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A Strangeonium Hybrid Meson? Digital Collections @ Dordt Faculty Work Comprehensive List 8-12-2019 Is the Y (2175) a Strangeonium Hybrid Meson? Jason Ho Dordt University, [email protected] R. Berg University of Saskatchewan T. G. Steele University of Saskatchewan W. Chen Sun Yat-sen University D. Harnett University of the Fraser Valley Follow this and additional works at: https://digitalcollections.dordt.edu/faculty_work Part of the Physics Commons Recommended Citation Ho, J., Berg, R., Steele, T. G., Chen, W., & Harnett, D. (2019). Is the Y (2175) a Strangeonium Hybrid Meson?. Physical Review D, 100 (3), 034012. https://doi.org/10.1103/PhysRevD.100.034012 This Article is brought to you for free and open access by Digital Collections @ Dordt. It has been accepted for inclusion in Faculty Work Comprehensive List by an authorized administrator of Digital Collections @ Dordt. For more information, please contact [email protected]. Is the Y (2175) a Strangeonium Hybrid Meson? Abstract QCD Gaussian sum rules are used to explore the vector (JPC=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). Keywords quantum chromodynamics, exotic mesons, hybrid mesons, mass Disciplines Physics Comments Access on publisher's site: https://journals.aps.org/prd/pdf/10.1103/PhysRevD.100.034012 This article is available at Digital Collections @ Dordt: https://digitalcollections.dordt.edu/faculty_work/1239 PHYSICAL REVIEW D 100, 034012 (2019) Is the Yð2175Þ a strangeonium hybrid meson? J. Ho, R. Berg, and T. G. Steele Department of Physics and Engineering Physics University of Saskatchewan Saskatoon, Saskatchewan, S7N 5E2, Canada W. Chen School of Physics Sun Yat-Sen University Guangzhou 510275, China D. Harnett Department of Physics University of the Fraser Valley Abbotsford, British Columbia, V2S 7M8, Canada (Received 18 June 2019; published 12 August 2019) QCD Gaussian sum rules are used to explore the vector (JPC ¼ 1−−) strangeonium hybrid interpretation of the Yð2175Þ. Using a two-resonance model consisting of the Yð2175Þ and an additional resonance, we find that the relative resonance strength of the Yð2175Þ 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 Yð2175Þ. DOI: 10.1103/PhysRevD.100.034012 3 I. INTRODUCTION was predicted to be 167 MeV in the P0 model and The initial state radiation (ISR) process in eþe− anni- 212 MeV in the flux tube breaking model [12]. Another Y 2175 hilation is a very useful technique to search for vector states possible interpretation of the ð Þ is that of a strang- −− eonium hybrid meson (i.e., sgs¯ ). Masses of vector strang- (i.e., JPC ¼ 1 ) in B-factories. In 2006, the BABAR eonium hybrid mesons have been computed using several Collaboration studied the cross sections for the ISR methodologies including the flux tube model [13–16], processes eþe− → KþK−πþπ− and eþe− → KþK−π0π0 lattice QCD [17], and QCD Laplace sum rules (LSRs) up to 4.5 GeV, aiming to confirm the existence of the [18]. The flux tube model calculation of [16] found a vector Yð4260Þ in the ϕππ channels. Instead of observing the strangeonium hybrid mass of 2.1–2.2 GeV. The lattice Yð4260Þ, however, they found a new resonance structure in QCD analysis of [17] found a vector strangeonium the ϕð1020Þf0ð980Þ channel, which was named the hybrid mass between 2.4 GeV and 2.5 GeV while the Yð2175Þ [1]. (It is also known as the ϕð2170Þ [2]). This LSRs calculation of [18] found a heavier mass of resonance was later confirmed by BABAR [3–5],BES[6], ð2.9 Æ 0.3Þ GeV. Yet another possible interpretation of and Belle [7] and recently by BESIII [8,9]. Its mass and the Yð2175Þ is that of a sss¯s¯ tetraquark. In [19], the masses decay width are M ¼ð2188 Æ 10Þ MeV and Γ ¼ð83 Æ of vector sss¯s¯ tetraquarks were investigated. Two states 12 MeV and its quantum numbers are IGJPC 0−1−− [2]. Þ ¼ were predicted with respective masses ð2.34 Æ 0.17Þ GeV To date, the nature of the Y 2175 is still unknown. ð Þ and ð2.41 Æ 0.25Þ GeV. Other LSRs analyses of sss¯s¯ Based on strange quarkonium mass predictions using a tetraquarks can be found in [20,21]. Furthermore, the 33 23 ¯ relativized potential model, only the S1 and D1 ss states Yð2175Þ has also been proposed as a molecular state of are expected to have masses close to that of the Y 2175 ð Þ ΛΛ¯ [22,23].In[22], a chromomagnetic interaction [10]. However, both interpretations are disfavored as the Hamiltonian was used to predict a hexaquark of mass corresponding resonance width predictions are signifi- 2.184 GeV that is strongly coupled to the ΛΛ¯ channel. In cantly larger than the width of the Yð2175Þ. The width 3 [23], a one-boson-exchange potential model was used to of the 3 S1 ss¯ state was predicted to be 378 MeV using the ¯ 3 3 predict a ΛΛ mass between 2.149 GeV and 2.181 GeV. P0 decay model [11] whereas the width of the 2 D1 ss¯ state Also, the Yð2175Þ has been interpreted as a dynamically generated resonance of ϕf0ð980Þ [24–27]. Decay modes and rates will be crucial to determining the Published by the American Physical Society under the terms of nature of the Yð2175Þ.In[11], it was predicted using the the Creative Commons Attribution 4.0 International license. 3 33 Further distribution of this work must maintain attribution to P0 model that the most important decay modes of the S1 ¯ à à à the author(s) and the published article’s title, journal citation, ss meson would be K K , KK ð1410Þ, and KK1ð1270Þ and DOI. Funded by SCOAP3. whereas the KK mode would be very weak. In [12],itwas 2470-0010=2019=100(3)=034012(7) 034012-1 Published by the American Physical Society HO, BERG, STEELE, CHEN, and HARNETT PHYS. REV. D 100, 034012 (2019) 3 gs ρ a ˜ a predicted using the P0 model that the most important jμ ¼ s¯γ γ5λ Gμρs: ð2Þ 3 2 decay modes of the 2 D1 ss¯ meson would be KKð1460Þ, à 1410 1270 à à KK ð Þ, KK1ð Þ, and K K . While not dominant, ˜ a In (2), s is a strange quark field and Gμρ is the dual gluon the KK decay mode was predicted to have a partial width of about 0.06. In [28], it was predicted using flux tube and field strength tensor, constituent gluon models that the most important decay 1 ˜ a a modes of a vector strangeonium hybrid would be Gμρ ¼ ϵμρωζGωζ; ð3Þ Ã 2 KK1ð1400Þ, KK1ð1270Þ, KK ð1410Þ, and KK2ð1430Þ, each containing a S-wave meson plus a P-wave meson, defined in terms of the Levi-Civita symbol, ϵμρωζ. – due to the S þ P selection rule [28 30]. Also, it was noted Between [18] and [41], the quantity Πðq2Þ from (1) has that the ϕf0ð980Þ mode could be significant. Of particular 2 been computed to leading-order (LO) in α gs within the interest are the KK, KÃKà and KKð1460Þ modes which are s ¼ 4π predicted to be zero for a strangeonium hybrid interpreta- operator product expansion. In [18], the perturbative and tion (the usual rule that suppresses or even forbids hybrid dimension-four (i.e., 4d) quark and gluon condensate decays to pairs of S-wave mesons [29,31,32]). For the sss¯s¯ contributions were calculated. In [41], the 5d mixed, 6d tetraquark interpretation, it has been suggested that the ηϕ quark, and 6d gluon condensate contributions were calcu- O 2 channel should be one of the dominant decay modes due to lated as well as ðms Þ corrections to perturbation theory the large phase space in the fall-apart mechanism [28]. where ms is the strange quark mass. Denoting the result as ΠQCD 2 However, in [33], it was argued that the ηϕ decay mode ðq Þ to emphasize that it is a QCD calculation, we ϕ 980 η have would be greatly suppressed and that the f0ð Þ, h1 , 0 ¯ 6 2 4 2 and h1η modes would be most important. For the ΛΛ α q 5m q 4q ΠQCD 2 s − s − ¯ interpretation of the Yð2175Þ, the KK decay mode was ðq Þ¼ π 240π2 þ 48π2 9 hmsssi predicted to dominate [34]. At present, the data concerning 2 19α − 2 decay modes and rates of the Yð2175Þ is incomplete, q α 2 sms ¯σ q þ h G iþ hgs Gsi log 2 making it difficult to draw any definitive conclusions [2]. 36π 72π μ 4260 As they are both observed in ISR processes, the Yð Þ ð4Þ and Yð2175Þ states have the same quantum numbers, and are often considered as analogous states in the hidden- where charm and hidden-strange sectors, respectively [1,35,36]. ¯ ¯α α Perhaps determining the nature of one will shed light on the hmsssi¼hmssi si ið5Þ other. Since the Yð4260Þ has been identified as a good α 2 α a a candidate for charmonium hybrid cgc¯ [37–39] or hidden- h G i¼h sGμνGμνið6Þ charm tetraquark state qcq¯c¯ [40], the Yð2175Þ meson may ¯σ ¯ασμνλa a β also be interpreted as a hybrid or tetraquark candidate.
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