1987 Fiscal Year Final Research Report Summary
Calculation of Hadron Masses in Lattice Gauge Theories
| Project/Area Number |
61540194
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
核・宇宙線・素粒子
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| Research Institution | University of Tsukuba |
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Principal Investigator |
IWASAKI Yoichi Institute of Physics, University of Tsukuba, 物理学系, 教授 (50027348)
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| Project Period (FY) |
1986 – 1987
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| Keywords | U(1) PROBLEM / Lattice gauge theory / Lattice QCD / Hadron / <phi> meson / Instantons / Quarks / Gluons |
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| Research Abstract |
We investigate in lattice OCD the U(1) problem that the <eta>' meson (960 MeV) is much heavier than the <pi> meson (140 MeV), taking Wilson fermions as quarks. We first derived the spectral representation of the quark propagator and investigate the Atiyah-Singer index theorem on a lattice. Then we calculate the propagators as well as the propagators for 10 configurations on an 8^3x16 lattice and show the following: The large splitting betwen the flavor singlet pseudo-scalar meson and the <pi> meson is caused both by the existence of topologically non-trivial configurations and by the fact that the u and d bare quark masses are very small. We further obtain that the mass of "<eta>"=(u<gamma>_5u + d<gamma>_5d)/ROO<2> and the mass of <eta>_s=s<gamma>_5s are both about 750 MeV: This is in accord with experiment, because if we assume the transition mass matrix between the two states is about 200 MeV, we obtain the correct masses for the <eta>' and <eta> mesons and the mixing angle <phi>=10゜ (<eta>'=<eta>_1 cos +<eta>_8 sin<phi>). On the other hand there is no noticeable splitting between the and <omega> mesons. We clarify the reason for the difference between the <pi>-<eta> splitting and the -<omega> splitting.
We point out that if the U(1) problem should be resolved both for Wilson quarks and for Kogut-Susskind quarks, the mechanisms would be completely different from each other. We also compare out results with the prediction of 1/N expanded QCD.
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Research Products
(4 results)
