We investigate a novel collider signature within the minimal Left-Right Symmetric Model, featuring a Higgs sector composed of a bi-doublet and two triplets. Our study focuses on a region of the parameter space where the SU(2) charged gauge boson $\textit{W}$ lies in the multi-TeV regime (3–100 TeV) and the additional Higgs states play a significant role. In this scenario, a heavy neutral Higgs boson ∆ with a dominant SU(2) triplet component can be produced in association with either a Standard Model Higgs boson or a massive weak boson. The subsequent decay of the heavy Higgs into Majorana neutrinos $\textit{N}$ results in displaced lepton signatures, providing a striking manifestation of lepton number violation. Additionally, we explore how the production of $\textit{b}$-jets in these processes can enhance hadron-collider sensitivity to such signals. A particularly compelling channel, $$ pp\to b\overline{b} NN $$ , offers the exciting possibility of simultaneously probing the spontaneous mass origin of both Dirac fermions and Majorana states. Based on an optimised event selection strategy and state-of-the-art Monte Carlo simulations, we outline the expected reach at the HL-LHC and future colliders. Our findings demonstrate that this channel probes a region of parameter space where the neutral Higgs triplet and heavy neutrino masses are relatively light ($\textit{m}$ ≲ 250 GeV, $\textit{m}$ ≲ 80 GeV), indirectly constraining the $\textit{W}$ boson to the deep multi-TeV domain, with sensitivity extending up to 70–80 TeV, effectively turning the LHC into a precision machine.

France

Benjamin Fuks

Slovenia

Jonathan Kriewald

Miha Nemevšek

Italy

Fabrizio Nesti

Beautiful Majorana Higgses at colliders

We derive simple expressions to regularise functional determinants from fluctuations of fields with spin 0, 1/2, and 1. These are important for the precise dimensionful determination of false vacuum decay rates. We work in $\textit{D}$ = 4 Euclidean dimensions and use familiar Feynman diagrammatic techniques with a double expansion in interactions and masses, together with dimensional regularisation in momentum space. We Fourier transform to coordinate space and end up with a simple regularisation prescription in terms of single integrals over the Euclidean radius of field-dependent masses and their derivatives. Our results apply to models with an arbitrary scalar potential and with any number of scalars, fermions, gauge bosons and associated ghosts. We exemplify this approach on the Standard Model with a streamlined calculation of the renormalisation and isolation of divergences in fluctuation determinants.

Pietro Baratella

Yutaro Shoji

Katarina Trailović

Lorenzo Ubaldi

Functional determinants for false vacuum decay

We consider a single real scalar field in flat spacetime with a polynomial potential up to $\textit{ϕ}$ , that has a local minimum, the false vacuum, and a deeper global minimum, the true vacuum. When the vacua are almost degenerate we are in the thin wall regime, while as their difference in potential energy increases, we approach the thick wall regime. We give explicit simple formulae for the decay rate of the false vacuum in 3 and 4 spacetime dimensions. Our results include a careful treatment both of the bounce action, which enters at the exponent of the decay rate, and of the functional determinant at one loop, which determines the prefactor. The bounce action is computed analytically as an expansion in the thin wall parameter in generic $\textit{D}$ dimensions. We find that truncating such an expansion at second order we obtain a remarkably accurate bounce action also deep into thick wall regimes. We calculate the functional determinant numerically in 3 and 4 dimensions and fit the results with simple polynomials of the same thin wall parameter. This allows us to write the complete one-loop decay rate as a compact expression, which works accurately from thin to thick wall regimes.

Marco Matteini

False vacuum decay rate from thin to thick walls

<p>We examine the prospect of observing genuine lepton-number-violating (LNV) signals at hadron colliders in the context of the type II seesaw mechanism. The model features smoking gun signals involving same-sign di-leptons and jets that may be the primary observable channel in certain regions of the parameter space. The flavor composition of final-state charged leptons is related to the origin of neutrino masses and is correlated with other rare processes, such as neutrinoless double-beta decay. We review existing collider limits and provide sensitivity estimates from LNV signals at upcoming Large Hadron Collider runs, including nonzero mass splittings between triplet components.</p>

Patrick D. Bolton

United States

Juan Carlos Vasquez

Hadron colliders signatures of lepton number violation in the type II seesaw model

We revisit the decay rate of the electroweak vacuum in the standard model with the full one-loop prefactor. We focus on the gauge degrees of freedom and derive the degeneracy factors appearing in the functional determinant using group theoretical arguments. Our treatment shows that the transverse modes were previously overcounted, so we revise the calculation of that part of the prefactor. The new result modifies the gauge fields’ contribution by 6% and slightly decreases the previously predicted lifetime of the electroweak vacuum, which remains much longer than the age of the Universe. Our discussion of the transverse mode degeneracy applies to any calculation of functional determinants involving gauge fields in four dimensions.

Revising the Full One-Loop Gauge Prefactor in Electroweak Vacuum Stability

We investigate the structure of the minimal left-right symmetric model that enables precise predictions in the gauge, scalar and neutrino sector. We revisit the complete set of mass spectra and mixings for the charged and neutral gauge bosons, would-be-Goldstones and gauge fixing, together with the ghost Lagrangian. In the scalar sector, we analytically re-derive all the massive states with mixings and devise a non-trivial physical input scheme, expressing the model couplings in terms of masses and mixing angles. Fermion couplings are also determined in closed form, including the Dirac mixing in the neutrino sector, evaluated explicitly using the Cayley–Hamilton theorem. These analytic developments are implemented in a comprehensive FeynRules model file. We calculate the one loop QCD corrections and provide a complete UFO file for NLO studies, demonstrated on relevant hadron-collider benchmarks. We provide various restricted variants of the model file with different gauges, massless states, neutrino hierarchies and parity violating $$g_L \ne g_R$$ gauge couplings.

Enabling precise predictions for left-right symmetry at colliders

Temporary matter domination and late entropy dilution, injected by a “long-lived” particle in the early Universe, serves as a standard mechanism for yielding the correct dark matter relic density. We recently pointed out the cosmological significance of diluting particle’s partial decay into dark matter. When repopulated in such a way, dark matter carries higher momentum than its thermal counterpart, resulting in a suppression of the linear matter power spectrum that is constrained by the large scale structure observations. In this work, we study the impact of such constraints on the minimal left-right symmetric model that accounts for the origin of neutrino mass. We map out a systematic anatomy of possible dilution scenarios with viable parameter spaces, allowed by cosmology and various astrophysical and terrestrial constraints. We show that to accommodate the observed dark matter relic abundance the spontaneous left-right symmetry breaking scale must be above PeV and cosmology will continue to provide the most sensitive probes of it. In case the dilutor is one of the heavier right-handed neutrinos, it can be much lighter and lie near the electroweak scale.

Canada

Yue Zhang

Anatomy of diluted dark matter in the minimal left-right symmetric model

We study the production of right-handed bosons <math><msub><mi>W</mi><mi>R</mi></msub></math> and heavy neutrinos <math><mi>N</mi></math> at a future 100 TeV high-energy hadron collider in the context of left-right symmetry, including the effects of <math><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>L</mi></mrow></msub><mtext>−</mtext><msub><mrow><mi>W</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></math> gauge boson mixing. We estimate the collider reach for up to <math><mrow><mn>3</mn><mo>/</mo><mi>ab</mi></mrow></math> integrated luminosity using a multibinned sensitivity measure. In the Keung-Senjanović and missing-energy channels, the <math><mrow><mn>3</mn><mi>σ</mi></mrow></math> sensitivity extends up to <math><msub><mi>M</mi><msub><mi>W</mi><mi>R</mi></msub></msub><mo>=</mo><mn>35</mn></math> and 37 TeV, respectively. We further clarify the interplay between the missing-energy channel and the (expected) limits from neutrinoless double beta decay searches and big bang nucleosynthesis (and dark matter).

Left-right symmetry at an FCC-hh

Entropy production is a necessary ingredient for addressing the overpopulation of thermal relics. It is widely employed in particle physics models for explaining the origin of dark matter. A long-lived particle that decays to the known particles, while dominating the universe, plays the role of the dilutor. We point out the impact of its partial decay to dark matter on the primordial matter power spectrum. For the first time, we derive a stringent limit on the branching ratio of the dilutor to dark matter from large scale structure observation using the sloan digital sky survey data. This offers a novel tool for testing models with a dark matter dilution mechanism. We apply it to the left-right symmetric model and show that it firmly excludes a large portion of parameter space for right-handed neutrino warm dark matter.