Identifying hadronic charmonium decays in hadron colliders

Identification of charmonium states at hadron colliders has mostly been limited to leptonic decays of the J/{\Psi}. In this paper we present and algorithm to identify hadronic decays of charmonium states (J/{\Psi}, {\Psi}(2S), \chi_{c0,1,2}) which make up the large majority of all decays.


Introduction
Charmonium states, in particular J/Ψ are used both as an analysis and a calibration tool in hadron colliders. The decay to two muons allows for an efficient identification of this state and its narrow peak in the invariant mass spectrum of the muons is a powerful probe of the momentum resolution of the detector. Only 6% of the J/Ψ states decay to a clean final state of µ + µ − with another 6% decaying to e + e − . The remaining 88% is decaying to hadronic states and are usually ignored. The other charmonium states are even harder to identify with a small fraction having a clean decay like Ψ(2S) → µ + µ − .
For some analyses it is desirable to obtain as many events as possible, like the search for the rare decay of the Higgs boson to charmonium and a photon, with a branching ratio of around 3 × 10 −6 for H → J/Ψγ. In this paper we aim to develop a tagging algorithm for hadronically decaying charmonium states to allow to obtain higher statistics for these rare decay measurements.
Looking at hadronic decays a couple of things can be noted. The process H → J/Ψγ does not involve QCD fragmentation and further hadronization like in quark and gluon jets. The invariant mass of the final state should be the J/Ψ mass, which is lower than the average mass of quark and gluon jets and the average multiplicity is also lower. This is similar to hadronic tau jets, although with a higher mass and multiplicity. Basically we are looking for a fat neutral tau and that is the starting point of our algorithm. This paper is organized as follows. Section 2 describes our simulation set-up. The observables used to distinguish hadronic charmonium jets are reviewed in Section 3. The neural network architecture and parameters are discussed in Section 4. In section 5 we present uur results and we investigate the performance of the network on different charmonium samples and the overal stability of the network.

Simulated samples
All simulations were performed with the Pythia 8 [1] program. The charmonium samples were generated using the gluon-gluon to cc plus photon or gluon processes (gg2ccbar(3S1) gm/g ) for the J/Ψ and Ψ(2S) states. The χ c states were simulated with the (gg2ccbar(3PJ) g, qg2ccbar(3PJ) q and qq2ccbar(3PJ) g processes. The minimum transverse momentum of the process was set to 30 GeV and the invariant mass of the process to within 2.5 GeV of the Z 0 mass, to obtain a similar momentum distribution as for the background quark jets from Z 0 decay. Background gluon jets were taken from the same sample, since they have very similar kinematics. Background quark jets were taken from a sample of simulated Z 0 decays. Long lived particles were allowed to decay if cτ < 100cm.
The events were passed through the Delphes [2] fast detector simulation using the AT-LAS detector configuration files where we used particle-flow jets clustered using the Anti-kt algorithm [3] with a distance parameter R = 0.4. Jets are said to be charmonium, quark or gluon if the angular distance to a truth charmonium meson, quark or gluon is ∆R < 0.2. Our entire configuration can be found here [4] 3 Observables Since we expect charmonium jets to be tau-like we start off with variables used in the identification of hadronic tau decays by the ATLAS experiment [5] These variables are using the fact that tau (and charmonium) jets have a lower mass (m j and m tr ), lower multiplicity (n ch and n 0 ), are narrower (∆ η , ∆ φ , R em , R track and are not surrounded by further hadronic activity from fragmentation (p core1,2 , f core1,2 ). To these variables we add the absolute values of the total charge and the jet-charge (p t weighted charge sum [6]), which are expected to peak at zero for charmonium and gluon jets, but to have a higher average value for jets originating from quarks. Using the output of the b-jet identification algorithm provides some discrimination against b-jets, since the lifetime of charmonium mesons is too short to produce a measurable decay length.
This list of variables is completed with a particular class of generalized angularities [7], which have demonstrated to be efficient in the distinguishing quark jets from gluon jets. The angularities depend on two parameters (κ, β) and are defined as: where z i is the momentum fraction of jet constituent i, and θ i is the normalized rapidityazimuth angle w.r.t. the jet axis. The variables are summarized in Table 1. Fig 1 shows the distribution for a number of the variables for J/Ψ signal data and a background samples composed of 50% quark jets and 50% gluon jets. invariant mass of all constituents of the jet n ch charged particle multiplicity n 0 neutral particle multiplicity abs(Q) absolute value of the total charge abs(q j ) jet charge (p t weighted charge sum, κ = 0.5) btag output of b-tagging algorithm: 1 = btagged jet, 0 = not b-tagged R em Average ∆ R w.r.t the jet axis weighted by electromagnetic energy: fraction of EM energy over total neutral energy of the jet p core1 ratio of sum p t in a cone of ∆R < 0.1 and the jet p t p core2 ratio of sum p t in a cone of ∆R < 0.2 and the jet p t f core1 ratio of sum E t in a cone of ∆R < 0.1 and the jet total E t f core2 ratio of sum E t in a cone of ∆R < 0.2 and the jet total E t (p D T ) 2

Machine Learning
We feed the classifying variables to a fully connected deep network using the TensorFlow [8] and Keras [9] libraries. The network architecture and parameters are listed in table 2. We used the standard technique of dropout layers to prevent overtraining. The network architecture and hyperparameters were optimized by hand on earlier simulation samples. The network performance turns out to be rather insensitive to their value. We use the receiver operating characteristic (ROC) curve as a measure the separation power of our classifier. For the training we use a sample of 17k simulated J/Ψ events, 17k Z 0 → qq events and 8k gluon events. To measure the performance we use independent samples with and equal amount of J/Ψ, Z 0 → qq and gluon events.

Results
Fig 2 shows the output distribution for our classifier for both signal and background and the ROC curve.s A good separation can be observed with an area under the curve of 0.927. This corresponds to a signal efficiency of 33% at a background rejection factor of 100. It should be noted that the performance of the classifier is significantly better against a background of gluon jets (AuC = 0.966, signal efficiency of 54% at 100x background rejection ) as against quarks jets (AuC = 0.889, efficiency of 25% at 100x background rejection). For gluons the performance against a single background can be further improved by using a single background training sample. The network performs well on jets from the hadronic decay of other charmonium states like Ψ(2S) and the χ c states, with the area under the curve only a few percent lower than for J/Ψ. Some of this difference can be recovered by including the heavier charmonium states in the training sample. An overview of the performance of the network for various training and test sets in given in table 3.
Finally we investigate the stability of the network performance under variations of the simulation parameters. For this we applied the recommended variations [10] of the Pythia8 parton shower and multiple parton interaction parameters based on the NNPDF23LO tune. These variations cover the a range of data observables from ATLAS Run 1. As can be seen in table 4, the network performance is very stable for different tunes.

Conclusion
We have presented an algorithm to identify jets from hadronic decay of charmonium states and have demonstrated that it works with a good efficiency especially against a background of gluons. The method works for J/Ψ and heavier charmonium states and is relatively insensitive to the simulation parameters. This opens the possibility to use hadronic decay modes of charmonium in the search for certain rare decays that suffer from low statistics.