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

Abstract
HTML
Reference
Related

PDF

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

[1]	Liang-Liang Liu , Su-Jun Cui , Jing Xu , Xin-Heng Guo . Forward-backward asymmetries in ${\boldsymbol \Lambda_{\boldsymbol b} \boldsymbol\rightarrow \boldsymbol\Lambda l^+ l^- }$ in the Bethe-Salpeter equation approach. Chinese Physics C, 2022, 46(9): 093106. doi: 10.1088/1674-1137/ac7041
[2]	Zi-Kan Geng , Yue Jiang , Tianhong Wang , Hui-Wen Zheng , Guo-Li Wang . Isgur-Wise function in B_c decays to charmonium with the Bethe-Salpeter method. Chinese Physics C, 2021, 45(1): 013104. doi: 10.1088/1674-1137/abc16b
[3]	Hong-Wei Ke , Xiao-Hai Liu , Xue-Qian Li . Study on the possible molecular state composed of $ {{D}^ * _s} {\bar{{D}}_{{s1}}}$ within the Bethe-Salpeter framework. Chinese Physics C, 2020, 44(9): 093104. doi: 10.1088/1674-1137/44/9/093104
[4]	Liang-Liang Liu , Xian-Wei Kang , Zhen-Yang Wang , Xin-Heng Guo . Rare ${{\Lambda_b \rightarrow \Lambda l^+ l^- }}$ decay in the Bethe-Salpeter equation approach. Chinese Physics C, 2020, 44(8): 083107. doi: 10.1088/1674-1137/44/8/083107
[5]	Ya-Peng Zhao , Rui-Rui Zhang , Han Zhang , Hong-Shi Zong . Chiral phase transition from the Dyson-Schwinger equations in a finite spherical volume. Chinese Physics C, 2019, 43(6): 063101. doi: 10.1088/1674-1137/43/6/063101
[6]	Rong Wang , Xu-Rong Chen . Dynamical parton distributions from DGLAP equations with nonlinear corrections. Chinese Physics C, 2017, 41(5): 053103. doi: 10.1088/1674-1137/41/5/053103
[7]	Jian Liang , Wei Sun , Ying Chen , Wei-Feng Qiu , Ming Gong , Chuan Liu , Yu-Bin Liu , Zhao-Feng Liu , Jian-Ping Ma , Jian-Bo Zhang . Spectrum and Bethe-Salpeter amplitudes of Ω baryons from lattice QCD. Chinese Physics C, 2016, 40(4): 041001. doi: 10.1088/1674-1137/40/4/041001
[8]	Arafat Gabareen , Stephen Lars . Z charmoniumlike mesons. Chinese Physics C, 2011, 35(7): 695-702. doi: 10.1088/1674-1137/35/7/017
[9]	G. Eichmann , A. Krassnigg , D. Nicmorus . Hadron properties from QCD bound-state equations: A status report. Chinese Physics C, 2010, 34(9): 1175-1180.
[10]	S.L.Olsen¹ , 2 . What's new with the XYZ mesons?. Chinese Physics C, 2008, 32(6): 455-462. doi: 10.1088/1674-1137/32/6/011
[11]	YUE RuiHong , FAN Heng , CAO JunPeng . Coordinate Bethe Ansatz for Generalized t-J Model. Chinese Physics C, 2000, 24(3): 203-207.
[12]	Bian Jianguo , Wang Jiahui . The Pseudo-scalar Solution of Bethe-Salpeter Equation in the Approximation of One Gluon Exchange. Chinese Physics C, 1994, 18(7): 591-600.
[13]	DONG Yu-Bing , SU Jun-Chen . BETHE-SALPETER EQUATION FOR qq SYSTEM AND CALCULATION OF MESON SPECTRA. Chinese Physics C, 1989, 13(11): 1007-1016.
[14]	Ma Zhongqi , Dai Anying . On the Hermitian of Hamiltonians of Radial Equations. Chinese Physics C, 1988, 12(S1): 27-36.
[15]	DAI You-Shan , SONG Xiao-Tong . THE BETHE-SALPETER EQUATION FOR SPIN (0—3/2) ELECTROMAGNETIC BOUND SYSTEM AND ITS APPROXIMATE SOLUTION. Chinese Physics C, 1986, 10(5): 527-535.
[16]	JU CHANG-SEN . THE DEPENDENCE OF OVERLAP INTEGRAL ON QUARK MASS IN BETHE-SALPETER THEORY. Chinese Physics C, 1982, 6(1): 25-29.
[17]	Ruan Tu-nan , Zhu Xi-quan , He Zho-xiu . DERIVATION OF A QUASIPOTENTIAL EQUATION FROM AN EQUATION OF THE BE THE-SALPETER TYPE. Chinese Physics C, 1980, 4(2): 186-190.
[18]	Li Bing-an , Xian Ding-chang , Yan Su , Chen Tian-lun , Yang Qing-zhu , Lu Jing-fa . THE INFLUENCE OF THE SELF-ENERGY DIAGRAMS ON THE SOLUTIONS OF A SCALAR BETHE SALPETER EQUATION. Chinese Physics C, 1980, 4(1): 33-42.
[19]	LI BING-AN . WARD IDENTITIES AND BETHE-SALPETER EQUATIONS AND THE ELECTROMAGNETIC TRANSITION ELEMENTS OF MESONS AND BARYONS. Chinese Physics C, 1979, 3(2): 141-151.
[20]	GAO CHONG-SHOU . BETHE-SALPETER EQUATION FOR STRATON AND ANTISTRATON WITH DIFFERENT MASSES AND SU(4)MASS RELATIONS FOR MESONS. Chinese Physics C, 1979, 3(2): 152-164.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(2356)
PDF Downloads(418)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.

HTML

Reference (1)

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

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article