Phenomenological study for the search of evidence for intrinsic charm at the COMPASS experiment

TL;DR

This paper investigates the potential evidence for intrinsic charm in double J/ψ production at COMPASS and reanalyzes NA3 data to understand charm production mechanisms in high-energy pion-nucleus collisions.

Contribution

It provides a phenomenological analysis of intrinsic charm signals in double J/ψ production at COMPASS and revisits previous NA3 data for comparison.

Findings

Potential evidence for intrinsic charm in COMPASS data

Reanalysis of NA3 data on double J/ψ production

Insights into charm production mechanisms in high-energy collisions

Abstract

In this paper we conduct a phenomenological study for the search of evidence for the intrinsic charm mechanism in double $J/\psi$ production at the COMPASS experiment using the CERN $\pi^-$ beam at 190 GeV/c. We also re-review the double $J/\psi$ production data provided by the NA3 experiment using the CERN $\pi^-$ beam at 150 and 280 GeV/c with incident on a platinum target.

Equations

$$\sigma (Q\bar{Q})={\int }_{2m_Q}^{2m_H}d{M}_{Q\bar{Q}}\frac{d{\sigma }_{Q\bar{Q}}}{d{M}_{Q\bar{Q}}},$$

$$\sigma (X)=\frac{1}{9}\cdot {\rho }_X\cdot \sigma (Q\bar{Q})$$

$${\rho }_X=\frac{2J_X+1}{{\sum }_i(2J_i+1)},$$

$${\rho }_{J/\psi }\approx \mathrm{0.2.}$$

$$\sigma (J/\psi J/\psi )=\frac{1}{9}\frac{1}{9}{\rho }_{J/\psi }{\rho }_{J/\psi }\cdot \sigma (c\bar{c}+c\bar{c}).$$

$$\frac{\sigma (c\bar{c}+c\bar{c})}{\sigma (c\bar{c})}>10^{-2}.$$

$${\sigma }_{J/\psi J/\psi }(150\text{mbox}GeV/c):{\sigma }_{J/\psi J/\psi }(190\text{mbox}GeV/c):{\sigma }_{J/\psi J/\psi }(280\text{mbox}GeV/c)\approx 1:2.06:3.34.$$

$${\sigma }_{J/\psi J/\psi }=f_{\psi /\pi }^2\frac{P_{icc}}{P_{ic}}{\sigma }_{ic},$$

Full text

1 Introduction

Almost four decades have passed since the intrinsic charm mechanism was proposed [1], stating that heavy quarks are present in the proton’s wavefunction from the outset.

The existence of heavy quarks in the proton’s light-front (LF) wavefunction at a large LF momentum fraction $x$ is in fact predicted by QCD if one analyzes the higher Fock states $|uudc\bar{c}\rangle$ and $|uudc\bar{c}c\bar{c}\rangle$ in the hadronic eigenstate, i.e. Fock states where the heavy quark pairs are multi-connected to the valence quarks. LF wavefunctions, the eigensolutions of the QCD LF Hamiltonian, are defined at fixed LF time $\tau=t+z/c$ and are thus off-shell in the invariant mass. For example in QED, positronium has an analogous Fock state $|e^{+}e^{-}\mu^{+}\mu^{-}\rangle$ due to the insertion of light-by-light scattering in the positronium self-energy amplitude. In such an “intrinsic charm” Fock state $|uudc\bar{c}\rangle$, the maximum kinematic configuration occurs at minimum invariant mass where all quarks are at rest in the hadron’s rest frame, i.e., at equal rapidity in the moving hadron. Equal rapidity implies $x_{i}\propto(m^{2}+{\vec{k}_{\perp}}^{2})^{1/2}$ for each quark, so that the heavy quarks in the Fock state carry most of the hadron’s LF momentum. The operator product expansion predicts that the probability of intrinsic heavy-quark Fock states $|uudQ\bar{Q}\rangle$ scales as $1/m_{Q}^{2}$ due to the non-Abelian couplings of QCD [2, 3].

Even though there is no clear observation of the mechanism, the baryonic states $\Lambda_{c}(udc)$ and $\Lambda_{b}(udb)$ were both discovered at the Intersecting Storage Rings at high values of the Feynman momentum fraction $x_{F}$ [4, 5, 6].111In this paper $x_{F}$ denotes the Feynman-$x$ in the laboratory frame while $x_{F}^{*}$ denotes the Feynman-$x$ in the center-of-mass system. The SELEX experiment provided the observation of a double charm baryon $|ccd\rangle$ at a large mean value for $x_{F}$ and a relatively small mean transverse momentum [7, 8]. In addition, the NA3 experiment measured both the single-quarkonium hadroproduction $\pi A\to J/\psi X$ [9] and the double-quarkonium hadroproduction $\pi A\to J/\psi J/\psi X$ [10] at high $x_{F}$. In fact, all of the $\pi A\to J/\psi J/\psi X$ events were observed with a total value of $x_{F}>0.4$.

As we show below, the NA3 kinematic features and the production rate can be a result of a misunderstanding of the detector acceptance. Fortunately, the NA3 measurement can be confirmed or disproved at the COMPASS experiment using the CERN $\pi^{-}$ beam at $190\mbox{\,GeV}/c$.

In this paper we discuss kinematic features and analysis strategies for the search of evidence for the intrinsic charm mechanism at the COMPASS experiment. We also estimate upper limits for the double $J/\psi$ production cross section for perturbative QCD (pQCD) and for the intrinsic charm (IC) mechanism.

2 Revisiting the double $J/\psi$ production at NA3

Using the CERN pion beam at $150$ and $280\mbox{\,GeV}/c$ to produce charm particles with incident on hydrogen and platinum targets, the NA3 experiment provided data on the production of the double $J/\psi$ on platinum target in the kinematic region $x_{F}^{*}(J/\psi)>0$ with the respective production cross sections of $18\pm 8\mbox{\,pb}$ and $30\pm 10\mbox{\,pb}$ per nucleon and the ratio $\sigma(J/\psi J/\psi)/\sigma(J/\psi)=(3\pm 1)\times 10^{-4}$ at both energies.

2.1 Acceptance of the NA3 detector

In order to understand the NA3 data, we give a short overview over the layout of the NA3 detector (see Ref. [11] for a more complete description). The NA3 detector consisted of a spectrometer with fixed targets of liquid hydrogen (proton target, 30 cm long) and platinum (nuclear target, 6 cm long). The targets were located at a distance of 45 cm.

For the measurements the NA3 experiment used the beams of $p$, $\bar{p}$, $K^{\pm}$, $\pi^{\pm}$ with intensities of $(3-5)\cdot 10^{7}$ particles per second. To reduce the particle flux through the spectrometer, a beam dump absorbing about 80% of the charged particle flux was installed behind the platinum target. The dump was made of a 1.5 m block of stainless steel and had a conical core made of tungsten and uranium. The aperture angle of the cone could be chosen as either 20 or 30 mrad. The stainless steel blocks surrounded the conical core of the dump. Along the beam behind the dump, other parts of the spectrometer were located such as a spectrometer magnet, tracking detectors, counter hodoscopes and trigger hodoscopes. At the end of the spectrometer an additional 1.8 m long iron absorber was placed which played the role of a muon filter and reduced the low energy particle background. Together with the other trigger hodoscopes, the trigger hodoscope placed behind the muon filter had the purpose to select muons originated from the targets. The trigger system imposed a condition on the vertical component of the transverse momentum of the muons. To be registered, a single muon had to satisfy the condition $p_{T}>1\mbox{\,GeV}/c$, while for two muons in the event one had to have $p_{T}>0.6\mbox{\,GeV}/c$ for each muon. Such requirements eliminated a large fraction of pion and kaon decays and rejected low mass resonances like $\rho$, $\phi$ and $\omega$ mesons.

In order to be registered, muons had to pass more than 3 m of iron. As charged particles, on this way they interacted with nucleons of the matter and spent some of their energy for ionization and radiative effects. For example, by passing through 3 m of iron a muon with energy of $150\mbox{\,GeV}/c$ looses more than $7.5\mbox{\,GeV}$ of its energy. This leads to an acceptance notion which mostly depends on the geometry of the setup, but also on the kinematics of the particles.

In the data analysis for single $J/\psi$ selection a criterium $x_{F}^{*}>0$ was used for both the $150\mbox{\,GeV}$ and $280\mbox{\,GeV}$ data samples. For $x_{F}^{*}<0$ the NA3 acceptance was dropping fast. This means that each of the $J/\psi$ should have had a minimal longitudinal momentum to pass the setup and to be detected. For the $150\mbox{\,GeV}$ beam this threshold was about $27\mbox{\,GeV}/c$, and $39\mbox{\,GeV}/c$ for the $280\mbox{\,GeV}$ beam. For the double $J/\psi$ state these thresholds should be multiplied roughly by two. Because the acceptance was dropping down near the threshold, there was a low probability to detect an event with a momentum close to the threshold. This means that it is not possible to detect a double $J/\psi$ state with $x_{F}\sim 27/150$ for $150\mbox{\,GeV}$ and with $x_{F}\sim 39/280$ for $280\mbox{\,GeV}$ i.e. $x_{F}<0.4$ and $x_{F}<0.3$ respectively, since low energy muons will either be absorbed by the matter of the setup or rejected by the trigger. In addition, because of the dropping of the acceptance, events detected de facto by NA3 have values of $x_{F}$ larger than the thresholds for both data samples (cf. Fig. 1). The estimate for the NA3 setup acceptance for the double $J/\psi$ production is done with a Monte Carlo approach using pairs of uncorrelated $J/\psi$’s. It is definitely interesting to investigate the correctness of the acceptance obtained by such a Monte Carlo simulation.

By investigating the kinematic distributions (cf. Fig. 2), one obtains a small difference in the momentum distribution between the $J/\psi$ for the Single Parton Scattering (SPS) mechanism and a higher momentum gap for the uncorrelated $J/\psi$’s sample. Such a gap in momentum and as the result of this also in the Feynman-$x$ distributions could lead to the erroneous interpretation of the NA3 acceptance. Indeed, keeping in mind that the $J/\psi$ pair has to carry a minimum $x_{F}$ to be detected, a situation is possible where one of the $J/\psi$ does not cary enough momentum to be triggered. Due to the larger momentum gap, the possibility of rejection can differ between SPS and the uncorrelated sample.

Concluding the above discussion we can say that the cross section values provided by the NA3 might be not fully correct and the high Feynman-$x$ region can be interpreted solely by the detector acceptance.

2.2 $\sigma(J/\psi J/\psi)$ production via Single Parton Scattering

Utilizing the fact that the double $J/\psi$ production cross section can be normalized with a special choice of the composition $(\alpha_{s}f_{\psi})^{4}$, where $\alpha_{s}$ is the strong coupling constant and $f_{\psi}$ is the decay constant of $J/\psi$, in Ref. [12] it was found that most of the measured cross section is due to $q\bar{q}\to J/\psi J/\psi$. However, as mentioned above, such a high production rate is unexpected at NA3 energies. Therefore, it is interesting to analyze the production rate instead of the double $J/\psi$ production cross section.

For our purpose it is sufficient to use the quark–hadron duality principle. Following Ref. [13], the cross section of quarkonium was obtained by calculating the production of a $Q\bar{Q}$ in the small invariant mass interval between $2m_{Q}$ and the threshold to produce open heavy-quark hadrons, $2m_{H}$.222For an estimate like this, generalizations of the method given in Refs. [14, 15, 16, 17] are not needed. The $Q\bar{Q}$ pair has $3\times\bar{3}=(1+8)$ color components, consisting of a color-singlet and a color-octet. Therefore, the probability that a color singlet is formed and produces a quarkonium state is given by $1/(1+8)$, and the model predicts

[TABLE]

where $\sigma_{Q\bar{Q}}$ is the production cross section of the heavy quark pairs and $\sigma(Q\bar{Q})$ is a sum of production cross sections of all quarkonium states in the duality interval. For example, in case of charmonium states one has $\sigma(Q\bar{Q})=\sigma(J/\psi)+\sigma(\psi(2S))+\ldots$ . According to a simple statistical counting, the fraction of the total color-singlet cross section into a quarkonium state is given by

[TABLE]

($X=J/\psi,\psi(2S),\ldots$) with

[TABLE]

where $J_{X}$ is the spin of the quarkonium state $X$ and the sum runs over all quarkonium states. In case of the $J/\psi$ meson the calculation gives

[TABLE]

These formulas can be easy generalized to the calculation of the production of double quarkonium,

[TABLE]

Using the NA3 rate it is easy to estimate that

[TABLE]

Even making the unrealistic assumption that all $c\bar{c}$ pairs in $\sigma(c\bar{c}+c\bar{c})$ are lying in the duality interval, the production rate seems to be absolutely untrusted. In essence, assuming SPS to be the only or even the leading mechanism for double $J/\psi$ production at NA3 energies should rise skepticism.

2.3 $\sigma(J/\psi J/\psi)$ production via the Intrinsic Charm mechanism

The production of double $J/\psi$ based on the intrinsic charm approach is discussed in detail in Refs. [22, 23, 24]. Perturbative QCD and intrinsic charm contributions populate different regions where the main statistic is expected (cf. the discussion in Ref. [25]). Based on this fact, in Ref. [22] it was assumed that all the NA3 data came from the intrinsic charm mechanism. However, as we have shown above this kinematic region is limited due to the detector acceptance. Therefore such interpretation is too ambitious.

Concluding this chapter it is important to note that none of the mechanisms discussed, neither pQCD nor the intrinsic charm mechanism, can be interpreted as the sole production mechanism. In addition, it is not possible to determine the relative contribution, as both calculations, the pQCD calculation [12] as well as the calculation based on the intrinsic charm mechanism [22], are normalized to the NA3 data, assuming either of these to be the sole production mechanism.

3 Double $J/\psi$ production

at the COMPASS experiment

3.1 The COMPASS detector: short description

COMPASS, a fixed target experiment at CERN, uses the high intensity $\pi^{-}$ beam of $190\mbox{\,GeV}$ at the Super Proton Synchrotron at CERN for Drell–Yan (DY) measurements to produce charmonium, possible exotic states and dimuons in the set of polarized targets [26]. The experiment had several DY runs in 2014, 2015 and 2018.

The COMPASS DY configuration setup is quite similar to the NA3 setup. It uses two cylindrical cells (of 55 cm length and 4 cm in diameter each) of ammonia as a target and a hadron absorber to reduce the particle flux through the setup. The absorber, made of alumina and stainless steel with the central tungsten plug, is placed downstream of the target. The outgoing charged particles are detected by two spectrometers (Large Angle Spectrometer and Small Angle Spectrometer). At each spectrometer, the muon identification was accomplished by a system of muon filters. To be detected, at least two muon candidates from the target region should hit the trigger hodoscopes of the first spectrometer ($25<\theta_{\mu}<160\mbox{\,mrad}$), or one should hit the trigger hodoscopes of the first and the other the trigger hodoscopes of the second spectrometer ($8<\theta_{\mu}<45\mbox{\,mrad}$). A muon passed through the peripheral part of the absorber and the material of one of two muon filters (stainless steel or concrete) loses an energy of about $10\mbox{\,GeV}$, defining the lower limit for its reconstruction.

3.2 Double $J/\psi$ production at the COMPASS

As the COMPASS has a similar detector setup as the one at NA3, we can estimate that double $J/\psi$ events detected by COMPASS should have $x_{F}>0.4$ as threshold. Therefore, COMPASS can give a significant contribution to the understanding of the double $J/\psi$ production mechanisms. In 2015 the COMPASS collaboration collected about one million dimuon events in the ${\rm NH}_{3}$ target [27], and a factor of at least $1.5$ more events are expected in the 2018 run [28]. Comparing the $J/\psi$ statistics collected by NA3 [9] and the acceptance of the COMPASS detector one can estimate up to 100 double $J/\psi$ events for the COMPASS experiment.

Taking into account that perturbative QCD and intrinsic charm contributions have principally different slopes and different regions where the main statistics is expected, we propose to use $x_{F}$ for the search for signals of the intrinsic charm mechanism and the determination of the relative contribution (cf. discussion in Chapter 3.3). The expected $x_{F}$ distribution for the COMPASS kinematics and for the different production mechanisms are shown in Fig. 3.

As we already mentioned above, it is not possible to predict the relative contribution of the mechanism. However, it is interesting to estimate upper limits for both SPS and IC mechanism. Note that Double Parton Scattering (DPS) contributions are suppressed compared to both SPS and IC [18].

3.2.1 Single Parton Scattering

Following calculations of the double $J/\psi$ production cross section in SPS from Ref. [29] we can find a ratio between the double $J/\psi$ production cross sections with a $\pi^{-}$ beam at NA3 and COMPASS energies:

[TABLE]

Using the mean values for the double $J/\psi$ production cross sections measured by NA3 of $18\pm 8\mbox{\,pb}$ and $30\pm 10\mbox{\,pb}$ per nucleon at $150$ and $280\mbox{\,GeV}/c$ as reference points, we find $\sigma(J/\psi J/\psi)\approx(12-29)\mbox{\,pb}$ per nucleon at $190\mbox{\,GeV}/c$ (cf. Fig. 4).

3.2.2 Intrinsic Charm

Following Ref. [22], we cast the double $J/\psi$ production cross section into the form

[TABLE]

where $f_{\psi/\pi}\approx 0.03$ is the fraction of $c\bar{c}$ quark pairs producing $J/\psi$, $P_{ic}$ and $P_{icc}$ are probabilities to produce intrinsic $c\bar{c}$ and $c\bar{c}c\bar{c}$ Fock states, respectively, and \sigma_{ic}\approx 0.5\mbox{\,\mub} is the intrinsic charm cross section for a $\pi^{-}$ beam momentum of $200\mbox{\,GeV}/c$. Assuming $P_{icc}$ to be independent of the projectile, the value $P_{icc}=4.4\%P_{ic}$ was found in Ref. [22], and assuming $\sigma(J/\psi J/\psi)/\sigma(J/\psi)$ to be independent of the projectile, $P_{icc}=10.6\%P_{ic}$ was found in the same Ref. [22]. It is easy to estimate the double $J/\psi$ production cross section at the COMPASS energy to be $(19.8-47.7)\mbox{\,pb}$ per nucleon (cf. Fig. 5).

3.3 Combination of Single Parton Scattering

and Intrinsic Charm contributions

As all researchers before us, up to this point we more or less quietly assumed the only possible production mechanism to be either SPS or DPS. However, it is interesting to investigate the case where both mechanisms can contribute to the production of double $J/\psi$ and to investigate the ability of the COMPASS experiments to separate them.

The possibility for COMPASS to identify the IC production mechanism based on the measured $x_{F}(J/\psi J/\psi)$ distribution is investigated using a toy Monte Carlo simulation where events are generated according to the SPS contribution shown in Fig. 3. The flat acceptance in the range $0.4<x_{F}(J/\psi J/\psi)<1$ and the absence of any other contributions is assumed. The double likelihood ratio distribution $R=2\log(L_{\rm IC}/L_{\rm SPS})$ based on $10^{5}$ runs is shown in Fig. 6 (left) for the COMPASS statistics of 12, 25 and 50 events. The likelihoods $L_{\rm IC}$ and $L_{\rm SPS}$ correspond to double $J/\psi$ production via pure IC and pure SPS mechanisms, respectively. In case of 50 double $J/\psi$ events an upper limit (CL=90%) for the relative IC mechanism contribution to the production cross section in the range $x_{F}(J/\psi J/\psi)>0.4$ could be established on the level of 29%. The obtained numbers should be treated just as an illustration as a non-flat acceptance and/or the presence of any additional significant contributions (e.g. background) could change these numbers significantly in both directions. The result of a single Monte Carlo run with the fitted SPS contribution and the curve corresponding to the obtained upper limit contribution of IC are shown as an example in Fig. 6 (right).

4 Conclusions

The analysis of this paper clearly shows that the NA3 data is puzzling and does not allow for a simple interpretation. We found that the calculation of the double $J/\psi$ production cross section is not very useful for the identification of the production mechanism. Instead, we have pointed out that the kinematic distributions provide opportunities for the COMPASS experiment using the $\pi^{-}$ beam of the Super Proton Synchrotron (CERN) at $190\mbox{\,GeV}/c$ to measure the effect of the intrinsic charm mechanism or to identify the production mechanism. We also estimated the double $J/\psi$ production cross section in assumption that all NA3 events came either from the SPS or from the IC mechanism. In addition, we give an estimate for the double $J/\psi$ events to be expected at COMPASS.

Acknowledgements

We would like to thank H.S. Shao for updating the HELAC-Onia generator. Also we would like to thank D. Bandurin for useful discussions. This research was supported by the Estonian Research Council under Grants No. TK133 and PRG356.