Low-energy theorems for nucleon-nucleon scattering

Cohen, Thomas D.; Hansen, James M.

doi:10.1103/PhysRevC.59.13

Low-energy theorems for nucleon-nucleon scattering

Aug, 1998

10 pages

Published in:

Phys.Rev.C 59 (1999) 13-20

e-Print:

nucl-th/9808038 [nucl-th]

DOI:

10.1103/PhysRevC.59.13

Report number:

DOE-ER-40762-156,
UMD-99-011

View in:

pdf

reference search96 citations

Citations per year

Abstract:

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both

m_\pi

and

1/a

(where

a

is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the

^1S_0

and

^3S_1

channels. Analogous theorems are developed for the energy dependence

\epsilon

parameter which describes

^3S_1 - ^3D_1

mixing. These theorems are also violated. These failures strongly suggest that the physical value of

m_\pi

is too large for the chiral expansion to be valid in this context. Comparisons of

m_\pi

with phenomenological scales known to arise in the two-nucleon problem support this conjecture.

nucleon nucleon: elastic scattering
partial wave analysis
approximation: effective range
low-energy theorem
expansion
pi: mass
nucleon nucleon: scattering length
numerical calculations: interpretation of experiments

References(51)

Figures(0)

Nuclear forces from chiral Lagrangians

Steven Weinberg
(
- Texas U.
)

- Phys.Lett.B 251 (1990) 288-292
•
DOI:
- 10.1016/0370-2693(90)90938-3

Effective chiral Lagrangians for nucleon - pion interactions and nuclear forces

Steven Weinberg
(
- Texas U.
)

- Nucl.Phys.B 363 (1991) 3-18
•
DOI:
- 10.1016/0550-3213(91)90231-L

Three body interactions among nucleons and pions

Steven Weinberg
(
- Texas U.
)

- Phys.Lett.B 295 (1992) 114-121
•
e-Print:
- hep-ph/9209257
•
DOI:
- 10.1016/0370-2693(92)90099-P

Chiral lagrangians and nuclear forces

C. Ordonez
(
- Texas U.
)
,
U. van Kolck
(
- Texas U.
)

- Phys.Lett.B 291 (1992) 459-464
•
DOI:
- 10.1016/0370-2693(92)91404-W

Excitation and decay of giant resonances in the Ca-40 (e, e'x) reaction

H. Diesener
(
- Darmstadt, Tech. Hochsch.
)
,
U. Helm
(
- Darmstadt, Tech. Hochsch.
)
,
G. Herbert
(
- Darmstadt, Tech. Hochsch.
)
,
V. Huck
(
- Darmstadt, Tech. Hochsch.
)
,
P. von Neumann-Cosel
(
- Darmstadt, Tech. Hochsch.
)

et al.

- Phys.Rev.Lett. 72 (1994) 1994-1997
•
DOI:
- 10.1103/PhysRevLett.72.1994

The Two nucleon potential from chiral Lagrangians

C. Ordonez
(
- Texas U. and
- Vanderbilt U.
)
,
L. Ray
(
- Texas U.
)
,
U. van Kolck
(
- Washington U., Seattle
)

- Phys.Rev.C 53 (1996) 2086-2105
•
e-Print:
- hep-ph/9511380
•
DOI:
- 10.1103/PhysRevC.53.2086

Few nucleon forces from chiral Lagrangians

U. van Kolck
(
- Washington U., Seattle
)

- Phys.Rev.C 49 (1994) 2932-2941
•
DOI:
- 10.1103/PhysRevC.49.2932

Radiative neutron - proton capture in effective chiral Lagrangians

- Phys.Rev.Lett. 74 (1995) 4153-4156
•
e-Print:
- nucl-th/9412025
•
DOI:
- 10.1103/PhysRevLett.74.4153

Chiral Lagrangian approach to exchange vector currents in nuclei

Tae-Sun Park
(
- Washington U., Seattle
)
,
Dong-Pil Min
(
- Washington U., Seattle
)
,
Mannque Rho
(
- Washington U., Seattle
)

- Nucl.Phys.A 596 (1996) 515-552
•
e-Print:
- nucl-th/9505017
•
DOI:
- 10.1016/0375-9474(95)00406-8

Nucleon - nucleon scattering from effective field theory

David B. Kaplan
(
- Washington U., Seattle
)
,
Martin J. Savage
(
- Carnegie Mellon U.
)
,
Mark B. Wise
(
- Caltech
)

- Nucl.Phys.B 478 (1996) 629-659
•
e-Print:
- nucl-th/9605002
•
DOI:
- 10.1016/0550-3213(96)00357-4

The p p ---> p p pi0 reaction near threshold: A Chiral power counting approach

Thomas D. Cohen
(
- Maryland U.
)
,
James Lewis Friar
(
- Los Alamos
)
,
Gerald A. Miller
(
- Washington U., Seattle
)
,
Ubirajara van Kolck
(
- Washington U., Seattle
)

- Phys.Rev.C 53 (1996) 2661-2673
•
e-Print:
- nucl-th/9512036
•
DOI:
- 10.1103/PhysRevC.53.2661

More effective field theory for nonrelativistic scattering

David B. Kaplan
(
- Washington U., Seattle
)

- Nucl.Phys.B 494 (1997) 471-484
•
e-Print:
- nucl-th/9610052
•
DOI:
- 10.1016/S0550-3213(97)00178-8

Nonperturbative regularization and renormalization: Simple examples from nonrelativistic quantum mechanics

- Annals Phys. 263 (1998) 255-275
•
e-Print:
- hep-th/9706070
•
DOI:
- 10.1006/aphy.1997.5771

Short range interactions in an effective field theory approach for nucleon-nucleon scattering

- Phys.Rev.C 56 (1997) 679-688
•
e-Print:
- nucl-th/9610049
•
DOI:
- 10.1103/PhysRevC.56.679

Dimensional power counting in nuclei

James Lewis Friar
(
- Los Alamos
)

- Few Body Syst. 22 (1997) 161
•
e-Print:
- nucl-th/9607020
•
DOI:
- 10.1007/s006010050059

- PRVA C 55 67

Bound states and power counting in effective field theories

Michael E. Luke
(
- Toronto U.
)
,
Aneesh V. Manohar
(
- UC, San Diego
)

- Phys.Rev.D 55 (1997) 4129-4140
•
e-Print:
- hep-ph/9610534
•
DOI:
- 10.1103/PhysRevD.55.4129

How to renormalize the Schrodinger equation

G.P. Lepage
(
- Cornell U., LNS
)

•
e-Print:
- nucl-th/9706029

Renormalization in nonrelativistic quantum mechanics

Sadhan K. Adhikari
(
- Sao Paulo, IFT
)
,
Angsula Ghosh
(
- Sao Paulo, IFT
)

- J.Phys.A 30 (1997) 6553-6564
•
e-Print:
- hep-th/9706193
•
DOI:
- 10.1088/0305-4470/30/18/029

Renormalization and power counting in effective field theories for nucleon-nucleon scattering

Keith G. Richardson
(
- Manchester U.
)
,
Michael C. Birse
(
- Manchester U.
)
,
Judith A. McGovern
(
- Manchester U.
)

e-Print:
- hep-ph/9708435

A Renormalization group treatment of two-body scattering

Michael C. Birse
(
- Manchester U.
)
,
Judith A. McGovern
(
- Manchester U.
)
,
Keith G. Richardson
(
- Manchester U.
)

- Phys.Lett.B 464 (1999) 169-176
•
e-Print:
- hep-ph/9807302
•
DOI:
- 10.1016/S0370-2693(99)00991-0

Nucleon deuteron scattering from an effective field theory

- Phys.Lett.B 428 (1998) 221-226
•
e-Print:
- nucl-th/9710073
•
DOI:
- 10.1016/S0370-2693(98)00430-4

Effective theory for neutron deuteron scattering: Energy dependence

Paulo F. Bedaque
(
- Washington U., Seattle
)
,
H.W. Hammer
(
- TRIUMF
)
,
U. van Kolck
(
- Caltech, Kellogg Lab
)

- Phys.Rev.C 58 (1998) R641-R644
•
e-Print:
- nucl-th/9802057
•
DOI:
- 10.1103/PhysRevC.58.R641

Nucleon-nucleon interaction and isospin violation

U. van Kolck
(
- Washington U., Seattle
)

- In *Mainz 1997, Chiral dynamics: Theory and experiment* 62-77,
- Lect.Notes Phys. 513 (1998) 62
•
e-Print:
- hep-ph/9711222
•
DOI:
- 10.1007/BFb0104898

Effective field theory of short range forces

U. van Kolck
(
- Caltech, Kellogg Lab and
- Washington U., Seattle
)

- Nucl.Phys.A 645 (1999) 273-302
•
e-Print:
- nucl-th/9808007
•
DOI:
- 10.1016/S0375-9474(98)00612-5

1-25 of 51
1
2
3
25 / page