# Dispersive analysis of low energy γN→πN process and studies on the N*(890) resonance

• We present a dispersive representation of the $\gamma N\rightarrow \pi N$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $\pi N$ final-state-interaction effects is taken into account via an Omnés formalism with elastic $\pi N$ phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed to pin down the involved subtraction constants. Good fit quality can be achieved with only one free parameter, and the experimental data regarding the multipole amplitude $E_{0}^+$ in the energy region below the $\Delta(1232)$ are well described. Furthermore, we extend the $\gamma N\rightarrow \pi N$ partial-wave amplitude to the second Riemann sheet to extract the couplings of the $N^\ast(890)$. The modulus of the residue of the multipole amplitude $E_{0}^+$ (S${_{11}pE}$) is $2.41\;\rm{mfm\cdot GeV^2}$, and the partial width of $N^*(890)\to\gamma N$ at the pole is approximately $0.369\ {\rm MeV}$, which is almost the same as that of the $N^*(1535)$ resonance, indicating that $N^\ast(890)$ strongly couples to the $\pi N$ system.
•  [1] G. F. Chew, M. L. Goldberger, F. E. Low et al., Phys. Rev. 106, 1345 (1957) doi: 10.1103/PhysRev.106.1345 [2] S. L. Adler, Annals Phys. 50, 189 (1968) [3] R. L. Walker, Phys. Rev. 182, 1729 (1969) doi: 10.1103/PhysRev.182.1729 [4] D. Drechsel, S. S. Kamalov, and L. Tiator, Eur. Phys. J. A 34, 69 (2007) [5] P. Benz et al., Nucl. Phys. B 65, 158 (1973) [6] M. Fuchs et al., Phys. Lett. B 368, 20 (1996) [7] G. Blanpied et al., Phys. Rev. C 64, 025203 (2001) [8] J. Ahrens et al., GDH, A2, Eur. Phys. J. A 21, 323 (2004) [9] INS Data Analysis Center, http://gwdac.phys.gwu.edu/ [10] V. Bernard, N. Kaiser, J. Gasser et al., Phys. Lett. B 268, 291 (1991) [11] V. Bernard, N. Kaiser, and U. G. Meissner, Nucl. Phys. B 383, 442 (1992) [12] V. Bernard, N. Kaiser, and U. G. Meissner, Eur. Phys. J. A 11, 209 (2001) [13] M. Hilt, S. Scherer, and L. Tiator, Phys. Rev. C 87, 045204 (2013) [14] M. Hilt, B. C. Lehnhart, S. Scherer et al., Phys. Rev. C 88, 055207 (2013) [15] A. N. Hiller Blin, T. Ledwig, and M. J. Vicente Vacas, Phys. Lett. B 747, 217 (2015) [16] A. N. Hiller Blin, T. Ledwig, and M. J. Vicente Vacas, Phys. Rev. D 93, 094018 (2016) [17] G. H. Guerrero Navarro, M. J. Vicente Vacas, A. N. Hiller Blin et al., Phys. Rev. D 100, 094021 (2019) [18] B. R. Martin, D. Morgan, G. L. Shaw et al., Pion-pion Interactions in Particle Physics, (Academic Press, London, 1976) [19] Y. F. Wang, D. L. Yao, and H. Q. Zheng, Chin. Phys. C 43, 064110 (2019) [20] Y. F. Wang, D. L. Yao, and H. Q. Zheng, Front. Phys. 14, 1 (2019) [21] Y. F. Wang, D. L. Yao, and H. Q. Zheng, Eur. Phys. J. C 78, 543 (2018) [22] Y. H. Chen, D. L. Yao, and H. Q. Zheng, Phys. Rev. D 87, 054019 (2013) [23] J. Alarcon, J. Martin Camalich, and J. Oller, Annals Phys. 336, 413 (2013) doi: 10.1016/j.aop.2013.06.001 [24] D. L. Yao et al., JHEP 05, 038 (2016) [25] D. Siemens et al., Phys. Rev. C 96, 055205 (2017) [26] Z. G. Xiao and H. Q. Zheng, Nucl. Phys. A 695, 273 (2001) [27] J. Y. He, Z. G. Xiao, and H. Q. Zheng, Phys. Lett. B 536, 59 (2002), [Erratum: Phys. Lett. B 549, 362 (2002)] [28] H. Q. Zheng et al., Nucl. Phys. A 733, 235 (2004) [29] H. Q. Zheng, Z. Y. Zhou, G. Y. Qin et al., AIP Conf. Proc. 717, 322 (2004) doi: 10.1063/1.1799725 [30] Z. Y. Zhou et al., JHEP 02, 043 (2005) [31] Z. Zhou and H. Zheng, Nucl. Phys. A 775, 212 (2006) [32] Y. Ma, W. Q. Niu, Y. F. Wang et al., Commun. Theor. Phys. 72, 105203 (2020) [33] O. Babelon, J.-L. Basdevant, D. Caillerie et al., Nucl. Phys. B 113, 445 (1976) [34] O. Babelon, J.-L. Basdevant, D. Caillerie et al., Nucl. Phys. B 114, 252 (1976) [35] Y. Mao, X. G. Wang, O. Zhang et al., Phys. Rev. D 79, 116008 (2009) [36] L. Y. Dai and M. R. Pennington, Phys. Rev. D 94, 116021 (2016) [37] J. Kennedy and T. D. Spearman, Phys. Rev. 126, 1596 (1962) doi: 10.1103/PhysRev.126.1596 [38] R. L. Workman, M. W. Paris, W. J. Briscoe et al., Phys. Rev. C 86, 015202 (2012) [39] A. Švarc et al., Phys. Rev. C 89, 065208 (2014) [40] R. Omnès, Nuovo Cim. 8, 316 (1958) doi: 10.1007/BF02747746 [41] K. M. Watson, Phys. Rev. 95, 228 (1954) doi: 10.1103/PhysRev.95.228 [42] S. Scherer and M. R. Schindler, Lect. Notes Phys. 830, 1 (2012) [43] M. Jacob and G. C. Wick, Annals Phys. 281, 404 (2000) [44] M. Tanabashi et al., Phys. Rev. D 98, 030001 (2018) [45] R. A. Arndt, W. J. Briscoe, I. I. Strakovsky et al., Phys. Rev. C 74, 1 (2006) [46] R. L. Workman, L. Tiator, and A. Sarantsev, Phys. Rev. C 87, 3 (2013) [47] R. A. Amdt, R. L. Workman, Z. Li et al., Phys. Rev. C 42, 1853 (1990) [48] A. Gasparyan and M. Lutz, Nucl. Phys. A 848, 126 (2010)

Figures(6) / Tables(4)

Get Citation
Yao Ma, Wen-Qi Niu, De-Liang Yao and Han-Qing Zheng. Dispersive Analysis of Low Energy γN→πN Process and Studies on the N*(890) Resonance[J]. Chinese Physics C. doi: 10.1088/1674-1137/abc169
Yao Ma, Wen-Qi Niu, De-Liang Yao and Han-Qing Zheng. Dispersive Analysis of Low Energy γN→πN Process and Studies on the N*(890) Resonance[J]. Chinese Physics C.
Milestone
Article Metric

Article Views(110)
Cited by(0)
Policy on re-use
To reuse of Open Access content published by CPC, for content published under the terms of the Creative Commons Attribution 3.0 license (“CC CY”), the users don’t need to request permission to copy, distribute and display the final published version of the article and to create derivative works, subject to appropriate attribution.
###### 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

Title:
Email:

## Dispersive analysis of low energy γN→πN process and studies on the N*(890) resonance

###### Corresponding author: De-Liang Yao, yaodeliang@hnu.edu.cn
• 1. Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
• 2. School of Physics and Electronics, Hunan University, Changsha 410082, China
• 3. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

Abstract: We present a dispersive representation of the $\gamma N\rightarrow \pi N$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $\pi N$ final-state-interaction effects is taken into account via an Omnés formalism with elastic $\pi N$ phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed to pin down the involved subtraction constants. Good fit quality can be achieved with only one free parameter, and the experimental data regarding the multipole amplitude $E_{0}^+$ in the energy region below the $\Delta(1232)$ are well described. Furthermore, we extend the $\gamma N\rightarrow \pi N$ partial-wave amplitude to the second Riemann sheet to extract the couplings of the $N^\ast(890)$. The modulus of the residue of the multipole amplitude $E_{0}^+$ (S${_{11}pE}$) is $2.41\;\rm{mfm\cdot GeV^2}$, and the partial width of $N^*(890)\to\gamma N$ at the pole is approximately $0.369\ {\rm MeV}$, which is almost the same as that of the $N^*(1535)$ resonance, indicating that $N^\ast(890)$ strongly couples to the $\pi N$ system.

Reference (48)

/