Bali, G. S.; Bruns, P. C.; Collins, S.; Deka, M.; Gläßle, B.; Göckeler, M.; Greil, L.; Hemmert, T. R.; Horsley, R.; Najjar, J.; Nakamura, Y.; Nobile, A.; Pleiter, D.; Rakow, P. E. L.; Schäfer, Andreas; Schiel, R.; Schierholz, G.; Sternbeck, A.; Zanotti, J. Nucleon mass and sigma term from lattice QCD with two light fermion flavors. (English) Zbl 1262.81254 Nucl. Phys., B 866, No. 1, 1-25 (2013). Summary: We analyze \(N_{f}=2\) nucleon mass data with respect to their dependence on the pion mass down to \(m_{\pi }=157\) MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion-nucleon \(\sigma\)-term. Our lattice data below \(m_{\pi }=435\) MeV is well described by \(O(p^{4})\) BChPT and we find \(\sigma =37(8)(6)\) MeV for the \(\sigma\)-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of \(r_{0}=0.501(10)(11)\) fm. Cited in 1 Document MSC: 81V35 Nuclear physics 81V05 Strong interaction, including quantum chromodynamics 81T15 Perturbative methods of renormalization applied to problems in quantum field theory Keywords:nucleon mass; pion-nucleon sigma term; Sommer scale; covariant baryon chiral perturbation theory; finite size corrections Software:Chroma PDFBibTeX XMLCite \textit{G. S. Bali} et al., Nucl. Phys., B 866, No. 1, 1--25 (2013; Zbl 1262.81254) Full Text: DOI arXiv Link References: [1] Koch, R., Z. Phys. C, 15, 161 (1982) [2] Pavan, M., PiN Newslett., 16, 110 (2002) [3] Gasser, J.; Leutwyler, H.; Sainio, M., Phys. Lett. B, 253, 252 (1991) [4] Borasoy, B.; Meissner, U.-G., Annals Phys., 254, 192 (1997) [5] Alarcon, J. M.; Camalich, J. Martin; Oller, J. A. (2011) [6] Babich, R., Phys. Rev. D, 85, 054510 (2012) [7] Bali, G. S., Phys. Rev. D, 85, 054502 (2012) [8] Dinter, S. (2012) [9] Horsley, R., Phys. Rev. D, 85, 034506 (2012) [10] Dürr, S., Phys. Rev. D, 85, 014509 (2012) [11] Shanahan, P.; Thomas, A.; Young, R. (2012) [13] Colangelo, G.; Dürr, S.; Haefeli, C., Nucl. Phys. B, 721, 136 (2005) [14] McGovern, J. A.; Birse, M. C., Phys. Rev. D, 74, 097501 (2006) [15] Colangelo, G., Eur. Phys. J. C, 71, 1695 (2011) [16] Meissner, U.-G., PoS, LAT2005, 009 (2006) [19] Bernard, V.; Meissner, U.-G., Phys. Lett. B, 639, 278 (2006) [20] Leinweber, D. B., Phys. Rev. D, 61, 074502 (2000) [21] Beane, S. R., Nucl. Phys. B, 695, 192 (2004) [22] Leinweber, D. B.; Thomas, A. W.; Young, R. D., Nucl. Phys. A, 755, 59 (2005) [24] Güsken, S., Phys. Rev. D, 59, 054504 (1999) [25] Procura, M.; Hemmert, T. R.; Weise, W., Phys. Rev. D, 69, 034505 (2004) [26] Procura, M., Phys. Rev. D, 73, 114510 (2006) [27] Ohki, H., Phys. Rev. D, 78, 054502 (2008) [28] Young, R.; Thomas, A., Phys. Rev. D, 81, 014503 (2010) [29] Ishikawa, K.-I., Phys. Rev. D, 80, 054502 (2009) [30] Alexandrou, C., Phys. Rev. D, 80, 114503 (2009) [31] Leinweber, D. B.; Thomas, A. W.; Young, R. D., Phys. Rev. Lett., 92, 242002 (2004) [32] Aubin, C., Phys. Rev. D, 70, 094505 (2004) [33] Göckeler, M., PoS, LAT2005, 063 (2006) [34] Göckeler, M., Phys. Rev. D, 73, 014513 (2006) [35] Fritzsch, P. (2012) [36] Edwards, R. G.; Joo, B., Nucl. Phys. B (Proc. Suppl.), 140, 832 (2005) [37] Boyle, P. A., Comp. Phys. Comm., 180, 2739 (2009) [38] Nakamura, Y.; Stüben, H., PoS, LATTICE2010, 040 (2010) [39] Gasser, J.; Leutwyler, H., Annals Phys., 158, 142 (1984) [40] Bellucci, S.; Gasser, J.; Sainio, M., Nucl. Phys. B, 423, 80 (1994) [41] Dorati, M.; Gail, T. A.; Hemmert, T. R., Nucl. Phys. A, 798, 96 (2008) [42] Becher, T.; Leutwyler, H., JHEP, 0106, 017 (2001) [43] Ali Khan, A., Nucl. Phys. B, 689, 175 (2004) [44] Schindler, M., Phys. Lett. B, 649, 390 (2007) [45] Becher, T.; Leutwyler, H., Eur. Phys. J. C, 9, 643 (1999) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.