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Masses of Scalar and Axial-Vector B Mesons Revisited

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Eur. Phys. J. C (2017) 77:668 DOI 10.1140/epjc/s10052-017-5252-4 Regular Article - Theoretical Physics Masses of scalar and axial-vector B mesons revisited Hai-Yang Cheng1, Fu-Sheng Yu2,a 1 Institute of Physics, Academia Sinica, Taipei 115, Taiwan, Republic of China 2 School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, People’s Republic of China Received: 2 August 2017 / Accepted: 22 September 2017 / Published online: 7 October 2017 © The Author(s) 2017. This article is an open access publication Abstract The SU(3) quark model encounters a great chal- 1 Introduction lenge in describing even-parity mesons. Specifically, the qq¯ quark model has difficulties in understanding the light Although the SU(3) quark model has been applied success- scalar mesons below 1 GeV, scalar and axial-vector charmed fully to describe the properties of hadrons such as pseu- mesons and 1+ charmonium-like state X(3872). A common doscalar and vector mesons, octet and decuplet baryons, it wisdom for the resolution of these difficulties lies on the often encounters a great challenge in understanding even- coupled channel effects which will distort the quark model parity mesons, especially scalar ones. Take vector mesons as calculations. In this work, we focus on the near mass degen- an example and consider the octet vector ones: ρ,ω, K ∗,φ. ∗ ∗0 eracy of scalar charmed mesons, Ds0 and D0 , and its impli- Since the constituent strange quark is heavier than the up or cations. Within the framework of heavy meson chiral pertur- down quark by 150 MeV, one will expect the mass hierarchy bation theory, we show that near degeneracy can be quali- pattern mφ > m K ∗ > mρ ∼ mω, which is borne out by tatively understood as a consequence of self-energy effects experiment. However, this quark model picture faces great due to strong coupled channels. Quantitatively, the closeness challenges in describing the even-parity meson sector: ∗ ∗0 of Ds0 and D0 masses can be implemented by adjusting two relevant strong couplings and the renormalization scale • Many scalar mesons with masses lower than 2 GeV appearing in the loop diagram. Then this in turn implies the have been observed and they can be classified into two mass similarity of B∗ and B∗0 mesons. The P∗ P inter- s0 0 0 1 nonets: one nonet with mass below or close to 1 GeV, action with the Goldstone boson is crucial for understand- such as f (500) (or σ ), K ∗(800) (or κ), f (980) and ing the phenomenon of near degeneracy. Based on heavy 0 0 0 a (980) and the other nonet with mass above 1 GeV quark symmetry in conjunction with corrections from QCD 0 such as K ∗(1430), a (1450) and two isosinglet scalar and 1/m effects, we obtain the masses of B∗ and B 0 0 Q (s)0 (s)1 mesons. Of course, the two nonets cannot be both low- mesons, for example, MB∗ = (5715 ± 1) MeV + δS, s0 lying 3 P qq¯ states simultaneously. If the light scalar = ( ± ) + δ δ / 0 MB 5763 1 MeV S with S being 1 m Q s1 nonet is identified with the P-wave qq¯ states, one will corrections. We find that the predicted mass difference of encounter two major difficulties: first, why are a (980) 48 MeV between B and B∗ is larger than that of 20– 0 s1 s0 and f (980) degenerate in their masses? In the qq¯ model, 30 MeV inferred from the relativistic quark models, whereas 0 the latter is dominated by the ss¯ component, whereas the difference of 15 MeV between the central values of MB s1 the former cannot have the ss¯ content since it is an and MB is much smaller than the quark model expectation 1 I = 1 state. One will expect the mass hierarchy pattern of 60–100 MeV.Experimentally, it is important to have a pre- ∗ m f (980) > m K ∗(800) > ma (980) ∼ m f (500). However, cise mass measurement of D mesons, especially the neutral 0 0 0 0 0 this pattern is not seen by experiment. In contrast, it is one, to see if the non-strange scalar charmed meson is heav- ≈ > ∗ > ma0(980) m f0(980) m K (800) m f0(500) experimen- ier than the strange partner as suggested by the recent LHCb (0 ) ∗( ) ∗± tally. Second, why are f0 500 and K0 800 so broad measurement of the D0 . compared to the narrow widths of a0(980) and f0(980) even though they are all in the same nonet? • ∗( ) In the scalar meson sector above 1 GeV, K0 1430 with mass 1425 ± 50 MeV [1] is almost degenerate in masses with a0(1450), which has a mass of 1474 ± 19 MeV [1] a e-mail: [email protected] despite having one strange quark for the former. 123 668 Page 2 of 13 Eur. Phys. J. C (2017) 77 :668 Table 1 Measured masses and J P Meson Mass (MeV) (MeV) Mass (MeV) widths of even-parity charmed mesons. The four p-wave + ∗( )0 ± ± 0 D0 2400 2318 29 267 40 2340–2410 Large charmed meson states are ∗ ± ∗, , ∗ D (2400) 2351 ± 7 230 ± 17 2340–2410 Large denoted by D0 D1 D1 and D2 , 0 respectively. In the heavy quark + ( )0 ± ± +107 ± 1 D1 2430 2427 26 25 384−75 74 2470–2530 Large limit, D has j = 1/2andD 1 1 1+ D (2420)0 2420.8 ± 0.531.7 ± 2.5 2417–2434 Small has j = 3/2with j being the 1 ± total angular momentum of the D1(2420) 2432.2 ± 2.425± 6 2417–2434 Small light degrees of freedom. The + ∗( )0 . ± . ± . 2 D2 2460 2460 57 0 15 47 7 1 3 2460–2467 Small data are taken from the Particle ∗ ± D (2460) 2465.4 ± 1.346.7 ± 1.2 2460–2467 Small Data Group [1]. The last two 2 + ∗ ( )± . ± . < columns are the predictions 0 Ds0 2317 2317 7 0 6 3.8 2400–2510 Large + ( )± . ± . < from the quark model [7,8]. 1 Ds1 2460 2459 5 0 6 3.5 2528–2536 Large “Large” means a broad width of + ± 1 Ds1(2536) 2535.10 ± 0.06 0.92 ± 0.05 2543–2605 Small order 100 MeV, while “small” + ∗ ( )± . ± . ± . implies a narrow width of order 2 Ds2 2573 2569 1 0 8169 0 8 2569–2581 Small 10 MeV 3 3 • In the even-parity charmed meson sector, we compare the χc1(1 P1) with a mass 3511 MeV [1]orχc1(2 P1) with experimentally measured masses and widths with what the predicted mass of order 3950 MeV [11]. Moreover, a are expected from the quark model (see Table 1). There pure charmonium for X(3872) cannot explain the large are some prominent features from this comparison: (i) the isospin violation observed in X(3872) → J/ψω, J/ψρ ∗, , ∗ ( ) measured masses of D0 D1 Ds0 and Ds1 are substan- decays. The extreme proximity of X 3872 to the thresh- tially smaller than the quark model predictions. (ii) The old suggests a loosely bound molecule state D0 D¯ ∗0 ∗ ( ) ( ) physical Ds0 mass is below the DK threshold, while Ds1 for X 3872 . On the other hand, X 3872 cannot be a is below DK∗. This means that both of them are quite nar- pure DD¯ ∗ molecular state either for the following rea- row, in sharp contrast to the quark model expectation of sons: (i) It cannot explain the prompt production of ∗( )0 ∗ ( ) ( ) large widths for them. (iii) D0 2400 and Ds0 2317 are X 3872 in high-energy collisions [12,13]. (ii) The ratio ∗( )± ≡ ( 0 → 0 ( ))/ ( − → − ( )) almost equal in their masses, while D0 2400 is heavier R1 B K X 3872 B K X 3872 ∗ 1 than Ds0 even though the latter contains a strange quark. is predicted to be much less than unity in the molecular , ∗, ∗ . ± . ± . (iv) The masses of D1 D2 Ds1 and Ds2 predicted by scenario, while it was measured to be 0 50 0 30 0 05 the quark model are consistent with experiment. These and 1.26 ± 0.65 ± 0.06 by Belle [14,15]. (iii) For the + + four observations lead to the conclusion that 0 and 1 ratio R2 ≡ (X(3872) → ψ(2S)γ )/ (X(3872) → charmed mesons have very unusual behavior not antici- J/ψ(1S)γ ), the molecular model leads to a very small pated from the quark model. value of order 3 × 10−3 [16–18], while the charmonium • The first XYZ particle, namely X(3872), observed by model predicts R2 to be of order of unity. The LHCb mea- ± ± + − Belle in 2003 in B → K + (J/ψπ π ) decays [9], surement yields R2 = 2.46 ± 0.64 ± 0.29 [19]. Hence, has the quantum numbers J PC = 1++ [10]. X(3872) X(3872) cannot be a pure DD¯ ∗ molecular state. The cannot be a pure charmonium as it cannot be identified as above discussions suggest that X(3872) is most likely an admixture of the S-wave DD¯ ∗ molecule and the P- wave charmonium as first advocated in [12], 1 Strictly speaking, the masses of the neutral and charged states of ∗( ) D0 2400 are not consistently determined due mainly to its broadness. 0 ∗0 The mass of the charged one is primarily from the LHCb measurements |X(3872)=c1|cc¯P-wave + c2|D D S-wave [2,3], while the neutral one is from BaBar [4], Belle [5]andFOCUS + ∗− [6]. It is worthwhile to notice that only FOCUS has measured both the +c3|D D S-wave +··· . (1.1) ∗( ) neutral and the charged D0 2400 , and their masses are quite similar, with a small difference of a few MeV.
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  • Pos(LATTICE2014)106 ∗ Andrea.Guerrieri@Roma2.Infn.It Speaker

    Pos(LATTICE2014)106 ∗ [email protected] Speaker

    Flavored tetraquark spectroscopy PoS(LATTICE2014)106 Andrea L. Guerrieri∗ Dipartimento di Fisica and INFN, Università di Roma ’Tor Vergata’ Via della Ricerca Scientifica 1, I-00133 Roma, Italy E-mail: [email protected] Mauro Papinutto, Alessandro Pilloni, Antonio D. Polosa Dipartimento di Fisica and INFN, ’Sapienza’ Università di Roma P.le Aldo Moro 5, I-00185 Roma, Italy Nazario Tantalo CERN, PH-TH, Geneva, Switzerland and Dipartimento di Fisica and INFN, Università di Roma ’Tor Vergata’ Via della Ricerca Scientifica 1, I-00133 Roma, Italy The recent confirmation of the charged charmonium like resonance Z(4430) by the LHCb ex- periment strongly suggests the existence of QCD multi quark bound states. Some preliminary results about hypothetical flavored tetraquark mesons are reported. Such states are particularly amenable to Lattice QCD studies as their interpolating operators do not overlap with those of ordinary hidden-charm mesons. The 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014 Columbia University New York, NY ∗Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Flavored tetraquark spectroscopy Andrea L. Guerrieri 1. Introduction The recent confirmation of the charged resonant state Z(4430) by LHCb [1] strongly suggests the existence of genuine compact tetraquark mesons in the QCD spectrum. Among the many phenomenological models, it seems that only the diquark-antidiquark model in its type-II version can accomodate in a unified description the puzzling spectrum of the exotics [2]. Although diquark- antidiquark model has success in describing the observed exotic spectrum, it also predicts a number of unobserved exotic partners.