes soft gluons, making the Monte Carlo parton distributions closer to inclusive parton distribution functions (PDFs), the resulting entropy starts to grow with decreasing x. This provides further evidence that the bulk of the measured entropy originates from initial-state effects.

M. Hentschinski

H. Jung

K. Kutak

Entanglement entropy, Monte Carlo event generators, and soft gluon discovery

High statistical precision is critical for Monte Carlo (MC) samples in high energy physics and is degraded by negatively weighted events. This paper investigates a procedure to learn the relationship between the negative and positive weight distributions of any sample, allowing the reduction of statistical uncertainty by reweighting kinematically equivalent events with the same sign. A robust uncertainty quantification method is required for the practical application of such method. Two methods for the estimation of the reweighting uncertainty are developed: one at the event and another one at the final observable level. The latter method is strongly favored. The gains in statistical precision are then quantified. The method is demonstrated on Sherpa vector boson plus jets samples when using all generated events and when restricted to the signal region of a mock analysis. It is demonstrated to significantly reduce stochastic behavior in sparse MC samples while decreasing the overall uncertainty with a sufficiently well-known reweighting function.

C. Palmer

B. Kronheim

Improving statistical precision in Monte Carlo samples with negative weights via reweighting and uncertainty quantification

Neutrino direct simulation Monte Carlo (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ν</mi><mi>DSMC</mi></math>) is a Monte Carlo method for solving the neutrino Boltzmann equation in the early Universe, designed to track the evolution of cosmic neutrinos across a wide range of cosmological scenarios. We develop a complete <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ν</mi><mi>DSMC</mi></math> solver that consistently incorporates the effects of the electron mass, three-flavor neutrino oscillations, and finite-temperature QED corrections to the thermodynamics of the electromagnetic plasma. As a first application, we perform a high-precision calculation of neutrino decoupling in the standard cosmological model and obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub><mo>=</mo><mn>3.0439</mn><mo>±</mo><mn>0.0006</mn></math>, in excellent agreement with state-of-the-art results.

Oleksii Ihnatenko

Maksym Ovchynnikov

Precision calculation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math> with neutrino direct simulation Monte Carlo

The IKKT model (or the type IIB matrix model) has been investigated as a promising nonperturbative formulation of superstring theory. One of the recent developments concerning this model is the discovery of the dual supergravity solution corresponding to the model obtained after supersymmetry-preserving mass deformation, which is dubbed the polarized IKKT model. Here we perform Monte Carlo simulations of this model in the case of matrix size <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math> for a wide range of the deformation parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Ω</mi></mrow></math>. While we reproduce precisely the known result for the partition function obtained by the localization method developed for supersymmetric theories, we also calculate the observables, which were not accessible by the previous work, in order to probe the spacetime structure emergent from the dominant matrix configurations. In particular, we find that the saddle point corresponding to the original IKKT model is smoothly connected to the saddle represented by the fuzzy sphere dominant at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Ω</mi></mrow></math>, whereas the dominant configurations become diverging commuting matrices at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Ω</mi></mrow></math>.

Chien-Yu Chou

Jun Nishimura

Cheng-Tsung Wang

Monte Carlo Studies of the Emergent Spacetime in the Polarized Type IIB Matrix Model

Lattice Monte Carlo simulations and the functional renormalization group (RG) are powerful approaches that allow for quantitative studies of nonperturbative phenomena such as bound-state formation, spontaneous symmetry breaking, and phase transitions. While results from both methods have recently shown remarkable agreement for many observables, e.g., in quantum chromodynamics, an analysis of deviations in certain quantities turns out to be challenging. This is because calculations with the two methods are based on different approximations, regularizations, and scale fixing procedures. In the present work, we present a framework for a more direct comparison by formulating the functional RG approach on a finite spacetime lattice. This removes all ambiguities of regularization, finite-size, and scale fixing procedures in concrete studies. By investigating the emergence of spontaneous symmetry breaking and phase transitions in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> scalar theory in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>1</mn></math>, 2, and 3 spacetime dimensions, we demonstrate at the example of the local potential approximation how this framework can be used to evaluate and compare the systematic errors of both approaches.

Niklas Zorbach

Jan Philipp Klinger

Owe Philipsen

Jens Braun

Lattice Monte Carlo meets the lattice functional renormalization group: A quantitative comparison

The LHCb collaboration amplitude analysis of the decays <math altimg='si32.svg'><mrow><msup><mi>B</mi><mo>+</mo></msup><mo>&#8594;</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>&#8722;</mo></msup><msup><mi>K</mi><mo>+</mo></msup></mrow></math>, <math altimg='si33.svg'><mrow><msup><mi>B</mi><mo>+</mo></msup><mo>&#8594;</mo><msup><mi>D</mi><mo>&#8722;</mo></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>&#960;</mi><mo>+</mo></msup></mrow></math>, and <math altimg='si34.svg'><mrow><msup><mi>B</mi><mn>0</mn></msup><mo>&#8594;</mo><msup><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup></mrow></math> suggested the existence of two new resonant <math altimg='si35.svg'><mrow><msup><mi>J</mi><mi>P</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>0</mn><mo>+</mo></msup></mrow></math> states with minimum quark content <math altimg='si21.svg'><mrow><mover accent='true'><mi>u</mi><mo>&#175;</mo></mover><mover accent='true'><mi>d</mi><mo>&#175;</mo></mover><mi>s</mi><mi>c</mi></mrow></math> and <math altimg='si23.svg'><mrow><mover accent='true'><mi>s</mi><mo>&#175;</mo></mover><mover accent='true'><mi>u</mi><mo>&#175;</mo></mover><mi>d</mi><mi>c</mi></mrow></math>/ <math altimg='si24.svg'><mrow><mover accent='true'><mi>s</mi><mo>&#175;</mo></mover><mover accent='true'><mi>d</mi><mo>&#175;</mo></mover><mi>u</mi><mi>c</mi></mrow></math>, named <math altimg='si1.svg'><msub><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow></msub></math> and <math altimg='si2.svg'><msub><mi>T</mi><mrow><mi>c</mi><mover accent='true'><mi>s</mi><mo>&#175;</mo></mover><mn>0</mn></mrow></msub></math>, respectively. In this work, we used the diffusion Monte Carlo (DMC) method to compute the masses of those tetraquarks within the framework of the constituent quark model. We describe the systems as compact structures, not as diquark/antidiquark or meson/meson arrangements. In this context, compact means that we used directly the eigenvectors of the spin, color and flavor operators without any splitting and/or (re)combination of smaller units. This allows us to deduce the existence of two distinct bound configurations for each composition, corresponding to ground and excited flavor states. In both cases, the excited flavor states are the ones with masses comparable to the ones observed by LHCb. In addition, our analysis allows us to assign unambiguously an isospin value of <math altimg='si20.svg'><mi>I</mi></math>=1 to the experimentally obtained <math altimg='si1.svg'><msub><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow></msub></math> tetraquark.

Spain

M.C. Gordillo

J. Segovia

Diffusion Monte Carlo calculation of compact <math altimg='si1.svg'><msub><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow></msub></math> and <math altimg='si2.svg'><msub><mi>T</mi><mrow><mi>c</mi><mover accent='true'><mi>s</mi><mo>&#175;</mo></mover><mn>0</mn></mrow></msub></math> tetraquarks

Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis of integrals in both double and quadruple precision, achieving significantly reduced computational times compared to existing tools. We demonstrate the performance of our integrator by evaluating one- and two-loop five-point Feynman integrals with up to nine complex kinematic scales. In particular, we apply our method to the radiative return process of massive electron-positron annihilation into pions plus an energetic photon within scalar QED, for which we also build the differential equation, and extend it to the case where virtual photons acquire an auxiliary complex mass under the Generalised Vector-Meson Dominance model. Furthermore, we validate our approach on two integral families relevant for the two-loop production of $$ t\overline{t} $$ + jet. The integrator achieves, in double precision, execution times of the order of milliseconds for one-loop topologies and hundreds of milliseconds for the two-loop families, enabling for on-the-fly computation of Feynman integrals in Monte Carlo generators and a more efficient generation of grids for the topologies with prohibitive computational costs.

Pau Petit Rosàs

William Torres Bobadilla

Fast evaluation of Feynman integrals for Monte Carlo generators

The neutrino energy reconstruction is crucial for reducing systematic uncertainties in neutrino oscillation experiments and improving cross section measurements. Kaon-decays-at-rest (KDAR) neutrinos provide a unique opportunity to probe neutrino-nucleus interactions at low energies with a precisely known energy of 235.5 MeV. This work presents Monte Carlo predictions of missing energy due to nuclear effects in the KDAR <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>μ</mi></msub></math> charged-current scattering on the carbon nucleus for the J-PARC sterile neutrino search at the J-PARC Spallation Neutron Source. The predictions from genie, nuwro, and gibuu show a significant impact of nuclear and final-state interaction (FSI) models, as well as nucleon removal energy, on missing energy reconstruction. Tuning the hA FSI model improves the predictions from genie. It is also observed that the nucleon elastic component of FSI leads to better predictions in nuwro compared to genie. nuwro shows the best agreement with data among the generators considered; however, the observed discrepancies with data across all generators highlight the limitations of current theoretical descriptions in the low-energy regime and the need for improvements in Monte Carlo modeling.

India

R.K. Pradhan

Israel

R. Lalnuntluanga

A. Giri

Monte Carlo study of KDAR <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>μ</mi></msub></math> charged-current scattering on carbon