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THE η(1405), η(1475), f1(1420), AND f1(1510)Revised November 2013 by C. Amsler (Bern) and A. Masoni(INFN Cagliari).
The first observation of the η(1440) was made in pp anni- hilation at rest into η(1440)π+π−, η(1440) → KKπ [1]. Thisstate was reported to decay through a0(980)π and K∗(892)Kwith roughly equal contributions. The η(1440) was also ob-served in radiative J/ψ(1S) decay into KKπ [2–4] and γρ [5].
There is evidence for the existence of two pseudoscalars inthis mass region, the η(1405) and η(1475). The former decaysmainly through a0(980)π (or direct KKπ) and the latter mainlyto K∗(892)K.
The simultaneous observation of two pseudoscalars is re- ported in three production mechanisms: π−p [6,7]; J/ψ(1S) decay [8,9]; and pp annihilation at rest [10–13]. Allof them give values for the masses, widths, and decay modesin reasonable agreement. However, Ref. 9 favors a state decay-ing into K∗(892)K at a lower mass than the state decayinginto a0(980)π. In J/ψ(1S) radiative decay, the η(1405) decaysinto KKπ through a0(980)π, and hence a signal is also ex-pected in the ηππ mass spectrum. This was indeed observed byMARK III in ηπ+π− [14], which reports a mass of 1400 MeV,in line with the existence of the η(1405) decaying into a0(980)π.
BES [15] reports an enhancement in K+K−π0 around 1.44 GeV in J/ψ(1S) decay, recoiling against an ω (but not a φ)without resolving the presence of two states nor performing aspin-parity analysis, due to low statistics. This state could alsobe the f1(1420) (see below). On the other hand, BES observesη(1405) → ηππ in J/ψ(1S) decay, recoiling against an ω [16].
The η(1405) is also observed in pp annihilation at rest into ηπ+π−π0π0, where it decays into ηππ [17]. The intermedi-ate a0(980)π accounts for roughly half of the ηππ signal, inagreement with MARK III [14] and DM2 [4].
However, the issue remains controversial as to whether two pseudoscalar mesons really exist. According to Ref. 18 thesplitting of a single state could be due to nodes in the decayamplitudes which differ in ηππ and K∗(892)K. Based on theisospin violating decay J/ψ(1S) → γ3π observed by BES [19] CITATION: J. Beringer et al. (Particle Data Group), PR D86, 010001 (2012) and 2013 update for the 2014 edition (URL: the splitting could also be due to a triangular singularity mixingηππ and K∗(892)K [20–21]. However, in a further paper [22],using the approach of [20], the authors concluded that theBES results can be reproduced either with the η(1405) or theη(1475)or by a mixture of the two states.
The η(1295) has been observed by four π−p experiments [7,23–25], and evidence is reported in pp annihilation [26–28].
In J/ψ(1S) radiative decay, an η(1295) signal is evident in the0−+ ηππ wave of the DM2 data [9]. Also BaBar [29] reportsevidence for a signal around 1295 MeV in B decays into ηππK.
However, the existence of the η(1295) is questioned in Refs.
[18] and [30]. The authors claim a single pseudoscalar mesonin the 1400 MeV region. This conclusion is based on propertiesof the wave functions in the 3P0 model (and on an unpublishedanalysis of the annihilation ¯ around 1400 MeV is then attributed to the first radial excitationof the η.
Assuming establishment of the η(1295), the η(1475) could be the first radial excitation of the η′, with the η(1295) beingthe first radial excitation of the η. Ideal mixing, suggestedby the η(1295) and π(1300) mass degeneracy, would thenimply that the second isoscalar in the nonet is mainly ss, andhence couples to K∗K, in agreement with properties of theη(1475). Also, its width matches the expected width for theradially excited ss state [31,32]. A study of radial excitationsof pseudoscalar mesons [33] favors the s¯ η(1475). However, due to the strong kinematical suppressionthe data are not sufficient to exclude a sizeable s¯ The KKπ and ηππ channels were studied in γγ collisions by L3 [34]. The analysis led to a clear η(1475) signal in KKπ,decaying into K∗K, very well identified in the untagged datasample, where contamination from spin 1 resonances is notallowed. At the same time, L3 [34] did not observe the η(1405),neither in KKπ nor in ηππ. The observation of the η(1475),combined with the absence of an η(1405) signal, strengthensthe two-resonances hypothesis. Since gluonium production ispresumably suppressed in γγ collisions, the L3 results [34] suggest that η(1405) has a large gluonic content (see also Refs.
[35] and [36]) .
The L3 result is somewhat in disagreement with that of CLEO-II, which did not observe any pseudoscalar signal inγγ → η(1475) → K0K±π∓ [37]. However, more data are required. Moreover, after the CLEO-II result, L3 performeda further analysis with full statistics [38], previous evidence for the η(1475). The CLEO upper limit [37]for Γγγ(η(1475)), and the L3 results [38], are consistent withthe world average for the η(1475) width.
[29] also reports the η(1475) in B decays into K∗ recoiling against a K, but upper limits only are given for the η(1405). As mentioned above, in B decays into ηππK theη(1295) → ηππ is observed while only upper limits are givenfor the η(1405). The f1(1420) (and the f1(1285)) are not seen.
The gluonium interpretation for the η(1405) is not favored by lattice gauge theories which predict the 0−+ state above2 GeV [39,40] (see also the article on the “Quark model” inthis issue of the Review). However, the η(1405) is an excellentcandidate for the 0−+ glueball in the fluxtube model [41]. Inthis model, the 0++ f0(1500) glueball is also naturally relatedto a 0−+ glueball with mass degeneracy broken in QCD. Also,Ref. [42] shows that the pseudoscalar glueball could lie ata lower mass than predicted from lattice calculation. In thismodel the η(1405) appears as the natural glueball candidate,see also Refs. [43–45]. A detailed review of the experimentalsituation is available in Ref. 46.
Let us now deal with 1++ isoscalars. The f1(1420), decaying into K∗K, was first reported in π−p reactions at 4 GeV/c [47].
However, later analyses found that the 1400–1500 MeV regionwas far more complex [48–50]. A reanalysis of the MARK IIIdata in radiative J/ψ(1S) decay into KKπ [8] shows thef1(1420) decaying into K∗K. Also, a C=+1 state is observedin tagged γγ collisions (e.g., Ref. 51).
In π−p → ηππn charge-exchange reactions at 8–9 GeV/c the ηππ mass spectrum is dominated by the η(1440) andη(1295) η(1295) and η(1440) decaying into ηπ0π0 with a weak f1(1285)signal, and no evidence for the f1(1420).
Axial (1++) mesons are not observed in pp annihilation at rest in liquid hydrogen, which proceeds dominantly throughS-wave annihilation. However, in gaseous hydrogen, P -waveannihilation is enhanced and, indeed, Ref. 11 reports f1(1420)decaying into K∗K. The f1(1420), decaying into KKπ, is alsoseen in pp central production, together with the f1(1285). Thelatter decays via a0(980)π, and the former only via K∗K, whilethe η(1440) is absent [53,54]. The K0K0π0 decay mode of the f1(1420) establishes unambiguously C=+1. On the other hand,there is no evidence for any state decaying into ηππ around1400 MeV, and hence the ηππ mode of the f1(1420) must besuppressed [55].
We now turn to the experimental evidence for the f1(1510).
Two states, the f1(1420) and f1(1510), decaying into K∗K,compete for the ss assignment in the 1++ nonet. The f1(1510)was seen in K−p → ΛKKπ at 4 GeV/c [56], GeV/c [57]. Evidence is also reported in π−p at 8 GeV/c, basedon the phase motion of the 1++ K∗K wave [50]. A somewhatbroader 1++ signal is also observed in J/ψ(1S) → γηπ+π− [58]as well as a small signal in J/ψ(1S) → γη′π+π−, attributed tothe f1(1510) [59].
The absence of f1(1420) in K−p [57] argues against the f1(1420) being the ss member of the 1++ nonet. However, thef1(1420) was reported in K−p but not in π−p [60], two experiments do not observe the f1(1510) in K−p [60,61].
The latter is also not seen in central collisions [54], although, surprisingly for an ss state, a signal is reported in 4π decays [63]. These facts lead to theconclusion that f1(1510) is not well established [64].
Assigning the f1(1420) to the 1++ nonet, one finds a nonet mixing angle of ∼ 50◦ [64]. However, arguments favoring thef1(1420) being a hybrid qqg meson, or a four-quark state, wereput forward in Refs. [65] and [66], respectively, while Ref. 67argued for a molecular state formed by the π orbiting in aP -wave around an S-wave KK state. The f1(1420) could alsobe an isoscalar K∗ ¯ K molecule. It is interesting to note that evidence for an isovector 1++ partner, a1(1420) decaying intof0(980)π, was reported recently by the COMPASS experimentin π−p → (3π)−p with 190 GeV/c pions [68].
Summarizing, there is convincing evidence for the f1(1420) decaying into K∗K, and for two pseudoscalars in the η(1440)region, the η(1405) and η(1475), decaying into a0(980)π andK∗K, respectively. Alternatively, these two structures couldoriginate from a single pole. Doubts have been expressed on theexistence of the η(1295). The f1(1510) is not well established.
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