Rare decays of η/η’ mesons to multiple leptons
The light unflavored mesons eta (η) and eta prime (η’) undergo a very rare decay called the double Dalitz where the meson decays into 4 muons. Currently the branching ratio of the eta prime decay is not established, and we hope to either tighten the bounds or get an exact ratio. This decay is particularly interesting because they could be sensitive to contributions from unknown particles; potentially being sensitive to MeV scale dark matter and hence serve as a test of lepton universality. Furthermore, since these decays proceed by virtual photons, they relate to the pseudoscalar meson transition form factors, which in turn are a major part of the hadronic light-by-light scattering contribution to g-2 of the muon. This project is being done under the supervision of Connor Henderson.
Theory and Methods:
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.
The eta and eta primes are combinations of quark and anti-quark pairs. On the left is the standard model of physics, which is our best understanding of fundamental particles, and how the forces relate and interact with each other. Focusing on the matter particles, they are further divided into two categories: Leptons and Quarks. Where leptons only interact via the weak force, while quarks interact via both the weak and strong forces.
Each group then consists of 6 particles, related in generations. Where moving up in generations, is going from lightest and most stable to heavier and less stable.
We are interested in this decay because it proceeds through an intermediate state of two virtual photons, and they help us understand the pseudoscalar transition form factor or TFF in short.
We are interested in this decay because it proceeds through an intermediate state of two virtual photons, and they help us understand the pseudoscalar transition form factor or TFF in short. Virtual photons are are particles exchanged during an electromagnetic interaction between charged particles. They can be temporarily created as intermediaries in interactions, to carry momentum, energy, and other properties. They cannot be directly observed but are inferred from their effects on measurable quantities. And Pseudoscalars are a type of elementary particle characterized by having zero spin and odd parity. They play a significant role in particle physics particularly in understanding strong interactions and structure of matter. Eta and eta prime are two such pseudoscalars. These TFFs are necessary inputs to calculate the pseudoscalar-meson-pole contributions to the hadronic light-by-light scattering, which causes the second largest uncertainty in the Standard Model determination of the muon anomalous magnetic moment. Which in its essence is a measure of how the magnetic moment of the muon differs from what is predicted by the Dirac equation within quantum field theory.
Side view of LHCb detector
Results and Conclusions:
Moreover, the high expected signal yield shows promise for future study around the branching ratio for the decay. Another aspect where improvements can be made in the future is accurate detector conditions. We weren’t nearly rigorous enough in recreating the LHCb conditions, and a study ran on more accurate conditions would be very interesting to see.
Standard Model of Physics Overview
The project is supposed to be running on data collected from the Large Hadron Collider experiment. It is a particle accelerator that consists of a 27-kilometre ring of superconducting magnets with a number of accelerating structures to boost the energy of the particles along the way. It is 100 meters underground, and is in Geneva, Switzerland. More specifically, we are interested in the LHCb experiment, which is a 5600-tonne detector 21m long, 10m high and 13m wide. The experiment uses a series of subdetectors to detect mainly forward-facing particles. with sophisticated movable tracking detectors. Being a single-arm forward spectrometer detector covering the pseudo rapidity range 2 < η < 5, it is designed for the study of particles containing b- or c-quarks.
The tools that were used for this project were C++, Pythia event generator, and ROOT data analysis framework. C++ was the language I used to code the particle interactions and simulate collision events. Pythia was our chosen simulator, which is a general-purpose monte Carlo event generator; and finally, all the data being produce was stored in ROOT structures.
Setting up the simulation, required us to add the double Dalitz decays into the Pythia framework since the decays didn’t have an established branching ration. After the addition, we wanted to maximize the number of eta and eta primes that we could observe, hence we forced all the eta and eta primes being produced to decay to 4 muons. With this large data sets we were able to perform cuts based off pseudo rapidity and transverse momentum requirements. The cuts that we ended up making were pseudo rapidity 2-5, and transverse momentum of the 2 leading muons >0.5 GeV and 2 trailing muons >0.1 GeV. Which after running 10,000 events gave us the following results.
From the 10,000 simulated events, we were producing 7.5 etas and 1 eta prime on average. The numbers would then go down after each subsequent application of a cut. For our final calculation of the expected signal yield, we used the data points from ‘Total decays when both meson and leptons are in acceptable pseudo rapidity range per event’, which is a condition that checks and confirms the presence of both the eta and all the 4 muons in the pseudo rapidity range of 2-5. The fractions came out to be 0.551 for eta and 0.052 for eta prime. For further calculations, we use the following numbers:
Cross section – 100 millibarn, Luminosity – 5 femtobarn-1, Branching ratios: Eta - 5e-9, Eta Prime - 1.7e-8
Where potential number of minimum bias events will be the product of cross section times luminosity, and the signal yield is finally given by frac x (500e12) x Branching Fraction. Which gives us the eta and eta primes values as 1,375,000 and 442,000 respectively which are significant number of observable events thus making the experiment a viable future endeavor.
Future Direction:
We attempted a background study with 30 million events from Pythia simulation but had to abandon that pursuit due to the insufficient statistics. The CPU power wasn’t enough, and the quality of the data wasn’t up to the expected standards. In the future, more accurate background data might be able to give us a branching ratio for the double Dalitz decay for the eta prime. Pulling data directly from the LHCb experiment instead of trying to simulate them through event generators.
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]
