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Phi meson
Phi meson
Phi meson
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Quark structure of the phi meson, is a vector meson formed of a strange quark and a strange antiquark.
Phi meson
Feynman diagram of the most common ϕ meson decay
Compositionϕ0
: ss
StatisticsBosonic
FamilyMesons
InteractionsStrong, Weak, Gravity, Electromagnetism
Symbolϕ, ϕ0
AntiparticleSelf
TheorizedSakurai (1962)
DiscoveredConnolly et al. (1963)
Types1
Mass1019.461±0.020 MeV/c2
Mean lifetime(1.55±0.01)×10−22 s
Decays into
Electric charge0
Spin1
Isospin0
Hypercharge0
Parity−1
C parity−1

In particle physics, the phi meson or ϕ meson is a vector meson formed of a strange quark and a strange antiquark. It was the ϕ meson's unexpected propensity to decay into K0
 and K0
 that led to the discovery of the OZI rule. It has a mass of 1019.461±0.020 MeV/c2 and a mean lifetime of 1.55±0.01 × 10−22 s .

Properties

[edit]

The most common decay modes of the ϕ meson are K+
K−
 at 48.9%±0.5%, K0
S+K0
L at 34.2%±0.4%, and various indistinguishable mixed combinations of rho mesons and pions at 15.3%±0.3%.[1] In all cases, it decays via the strong force. The pion channel would naïvely be the dominant decay channel because the collective mass of the pions is smaller than that of the kaons, making it energetically favorable; however, that decay route is suppressed by the OZI rule.

Technically, the quark composition of the ϕ meson can be thought of as a mix between ss, uu, and dd states, but it is very nearly a pure ss state.[2] This can be shown by deconstructing the wave function of the ϕ into its component parts. We see that the ϕ and ω mesons are mixtures of the SU(3) wave functions as follows.

,
,

where

is the nonet mixing angle,
and

The mixing angle at which the components decouple completely can be calculated to be The mixing angle of the ϕ and ω states is calculated from the masses of each state to be about 35˚, which is very close to maximum decoupling. Therefore, the ϕ meson is nearly a pure ss state.[2]

History

[edit]

The existence of the ϕ meson was first proposed by the Japanese American particle physicist, J. J. Sakurai, in 1962 as a resonance state between the K0
 and the K0
.[3] It was discovered later by Connolly et al. (1963) in a 20 inch hydrogen bubble chamber at the Alternating Gradient Synchrotron (AGS) in Brookhaven National Laboratory in Upton, NY while they were studying K−
p+
 collisions at approximately 2.23 GeV/c.[4][5] In essence, the reaction involved a beam of K−
s being accelerated to high energies to collide with protons.

The ϕ meson has several possible decay modes. The most energetically favored mode involves the ϕ meson decaying into three pions, which is what would naïvely be expected. However, we instead observe that it decays most frequently into two kaons.[6] Between 1963 and 1966, three people, Susumu Okubo, George Zweig, and Jugoro Iizuka, each independently proposed a rule to account for the observed suppression of the three pion decay.[7][8][9] This rule is now known as the OZI rule and is also the currently accepted explanation for the unusually long lifetimes of the J/ψ and ϒ mesons.[6] Namely, on average they last ~ 7 × 10−21 s and ~ 1.5 × 10−20 s respectively.[6] This is compared to the normal mean lifetime of a meson decaying via the strong force, which is on the order of 10−23 s .[6]

In 1999, a ϕ factory named DAFNE (or DAϕNE since the F stands for "ϕ Factory") began operation to study the decay of the ϕ meson in Frascati, Italy.[5] It produces ϕ mesons via electron-positron collisions. It has numerous detectors, including the KLOE detector which was in operation at the beginning of its operation.

Particle name Particle
symbol 		Antiparticle
symbol 		Quark
content 		Rest mass (MeV/c2) IG JPC S C B' Mean lifetime (s) Commonly decays to

(>5% of decays)

Phi meson[10] ϕ(1020) Self ss 1,019.461 ± 0.020 0− 1−− 0 0 0 1.55 ± 0.01 × 10−22 [f] K+
 + K−
 or
K0
S + K0
L or
(ρ + π) / (π+
 + π0
 + π−
)

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Phi meson

View on Grokipedia
from Grokipedia
The φ meson, also denoted as φ(1020), is a subatomic particle classified as a vector meson in the quark model of hadrons, primarily composed of a strange quark and its antiquark (s\bar{s}). It possesses a rest mass of 1019.461 ± 0.016 MeV/c² and a total decay width of 4.249 ± 0.013 MeV, indicating a short lifetime on the order of ħ / Γ ≈ 1.55 × 10^{-22} s. With quantum numbers J^{PC} = 1^{--}, I^G = 0^-, the φ meson belongs to the light vector nonet and decays almost exclusively (approximately 83%) into kaon-antikaon pairs, such as K^+ K^- (49.1 ± 0.5%) and K_S^0 K_L^0 (33.9 ± 0.4%), with rarer modes including 3π (15.4 ± 0.4%) and η γ ((2.95 ± 0.10) × 10^{-4}) %. Discovered in 1963 at through the reaction K^- p → K^0 \bar{K}^0 n and confirmed at Lawrence Berkeley Laboratory in the decay K^- p → φ n → K^+ K^- π^- p, the φ meson's existence and properties were reported in simultaneous publications that highlighted its narrow peak near 1020 MeV. Predicted theoretically by Jun John Sakurai in 1962 as part of vector meson dominance in electromagnetic interactions, its identification resolved puzzles in kaon-nucleon scattering data and provided early evidence for flavor SU(3) in particle . The φ meson's significance extends to validating the quark model, proposed independently by and in 1964, due to its nearly ideal mixing with the isoscalar ω(782) meson. In the quark model framework, the vector mesons form a nonet where the φ is predominantly s\bar{s} (with mixing angle θ_V ≈ 36.5°, close to the ideal value of arcsin(1/√3) ≈ 35.3°), while the ω is approximately (u\bar{u} + d\bar{d})/√2; this "ideal mixing" explains the φ's suppressed decays into non-strange hadrons via the Okubo-Zweig-Iizuka (OZI) rule and supports the three-quark flavor structure of hadrons. Modern studies utilize the φ as a probe for (QCD) phenomena, including and the quark-gluon plasma in relativistic heavy-ion collisions, owing to its clean strange-sector signature and small hadronic width.

Definition and Properties

Composition and Classification

The φ meson is a composed of a (s) and a corresponding strange antiquark (sˉ\bar{s}), forming a nearly pure ssˉs\bar{s} state in the . This flavor-specific composition distinguishes it from other light vector mesons that involve up and down mixtures. In the , the φ meson is classified as a with quantum numbers JPC=1−−J^{PC} = 1^{--}, where JJ is the total , PP is parity, and CC is charge conjugation. It belongs to the vector nonet of light mesons under SU(3) flavor symmetry, which arises from the of the fundamental triplet and antiquark antitriplet representations (3⊗3ˉ=8⊕13 \otimes \bar{3} = 8 \oplus 1), grouping it with particles like the ρ, ω, and K* mesons. Due to its neutral charge and identical quark-antiquark content, the φ meson is its own antiparticle. The particle was identified experimentally in 1963 and designated with the Greek letter φ in accordance with conventions for naming resonances observed in particle spectra.

Fundamental Physical Properties

The φ meson, denoted as φ(1020), has a rest mass of 1019.461 ± 0.016 MeV/c². Its mean lifetime is approximately 1.55 × 10^{-22} s, derived from the total decay width of 4.249 ± 0.013 MeV via the relation τ = ħ / Γ. These values reflect the particle's stability relative to lighter mesons and are established through precision measurements in e⁺e⁻ annihilation and hadronic collisions. The φ meson possesses well-defined quantum numbers consistent with its classification as a : total J = 1, parity P = -1, charge conjugation C = -1, I = 0, G-parity G = -1, Y = 0, B = 0, and S = 0. These assignments arise from the particle's observed decay patterns and spectroscopic analyses, confirming its I^G (J^{PC}) = 0^- (1^{--}) quantum numbers. Its mass exceeds that of the lighter ρ meson (approximately 775 MeV/c²) by about 244 MeV/c², highlighting the effect of content on the .

Historical Development

Theoretical Prediction

In the early 1960s, the development of SU(3) flavor symmetry, known as the Eightfold Way, provided a framework for classifying hadrons into multiplets based on their quantum numbers. Independently proposed by and , this scheme organized observed particles and predicted the existence of additional states to complete the symmetry representations. Specifically, it anticipated a nonet of vector mesons in the 1 GeV mass range, comprising an isovector triplet (rho mesons), a light isoscalar (), and a heavier isoscalar strange partner () to maintain SU(3) invariance. Building on this symmetry, J.J. Sakurai extended the vector meson dominance (VMD) theory in December 1962 to incorporate the predicted phi meson. In VMD, vector mesons mediate photon-hadron interactions, and Sakurai calculated that the phi, as the strange isoscalar, would have a mass around 1020 MeV, arising from mixing between octet and singlet states under SU(3). This prediction linked the phi to electromagnetic processes, such as vector meson photoproduction, and emphasized its role in testing the symmetry breaking patterns observed in lighter mesons. Although formulated after the phi's experimental observation, George Zweig's 1964 offered foundational insights into its composition. Zweig proposed that mesons consist of -antiquark pairs, with the phi emerging as a nearly pure -antiquark (s\bar{s}) state due to the heavier of the compared to up and down quarks. This interpretation reinforced the SU(3) predictions by attributing the phi-omega splitting and mixing to flavor differences in the quark constituents.

Experimental Discovery

The phi meson was first observed in 1963 at the through a study of K^- p interactions at a beam momentum of 2.43 GeV/c. The experiment, conducted by a team including M. Goldberg, M. Gundzik, S.M. Lichtman, J. Leitner, C. Llewellyn Smith, L. Matos, J. Nee, F. Oliveira (often cited as Connolly et al.), utilized a combined with scintillation counters to detect and track charged particles from the reaction K^- p → K^+ K^- n. Analysis of the data revealed a narrow in the spectrum of K^+ K^- pairs centered at 1.02 GeV, with a of approximately 4 MeV and a exceeding 5 standard deviations based on roughly 20 events in the peak. This evidence indicated the presence of a new state, distinct from previously known resonances due to its narrow width and preferred decay to kaons. The findings were reported in a seminal paper published in on 15 April 1963, marking a key breakthrough in hadron spectroscopy and providing experimental support for predictions of SU(3) flavor symmetry in the vector nonet. The discovery was rapidly confirmed by independent groups at using electron-positron annihilation data and at through kaon-proton scattering experiments later in 1963, solidifying the phi meson's existence and properties.

Production Mechanisms

Hadronic Production

The φ meson can be produced in hadronic collisions through processes, where the center-of-mass energy must exceed the kinematic threshold of approximately 2.04 GeV to allow for its creation, corresponding to twice the φ mass of 1019.46 MeV. Near-threshold production occurs in kaon-nucleon interactions, such as K⁻ p → φ N, typically requiring beam energies of 2–5 GeV to access the reaction channel. In these low-energy collisions, the cross section is influenced by exchange mechanisms, with measurements showing total cross sections on the order of microbarn at excess energies around 100 MeV above threshold. At high energies, such as in proton-proton (pp) collisions at the LHC, φ mesons are primarily produced inclusively via fusion or quark-antiquark annihilation, with diffractive and central exclusive processes contributing at forward rapidities. Measurements by the ALICE collaboration in pp collisions at √s = 13 TeV report differential cross sections d²σ/dp_T dy ≈ 10–20 mb/(GeV/c)² at mid-rapidity for p_T < 5 GeV/c, showing a scaling behavior with energy consistent with Regge-inspired models. Similarly, ATLAS data at √s = 7 TeV yield a fiducial integrated cross section σ(φ → K⁺K⁻) ≈ 570 ± 74 μb (stat. and syst. combined) for p_T^φ < 1.2 GeV/c and |y^φ| < 0.8, highlighting the dominance of soft QCD processes in the low-p_T regime. Recent studies at √s = 13.6 TeV using Run 3 data continue to probe φ production, extending the energy range for soft QCD investigations. In heavy-ion collisions, such as Au-Au at RHIC (√s_NN = 200 GeV) and Pb-Pb at LHC (√s_NN = 2.76–5.02 TeV), φ production is enhanced due to the higher strange quark density in the quark-gluon plasma, where coalescence of s s-bar pairs from the medium becomes a key mechanism alongside initial hard scattering. STAR measurements at RHIC indicate elliptic flow v₂(φ) ≈ 0.02–0.05 for p_T = 0.5–2 GeV/c in mid-central collisions, supporting coalescence as the primary formation process in the intermediate p_T range, with yields scaling with the number of binary collisions for high-p_T φ. ALICE results in Pb-Pb collisions further show a strangeness enhancement factor of ≈2–3 relative to pp, attributed to thermal s quark production in the plasma.

Electromagnetic Production

The dominant method for the electromagnetic production of the φ meson involves electron-positron annihilation into the φ resonance, e+e−→ϕe^+ e^- \to \phi, at a center-of-mass energy s=mϕ≈1.02\sqrt{s} = m_\phi \approx 1.02
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