Leading order relativistic chiral nucleon-nucleon interaction

Xiu-Lei Ren; Kai-Wen Li; Li-Sheng Geng; Bingwei Long; Peter Ring; Jie Meng

doi:10.1088/1674-1137/42/1/014103

Chinese Physics C> 2018, Vol. 42> Issue(1) : 014103 DOI: 10.1088/1674-1137/42/1/014103

Leading order relativistic chiral nucleon-nucleon interaction

Xiu-Lei Ren ^1,2 ,
Kai-Wen Li ³ ,
Li-Sheng Geng ^3,4,, ,
Bingwei Long ⁵ ,
Peter Ring ^1,6 ,
Jie Meng ^1,3,,

1.
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
2.
Institut fü
3.
School of Physics and Nuclear Energy Engineering &
4.
School of Physics and Nuclear Energy Engineering &
5.
Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 100191, China
6.
Center for Theoretical Physics, Department of Physics, Sichuan University, Chengdu, Sichuan 610064, China
7.
Physik Department, Technische Universitä
8.
School of Physics and Nuclear Energy Engineering &

Abstract
HTML
Reference
Related

PDF

Abstract：
Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian. We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of the partial wave potentials shows a better description of the ¹S₀ and ³P₀ phase shifts than the leading order Weinberg approach, and similar to that of the next-to-leading order Weinberg approach. For the other partial waves with angular momenta J ≥ 1, the relativistic results are almost the same as their leading order non-relativistic counterparts.
- covariant chiral perturbation theory ,
- nucleon-nucleon interaction ,
- relativistic scattering equation

References

[1]	P. Schwerdtfeger, ed., Relativistic Electronic Structure Theory, Part I. Fundamentals, Theoretical and Computational Chemistry Vol. 11 (Elsevier Science B.V., 2002)
[2]	J. Meng, ed., In Relativistic Density Functional for Nuclear Structure, International Review of Nuclear Physics Vol. 10 (Singapore:World Scientific, 2016)
[3]	M. Mayer and J. Jensen, Elementary Theory of Nuclear Shell Structure, Structure of matter series (John Wiley Sons, 1955)
[4]	M. Karplus, M. Levitt, and A. Warshel, The Nobel Prize in Chemistry (2013)
[5]	S. Elhatisari, D. Lee, G. Rupak, E. Epelbaum, H. Krebs, T. A. Lhde, T. Luu, and U.-G. Meiner, Nature, 528:111 (2015)
[6]	V. Lapoux, V. Som, C. Barbieri, H. Hergert, J. D. Holt, and S. Stroberg, Phys. Rev. Lett., 117:052501 (2016)
[7]	T. D. Cohen, R. J. Furnstahl, and D. K. Griegel, Phys. Rev. Lett., 67:961 (1991)
[8]	T. D. Cohen, R. J. Furnstahl, and D. K. Griegel, Phys. Rev. C, 45:1881 (1992)
[9]	T. D. Cohen, R. J. Furnstahl, K. Griegel, and S. Jin, Prog. Part. Nucl. Phys., 35:221 (1995)
[10]	H. Yukawa, Proc. Phys. Math. Soc. Jap., 17:48 (1935),[Prog. Theor. Phys. Suppl.1,1(1935)]
[11]	V. G. J. Stoks, R. A. M. Klomp, C. P. F. Terheggen, and J. J. de Swart, Phys. Rev. C, 49:2950 (1994)
[12]	R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C, 51:38 (1995)
[13]	E. Epelbaum, H. Krebs, and U.-G. Meiner, Phys. Rev. Lett., 115:122301 (2015)
[14]	D. R. Entem, R. Machleidt, and Y. Nosyk (2017), 1703.05454
[15]	R. Machleidt, Adv. Nucl. Phys., 19:189 (1989)
[16]	R. Machleidt, Phys. Rev. C, 63:024001 (2001)
[17]	F. Gross, J. W. Van Orden, and K. Holinde, Phys. Rev. C, 45:2094 (1992)
[18]	F. Gross and A. Stadler, Phys. Rev. C, 78:014005 (2008)
[19]	R. Higa and M. R. Robilotta, Phys. Rev. C, 68:024004 (2003)
[20]	R. Higa, M. Pavon Valderrama, and E. Ruiz Arriola, Phys. Rev. C, 77:034003 (2008)
[21]	T. Becher and H. Leutwyler, Eur. Phys. J. C, 9:643 (1999)
[22]	B. Ter Haar and R. Malfliet, Phys. Rept., 149:207 (1987)
[23]	R. Brockmann and R. Machleidt, Phys. Rev. C, 42:1965 (1990)
[24]	S. Shen, J. Hu, H. Liang, J. Meng, P. Ring, and S. Zhang, Chin. Phys. Lett., 33:102103 (2016)
[25]	S. Shen, H. Liang, J. Meng, P. Ring, and S. Zhang, Phys. Rev. C, 96:014316 (2017)
[26]	S. Weinberg, Physica A, 96:327 (1979)
[27]	E. E. Jenkins and A. V. Manohar, Phys. Lett. B, 255:558 (1991)
[28]	S. Weinberg, Phys. Lett. B, 251:288 (1990)
[29]	S. Weinberg, Nucl. Phys. B, 363:3 (1991)
[30]	C. Ordonez and U. van Kolck, Phys. Lett. B, 291:459 (1992)
[31]	C. Ordonez, L. Ray, and U. van Kolck, Phys. Rev. Lett., 72:1982 (1994)
[32]	U. van Kolck, Phys. Rev. C, 49:2932 (1994)
[33]	N. Kaiser, R. Brockmann, and W. Weise, Nucl. Phys. A, 625:758 (1997)
[34]	N. Kaiser, Phys. Rev. C, 61:014003 (2000)
[35]	N. Kaiser, Phys. Rev. C, 65:017001 (2002)
[36]	N. Kaiser, Phys. Rev. C, 64:057001 (2001)
[37]	E. Epelbaum, W. Gloeckle, and U.-G. Meiner, Nucl. Phys. A, 637:107 (1998)
[38]	E. Epelbaum, W. Gloeckle, and U.-G. Meiner, Nucl. Phys. A, 671:295 (2000)
[39]	D. R. Entem and R. Machleidt, Phys. Lett. B, 524:93 (2002)
[40]	D. R. Entem and R. Machleidt, Phys. Rev. C, 66:014002 (2002)
[41]	D. R. Entem and R. Machleidt, Phys. Rev. C, 68:041001 (2003)
[42]	E. Epelbaum, W. Glockle, and U.-G. Meiner, Nucl. Phys. A, 747:362 (2005)
[43]	E. Epelbaum, H. Krebs, and U. G. Meiner, Eur. Phys. J. A, 51:53 (2015)
[44]	P. F. Bedaque and U. van Kolck, Ann. Rev. Nucl. Part. Sci., 52:339 (2002)
[45]	E. Epelbaum, H.-W. Hammer, and U.-G. Meiner, Rev. Mod. Phys., 81:1773 (2009)
[46]	R. Machleidt and D. R. Entem, Phys. Rept., 503:1 (2011)
[47]	D. R. Entem, N. Kaiser, R. Machleidt, and Y. Nosyk, Phys. Rev. C, 91:014002 (2015)
[48]	D. R. Entem, N. Kaiser, R. Machleidt, and Y. Nosyk, Phys. Rev. C, 92:064001 (2015)
[49]	M. J. Savage, in Nuclear physics with effective field theory. Proceedings, Joint Caltech/INT Workshop, Pasadena, USA, February 26-27, 1998 (1998), pp. 247-267, nucl-th/9804034
[50]	D. B. Kaplan, M. J. Savage, and M. B. Wise, Phys. Lett. B, 424:390 (1998)
[51]	D. B. Kaplan, M. J. Savage, and M. B. Wise, Nucl. Phys. B, 534:329 (1998)
[52]	J. Gegelia (1998), nucl-th/9806028
[53]	T. D. Cohen and J. M. Hansen, Phys. Rev. C, 59:13 (1999)
[54]	J. Gegelia, Phys. Lett. B, 463:133 (1999)
[55]	S. Fleming, T. Mehen, and I. W. Stewart, Nucl. Phys. A, 677:313 (2000)
[56]	T. Frederico, V. S. Timoteo, and L. Tomio, Nucl. Phys. A, 653:209 (1999)
[57]	S. R. Beane, P. F. Bedaque, L. Childress, A. Kryjevski, J. McGuire, and U. van Kolck, Phys. Rev. A, 64:042103 (2001)
[58]	S. R. Beane, P. F. Bedaque, M. J. Savage, and U. van Kolck, Nucl. Phys. A, 700:377 (2002)
[59]	A. Nogga, R. G. E. Timmermans, and U. van Kolck, Phys. Rev. C, 72:054006 (2005)
[60]	M. C. Birse, Phys. Rev. C, 74:014003 (2006)
[61]	V. S. Timoteo, T. Frederico, A. Delfino, and L. Tomio, Phys. Lett. B, 621:109 (2005)
[62]	M. C. Birse, Phys. Rev. C, 76:034002 (2007), 0706.0984
[63]	C. J. Yang, C. Elster, and D. R. Phillips, Phys. Rev. C, 77:014002 (2008), 0706.1242
[64]	C. J. Yang, C. Elster, and D. R. Phillips, Phys. Rev. C, 80:034002 (2009)
[65]	C. J. Yang, C. Elster, and D. R. Phillips, Phys. Rev. C, 80:044002 (2009), 0905.4943.
[66]	M. P. Valderrama, Phys. Rev. C, 83:024003 (2011)
[67]	M. P. Valderrama, Phys. Rev. C, 84:064002 (2011)
[68]	B. Long and C. J. Yang, Phys. Rev. C, 84:057001 (2011)
[69]	B. Long and C. J. Yang, Phys. Rev. C, 86:024001 (2012)
[70]	E. Epelbaum and J. Gegelia, Phys. Lett. B, 716:338 (2012)
[71]	E. Epelbaum, A. M. Gasparyan, J. Gegelia, and H. Krebs, Eur. Phys. J. A, 51:71 (2015)
[72]	L.-S. Geng, J. Martin Camalich, L. Alvarez-Ruso, and M. J. Vicente Vacas, Phys. Rev. Lett., 101:222002 (2008)
[73]	X.-L. Ren, L.-S. Geng, J. Martin Camalich, J. Meng, and H. Toki, JHEP, 12:073 (2012)
[74]	X.-L. Ren, L.-S. Geng, and J. Meng, Phys. Rev. D, 91:051502 (2015), 1404.4799
[75]	A. H. Blin, T. Gutsche, T. Ledwig, and V. E. Lyubovitskij, Phys. Rev. D, 92:096004 (2015)
[76]	D.-L. Yao, D. Siemens, V. Bernard, E. Epelbaum, A. M. Gasparyan, J. Gegelia, H. Krebs, and U.-G. Meiner, JHEP, 05:038 (2016)
[77]	M. Altenbuchinger, L.-S. Geng, and W. Weise, Phys. Rev. D, 89:014026 (2014)
[78]	L.-S. Geng, Front. Phys., (Beijing) 8:328 (2013), 1301.6815
[79]	M. H. Partovi and E. L. Lomon, Phys. Rev. D, 2:1999 (1970)
[80]	K. Erkelenz, Phys. Rept., 13:191 (1974)
[81]	R. J. Yaes, Phys. Rev. D 3:3086 (1971)
[82]	R. H. Thompson, Phys. Rev. D, 1:110 (1970)
[83]	R. Blankenbecler and R. Sugar, Phys. Rev., 142:1051 (1966)
[84]	V. G. Kadyshevsky, Nucl. Phys. B, 6:125 (1968)
[85]	F. Gross, Phys. Rev., 186:1448 (1969)
[86]	R. M. Woloshyn and A. D. Jackson, Nucl. Phys. B, 64:269 (1973)
[87]	K.-W. Li, X.-L. Ren, L.-S. Geng, and B. Long, Phys. Rev. D, 94:014029 (2016)
[88]	D. Djukanovic, J. Gegelia, S. Scherer, and M. R. Schindler, Few Body Syst., 41:141 (2007)
[89]	L. Girlanda, S. Pastore, R. Schiavilla, and M. Viviani, Phys. Rev. C, 81:034005 (2010)
[90]	K. A. Olive, Chin. Phys. C, 40:100001 (2016)
[91]	H. Polinder, J. Haidenbauer, and U.-G. Meiner, Nucl. Phys. A, 779:244 (2006)
[92]	S. Petschauer and N. Kaiser, Nucl. Phys. A, 916:1 (2013)
[93]	J. Goto and S. Machida, Progr. Theor. Phys., 25, 64 (1961)
[94]	E. Epelbaum, Ph.D. thesis, Julich, Forschungszentrum (2000)
[95]	H. P. Stapp, T. J. Ypsilantis, and N. Metropolis, Phys. Rev., 105:302 (1957)
[96]	V. G. J. Stoks, R. A. M. Klomp, M. C. M. Rentmeester, and J. J. de Swart, Phys. Rev. C, 48:792 (1993)
[97]	R. A. Arndt, I. I. Strakovsky, and R. L. Workman, Phys. Rev. C, 50:2731 (1994)
[98]	J. Soto and J. Tarrus, Phys. Rev. C, 78:024003 (2008)
[99]	B. Long, Phys. Rev. C, 88:014002 (2013)
[100]	H. Kamada, W. Gloeckle, J. Golak, and C. Elster, Phys. Rev. C, 66:044010 (2002)

[1]	Víctor Miguel Banda Guzmán , Rubén Flores-Mendieta , Johann Hernández . Use of SU(3) flavor projection operators to construct baryon-meson scattering amplitudes in the 1/N_c expansion. Chinese Physics C, 2026, 50(2): 1-25.
[2]	N. Amangeldi , N. Burtebayev , G. Yergaliuly , Maulen Nassurlla , B. Balabekov , Abylay Tangirbergen , Awad A. Ibraheem , Mohamed A. Dewidar , Sh. Hamada . Breakup of ⁷Li in the field of ^118,120Sn nuclei and its effect on the elastic scattering channel. Chinese Physics C, 2026, 50(2): 1-12.
[3]	. Soft pattern of gravitational Rutherford scattering from heavy target mass expansion. Chinese Physics C, 2026, 50(1): 013102. doi: 10.1088/1674-1137/ad62d6
[4]	. Correlation between Zero-Sound modes and nuclear equation of state stiffness detected by light vector boson. Chinese Physics C, 2026, 50(1): 014101. doi: 10.1088/1674-1137/adfa81
[5]	Yugen Lin , Yu Gao . Dark matter subhalo evaporation by Coulomb-like interaction with galactic gas. Chinese Physics C, 2026, 50(1): 015104. doi: 10.1088/1674-1137/ae07be
[6]	Wentao Zeng , Zehao Lin , Yiran Wang , Shuangquan Zhang , Jinniu Hu , Ying Zhang . Resonant states in the Schrödinger equation solved by the Green's function method. Chinese Physics C, 2026, 50(2): 1-10.
[7]	Huixiao Duan , Fan Zhang , Kailei Wang , Jun Su . Nuclear temperature of spectator source extracted by neutron spectra in ¹²⁴Sn,¹⁰⁷Sn + ¹²⁰Sn collisions at 600 MeV/nucleon. Chinese Physics C, 2026, 50(2): 1-10.
[8]	Renli Xu , Chen Wu , Jian Liu , Bin Hong , Jie Peng , Xiong Li , Ruxian Zhu , Zhizhen Zhao , Zhongzhou Ren . Ground-state properties of finite nuclei in relativistic Hartree-Bogoliubov theory with an improved quark mass density-dependent model. Chinese Physics C, 2026, 50(2): 1-12.
[9]	Y. P. Wang , Y. K. Wang , P. W. Zhao . Tilted-axis-cranking covariant density functional theory for the high-spin spectroscopy in ⁶⁹Ga. Chinese Physics C, 2026, 50(2): 1-5. doi: 10.1088/1674-1137/ae07b8
[10]	Yiming Gao , Yoshiki K. Tanaka , Vasyl Drozd , Hiroyuki Ekawa , Samuel Escrig , Yan He , Ayumi Kasagi , Enqiang Liu , Manami Nakagawa , Christophe Rappold , Takehiko R. Saito , Ryohei Sekiya , He Wang , Ayari Yanai , Xiaohong Zhou . Feasibility study of measuring interaction cross sections of hypernuclei produced in projectile fragmentation reactions with WASA-FRS setup. Chinese Physics C, 2025, 49(12): 124003. doi: 10.1088/1674-1137/adf4b2
[11]	Wei-Xi Kong , Ben-Wei Zhang . Fox-Wolfram moment of jet production in relativistic heavy-ion collisions. Chinese Physics C, 2025, 49(9): 094101. doi: 10.1088/1674-1137/add5d8
[12]	Yu-Chen Wu , Man Bao . Low-lying states of odd-even N = 79 isotones within the nucleon-pair approximation. Chinese Physics C, 2025, 49(12): 124109. doi: 10.1088/1674-1137/adf1f6
[13]	Qu-Zhi Li , Zhiguang Xiao , Han-Qing Zheng . On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses. Chinese Physics C, 2025, 49(12): 123103. doi: 10.1088/1674-1137/adfa02
[14]	O. A. Rubtsova , V. N. Pomerantsev , L. D. Blokhintsev . Universal momentum distributions for the spin-singlet NN channels. Chinese Physics C, 2025, 49(10): 104104. doi: 10.1088/1674-1137/addaaf
[15]	Jian Liu , Qiang Su , Qinglin Niu , Lei Wang , Zhongzhou Ren . Charged-current quasielastic neutrino scattering off nuclei with nucleon-nucleon short-range correlations. Chinese Physics C, 2025, 49(10): 104102. doi: 10.1088/1674-1137/ade126
[16]	BAO Ai-Dong , YAO Hai-Bo , WU Shi-Shu . Topological approach to examine the singularity of the axial-vector current in an Abelian gauge field theory (QED). Chinese Physics C, 2009, 33(3): 177-180. doi: 10.1088/1674-1137/33/3/003
[17]	Yang Jianjun , Ma Boqiang , Li Guanglie . Non-perturbative Quark Propagator and the Study of the Non-trivial Q² Dependence in the Nucleon Structure Functions. Chinese Physics C, 1997, 21(2): 146-156.
[18]	Li Yangguo . Antiproton -Nucleus Charge Exchange Reaction and Inelastic Scattering. Chinese Physics C, 1996, 20(11): 1021-1027.
[19]	HOU Ren-Chang , ZHAO Xuan . QUADRUPOLE-OCTUPOLE TWO-PHONON EXCITATIONS IN INELASTIC SCATTERING. Chinese Physics C, 1983, 7(2): 236-244.
[20]	CHANG KONG-LIANG . DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS. Chinese Physics C, 1978, 2(3): 200-210.

Access

Get Citation

Xiu-Lei Ren, Kai-Wen Li, Li-Sheng Geng, Bingwei Long, Peter Ring and Jie Meng. Leading order relativistic chiral nucleon-nucleon interaction[J]. Chinese Physics C, 2018, 42(1): 014103. doi: 10.1088/1674-1137/42/1/014103

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2017-07-12
Revised: 2017-09-08

Fund

Supported by National Natural Science Foundation of China (11375024, 11522539, 11335002, 11375120), DFG and NSFC through funds provided to the Sino-German CRC 110 Symmetries and the Emergence of Structure in QCD (NSFC Grant No. 11621131001, DFG Grant No. TRR110), the Major State 973 Program of China (2013CB834400), the China Postdoctoral Science Foundation (2016M600845, 2017T100008), the Fundamental Research Funds for the Central Universities, and by the DFG cluster of excellence Origin and Structure of the Universe (www.universe-cluster.de)

Article Metric

Article Views(3166)
PDF Downloads(57)
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

Leading order relativistic chiral nucleon-nucleon interaction

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Leading order relativistic chiral nucleon-nucleon interaction

Corresponding author: Li-Sheng Geng,

Corresponding author: Jie Meng,

HTML

目录