Charge symmetry breaking of the nucleon-nucleon interaction: ρ-ω mixing versus nucleon mass splitting

R. Machleidt; H. Müther

doi:10.1103/PhysRevC.63.034005

Access by Xinjiang University

Charge symmetry breaking of the nucleon-nucleon interaction: ρ-ω mixing versus nucleon mass splitting

R. Machleidt^1,* and H. Müther^2,†

¹Department of Physics, University of Idaho, Moscow, Idaho 83844
²Institut für Theoretische Physik, Universität Tübingen, D-72076 Tübingen, Germany

^*Electronic address: machleid@uidaho.edu
^†Electronic address: herbert.muether@uni-tuebingen.de

PDF

Phys. Rev. C 63, 034005 – Published 22 February, 2001

DOI: https://doi.org/10.1103/PhysRevC.63.034005

Abstract

We investigate three models for the charge symmetry breaking (CSB) of the nucleon-nucleon $(NN)$ interaction (based upon $ρ - ω$ mixing, nucleon mass splitting, and phenomenology) that all reproduce the empirical value for the CSB of the $^{1} S_{0}$ scattering length $(Δ a_{CSB})$ accurately. We reveal that these models make very different predictions for CSB in $^{3} P_{J}$ waves and examine the impact of this on some observable quantities of $A >~ 3$ nuclear systems. It turns out that the $^{3} H -^{3} He$ binding energy difference is essentially ruled by $Δ a_{CSB}$ and not very sensitive to CSB from P waves. However, the Coulomb displacement energies (which are the subject of the Nolen-Schiffer anomaly) receive about 50% of their CSB contribution from $NN$ partial waves beyond $^{1} S_{0} .$ Consequently, the predictions by the various CSB models differ here substantially (10%–20%). Unfortunately, the evaluation of the leading Coulomb contributions carries a large uncertainty such that no discrimination between the competing CSB models can presently be made. To decide the issue we suggest looking into nuclear few-body reactions that are sensitive to CSB of the nuclear force.

References (45)

C.R. Howell et al., Phys. Lett. B 444, 252 (1998).
D.E. González Trotter et al., Phys. Rev. Lett. 83, 3788 (1999).
G.A. Miller, M.K. Nefkens, and I. Slaus, Phys. Rep. 194, 1 (1990).
R. Machleidt, Adv. Nucl. Phys. 19, 189 (1989).
G. A. Miller and W. H. T. van Oers, in Symmetries and Fundamental Interactions in Nuclei, edited by W. C. Haxton and E. M. Henley (World Scientific, Singapore, 1995), p. 127.
S.A. Coon and R.C. Barrett, Phys. Rev. C 36, 2189 (1987).
S.A. Coon and M.D. Scadron, Phys. Rev. C 26, 562 (1982).
T. Goldman, J.A. Henderson, and A.W. Thomas, Few-Body Syst. 12, 193 (1992).
J. Piekarewicz and A.G. Williams, Phys. Rev. C 47, 2462 (1993).
G. Krein, A.W. Thomas, and A.G. Williams, Phys. Lett. B 317, 293 (1993).
H.B. O’Connell, B.C. Pearce, A.W. Thomas, and A.G. Williams, Phys. Lett. B 336, 1 (1994).
S.A. Coon, B.H.J. McKellar, and A.A. Rawlinson, in Intersections Between Particle and Nuclear Physics, edited by T. W. Donelly, AIP Conf. Proc. No. 412 (AIP, Woodbury, NY, 1997), p. 368.
H.B. O’Connell, B.C. Pearce, A.W. Thomas, and A.G. Williams, Prog. Part. Nucl. Phys. 39, 201 (1997).
S. A. Coon and M. D. Scadron, Proceedings of the XXIII Symposium on Nuclear Physics, Oaxtepec, Mexico, 2000 (Revista Mexicana de Fisica, to be published).
R. Machleidt, K. Holinde, and Ch. Elster, Phys. Rep. 149, 1 (1987).
S.A. Coon and J.A. Niskanen, Phys. Rev. C 53, 1154 (1996).
G.Q. Li and R. Machleidt, Phys. Rev. C 58, 1393 (1998).
U. van Kolck, M.C.M. Rentmeester, J.L. Friar, T. Goldman, and J.J. de Swart, Phys. Rev. Lett. 80, 4386 (1998).
H. Müther, A. Polls, and R. Machleidt, Phys. Lett. B 445, 259 (1999).
J.A. Nolen and J.P. Schiffer, Annu. Rev. Nucl. Sci. 19, 471 (1969).
R.B. Wiringa, V.G.J. Stoks, and R. Schiavilla, Phys. Rev. C 51, 38 (1995).
P.C. McNamee, M.D. Scadron, and S.A. Coon, Nucl. Phys. A249, 483 (1975).
R. Blankenbecler and R. Sugar, Phys. Rev. 142, 1051 (1966).
E.E. Salpeter and H.A. Bethe, Phys. Rev. 84, 1232 (1951).
R. Machleidt, Phys. Rev. C 63, 024001 (2001).
Particle Data Group, C. Caso et al., Eur. Phys. J. C 3, 1 (1998).
The convention used in Ref. [6] for $g_{α}^{2}$ differs by a factor of 4 from ours.
R.V. Reid, Ann. Phys. (N.Y.) 50, 411 (1968).
Based upon the Bonn Full Model [15], the original investigation [17] of the effect of nucleon mass splitting uses the $π NN$ coupling constant $g_{π}^{2} / 4 π = 14.4$ which is not current. For that reason we have revised the Bonn Full Model using $g_{π}^{2} / 4 π = 13.6$ and then repeated the CSB calculations of Ref. [17]. The total $Δ a_{CSB}$ predicted by the revised model is 1.508 fm (about 5% less than what was reported in Ref. [17]). Similarly, the phase shift differences created by nucleon mass splitting shown in Fig. 44 by the dashed curve are, in general, a few percent smaller than those given in Ref. [17].
W. A. van der Sanden, A. H. Emmen, and J. J. de Swart, Report No. THEF-NYM-83.11, Nijmegen, 1983 (unpublished), quoted in Ref. [31].
J.R. Bergervoet, P.C. van Campen, W.A. van der Sanden, and J.J. de Swart, Phys. Rev. C 38, 15 (1988).
R.A. Brandenburg, G.S. Chulick, Y.E. Kim, D.J. Klepacki, R. Machleidt, A. Picklesimer, and R.M. Thaler, Phys. Rev. C 37, 781 (1988).
J.L. Friar, B.F. Gibson, and G.L. Payne, Phys. Rev. C 35, 1502 (1987).
Y. Wu, S. Ishikawa, and T. Sasakawa, Phys. Rev. Lett. 64, 1875 (1990).
R.A. Brandenburg, S.A. Coon, and P.U. Sauer, Nucl. Phys. A294, 305 (1978).
J.L. Friar, B.F. Gibson, and G.L. Payne, Phys. Rev. C 42, 1211 (1990).
N. Auerbach, J. Hüfner, C.M. Shakin, and A.K. Kerman, Rev. Mod. Phys. 44, 48 (1972).
H. Sato, Nucl. Phys. A269, 378 (1976).
P.G. Blunden and M.J. Iqbal, Phys. Lett. B 198, 14 (1987).
K.C. Tam, H. Müther, H.M. Sommermann, T.T.S. Kuo, and A. Faessler, Nucl. Phys. A361, 412 (1981).
C. Harzer, H. Müther, and R. Machleidt, Phys. Lett. B 459, 1 (1999).
K.W. Schmid, H. Müther, and R. Machleidt, Nucl. Phys. A530, 14 (1991).
H. Müther and L.D. Skouras, Nucl. Phys. A581, 247 (1995).
T. Suzuki, H. Sagawa, and A. Arima, Nucl. Phys. A536, 141 (1992).
W. Glöckle, H. Witała, D. Hüber, H. Kamada, and J. Golak, Phys. Rep. 274, 107 (1996), and references therein.

[c1] C.R. Howell et al., Phys. Lett. B 444, 252 (1998).

[c2] D.E. González Trotter et al., Phys. Rev. Lett. 83, 3788 (1999).

[c3] G.A. Miller, M.K. Nefkens, and I. Slaus, Phys. Rep. 194, 1 (1990).

[c4] R. Machleidt, Adv. Nucl. Phys. 19, 189 (1989).

[c5] G. A. Miller and W. H. T. van Oers, in Symmetries and Fundamental Interactions in Nuclei, edited by W. C. Haxton and E. M. Henley (World Scientific, Singapore, 1995), p. 127.

[c6] S.A. Coon and R.C. Barrett, Phys. Rev. C 36, 2189 (1987).

[c7] S.A. Coon and M.D. Scadron, Phys. Rev. C 26, 562 (1982).

[c8] T. Goldman, J.A. Henderson, and A.W. Thomas, Few-Body Syst. 12, 193 (1992).

[c9] J. Piekarewicz and A.G. Williams, Phys. Rev. C 47, 2462 (1993).

[c10] G. Krein, A.W. Thomas, and A.G. Williams, Phys. Lett. B 317, 293 (1993).

[c11] H.B. O’Connell, B.C. Pearce, A.W. Thomas, and A.G. Williams, Phys. Lett. B 336, 1 (1994).

[c12] S.A. Coon, B.H.J. McKellar, and A.A. Rawlinson, in Intersections Between Particle and Nuclear Physics, edited by T. W. Donelly, AIP Conf. Proc. No. 412 (AIP, Woodbury, NY, 1997), p. 368.

[c13] H.B. O’Connell, B.C. Pearce, A.W. Thomas, and A.G. Williams, Prog. Part. Nucl. Phys. 39, 201 (1997).

[c14] S. A. Coon and M. D. Scadron, Proceedings of the XXIII Symposium on Nuclear Physics, Oaxtepec, Mexico, 2000 (Revista Mexicana de Fisica, to be published).

[c15] R. Machleidt, K. Holinde, and Ch. Elster, Phys. Rep. 149, 1 (1987).

[c16] S.A. Coon and J.A. Niskanen, Phys. Rev. C 53, 1154 (1996).

[c17] G.Q. Li and R. Machleidt, Phys. Rev. C 58, 1393 (1998).

[c18] U. van Kolck, M.C.M. Rentmeester, J.L. Friar, T. Goldman, and J.J. de Swart, Phys. Rev. Lett. 80, 4386 (1998).

[c19] H. Müther, A. Polls, and R. Machleidt, Phys. Lett. B 445, 259 (1999).

[c20] J.A. Nolen and J.P. Schiffer, Annu. Rev. Nucl. Sci. 19, 471 (1969).

[c21] R.B. Wiringa, V.G.J. Stoks, and R. Schiavilla, Phys. Rev. C 51, 38 (1995).

[c22] P.C. McNamee, M.D. Scadron, and S.A. Coon, Nucl. Phys. A249, 483 (1975).

[c23] R. Blankenbecler and R. Sugar, Phys. Rev. 142, 1051 (1966).

[c24] E.E. Salpeter and H.A. Bethe, Phys. Rev. 84, 1232 (1951).

[c25] R. Machleidt, Phys. Rev. C 63, 024001 (2001).

[c26] Particle Data Group, C. Caso et al., Eur. Phys. J. C 3, 1 (1998).

[c27] The convention used in Ref. [6] for $g_{α}^{2}$ differs by a factor of 4 from ours.

[c28] R.V. Reid, Ann. Phys. (N.Y.) 50, 411 (1968).

[c29] Based upon the Bonn Full Model [15], the original investigation [17] of the effect of nucleon mass splitting uses the $π NN$ coupling constant $g_{π}^{2} / 4 π = 14.4$ which is not current. For that reason we have revised the Bonn Full Model using $g_{π}^{2} / 4 π = 13.6$ and then repeated the CSB calculations of Ref. [17]. The total $Δ a_{CSB}$ predicted by the revised model is 1.508 fm (about 5% less than what was reported in Ref. [17]). Similarly, the phase shift differences created by nucleon mass splitting shown in Fig. 44 by the dashed curve are, in general, a few percent smaller than those given in Ref. [17].

[c30] W. A. van der Sanden, A. H. Emmen, and J. J. de Swart, Report No. THEF-NYM-83.11, Nijmegen, 1983 (unpublished), quoted in Ref. [31].

[c31] J.R. Bergervoet, P.C. van Campen, W.A. van der Sanden, and J.J. de Swart, Phys. Rev. C 38, 15 (1988).

[c32] R.A. Brandenburg, G.S. Chulick, Y.E. Kim, D.J. Klepacki, R. Machleidt, A. Picklesimer, and R.M. Thaler, Phys. Rev. C 37, 781 (1988).

[c33] J.L. Friar, B.F. Gibson, and G.L. Payne, Phys. Rev. C 35, 1502 (1987).

[c34] Y. Wu, S. Ishikawa, and T. Sasakawa, Phys. Rev. Lett. 64, 1875 (1990).

[c35] R.A. Brandenburg, S.A. Coon, and P.U. Sauer, Nucl. Phys. A294, 305 (1978).

[c36] J.L. Friar, B.F. Gibson, and G.L. Payne, Phys. Rev. C 42, 1211 (1990).

[c37] N. Auerbach, J. Hüfner, C.M. Shakin, and A.K. Kerman, Rev. Mod. Phys. 44, 48 (1972).

[c38] H. Sato, Nucl. Phys. A269, 378 (1976).

[c39] P.G. Blunden and M.J. Iqbal, Phys. Lett. B 198, 14 (1987).

[c40] K.C. Tam, H. Müther, H.M. Sommermann, T.T.S. Kuo, and A. Faessler, Nucl. Phys. A361, 412 (1981).

[c41] C. Harzer, H. Müther, and R. Machleidt, Phys. Lett. B 459, 1 (1999).

[c42] K.W. Schmid, H. Müther, and R. Machleidt, Nucl. Phys. A530, 14 (1991).

[c43] H. Müther and L.D. Skouras, Nucl. Phys. A581, 247 (1995).

[c44] T. Suzuki, H. Sagawa, and A. Arima, Nucl. Phys. A536, 141 (1992).

[c45] W. Glöckle, H. Witała, D. Hüber, H. Kamada, and J. Golak, Phys. Rep. 274, 107 (1996), and references therein.

Physical Review C

Export citation

Export citation

Charge symmetry breaking of the nucleon-nucleon interaction: ρ-ω mixing versus nucleon mass splitting

Abstract

References (45)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation