Mass and the [ital E]1 decay rate of the singlet [ital P] state of charmonium

Journal Article · Tue Feb 01 04:00:00 EST 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.49.1639· OSTI ID:5408669

Grotch, H ^[1]; Sebastian, K J ^[2]; Zhang, X ^[3]

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1. Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
2. Department of Physics, University of Massachusetts, Lowell, Lowell, Massachusetts 01854 (United States)
3. Department of Physics, Pennsylvania State University, Hazelton Campus, Hazelton, Pennsylvania 18201 (United States)

We calculate the hyperfine splitting of the [ital P] states of charmonium using the perturbative QCD hyperfine interaction to order [alpha][sub [ital s]][sup 2], in an improved quasistatic approximation whereby the quark-antiquark scattering amplitude is expanded in powers of [ital p][sup 2]/[ital p][sub 0][sup 2] instead of [ital p][sup 2]/[ital m][sup 2] and terms of up to first order in [ital p][sup 2]/[ital p][sub 0][sup 2] are kept. We evaluated the hyperfine splitting using the wave functions obtained from the unperturbed Hamiltonian of Gupta, Radford, and Suchyta. We find the splitting [Delta][ital M][sub [ital P]]=[ital M][sub c.o.g.][sup 3][ital P][sub [ital J]][minus][ital M][sup 1][ital P][sub 1] to be [minus]0.63 MeV. Our result is very similar to the result of Halzen, Olson, Olsson, and Stong who find [Delta][ital M][sub [ital P]]=[minus]0.7[plus minus]0.2 MeV, using various potential models. It also confirms the recent published experimental result on [Delta][ital M][sub [ital P]]. We also note that if we had used the improved quasistatic approximation of Gupta to extract the hyperfine interaction from the [ital q[bar q]] scattering amplitude to order [alpha][sub [ital s]][sup 2] in QCD, we would have obtained entirely different results for the [ital P]-wave hyperfine splitting in charmonium. We also calculate the electric dipole decay rate of the process 1 [sup 1][ital P][sub 1][r arrow]1 [sup 1][ital S][sub 0]+[gamma] and find it to be about 630 keV for charmonium.

• OSTI ID: 5408669
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 49:3; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
BOSONS
CHARMONIUM
E1-TRANSITIONS
ELEMENTARY PARTICLES
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
FIELD THEORIES
FUNCTIONS
HADRONS
HYPERFINE STRUCTURE
INTERACTIONS
MASS
MESONS
MULTIPOLE TRANSITIONS
P STATES
PARTICLE INTERACTIONS
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK-ANTIQUARK INTERACTIONS
QUARKONIUM
SCATTERING AMPLITUDES
WAVE FUNCTIONS