Fundamentals
Definition and composition
The Upsilon meson is a flavorless meson formed by a bottom quark (b) and its antiquark (\bar{b}) bound together in a color-singlet state, making it a member of the bottomonium family of quarkonia. This composition arises from the strong interaction, where the quark and antiquark annihilate their color charges to form a neutral hadron.[1] Like the charmonium states such as the J/ψ meson (composed of a charm quark and antiquark), the Upsilon system benefits from the heavy mass of its constituents, allowing a non-relativistic treatment, but the bottom quark's greater mass leads to a more compact bound state with a size on the order of 0.2 fm and higher overall masses compared to charmonium's approximately 0.3 fm extent.[2] The increased heaviness enhances the validity of potential models for describing the internal dynamics.[1] The binding mechanism relies on the exchange of gluons via the strong force, modeled within quantum chromodynamics (QCD) as a non-relativistic quantum mechanical system akin to positronium in quantum electrodynamics, though distinguished by QCD's asymptotic freedom at short distances and confinement at larger scales that prevents dissociation into free quarks.[1] This framework captures the Upsilon's stability as a colorless excitation of the QCD vacuum.Notation and quantum numbers
The Upsilon meson, as a vector state in the bottomonium spectrum, is labeled using the standard spectroscopic notation for quarkonia, ^{2S+1}L_J, where S denotes the total spin quantum number of the quark-antiquark pair, L the orbital angular momentum quantum number (with S, P, D, etc., corresponding to L = 0, 1, 2, \ldots), and J the total angular momentum quantum number.[3] For the Upsilon family, the states are spin triplets with S = 1, hence ^{3}L_J, reflecting the parallel spins of the bottom quark and antiquark.[3] The ground state Upsilon mesons correspond to S-wave configurations where L = 0, yielding the symbol \Upsilon for the vector meson with J = 1.[3] Radial excitations are distinguished by the principal quantum number n = 1, 2, 3, \ldots, as in \Upsilon(nS) for these ^{3}S_1 states.[3] The intrinsic quantum numbers of the Upsilon meson are fixed by its quark content and the non-relativistic quark model. It has total spin J = 1, negative parity P = -1, negative charge conjugation C = -1, zero isospin I = 0 due to the identical flavor of the b\bar{b} pair, and G-parity G = -1 (since G = C (-1)^I for I = 0).[4] These combine to give the full set I^G (J^{PC}) = 0^- (1^{--}), characteristic of neutral vector mesons in quantum chromodynamics.[3] The parity arises from P = (-1)^{L+1} for quarkonia, which for L = 0 yields P = -1, while C = (-1)^{L+S} gives C = -1 for S = 1.[4] Within the broader bottomonium spectrum, the Upsilon states are distinguished from pseudoscalar singlet counterparts like the \eta_b, which have S = 0 and thus J^{PC} = 0^{-+}, or from scalar ^3P_0 states like the \chi_{b0} with J^{PC} = 0^{++}.[3] This notation framework, rooted in the quark model's classification of hadron quantum numbers, provides the basis for identifying excited states such as \Upsilon(1S), though specific assignments require experimental confirmation of their J^{PC}.[3]History
Discovery at Fermilab
The E288 experiment at Fermilab, conducted in 1977, provided the first evidence for the Upsilon meson through the detection of dimuon events in high-energy proton-nucleus collisions. The setup utilized a 400 GeV proton beam directed at fixed copper and platinum targets, with a magnetic spectrometer equipped with multiwire proportional chambers to track and identify muon pairs (μ⁺μ⁻). This configuration, an upgrade from an earlier phase of the experiment, was optimized for sensitivity to high-mass dileptons, analyzing approximately 9000 events with invariant masses above 5 GeV.[5] Key evidence emerged from a narrow resonance peak centered at approximately 9.5 GeV in the dimuon mass spectrum, specifically within the 9.4–10.4 GeV range, indicating a strong enhancement consistent with a short-lived particle decay. The experiment, led by Leon Lederman as spokesman in collaboration with researchers from Fermilab, Columbia University, and Stony Brook University, interpreted this resonance as the ground-state bound state of a bottom quark and its antiquark (b\overline{b}), providing direct experimental confirmation of the bottom quark's existence and completing the third generation of quarks predicted by the standard model.[5][6] The discovery aligned with theoretical expectations for a heavier analog to the J/ψ meson (c\overline{c} bound state), following predictions of sequential quark generations to address flavor-changing neutral currents, as proposed by Glashow, Iliopoulos, and Maiani in 1970, and motivated by searches for higher-mass quarkonia anticipated by groups including Samuel C. C. Ting's. Internal analysis identified the signal by mid-June 1977, leading to a seminar announcement at Fermilab on July 1, 1977, and formal publication in August 1977. This breakthrough built on the 1974 J/ψ discovery, for which Samuel C. C. Ting and Burton Richter shared the 1976 Nobel Prize in Physics.[7][8][9]Confirmation and early spectroscopy
Following the initial observation at Fermilab, the Υ(1S) resonance was independently verified in 1978 at DESY's DORIS e⁺e⁻ storage ring by the PLUTO and DASP collaborations, which detected resonant production in electron-positron annihilations at a center-of-mass energy corresponding to the resonance mass of 9.46 GeV.[10] The experiment measured a narrow width of about 8 MeV, consistent with the DORIS beam energy resolution, thereby confirming the particle's existence and vector quantum numbers through the enhanced hadronic cross section at the peak.[11] In the late 1970s, energy scans at DORIS further identified the first excited state, Υ(2S), at a mass of 10.02 GeV, observed as a distinct peak in the ratio R of hadronic to muonic cross sections during systematic variation of the center-of-mass energy by the PLUTO and DASP collaborations.[11] These R-scan measurements, which probed the total e⁺e⁻ annihilation cross section versus energy, revealed the resonance's leptonic branching fraction and narrow width, supporting its interpretation as a radial excitation of the ground-state bottomonium.[11] The Υ(3S) state was discovered in 1980 at Cornell's CESR e⁺e⁻ collider using the CLEO and CUSB detectors, where R-scan data showed a resonance at 10.36 GeV with a measured mass and width aligning with expectations for the next radial excitation.[12] This observation extended the bottomonium spectrum and provided early evidence for higher-lying states through resonant enhancements in the hadronic cross section.[11] These confirmations solidified the Υ mesons as bound states of a bottom quark and antiquark, with the measured masses enabling initial refinements to the bottom quark mass in non-relativistic potential models, yielding estimates around 4.5 GeV after accounting for binding effects and spin-averaged spectra.[11]General properties
Mass spectrum overview
The Upsilon meson resonances form a series of radially excited vector bottomonium states (b\bar{b}) exhibiting a well-defined mass hierarchy, as established through high-precision measurements in e⁺e⁻ collisions and hadron colliders. The ground state, Υ(1S), has a mass of 9.46040 ± 0.00013 GeV/c². Subsequent radial excitations display progressively smaller level spacings, with the mass increasing by approximately 0.5–0.6 GeV from the 1S to 2S transition, decreasing thereafter due to the confining nature of the strong interaction.[13] The full empirical spectrum spans from the Υ(1S) at ~9.46 GeV/c² to the Υ(6S) at ~11.00 GeV/c², encompassing three observed S-wave vector states below the B\bar{B} threshold (Υ(1S)–Υ(3S)) and higher excitations above it influenced by open-flavor channels. Fine structure splittings, arising from spin-dependent interactions, are generally small (<10 MeV) for the dominant vector levels, reflecting the heavy quark mass and non-relativistic dynamics. The following table summarizes the measured masses of the principal Upsilon resonances:| State | Mass (GeV/c²) |
|---|---|
| Υ(1S) | 9.46040 ± 0.00013 |
| Υ(2S) | 10.0234 ± 0.0005 |
| Υ(3S) | 10.3551 ± 0.0005 |
| Υ(4S) | 10.5794 ± 0.0012 |
| Υ(5S) | 10.8852 +0.0026/-0.0016 |
| Υ(6S) | 11.000 ± 0.004 |