Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation

Richard Williams; Christian S

doi:10.1088/1674-1137/34/9/084

Chinese Physics C> 2010, Vol. 34> Issue(9) : 1500-1503 DOI: 10.1088/1674-1137/34/9/084

Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation

Richard Williams ^, ,
Christian S

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Abstract：
We investigate masses of light mesons from a coupled system of Dyson—Schwinger (DSE) and Bethe—Salpeter equations (BSE), taking into account dominant non-Abelian, sub-leading Abelian, and dominant pion cloud contributions to the dressed quark-gluon vertex. The axial-vector Ward-Takahashi identity preserving Bethe-Salpeter kernel is constructed and the spectrum of light mesons calculated. Our model goes significantly beyond the rainbow-ladder. We find that sub-leading Abelian corrections are further dynamically suppressed, and that our results supersede early qualitative predictions from simple truncation schemes.

References

[1]

. Maris P, Roberts C D, Tandy P C. Phys. Lett. B, 1998,420: 267 [arXiv:nucl-th/9707003]2. Maris P, Roberts C D. Phys. Rev. C, 1997, 56: 3369 [arXiv:nucl-th/9708029]3. Maris P,Tandy P C. Phys. Rev. C, 1999, 60: 055214 [arXiv:nucl-th/9905056]4. Maris P,Tandy P C. Phys. Rev. C, 2000, 62: 055204 [arXiv:nucl-th/0005015]5. Bhagwat M S, Maris P. Phys. Rev. C,2008, 77: 025203[arXiv:nucl-th/0612069]6. Nicmorus D, Eichmann G, Krassnigg A, Alkofer R. Phys.Rev. D, 2009, 80: 054028 [arXiv:0812.1665 [hep-ph]]7. Eichmann G, Alkofer R, Krassnigg A, Nicmorus D. Phys.Rev. Lett., 2010, 104: 201601 [arXiv:0912.2246 [hep-ph]]8. Alkofer R, Eichmann G, Krassnigg A, Nicmorus D. arXiv:0912.3105 [hep-ph]9. Munczek H J. Phys. Rev. D, 1995, 52: 4736 [arXiv:hepth/9411239]10. Bender A, Roberts C D, Smekal L Von. Phys. Lett. B,1996,380: 7 [arXiv:nucl-th/9602012]11. Bender A, Detmold W, Roberts C D, Thomas A W. Phys.Rev. C,2002, 65: 065203 [arXiv:nucl-th/0202082]12. Bhagwat M S, Holl A, Krassnigg A, Roberts C D,Tandy PC. Phys. Rev. C,2004, 70: 035205 [arXiv:nucl-th/0403012]13. Watson P, Cassing W, Tandy P C. Few Body Syst., 2004,35: 129 [arXiv:hep-ph/0406340]14. Matevosyan H H, Thomas A W ,Tandy P C. Phys. Rev.C,2007, 75: 045201 [arXiv:nucl-th/0605057]15. Alkofer R, Fischer C S, Llanes-Estrada F J, Schwenzer K.Annals Phys., 2009, 324: 106 [arXiv:0804.3042 [hep-ph]]16. Fischer C S, Williams R. Phys. Rev. Lett. 2009, 103:122001. [arXiv:0905.2291 [hep-ph]]17. Fischer C S, Williams R. Phys. Rev. D,2008, 78: 074006[arXiv:0808.3372 [hep-ph]]18. Williams R. arXiv:0912.3494 [hep-ph]19. Bhagwat M S, Tandy P C. Phys. Rev. D, 2004, 70: 094039[arXiv:hep-ph/0407163]20. Chang L, Roberts C D. Phys. Rev. Lett. 2009, 103: 081601[arXiv:0903.5461 [nucl-th]].21. Fischer C S, Nickel D, Wambach J. Phys. Rev. D , 2007,76: 094009 [arXiv:0705.4407 [hep-ph]]22. Fischer C S, Nickel D, Williams R. Eur. Phys. J. C,2008,60: 1434 [arXiv:0807.3486 [hep-ph]]23. Llewellyn-Smith C H. Annals Phys., 1969, 53: 52124. Maris P, Tandy P C. Nucl. Phys. Proc. Suppl., 2006, 161:136. [arXiv:nucl-th/0511017]25. Amsler C et al. [Particle Data Group], Phys. Lett. B, 2008,667: 1

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Richard Williams and Christian S. Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation[J]. Chinese Physics C, 2010, 34(9): 1500-1503. doi: 10.1088/1674-1137/34/9/084

Richard Williams and Christian S. Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation[J]. Chinese Physics C, 2010, 34(9): 1500-1503. doi: 10.1088/1674-1137/34/9/084 shu

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Received: 2010-02-09
Revised: 1900-01-01

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation

Corresponding author: Richard Williams,

Received Date: 2010-02-09

Accepted Date: 1900-01-01

Available Online: 2010-09-05

Abstract: We investigate masses of light mesons from a coupled system of Dyson—Schwinger (DSE) and Bethe—Salpeter equations (BSE), taking into account dominant non-Abelian, sub-leading Abelian, and dominant pion cloud contributions to the dressed quark-gluon vertex. The axial-vector Ward-Takahashi identity preserving Bethe-Salpeter kernel is constructed and the spectrum of light mesons calculated. Our model goes significantly beyond the rainbow-ladder. We find that sub-leading Abelian corrections are further dynamically suppressed, and that our results supersede early qualitative predictions from simple truncation schemes.

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Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation

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