1

84. Pentaquarks

84. Pentaquarks
Revised March 2024 by M. Karliner (Tel Aviv U.) and T. Skwarnicki (Syracuse U.).
Experimental searches for pentaquark hadrons comprised of light flavors have a long and vivid
history. No undisputed candidates had been found in 50 years. The first wave of claimed observations of pentaquark candidates containing a strange antiquark occurred in the early seventies,
see e.g. a review in the 1976 edition of Particle Data Group listings for Z0 (1780), Z0 (1865) andZ1 (1900) [1]. The last mention of these candidates can be found in the 1992 edition [2] with theperhaps prophetic comment “the results permit no definite conclusion - the same story for 20 years.
[...] The skepticism about baryons not made of three quarks, and lack of any experimental activity
in this area, make it likely that another 20 years will pass before the issue is decided.” A decade
later, a second wave of observations occurred, possibly motivated by specific theoretical predictions
for their existence [3–5]. The evidence for pentaquarks was based on observations of peaks in theinvariant mass distributions of their decay products. More data and subsequent more sensitive
experiments did not confirm these claims [6]. In the last mention of the best known candidatefrom that period, Θ(1540)+ , the 2006 Particle Data Group listing [7] included a statement: “Theconclusion that pentaquarks in general, and that Θ+ , in particular, do not exist, appears compelling.” which well reflected the prevailing mood in the particle physics community until a studyof Λ0b → J/ψ pK − (J/ψ → µ+ µ− ) decays by LHCb [8] (charge conjugate modes are implied). Froman analysis of 3 fb−1 Run 1 data at 7 and 8 TeV at the LHC, the LHCb collaboration reported
a significant J/ψ p structure in Λ0b → J/ψ pK − decays [8]. The exotic character of this structure,with the minimal quark content of uudcc̄, was demonstrated in a nearly model-independent way inRef. [9], where it was shown that the J/ψ p mass (mJ/ψ p ) peak near 4450 MeV was too narrow to beaccounted for by Λ∗ → pK − reflections (Λ∗ denotes a generic Λ excitation), reinforcing the resultsfrom the earlier model-dependent six-dimensional amplitude analysis of invariant masses and decay
angles describing the Λ0b decay in the same data [8]. The LHCb 6 fb−1 Run 2 LHC data at 13 TeV,
together with the improvements in the data selection for both runs, resulted in a nine-fold increasein the number of reconstructed Λ0b → J/ψ pK − decays (246,000 events) [10] and observation of new
narrow J/ψ p structures which were too faint to had been significant in the Run 1 data analysis. A
second horizontal band is observed in the Dalitz plot (Fig. 84.1) near 4312 MeV in the J/ψ p mass.
The 4450 MeV structure also appears to consist of two narrower peaks at 4440 and 4457 MeV.
Performing a rigorous six-dimensional amplitude analysis of these faint J/ψ p structures is challenging and has not been accomplished yet. Fortunately, the newly observed peaks are so narrow that
it is not necessary to construct an amplitude model to prove that these states are not artifacts
of interfering Λ∗ resonances, as was previously demonstrated in Ref. [9]. Their masses and widths
have been characterized by the LHCb (see Table 84.1) from one-dimensional fits to J/ψ p mass distributions, with different levels of suppression of the Λ∗ contributions, which peak at the lower pK −masses (Fig. 84.1). Such analysis is not sensitive to any broad J/ψ p contributions. The histograms
analyzed by the LHCb are available in tabular form at https://www.hepdata.net/record/89271.
The fit chosen by the LHCb for the central mass and width values is displayed in Fig. 84.2. The
Pcc̄ (4312)+ state (formerly known as Pc (4312)+ ) peaks right below the Σc+ D0 threshold and has
statistical significance over 7.6σ. The Pcc̄ (4457)+ state peaks right below the Σc+ D∗0 threshold,while the Pcc̄ (4440)+ state peaks about 20 MeV below it. The significance of the two-peak versus
one-peak hypothesis for the 4450 MeV structure is over 5.4σ, rendering the single peak interpretationof this region obsolete. The six-dimensional amplitude analysis reported in Ref. [8], which inaddition to the structure near 4450 MeV, provided also evidence for the broad Pcc̄ (4380)+ state, isobsolete since it used the single Pcc̄ (4450)+ state and it lacked the Pcc̄ (4312)+ state. Furthermore,
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
31st May, 2024 10:18am

m2J/ ψ p [GeV2]

26
LHCb

102

24
22
10
20
18
16
2

2.5

3

3.5

4

4.5

5

5.5 6 6.5
m2Kp [GeV2]

Candidates/(0.105×0.045 GeV4)

84. Pentaquarks

2

1

Figure 84.1: Dalitz plot distributions for Λ0b → J/ψ pK − decays as observed by LHCb.
it used the helicity formalism in which the half-integer spin of the proton was not aligned properly
between the different Λ0b decay chains [11, 12]. The newer one-dimensional analysis by LHCb [10]+was not sensitive to wide Pcc̄states. The LHCb result from the six-dimensional amplitude analysisof the Cabibbo suppressed channel Λ0b → J/ψ pπ − [13], which contains a statistically marginal−+
evidence for the sum of the Pcc̄and the Tcc̄1(formerly known as Zc (4200)− ) contributions, took
extensive input from Ref. [8] and, like the Pcc̄ (4380)+ state, should be treated with caution until
the both amplitude analyses are completed on the enlarged data sets with the modified helicity
formalism.
While Σc D̄(∗) states had been predicted [14–17] before the first LHCb results [8], after theseresults became known, many theoretical groups interpreted the Pcc̄ (4450)+ and Pcc̄ (4380)+ statesin terms of diquarks and triquarks as building blocks of a compact pentaquark [18–24]. In adifferent strategy, a tentative attempt has been made to treat the full 5-body dynamics, leading
to states below the lowest threshold for spontaneous dissociation [25]. In the first implementationof the former approach [18], the pentaquark mass splitting was generated mostly by the changeof angular momentum between the sub-components (L) from zero to one, which would also makethe heavier state narrower and of opposite parity. Explicit modeling of multiquark systems [26]questions if centrifugal barrier factor provides enough width suppression via spatial separation ofc and c̄ quarks at these masses, as the phase space for J/ψp decay is very large (more than 400
MeV). Also, the observed mass splitting was too small to be only due to the mechanism proposed
in Ref. [18] and required fine-tuning of such models. A variation of this model, in which the
31st May, 2024

84. Pentaquarks

3+
Table 84.1: Summary of the narrow Pcc̄(formerly known as Pc+ ) properties, interpreted as Breit-Wigner resonances. The central values are basedon the fit displayed in Fig. 84.2.

StatePcc̄ (4312)+
Pcc̄ (4440)+
Pcc̄ (4457)+

M [ MeV ]4311.9 ± 0.7+6.8−0.6
4440.3 ± 1.3+4.1−4.7
4457.3 ± 0.6+4.1−1.7

Γ [ MeV ] (95% CL)
3.7
9.8 ± 2.7+
− 4.5 (< 27)
8.7
20.6 ± 4.9+
−10.1 (< 49)+ 5.7
6.4 ± 2.0− 1.9 (< 20)

R [%]0.30 ± 0.07+0.34−0.09
1.11 ± 0.33+0.22−0.10
0.53 ± 0.16+0.15−0.13

heavy (cu) diquark couples with heavy c̄ to form colored triquark attracting the light diquark+(ud), has been re-implemented for the narrow Pcc̄states [27]. In this model, the Pcc̄ (4440)+ andPcc̄ (4457)+ states are accommodated via spin-orbit interactions for the L = 1 states, while thePcc̄ (4312)+ is one of the L = 0 states. However, the mass prediction for the latter is off by(−72 ± 29) MeV [27]. This work was later extended to SU (3)F [28]. The width dilemma becomes
more severe in view of the narrow widths of the newly observed states (Table 84.1), especially for
the L = 0 Pcc̄ (4312)+ state, and requires a different origin of potential barrier between c and c̄ thanangular momentum [27, 29], which remains a subject of theoretical controversy. Measurement of
spin-parity of Pcc̄ (4312)+ , Pcc̄ (4440)+ and Pcc̄ (4457)+ will be crucial for testing these and alternative
theoretical ideas discussed in the following.
More effective width suppression mechanism is offered by a loosely bound charmed baryonanticharmed meson molecular model, in which c and c̄ can be separated by much larger distances,resulting in a smaller probability of them getting close enough to each other in order to make a
J/ψ. Since molecular binding energy cannot be large, such molecules are in S-wave, so it has beenrealized early on that their masses must be near the sum of the baryon and meson masses and theirspin and parity are inherited from their constituent hadrons, see e.g. discussion in [17]. The mass
coincidence of the Pcc̄ (4312)+ and of Pcc̄ (4457)+ states, with the two related thresholds, Σc+ D0
and Σc+ D∗0 , provides very strong experimental evidence in favor of this interpretation. Given how
close Pcc̄ (4312)+ is to the Σc+ D0 threshold, it might be a virtual rather than a bound state [30].
Since the spins of Σc+ and of D∗0 can be combined in two different ways, the narrow Pcc̄ (4440)+
peak also finds natural explanation in this physical picture. It cannot be a virtual state since it issufficiently below the Σc+ D∗0 threshold.
(∗)+
It is worth stressing that other baryon-meson combinations, Λc D̄(∗)0 and χcJ p are not expected to bind [14, 31]. Before the first pentaquark observation [8] heavy quark symmetry wasused to show that, in addition to the three Σc D̄(∗)0 states, one expects four Σc∗ D̄(∗)0 states, for a
total of seven [32]. Indeed, additional states at, or below, the Σc∗+ D and Σc∗+ D∗ thresholds, areexpected [33–36]. Since Σc∗+ width is likely around 15 MeV [37], more than the width of either
Pcc̄ (4312)+ or Pcc̄ (4457)+ , it is important to keep in mind that a molecule is typically as broad as
the constituents1 [38–40]. There is no significant evidence for Σc∗ D̄(∗) states in the present LHCb
data set [10,41]. Larger data sets are expected from the Upgraded LHCb experiment. For a review
on hadronic molecules, and a recent survey in a particular approach, see respectively Refs. [42, 43].
It is useful to consider the Pcc̄ (4312)+ , Pcc̄ (4440)+ and Pcc̄ (4457)+ narrow pentaquarks together
with several analogous exotic states with hidden charm and bottom in the meson sector. This
provides additional significant motivation for the molecular model. At least five exotic mesons areclose to thresholds of two heavy-light mesons: χc1 (3872) (formerly known as X(3872)) [44–47],
Tbb̄1 (10610) and Tbb̄1 (10650) (formerly Zb (10610) and Zb (10650)) in the bottomonium sector [48–1This feature gets changed if systems are more deeply bound.

31st May, 2024

84. Pentaquarks

Weighted candidates/(2 MeV)

4

+ 0
ΣcD

Σ +c D * 0

1200
1000

LHCb

data
total fitbackground

800
600
400

+

+

P c (4312)

P c (4440)+

P c (4457)

200
04200 4250 4300 4350 4400 4450 4500 4550 4600
m J / ψp [MeV]
Figure 84.2: Fit to the J/ψ p mass distribution, in which events were weighted to suppress Λ∗ →pK − backgrounds, of three Breit-Wigner functions and a sixth-order polynomial background. This+fit was used to determine the central values of the masses and widths of the Pcc̄states (formerly
+
+
0
+
∗0
known as Pc ) reported by LHCb. The mass thresholds for the Σc D and Σc D final states aresuperimposed.

52] and Tcc̄1 (3900) (formerly Zc (3900)) [53–57] and Tcc̄1 (4020) (formerly Zc (4020)) [58–60] in thecharmonium sector (see Table II in Ref. [61]; for reviews of experimental information see Ref. [62,63],
as well as Spectroscopy of Mesons Containing Two Heavy Quarks and Heavy Non-q q̄ Mesons in thecurrent Review of Particle Properties. These states share several important features: a) their masses
are near thresholds and their spin and parity correspond to S-wave combination of the two mesons;b) they are very narrow, despite very large phase space for decay into quarkonium + pion(s); c) the
branching fractions for “fall apart” mode into two mesons are much larger than branching fractions
for decay into quarkonium and pion(s). So far, there is no experimental evidence for states at
two pseudoscalar thresholds (DD̄ and B B̄), suggesting that pseudoscalar exchange is essential for
31st May, 2024

584. Pentaquarks

binding in meson-meson systems.
The above provide a strong hint that these states are deuteron-like loosely bound states of two
heavy mesons [64–72]. It is then natural to conjecture that similar bound states might exist of two
heavy baryons [73,74], or a meson and a baryon or a baryon and an antibaryon, leading to a rather
accurate prediction of the Pcc̄ (4457)+ mass as 3/2− Σc D̄∗ molecule (the mass threshold is 4460
MeV for Σc+ D̄∗0 and 4464 MeV for Σc++ D∗− ) [17, 61], following similar predictions obtained in a
wider framework of doubly heavy baryon-meson hadronic molecules, which might include mixturesof various two-hadron states [14–16, 31]. However, single pion exchange is not possible in Σc+ D0
system. Thus the existence of Pcc̄ (4312)+ suggests a more general binding mechanism in baryonmeson molecules, e.g. vector or two-pion exchanges, and/or coupled-channel interactions. Two-pionexchange in DD̄ system is highly suppressed, because the intermediate state is D∗ D̄∗ , which is 282∗
MeV heavier than DD̄. On the other hand, in the Σc D̄ system the intermediate Λ+c D̄ state is only
25 MeV lighter than Σc D̄, and therefore does not have to suffer significant suppression, providing a
possible binding mechanism [75]. In a generic hadronic molecule it is essential that the two hadrons
are heavy, in order to minimize the repulsive kinetic energy [73, 74, 76].
Following the initial LHCb discovery [8], several groups carried out a detailed analysis of the+
Pcc̄ states as hadronic molecules [77–86] followed by further analyses [35, 87–111] after the updated
LHCb results [10]. Partial widths of all the allowed decay channels for the Pcc̄ states have been
estimated within a specific model in the molecular picture [112]. The most striking suggestion is that∗0
Pcc̄ (4312)+ decays are totally dominated by the Λ+c D̄ channel. This channel is also suggested to be+very prominent in decays of Pcc̄ (4440) and Pcc̄ (4457)+ . But other scenarios are possible, as shownby a recent theoretical analysis, allowing for the most general scattering potential of the baryonmeson system consistent with QCD symmetries at leading order in a momentum counting [113].
(∗)0 channels are allowed. Clearly,
They found that both large and vanishing transitions to Λ+c D̄experimental determination of the branching fraction of these channels is of high priority.
The Pcc̄ states have also been-interpreted as so called hadro-charmonium [114], a bound state ofrelatively compact charmonium states with light hadronic matter. It was proposed that Pcc̄ (4440)+−−
and Pcc̄ (4457)+ are spin-split ψ(2S)p bound states with J P = 21 and 32 , while Pcc̄ (4312)+ is a χc0 p+
bound state with J P = 12 [115]. While very interesting from the theoretical point of view, it is not
at all clear why the binding energies between charmonia and the nucleon should conspire to produce
states so close to the Σc D̄ and Σc D̄∗ thresholds. Moreover, the predicted widths of Pcc̄ (4440)+ andPcc̄ (4457)+ are too big by a factor ∼ 2-3. One should also keep in mind that the molecular andhadro-charmonium pictures provide opposite predictions for the parity of Pcc̄ (4312)+ . In principle
LHCb can check the spin and parity through partial wave analysis, but at present it is not known
if systematic uncertainties can be sufficiently reduced to make such an analysis conclusive.
Shortly after the initial experimental discovery it was conjectured that the Pcc̄ (4450)+ reflects
the presence of a triangle singularity near the χc1 p threshold [116–119]. These explanations are nolonger viable, since the Pcc̄ (4440)+ mass is not at any threshold and the Pcc̄ (4312)+ and Pcc̄ (4457)+
0peak slightly below the Σc+ D0 and Σc+ D∗0 thresholds. The Pcc̄ (4457)+ mass is exactly at Λ∗+c D
threshold, but LHCb has demonstrated that the observed peaking is narrower in the data than
expected from the triangle-diagram when a realistic width of the excited Ds− state exchanged in
the triangle is used (Supplemental Material in Ref. [10]).
More extensive pre-2019 reviews of some of the theoretical issues can be found in Refs. [120,121].
Two recent relevant reviews are Refs. [122, 123].
+
So far the Pcc̄states have been observed by only one experiment in only one channel. It is+(∗)0 , η p [113]. Theseessential to explore other possible experimental channels, such as Pcc̄
→ Λ+
c
c D̄
+
channels are however much more experimentally challenging than Pcc̄ → J/ψp. Proposals have
31st May, 2024

6

84. Pentaquarks

also been made to search for heavy pentaquarks in photo-production [124–131]. Ref. [132] discusses
photoproduction within the string-junction physical picture of the pentaquarks. Photoproductionis also related to recent work on J/ψ(ηc )N scattering on the lattice [133] and on computation ofJ/ψ(ηc )N and Υ (ηb )N cross sections [134]. In addition, pentaquark production has been discussed
in the context of antiproton-deuterium collisions [135], of heavy ion collisions at LHC [136], in pA
collisions [137] and in pion-induced processes [138–140]. The GlueX Collaboration reported negative+
search results for the Pcc̄states in photo-production at JLAB [141, 142], γp → (J/ψ → e+ e− )p.
Within the large experimental errors and considerable theoretical model dependence these results+
do not contradict the molecular interpretations of the narrow Pcc̄states. In particular, vector-meson
dominance often assumed in theoretical modelling may not hold for near-threshold J/ψ production,and Λc D̄(∗)0 intermediate states may significantly contribute to the J/ψ p production complicating+probing for the Pcc̄states [143, 144].
+
As noted in e.g. [17], bottom analogues of the Pcc̄might well exist, but experimental search forsuch states involves very significant challenges. It is therefore hardly surprising that they have notbeen observed so far. A detailed discussion is beyond the scope of the current review.
+
The LHCb collaboration obtained a 3.1σ evidence for a Pcc̄→ J/ψ p state in the four-dimensional
amplitude analysis of about 800 Bs0 → J/ψ pp̄ (J/ψ → µ+ µ− ) decays [145]. The mass of the state,+4337+7−4 ± 2 MeV, is not compatible with the the Pcc̄ (4312) state at 3.1 standard deviations. The
width is relatively small, 29+26−12 ±14 MeV. The present data do not provide sufficient discrimination
between various J P assignments. Its mass is about 19 MeV higher than the Σc+ D̄0 threshold andabout 16 MeV lower than the χc0 p threshold. At present, no specific explanation for this structure
has been proposed, but some intriguing ideas have been raised in Ref. [146]. Since the statisticalsignificance of this evidence is marginal, more data are required before this state is consideredexperimentally established.
0 → J/ψ Λ structure was observed by the LHCb
Similarly inconclusive 3.1σ evidence for a Pcc̄scollaboration in the six-dimensional amplitude analysis of about 1750 Ξb− → J/ψ ΛK − (J/ψ →+µ+ µ− , Λ → pπ − decays [12]. The strange counterparts of Pcc̄states have been predicted in both
molecular and compact pentaquark models [15, 99, 101, 147–149]. When interpreted as a single
00 0
peak, its mass, 4458.8 ± 2.9+4.7−1.1 MeV, is 15 MeV above the Ξc D̄ threshold and 18 MeV below
+8.0
∗0
0
the Ξc D̄ threshold. Its width, 17.3 ± 6.5−5.7 MeV, is relatively narrow, thus plausibly could beinterpreted as a loosely bound Ξc0 D̄∗0 state. However, in the latter model two states are expectedwith J P equal to 1/2− and 3/2− . In fact, the LHCb data are consistent with such hypothesis,
under which 4454.9 ± 2.7 MeV (Γ = 7.5 ± 9.7 MeV) and 4467.8 ± 3.7 MeV (Γ = 5.2 ± 5.3 MeV)
mass (width) estimates are obtained (statistical errors only). It is worth noting, that the SU (3)flavor structure of Ξc0 D̄∗0 states is different from that of Σc+ D̄∗0 states, since Ξc0 belongs to thecharmed baryon triplet, together with Ξc+ and Λ+
c , where the two light quarks form a spin-zero+
00
diquark, unlike Σc , which together with Ξc and Ωc0 belongs to the charmed baryon sextet, where
the two light quarks form a spin-1 diquark. More data are required to experimentally establish thisstructure, clarify its composition, and determine the related quantum numbers.
If the two states at 4455 MeV and 4468 MeV indeed correspond to a Ξc0 D̄∗0 molecule, there
perhaps exist two other states, corresponding to Ξc0 D̄∗ [15, 99, 101, 147–149], with a mass shifted
upwards by approximately Ξc0 − Ξc mass difference [150, 151], i.e. about 108 MeV [37].
More recently, the LHCb experiment observed highly significant (> 14σ) pentaquark statePcc̄s (4338)0 → J/ψ Λ (formerly known as Pcs (4338)) in the six-dimensional amplitude analysis of
4620 ± 70 B − → J/ψ Λp̄ decays [152]. Its mass 4338.2 ± 0.7 ± 0.4 MeV is right at the Ξc D̄ threshold(Fig. 84.3), its width is narrow 7.0 ± 1.2 ± 1.3 MeV, and its spin is 1/2, with a preference fornegative parity, which all fits the molecular model very well. This makes the Pcc̄s (4338)0 state alikely Ξc0 D̄0 analog of the Pcc̄ (4312)+ state in Σc0 D̄0 system. In addition, as in the Pcc̄s (4459)0 case,
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84. Pentaquarks

7

Candidates/(2 MeV)a Ξc0 D̄ state is expected, for a total of three additional strange pentaquarks [151]. Experimental(∗,0)
determination whether yet additional Ξc D̄(∗)0 states actually exist will provide a useful testing
ground for the various theoretical approaches which have been used to predict them.

180
160

LHCb
9 fb-1Data
Nominal fit
Baseline fit
NR(J/ψ p )NR(Λ p )PΛψs0
Background

140
120
100
80
60
40
20
0
4.2

4.25

4.3

4.35

m(J/ψ Λ) [GeV]

Figure 84.3: Distribution of invariant J/ψ Λ mass, with the projection of the amplitude fit modelΛ 0 ) is also shown in grey.
superimposed. The model without the Pcc̄s (4338)0 state (labeled as PψsThe Ξc+ D− baryon-meson threshold is indicated with a vertical dashed line.
In hidden-charm exotics discussed above, the charmed and the anticharmed quarks can forma charmonium and thereby decouple from the light quarks. The molecular model provides anefficient mechanism to suppress such decays, thus making these states narrow. Compact direct color
couplings between quarks are missing an obvious width suppression mechanism, thus could lead tobroader states. In fact, there is plenty of evidence for them in form of broader tetraquark mass
structures in J/ψ φ [153–159], J/ψ J/ψ [160–162], Tcc̄1 (4430)+ → ψ(2S)π + (formerly Zc (4430)+ )[163–165] and others, although alternative explanations of these structures have been also proposed.
Analogous configurations may also exist for pentaquarks, but there is no firm evidence for them
31st May, 2024

884. Pentaquarks

yet.
The hidden-charm exotic states, should not be confused with exotic hadrons containing two
heavy quarks, rather than a heavy quark and a heavy antiquark. Decoupling from the light quarks
is impossible in exotics which contain two heavy quarks. This has far-reaching consequences.
The first tetraquark of the latter type, i.e. containing two heavy quarks, has been reported by
LHCb [166, 167]. A comprehensive discussion of tetraquark candidates can be found in the “Heavy
non-QQ̄ Mesons” review.
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