IN-Medium Effective Chiral Lagrangian and the Pion Mass in Nuclear Matter

TANG Shu-Pian; XU Yuan

Chinese Physics C> 2001, Vol. 25> Issue(12) : 1197-1205

IN-Medium Effective Chiral Lagrangian and the Pion Mass in Nuclear Matter

TANG Shu-Pian ^, ,
XU Yuan

College of Basic Science, Hebei Science and Technology University, Shijiazhuang 050054, China2 Department of Mathematics and Physics, Hehai Univgrsity, Nanjing 210024, China

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Abstract：
We argue that effective pion mass in nuclear matter obtained from chiral effective lagrangians is unique and does not depend on off-mass-shell extensions of the pion fields as e. g. the PCAC choice. How chiral perturbation theory can be applied to the analysis of s-wave pion propagation is discussed. We consider tree level lagrangians throughout, working to O(Q 2). We illustrate the results for homogeneous, isotropic, isospin symmetric and spin-unpolarized nuclear matter, and evaluate nucleon operators in the mean field approximation, such that the corresponding results hold modulo nuclear correlation corrections. The effective pion mass in isospin symmetric nuclear matter is predicted to increase slightly with increasing nuclear density, whereas the effective time-like pion decay constant and the magnitude of the density-dependent quark condensate decrease appreciably. We work out the in-medium pion mass, the effective pion decay constant, the in-medium quark condensate, the Gell-Mann-Oakes-Renner relation and the PCAC relation in nuclear matter. The in-medium GMOR relation as well as other in-medium identities are studied in addition. Finally, we discuss how the new developments about non-relativistic chiral lagrangians and generalizations to four-quark condensates constrain the structure of the in-medium chiral lagrangians, sevral constraints on effecttive lagrangians for the description of the pion propagation in isospin symmetric, isotropic and homogenous nuclear matter.

References

[1]

. Kaplan D B .Nelson A E .Phys.Lett.,1986,B175:572. Brown G E ,Koch V ,Rho M .Nucl.Phys.,1991,A535:701 3. Delorme J,Ericson M ,Ericson T E O .Phys.Lett.,1992,B291:379 4. Brown B E et al.Nucl.Phys.,1993,A567:937 5. Yabu H et al.Phys.Lett.,1993,B315:17;Yabu H ,Nakamura S,Kubodera K .Phys.Lett.,1993,B317:269;Yabu H ,Myhrer F ,Kubdera K .Phys.Rev.,1994,D50:35496. Thorsson V ,Wirzba A .Nucl.Phys.,1995,A589:633 7. Coleman S ,Wess J,Zumino B .Phys.Rev.,1969,177:2239 8. Gasser J, Leutwyler H .Ann.Phys.(N .Y .),1984,158:142 9. Gasser J, Sainio M E ,Svarc A .Nucl.Phys.,1988,B307:779 10. Weinberg S .Phisica,1979,A96:327;Phys.Lett.,1990,B251:288;Nucl.Phys.,1991,B363:3 11. Knecht M ,Stern J. Generalized Chiral Perturbation Theory. In the Second Edition of the DAPHNE Physics Handbook,eds.L .Maini,G .Pancheri,N .Paver(Frascati,May1995)12. Jenkins E ,Manohar A .Phys.Lett.,1991,B255:55813. Bernard V ,Kaiser N ,Kambor J et al.Nucl.Phys.,1992,B388:31514. Bernard V ,Kaiser N ,Meiβner U G .Phys.Lett.,1993,B309:421 15. Gasser J, Leutwyler H ,Sainio M E .Phys.Lett.,1991,B253:25216. Koch R .Nucl.Phys.,1986,A448:707 17. Baym G ,Flowers E .Nucl.Phys.,1974,A222:29;Nelson A E ,Kaplan D B .Phys.Lett.,1987,B192:193;Muto T, Tatsumi T .Phys.Lett.,1992,B283:165;Thorsson V ,Prakash M ,Lattimer J M .Nucl.Phys.,1994,A572:693;1994,A574:85118. Gell-Mann M ,Oakes R J,Renner B .Phys.Rev.,1968,175:2195 19. Kirchbach M ,Riska D O .Nucl.Phys.,1994,A578:511 20. Drukarev E G ,Levin E M .Nucl.Phys.,1988,A511:697;Cohen T D ,Furnstahl R J,Griegel D K .Phys.Rev.Lett.,1991,67:961;Phys.Rev.,1992,C45:1881;Birse M C .J.Phys.,1994,G20:1537 21. Bernard V ,Meiβner U G .Nucl.Phys.,1988,A489:647;Lutz M ,Steiner A ,Weise W .Nucl.Phys.,1992,A542:521;1994,A574:755 22. Leutwyler H .Phys.Rev.,1994,D49:3033

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[19]	ZHU Wei . NUCLEON PROPERTIES IN NUCLEAR MEDIUM. Chinese Physics C, 1986, 10(4): 505-507.
[20]	ZHANG QI-REN . PARTIAL RESTORATION OF THE CHIRAL SYMMETRY AND THE π CONDENSATION IN NUCLEAR MATTER. Chinese Physics C, 1981, 5(3): 314-320.

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TANG Shu-Pian and XU Yuan. IN-Medium Effective Chiral Lagrangian and the Pion Mass in Nuclear Matter[J]. Chinese Physics C, 2001, 25(12): 1197-1205.

TANG Shu-Pian and XU Yuan. IN-Medium Effective Chiral Lagrangian and the Pion Mass in Nuclear Matter[J]. Chinese Physics C, 2001, 25(12): 1197-1205. shu

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Received: 2000-06-05
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

IN-Medium Effective Chiral Lagrangian and the Pion Mass in Nuclear Matter

Corresponding author: TANG Shu-Pian,

College of Basic Science, Hebei Science and Technology University, Shijiazhuang 050054, China2 Department of Mathematics and Physics, Hehai Univgrsity, Nanjing 210024, China

Received Date: 2000-06-05

Accepted Date: 1900-01-01

Available Online: 2001-12-05

Abstract: We argue that effective pion mass in nuclear matter obtained from chiral effective lagrangians is unique and does not depend on off-mass-shell extensions of the pion fields as e. g. the PCAC choice. How chiral perturbation theory can be applied to the analysis of s-wave pion propagation is discussed. We consider tree level lagrangians throughout, working to O(Q 2). We illustrate the results for homogeneous, isotropic, isospin symmetric and spin-unpolarized nuclear matter, and evaluate nucleon operators in the mean field approximation, such that the corresponding results hold modulo nuclear correlation corrections. The effective pion mass in isospin symmetric nuclear matter is predicted to increase slightly with increasing nuclear density, whereas the effective time-like pion decay constant and the magnitude of the density-dependent quark condensate decrease appreciably. We work out the in-medium pion mass, the effective pion decay constant, the in-medium quark condensate, the Gell-Mann-Oakes-Renner relation and the PCAC relation in nuclear matter. The in-medium GMOR relation as well as other in-medium identities are studied in addition. Finally, we discuss how the new developments about non-relativistic chiral lagrangians and generalizations to four-quark condensates constrain the structure of the in-medium chiral lagrangians, sevral constraints on effecttive lagrangians for the description of the pion propagation in isospin symmetric, isotropic and homogenous nuclear matter.

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IN-Medium Effective Chiral Lagrangian and the Pion Mass in Nuclear Matter

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