General Treatment of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi><mml:mo>→</mml:mo><mml:mi>π</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>in the Veneziano Model

Rosner, Jonathan L.; Suura, H.

doi:10.1103/physrev.187.1905

Cited by 16 publications

(1 citation statement)

References 25 publications

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“…If Veneziano forms are to be taken seriously we might expect to find sequences of 77 and A mesons whose poles should be included if we wish to treat the intermediate range for t. 6 Such a discussion is beyond the scope of this paper but it appears that the arbitrariness of F^{t) will still be maintained as long as we require that the matrix element in Eq. (4) has no subtractions in p 2 or k 2 . In any case, unless we impose some symmetry constraint on F^{t) such as proposed by Suura,6 F^{t) will now depend on many unknown inelastic amplitudes involving the heavy IT and A mesons.…”

Section: + (Sj) = C-(ts) = -(Ybf a /M A 2 )(T-mmtb2 11 (St)-(mentioning

confidence: 99%

Connection BetweenFπ(t)and the Amplitudes forππ→ππand
Geffen
¹

1969
Phys. Rev. Lett.
11
0
1
0
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We have studied this background process since it provides a test of charge independence. We have found that both the energy dependence of the total cross sec-tion and the angular distributions are in excellent agreement with existing data for n +p -*d + 7r° andp +p -*-d + TT + c I. Hammerman, thesis, Princeton University, Palmer Physical Laboratory Report No. PURC-2137-9 (unpublished). 6 Monte Carlo program based on technique of J. Butcher and H. Messell, NucL Phys. 20, 15 (1960). We have checked this calculation by using y rays from the reaction n+p-^d + ir 0 . 7 To Devlin, P. Shepard, R" Mischke, and J. Solomon, private communication 0 8 A possible source of systematic error could arise if the neutron beam were polarized. Reciprocity requires that the angular distributions for Reactions (1) and (2) be the same if initial-state spins are averaged and final-state spins summed. We have measured the polarization of the incident neutrons in our beam and found it to be 0.04 ±0.02 (T n & 600 MeV), a value too small to yield significant asymmetries. Our detector is insensitive to the spin of either the deuteron or the photon. A parallel situation holds for the measurement of Reaction (2).The current-algebra connection between the pion electromagnetic form factor F v (t) and the amplitudes for 7T7r-*7T7T and Tnr-*TrA i is examined by explicitly extrapolating off the pion mass shell the matrix element (^{A^l TTTT) which is taken to be dominated by ir and A t poles and possible subtractions. It is found that the connection is broken by the presence of an almost arbitrary subtraction function. In particular the Apir interaction remains arbitrary as well as the form for F^(t). The results are applied briefly to the Veneziano model. Several authors 1 have recently explored the connection between the amplitudes 7T7T -^-mr and TTTT •*irA 1 that follows from the assumptions that the matrix element <7T7T lA M | 7r> is dominated by ir and A x poles and that the scattering amplitudes are given by the Veneziano model. 2 Oyanagi 3 has extended the analysis by extrapolating to zero the momentum of one of the pions in the matrix element and thereby obtaining a Veneziano-like expression for F^(t). One result of this work, and that of a subsequent analysis, 4 has been to propose a vanishing D-wave Apu interaction, either to yield a more convergent F^it) for large t or to eliminate satellites from the int -7nr and -nil -^,nA 1 scattering amplitudes. In all these treatments, however, the extrapolation of one pion off the mass shell of the amplitude <7T7T IA M |7T> has not been done in a consistent way. 5 We intend to summarize the results of such a consistent treatment in this Letter and show that the use of the Veneziano model for this example imposes no restriction on the Z>-wave Apir interaction and that one is free to obtain almost any asymptotic behavior for F^(t).Consider the amplitude for Tr + {p) + 7r~ (q)-A^(k) + TT~ (q') with the TT + extrapolated off the mass shell,

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Section: + (Sj) = C-(ts) = -(Ybf a /M A 2 )(T-mmtb2 11 (St)-(mentioning

confidence: 99%

Connection BetweenFπ(t)and the Amplitudes forππ→ππand
Geffen
¹

1969
Phys. Rev. Lett.
11
0
1
0
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Nucleon form factors in the veneziano model

Konetschny¹,

Majerotto

1971

Nuov Cim A

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The Goldberger-Treiman relation: a probe of the chiral symmetries of quantum chromodynamics

Domínguez

1985

Riv. Nuovo Cim.

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General Treatment ofππ→πA1in the Veneziano Model

Abstract: A two-parameter Veneziano-type model for Tnr-^wAi is discussed from the standpoints of (1) constraints due to partial conservation of axial-vector current, (2) the pion electromagnetic form factor, and (3) partial widths r (X -» A IT) for X along the leading trajectory.

Cited by 16 publications

References 25 publications

Connection BetweenFπ(t)and the Amplitudes forππ→ππand
Geffen
¹

1969
Phys. Rev. Lett.
11
0
1
0
View full text Add to dashboard Cite

Connection BetweenFπ(t)and the Amplitudes forππ→ππand
Geffen
¹

1969
Phys. Rev. Lett.
11
0
1
0
View full text Add to dashboard Cite

Nucleon form factors in the veneziano model

The Goldberger-Treiman relation: a probe of the chiral symmetries of quantum chromodynamics

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General Treatment ofππ→πA1in the Veneziano Model

Abstract: A two-parameter Veneziano-type model for Tnr-^wAi is discussed from the standpoints of (1) constraints due to partial conservation of axial-vector current, (2) the pion electromagnetic form factor, and (3) partial widths r (X -» A IT) for X along the leading trajectory.

Cited by 16 publications

References 25 publications

Connection BetweenFπ(t)and the Amplitudes forππ→ππandGeffen1 1969Phys. Rev. Lett.11010View full textAdd to dashboardCite

Connection BetweenFπ(t)and the Amplitudes forππ→ππandGeffen1 1969Phys. Rev. Lett.11010View full textAdd to dashboardCite

Nucleon form factors in the veneziano model

The Goldberger-Treiman relation: a probe of the chiral symmetries of quantum chromodynamics

Contact Info

Product

Resources

About

Connection BetweenFπ(t)and the Amplitudes forππ→ππand
Geffen
¹

1969
Phys. Rev. Lett.
11
0
1
0
View full text Add to dashboard Cite

Connection BetweenFπ(t)and the Amplitudes forππ→ππand
Geffen
¹

1969
Phys. Rev. Lett.
11
0
1
0
View full text Add to dashboard Cite