QCD Gaussian sum-rules are used to explore the vector (J PC = 1 −− ) strangeonium hybrid interpretation of the Y(2175). Using a two-resonance model consisting of the Y(2175) and an additional resonance, we find that the relative resonance strength of the Y(2175) in the Gaussian sum-rules is less than 5% that of a heavier 2.9 GeV state. This small relative strength presents a challenge to a dominantly-hybrid interpretation of the Y(2175).
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I. INTRODUCTIONThe initial state radiation (ISR) process in e + e − annihilation is a very useful technique to search for vector states (i.e., J PC = 1 −− ) in B-factories. In 2006, the BaBar Collaboration studied the cross sections for the ISR processes e + e − → K + K − π + π − and e + e − → K + K − π 0 π 0 up to 4.5 GeV, aiming to confirm the existence of the Y(4260) in the φππ channels. Instead of observing the Y(4260), however, they found a new resonance structure in the φ(1020) f 0 (980) channel, which was named the Y(2175) [1]. (It is also known as the φ (2170) [2]). This resonance was later confirmed by BaBar [3][4][5], BES [6], and Belle [7] and recently by BESIII [8,9]. Its mass and decay width are M = (2188 ± 10) MeV and Γ = (83 ± 12) MeV and its quantum numbers areTo date, the nature of the Y(2175) is still unknown. Based on strange quarkonium mass predictions using a relativized potential model, only the 3 3 S 1 and 2 3 D 1 ss states are expected to have masses close to that of the Y(2175) [10]. However, both interpretations are disfavoured as the corresponding resonance width predictions are significantly larger than the width of the Y(2175). The width of the 3 3 S 1 ss state was predicted to be 378 MeV using the 3 P 0 decay model [11] whereas the width of the 2 3 D 1 ss state was predicted to be 167 MeV in the 3 P 0 model and 212 MeV in the flux tube breaking model [12]. Another possible interpretation of the Y(2175) is that of a strangeonium hybrid meson (i.e.,sgs). Masses of vector strangeonium hybrid mesons have been computed using several methodologies including the flux tube model [13][14][15][16], lattice QCD [17], and QCD Laplace sum-rules (LSRs) [18]. The flux tube model calculation of [16] found a vector strangeonium hybrid mass of 2.1-2.2 GeV. The lattice QCD analysis of [17] found a vector strangeonium hybrid mass between 2.4 GeV and 2.5 GeV while the LSRs calculation of [18] found a heavier mass of (2.9 ± 0.3) GeV. Yet another possible interpretation of the Y(2175) is that of a ssss tetraquark. In [19], the masses of vector ssss tetraquarks were investigated. Two states were predicted with respective masses (2.34±0.17) GeV and (2.41±0.25) GeV. Other LSRs analyses of ssss tetraquarks can be found in [20,21]. Furthermore, the Y(2175) has also been proposed as a molecular state of ΛΛ [22,23]. In [22], a chromomagnetic interaction Hamiltonian was used to predict a hexaquark of mass 2.184 GeV that is strongly coupled to the ΛΛ channel. In [23], a one-boson-exchange potential model was used to predict a ΛΛ mass between 2.