The U(1) Problem

Weinberg, Steven

doi:10.1103/PhysRevD.11.3583

The U(1) Problem

Steven Weinberg
(
- Harvard U.
)

Mar, 1975

37 pages

Published in:

Phys.Rev.D 11 (1975) 3583-3593

DOI:

10.1103/PhysRevD.11.3583

Report number:

Print-75-0266 (HARVARD)

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Abstract: (APS)

A detailed analysis of the problems associated with the conserved U(1) axial-vector current in quark-gluon models is presented. It is shown that such models involve a light isoscalar pseudoscalar boson, with a mass less than 3mπ. The existence of this boson would produce a strong off-shell variation in the η→3π matrix element, thus invalidating the usual conclusions about the rate and energy dependence of this decay. Following Kogut and Susskind, it is proposed that the light Goldstone boson is actually a dipole, with positive- and negative-metric parts, which cancel in matrix elements of gluon-gauge-invariant operators but not in operators such as the U(1) current. It is shown that the masses of the observable pseudoscalar bosons and the η decay rate are then just as they would be in a theory without the U(1) symmetry, and in fair agreement with experiment. The application of current algebra to theories with charmed quarks is briefly discussed.

FIELD THEORY: UNIFIED INTERACTION
CURRENT ALGEBRA
QUARK: CHARM
MODEL: GLUON
SYMMETRY: U(1)
MODEL: CONSERVED A-V CURRENT
FIELD THEORY: GOLDSTONE THEOREM
FIELD THEORY: OPERATOR ALGEBRA
POSTULATED PARTICLE: ISOSCALAR BOSON
POSTULATED PARTICLE: PSEUDOSCALAR

References(49)

Figures(0)

Reliable Perturbative Results for Strong Interactions?

H.David Politzer
(
- Harvard U.
)

- Phys.Rev.Lett. 30 (1973) 1346-1349,
- Also in *Mohapatra, R. N. (Ed.), Lai, C. H. (Ed.): Gauge Theories Of Fundamental Interactions*, 333-336, and in *Rebbi, C. (Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 237-240,
- In *Lichtenberg, D. B. (Ed.), Rosen, S. P. (Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 243-246,
•
DOI:
- 10.1103/PhysRevLett.30.1346

Ultraviolet Behavior of Nonabelian Gauge Theories

David J. Gross
(
- Princeton U.
)
,
Frank Wilczek
(
- Princeton U.
)

- Phys.Rev.Lett. 30 (1973) 1343-1346,
- Also in *Rebbi, C. (Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 233-236,
•
DOI:
- 10.1103/PhysRevLett.30.1343

New approach to the renormalization group

Steven Weinberg
(
- Harvard U.
)

- Phys.Rev.D 8 (1973) 3497-3509
•
DOI:
- 10.1103/PhysRevD.8.3497

- Phys.Rev.D 9 908

Price of asymptotic freedom

Sidney R. Coleman
(
- Princeton U.
)
,
David J. Gross
(
- Princeton U.
)

- Phys.Rev.Lett. 31 (1973) 851-854
•
DOI:
- 10.1103/PhysRevLett.31.851

Hierarchy of Interactions in Unified Gauge Theories

- Phys.Rev.Lett. 33 (1974) 451-454
•
DOI:
- 10.1103/PhysRevLett.33.451

Nonabelian Gauge Theories of the Strong Interactions

Steven Weinberg
(
- Harvard U.
)

- Phys.Rev.Lett. 31 (1973) 494-497,
- Also in *Mohapatra, R. N. (ed.), Lai, C. H. (ed.): Gauge Theories Of Fundamental Interactions*, 357-360, and in *Froggatt, C.D., Nielsen, H.B.: Origin of symmetries* 256-259
•
DOI:
- 10.1103/PhysRevLett.31.494

Current algebra and gauge theories. 1.

Steven Weinberg
(
- MIT, LNS
)

- Phys.Rev.D 8 (1973) 605-625
•
DOI:
- 10.1103/PhysRevD.8.605

Current algebra and gauge theories. 2. NonAbelian gluons

Steven Weinberg
(
- Harvard U.
)

- Phys.Rev.D 8 (1973) 4482-4498
•
DOI:
- 10.1103/PhysRevD.8.4482

Mass-shell evaluation of the amplitude, partial conservation of axial-vector current, and equal time commutators in low-energy k-plus-minus p scattering

- Phys.Rev. 179 (1969) 1449-1456
•
DOI:
- 10.1103/PhysRev.179.1449

Electrodynamic properties of baryons in the unitary symmetry scheme

Sidney R. Coleman
(
- Caltech
)
,
Sheldon Lee Glashow
(
- Caltech
)

- Phys.Rev.Lett. 6 (1961) 423
•
DOI:
- 10.1103/PhysRevLett.6.423

Departures from the eightfold way: Theory of strong interaction symmetry breakdown

Sidney R. Coleman
(
- Harvard U.
)
,
S.L. Glashow
(
- Harvard U.
)

- Phys.Rev. 134 (1964) B671-B681
•
DOI:
- 10.1103/PhysRev.134.B671

Current algebra and the decay $\eta \to 3\pi$

D.G. Sutherland

- Phys.Lett. 23 (1966) 384-385
•
DOI:
- 10.1016/0031-9163(66)90477-X

Current algebra and eta ---> 3 pi

J.S. Bell
(
- CERN
)
,
D.G. Sutherland
(
- CERN
)

- Nucl.Phys.B 4 (1968) 315-325,
- *Bell, M. (ed.) et al.: Quantum mechanics, high energy physics and accelerators* 328-338
•
DOI:
- 10.1016/0550-3213(68)90316-7

- Phys.Rev. 187 1416

Gauge theories based on quarks and the eta ---> 3pi problem

R.N. Mohapatra
(
- Maryland U.
)
,
Jogesh C. Pati
(
- Maryland U.
)

- Phys.Rev.D 8 (1973) 4212-4217
•
DOI:
- 10.1103/PhysRevD.8.4212

Advantages of the Color Octet Gluon Picture

- Phys.Lett.B 47 (1973) 365-368,
- Also in *Lichtenberg, D. B. (Ed.), Rosen, S. P. (Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 151-154
•
DOI:
- 10.1016/0370-2693(73)90625-4

Eta ---> 3pi in a renormalizable su(3) sigma model

W. Hudnall
(
- Syracuse U.
)
,
J. Schechter
(
- Syracuse U.
)

- Phys.Rev.D 9 (1974) 2111-2118
•
DOI:
- 10.1103/PhysRevD.9.2111

Pi-eta Degeneracy Problem in Gauge Theories

Itzhak Bars
(
- Stanford U., ITP
)
,
M.B. Halpern
(
- UC, Berkeley
)

- Phys.Rev.D 9 (1974) 3430
•
DOI:
- 10.1103/PhysRevD.9.3430

Axial vector vertex in spinor electrodynamics

Stephen L. Adler
(
- Princeton U.
)

- Phys.Rev. 177 (1969) 2426-2438,
•
DOI:
- 10.1103/PhysRev.177.2426

A PCAC puzzle: $\pi^0 \to \gamma \gamma$ in the $\sigma$ model

J.S. Bell
(
- CERN
)
,
R. Jackiw
(
- CERN
)

- Nuovo Cim.A 60 (1969) 47-61
•
DOI:
- 10.1007/BF02823296

Phase transitions in vector - gluon models: A solution to the U(3) problem

Paul Langacker
(
- Rockefeller U.
)
,
Heinz Pagels
(
- Rockefeller U.
)

- Phys.Rev.D 9 (1974) 3413-3427
•
DOI:
- 10.1103/PhysRevD.9.3413

Weak Interactions with Lepton-Hadron Symmetry

- Phys.Rev.D 2 (1970) 1285-1292,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 203-210,
- In *Rosner, J.L. (ed.): New Particles*, 18-25,
- In *Lichtenberg, D. B. (Ed.), Rosen, S. P. (Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 193-200.,
- In *Bologna 1984, Proceedings, Fifty Years of Weak-Interaction Physics* 687-694
•
DOI:
- 10.1103/PhysRevD.2.1285

Behavior of current divergences under SU(3) x SU(3)

- Phys.Rev. 175 (1968) 2195-2199
•
DOI:
- 10.1103/PhysRev.175.2195

Breaking chiral symmetry

S.L. Glashow
(
- Harvard U.
)
,
Steven Weinberg
(
- MIT, LNS
)

- Phys.Rev.Lett. 20 (1968) 224-227
•
DOI:
- 10.1103/PhysRevLett.20.224

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