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2Physics Quote:
"Today’s most precise time measurements are performed with optical atomic clocks, which achieve a precision of about 10-18, corresponding to 1 second uncertainty in more than 15 billion years, a time span which is longer than the age of the universe... Despite such stunning precision, these clocks could be outperformed by a different type of clock, the so called “nuclear clock”... The expected factor of improvement in precision of such a new type of clock has been estimated to be up to 100, in this way pushing the ability of time measurement to the next level."
-- Lars von der Wense, Benedict Seiferle, Mustapha Laatiaoui, Jürgen B. Neumayr, Hans-Jörg Maier, Hans-Friedrich Wirth, Christoph Mokry, Jörg Runke, Klaus Eberhardt, Christoph E. Düllmann, Norbert G. Trautmann, Peter G. Thirolf
(Read Full Article: "Direct Detection of the 229Th Nuclear Clock Transition"

Sunday, May 23, 2010

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

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 and e+e
ϒ(2S+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 and ϒ(2S+π arising from the production and decays of the lower bottomonia states, such as ϒ(4S) → ϒ(1S+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- and ϒ(2S+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- and ϒ(2S+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 ϒb 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- and ϒ(2S+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+ebb 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- and ϒ(2S+π- are concentrated around 10.90 GeV, and hence we tentatively identified the states in our analysis of the Rb-scan with the state Yb(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 Yb → ϒ(1S+π-, ϒ(2S+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 Yb(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+ebb 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.

K. F. Chen et al. [Belle Collaboration], "Observation of Anomalousϒ(1S+π- and ϒ(2S+π- Production near the ϒ(5S) Resonance", Phys. Rev. Lett. 100, 112001 (2008) Abstract ; K.-F. Chen et al. [Belle Collaboration], "Observation of an enhancement in e+e → ϒ(1S)π+π-, ϒ(2S)π+π-, and ϒ(3S)π+π- production around √s = 10.89 GeV at Belle", arXiv:0808.2445 [hep-ex] (2010). Article.
[2] L. S. Brown and R. N. Cahn, "Separation of ψ → π+π-γ from ψ → π+π-π0 ", Phys. Rev. Lett. 35, 1 (1975) Abstract; M. B. Voloshin, "Possible four-quark isovector resonance in the family of ϒ particles" JETP Lett. 21, 347 (1975) Pisma Zh. Eksp. Teor. Fiz. 21, 733 (1975)] Article ; K. Gottfried, "Hadronic Transitions between Quark-Antiquark Bound States", Phys. Rev. Lett. 40, 598 (1978) Abstract ; V. A. Novikov and M. A. Shifman, "Comment on the ψ′ → J/ψππ decay", Z. Phys. C 8, 43 (1981) Abstract ; Y. P. Kuang and T. M. Yan, "Predictions for hadronic transitions in the bb system", Phys. Rev. D 24, 2874 (1981). Abstract.
[3] A. Sokolov et al. [Belle Collaboration], "Measurement of the branching fraction for the decay Υ(4S)→ Υ(1S+π-", Phys. Rev. D 79, 051103 (2009). Abstract.
[4] A. Ali, C. Hambrock and M. J. Aslam, "Tetraquark Interpretation of the BELLE Data on the Anomalous Υ(1S)π+π- and Υ(2S)π+π- Production near the Υ(5S) Resonance", Phys. Rev. Lett, 104, 162001 (2010). Abstract.
[5] R. L. Jaffe, "Multiquark hadrons. II. Methods", Phys. Rev. D 15, 281 (1977), Abstract ; R. L. Jaffe and F. E. Low, "Connection between quark-model eigenstates and low-energy scattering", Phys. Rev. D 19, 2105 (1979). Abstract.
[6] L. Maiani, F. Piccinini, A. D. Polosa and V. Riquer, "Diquark-antidiquark states with hidden or open charm and the nature of X(3872)", Phys. Rev. D 71, 014028 (2005). Abstract.
[7] G. ’t Hooft, G. Isidori, L. Maiani, A. D. Polosa and V. Riquer, "A theory of scalar mesons", Phys. Lett. B 662, 424 (2008). Abstract.
[8] A. Ali, C. Hambrock, I. Ahmed and M. J. Aslam, "A Case for Hidden bb Tetraquarks Based on e+ebb Cross Section Between √s = 10.54 and 11.20 GeV", Phys. Lett. B 684, 28 (2010). Abstract.
[9] B. Aubert et al. [BaBar Collaboration], "Measurement of the e+ebb Cross Section between √s=10.54 and 11.20 GeV", Phys. Rev. Lett. 102, 012001 (2009). Abstract.



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