Semileptonic Decays of Charmed Mesons to Light Scalar Mesons

PHYSICAL REVIEW D 102, 016013 (2020) Semileptonic decays of charmed mesons to light scalar mesons N. R. Soni * Department of Physics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara 390002, Gujarat, India † A. N. Gadaria , J. J. Patel , and J. N. Pandya Applied Physics Department, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara 390001, Gujarat, India (Received 4 February 2020; accepted 30 June 2020; published 20 July 2020) Within the framework of covariant confined quark model, we compute the transition form factors of D and Ds mesons decaying to light scalar mesons f0ð980Þ and a0ð980Þ. The transition form factors are then utilized to compute the semileptonic branching fractions. We study the channels, namely, þ → ð980Þlþν → ð980Þlþν l ¼ μ DðsÞ f0 l and D a0 l for e and . For computation of semileptonic branching fractions, we consider the a0ð980Þ meson to be the conventional quark-antiquark structure and the f0ð980Þ meson as the admixture of ss¯ and light quark-antiquark pairs. Our findings are found to support the recent BESIII data. DOI: 10.1103/PhysRevD.102.016013 I. INTRODUCTION the ss¯ counterpart. Recently, BESIII Collaboration reported the first ever experimental observation for the semileptonic Charmed semileptonic decays are important for the study þ branching fraction of D → a0ð980Þe ν [5]. The notable of open flavor hadron spectroscopy in general and heavy e results on these channels read quark decay properties in particular. More specifically, the scalar mesons below 1 GeV in final product can provide the þ þ þ − −5 BðD →f0ð980Þe ν ;f0ð980Þ→π π Þ<2.5×10 ½4 key information regarding their internal structure as well as e þ þ þ − the chiral symmetry in the low energy region of non- BðDs →f0ð980Þe νe;f0ð980Þ→π π Þ perturbative QCD [1]. The internal structure of these ¼ð0.13Æ0.04Æ0.01Þ% ½3 mesons is yet to be clearly understood from the theoretical 0 − þ − − studies attempted so far. BðD →a0ð980Þ e νe;a0ð980Þ →ηπ Þ ð980Þ Conventionally, the structure of f0 meson was ¼ð1.33þ0.33 Æ0.09Þ×10−4 ½5 thought to be a bound state of quark-antiquark pair. CLEO −0.29 Bð þ → ð980Þ0 þν ð980Þ0 →ηπ0Þ was the first to have studied the semileptonic decays of D a0 e e;a0 þ D → f0ð980Þe ν [2,3] and recently, BESIII has reported þ0.81 −4 s e ¼ð1.66−0 66 Æ0.11Þ×10 ½5: ð1Þ branching fractions for the semileptonic decays of Dþ → . ð980Þ þν f0 e e [4] suggesting that the internal structure of On experimental front, BESIII and other worldwide exper- ð980Þ bound state of f0 meson may not be the conventional imental facilities have reported the most precise results quark-antiquark pair. These experimental results also indi- on semileptonic decay of DðsÞ to pseudoscalar and vector f0ð980Þ cate that the internal structure of meson could be mesons. From theory point of view, these channels are ss¯ admixture of lighter quark state and state. For the straightforward to study because the internal structure/ D → f0ð980Þ, the dominant contribution is from the lighter → ð980Þ quark content of the daughter meson is a typical quark- quarks, whereas that for the Ds f0 channel is from antiquark system. But the quark structure of the scalar mesons below 1 GeV has varied explanations (see note *[email protected] on scalar mesons below 2 GeV in Particle Data Group † [email protected] Ref. [6]). The computation of branching fractions of DðsÞ mesons decaying to a0ð980Þ and f0ð980Þ is highly sensi- Published by the American Physical Society under the terms of tive to the internal structure of these mesons. The theo- the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to retical approaches so far include lattice quantum the author(s) and the published article’s title, journal citation, chromodynamics [7–12], QCD sum rules [13–17], chiral and DOI. Funded by SCOAP3. unitary approach [18], and different quark models [19–24]. 2470-0010=2020=102(1)=016013(9) 016013-1 Published by the American Physical Society SONI, GADARIA, PATEL, and PANDYA PHYS. REV. D 102, 016013 (2020) There are different ways in which these scalar mesons are fractions, and other physical observables such as forward studied globally, viz. conventional quark-antiquark states backward asymmetry and lepton polarization. The present [25–27] and compact multiquark states including diquark- study will help understand the essential dynamics of diantiquark [28], meson-meson composite molecule charmed semileptonic decays and the possible structure [29–37], as well as compact structure of tetra quarks of the scalar mesons below 1 GeV, namely, f0ð980Þ and [38–46]. In this mass range, one can also consider the a0ð980Þ. possibility of scalar glueball bound state [47,48]. This paper is organized in the following way: after In quark-antiquark picture, several theories have been introducing the requirement for the study of scalar mesons proposed including the constituent quark model [25]. The in the semileptonic decays with the literature in Sec. I,we semileptonic branching fractions for Ds → f0ð980Þ were briefly introduce the essential components of covariant considered in the light front quark model [26] and semi- confined quark model employed here for computation of leptonic as well as rare decays of the BðsÞ have also been the hadronic form factors in Sec. II. Using the transition studied in the formalism of covariant quark model [27].In form factors, we compute the semileptonic branching composite structure, there are several ways in which the fractions. In Sec. III, we present our numerical results of structure of scalar mesons is proposed. Fariborz et al. semileptonic branching fractions in comparison with other studied the light scalar mesons considering diquark- theoretical results and available experimental data. Finally, diantiquark state in the formalism of linear sigma model in Sec. IV, we summarize and conclude the present work. [28]. The scalar mesons have been considered to be the ¯ bound states of KK molecules in the potential model II. FORM FACTORS AND SEMILEPTONIC approach [29,30]. Achasov et al. considered the scalar BRANCHING FRACTIONS meson to be the KK¯ molecule in the radiative decays of ϕ meson [31]. The assignment of f0ð980Þ as the molecular Within standard model, the semileptonic decays are structure of KK¯ has also been used in the phenomeno- very well separated by strong and weak interactions. logical Lagrangian approach by studying the strong decays The charmed meson semileptonic decays to light scalar of f0ð980Þ to ππ and γγ channels [32]. The multiquark meson can be written as structure was also attempted in the unitarized meson model [33], effective field theory [34,35], as well as þ GF μ þ MðDð Þ → Sl νlÞ¼pffiffiffi V hSjqO¯ cjDð Þi½l Oμνl; chiral perturbation theory [36,37]. Maiani et al. studied s 2 cq s the diquark-diantiquark structure via strong decay of DðsÞ μ μ mesons [42,43]. Light scalar mesons are also studied in the with O ¼ γ ð1 − γ5Þ and q ∈ d; s. The matrix element in framework of tetraquark mixing [44–46]. this process is very well parametrized in terms of transition Lattice quantum chromodynamics investigations of these form factors given by scalar mesons are reported employing the four quark Mμ ¼ μ ð 2Þþ μ ð 2Þ ð Þ [49,50] and diquark-diantiquark pictures [51]. The tran- S P Fþ q q F− q : 2 sition form factors for the decays with scalar mesons as daughter products are also computed in the framework of Here P ¼ p1 þ p2 and q ¼ p1 − p2 with p1 and p2 to be – QCD sum rules [52 54] and light cone sum rules [55,56]. the momentum of DðsÞ meson of mass m1 and momentum Cheng et al. studied the transition form factors and semi- of scalar (S) meson of mass m2, respectively. The form → ð980Þ leptonic branching fractions for the channel D a0 factors Fþ and F− are computed in the entire accessible in the light cone sum rule approach where they considered physical range of momentum transfer in the formalism of a0ð980Þ to be the conventional quark-antiquark state [57]. CCQM. The Lagrangian describing the coupling of the The transition form factors are also determined in the light constituent quarks to the meson can be written as [58–61] front quark model considering them as a four quark state Z [22]. Jaffe considered the diquark-diantiquark structure of L ¼ ð Þ ð ; Þ¯ ð ÞΓ ð Þ these mesons in the formalism of MIT bag model [1]. int gM M x dx1dx2FM x x1;x2 q2 x2 Mq1 x1 The present work is focused on the semileptonic decay þ H:c: ð3Þ of D and Ds mesons to the light scalar mesons, namely, f0ð980Þ and a0ð980Þ in the framework of covariant Γ confined quark model (CCQM) [58–61]. The CCQM is Here, M is the Dirac matrix projecting onto spin of Γ ¼ the effective field theory approach with the built-in infrared corresponding mesonic state. It should read, i.e., M I, 5 confinement for the hadronic interactions to their constitu- γ , γμ for scalar, pseudoscalar, and vector mesons, respec- ents. Recently, we studied the semileptonic decays of tively. gM is the coupling strength of the meson with its D and Ds mesons to the pseudoscalar and vector mesons constituent quarks. FM, the translation invariant vertex in this formalism in great detail [62–66]. In these papers, function characterizing the effective physical size of the we investigated the transition form factors, branching hadron, is given by 016013-2 SEMILEPTONIC DECAYS OF CHARMED MESONS TO LIGHT … PHYS.

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