Growing evidence of Tetraquarks

Ahmed Ali, Christian Hambrock, M. Jamil Aslam
(from Left to Right)




[This is an invited article based on a recent work by the authors. -- 2Physics.com]

Authors: Ahmed Ali¹, Christian Hambrock¹, M. Jamil Aslam²
Affiliation:
¹ Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany.
² Physics Department, Quaid-i-Azam University, Islamabad, Pakistan.

In December 2007, the Belle collaboration working at the KEKB e⁺e⁻ collider in Tsukuba, Japan, reported the first observation of the processes e⁺e⁻ → ϒ(1S)π⁺π⁻ and e⁺e⁻ →
ϒ(2S)π⁺π⁻ near the peak of the ϒ(5S) resonance at the center-of-mass energy √s of about 10.87 GeV [1]. The ϒ(nS) states (n being the principal quantum number and S stands for the orbital angular momentum l = 0, borrowing the language of atomic physics) are called “bottomonia” - bb bound states of the bottom quark and its antiparticle. Production and decays of the ϒ(nS) are popular theoretical laboratories to test Quantum Chromo Dynamics (QCD), the theory of strong interactions. In particular, the final states ϒ(1S)π⁺π⁻ and ϒ(2S)π⁺π⁻ arising from the production and decays of the lower bottomonia states, such as ϒ(4S) → ϒ(1S)π⁺π⁻, have been studied in a number of experiments over the last thirty years and are theoretically well-understood in QCD [2].

Belle measurements near the ϒ(5S), however, did not fall in line with theoretical expectations [1]. Their data were enigmatic in that the partial decay widths for ϒ(5S) →
ϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- were typically three orders of magnitude larger than anticipated in QCD [2]. In addition, the dipion invariant mass distributions in these events were distinctly different from theoretical expectations as well as from the corresponding measurements at the ϒ(4S), undertaken previously by them [3]. The measurements in question are robust, with the ϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- channels having a significance of 20σ and 14σ [1], respectively.

To be precise, two aspects of the Belle data had to be explained: (a) the anomalously
large partial decay rates and (b) the invariant mass distributions of the dipions. A related and important issue is whether the puzzling events seen by Belle stem from the decays of the ϒ(5S), or from another particle ϒ_b having a mass close enough to the mass of the
ϒ(5S). In the conventional Quarkonium theory, there is no place for such a nearby additional bb resonance having the quantum numbers of ϒ(5S).

Our interpretation [4] of the Belle data is that the anomalous ϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- events are not due to the production and decays of the ϒ(5S), but rather from the production of a completely different hadron species, tetraquark hadrons with the quark structure Y_[bu] = [bu][b u ] and Y_[bd] = [bd][b d ], and their subsequent decays. The constituents of the tetraquarks, diquarks and antidiquarks (see the sketch below), have well-defined properties, characterized by their color and electromagnetic charges, spin and flavor quantum numbers. The tetraquark hadrons Y_[bu] and Y_[bd] are singlets in color (pictured white), and hence they participate as physical states in scattering and decay processes. This is not too dissimilar a situation from the well-known mesons, which are color singlet (white) bound states of the confined colored quarks and antiquarks.

The idea that diquarks and antidiquarks may play a fundamental role in hadron spectroscopy is rather old and goes back to well over thirty years [5]. This suggestion was lying dormant for most of this period for lack of experimental evidence. Tetraquarks resurfaced as possible explanations of the exotic hadronic states in the charm quark sector, such as X(3872) and the
Y(4660), which are interpreted as [cu][c u ] states [6]. Lately, also the perception about the light scalar mesons, such as f₀(600) and f₀(980) (there is an entire nonet of them) has changed. They are now interpreted as being dominantly tetraquark [qq′][q q′ ] states instead of the usual qq mesons [7]. Y_[bu] and Y_[bd] are the first tetraquarks in the bottom quark sector – harbingers of an entirely new world of bound and open beauty hadrons.

In an earlier paper [8], we (togeher with Ishtiaq Ahmed) were able to identify tetraquark states which can be produced in e⁺e⁻ annihilation directly. Of these, Y_[bu] and Y_[bd] are estimated to have the right masses to be produced in the vicinity of the ϒ(5S). The physical particles called Y_[b,l] and Y_[b,h], for lighter and heavier of the two, are mixed states. They have masses around 10.90 GeV and are split in mass by about 6 MeV. To search for them we analyzed the BaBar data, obtained during the energy scan of the e⁺e⁻ → bb cross section in the range of √s = 10.54 GeV to 11.20 GeV [9]. Our inference was that the BaBar data are consistent with the presence of additional bb states
Y_[b,l] and Y_[b,h] with a mass of about 10.90 GeV and a decay width of about 30 MeV, apart from the ϒ(5S) and ϒ(6S) resonances. It struck us that most of the enigmatic events in the Belle data in the final states ϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- are concentrated around 10.90 GeV, and hence we tentatively identified the states in our analysis of the R_b-scan with the state Y_b(10890) in the Belle analysis.

To pursue our theoretical hypothesis, we developed a dynamical theory to make quantitative predictions and undertake an analysis of the Belle data. Explaining the larger decay rates for the transitions Y_b → ϒ(1S)π⁺π^-, ϒ(2S)π⁺π^- was not so difficult, as the decays of
Y_[b,l] and Y_[b,h] involve a recombination of the initial four quarks, as exemplified below by the process Y_[bu] ≡ [bu][b u] → (bb)(uu), with the subsequent projection (bb) → ϒ(1S) and (uu) → π⁺π^-.

Such quark recombination processes do not require the emission and absorption of gluons, and are appropriately called Zweig-allowed, after the co-discoverer of the quark-model, George Zweig. On the other hand, the dipionic transitions from a higher bottomonium state, such as ϒ(5S), to lower bottomonium states, such as ϒ(1S), are very rare QCD processes, needing the radiation of two gluons and their conversion to the π⁺π^- final state (see the sketch above).

The measured decay distributions, such as the dipion invariant mass spectra, are also easily understood in terms of the affinity of the tetraquark states Y_[b,l] and Y_[b,h] to decay preferentially into ϒ(1S) or ϒ(2S) and lighter tetraquark states, the light 0⁺⁺ states f₀(600)and f₀(980), mentioned earlier. They are indicated in the relevant figure by the intermediate state f₀. Hence, one expects a resonant structure in the dipion invariant mass, reflecting these and other known resonances allowed by the phase space. This is indeed the case, as can be seen in the figures below adapted from our PRL paper [4]. In these plots Belle data are indicated by crosses; the shaded histograms are our theoretical calculations for the tetraquark case (best fits) and the solid curves are the shapes from the corresponding decays of the ϒ(5S), which do not fit the data. In summary, tetraquark interpretation of the Y_b(10890) provides an excellent description of the decay distributions measured by Belle.

Exciting and plausible as our interpretation of the Belle and BaBar data is, we stress that a number of measurements has to be undertaken to confirm the tetraquark interpretation of the Belle anomaly. The first and foremost is that two almost degenerate states Y_[b,l] and Y_[b,h], predicted in the tetraquark theory as members of an isodoublet, have to be confirmed experimentally. We wait anxiously for the analysis of the new data which Belle is currently accumulating around the ϒ(5S) region. Improved measurements of the cross section e⁺e⁻ → bb in dedicated energy scans, which will be carried out at the Super-B factories being planned at KEK and Frascati in Italy, may also greatly help in resolving this structure and perhaps establish other tetraquark resonances predicted in that region.

Last, but by no means least, these and other tetraquark states should be measured in
experiments at the Tevatron and the LHC. Final states -- such as seen in the Belle experiment -- are easy enough to be measured even in the noisy backgrounds in hadron colliders; calculating the production cross section requires theoretical work. We look forward to data from the ongoing run by the Belle collaboration and eventually from the two hadron colliders and the Super-B factories.

References
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