Mesons with Beauty and Charm: New Horizons in Spectroscopy

PHYSICAL REVIEW D 99, 054025 (2019) Editors' Suggestion Mesons with beauty and charm: New horizons in spectroscopy † Estia J. Eichten* and Chris Quigg Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510, USA (Received 8 March 2019; published 28 March 2019) þ ¯ The Bc family of ðcbÞ mesons with beauty and charm is of special interest among heavy quarkonium þ ¯ systems. The Bc mesons are intermediate between ðcc¯Þ and ðbbÞ states both in mass and size, so many features of the ðcb¯Þ spectrum can be inferred from what we know of the charmonium and bottomonium systems. The unequal quark masses mean that the dynamics may be richer than a simple interpolation would imply, in part because the charmed quark moves faster in Bc than in the J=ψ. Close examination of þ the Bc spectrum can test our understanding of the interactions between heavy quarks and antiquarks and may reveal where approximations break down. Whereas the J=ψ and ϒ levels that lie below the flavor threshold are metastable with respect to strong decays, the Bc ground state is absolutely stable against strong or electromagnetic decays. Its dominant weak decays arise from b¯ → cW¯ ⋆þ, c → sW⋆þ, and cb¯ → W⋆þ transitions, where W⋆ designates a virtual weak boson. Prominent examples of the first þ þ þ þ category are quarkonium transmutations such as Bc → J=ψπ and Bc → J=ψl νl, where J=ψ designates the ðcc¯Þ 1S level. The high data rates and extraordinarily capable detectors at the Large Hadron Collider give renewed impetus to the study of mesons with beauty and charm. Motivated by the recent experimental searches for the radially excited Bc states, we update the expectations for the low-lying spectrum of the Bc system. We make use of lattice QCD results, a novel treatment of spin splittings, and an improved quarkonium potential to obtain detailed predictions for masses and decays. We suggest promising modes in which to observe excited states at the LHC. The 3P and 3S states, which lie close to or just above the threshold for strong decays, may provide new insights into the mixing between quarkonium bound states and nearby two-body open-flavor channels. Searches in the BðÞDðÞ final states could well reveal narrow resonances in the JP ¼ 0−, 1−, and 2þ channels and possibly in the JP ¼ 0þ and 1þ channels at threshold. Looking further ahead, the prospect of very-high-luminosity eþe− colliders capable of producing tera-Z samples raises the possibility of investigating Bc spectroscopy and rare decays in a controlled environment. DOI: 10.1103/PhysRevD.99.054025 I. INTRODUCTION shows the way toward exploiting the potential of ðcb¯Þ spectroscopy. Although the lowest-lying ðcb¯Þ meson has long been established, the spectrum of excited states is little B explored. The ATLAS experiment at CERN’s Large A. What we know of the c mesons Hadron Collider reported the observation of a radially The possibility of a spectrum of narrow Bc states was excited Bc state [1], but this sighting was not confirmed first suggested by Eichten and Feinberg [5]. Anticipating by the LHCb experiment [2]. The unsettled experimental the copious production of b-quarks at Fermilab’s Tevatron situation and the large datasets now available for analysis Collider and CERN’s Large Electron-Positron Collider make it timely for us to provide up-to-date theoretical (LEP), we presented a comprehensive portrait of the expectations for the spectrum and decay patterns of spectroscopy of the Bc meson and its long-lived excited narrow ðcb¯Þ states and for their production in hadron states [6], based on then-current knowledge of the inter- colliders [3]. New work from the CMS Collaboration [4] action between heavy quarks derived from ðcc¯Þ and ðbb¯Þ bound states, within the framework of nonrelativistic quan- *[email protected] tum mechanics [7]. Surveying four representative poten- † P − [email protected] tials, we characterized the mass of the J ¼ 0 ground state as MðBcÞ ≈ 6258 Æ 20 MeV. A small number of Bc can- Published by the American Physical Society under the terms of 0 the Creative Commons Attribution 4.0 International license. didates appeared in hadronic Z decays at LEP. The CDF Æ → ψlÆν Further distribution of this work must maintain attribution to Collaboration observed the decay Bc J= in 1.8- the author(s) and the published article’s title, journal citation, TeV pp¯ collisions at the Fermilab Tevatron [8], estima- 3 and DOI. Funded by SCOAP . ting the mass as MðBcÞ ≈ 6400 Æ 411 MeV. (The generic 2470-0010=2019=99(5)=054025(15) 054025-1 Published by the American Physical Society ESTIA J. EICHTEN and CHRIS QUIGG PHYS. REV. D 99, 054025 (2019) Ã lepton l represents an electron or muon.) Subsequent work the low-energy photon from the subsequent Bc → Bcγ by the CDF [9],D0[10], and LHCb [11] Collaborations decay, and that the signal is an unresolved combination 3 1 has refined the mass to MðBcÞ¼6274.9 Æ 0.8 MeV [12], of 2 S1 and 2 S0 peaks. A search by the LHCb collabo- with the most precise determinations coming from fully ration in 2 fb−1 of 8-TeV pp data yielded no evidence for ψπþ reconstructed final states such as J= . either Bcð2SÞ state [2]. As we prepared this article for Investigations based on the spacetime lattice formulation publication, the CMS Collaboration provided striking ab initio of QCD aim to provide calculations that incor- evidence for both Bcð2SÞ levels, in the form of well- þ − porate the full dynamical content of the theory of strong separated peaks in the Bcπ π invariant mass distribution, interactions. Before the nonleptonic Bc decays had been closely matching the theoretical template [4]. We incorpo- observed, a first unquenched lattice QCD prediction, incor- rate these new observations into the discussion that follows porating 2 þ 1 dynamical quark flavors ðu=d; sÞ found in Sec. VA. þ18 MðBcÞ¼6304 Æ 12−0 MeV [13], where the first error bar represents statistical and systematic uncertainties and the B. Analyzing the (cb¯) bound states second characterizes heavy-quark discretization effects. The nonrelativistic potential picture, motivated by the 2 1 1 Calculations incorporating þ þ dynamical quark fla- asymptotic freedom of QCD [20], gave early insight into 11 6278 9 vors ðu=d; s; cÞ [14] yield Mð S0Þ¼ Æ MeV, in the nature of charmonium and generated a template for impressive agreement with the measured Bc mass, and 1 the spectrum of excited states [21]. For more than four predict Mð2 S0Þ¼6894 Æ 19 Æ 8 MeV [15]. decades, it has served as a reliable guide to quarkonium Three distinct elementary processes contribute to the spectroscopy, including the states lying near or just above ¯ ¯ ⋆þ decay of Bc: the individual decays b → cW and c → flavor threshold for fission into two heavy-light mesons sW⋆þ of the two heavy constituents, and the annihilation that are significantly influenced by coupled-channel cb¯ → W⋆þ through a virtual W-boson. Several examples effects [22,23]. of the b¯ → c¯ transition have been observed, including We view the nonrelativistic potential-model treatment as þ þ þ þ þ − the final states J=ψl νl, J=ψπ , J=ψK , J=ψπ π π , a stepping stone, not a final answer, however impressive its þ þ − þ þ þ − − þ ⋆þ record of utility. Potential theory does not capture the full J=ψπ K K , J=ψπ π π π π , J=ψDs , J=ψDs , and þ þ 0 þ dynamics of the strong interaction, and while the standard J=ψπ pp¯ ; and ψð2SÞπ . A single channel, Bsπ , repre- senting the c → s transition is known. The annihilation coupled-channel treatment is built on a plausible physical þ picture, it is not derived from first principles. Moreover, mechanism, which would lead to final states such as τ ντ ¯ ¯ πþ relativistic effects may be more important for ðcbÞ than for and pp , has not yet been established. The observed ¯ τ 0 507 0 009 ðccÞ. The c-quark moves faster in the Bc meson than in the lifetime, ðBcÞ¼ð . Æ . Þ ps [12], is consistent J=ψ, because it must balance the momentum of a more with theoretical expectations [16,17]. Predictions for partial massive b-quark. One developing area of theoretical decay rates (or relative branching fractions) await exper- research has been to explore methods more robust than imental tests. Some recent theoretical works explore the nonrelativistic quantum mechanics [17,24,25]. potential of rare B decays [18]. c ¯ Nonperturbative calculations on a spacetime lattice in Until recently, the only evidence reported for a ðcbÞ principle embody the full content of QCD. This approach is excited state was presented by the ATLAS Collaboration yielding increasingly precise predictions for the masses of [1] in pp collisions at 7 and 8 TeV, in samples of 4.9 ¯ 0 23 −1 ðcbÞ levels up through the Bc ð S1Þ state. It is not yet and 19.2 fb . They observed a new state at 6842 Æ 7 MeV possible to extract reliable signals for higher-lying states Æπþπ− − Æ − 2 πÆ in the MðBc Þ MðBc Þ Mð Þ mass difference, from the lattice, so we rely on potential-model methods to Æ ψπÆ 3 with Bc detected in the J= mode. The mass construct a template for the Bc spectrum through the 4 S1 (527 Æ 7 MeV above hMð1SÞi) and decay of this state level. If experiments should uncover systematic deviations are broadly in line with expectations for the second s-wave from the expectations we present, they may be taken as Æ state, Bc ð2SÞ.

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