Collider-testable type I seesaw extensions of the Standard Model are generally protected by an approximate lepton number (LN) symmetry. Consequently, they predict pseudo-Dirac heavy neutral leptons (HNLs) composed of two nearly degenerate Majorana fields. The interference between the two mass eigenstates can induce heavy neutrino-antineutrino oscillations (  <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>Os</mi> </math>  $$ N\overline{N}\textrm{Os} $$ ) leading to observable lepton number violation (LNV), even though the LN symmetry is approximately conserved. These   <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>Os</mi> </math>  $$ N\overline{N}\textrm{Os} $$  could be resolved in long-lived HNL searches at collider experiments, such as the proposed Future Circular e + e  −  Collider (FCC-ee) or Circular Electron Positron Collider (CEPC). However, during their Z-pole runs, the LN carried away by the light (anti)neutrinos produced alongside the HNLs prevents LNV from being observed directly. Nevertheless,   <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>Os</mi> </math>  $$ N\overline{N}\textrm{Os} $$  materialise as oscillating signatures in final state distributions. We discuss and compare a selection of such oscillating observables, and perform a Monte Carlo simulation to assess the parameter space in which   <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>Os</mi> </math>  $$ N\overline{N}\textrm{Os} $$  could be resolved.

Switzerland

Stefan Antusch

Portugal

Jan Hajer

Bruno Oliveira

Discovering heavy neutrino-antineutrino oscillations at the Z-pole

Under the assumption that the recent pulsar timing array evidence for a stochastic gravitational wave (GW) background at nanohertz frequencies is generated by metastable cosmic strings, we analyze the potential of present and future GW observatories for probing the change of particle degrees of freedom caused, e.g., by a supersymmetric (SUSY) extension of the Standard Model (SM). We find that signs of the characteristic doubling of degrees of freedom predicted by SUSY could be detected at Einstein Telescope and Cosmic Explorer even if the masses of the SUSY partner particles are as high as about 10$^{4}$ TeV, far above the reach of any currently envisioned particle collider. We also discuss the detection prospects for the case that some entropy production, e.g. from a late decaying modulus field inducing a temporary matter domination phase in the evolution of the universe, somewhat dilutes the GW spectrum, delaying discovery of the stochastic GW background at LIGO-Virgo-KAGRA. In our analysis we focus on SUSY, but any theory beyond the SM predicting a significant increase of particle degrees of freedom could be probed this way.

Kevin Hinze

Shaikh Saad

Germany

Jonathan Steiner

Probing SUSY at gravitational wave observatories

We posit that the distinct patterns observed in fermion masses and mixings are due to a minimally broken <math><mrow><mi>U</mi><mo>(</mo><mn>2</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>q</mi><mo>+</mo><mi>e</mi></mrow></msub></mrow></math> flavor symmetry acting on left-handed quarks and right-handed charged leptons, giving rise to an accidental <math><mi>U</mi><mo>(</mo><mn>2</mn><msup><mo>)</mo><mn>5</mn></msup></math> symmetry at the renormalizable level without imposing selection rules on the Weinberg operator. We show that the symmetry can be consistently gauged by explicit examples and comment on realizations in SU(5) unification. Via a model-independent analysis of a standard model viewed as an effective field theory, we find that selection rules due to <math><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mrow><mi>q</mi><mo>+</mo><mi>e</mi></mrow></msub></math> enhance the importance of charged lepton flavor violation as a probe, where significant experimental progress is expected in the near future.

Admir Greljo

United Kingdom

Ben A. Stefanek

Anders Eller Thomsen

U(2) Is Right for Leptons and Left for Quarks

Embedding inflation within a grand unified theory is an intriguing idea towards a more fundamental understanding of particle physics and cosmology. However, within the framework of supersymmetric <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> grand unified theory inflation, models typically feature light color octets and weak triplets that ruin the successful gauge coupling unification of the mimimal supersymmetric Standard Model. We present a new possibility for naturally splitting the electronlike states from the colored ones within vectorlike 10-plets by utilizing their couplings with 40-plets that lack electronlike states. Together with the extra light weak doublets from the double missing partner mechanism, the appearance of the light electronlike states from our proposed generalized missing partner mechanism restores gauge coupling unification. Remarkably, the same vectorlike 10-plets cure the bad mass relations between the down quarks and the charged leptons. Discovering the light relic states at future colliders would provide a “smoking gun” signal of the scenario.

Generalized missing partner mechanism for <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> GUT inflation

In this work, we construct promising model-building routes towards SO(10) grand unified theory inflation and examine their ability to explain the recent pulsar timing arrays (PTAs) results hinting at a stochastic gravitational wave (GW) background at nanohertz frequencies. We consider a supersymmetric framework within which the so-called doublet-triplet splitting problem is solved without introducing fine-tuning. Additionally, realistic fermion masses and mixings, gauge coupling unification, and cosmic inflation are incorporated by utilizing superfields with representations no higher than the adjoint representation. Among the three possible scenarios, two of these cases require a single adjoint Higgs field, and do not lead to cosmic strings. In contrast, the third scenario featuring two adjoints, can lead to a network of metastable cosmic strings that generates a GW background contribution compatible with the recent PTA findings and testable by various ongoing and upcoming GW observatories.

Singling out SO(10) GUT models using recent PTA results

We study decoherence effects and phase corrections in heavy neutrino-antineutrino oscillation (  <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>O</mi> </math>  $$ N\overline{N}O $$ s), based on quantum field theory with external wave packets. Decoherence damps the oscillation pattern, making it harder to resolve experimentally. Additionally, it enhances lepton number violation (LNV) for processes in symmetry-protected low-scale seesaw models by reducing the destructive interference between mass eigenstates. We discuss a novel time-independent shift in the phase and derive formulae for calculating decoherence effects and the phase shift in the relevant regimes, which are the no dispersion regime and transverse dispersion regime. We find that the phase shift can be neglected in the parameter region under consideration since it is small apart from parameter regions with large damping. In the oscillation formulae, decoherence can be included by an effective damping parameter. We discuss this parameter and present averaged results, which apply to simulations of   <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>O</mi> </math>  $$ N\overline{N}O $$ s in the dilepton-dijet channel at the HL-LHC. We show that including decoherence effects can dramatically change the theoretical prediction for the ratio of LNV over LNC events.

Johannes Rosskopp

Decoherence effects on lepton number violation from heavy neutrino-antineutrino oscillations

In this paper, the existence of a massive dark photon, associated with a new gauge group is considered. The dark photon can be kinetically mixed with the photon. To study some applications, the thermo field dynamics formalism is used. Exploring the topological structure of this approach, the influence of dark photons on the Stefan–Boltzmann law and the Casimir effect at zero and finite temperature is calculated.

Brazil

V. Prata

A. Santos

Canada

Faqir Khanna

Stefan–Boltzmann law and Casimir effect for dark photons

In this work, we attempt to answer the question, “What is the minimal viable renormalizable <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> grand unified theory with representations no higher than adjoints?” We find that an <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> model with a pair of vectorlike fermions <math><msub><mn>5</mn><mi>F</mi></msub><mo>+</mo><msub><mover><mn>5</mn><mo>¯</mo></mover><mi>F</mi></msub></math>, as well as two copies of <math><mn>1</mn><msub><mn>5</mn><mi>H</mi></msub></math> Higgs fields, is the minimal candidate that accommodates for correct charged fermion and neutrino masses and can also address the matter-antimatter asymmetry of the Universe. Our results show that the presented model is highly predictive and will be fully tested by a combination of upcoming proton decay experiments, collider searches, and low-energy experiments in search of flavor violations. Moreover, we also entertain the possibility of adding a pair of vectorlike fermions <math><mn>1</mn><msub><mn>0</mn><mi>F</mi></msub><mo>+</mo><msub><mover><mn>10</mn><mo>¯</mo></mover><mi>F</mi></msub></math> or <math><mn>1</mn><msub><mn>5</mn><mi>F</mi></msub><mo>+</mo><msub><mover><mn>15</mn><mo>¯</mo></mover><mi>F</mi></msub></math> (instead of a <math><msub><mn>5</mn><mi>F</mi></msub><mo>+</mo><msub><mover><mn>5</mn><mo>¯</mo></mover><mi>F</mi></msub></math>). Our study reveals that the entire parameter space of these two models, even with minimal particle content, cannot be fully probed due to a possible longer proton lifetime beyond the reach of Hyper-Kamiokande.

Minimal <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> GUTs with vectorlike fermions

We discuss the impact of heavy neutrino-antineutrino oscillations (  <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>Os</mi> </math>  $$ \textrm{N}\overline{\textrm{N}}\textrm{Os} $$ ) on heavy neutral lepton (HNL) searches at proposed electron-positron colliders such as the future circular e + e  −  collider (FCC-ee). During the Z pole run, HNLs can be produced alongside a light neutrino or antineutrino that escapes detection and can decay into a charged lepton or antilepton together with an off-shell W boson. In this case, signals of lepton number violation (LNV) only show up in the final state distributions. We discuss how   <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>Os</mi> </math>  $$ \textrm{N}\overline{\textrm{N}}\textrm{Os} $$ , a typical feature of collider-testable low-scale seesaw models where the heavy neutrinos form pseudo-Dirac pairs, modify such final state distributions. For example, the forward-backward asymmetry (FBA) of the reconstructed heavy (anti)neutrinos develops an oscillatory dependence on the HNL lifetime. We show that these oscillations can be resolvable for long-lived HNLs. We also discuss that when the   <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>Os</mi> </math>  $$ \textrm{N}\overline{\textrm{N}}\textrm{Os} $$  are not resolvable, they can nevertheless significantly modify the theory predictions for FBAs and observables such as the ratio of the total number of HNL decays into ℓ  −  over ones into ℓ +, in an interval of the angle θ between the HNL and the beam axis. Our results show that   <math> <mi>N</mi> <mover> <mi>N</mi> <mo>¯</mo> </mover> <mi>Os</mi> </math>  $$ \textrm{N}\overline{\textrm{N}}\textrm{Os} $$  should be included in collider simulations of HNLs at the FCC-ee.

Heavy neutrino-antineutrino oscillations at the FCC-ee

Collider testable low-scale seesaw models predict pseudo-Dirac heavy neutrinos, that can produce an oscillating pattern of lepton number conserving and lepton number violating events. We explore if such heavy neutrino-antineutrino oscillations can be resolved at the HL-LHC. To that end, we employ the first ever full Monte Carlo simulation of the oscillations, for several example benchmark points, and show under which conditions the CMS experiment is able to discover them. The workflow builds on a FeynRules model file for the phenomenological symmetry protected seesaw scenario (pSPSS) and a patched version of MadGraph, able to simulate heavy neutrino-antineutrino oscillations. We use the fast detector simulation Delphes and present a statistical analysis capable of inferring the significance of oscillations in the simulated data. Our results demonstrate that, for heavy neutrino mass splittings smaller than about 100 μeV, the discovery prospects for heavy neutrino-antineutrino oscillation at the HL-LHC are promising.