Theoretical Formalism and Simulation Setup

  • Kadir Utku Can
Part of the Springer Theses book series (Springer Theses)


This chapter consists of two parts where we, first, discuss the essential theoretical formalism to investigate the observables we are interested in. Mainly, we provide the formulations to extract the mass and the electromagnetic form factors of spin-1/2 and spin-3/2 baryons. A brief account on data analysis is also given. Second part focuses on the technical, computaional aspects of the lattice method where we detail our setup. Information about the gauge configurations, parameter tunings, propagator inversions and statistical improvements are all given in this part.


Hadron mass Electromagnetic form factor Spin-1/2 and spin-3/2 baryons Lattice simulations Parameter tuning 


  1. 1.
    S. Aoki, M. Fukugita, S. Hashimoto, Y. Iwasaki, K. Kanaya, Y. Kuramashi, H. Mino, M. Okawa, A. Ukawa, T. Yoshie, Analysis of hadron propagators with 1000 configurations on a \(24**3 x 64\) lattice at beta \(= 6\). Nucl. Phys. Proc. Suppl. 47, 354–357 (1996). Scholar
  2. 2.
    C. Alexandrou, M. Brinet, J. Carbonell, M. Constantinou, P.A. Harraud, et al., Nucleon electromagnetic form factors in twisted mass lattice QCD. Phys. Rev., D83: 0 094502 (2011a).
  3. 3.
    R. William, J. Schwinger, On a theory of particles with half-integral spin. Phys. Rev. 60, 61–61 (1941).
  4. 4.
    S. Nozawa, D.B. Leinweber, Electromagnetic form-factors of spin 3/2 baryons. Phys. Rev. D 42, 3567–3571 (1990). Scholar
  5. 5.
    C. Alexandrou, V. Drach, K. Jansen, C. Kallidonis, G. Koutsou, Baryon spectrum with \(N_f = 2+1+1\) twisted mass fermions. Phys. Rev. D90 0 (7): 0 074501 (2014).
  6. 6.
    S. Boinepalli, D.B. Leinweber, P.J. Moran, A.G. Williams, J.M. Zanotti, J.B. Zhang, Electromagnetic structure of decuplet baryons towards the chiral regime. Phys. Rev. D 80: 0 054505 (2009).
  7. 7.
    C. Alexandrou, T. Korzec, G. Koutsou, J.W. Negele, and Y. Proestos. The Electromagnetic form factors of the \(\Omega ^-\) in lattice QCD. Phys.Rev. D82: 0 034504, 2010.
  8. 8.
    L. Lyons, Statistics for nuclear and particle physicists, (Cambridge University Press, 1986).
  9. 9.
    J.W. Tukey, Abstracts of papers. Ann. Math. Statistics 29 0(2): 0 614–623 (1958). ISSN 00034851.
  10. 10.
    M.H. Quenouille, Approximate tests of correlation in time-series. J. R. Statistical Soc. Series B (Methodological), 11 0 (1): 0 68–84 (1949). ISSN 00359246.
  11. 11.
    C. Michael, Fitting correlated data. Phys. Rev. D 49, 2616–2619 (1994).
  12. 12.
    C. Michael, A. McKerrell, Fitting correlated hadron mass spectrum data. Phys. Rev. D 51, 3745–3750 (1995).
  13. 13.
    S. Aoki, K.-I. Ishikawa, N. Ishizuka, T. Izubuchi, D. Kadoh, K. Kanaya, Y. Kuramashi, Y. Namekawa, M. Okawa, Y. Taniguchi, A. Ukawa, N. Ukita, T. Yoshie, 2+1 Flavor Lattice QCD toward the Physical Point. Phys. Rev. D79: 0 034503 (2009).
  14. 14.
    Aida X. El-Khadra, Andreas S. Kronfeld, Paul B. Mackenzie, Massive fermions in lattice gauge theory. Phys. Rev. D 55, 3933–3957 (1997). Scholar
  15. 15.
    T. Burch, C. DeTar, M. Di Pierro, A.X. El-Khadra, E.D. Freeland, et al., Quarkonium mass splittings in three-flavor lattice QCD. Phys.Rev. D81: 0 034508 (2010).
  16. 16.
    C. Bernard, C. DeTar, M. DiPierro, A.X. El-Khadra, R.T. Evans, E.D. Freeland, E. Gamiz, S. Gottlieb, U.M. Heller, J.E. Hetrick, A.S. Kronfeld, J. Laiho, L. Levkova, P. B. Mackenzie, J.N. Simone, R. Sugar, D. Toussaint, R.S./ VandeWater, Tuning fermilab heavy quarks in 2+1 flavor lattice QCD with application to hyperfine splittings. Phys.Rev. D83: 0 034503 (2011).
  17. 17.
    D. Mohler, R.M. Woloshyn, \(D\) and \(D_s\) meson spectroscopy. Phys.Rev. D84: 0 054505 (2011).
  18. 18.
    D. Mohler, S. Prelovsek, R.M. Woloshyn, \(D \pi \) scattering and \(D\) meson resonances from lattice QCD. Phys.Rev. D87 0(3): 0 034501 (2013a).
  19. 19.
    D. Mohler, C.B. Lang, L. Leskovec, S. Prelovsek, R.M. Woloshyn, \(D_{s0}^*(2317)\) meson and \(D\)-meson-kaon scattering from lattice QCD. Phys. Rev. Lett. 111 0(22): 0 222001 (2013b).
  20. 20.
    A. Ali Khan, S. Aoki, G. Boyd, R. Burkhalter, S. Ejiri, M. Fukugita, S. Hashimoto, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneko, Y. Kuramashi, T. Manke, K. Nagai, M. Okawa, H.P. Shanahan, A. Ukawa, T. Yoshié, Light hadron spectroscopy with two flavors of dynamical quarks on the lattice. Phys. Rev. D 65 0(5): 0 054505 (2002).
  21. 21.
    Y. Namekawa et al., Charm quark system at the physical point of 2+1 flavor lattice QCD. Phys.Rev. D84: 0 074505 (2011).
  22. 22.
    C. Alexandrou, M. Brinet, J. Carbonell, M. Constantinou, P.A. Harraud, P. Guichon, K. Jansen, T. Korzec, M. Papinutto, Axial nucleon form factors from lattice QCD. Phys. Rev. D83: 0 045010 (2011b).
  23. 23.
    B. Bunk, K.H. Mutter, K. Schilling, Lattice gauge theory. A challenge in large scale computing, in Proceedings, NATO workshop, ed. by F.R. Wuppertal, Germany, November 5–7 (1985). NATO Sci. Ser. B 140: 0 pp. 1–334 (1986)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Strangeness Nuclear Physics Laboratory, Nishina CenterRIKENWakoJapan

Personalised recommendations