Lepton number violating meson decays, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>M</mi><mn>1</mn><mo>−</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>M</mi><mn>2</mn><mo>+</mo></msubsup><msubsup><mo>ℓ</mo><mn>1</mn><mo>−</mo></msubsup><msubsup><mo>ℓ</mo><mn>2</mn><mo>−</mo></msubsup></math>, provide constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>9</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>L</mi><mo>=</mo><mn>2</mn></math> operators. Renormalization group equation (RGE)-improved bounds on the Wilson coefficients of these operators have been presented in the literature, taking into account perturbative quantum chromodynamics (QCD) one-loop corrections and the corresponding operator mixing. Here, we present for the first time the contribution of connected diagrams to the hadronic matrix elements <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">|</mo><msub><mrow><mi mathvariant="script">O</mi></mrow><mrow><mi>h</mi></mrow></msub><mo stretchy="false">|</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">⟩</mo></mrow></math>. These diagrams, usually overlooked under the assumption that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><msub><mi>M</mi><mn>2</mn></msub><mo stretchy="false">|</mo><msub><mi mathvariant="script">O</mi><mi>h</mi></msub><mo stretchy="false">|</mo><msub><mi>M</mi><mn>1</mn></msub><mo stretchy="false">⟩</mo><mo>∼</mo><mo stretchy="false">⟨</mo><msub><mi>M</mi><mn>2</mn></msub><mo stretchy="false">|</mo><msub><mi>J</mi><mrow><msub><mi>q</mi><mn>3</mn></msub><msub><mi>q</mi><mn>4</mn></msub></mrow></msub><mo stretchy="false">|</mo><mn>0</mn><mo stretchy="false">⟩</mo><mo>×</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">⟨</mo><mn>0</mn><mo stretchy="false">|</mo><msub><mi>J</mi><mrow><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub></mrow></msub><mo stretchy="false">|</mo><msub><mi>M</mi><mn>1</mn></msub><mo stretchy="false">⟩</mo><mo>≫</mo><mo stretchy="false">⟨</mo><msub><mi>M</mi><mn>2</mn></msub><mo stretchy="false">|</mo><msub><mi>J</mi><mrow><msub><mi>q</mi><mn>3</mn></msub><msub><mi>q</mi><mn>2</mn></msub></mrow></msub><mo>×</mo><msub><mi>J</mi><mrow><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>4</mn></msub></mrow></msub><mo stretchy="false">|</mo><msub><mi>M</mi><mn>1</mn></msub><mo stretchy="false">⟩</mo></math>, can give indeed a significant contribution to the matrix element. Including these connected diagrams is but the first step toward a full nonperturbative computation of the long-range QCD effects in these operators, that should be performed using lattice field theory techniques. However, connected diagrams represent the leading order in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math> expansion of the QCD nonperturbative effects and thus our work can be understood as a realistic, first approximation to a complete calculation of the long-range part of the matrix elements.

Spain

Andrea Donini

Chile

Marcela González

Martin Hirsch

Nicolás A. Neill

Leading large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> contributions to lepton number violating meson decays

Heavy neutral leptons (HNLs) and axion-like particles (ALPs) are both considered well-motivated candidates for beyond the standard model (BSM) physics. If ALPs with sizable couplings to gluons exist, they will be abundantly produced at the LHC. Therefore, HNLs produced via the ALP portal may provide unprecedented sensitivities to HNL parameters. Here, we study the prospects for the high-luminosity LHC to search for long-lived HNLs. We consider future far detectors as well as ATLAS in our simulations. In the limit where the ALP mass is above the TeV scale, HNLs are effectively produced by a dimension-8 operator connecting HNL pairs to gluons. For completeness, we therefore also calculate future LHC sensitivities for HNLs produced via $\textit{N}$ SMEFT operators with gluons.

Cyprus

Rebeca Beltrán

Chandan Hati

Ana Martín-Galán

Long-lived HNLs via ALP portal at the LHC

We present a novel strategy to uncover indirect signs of new physics in collider data using the standard model effective field theory (SMEFT) framework, offering notably improved sensitivity compared to traditional global analyses. Our approach leverages genetic algorithms to efficiently navigate the high-dimensional space of operator subsets, identifying deformations that improve agreement with data without relying on prior ultraviolet (UV) assumptions. This enables the systematic detection of SMEFT scenarios that outperform the standard model in explaining observed deviations. We validate the approach on current large hadron collider and large electron-positron collider measurements, perform closure tests with injected UV signals, and assess performance under high-luminosity projections. The algorithm successfully recovers relevant operator subsets and highlights directions in parameter space where deviations are most likely to emerge. Our results demonstrate the potential of SMEFT-based discovery searches driven by model selection, providing a scalable framework for future data analyses.

Luca Mantani

Veronica Sanz

Data-Driven Discovery Strategy for Standard Model Effective Field Theory Searches

A correction to this paper has been published: https://doi.org/10.1007/JHEP05(2025)238

Giovanna Cottin

Germany

Julian Günther

Italy

Arsenii Titov

China

Zeren Wang

Erratum to: Heavy neutral leptons and top quarks in effective field theory

We study the phenomenology of heavy neutral leptons (HNLs) at the LHC in effective field theory, concentrating on $\textit{d}$ = 6 operators with top quarks. Depending on the operator choice and HNL mass, the HNLs will be produced either from proton-proton collisions in association with a single top, or via non-standard decays of top quarks. For long-lived HNLs we estimate the sensitivity reach of different detectors to various operators with top quarks and the HNLs for the high-luminosity phase of the LHC. For certain operators, ATLAS and some far detectors (MATHUSLA and ANUBIS) will be able to probe the associated new-physics scale as large as 12 TeV and 4.5 TeV, respectively, covering complementary HNL-mass ranges.

Heavy neutral leptons and top quarks in effective field theory

We present analytical expressions for the transverse momentum dependent (unintegrated) gluon and quark densities in a proton derived at leading order of QCD running coupling and valid at both small and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The calculations are performed using the Kimber-Martin-Ryskin/Watt-Martin-Ryskin prescription (in both differential and integral formulations) with different treatment of kinematical constraint, which reflects the angular and strong ordering conditions for parton emissions. As an input, the analytical solution of QCD evolution equations for conventional (collinear) parton distributions is applied, where the valence and nonsinglet quark parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, and momentum conservation for the singlet quark and gluon densities is taken into account. Several phenomenological parameters are extracted from the combined fit to precision data on the proton structure function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> collected by the BCDMS, H1, and ZEUS Collaborations, comprising a total of 933 points from 5 datasets. Comparison with the numerical results obtained by other groups is presented, and the phenomenological application to the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-jet production at the LHC is given.

JINR

A.V. Kotikov

Russia

A.V. Lipatov

Updating TMD parton densities in a proton within the Kimber-Martin-Ryskin approach

We discuss an extension of the standard model with a real scalar triplet, $\textit{T}$, including non-renormalizable operators (NROs) up to $\textit{d}$ = 6. If $\textit{T}$ is odd under a $\textit{Z}$ symmetry, the neutral component of $\textit{T}$ is a good candidate for the dark matter (DM) of the universe. We calculate the relic density and constraints from direct and indirect detection on such a setup, concentrating on the differences with respect to the simple model for a DM $\textit{T}$ with only renormalizable interactions. Bosonic operators can change the relic density of the triplet drastically, opening up new parameter space for the model. Indirect detection constraints, on the other hand, rule out an interesting part of the allowed parameter space already today and future CTA data will, very likely, provide a decisive test for this setup.

Carolina Arbeláez

Nicolás Neill

Colombia

Diego Restrepo

Effective field theory and scalar triplet dark matter

Romania

Victor E. Ambrus

France

Maxim N. Chernodub

Corrigendum to “Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism” [Physics Letters B 855 (2024) 138757/PLB 138795]

Neutrino masses and dark matter (DM) might have a common origin. The $\textit{scotogenic}$ model can be considered the proto-type model realizing this idea, but many other variants exist. In this paper we explore the phenomemology of a particular DM neutrino mass model, containing a triplet scalar. We calculate the relic density and check for constraints from direct detection experiments. The parameter space of the model, allowed by these constraints, contains typically a long-lived or quasi-stable doubly charged scalar, that can be searched for at the LHC. We reinterpret existing searches to derive limits on the masses of the scalars of the model and estimate future sensitivities in the high-luminosity phase of the LHC. The searches we discuss can serve to constrain also many other 1-loop neutrino mass models.

Juan Helo

Téssio Melo

Long-lived particle phenomenology in one-loop neutrino mass models with dark matter

Searches for anomalous neutral triple gauge boson couplings (NTGCs) provide important tests for the gauge structure of the standard model. At the LHC, NTGCs are searched for via the process $\textit{pp}$ → $\textit{ZZ}$ → 4$\textit{l}$, where the two $\textit{Z}$-bosons are on-shell. In this paper, we discuss how the same process can occur through tree-level diagrams just adding a vector-like quark (VLQ) to the standard model. Since NTGCs are generated in standard model effective theory (SMEFT) only at 1-loop order, vector like quarks could be an important alternative interpretation to, and background for, NTGC searches. Here, we construct a simple example model, discuss low-energy constraints and estimate current and future sensitivities on the model parameters from $\textit{pp}$ → $\textit{ZZ}$ → 4$\textit{l}$ searches.

Ricardo Cepedello

Fabian Esser

Faking ZZZ vertices at the LHC