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 &

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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)

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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

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

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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)

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Leading order relativistic chiral nucleon-nucleon interaction

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Leading order relativistic chiral nucleon-nucleon interaction

Corresponding author: Li-Sheng Geng,

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