I=2 pion scattering length from two-pion wave functions

Journal Article · Sun May 01 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.71.094504· OSTI ID:20709387

Aoki, S; Iwasaki, Y; Kanaya, K; Yamazaki, T ^[1]; Fukugita, M ^[2]; Ishikawa, K-I; Okawa, M ^[3]; Ishizuka, N; Kuramashi, Y; Ukawa, A; Yoshie, T ^[1]; Kaneko, T ^[4]

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1. Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571 (Japan)
2. Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277 8582 (Japan)
3. Department of Physics, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526 (Japan)
4. High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801 (Japan)

We calculate the two-pion wave function in the ground state of the I=2 S-wave system and find the interaction range between two pions, which allows us to examine the validity of the necessary condition for the finite-volume method for the scattering length proposed by Luescher. We work in the quenched approximation employing a renormalization group improved gauge action for gluons and an improved Wilson action for quarks at 1/a=1.207(12) GeV on 16{sup 3}x80, 20{sup 3}x80, and 24{sup 3}x80 lattices. We conclude that the necessary condition is satisfied within the statistical errors for the lattice sizes L{>=}24 (3.92 fm) when the quark mass is in the range that corresponds to m{sub {pi}}{sup 2}=0.273-0.736 GeV{sup 2}. We obtain the scattering length with a smaller statistical error from the wave function than from the two-pion time correlator.

• OSTI ID: 20709387
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 9 Vol. 71; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ERRORS
GEV RANGE
GLUONS
GROUND STATES
INTERACTION RANGE
LATTICE FIELD THEORY
PIONS
QUARKS
RENORMALIZATION
REST MASS
S WAVES
SCATTERING LENGTHS
WAVE FUNCTIONS