63. Spectroscopy of Light Meson Resonances

1

63. Spectroscopy of Light Meson Resonances
Revised March 2024 by C. Amsler (Stefan Meyer Inst.), A. Masoni (INFN, Cagliari) and G. Venanzoni (Liverpool U.; INFN, Pisa).

63.1
63.2
63.3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scalar mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Glueballs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.3.1 Scalar glueballs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.3.2 Tensor glueballs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.4 Pseudoscalar mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.5 Vector mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.5.1 The ρ(770) meson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.5.2 The ρ(770) excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.6 Axial-vector mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.7 Hybrid mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.8 Tetraquark states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.9 Baryonia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
3
5
5
7
8
10
10
11
13
13
15
16
17

63.1 Introduction
According to the constituent quark model, a light meson consists of a color singlet quarkantiquark pair made of the u, d, or s quarks and the u, d, or s antiquarks, grouped into a flavor
multiplet of SU(3). However, additional mesons made of bound gluons (glueballs) could exist in
the same mass range, suggested by the self coupling of gluons in QCD. Multiquark structures arealso possible, such as quark-antiquark pairs with an excited gluon (hybrid mesons). Tetraquarks
are compact color singlets of diquark-antidiquark pairs (qqqq) or ‘molecular’ bound states of two
mesons (qqqq). More complex systems such as qqqqqq (baryonia) are also predicted.
Fundamentals on the constituent quark model on light and heavy mesons and baryons (including hadrons with charm and bottom quarks), and on predictions from lattice gauge theories,
are described in ‘Quark Model’ in this issue of the Review of Particle Physics, henceforth called
the Review. In the present text we describe the experimental spectrum of light mesons and theirclassifications within the constituent quark model, with emphasis on states exhibiting properties
incompatible with q q̄ structures. The discussion is driven by the results entered in the databaseof the Review. The spectrum of kaon excitations is much less clear cut and therefore deferred toa future edition, when further data might become available. More detailed discussions on exotic
mesons – including those involving the c and b quarks – can be found in Refs. [1–7] and in ‘Heavy
Non-q q̄ Mesons’ of the Review. For more information on the meson (and baryon) spectrum of light(and heavy) quarks we refer to one of the textbooks [8].
Figure 63.1 shows the mass spectrum of q q̄ mesons. The mass (vertical axis) increases withorbital excitations ` (horizontal axis) and radial excitation n. In the quark model one uses thenotation nS, nP , nD... for the radial excitations (n = 1 for the ground states), in contrast to
the usual 1s, 2p, 3d... notation in atomic physics. Each box represents an SU(3) nonet containing
multiplets of the isospin i, three isovectors, two strange isodoublets, and two isosinglets (one SU(3)singlet and one SU(3) octet). The spin, parity [P = −(−1)` ] and C-parity [C = (−1)`+s ] take the
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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63. Spectroscopy of Light Meson Resonances

possible values J P C = 0++ (scalar), 0−+ (pseudoscalar), 1−− (vector), 1+± (axial- or pseudovector),2++ (tensor), etc. Therefore mesons with the exotic quantum numbers 0−− , 0+− , 1−+ , 2+− , 3−+ ,etc. cannot be q q̄ states. Note that the C-parity is defined only for the electrically neutral nonstrange nonet members.
The two isosinglets in each nonet mix with an angle θ close to the ideal value of 35.3◦ for the
1−− , 1+± , 2++ and 3−− nonets, in which case the isosinglets decouple to uu + dd and ss. The
orbital excitations ` ≥ 1 consist of four nonets for each value of n, since j = ` for antiparallel quark
spins and j = `−1, ` or `+1 for parallel spins. Since the C-parity is not defined for strange mesons,the K1A and K1B in the axial vector 1++ and 1+− nonets of fig. 63.1 are mathematical constructs
which mix to give the observed K1 (1270) and K1 (1400) mesons. A similar scenario occurs for theobserved 2−+ K2 (1770) and 2−− K2 (1820) mesons.
a4(1970)
K*4(2045)
f4(2050)
f4(2300)

Mass(23P2 ) 1++(23P1) 3--(13D3)

K1(1650)f0(2020)h1(1595)++--

1 (23S1)r(1450)K*(1410)2v(1420)f(1680)0++K(1460)h(1295)h(1440) 1)(13P0 )

p(1300)a0(1450)
K0*(1430)
f0(1370,
1500,1710)b1(1235)
K1B
h1(1170)h1(1415) 3)r(770)
K*(892)hh'v(782)
f(1020)0p2(1670)r(1700)K2(1770)h2(1645)h2(1870)

K*(1680)v(1650)f(2170)-+--1(13F4)

6)

3

2 (1 D2) 1 (1 D1)

2)

-+

K

1

a2(1320)
K2*(1430)
f2(1270)
f2'(1525)

0 (11S0 ) 1-- (13S1)

p(23P0 ) 1+-(21P )a1(1260)
K1A
f1(1285)
f1(1420) 4)++-+

0 (21S0 )(13P2 )0

K2(1820)(13P1)a0(1950)

K3*(1780)v3(1670)
f3(1850)++

f2(1640)
f2(1950)

7)

++

4

r3(1690)1p(1800) 5)

a1(1640)--

2 (13D2)+-

a2(1700)
K2*(1980)---+
0 (31S0 ) 1 (33S1)
K(1830)h(1760)++1 (11P1)

2

i=1
i=1/2
i=0

1

2

3

Orbital excitationlFigure 63.1: The mesons made of the u, d, and s light quarks are organised in J P C (n2s+1 `j )nonets with isospin i. The established mesons (which appear in the Summary Table of the Review)are shown in the dark (blue) areas. The white areas contain those omitted in the Summary Table
but reported in the Listings. States with the same J P C mix, such as the 23 S1 and 13 D1 mesons.
The states become broad and overlap with increasing masses, which complicates the determinationof the resonance parameters e.g. mass, width and spin. For a complete list of mesons see the
Listings.
1 The η(1440) stands for the η(1405) and the η(1475), section 63.4.
2 The classification of the scalar nonet is controversial. In alternative schemes the 13 P nonet
0
contains the light scalars below 1 GeV, section 63.2.
3 Considered established, but more data would be desirable.
4 An alternative to the f (1420) is the f (1510), section 63.6.
1
1
5 The π(1800) has also been proposed as a hybrid meson, section 63.7.
6 The φ(2170) has also been proposed as a tetraquark state, section 63.8.
7 The f (1950) has also been proposed as a tensor glueball, section 63.3.2.
2
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63. Spectroscopy of Light Meson Resonances

As described in more detail below (section 63.2), it is hard to accommodate all the known scalarmesons in the lower q q̄ nonets: The light scalar mesons a0 (980), K0∗ (700) (also known as κ), thef0 (500) (also known as σ), and the f0 (980), not shown in the figure, could build the lightest nonet,
but could also be two-meson resonances or tetraquarks (section 63.8). Three isoscalars are known
in the 1500 MeV region, the f0 (1500) or f0 (1710) being proposed as gluonic states mixing withthe f0 (1370) (section 63.3.1). The pseudoscalar labeled η(1440) may consist of two states (section
63.4). The status of vector meson excitations is described in section 63.5. The axial-vector meson
f1 (1420) could be replaced in the 1++ nonet by the f1 (1510) which, however, needs confirmation(see the Listings and section 63.6). Mesons with exotic quantum numbers are discussed in section
63.7.

63.2 Scalar mesons
Scalar mesons decay dominantly into pairs of pseudoscalar mesons (ππ, KK, πη, ηη or ηη 0 ).
The widths tend to be large for those decaying into ππ, due to the absence of angular momentum
barrier and the large available phase space. Broad overlapping states decaying into the same final
state interfere, which complicates the determination of their masses and widths. Furthermore, theground state glueball, a 0++ expected below 2 GeV, will mix with the isoscalar 0++ q q̄ states.
The onset of the KK, ηη or ηη 0 thresholds also distorts the line shapes and produces cusps. Thisrequires high statistics data and the use of coupled channel analyses taking into account unitarity
and analyticity (see ‘Resonances’ in the Review).
Two isovector scalars are established, the a0 (980) and the a0 (1450), together with five isoscalars:
the very broad f0 (500), the f0 (980), the broad f0 (1370), and the comparatively narrow f0 (1500)
and f0 (1710). The strange partners are the K0∗ (700) and the K0∗ (1430). The f0 (500) and K0∗ (700)deserve a separate treatment and can be found in ‘Scalar Mesons below 1 GeV’, which contains
more details on the a0 (980) and f0 (980), briefly reviewed in section 63.8.
The a0 (1450) was first reported by the Crystal Barrel experiment in p̄p annihilation with stopped
antiprotons [9, 10] (see [11] for a review of Crystal Barrel results). An isovector scalar, possibly thea0 (1450) (albeit at a lower mass of 1317 MeV) is observed by Belle in γγ collisions leading to ηπ 0 [12].
The state interferes destructively with the non-resonant background. Its γγ coupling is comparable
to that of the a2 (1320), in accord with simple predictions (see e.g. [13]). A contribution froma0 (1450) → K K̄ is also found in the CLEO-c analysis of D± → K + K − π ± [14] and D0 → KS0 K ± π ∓from LHCb [15]. The a0 (1450) is reported at a lower mass in p̄p annihilation in flight, overlappingwith the a2 (1320) [16, 17].
The f0 (1370) and f0 (1500) were observed by Crystal Barrel [18–20] and by WA102 in central
production with 450 GeV protons [21,22]. They decay mostly into 2π and 4π. The f0 (1500) was also
observed to decay into ηη [23–25] and ηη 0 [26]. All data agree that the 4π decay mode represents
about half of the f0 (1500) decay width, but is dominant for f0 (1370).
The determination of the ππ coupling of the very broad f0 (1370) is complicated by its interference with the f0 (500). The existence of the f0 (1370) was questioned by COMPASS from00
π − p → π − π − π + p data [27] and by LHCb in B s → J/ψ(1S)π + π − [28]. In B → J/ψ(1S)π + π − theππ mass spectrum does not show any significant scalar component above ∼1.2 GeV [29] (an analysis
that is challenged in [30]). The existence of the f0 (1370) has been disputed by a reassessment ofvarious production modes [31] (the K0∗ (700) is also not needed in Kπ scattering). This contrasts
with its ππ decay analyzed in Ref. [32]). However, data from CLEO-c in D0 → π + π − π + π − require
a contribution from f0 (500)f0 (1370) → 4π [33]. A broad 2π signal is also observed by BaBar around
1400 MeV in the decay B ± → π ± π ± π ∓ [34] which is attributed to the f0 (1370) (but could also be
due to the f0 (1500)). The existence of the f0 (1370) is confirmed by a recent dispersive analysis of
ππ scattering data, which leads to a complex pole around 1245 MeV with a very large width of
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463. Spectroscopy of Light Meson Resonances

about 600 MeV [35].
In Refs. [36, 37] the f0 (1370) and f0 (1710) (together with the f2 (1270) and f20 (1525)) are interpreted as bound systems of two vector mesons. This view is challenged in Ref. [38] where in a
covariant formalism, e.g. the f2 (1270) does not appear as a ρρ bound state. Photoproduction dataof the f2 (1270) in γp → π 0 π 0 p from CLAS [39], as a function of momentum transfer, also disagreewith predictions [40] for the f2 (1270) to be a ρρ bound state.
While the K K̄ decay branching ratio of the f0 (1500) is small [21] [41], the f0 (1710) decays
dominantly into KK. The f0 (1710) is not observed in pp annihilation at rest [41] and only weakly
produced in pp̄ annihilation in flight [42], with a rate strongly suppressed compared to that of thef0 (1500) (∼7%). For comparison, the rate for the (ss̄) f20 (1525) production is about 9% that of the¯ f2 (1270), as expected from the OZI rule [42]. On the other hand the f0 (1370) does not(uū + dd)¯ for the f0 (1370) and ss̄ forcouple strongly to K K̄ [21]. This suggests an nn̄ structure (uū + dd)
the f0 (1710). The f0 (1500) would also qualify as an nn̄ state, although it is very narrow comparedto the other states. Occam’s razor principle therefore suggests that the f0 (1370), a0 (1450), and thef0 (1710) are in the 13 P0 q q̄ SU(3) flavor nonet, the f0 (1370) and a0 (1450) being the two (mostly)nn̄ states, and the f0 (1710) the (dominantly) ss̄ one. The nature of the f0 (1500) is discussed along
this scheme in section 63.3.1.
There is long-time evidence for the existence of two scalar nonets and one glueball below 2
GeV [43]. The ground state 13 P0 q q̄ nonet and a lighter one made of four-quark states which
recombine at large distances to become meson-meson resonances, the a0 (980), a0 (980), f0 (500) andK0∗ (700), see section 63.8. For a review see Ref. [1] and for the f0 (500) Ref. [44].
Other schemes have been proposed, for example a tetraquark for the f0 (1500) [45] or flavor octets
for the f0 (1500) and f0 (1710) [3]. In Ref. [46] the a0 (1450), f0 (1370), f0 (1500) and K0∗ (1430) areradial excitations of the scalar nonet below 1 GeV. In Ref. [47] the light and 13 P0 scalar nonets
are interpreted as mixing of two tetraquark nonets. In the unitarized quark model with coupledq q̄ and meson-meson channels, the scalars below 1 GeV are manifestations of bare q q̄ confinement
states, mass shifted from the 1.4 GeV region and distorted by the strong 3 P0 coupling to S-wave
two-meson decay channels [48,49]. Thus, in these models the light scalar nonet comprising the lightand 13 P0 scalar nonets are manifestations of the same bare input states (see also [50]). Surprisingly
for a state decaying strongly into 2π and 4π, the f0 (1370) is assumed to be an ss̄ state in Ref. [51].
The f0 (1500) is then a radial excitation.
There is evidence for the existence of two further 0++ mesons in the 1700 – 1800 MeV range,
one isoscalar (f0 (1770)) and one isovector (a0 (1710)), which could be the isovector partner of thef0 (1710). The f0 (1770), claimed by BESII/III [52–54], and also observed in π − p → nωφ [55],has been interpreted as a radial excitation [56]. Two isoscalars are also reported by a re-analysisof BESIII radiative J/ψ(1S) decay data [57, 58]. Evidence for the a0 (1710) is inferred from theinterference of the K + K − and KS0 KS0 decays of the f0 (1710) in Ds+ → f0 (1710)π + , leading to a
relative branching ratio an order of magnitude larger than expected from isospin symmetry [59,60].
A signal for a0 (1710) → KS0 K + is indeed reported by BESIII [61], albeit at 1817 MeV, in contrast
to the state observed by BaBar in ηπ at 1704 MeV [62].
From a study of the vector-vector interaction the authors of Ref. [63], predict an isovector poleat 1780 MeV, while the f0 (1710) is a K ∗ K̄ ∗ molecule, a view also supported by Refs. [64–67].
Thus the f0 (1710) and a0 (1710) might be K ∗ K̄ ∗ molecules, similar to the f0 (980) and a0 (980)
which have been interpreted as K K̄ molecules. Scalar resonances near the D0 mass such as thef0 (1710) and the f0 (1770) are also suggested to produce CP violation enhancements in the charmsystem [68]. Unfortunately, the spectrum of scalar mesons above the f0 (1710) is not well establishedexperimentally and more data are needed to confirm the f0 (1770) and a0 (1710).
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563. Spectroscopy of Light Meson Resonances

63.3 Glueballs
Lattice calculations, QCD sum rules, flux tube, and constituent glue models agree that thelightest glueball has quantum numbers J P C = 0++ and the first excited state 2++ . Lattice calculations predict for the ground state (0++ ) a mass around 1600 – 1700 MeV [69–72], while the2++ state lies around 2300 MeV. For more information on lattice calculations see ‘Quark Model’ in
the Review and fig. 15.3 therein for an example of mass spectrum. These predictions were madein the quenched approximation, neglecting q q̄ loops. However quenched predictions and full QCD
calculations lead to small mass shifts (see ‘Quark Model’ and fig. 15.15 therein).
Heavier glueballs with quantum numbers 0−+ , 2−+ , 1+− , etc. are predicted above 2500 MeV
and the lowest exotic ones (with exotic quantum numbers such as 0+− and 2+− ) are expected
above 4000 MeV [72]. In holographic QCD the 0−+ is predicted to be very broad [73] and the
1+− is at least as broad as its width [74]. Calculations of the three lowest scalar and pseudoscalar
glueballs masses in pure Yang-Mills theory are in quantitative agreement with lattice results [75].
The lightest glueballs lie in the same mass region as ordinary isoscalar q q̄ states, in the mass rangeof the 13 P0 (0++ ), 23 P2 (2++ ), 33 P2 (2++ ), and 13 F2 (2++ ) q q̄ states. Therefore, mixing of glueballswith nearby qq states of the same quantum numbers leads to supernumerary isoscalar state in the
qq nonets (however, see Ref. [57] discussed in section 63.3.1).
Among the signatures naively expected for glueballs are (i) isoscalar states that do not fit
into qq nonets, (ii) enhanced production in gluon-rich channels such as central production andradiative J/ψ(1S) decay, (iii) decay branching fractions incompatible with SU(3) predictions for
qq states, and (iv) reduced γγ couplings (see however [76, 77]). Mixing effects with isoscalar qq
mesons [31, 69, 76, 78–84] and decay form factors [85] can also obscure these simple signatures.
According to SU(3) the decay branching ratios for q q̄ mesons and pure glueballs are different,
and therefore useful to determine the internal structures of mesons. For pure glueballs with flavor
symmetric couplings the decay ratios are ππ : K K̄ : ηη : ηη 0 = 3 : 4: 1 : 0, apart from phase spacefactors. The partial widths for the decay of a scalar (or a tensor) meson into a pair of pseudoscalarmesons are given in fig. 63.2 (for a derivation see e.g. [8]). The decay of a q q̄ meson into a pair ofmesons involves the creation of a q q̄ pair, and SU(3) symmetry assumes that the matrix elements
for the creation of ss̄, uū, and dd¯ pairs are equal. (The generalization to unequal ss̄, uū, and dd¯couplings is given in Ref. [78].) An excellent fit to the tensor meson decay widths is obtained with
β ' 0.5 GeV/c, θV ' 26 ◦ and θP ' –17 ◦ [78].
Note that the assumption of flavor symmetric couplings may not apply in models describing
the scalar glueball by a dilaton field, which lead to mass dependent couplings [86, 87] (see Ref. [88]which predicts that a scalar glueball above 1 GeV would be unobservably wide).
Another way to determine the flavor contents of neutral mesons is the decay B → J/ψ(1S)X
which filters out the dd content of X, while Bs0 → J/ψ(1S)X selects its ss component [89]. More
0 → J/ψ(1S)[f (1370), f (1500), f (1710)] would help to pin down the nature of
precise data on B(s)000these scalar mesons [90].
63.3.1 Scalar glueballs
One of the three isoscalars, the f0 (1370), f0 (1500) or f0 (1710), appears to be supernumerary.
The branching ratios in fig. 63.2 can be used to deduce the structures of these states, assumingthat they are q q̄. The comparison of decay branching ratios from Crystal Barrel annihilation andWA102 central collision data shows that the f0 (1500) is compatible with an nn̄ structure, while thef0 (1710) is mostly ss̄ [13]. However, the close vicinity of the very broad nn̄ f0 (1370), its narrow
width, enhanced production at low transverse momentum transfer in central collisions [91–93] favor
the f0 (1500) to be the supernumerary non-qq state. According to [78,83] the f0 (1370) and f0 (1710)
would be dominantly q̄q states mixing with glue, while the f0 (1500) would be dominantly a glueball31st May, 2024

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63. Spectroscopy of Light Meson Resonances

Figure 63.2: Left: SU(3) couplings γ 2 for scalar (or tensor) q q̄ meson decays. The angles αand φ are defined as α = 54.7◦ + θ and φ = 54.7◦ + θP , where θ is the mixing angle of the
decaying isoscalars and θP the mixing angle in the 0−+ nonet. The partial decay width is given byΓ = C × γ 2 × |F (q)|2 × q, where C is a nonet constant, q the momentum of the decay products
and F (q) a form factor which may be taken as |F (q)|2 = q 2` × exp(−q 2 /8β 2 ) with β= 0.5 GeV/c,
and where ` is the relative angular momentum between the decay products (` = 0 for scalars and` = 2 for tensors). Right: SU(3) couplings as a function of mixing angle α for isoscalar decays forθP = −17.3◦ (from [78]).

mixing with q q̄ states. Its suppressed K K̄ decay would be due to interferences with the f0 (1370)
and f0 (1710). In the analogous mixing scheme of Ref. [56], which uses central production datafrom WA102 and the hadronic J/ψ(1S) decay data from BES [94, 95], glue is shared between thef0 (1370) (mainly nn̄), f0 (1500)(mainly glue) and f0 (1710) (dominantly ss̄). This agrees with theanalyses [78, 83]. In the mixing scheme of Ref. [96] the QCD spectral sum rule also leads to a large
gluonic component in the f0 (1500) (satisfying the observed strong ππ and f0 (500)f0 (500) → 4π
decays).
However, not everybody agrees that the strong K K̄ signal is indicative of an ss̄ structure forthe f0 (1710). The f0 (1710) could still be the glueball, since the two-gluon coupling to nn̄ appears
to be suppressed by chiral symmetry [97], thus K K̄ would be enhanced compared to ππ. It wasargued that chiral symmetry constraints in a multichannel analysis imply that the f0 (1710) is anunmixed scalar glueball [98]. However, this view is challenged in [63].
The K K̄ decay is also naturally enhanced in the extended linear sigma model with a dilaton asglueball [86] and in the holographic model of [87,99] which both prefer the f0 (1710) as the glueball.
For a scalar glueball Ref. [87] finds a strong enhancement of the decays into K K̄ and ηη, in fairly
close agreement with the measured branching ratios of the f0 (1710), while Ref. [99] predicts the(so far not measured) rate into ηη 0 to be very small.
In γγ collisions leading to KS KS [100] and K + K − [101] a spin-0 signal is observed at thef0 (1710) mass (together with a dominant spin-2 component), while the f0 (1500) is not observed inγγ → K K̄ nor π + π − [102]. The f0 (1500) is also not observed by Belle in γγ → π 0 π 0 , although ashoulder is seen which could also be due to the f0 (1370) [103]. The absence of f0 (1500) signal inthe ππ channel in γγ collisions does not favor an nn interpretation for the f0 (1500). The upper
limit for Γ2γ (< 1.4 keV) in π + π − [13]) excludes a large nn content, and hence points to a mainly
ss content [13], which contradicts the small KK decay branching ratio of the f0 (1500) [10, 21, 41].
Belle finds that in γγ → KS KS collisions the 1500 MeV region is dominated by the f20 (1525).
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63. Spectroscopy of Light Meson Resonances

The f0 (1710) is also observed with a production rate × branching ratio compatible with an ss̄
state [104]. Note, however, that the γγ couplings of glueballs are sensitive to glue mixing withq q̄ [56]. Ref. [76] predict the glueball γγ partial width in the few keV range (comparable to thatof q q̄ mesons) due to couplings of vector mesons to γ via VDM, in agreement with holographic
models [77].
Alternative assignments for the scalar glueball have been proposed: In Ref. [80] the gluonicsignal is distributed over f0 (1370), f0 (1500) and another broad isoscalar around 1530 MeV, while thegluonic contribution to the f0 (1710) is small. As mentioned already, in Ref. [69,86,87] the f0 (1710)
is the glueball state, as in Ref. [84], where the f0 (1500) is the q q̄ octet state degenerate with thea0 (1450). In the generalized linear sigma model [105] the a0 (980) is dominantly a tetraquark anda0 (1450) a q q̄ state. The f0 (980), f0 (1370) and f0 (1500) (or f0 (1710)) are dominantly tetraquark,q q̄ and glue.
In Ref. [82] the f0 (500) and f0 (1370) are signals from a single broad resonance proposed as
the scalar glueball. The ground state scalar nonet then consists of the f0 (980), a0 (980), K0∗ (1430),
f0 (1500) and f0 (1710) [31]. The f0 (980) and f0 (1500) mix (similarly to the η and η 0 in the pseudoscalar nonet), while the f0 (1500) mixes with a glueball in the 500 – 1000 MeV mass range, which
is identified as the f0 (500).
In Ref. [106], a large K + K − scalar signal reported by Belle in B decays into KK K̄ [107],
compatible with the f0 (1500), is explained as due to constructive interference of a flavor octet with abroad glueball background. However, the Belle data are inconsistent with the BaBar measurements
which show instead a broad scalar at this mass for B decays into both K ± K ± K ∓ [108] and K + K − π 0[109].
The f0 (1500) is observed by BESII in J/ψ(1S) → γππ [110] and by BESIII in J/ψ(1S) →γηη [111] with a much smaller rate than for the f0 (1710), which would speak against a glueballinterpretation of the former, although the systematic errors are large. Also, the f0 (1500) appears
at a lower mass and the f0 (1710) at a higher mass than the accepted values. However, the coupledchannel analysis of more data on radiative J/ψ(1S) decay from BESIII [57] (described in the next
paragraph) finds comparable contributions from f0 (1500) and f0 (1710) with a preference for ππdecay over K K̄ for the former and K K̄ over ππ for the latter.
The authors of Ref. [57] have analyzed the high statistics data from J/ψ(1S) radiative decays
into π 0 π 0 , KS0 KS0 , ηη and ωφ from BESIII, including data on ππ, ηη and ηη 0 from the CERN SPS,
BNL data on ππ → KS0 KS0 and p̄p annihilation data from LEAR into various final states. The
coupled channel analysis requires ten scalar mesons, the established ones in the Review and thef0 (2020, as well as the isoscalars f0 (2100, 2200, 2330) so far omitted from the Summary Table. As
a new feature, the f0 (1710) splits into two states, one at about 1700 MeV, the former f0 (1710),
and the new f0 (1770 discussed above, being mandatory to obtain a good fit. A broad (∼370
MeV) enhancement is observed in J/ψ(1S) radiative decays around 1865 MeV, attributed to thecontribution of glue distributed among the scalar mesons, with a very strong contribution fromthe 1770 MeV state [58]. In this model there are no supplementary states as the glue ‘fragments’between the various isoscalars.
Ref. [112] reports on a very recent re-analysis of the BESIII J/ψ(1S) radiative decay data intoπ 0 π 0 and KS0 KS0 . A good fit is obtained with only two scalar resonances below 2 GeV, the f0 (1500)
and f0 (1710). The latter is more strongly produced, which points to a sizeable glueball component.
63.3.2 Tensor glueballs
Above the well known f2 (1270) and f20 (1525) q q̄ mesons, the f2 (1640) and f2 (1950) are tentatively assigned to the 23 P2 nonet (see fig. 63.1). The broad f2 (1950) has been observed by several
experiments, e.g. in central production [22] and in pp annihilation in flight [17] and is often identi31st May, 2024

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63. Spectroscopy of Light Meson Resonances

fied as a glueball [113], the ground state of the pomeron [114, 115]. Three further isoscalar tensors
are established, the f2 (2010), f2 (2300) and f2 (2340), which are in the range of the 13 F2 and 33 P2
nonets. The large φφ cross section in pp just above threshold [116] could be due to the productionof the 2++ glueball, in accord with earlier observations in π − N → φφn reactions [117, 118] and incentral collisions [119].
The f2 (2010), f2 (2300) and f2 (2340) have been observed by BESIII in J/ψ(1S) → γφφ [120].
The production rate of a tensor glueball in J/ψ(1S) radiative decay has been calculated in quenchedlattice QCD to be large (around 1%) [121] and is claimed by BESIII [120] to be compatible with
their rates measured in J/ψ(1S) → f2 (2340), f2 (2340) → ηη [111], and f2 (2340) → φφ [120]. The
authors of Ref. [122] have re-analyzed the J/ψ(1S) radiative decay into π 0 π 0 and KS KS fromBESIII and found an enhancement described by a 360 MeV broad pole around 2210 MeV, possiblycomposed of the resonances observed earlier in φφ.
The relatively narrow f2 (2300) with a measured width of 149 MeV [118] is preferred by theholographic QCD model of Ref. [123]. However, the tensor glueball is predicted to be much broader(600-900 MeV) by the holographic model of Ref. [124].
There is no evidence for a narrow meson, fJ (2220) (a tensor candidate) in pp annihilation (seethe note under the fJ (2220) in the 2004 issue of the Review). The measured partial width to pp inradiative J/ψ(1S) decay [125] is too large and inconsistent with the upper limit from pp annihilation
into ππ [126].

63.4 Pseudoscalar mesons
We now deal with the first radial excitations of the 0−+ nonet (fig. 63.1). The π(1300) is avery broad resonance (200–600 MeV) decaying into 3π. The K(1460) was recently confirmed withhigh statistics data from LHCb in D0 → K3π decays [127] and has become an established kaon
excitation. The first observation of an isoscalar resonance around 1425 MeV – the E-meson – wasmade in pp annihilation at rest into E π + π − , E → KKπ [128]. This state was reported to decay
into a0 (980)π and K ∗ (892)K with roughly equal contributions. An isoscalar state, the ι meson,
was observed in radiative J/ψ(1S) decay into KKπ [129–131] and γρ [132], and was considered atthat time as a glueball candidate, owing to its strong signal in radiative J/ψ(1S) decay. The E
and ι were later assumed to be the same state, called η(1440).
The η(1295) has been observed in various production mechanisms, in π − p experiments [133–136],
and possibly in pp annihilation [137, 138]. In J/ψ(1S) radiative decay, the η(1295) signal is also
evident in the 0−+ ηππ wave of the DM2 data [139]. Also BaBar reports a signal around 1295 MeV
in B decays into ηππK [140]. We therefore assume that the η(1295) is one of the isoscalars in thisnonet.
However, two isoscalars were later observed in this mass region, the η(1405) and η(1475).
The former decays mainly into a0 (980)π (or direct KKπ) and the latter mainly into K ∗ (892)K.
The simultaneous observation of two pseudoscalars is reported in three production mechanisms:
π − p [133,141], radiative J/ψ(1S) decay [139,142], and pp annihilation at rest [143–146]. All of them
give values for the masses, widths, and decay modes that are in reasonable agreement. (However,Ref. [139] favors a state decaying into K ∗ (892)K at a lower mass than the state decaying into
a0 (980)π.) In J/ψ(1S) radiative decay, the η(1405) decays into KKπ through a0 (980)π, and hencea signal is also expected in the ηππ mass spectrum. This was indeed observed by MARK III
in ηπ + π − [147], which reported a mass of 1400 MeV, in line with the existence of the η(1405)
decaying into a0 (980)π. The η(1405) decaying into ηππ is also observed by Crystal Barrel [138].
Two states were also reported by BES: Around 1452 MeV BESII observed a K K̄π enhancement in
J/ψ(1S) → ωK K̄π but not in J/ψ(1S) → φK K̄π [148], while BESIII reported a 52 MeV broadstate in ψ(2S) → ωK ∗ K [149], both left without J P C determination.
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The KKπ and ηππ channels were studied in γγ collisions by L3 [150]. (For the 2γ couplingsof glueballs and q q̄ mesons see [76, 77, 151, 152].) The analysis led to a clear η(1475) signal in
KKπ, decaying into K ∗ K, well identified in the untagged data sample, where spin 1 resonances
are not allowed. At the same time, L3 did not observe the η(1405), neither in KKπ nor inηππ [150]. On the other hand, CLEO-II did not observe any pseudoscalar signal with tagged
γ’s in γγ → η(1475) → KS0 K ± π ∓ [153], with an upper limit slightly smaller than the signal
observed by L3. After the CLEO-II result, L3 performed a further analysis with full statistics [154],
confirming their previous evidence for the η(1475). The CLEO upper limit [153] for Γγγ , and theL3 results [154], are consistent with the world average for the η(1475) width. BaBar [140] also
reported the η(1475) in B decays into K K̄ ∗ recoiling against a K, while upper limits only were
given for the η(1405).
Hence, in radiative J/ψ(1S) decay, π − p and pp annihilation at rest two isoscalar signals areobserved in the 1400 – 1500 MeV mass region, while the η(1405) is not seen in γγ interactions nor in
B decays. The η(1475) could be the first radial excitation of the η 0 , with the η(1295) being the firstradial excitation of the η. Ideal mixing, suggested by the η(1295) and π(1300) mass degeneracy,
would then imply that the second isoscalar in the nonet is mainly ss, and hence couples to K ∗ K,
in agreement with properties of the η(1475). Also, its width agrees with the expected one for theradially excited ss state [85, 91]. A study of radial excitations of pseudoscalar mesons [155] alsofavors the ss̄ interpretation of the η(1475). However, due to the strong kinematical suppression inη(1405) → K ∗ K the data are not sufficient to exclude a sizeable ss̄ admixture also in the η(1405).
The supernumerary isoscalar η(1405) would be a candidate for the 0−+ glueball in the fluxtube
model [156], in which the 0++ glueball is also naturally related to a 0−+ glueball with mass degeneracy broken in QCD. However, this scenario is not favored by lattice gauge theories which predictthe 0−+ state above 2 GeV [70, 157] (see ‘Quark model’ in this issue of the Review). Nevertheless,the pseudoscalar glueball could lie at a lower mass than predicted from lattice calculation [158], seealso Refs. [159–161]. The holographic model of Ref. [77] predicts the pseudoscalar glueball below
2600 MeV, decaying dominantly into two vector mesons. A detailed review of the experimental
situation on the pseudoscalar glueball is available in Ref. [162].
Here also, there are alternative explanations. The mere existence of the η(1295) is questioned inRefs. [3, 163], in which the authors also propose a single pseudoscalar meson at 1440 MeV, the firstradial excitation of the η. According to Ref. [3] the splitting of the 1440 MeV state into η(1405)
and η(1475) is due to nodes in the decay amplitudes, which differ in ηππ and K ∗ (892)K. The
splitting could also be due to a triangle singularity, hence the manifestation of one state only (fig.
63.3) [164–166]. The importance of the triangle singularity for the η(1295) and η(1405/1475) inthe ηππ and K K̄π channels is stressed in Ref. [167].
In Ref. [168], using the triangle singularity approach of [164], the authors conclude that the
BESIII results can be reproduced either with the η(1405) or the η(1475), or by a mixture ofthese two states. From a high statistics data sample in J/ψ(1S) → γKS KS π 0 BESIII reports theobservation of both η(1405) and η(1475) [169]. A one resonance parametrization is ruled out andtriangle singularity models do not describe the data satisfactorily. This radiative decay channel
has been studied in a three-body unitary coupled-channel analysis and compared to the BESIII
data, including ratios of radiative branching ratios into ηπ + π − and K K̄π through the η(1405/1475)
intermediate states [170]. Two poles emerge for K ∗ K̄ in different Riemann sheets around 1400 MeV
and only one pole around 1500 MeV.
To summarise this section, the experimental data on the 1400 — 1500 MeV region span several
decades, various production mechanisms and decay modes, with models for data analysis evolving
with time. A comprehensive coherent picture of all available data is therefore difficult. We believethat there is sufficient evidence to consider the 0−+ nonet with the η(1440) in fig. 63.1 as established.
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63. Spectroscopy of Light Meson Resonances

Whether one or two different states – η(1405) and η(1475) – exist is an open question, in which casethe η(1405) would be supernumerary. The most recent high statistics data and their theoreticalinterpretation seem to favor the two-resonance scenario.

Figure 63.3: Triangle singularity: a state A decays into K ∗ K. The K from K ∗ decay catches up
with the K and excites the a0 (980) resonance which in turn decays into ηπ. This mechanism canlead to two distinct peaks (depending on the width of A), one in K ∗ K and the other via rescatteringin ηππ. Similarly, the virtual K ∗ K loop can couple to f0 (980) which, decaying into ππ, leads to apeak in the 3π final state.

63.5 Vector mesons
In this section we restrict ourselves to the more interesting isovector spectrum which contains
broad and overlapping states.
63.5.1 The ρ(770) meson
The determination of the parameters of the ρ(770) is beset with many difficulties because of its
large width. The line shape depends on the production process and is not described by a relativistic
Breit-Wigner function with a P -wave width, but requires some additional shape parameter. Thisdependence on parameterization was demonstrated long ago [171]. Bose-Einstein correlations areanother source of shifts in the ρ(770) line shape, particularly in multiparticle final-state systems[172].
The same model dependence afflicts any other source of resonance parameters, such as theenergy dependence of the phase shift δ11 , or the pole position. It is, therefore, not surprising thata study of ρ(770) dominance in the decays of the η and η 0 reveals the need for specific dynamical
effects, in addition to the ρ(770) pole [173, 174].
The cleanest determination of the ρ(770) mass and width comes from e+ e− annihilation andτ -lepton decays. ALEPH data [175] showed that the charged ρ(770) parameters measured fromτ -lepton decays are consistent with those of the neutral one determined from e+ e− data [176]. Thisconclusion is qualitatively supported by the later studies of CLEO [177] and Belle [178]. However,a comparison of the two-pion mass spectrum in τ decays from OPAL [179], CLEO [177], and
ALEPH [180, 181], and the e+ e− → π + π − cross section from CMD-2 [182, 183], showed significant
discrepancies between the two shapes which can be as high as 10% above the ρ meson mass [184,185].
This discrepancy remains after measurements of the two-pion cross section in e+ e− annihilation
at KLOE [186–189], SND [190, 191], BaBar [192] and, more recently BESIII [193]. The effectis not accounted for by isospin breaking [194–197], but the accuracy of its calculation may beoverestimated [198, 199].
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63. Spectroscopy of Light Meson Resonances

Two recent measurements of the e+ e− → π + π − cross section by SND [200] and CMD-3 [201,202]
show discrepancies in the ρ region: while SND is consistent with previous e+ e− experiments,
CMD-3 finds differences as high as 5% around the ρ meson mass. In addition, in the fit of thee+ e− → π + π − cross section CMD-3 reports values for the mass of the ω and the mass and widthof the φ, which differ slightly from the PDG values, showing for the first time the effect of the
φ → π + π − interference.
The problem of the difference in the π + π − shapes between e+ e− and τ decays seems to besolved after a recent analysis by [203], which showed that, after correcting the τ data for the
missing ρ−γ mixing contribution, besides the other known isospin symmetry violating corrections,the ππ isospin 1 part of the hadronic vacuum polarization contribution to the muon g − 2 is fullycompatible between τ -based and e+ e− -based evaluations. The global fit of the whole set of the ρ, ω,and φ decays, taking into account mixing effects in the hidden local symmetry model, also showed
consistency of the two-pion data in τ decay and e+ e− annihilation [204, 205]. However, becauseof the progress in e+ e− data, the τ input is now less precise and less reliable due to additional
theoretical uncertainties [206] decreasing the importance of τ decay for the determination of theρ(770) parameters.
63.5.2 The ρ(770) excitations
In our 1988 edition, we replaced the ρ(1600) entry with two new ones, the ρ(1450) and theρ(1700), because there was emerging evidence that the 1600-MeV region actually contains two ρlike resonances. This possibility was pointed out by a theoretical analysis [207] on the consistencyof the 2π and 4π electromagnetic form factors and the ππ scattering length. A consistent picture ofe+ e− → 2π, 4π and diffractive photoproduction is obtained with two resonances [208]. The existenceof the ρ(1450) was supported by the analysis of ηρ0 mass spectra obtained in photoproduction ande+ e− annihilation [209], as well as that of e+ e− → ωπ [210].
The analysis of [208] was further extended by [211, 212] to include new data on 4π-systems
produced in e+ e− annihilation, and in τ decays (τ → 4π and e+ e− → 4π are related by theConserved Vector Current hypthesis). These systems were successfully analyzed using interfering
contributions from two ρ-like states, and from the tail of the ρ(770) two-body decay. While specificconclusions on ρ(1450) → 4π were obtained, little could be said about the ρ(1700). Independent
evidence for two 1− states is provided by [213] in 4π electroproduction at hQ2 i = 1 (GeV/c)2 , andby [214] in a high-statistics sample of the ηππ system in π − p charge exchange.
This scenario with two overlapping resonances is supported by other data. DM2 [215] measured
the pion form factor in the interval 1.35–2.4 GeV, and observed a deep minimum around 1.6 GeV.
The best fit was obtained with the hypothesis of ρ-like resonances at 1420 and 1770 MeV, withwidths of about 250 MeV. DM2 [216] found that the e+ e− → η π + π − cross section is better fittedwith two fully interfering Breit-Wigners, with parameters in fair agreement with those of [208]and [215]. These results can be considered as a confirmation of the ρ(1450).
Decisive evidence for the ππ decay mode of both ρ(1450) and ρ(1700) comes from pp annihilation
at rest [217]. It has been shown that these resonances possess a KK decay mode [10, 218, 219].
This decay mode has also been studied in three-body hadronic B decays [220]. High-statistics
studies of the decays τ → ππντ [175, 177], and τ → 4πντ [221] also require the ρ(1450), but are notsensitive to the ρ(1700), being too close to the τ mass. A recent very-high-statistics study of theτ → ππντ from Belle [178] reports the first observation of both ρ(1450) and ρ(1700) in τ decays.
A clear picture of the two π + π − resonances interfering with the ρ(770) in e+ e− annihilation was
also reported by BaBar using the ISR (Initial State Radiation) method [222], and more recently by
CMD-3 [201].
The structure of these ρ states is not yet completely clear. The authors of Refs. [85, 223] claim
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63. Spectroscopy of Light Meson Resonancesthat ρ(1450) has a mass consistent with radial 2S, but its decays show characteristics of hybrids,
and suggest that this state may be a 2S-hybrid mixture. Hybrid states could have a 4π decay
mode dominated by the a1 π [224]. Such behavior has been observed by [225] in e+ e− → 4π in theenergy range 1.05–1.38 GeV, and by [221] in τ → 4π decays. CLEO [226] and Belle [227] observethe ρ(1450) → ωπ decay mode in B-meson decays, however, do not find ρ(1700) → ωπ 0 . A similar
conclusion is made in Refs. [228, 229], which studied the process e+ e− → ωπ 0 and do not observe a
statistically significant signal of the ρ(1700). Various decay modes of the ρ(1450) and ρ(1700) are
observed in pn and pp annihilation [230, 231], but no definite conclusions can be drawn. More data
should be collected to clarify the nature of the ρ states, particularly in the energy range above 1.6
GeV.
We now list under a separate entry the ρ(1570), the φπ state with J P C = 1−− earlier observedin [232] – referred to as C(1480) – also reported in [233] and possibly seen in [234]. While thismay be due to a threshold effect [235], Refs. [211] and [236] suggest two independent vector stateswith this decay mode. The C(1480) has not been seen in pp [237] nor in other e+ e− [238, 239]
experiments. However, the sensitivity of the two latter is an order of magnitude lower than that ofRef. [234] which cannot exclude that the observation is due to an OZI-suppressed decay mode ofthe ρ(1700).
Several observations on the ωπ system in the 1200 MeV region [240–246] may be interpreted
in terms of either J P = 1− ρ(770) → ωπ production [247], or J P = 1+ b1 (1235) production[245, 246]. The LASS amplitude analysis [248] showing evidence for ρ(1270) is preliminary andneeds confirmation. Evidence for a ρ(1250) from a reanalysis of elastic scattering data is claimed
in Ref. [249].
Ref. [250] reported a very broad 1−− resonance-like K + K − state in J/ψ → K + K − π 0 decays.
Its pole position corresponds to mass of 1576 MeV and width of 818 MeV. Its exotic structure(molecular or multiquark) is suggested [251–253], while in Refs. [254] and [255] this is explained by
the interference between the ρ(1450) and ρ(1700). The latter statement is qualitatively supported
by BaBar [256] and SND [257]. We quote the state reported by [250] as X(1575) in the section“Further States.” Another state observed in J/ψ → K + K − π 0 is the φ(2170) [258] which has beeninterpreted as exotic, e.g. as tetraquark, see section 63.8.
Evidence for ρ-like mesons decaying into 6π was first noted by [259] in the analysis of e+ e− → 6π
[260,261] and diffractive photoproduction [262]. The authors of Ref. [259] argued that two states atabout 2.1 and 1.8 GeV exist: while the former is a candidate for the ρ(2150), the latter could be amanifestation of the ρ(1700) distorted by threshold effects. BaBar reported observations of the new
decay modes of the ρ(2150) in the channels η 0 (958)π + π − , f1 (1285)π + π − [263] and π + π − [264]. The
decay of the ρ(2150) into K + K − has been observed by BESIII [265] and confirmed by BaBar [266].
The relativistic quark model [267] predicts the 23 D1 state with J P C = 1−− at 2.15 GeV which canbe identified with the ρ(2150).
Under ρ(1900) we list various observations of irregular behavior of the cross sections near the
N N̄ threshold. Dips of various width around 1.9 GeV were reported by the E687 Collaboration(a narrow one in the 3π + 3π − diffractive photoproduction [268, 269]), by the FENICE experimentreporting a narrow dip [270], by BaBar in ISR (a narrow structure in e+ e− → φπ final state [234],
but much broader in e+ e− → 3π + 3π − and e+ e− → 2(π + π − π 0 ) [271]), by CMD-3 (also a rather
broad dip in e+ e− → 3π + 3π − [272]). A dedicated scan of the N N̄ -threshold region by CMD-3
confirms this effect in the e+ e− → 3π + 3π − and e+ e− → K + K − π + π − final states, but does notsee it in the cross section of e+ e− → 2π + 2π − [273]. Most probably, these structures emerge asa threshold effect due to the opening of the N N̄ channel [274–276]. A similar enhancement isobserved by BESIII in e+ e− → ΛΛ̄ near the ΛΛ̄ threshold [277, 278] which can be described as ΛΛ̄final state interaction [279].
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63. Spectroscopy of Light Meson Resonances

63.6 Axial-vector mesons
The J P C = 1++ nonet consists of the isovector a1 (1260), the isoscalars f1 (1285) and f1 (1420),
and the K1A , which is a superposition of the physical states K1 (1270) and K1 (1400) with a mixing
angle of about 35◦ [280]. The nonet mixing angle θ1++ is around 23◦ . The orthogonal combination– the K1B – belongs to the 1+− nonet with a mixing angle θ1+− of about 28◦ [280]. f1 (1510).
However, a two-pole structure for the K1 (1270) emerges when using the unitary extension of chiralperturbation theory [281].
The mass region above 1400 MeV is rather complex [282–284]. The f1 (1420) was first reported
in π − p reactions at 4 GeV/c, decaying into K ∗ K [285]. The f1 (1420) → KKπ was also observedin a reanalysis of the MARK III data [142], and a C=+1 state seen in tagged γγ collisions [286].
Axial-vector mesons are not observed in pp annihilation at rest in liquid hydrogen, which proceeds
dominantly through S-wave annihilation. However, in gaseous hydrogen, P -wave annihilation isenhanced and the f1 (1420) is indeed observed, decaying into K ∗ K [144]. The f1 (1420), decaying
into KKπ, is also seen in pp central production, together with the f1 (1285). The latter decays
via a0 (980)π, and the former only via K ∗ K. The KS0 KS0 π 0 decay mode of the f1 (1420) establishes
unambiguously C=+1. Neither central production [287] nor π − p interactions at 100 GeV [135] findany evidence for a ηππ decay mode of the f1 (1420).
The f1 (1285) has been suggested to be a K ∗ K molecule [288]. However, LHCb has determinedthe 1++ nonet mixing angle to be consistent with a mostly nn̄ structure for the f1 (1285) from
00
B /B → J/ψ(1S)f1 (1285), independent of the identity of its isoscalar partner [289]. The mixing
00angle θ1++ = 24◦ agrees with that of Ref. [280] quoted above. The ratio of B /B s decay rates
also excludes the tetraquark interpretation of the f1 (1285) [289]. This is consistent with earlier
determinations assuming that the f1 (1420) is the other isoscalar in the nonet [290].
The resonance candidate a1 (1420) decaying into 3π, reported earlier by COMPASS at 1420 MeV
in π − p → π − π − π + p [291, 292], appears to originate from a triangle singularity: the decay of thea1 (1260) into K ∗ (→ Kπ)K̄ is followed by rescattering into the f0 (980)π channel, f0 (980) → ππ [293](see the caption of fig. 63.3). A similar triangle singularity is proposed for the f1 (1420), resulting
from the K ∗ K and a0 (980)π decay modes of the f1 (1285) [294]. The f1 (1420) was also suggested to
be a hybrid qqg meson [295] or a K ∗ K molecule, due to the proximity of the K ∗ K threshold [296].
The f1 (1420) is not seen in the K − p data [297], which would argue against this state being the ss
member of the 1++ nonet. Note, however, that Ref. [298] reports a signal from f1 (1420) in K − p,but not in π − p.
The ss̄ partner of the f1 (1285) could also be the (not well established) f1 (1510) [299]. This state
was seen to decay into K K̄π in K − p interactions at 4 and 11 GeV/c, recoiling against a Λ [297,300],
which indeed points to an ss̄ state. Evidence was reported in π − p interactions, based on the phasemotion of the 1++ K ∗ K wave [284]. The f1 (1510) is also needed by CMD-3 in e+ e− → f1 ρ(770),
together with the f1 (1285) and f1 (1420) peaks, to describe the shoulder in the KS K ± π ∓ massaround 1500 MeV [301]. A somewhat broader 1++ signal is observed in J/ψ(1S) → γηπ + π − [302]and a small signal in J/ψ(1S) → γη 0 π + π − [303].
However, there is no evidence for the f1 (1510) in other K − p experiments [298,304]. The f1 (1510)
is not seen in central collisions [305], nor in γγ collisions [306], although surprisingly for an assumed
ss̄ meson, a signal is reported in 4π decays [307]. Given this confusing experimental situation, themeson classification in the 1++ nonet is not entirely settled.

63.7 Hybrid mesons
Hybrids may be viewed as qq mesons with a vibrating gluon flux tube. In contrast to glueballs,
they can have isospin 0 or 1 and be electrically charged. The mass spectrum of hybrids withexotic (non-qq) quantum numbers was predicted in Ref. [308], while Ref. [309] also deals with non31st May, 2024

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63. Spectroscopy of Light Meson Resonances

exotic quantum numbers. The ground-state hybrids with quantum numbers (0−+ , 1−+ , 1−− , and2−+ ) are expected around 1.7 to 1.9 GeV. Lattice calculations predict that the hybrid with exotic
quantum numbers 1−+ lies at a mass of 1.9 ± 0.2 GeV [310, 311]. Most hybrids are expected to berather broad, but some can be as narrow as 100 MeV [312]. They prefer to decay into a pair of Sand P -wave mesons. The lattice study in [313, 314], based on full QCD with pion masses around
400 MeV, finds that several of the high-lying states observed in their spectrum show significant
overlap with gluon rich source terms interpreted as hybrid states. A very broad 1−+ structure ispredicted by a recent lattice calculation [315]. The main decay mode is b1 (1235)π (a pair of S- andP -wave mesons), while other modes, such as ρπ, ηπ and η 0 π, are suppressed by at least an order ofmagnitude. For an experimental and theoretical review on hybrid mesons see [4, 316].
Two isovector 1−+ candidates have been reported, one around 1400 MeV (the π1 (1400) in
previous versions on this Review) and the π1 (1600). The ∼350–400 MeV broad π1 (1400), wasreported in π − p → ηπ − p [317, 318] and in π − p → ηπ 0 n [319]. It was observed as an interference
between the angular momentum L = 1 and L = 2 ηπ amplitudes, leading to a forward/backward
asymmetry in the ηπ angular distribution. This state had been reported earlier in π − p reactions[320], but ambiguous solutions in the partial wave analysis were pointed out [321,322]. A resonating
1−+ contribution to the ηπ P -wave is also required in the Dalitz plot analysis of pn annihilation
into π − π 0 η [323], and in pp annihilation into π 0 π 0 η [324]. Mass and width are consistent with theresults of Ref. [317]. A coupled channel re-analysis of the π 0 π 0 η, π 0 ηη and K + K − π 0 Crystal Barrel
data at 900 MeV/c, supplemented with data from other collaboration in ππ → ππ, K K̄, ηη and ηη 0 ,leads to a single 1−+ ∼600 MeV broad state with a pole around 1400 MeV, decaying into ηπ 0 [16].
Ref. [325] suggested for the production in π − p that a Deck-generated ηπ background from final
state rescattering in π1 (1600) decay could mimic π1 (1400), a mechanism that is, however, absent
in pp annihilation.
The π1 (1600), decaying into ρπ, was reported by COMPASS with 190 GeV pions hitting a leadtarget [326, 327]. It had already been observed in π − p interactions in the decay modes η 0 π [328],
f1 (1285)π [329], and ωππ [330], b1 (1235)π, but not ηπ [331]. A strong enhancement in the 1−+ η 0 π
wave, compared to ηπ, was reported at this mass in [332]. The enhancement is also observed by
COMPASS in π − p → η 0 π but in ηπ a peak appears at 1400 MeV and in η 0 π at 1600 MeV [333].
A coupled channel analysis of the ηπ and η 0 π COMPASS data leads to a single pole at 1564 ± 89
MeV, with a width of 492 ± 115 MeV [334]. The predicted width from the lattice calculation [315]is compatible with the COMPASS result. Furthermore, a combined analysis of the COMPASS
and Crystal Barrel data at 900 MeV/c leads to similar results, a single pole around 1623 MeV,
with a width of about 455 MeV, although a two-pole scenario cannot be completely excluded [335].
Accordingly, in the current review we have moved the former π1 (1400) data into the π1 (1600)
section.
Very recently, BESIII reported a 188 MeV broad enhancement at 1855 MeV in J/ψ(1S) radiative
decay into the ηη 0 P-wave [336], hence with exotic quantum numbers 1−+ . This isoscalar resonanceis needed with very high significance, albeit the contribution to γηη 0 is weak and several otherisoscalars expected to contribute are absent [337]. Hence this state needs confirmation. In thepast there had been claims for such a state decaying into ηη 0 in this mass range, which we havelisted under the f2 (1910) (see e.g. Ref. [26] from WA102 central production, suggesting 1−+ asan alternative to 2++ ). If confirmed, the η(1855) could be one of the isospin 0 partners of theπ1 (1600), a member of the 1−+ hybrid nonet [338–340] or a K K̄1 (1400) molecule [341].
Hybrid candidates with the non-exotic quantum numbers 0−+ , 1−− , and 2−+ have also beenreported: the π(1800) is somewhat narrow if interpreted as the second radial excitation of thepion. It decays mostly into a pair of S- and P -wave mesons [342, 343], in line with expectations for
0−+ hybrid mesons. The evidence for 1−− hybrids in e+ e− annihilation and in τ decays has been
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63. Spectroscopy of Light Meson Resonances

discussed in [224]. The near degeneracy of the η2 (1645) and π2 (1670) suggests ideal mixing in the
2−+ qq nonet, and hence, the second isoscalar, presumably the η2 (1870), should be mainly ss (fig.
63.1). However, the η2 (1870) is also observed in pp annihilation and decays mainly into a2 (1320)πand f2 (1270)π [344], with a relative rate compatible with a hybrid state [309].
Evidence for another exotic π1 (2015) has been claimed in π − p interactions [329, 330]. A flavor
multiplet of vector hybrids between 2200 and 2300 MeV is predicted by the constituent gluon
model [340].
Summarizing, there is evidence for a very broad 1−+ enhancement in the 1400–1600 MeV region,
which consists in one (or pssibly two) exotic states, the lowest mass one favored by p̄p annihilation
data, the highest one by high energy π − p data. As isovectors, these states cannot be glueballs.
The coupling to ηπ of the lighter one points to a four-quark state [345], while the η 0 π coupling of
the heavier one is favored for hybrid states [346, 347]. The mass of the latter, the π1 (1600), is not
far below the lattice and flux tube model predictions. The η1 (1855) is an isoscalar candidate forthe ground state 1−+ hybrid nonet.

63.8 Tetraquark states
The existence of multiquark states was suggested a long time ago, based on duality arguments[348, 349]. The most prominent light tetraquark candidates are the a0 (980) and f0 (980) [350–352].
A remarkable prediction for the existence of low-lying four quarks states is based on color hyperfine
splitting. The lowest ground state (L = 0) tetraquark multiplet is predicted to be a scalar nonet.
The scalar nonet lies just below 1 GeV when one assumes as mass scale the hyperfine color splitting
between the ρ and the π (for a simple derivation see [8]). One then gets the nonet structures¯ √1 |(uū − dd)ss̄i,¯|a0 (980)i = |usds̄i,|ūs̄dsi,
21¯|f0 (980)i = √ |(uū + dd)ss̄i,2¯|f0 (500)i = |ūdudi,¯¯¯|K0∗ (700)i = |s̄dudi,|s̄ūudi and |ūdusi,|ūddsi.

(63.1)The two isoscalars are expected to mix with the angle ϕ:|f0 (980)i = cos ϕ|ss̄i + sin ϕ|nn̄i,|f0 (500)i = − sin ϕ|ss̄i + cos ϕ|nn̄i.

(63.2)

Table 63.1:
Coupling amplitudes for B̄ 0 and B̄s0 decays intoJ/ψ(1S)f0 (500)/f0 (980), depending on the q q̄ or tetraquark structures ofthe f0 (500) and f0 (980) (from [353] where illustrative decay diagrams canbe found). The angle ϕ is defined in Eq. 63.2.
B̄ 0
f0 (980)
f0 (500)q q̄
qq q̄ q̄√sin ϕ/√2
1/ 2√
cos ϕ/ 2
1

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f0 (980) f0 (500)
cos
√ϕ
2

sin ϕ
0

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63. Spectroscopy of Light Meson Resonances

Whether these mesons are really tetraquark states or q q̄ mesons, is still an open issue. The
f0 (980) is strongly produced in Ds+ decay [354], which suggests a large ss component, due to the
Cabibbo-favored c → s coupling. However, the mainly nn̄ f0 (1370) is also strongly produced in
Ds+ decay, hence additional graphs must contribute [355].
The relative branching ratios for B̄ 0 and B̄s0 → J/ψ(1S)f0 (500) and J/ψ(1S)f0 (980) can be used
to probe the q q̄ or tetraquark natures of the f0 (500) and f0 (980), as proposed in Refs. [353, 356].
LHCb observes the f0 (980) in B̄s0 decays, but not the f0 (500) [28], as would be expected fortetraquarks (see Table 63.1). In contrast, LHCb also observes the f0 (500) in B̄ 0 decays, but not
the f0 (980) with an upper limit eight standard deviations below the predicted value for a tetraquark
state [29]. However, these contradicting findings have been challenged by a dispersive analysis [357],
using a model independent inclusion of hadronic final state interactions, in which a substantial
f0 (980) contribution is nevertheless found in B̄ 0 -decays, thus still leaving the tetraquark structure
as an open possibility. The ALICE collaboration reports a much stronger KS KS femtoscopic
correlation than for KS K ± in high energy pp collisions, indicative of the a0 (980) being a tetraquark
state [358].
The f0 (980) and a0 (980) could also be KK molecular states [359–361], being close to the KK
threshold and decaying strongly into KK. For qq states, the expected γγ widths [362, 363] arenot significantly larger than for molecular states [362, 364] and both predictions are consistent
with data. Radiative decay of the φ(1020) into a0 (980) and f0 (980) were proposed to disentangle
compact (tetraquark) structures from hadronic molecules. Following Refs. [365, 366] the data fromKLOE [367, 368], CMD-2 [369] and SND [370] seem to favor these mesons to be tetraquark states.
This is also supported by a BESIII analysis of J/ψ(1S) → γπ 0 π 0 data [371] and by a measurementof a0 (980) − f0 (980) mixing at BESIII [372]. In Ref. [43] these states are made of four-quark
cores and virtual K K̄ clouds at the periphery, a view that is challenged in Ref. [373] showing thatradiative φ decay data are consistent with molecular structures of light scalars.
As mentioned already, the f0 (1500) [45] and the f1 (1285) [353] have been proposed as tetraquarks,
the latter also as K ∗ K molecule [288], together with the f1 (1420) [296].
Another potential candidate for a tetraquark is the φ(2170). As an excited q q̄ state of theφ(1020), this meson should decay strongly into K + K − and KS0 KL0 , and also K ∗ K̄ ∗ . However,these decays are not observed. Hence, based on its observed decay into f0 (980)φ(1020) this meson
could be sss̄s̄ [374], where relative decay rates into various channels are predicted for both q q̄ andtetraquark structures of the f0 (980). However Refs. [375, 376] claim that the φ(2170) may not bea good candidate for the sss̄s̄ state, but could qualify as an sus̄ū tetraquark [376].
More information on the a0 (980), f0 (980), f0 (500) and K0∗ (700) is provided by ‘Scalar Mesons
below 1 GeV’ in the Review.

63.9 Baryonia
Nucleon-antinucleon (N N̄ ) bound states and resonances (baryonium) were predicted a long timeago [377, 378], based on the strongly attractive N N̄ meson exchange potential, which is obtained
from the N N one by multiplying with the G-parity of the exchanged meson. Several candidates
had been reported in the seventies by experiments at CERN, BNL and KEK, some of them being
indisputably statistically significant (for details on the model and on experiments, see [379,380] andreferences therein). Most potential models predict a sequence of deeply bound isoscalar baryonia
with quantum numbers J P C = 2++ , 1−− and 0++ , the latter being the mostly bound [381, 382].
The f2 (1565) which is observed in pp annihilation only [383, 384], is a good candidate for the 2++p̄p bound state.
Enhancements close to the p̄p threshold have also been reported in B decays [385–387]. The
strong signal in J/ψ(1S) → γ p̄p [388–390] could be due to a 0−+ baryonium [391], but could also
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63. Spectroscopy of Light Meson Resonances

be generated by the N N̄ final state interaction [392–395]. The strong energy dependence of thecross section in e+ e− → p̄p [396, 397] and p̄p → e+ e− [398] is attributed to the N N̄ final stateinteraction [399] (see also our comments on the ρ(1900) at the end of section 63.5.2). Alternative
explanations to baryonia have been proposed for the signals in B → p̄pK, such as the dynamics ofthe fragmentation mechanism [386].

63.10 Conclusions
The ground state nonets 11 S0 , 13 S1 , 11 P1 , 13 P2 , 11 D2 and 13 D3 (see fig. 63.1) are established(although more data are desirable for the h1 (1415) in the 11 P1 nonet). There are uncertainties andambiguities in all other nonets. In the pseudoscalar sector the η(1440) consists of two states, one
at 1405 MeV, the other at 1475 MeV, which could also be the manifestation of a single resonancedecaying into two different final states. In this case the 1475 one could be the radial excitation ofthe η 0 and the 1405 the pseudoscalar ground state glueball predicted a long time ago by the bag
model, although the lattice puts it above 2 GeV. In the 1++ nonet two isoscalars – the f1 (1420)
and f1 (1510) – compete for the ss̄ slot. The first radial excitation 23 S1 is complete, but questions
have been raised as to the nature of the ρ(1450) and its relation to the ρ(1700). The classificationof scalar mesons is not settled, with the ones below 1 GeV being tetraquark states or building the
ground state nonet. The nature of the scalars in the 1.5 – 1.8 GeV region is unclear, obscured by
the interference with the ground state scalar glueball predicted in this mass region. For example,
the f0 (1500) and the f0 (1710) could be q q̄ states (nn̄ and ss̄, respectively) or made of gluons mixed
with q q̄. The f0 (1500), or alternatively the f0 (1710), have been proposed as mostly gluonic. Scalarmesons above the f0 (1710) need experimental confirmation. Another pair of scalars, a0 (1710) andf0 (1770), has been reported. An isovector meson with exotic (1−+ ) quantum numbers, π1 (1600),
is observed around 1.6 GeV with mass not far below theoretical predictions, although a further
1−+ state, decaying into ηπ, cannot be entirely excluded around 1.4 GeV. An isoscalar partner,the η1 (1855), has been reported. Above 1.8 GeV mesons are broad and overlap, which complicatesthe data analyses. This makes the classification difficult, in particular the identification of the 2++
glueball, expected in 2200 – 2300 MeV mass range.
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