ATLAS results on exotic hadronic resonances††thanks: Copyright 2022 CERN for
the benefit of the ATLAS Collaboration. CC-BY-4.0 license.

Yue Xu1,2$\star$

1 On behalf of the ATLAS collaboration

2 Department of Physics, Tsinghua University, Beijing 100084, China

*<EMAIL_ADDRESS>
51st International Symposium on Multiparticle Dynamics (ISMD2022)
Pitlochry, Scottish Highlands, 1-5 August 2022 10.21468/SciPostPhysProc.?

## Abstract

Recent results from the proton-proton collision data taken by the ATLAS
experiment on exotic resonances are presented. A search for $J/\psi p$
resonances in $\Lambda_{b}\rightarrow J/\psi pK$ decays with large $pK$
invariant masses is reported. A search for exotic resonances in the four-muon
final state is shown.

###### Contents

  1. 1  Introduction
  2. 2  Study of $J/\psi p$ resonances in the $\Lambda_{b}^{0}\rightarrow J/\psi pK^{-}$ decays
  3. 3  Observation of di-charmonium events
  4. 4  Conclusion

##  1  Introduction

The quark model proposed by Gell-Mann and Zweig successfully describes
conventional hadrons as being composed of two or three valence quarks [1, 2].
At the same time, theorists also predicted the existence of exotic hadrons
with more than three quarks, whose properties would not fit the standard
picture of quark model. The study of exotic hadrons can provide a unique
insight into the nature of strong interaction. This proceeding overviews the
recent studies of exotic hadronic resonances with proton-proton ($pp$)
collision data collected by ATLAS detector [3] at centre-of-mass energies
$\sqrt{s}=7$ [4], $8$ [5] and $13$ [6] TeV.

##  2  Study of $J/\psi p$ resonances in the $\Lambda_{b}^{0}\rightarrow
J/\psi pK^{-}$ decays

The search of potential pentaquark is carried out through
$\Lambda_{b}^{0}\rightarrow J/\psi pK^{-}$ decays , using
$4.9~{}\text{fb}^{-1}$ and $20.6~{}\text{fb}^{-1}$ of $pp$ collision data at
$\sqrt{s}=7$ [4] and $8$ [5] TeV. The $\Lambda^{0}_{b}\rightarrow J/\psi
pK^{-}$ decays are reconstructed together with $B^{0}\rightarrow J/\psi
K^{+}\pi^{-}$, $B^{0}\rightarrow J/\psi\pi^{+}\pi^{-}$, $B^{0}_{s}\rightarrow
J/\psi K^{+}K^{-}$ and $B^{0}_{s}\rightarrow J/\psi\pi^{-}\pi^{+}$ decays, due
to lack of particle identification for charged hadrons. $J/\psi$ candidate is
reconstructed through $J/\psi\rightarrow\mu^{+}\mu^{-}$ decays. Both muons are
required to have $p_{T}>4$ GeV and $|\eta|<2.3$. The invariant mass of two
muons is required to be $2807<m_{\mu^{+}\mu^{-}}<3387$ MeV. To form B-hadron
($H_{b}$) candidates, $J/\psi$ candidate and two additional tracks from
hadrons are refitted to a common vertex with $J/\psi$ mass constraint.

Multi-dimensional fits are performed to estimate background contributions and
extract pentaquark parameters. The fit procedure is complex. It’s iterative
with four steps in each iteration. Parameters obtained in previous step are
used in the current step. After the fit, all the pentaquark parameters can be
obtained. Two hypotheses are tested in the fit:

  1. 1.

Hypothesis with two pentaquarks with spin parity of $3/2^{-}$ and $5/2^{+}$,
respectively.

  2. 2.

Hypothesis with four pentaquarks with masses, widths and relative yields fixed
to the results from LHCb [7].

Figure 1 shows the $\chi^{2}$ fit results of the $m(J/\psi p)$ distribution
for the two hypotheses. The data description by hypotheses of two pentaquarks
and four pentaquarks are both good ($\chi^{2}/N_{\text{dof}}=37.1/39$ and
$\chi^{2}/N_{\text{dof}}=37.1/42$).

(a)(b)

Figure 1: The $\chi^{2}$ fit results of the $m(J/\psi p)$ distribution in the
signal region with the hypothesis of two pentaquarks (a) and with the
hypothesis of four pentaquarks (b) [8].

Table 1 summarizes the obtained pentaquark masses and widths for the
hypothesis of two pentaquarks and compares to the LHCb values [9]. The
extracted pentaquark masses and widths are consistent with the LHCb values
within uncertainties.

Table 1: Extracted pentaquarks masses and widths in $\Lambda_{b}\rightarrow P_{c}^{+}K^{-}$ decays for the hypothesis of two pentaquarks [8]. Parameter | Value [8] | LHCb value [9]
---|---|---
$m(P_{c1})$ | $4282^{+33}_{-26}\text{(stat)}^{+28}_{-7}\text{(syst)}$ MeV | $4380\pm 8\pm 29$ MeV
$\Gamma(P_{c1})$ | $140^{+77}_{-50}\text{(stat)}^{+41}_{-33}\text{(syst)}$ MeV | $205\pm 18\pm 86$ MeV
$m(P_{c2})$ | $4449^{+20}_{-29}\text{(stat)}^{+18}_{-10}\text{(syst)}$ MeV | $4449.8\pm 1.7\pm 2.5$ MeV
$\Gamma(P_{c1})$ | $51^{+59}_{-48}\text{(stat)}^{+14}_{-46}\text{(syst)}$ MeV | $39\pm 5\pm 19$ MeV

##  3  Observation of di-charmonium events

This analysis searches for potential tetraquark (TQ) in the $4\mu$ final state
through the di-$J/\psi$ and $J/\psi+\psi(2S)$ channels, using
$139~{}\text{fb}^{-1}$ of $pp$ data at $\sqrt{s}=13$ TeV.

Combinations of di-muon and tri-muon triggers with $J/\psi$ or $\psi(2S)$ mass
window requirement are applied for the largest acceptance. Events should
contain at least two opposite-charge muon pairs. The TQ vertex is
reconstructed by fitting the muon tracks in the inner detector. Then, each
muon pair is revertexed with a $J/\psi$ or $\psi(2S)$ mass constraint to
achieve best TQ mass resolution. The TQ mass obtained with mass constraints
($m_{4\mu}^{\text{con}}$) and the one without mass constraints ($m_{4\mu}$)
are both used in the analysis. The dominant backgrounds are di-charmonium
production through single parton scattering (SPS) process [10] and double
parton scattering (DPS) process [11], modelled by Monte Carlo (MC) simulations
with normalisations and kinematics corrected in SPS and DPS control regions
(CRs). The detailed event selection requirements for signal region (SR) and
CRs are summarized in Table 2 [12].

Table 2: Summary of event selection requirements for the signal and control regions [12]. Conditions | SR | SPS CR | DPS CR
---|---|---|---
Baseline | Di-muon or tri-muon triggers,
Opposite charged muons from the same $J/\psi$ or $\psi$(2S) vertex,
Loose muon ID
$p_{\text{T}}^{\mu_{1},\mu_{2},\mu_{3},\mu_{4}}>4,4,3,3$ GeV and
$|\eta_{\mu_{1},\mu_{2},\mu_{3},\mu_{4}}|<2.5$
$m_{J/\psi}\in\\{2.94,3.25\\}$ GeV, or $m_{\psi(2S)}\in\\{3.56,3.80\\}$ GeV,
Loose vertex cuts $\chi^{2}_{4\mu}/N<40$ and $\chi^{2}_{\text{di-}\mu}/N<100$,
Vertex $\chi^{2}_{4\mu}/N<3$,
$L_{xy}^{4\mu}<0.2$ mm, $|L_{xy}^{\text{di-}\mu}|<0.3$ mm,
$m_{4\mu}$ | <7.5 GeV, | (7.5, 12.0) GeV | (14.0, 25.0) GeV
$\Delta R$ between charmonia | <0.25 | $-$ | $-$

Unbinned maximum likelihood fits are used to obtain TQ masses and widths in
the $4\mu$ mass spectra of fit regions. Two fit regions (fit SR with
$m_{4\mu}^{\text{con}}<11~{}\text{GeV}$ and $\Delta R<0.25$, and fit CR with
$m_{4\mu}^{\text{con}}<11~{}\text{GeV}$ and $\Delta R\geq 0.25$) are defined
based on the baseline conditions in Table 2.

In the di-$J/\psi$ channel, three-resonance signal model with interferences
among signal resonances is applied. The signal model reads

$\displaystyle
f_{s}(x)=\left|\sum_{i=0}^{2}\frac{z_{i}}{x^{2}-m_{i}^{2}+im_{i}\Gamma_{i}}\right|^{2}\sqrt{1-\frac{4m_{J/\psi}^{2}}{x^{2}}}\otimes
R(\alpha),$ (1)

where $m_{i}$ and $\Gamma_{i}$ are the masses and widths of each resonance,
$z_{i}$’s are complex numbers representing the amplitudes ($z_{1}$ is fixed to
unity with zero phase), the square root factor is the phase space factor, and
$R(\alpha)$ is a resolution function.

In the $J/\psi+\psi(2S)$ channel, two models (model A and model B) are used,
due to lower statistics. Model A considers the same resonances in the
di-$J/\psi$ channel which can also contribute to $J/\psi+\psi(2S)$, plus a
standalone resonance. It reads

$f_{s}(x)=\left(\left|\sum_{i=0}^{2}\frac{z_{i}}{x^{2}-m_{i}^{2}+im_{i}\Gamma_{i}}\right|^{2}+\left|\frac{z_{3}}{x^{2}-m_{3}^{2}+im_{3}\Gamma_{3}}\right|^{2}\right)\sqrt{1-\left(\frac{m_{J/\psi}+m_{\psi(2S)}}{x}\right)^{2}}\otimes
R(\alpha),$ (2)

Where the first three resonances are fixed to the results obtained in the
di-$J/\psi$ channel. Model B only assumes a standalone resonance.

Figure 2 shows the fitted $4\mu$ mass spectra in the di-$J/\psi$ and
$J/\psi$+$\psi$(2S) channels. The obtained masses and widths of resonances are
summarized in Table 3. In the di-$J/\psi$ channel, a broad structure at
threshold and a resonance at $6.9$ GeV which is consistent with the $X(6900)$
observed by LHCb [13] are observed with a significance far above $5\sigma$.
Although the near threshold structure is explained by two interfering
resonances, it could result from other physical processes e.g. feed down from
di-charmonium resonances with higher masses.

In the $J/\psi+\psi(2S)$ channel, model A describes data better than model B,
with a combined significance of $4.6\sigma$. The second resonance around $7.2$
GeV with significance of $3.2\sigma$ is also hinted by LHCb [13].

(a)(b)
(c)(d)

Figure 2: The fitted $4\mu$ mass spectra in the fit signal regions of the di-$J/\psi$ (a,b) and $J/\psi$+$\psi$(2S) (c,d) channels. The purple (green) dashed lines represent the components of individual resonances (interferences among them). Fits in (a) and (b) have the same likelihood but different resonances magnitudes and interferences due to degenerate solutions. In the $J/\psi$+$\psi$(2S) channel, both model A (c) and B (d) fit results are shown [12]. Table 3:  The extracted masses and widths of the resonances in the di-$J/\psi$ and $J/\psi$+$\psi$(2S) channels. The first errors in each value are statistical while the second ones are systematic [12]. (GeV) | $m_{0}$ | $\Gamma_{0}$ | $m_{1}$ | $\Gamma_{1}$
---|---|---|---|---
di-$J/\psi$ | $6.22\pm 0.05_{-0.05}^{+0.04}$ | $0.31\pm 0.12_{-0.08}^{+0.07}$ | $6.62\pm 0.03_{-0.01}^{+0.02}$ | $0.31\pm 0.09_{-0.11}^{+0.06}$
$m_{2}$ | $\Gamma_{2}$ | —
| $6.87\pm 0.03_{-0.01}^{+0.06}$ | $0.12\pm 0.04_{-0.01}^{+0.03}$ | —
(GeV) |  | $m_{3}$ | $\Gamma_{3}$ |
$J/\psi$+$\psi$(2S) | model A | $7.22\pm 0.03_{-0.03}^{+0.02}$ | $0.10_{-0.07-0.05}^{+0.13+0.06}$ | —
model B | $6.78\pm 0.36_{-0.54}^{+0.35}$ | $0.39\pm 0.11_{-0.07}^{+0.11}$ | —

##  4  Conclusion

The recent ATLAS results on exotic hadronic resonances, including pentaquark
and tetraquark searches, are highlighted in this proceeding. The extracted
pentaquark masses and widths are consistent with LHCb values. The potential
tetraquark $X(6900)$ is observed with ATLAS data collected during Run 2. More
results of exotic hadrons at ATLAS are expected in the near future with Run 2
and Run 3 data.

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