Abstract
I analyze the lattice simulation data of the Domain Wall Fermion in quaternion basis. As pointed out by Atiyah and Ward, the minimum action solution for SU(2) Yang–Mills fields in Euclidean 4-space correspond, via Penrose twistor transform, to algebraic bundles on the complex projective 3-space. Assuming dominance of correlation between the fermions on the domain walls via exchange of instantons, I extract parameters necessary for defining gauge fields of Atiyah–Ward ansatz. The QCD effective coupling in the infrared and the relation between the number of flavors and the infrared fixed point is investigated. Consequence of this lepton flavor assignment to phenomenology of baryons is also discussed.
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Banks T., Zaks A.: On the phase structure of vector-like gauge theories with massless fermion. Nucl. Phys. B 196, 189 (1982)
Appelquist, T., Fleming, G.T., Neil, E.T.: Lattice study of the conformal window in QCD-like theories. Phys. Rev. Lett. 100, 171607 (2008); Errata Phys. Rev. Lett. 102, 149902 (2009)
Appelquist T.: Lattice explorations of TeV physics. Prog. Theor. Phys. (Kyoto) 180, 79 (2009)
Rubio, P.P., Sint, S.: Non-perturbative running of the coupling from four flavour lattice QCD with staggered quarks. In: Lattice 2010 Conference Proceedings. arXiv:1011.6580[hep-lat]
Fodor, Z., Holland, K., Kuti, J., Nógrádi, D., Schroeder, Ch.: Twelve massless flavors and three colors below the conformal window. arXiv:1104.3124[hep-lat]
Dietrich D., Sannino F.: Conformal window of SU(N) gauge theories with fermions in higher dimensional representations. Phys. Rev. D 75, 085018 (2007)
Ryttov T.A., Sannino F.: Supersymmetry inspired QCD beta function. Phys. Rev. D 78, 065001 (2008)
Grunberg G.: A proposal to solve the Landau ghost and renormalon problems. Phys. Lett. B 349, 469 (1995)
Gardi E., Grunberg G.: Conformal expansion and renormalons. Phys. Lett. B 517, 215 (2001) arXiv:hep-ph/0107300
Grunberg G.: Conformal window and Landau singularity. JHEP 0108, 019 (2001) arXiv:hep-ph/0104098v2
Allton C. et al.: (RBC/UKQCD collaboration): 2+1 flavor domain wall QCD on a (2fm)3 lattice, light meson spectroscopy with L s = 16. Phys. Rev. D 76, 014504 (2007) arXiv:hep-lat/0701013
Furui, S., Nakajima, H.: Roles ofthe quark field in the infrared lattice Coulomb gauge and Landau gauge QCD. In: PoS (Lattice 2007), 301 (2007). arXiv:0708.1421[hep-lat]
Deur A., Burkert V., Chen J.P., Korsch W.: Experimental determination of the effective strong coupling constant. Phys. Lett. B 650, 244 (2006)
Deur, A., Burkert, V., Chen, J.P., Korsch, W.: Determination of effective strong coupling constant α s, g1(Q *2) from CLAS spin structure function data. Phys. Lett. B 665, 349 (2008). arXiv: 0803.4119[hep-ph]
Wolfram, S.: Mathematica 8. Wolfram Research (2010)
Brodsky S.J., de Téramond G., Deur A.: Nonperturbative QCD coupling and its β function from light-front holography. Phys. Rev. D 81, 096010 (2010) arXiv:1002.3948[hep-ph]
Téramond G.F., Brodsky S.J.: Hadronic spectrum of a holographic dual of QCD. Phys. Rev. Lett. 94, 201601 (2005)
Brodsky S.J., Lepage G.P., Mackenzie P.B.: On the elimination of scale ambiguities in perturbative quantum chromodynamics. Phys. Rev. D 28, 228 (1983)
Brodsky S.J., Menke S., Merino C., Rathsman J.: On the behavior of effective QCD coupling ατ(s) at low energy. Phys. Rev. D 67, 055008 (2003) arXiv: hep-ph/0212078
Beneke, M., Braun, V.N.: Naive nonabelianization and resummation of fermion bubble chains. Phys. Lett. B 348, 513 (1995). arXiv:hep-ph/9411229
Brodsky S.J., Gardi E., Grunberg G., Rathman J.: Disentangling running coupling and conformal effects in QCD. Phys. Rev. D 63, 094017 (2001)
Brodsky S.J., Shrock R.: Maximum wavelength of confined quarks and gluons and properties of quantum chromodymnamics. Phys. Lett. B 666, 95 (2008) arXiv:0806.1535 [hep-th]
Lüscher M., Narayanan R., Weisz P., Wolff U.: The Schrödinger functional—a renormalizable probe for non-abelian gauge theories. Nucl. Phys. B 384, 168 (1992)
t’Hooft G.: Computation of the quantum effects due to a four dimensional pseudoparticles. Phys. Rev. D 14, 3432 (1976)
Atiyah M.F., Ward R.S.: Instantons and algebraic geometry. Commun. Math. Phys. 55, 117 (1977)
Penrose R.: Twistor algebra. J. Math. Phys. 8, 345 (1967)
Furui S.: The self-dual gauge fields and the domain wall fermion zero modes. Few Body Syst. 46, 211 (2009)
Louno P.: Clifford Algebras and Spinors. 2nd edn. Cambridge University Press, Cambridge (2000)
Kaplan D.B.: A method for simulating chiral fermion on the lattice. Phys. Lett. B 288, 342 (1992)
Narayanan R., Neuberger H.: Infinitely many regulator fields for chiral fermions. Phys. Lett. B 302, 93 (1993)
Shamir Y.: The euclidean spectrum of Kaplan’s lattice chiral fermions. Phys. Lett. B 305, 357 (1993)
Cartan, É.: The theory of Spinors. p. 118. Dover Publications, New York (1966). [La Theorie des Spineurs. Hellman, Paris (1938)]
Corrigan E., Goddard P.: An n monopole solutions with 4n-1 degrees of freedom. Commun. Math. Phys. 80, 575 (1981)
Takasaki, K.: The World of Twistors. Kyouritu Shuppan Publications, Tokyo (2005) (in Japanese)
Furui S., Nakajima H.: Correlation of the ghost and the quark in the lattice landau gauge QCD. Braz. J. Phys. 37, 186 (2007) arXiv:hep-lat.0609024
Ma E.: A 4 symmetry and neutrinos with very different masses. Phys. Rev. D 82, 037301 (2010)
Becher, P., Böhm, M., Joos, H.: Eichtheorien. Teubner, Stuttgart (1982)
Glashow S.L., Iliopoulos J., Maiani L.: Weak interactions with Lepton–Hadron symmetry. Phys. Rev. D 2, 1285 (1970)
Ipp A., Kajantie K., Rebhan A., Vuorinen A.: Pressure of deconfined QCD for all temperatures and quark chemical potentials. Phys. Rev. D 74, 045016 (2006)
Furui, S.: Lattice Simulations in MOM v.s. Schrödinger Functional Scheme and Triality. In: AIP Conference Proceedings No 1343. p. 534. Baryons’10, RCNP Osaka University, December 2010
Linde A.D.: Infrared problem in the thermodynamics of the Yang–Mills gas. Phys. Lett. B 96, 289 (1980)
Nakamura K. et al.: (Particle Data Group), Review of particle physics. J. Phys. G 37, 075021 (2010)
Hara, K., et al. (The Belle collaboration): Evidence of \({B\to \tau\bar\nu}\) with a semileptonic tagging method. Phys. Rev. D82,071101 (2010). arXiv:1006.4201v3[hep-ex]
Lunghi E., Soni A.: Possible evidence for the breakdown of the CKM-paradigm of CP-violation. Phys. Lett. B 697, 323 (2011) arXiv:1010.6092v2[hep-ph]
Labelle P.: Supersymmetry Demystified. McGrawHill, NewYork (2010)
Georgi H.: Unparticle physics. Phys. Rev. Lett. 98, 221601 (2007)
Eichten E., Lane K.: Dynamical breaking of weak interaction symmetries. Phys. Lett. B 90, 125 (1980)
Chivukula, R.S., Simmons, E.H.: Technicolor and lattice gauge theory. In: PoS Lattice 2010. arXiv:1011.2535v1 (2010)
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Furui, S. Fermion Flavors in Quaternion Basis and Infrared QCD. Few-Body Syst 52, 171–187 (2012). https://doi.org/10.1007/s00601-011-0274-1
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DOI: https://doi.org/10.1007/s00601-011-0274-1