Bottomonium Spectroscopy Research Articles

Charmonium and bottomonium spectroscopy at Belle II

The Belle II experiment at the SuperKEKB energy-asymmetric e^{+}e^{-}e+e− collider is an upgrade of the BB factory facility at KEK in Tsukuba, Japan. The experiment began operation in 2019 and aims to record a factor of 50 times more data than its predecessor. Belle II is uniquely capable of studying the so-called “XYZ” particles: heavy exotic hadrons consisting of more than three quarks. First discovered by Belle, these now number in the dozens, and represent the emergence of a new category within quantum chromodynamics. We present recent results obtained from Belle II data, and the future prospects to explore both exotic and conventional quarkonium physics.

Excited and exotic bottomonium spectroscopy from lattice QCD

We explore the spectrum of excited and exotic bottomonia using lattice QCD. Highly excited states are identified with masses up to 11,000 MeV, many of which can be grouped into supermultiplets matching those of the quark model while exotic spin-parity-charge-conjugation quantum numbers JPC = 0+−, 1−+, 2+− that cannot be formed from overline{q}q alone are also identified. Single-meson operator constructions are used that have good JPC in the continuum, these are found to overlap well onto heavy quark states up to J ≤ 4. A continuum JPC is assigned to each level, based on the distribution amongst lattice irreps and dominant operator overlaps. States with a dominant gluonic component are identified and form a hybrid supermultiplet with JPC = (0, 1, 2)−+, 1−−, approximately 1500 MeV above the ground-state ηb, similar to previous computations with light, strange and charm quark systems.

Importance of confinement in instanton induced potential for bottomonium spectroscopy

Mass spectra of bottomonium states are computed using the Instanton Induced potential obtained from Instanton Liquid Model for QCD vacuum and incorporating a stronger confinement term. Spin dependent interactions through confined one gluon exchange potential are incorporated to remove the mass degeneracy. The mass spectra of the bbar{b} states up to 4S states are found to be in good agreement with the values reported by PDG(2020). Mixing of nearby isoparity states are also studied. We found the state varUpsilon (10{,}860) as an admixture of 5^3S_1 and 6^3D_1 Upsilon states with mixing angle theta = 39.98^{circ } and the mixed state di-leptonic decay width is found to be 0.25 keV as against the width of 0.31 pm 0.07 keV reported by PDG. Further the state varUpsilon (11{,}020) is also found to be the admixture of 6^3S_1 and 5^3D_1 Upsilon states with the mixing angle theta = 51.69^{circ } and the di-leptonic decay width of the mixed state is obtained as 0.14 keV which is very close to the width of 0.13 pm 0.03 keV reported by PDG. Present results indicates that addition of confinement to the instanton potential is crucial for the determination of the mass spectroscopy of heavy hadrons.

Bottomonium spectroscopy motivated by general features of pNRQCD

The bottomonium mass spectra are computed in the framework of potential non-relativistic quantum chromodynamics. The potential consists of a static term incorporating the Coulomb plus confinement part along with a correction term added non-perturbatively from pNRQCD, which is classified in powers of the inverse of the heavy quark mass O(1/m). The masses of excited bottomonia are calculated by perturbatively adding spin–hyperfine, spin–orbit and tensor components of one-gluon exchange interactions in powers of O(1/m 2). Calculated masses are found to be consistent with other theoretical studies and experimental data. The Regge trajectories of the calculated mass spectra are also constructed. The values of the wave functions are extracted and employed to calculate the electromagnetic transition widths and γγ, e + e −, light hadron and γγγ decay widths of several states at various leading orders, within the non-relativistic QCD formalism. Some of the experimentally reported states of bottomonium family like ϒ(10 860), ϒ(11 020) and X(10 610) are identified as mixed S–D wave and P wave states.

Search for exotics atBABAR

One of the most intriguing puzzles in hadron spectroscopy are the numerous charmonium-like states observed in the last decade, including charged states that are manifestly exotic. Over the years, the experiment BABAR has extensively studied those in B meson decays, initial state radiation processes and two photon reactions. We report in this paper new and additional studies on some of those states, performed using the entire data sample collected by BABAR in e+e− collisions, at center of mass energies near 10.58 GeV/c2. Among these, the study of the process B → J/ψϕK, with a search for the resonant states X(4140) and X(4270) in their decays to J/ψϕ, will be highlighted. The recent BABAR results of the Dalitz analysis of ηc to 3 pseudoscalar mesons, via 2-photon interactions, will be also presented in this report. Preliminary results on χbJ in the field of bottomonium spectroscopy will be introduced.

Bottomonium spectroscopy and radiative transitions involving theχbJ(1P,2P)states atBaBar

We use $(121\pm1)$ million $\Upsilon(3S)$ and $(98\pm1)$ million $\Upsilon(2S)$ mesons recorded by the BABAR detector at the PEP-II $e^+e^-$ collider at SLAC to perform a study of radiative transitions involving the $\chi_{b\mathrm{J}}(1P,2P)$ states in exclusive decays with $\mu^+\mu^-\gamma\gamma$ final states. We reconstruct twelve channels in four cascades using two complementary methods. In the first we identify both signal photon candidates in the Electromagnetic Calorimeter (EMC), employ a calorimeter timing-based technique to reduce backgrounds, and determine branching-ratio products and fine mass splittings. These results include the best observational significance yet for the $\chi_{b0}(2P)\rightarrow\gamma\Upsilon(2S)$ and $\chi_{b0}(1P)\rightarrow\gamma\Upsilon(1S)$ transitions. In the second method, we identify one photon candidate in the EMC and one which has converted into an $e^+e^-$ pair due to interaction with detector material, and we measure absolute product branching fractions. This method is particularly useful for measuring $\Upsilon(3S)\rightarrow\gamma\chi_{b1,2}(1P)$ decays. Additionally, we provide the most up-to-date derived branching fractions, matrix elements and mass splittings for $\chi_b$ transitions in the bottomonium system. Using a new technique, we also measure the two lowest-order spin-dependent coefficients in the nonrelativistic QCD Hamiltonian.

Recent bottomonium studies at Belle

We report the recent studies of bottomonium spectroscopy and transitions using the data sample collected with the Belle detector. Unambiguous π+π−π0χb1 (J = 1, 2), ωχb1 signals are observed near the Υ(5S) resonance mass region. In the invariant mass distribution, some (π+π−π0)non-ω events are observed besides clear ω signal events. A X(3872)- like state in bottom sector is searched for in the final state ωΥ(1S). The Belle collaboration also searches for the η transitions with the Υ(4S) and Υ(5S) data samples. The Υ(4S) → ηhb(1P) process is observed and evidences of η transitions from Υ(5S) to lower bottomonium are found. The ηb(1S) resonance parameters are updated based on the decay mode hb(1P) → γηb(1S) in the same work.

New bottomonium(-like) resonances’ spectroscopy and decays at Belle

We report the recent progresses in the study of bottomonium spectroscopy and decays obtained with the ϒ(1S ), ϒ(2S ), and ϒ(5S ) samples collected by the Belle experiment. Among these results, particular interest is generated by the observation, with high significance, of the missing singlet states hb (1P ) and hb (2P ) in ϒ(5S ) hadronic decays. The transition ϒ(5S ) → π+ π− hb (1, 2P ) in particular is found to be mediated by two new, bottomonium-like, charged state Zb and Zb ′ , whose nature is still argument of discussion. The large samples of hb (1P ) and hb (2P ) provided by these transitions allow the word most precise measurement of the hyperfine splitting in the 1S system and the first measurement of this quantity in the 2S system, together with a new high significance observation of the ηb (1S ) and a new, precise measurements of its parameters. The study of the radiative transition hb (2P ) → ηb (2S ) resulted in the first evidennce of the 2S singlet state. We report also new studies of the ϒ(nS ) → η ϒ(mS ) transitions, the results of an intensive search for bottomonium decays to charmonium and the first observation of ϒ(1S ) and ϒ(2S ) decaying in low multiplicity, mesonic final states.

The search for a light CP-odd Higgs and light dark matter at colliders

The possible existence of a light CP-odd Higgs boson in the NMSSM, mixing with ηb resonances, can yield sizable effects on the bottomonium spectroscopy and decays to be observed at (Super) B factories. On the other hand, recent findings from astroparticle and cosmology favoring a light dark matter constituent with mass about 10 GeV or less cast a new interest into the search for invisible decays of Υ resonances performed ar B factories.

B- and ϒ-Phenomenology in the NMSSM

The Next-to-Minimal Supersymmetric Standard Model is a well-motivated singlet extension of the MSSM, liable, e.g., to solve the “ μ -problem”. A remarkable feature of this NMSSM lies in the possibility of very light CP-odd Higgs states (below the B − B ¯ threshold). While most of the aspects of the phenomenology of the NMSSM at low energy remain similar to the effects expected in the MSSM, such light particles may lead to significant new contributions. We shall here review a few aspects of the low energy phenomenology of the NMSSM, focussing on rare B decays and bottomonium spectroscopy and decays. Special emphasis shall be given to the specific effects associated with a light CP-odd Higgs.

Bottomonium Spectroscopy with Mixing ofηbStates and a LightCP-Odd Higgs Boson

The mass of the ${\ensuremath{\eta}}_{b}(1S)$, measured recently by the BABAR Collaboration, is significantly lower than expected from QCD predictions for the $\ensuremath{\Upsilon}(1S)\mathrm{\text{\ensuremath{-}}}{\ensuremath{\eta}}_{b}(1S)$ hyperfine splitting. We suggest that the observed ${\ensuremath{\eta}}_{b}(1S)$ mass is shifted downwards due to a mixing with a $CP$-odd Higgs boson $A$ with a mass ${m}_{A}$ in the range 9.4--10.5 GeV compatible with LEP, CLEO, and BABAR constraints. We determine the resulting predictions for the spectrum of the ${\ensuremath{\eta}}_{b}(nS)\mathrm{\text{\ensuremath{-}}}A$ system and the branching ratios into ${\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ as functions of ${m}_{A}$.

SPECTROSCOPY AT B-FACTORIES USING HARD PHOTON EMISSION

The process of hard photon emission by initial electrons (positrons) at B-factories is discussed. It is shown that studies of the bottomonium spectroscopy will be feasible for the planned integrated luminosity of the B-factory experiments.

Probing QCD with heavy quarkonia

The sensitivity of the charmonium and bottomonium spectroscopy to the short distance part of the interquark potential is critically re-examined using the latest data. We confirm that the data cannot accomodate a QCD scale parameter\(\left( {\Lambda _{\overline {MS} } } \right)\) smaller than about 150 MeV, whereas we find no constraint on larger values for the scale parameter, contrary to a previous analysis. The effect of dynamical heavy quark masses in the loop correction to the perturbative potential is studied in detail and the effective four quark theory with a massive charmed quark is found to give an accurate description of the perturbative potential for quarkonia of mass up to about 200 GeV. It is argued that the experimental determination of the mass ande+e− decay width of the 1S and 2S toponium resonances (of mass round 80 GeV) with the accuracy anticipated at the forthcominge+e− colliders should enable the QCD scale parameter to be determined to within ±100 MeV.