Rare Decays η and η′ Mesons
By Akash Khanikor, under the supervision of Connor Henderson.
The light unflavored mesons η (eta) and η′ (eta prime) can undergo an exceedingly rare decay mode known as the double Dalitz decay, where each meson decays into four muons via two virtual photons. The branching ratio for this decay is extremely small—so small, in fact, that it has not yet been experimentally established for the η′. Measuring or constraining this decay is scientifically compelling because it can:
Probe New Physics: Even a small deviation from Standard Model predictions might indicate contributions from exotic particles, potentially including MeV-scale dark matter.
Test Lepton Universality: Rare decays are precise ways to see if all leptons “behave” the same way under fundamental forces.
Refine Muon g−2 Calculations: These decays proceed via virtual photons and are tied to the pseudoscalar meson transition form factors, which are pivotal in reducing the uncertainty in the hadronic light-by-light scattering contribution to the muon’s anomalous magnetic moment (g−2).
Theoretical Background:
Feynman diagram representing the η meson decay into four leptons. This decay belongs to the class of “Dalitz decays”, where one or more photons are emitted before converting to a pair of leptons.
Mesons like η and η′ are quark–antiquark pairs. Within the Standard Model, quarks interact through both the strong and weak forces, whereas leptons interact only through the weak force (and electromagnetism if charged). These mesons are pseudoscalar particles, meaning they have zero spin and odd parity. Their decays involving virtual photons (i.e., photons that exist only briefly as mediators of electromagnetic interactions) offer a unique laboratory for studying how quarks bind into mesons and how these mesons couple to photons.
The transition form factor (TFF) describes how a pseudoscalar meson couples to two photons—real or virtual—and plays a crucial role in theoretical calculations of the muon g−2. Better measurements of η and η′ decays can thus sharpen our understanding of (g−2) and potentially point to new physics.
Side view of LHCb detector
Results and Conclusions:
After running 10,000 simulated events:
We produced an average of 7.5 η mesons and 1 η′ meson per event before cuts.
Subsequent selection criteria reduced these numbers, but we still found that about 55.1% of η and 5.2% of η′ events passed final acceptance cuts, ensuring all four muons and the mother meson were within the detector’s pseudorapidity range.
Using a cross section of 100 millibarns, an integrated luminosity of 5 fb^(−1), and branching ratios of 5e-9 for η and 1.7e-8 for η′ we estimated:
1,375,000 η→4μ events
442,000 η′→4μ events
These are large enough yields to suggest that, with sufficient data and careful analysis, the double Dalitz decays could indeed be observed or at least tightly constrained at LHCb.
Future Direction:
Obtain More Accurate Background Data: Either through larger-scale simulations with increased CPU power or by using direct LHCb data.
Improve Detector Realism: We seek better modeling of the LHCb environment, including tracking and trigger conditions.
Refine the η′ Branching Ratio: A direct measurement or tighter bound on η′→4μ would impact both precision QCD studies and new physics searches.
We attempted a background study using 30 million Pythia events but could not achieve the necessary statistics without more computing resources. In the future, we plan to:
Overall, our simulation demonstrates that, despite being extremely rare, the double Dalitz decays of η and η′ are within experimental reach. A dedicated analysis of LHCb data could solidify our understanding of these decays and potentially open new windows on the search for physics beyond the Standard Model.
Histogram of invariant mass for background study.
References:
The REDTOP experiment: Rare η/η′ Decays To Probe New Physics, REDTOP Collaboration, 2022 [1]
Measurement of J/ψ√ pair production in pp collisions at s = 13 TeV and study of gluon transverse-momentum dependent PDFs, LHCb collaboration, 2024 [2]
Dalitz decays of π0, η and η′ mesons, Rafel Escribano, 2017 [3]
Observation of the double Dalitz decay, BESIII Collaboration, 2022 [4]
Search for the process e+e−→ηη, SND Collaboration, 2018 [5]
Observation of the rare eta->e+e-e+e- decay with the KLOE experiment, KLOE Collaboration, 2011 [6]
Measurement of eta meson decays into lepton-antilepton pairs, CELSIUS/WASA Collaboration, 2008 [7]
What is interesting in eta and eta' Meson Decays?, Andrzej Kupsc, 2007 [8]
Anomalous decays of pseudoscalar mesons, Thimo Petri, 2010 [9]
First observation of the rare 4 μμ decay of the ηη meson, CMS Collaboration, 2023 [10]
