Abstract
Dyson-Schwinger equations furnish a Poincaré covariant framework within which to study hadrons. A particular feature is the existence of a nonperturbative, symmetry preserving truncation that enables the proof of exact results. Key to the DSE’s efficacious application is their expression of the materially important momentum-dependent dressing of parton propagators at infrared length-scales, which is responsible for the magnitude of constituent-quark masses and the length-scale characterising confinementin bound states. A unified quantitative description of light- and heavy-quark systems is achieved by capitalising on these features.
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1. C.D. Roberts and A.G. Williams, Prog. Part. Nucl. Phys. 33, 477 (1994).
2. C.D. Roberts and S.M. Schmidt, Prog. Part. Nucl. Phys. 45, S1 (2000).
3. R. Alkofer and L.v. Smekal, Phys. Rept. 353, 281 (2001).
4. P. Maris and C.D. Roberts, “Dyson-Schwinger equations: A tool for hadron physics,” nucl-th/0301049.
5. P. Maris, C.D. Roberts and P.C. Tandy, Phys. Lett. B 420, 267 (1998). Rmrt98
6. P. Maris and C.D. Roberts, Phys. Rev. C 56, 3369 (1997).
7. P. Maris, A. Raya, C.D. Roberts and S.M. Schmidt, “Facets of confinement and dynamical chiral symmetry breaking,” nucl-th/0208071.
8. A. Bender, C.D. Roberts and L.v. Smekal, Phys. Lett. B 380, 7 (1996).
9. A. Bender, W. Detmold, C.D. Roberts and A.W. Thomas, Phys. Rev. C 65, 065203 (2002).
10. P. Maris and C.D. Roberts, “QCD bound states and their response to extremes of temperature and density.” In: Proc. of the Wkshp. on Nonperturbative Methods in Quantum Field Theory, Adelaide, Australia, 2-13 Feb., 1998, ed. by A.W. Schreiber, A.G. Williams and A.W. Thomas (World Scientific, Singapore 1998) pp. 132–151.
11. M.A. Ivanov, Yu.L. Kalinovsky and C.D. Roberts, Phys. Rev. D 60, 034018 (1999).
12. H.J. Munczek and A.M. Nemirovsky, Phys. Rev. D 28, 181 (1983).
13. C.H. Llewellyn-Smith, Annals Phys. (NY) 53, 521 (1969).
14. H.J. Munczek, Phys. Rev. D 52, 4736 (1995).
15. R.W. Haymaker, Riv. Nuovo Cim. 14N8, 1 (1991).
16. K.D. Lane, Phys. Rev. D 10, 2605 (1974); H.D. Politzer, Nucl. Phys. B 117, 397 (1976).
17. K. Langfeld, R. Pullirsch, H. Markum, C.D. Roberts and S.M. Schmidt, “Concerning the quark condensate,” nucl-th/0301024.
18. C.D. Roberts, “Continuum strong QCD: Confinement and Dynamical Chiral Symmetry Breaking,” nucl-th/0007054.
19. C. Alexandrou, P. De Forcrand and E. Follana, Phys. Rev. D 65, 117502 (2002); P.O. Bowman, U.M. Heller, D.B. Leinweber and A.G. Williams, Phys. Rev. D 66, 074505 (2002); and references therein.
20. J.C.R. Bloch, Phys. Rev. D 64, 116011 (2001).
21. R. Alkofer, C.S. Fischer and L.v. Smekal, Acta Phys. Slov. 52, 191 (2002).
22. J. Skullerud and A. Kızılersü, JHEP 0209, 013 (2002); J.I. Skullerud, P.O. Bowman, A. Kızılersü, D.B. Leinweber, A.G. Williams, “Nonperturbative structure of the quark-gluon vertex,” hep-ph/0303176.
23. J.C.R. Bloch, A. Cucchieri, K. Langfeld and T. Mendes, “Running coupling constant and propagators in SU(2) Landau gauge,” hep-lat/0209040.
24. P. Maris and P.C. Tandy, Phys. Rev. C 60, 055214 (1999).
25. L. Montanet, et al. [Part. Data Group Coll.], Phys. Rev. D 50, 1173 (1994); C. Caso et al. [Part. Data Group Coll.], Eur. Phys. J. C 3, 1 (1998).
26. P.O. Bowman, U.M. Heller and A.G. Williams, Phys. Rev. D 66, 014505 (2002).
27. K. Johnson, M. Baker and R. Willey, Phys. Rev. 136, B1111 (1964).
28. M.S. Bhagwat, M.A. Pichowsky, C.D. Roberts and P.C. Tandy, “Analysis of a quenched lattice-QCD dressed-quark propagator,” nucl-th/0304003.
29. P. Maris, “Continuum QCD and Light Mesons.” In: Wien 2000, Quark Confinement and the Hadron Spectrum — Proc. of the 4th Int. Conf., Vienna, Austria, 3-8 Jul 2000, ed. by W. Lucha and K. Maung Maung (World Scientific, Singapore 2002) pp. 163-175.
30. M.B. Hecht, C.D. Roberts and S.M. Schmidt, “Contemporary Applications of Dyson-Schwinger Equations.” In: Wien 2000, Quark Confinement and the Hadron Spectrum – Proc. of the 4th Int. Conf., Vienna, Austria, 3-8 Jul 2000, ed. by W. Lucha and K. Maung Maung (World Scientific, Singapore 2002) pp. 27-39.
31. K.C. Bowler, et al. [UKQCD Coll.], Phys. Rev. D 62, 054506 (2000).
32. P.C. Tandy, “Covariant QCD modeling of light meson physics,” nucl-th/0301040.
33. P. Maris and P.C. Tandy, Phys. Rev. C 61, 045202 (2000).
34. P. Maris and P.C. Tandy, Phys. Rev. C 62, 055204 (2000).
35. P. Brauel, et al., Z. Phys. C 3, 101 (1979).
36. S.R. Amendolia, et al. [NA7 Coll.], Nucl. Phys. B 277, 168 (1986).
37. J. Volmer, et al. [JLab F π Coll.], Phys. Rev. Lett. 86, 1713 (2001).
38. P. Maris, π N Newslett. 16, 213 (2002).
39. C.D. Roberts, Nucl. Phys. A 605, 475 (1996).
40. P. Maris and C.D. Roberts, Phys. Rev. C 58, 3659 (1998).
41. G.R. Farrar and D.R. Jackson, Phys. Rev. Lett. 43, 246 (1979).
42. G.P. Lepage and S.J. Brodsky, Phys. Rev. D 22, 2157 (1980).
43. M.S. Bhagwat, M.A. Pichowsky and P.C. Tandy, Phys. Rev. D 67, 054019 (2003).
44. S.R. Cotanch and P. Maris, Phys. Rev. D 66, 116010 (2002); P. Bicudo, Phys. Rev. C 67, 035201 (2003).
45. J. Praschifka, C.D. Roberts and R.T. Cahill, Phys. Rev. D 36, 209 (1987); C.D. Roberts, R.T. Cahill and J. Praschifka, Annals Phys. (NY) 188, 20 (1988).
46. M. Bando, M. Harada and T. Kugo, Prog. Theor. Phys. 91, 927 (1994).
47. R. Alkofer and C.D. Roberts, Phys. Lett. B 369, 101 (1996); B. Bistrović and D. Klabučar, Phys. Lett. B 478, 127 (2000).
48. P. Maris and P.C. Tandy, Phys. Rev. C 65, 045211 (2002).
49. E.S. Ackleh, T. Barnes and E.S. Swanson, Phys. Rev. D 54, 6811 (1996).
50. G.S. Adams et al. [E852 Coll.], Phys. Rev. Lett. 81, 5760 (1998). S.U. Chung et al., Phys. Rev. D 65, 072001 (2002).
51. C.J. Burden, Lu Qian, C.D. Roberts, P.C. Tandy and M.J. Thomson, Phys. Rev. C 55, 2649 (1997).
52. C.J. Burden and M.A. Pichowsky, Few Body Syst. 32, 119 (2002).
53. J.C.R. Bloch, Yu.L. Kalinovsky, C.D. Roberts and S.M. Schmidt, Phys. Rev. D 60, 111502 (1999).
54. M.A. Ivanov, Yu.L. Kalinovsky, P. Maris and C.D. Roberts, Phys. Lett. B 416, 29 (1998).
55. M.A. Ivanov, Yu.L. Kalinovsky, P. Maris and C.D. Roberts, Phys. Rev. C 57, 1991 (1998).
56. M. Neubert, Phys. Rep. 245, 259 (1994); M. Neubert, “Heavy quark masses, mixing angles, and spin flavor symmetry.” In: The Building Blocks of Creation: From Microfermis to Megaparsecs, Boulder, Colorado, 6/Jun - 2/Jul 1993, ed. by S. Raby and T. Walker (World Scientific, Singapore 1994) pp. 125-206; and references therein.
57. J.M. Flynn and C.T. Sachrajda, Adv. Ser. Direct. High Energy Phys. 15, 402 (1998).
58. C. McNeile, “Heavy quarks on the lattice,” hep-lat/0210026.
59. C.D. Roberts, Nucl. Phys. Proc. Suppl. 108, 227 (2002).
60. Yu.L. Kalinovsky, K.L. Mitchell and C.D. Roberts, Phys. Lett. B 399, 22 (1997); C.R. Ji and P. Maris, Phys. Rev. D 64, 014032 (2001).
61. H. Munczek, Phys. Lett. B 175, 215 (1986); C.J. Burden, C.D. Roberts and A.G. Williams, ibid 285, 347 (1992).
62. M.A. Pichowsky and T.-S.H. Lee, Phys. Lett. B 379, 1 (1996); M.A. Pichowsky and T.-S.H. Lee, Phys. Rev. D 56, 1644 (1997).
63. F.T. Hawes and M.A. Pichowsky, Phys. Rev. C 59, 1743 (1999).
64. G. Buchalla, A.J. Buras and M.E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996).
65. N. Isgur and M.B. Wise, Phys. Lett. B 232, 113 (1989); ibid B 237, 527 (1990).
66. The fitting used [25]: V ub =0.0033, V cd = 0.2205, V cs = 0.9745 and V cb = 0.039; and, in GeV, M ρ = 0.77, MK*=0.892 and, except in the kinematic factor λ(m12,m22,t) where the splittings are crucial, averaged D- and B-meson masses: m D = 1.99, m B =5.35 (from m D =1.87, m Ds =1.97, MD*=2.01, M Ds *=2.11, and m B =5.28, m Bs =5.37, MB*=5.32, M Bs *=5.42). Furthermore, b0u=0.131, b0s=0.105, b3u=0.185=b3s and ε = 10-4 were not varied, being instead fixed at the values determined in [67].
67. C.J. Burden, C.D. Roberts and M.J. Thomson, Phys. Lett. B 371, 163 (1996).
68. J.D. Richman and P.R. Burchat, Rev. Mod. Phys. 67, 893 (1995).
69. J.E. Duboscq et al. [CLEO Coll.], Phys. Rev. Lett. 76, 3898 (1996).
70. D.R. Burford, et al., [UKQCD Coll.], Nucl. Phys. B 447, 425 (1995).
71. V.M. Belyaev, V.M. Braun, A. Khodjamirian and R. Rückl, Phys. Rev. D 51, 6177 (1995).
72. A. Anastassov et al. [CLEO Coll.], Phys. Rev. D 65, 032003 (2002).
73. W.R. Molzon et al., Phys. Rev. Lett. 41, 1213 (1978) [Erratum-ibid. 41, 1523 (1978)]; S.R. Amendolia et al., Phys. Lett. B 178, 435 (1986).
74. H. Albrecht et al. [ARGUS Coll.], Z. Phys. C 57, 533 (1993).
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Roberts, C.D. Unifying Aspects of Light- and Heavy-Systems. In: Blaschke, D., Ivanov, M.A., Mannel, T. (eds) Heavy Quark Physics. Lecture Notes in Physics, vol 647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40975-5_6
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