- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Chiral symmetry breaking and confinement: Separating the scales

Nick Evans* and Konstantinos S. Rigatos†

  • School of Physics & Astronomy and STAG Research Centre, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom

  • *n.j.evans@soton.ac.uk
  • †k.c.rigatos@soton.ac.uk
PDF

Phys. Rev. D 103, 094022 – Published 18 May, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.094022

Abstract

We review arguments that chiral symmetry breaking is triggered when the quark bilinear condensate’s dimension passes through one (γ=1). This is supported by gap equations and more recently holographic models. Confinement may then be a separate property of the pure Yang-Mills theory below the scale of the dynamically generated quark mass, occurring at the scale of the pole in the deep IR running. Here, we use perturbative results for the running of the gauge coupling and γ in asymptotically free SU(N) gauge theories with matter in higher dimension representations to seek the best candidate theories where confinement and chiral symmetry breaking can be maximally separated. For example, SU(2) gauge theory with a single Weyl quark in the S3 (dimension 4) representation may have a factor of 20 separation in scale. Such a theory could be simulated on the lattice to test the separation. We also propose studying multirepresentation theories where the higher dimension representation forms a condensate at one scale that can be quite separate from the condensation scale of the second representation matter. The confinement scale would presumably be below the second scale. For example, SU(3) gauge theory with a Weyl adjoint fermion and ten fundamental quarks may have a separation of a factor of 20 also.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (74)

  1. S. Weinberg, Phys. Rev. D 13, 974 (1976); 19, A1277 (1979).
  2. G. ’t Hooft, in High-Energy Particle Physics Divisional Conference of EPS (includes 8th biennial conf on Elem. Particles) (1975).
  3. S. Mandelstam, Phys. Rev. D 19, 2391 (1979).
  4. A. Casher, Phys. Lett. 83B, 395 (1979).
  5. E. V. Shuryak, Phys. Lett. 107B, 103 (1981).
  6. F. Gross and J. Milana, Phys. Rev. D 45, 969 (1992).
  7. D. Bak and H.-U. Yee, Phys. Rev. D 71, 046003 (2005).
  8. F. Synatschke, A. Wipf, and K. Langfeld, Phys. Rev. D 77, 114018 (2008).
  9. C. Lang and M. Schrock, Phys. Rev. D 84, 087704 (2011).
  10. L. Glozman, Acta Phys. Pol. B Proc. Suppl. 6, 245 (2013).
  11. H. Suganuma, T. M. Doi, K. Redlich, and C. Sasaki, J. Phys. G 44, 124001 (2017).
  12. Y. Yang and P.-H. Yuan, arXiv:2011.11941.
  13. Y. Aoki, Z. Fodor, S. Katz, and K. Szabo, Phys. Lett. B 643, 46 (2006).
  14. F. Karsch, Lect. Notes Phys. 583, 209 (2002).
  15. D. Sinclair, Phys. Rev. D 78, 054512 (2008).
  16. K. Higashijima, Phys. Rev. D 29, 1228 (1984).
  17. V. Miransky, Nuovo Cimento A 90, 149 (1985).
  18. T. W. Appelquist, D. Karabali, and L. Wijewardhana, Phys. Rev. Lett. 57, 957 (1986).
  19. A. G. Cohen and H. Georgi, Nucl. Phys. B314, 7 (1989).
  20. M. Hopfer, C. S. Fischer, and R. Alkofer, J. High Energy Phys. 11 (2014) 035.
  21. J. M. Maldacena, Int. J. Theor. Phys. 38, 1113 (1999); Adv. Theor. Math. Phys. 2, 231 (1998).
  22. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
  23. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998).
  24. J. Babington, J. Erdmenger, N. J. Evans, Z. Guralnik, and I. Kirsch, Phys. Rev. D 69, 066007 (2004).
  25. P. Breitenlohner and D. Z. Freedman, Ann. Phys. (N.Y.) 144, 249 (1982).
  26. V. G. Filev, C. V. Johnson, R. Rashkov, and K. Viswanathan, J. High Energy Phys. 10 (2007) 019.
  27. J. Erdmenger, R. Meyer, and J. P. Shock, J. High Energy Phys. 12 (2007) 091.
  28. R. Alvares, N. Evans, and K.-Y. Kim, Phys. Rev. D 86, 026008 (2012).
  29. M. Jarvinen and E. Kiritsis, J. High Energy Phys. 03 (2012) 002.
  30. D. Kutasov, J. Lin, and A. Parnachev, Nucl. Phys. B858, 155 (2012).
  31. T. Alho, N. Evans, and K. Tuominen, Phys. Rev. D 88, 105016 (2013).
  32. W. J. Marciano, Phys. Rev. D 21, 2425 (1980).
  33. A. Mocsy, F. Sannino, and K. Tuominen, Phys. Rev. Lett. 92, 182302 (2004).
  34. A. Mocsy, F. Sannino, and K. Tuominen, J. Phys. G 30, S1255 (2004).
  35. T. Appelquist, J. Terning, and L. Wijewardhana, Phys. Rev. Lett. 77, 1214 (1996).
  36. T. A. Ryttov and F. Sannino, Phys. Rev. D 78, 065001 (2008).
  37. B. Holdom, Phys. Rev. D 24, 1441 (1981).
  38. G. Bergner, P. Giudice, G. Münster, P. Scior, I. Montvay, and S. Piemonte, J. High Energy Phys. 01 (2018) 119.
  39. S. Piemonte, G. Bergner, and C. López, Phys. Rev. D 102, 014503 (2020).
  40. D. J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973).
  41. H. Politzer, Phys. Rev. Lett. 30, 1346 (1973).
  42. R. Feger and T. W. Kephart, Comput. Phys. Commun. 192, 166 (2015).
  43. T. Appelquist, G. T. Fleming, and E. T. Neil, Phys. Rev. Lett. 100, 171607 (2008); 102, 149902(E) (2009).
  44. T. Appelquist et al. (LSD Collaboration), Phys. Rev. D 90, 114502 (2014).
  45. T. Appelquist et al. (Lattice Strong Dynamics Collaboration), Phys. Rev. D 99, 014509 (2019).
  46. T. Appelquist et al., arXiv:1204.6000.
  47. C. J. D. Lin, K. Ogawa, and A. Ramos, J. High Energy Phys. 12 (2015) 103.
  48. Z. Fodor, K. Holland, J. Kuti, S. Mondal, D. Nogradi, and C. H. Wong, Phys. Rev. D 94, 091501 (2016).
  49. A. Cheng, A. Hasenfratz, Y. Liu, G. Petropoulos, and D. Schaich, J. High Energy Phys. 05 (2014) 137.
  50. A. Hasenfratz, C. Rebbi, and O. Witzel, Phys. Rev. D 101, 114508 (2020).
  51. T. Karavirta, J. Rantaharju, K. Rummukainen, and K. Tuominen, J. High Energy Phys. 05 (2012) 003.
  52. F. Karsch and M. Lutgemeier, Nucl. Phys. B550, 449 (1999).
  53. T. DeGrand, Y. Shamir, and B. Svetitsky, Phys. Rev. D 88, 054505 (2013).
  54. L. Del Debbio, A. Patella, and C. Pica, Phys. Rev. D 81, 094503 (2010).
  55. T. DeGrand, Y. Shamir, and B. Svetitsky, Phys. Rev. D 83, 074507 (2011).
  56. J. Rantaharju, T. Rantalaiho, K. Rummukainen, and K. Tuominen, Phys. Rev. D 93, 094509 (2016).
  57. A. Athenodorou, E. Bennett, G. Bergner, and B. Lucini, Phys. Rev. D 91, 114508 (2015).
  58. G. Bergner, P. Giudice, G. Münster, S. Piemonte, and D. Sandbrink, J. High Energy Phys. 11 (2014) 049.
  59. G. Veneziano and S. Yankielowicz, Phys. Lett. 113B, 231 (1982).
  60. T. DeGrand, Y. Shamir, and B. Svetitsky, Phys. Rev. D 79, 034501 (2009).
  61. J. Kogut and D. Sinclair, Phys. Rev. D 81, 114507 (2010).
  62. J. Kogut and D. Sinclair, Phys. Rev. D 92, 054508 (2015).
  63. Z. Fodor, K. Holland, J. Kuti, S. Mondal, D. Nogradi, and C. H. Wong, J. High Energy Phys. 09 (2015) 039.
  64. M. Hansen and C. Pica, EPJ Web Conf. 175, 08018 (2018).
  65. G. Ferretti and D. Karateev, J. High Energy Phys. 03 (2014) 077.
  66. F. Sannino, Acta Phys. Pol. B 40, 3533 (2009).
  67. P. Channuie, J. J. Joergensen, and F. Sannino, J. Cosmol. Astropart. Phys. 05 (2011) 007.
  68. V. Ayyar, T. DeGrand, D. C. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky, Phys. Rev. D 97, 114502 (2018).
  69. J. Engels, S. Holtmann, and T. Schulze, Proc. Sci., LAT2005 (2006) 148.
  70. G. Bergner and S. Piemonte, Phys. Rev. D 103, 014503 (2021).
  71. J. Braun and T. K. Herbst, arXiv:1205.0779.
  72. K. Bitaghsir Fadafan, J. Cruz Rojas, and N. Evans, Phys. Rev. D 101, 126005 (2020).
  73. K. Bitaghsir Fadafan, J. Cruz Rojas, and N. Evans, Phys. Rev. D 103, 026012 (2021).
  74. L. McLerran and R. D. Pisarski, Nucl. Phys. A796, 83 (2007).

Outline

Information

Phys. Rev. D 103, 094022– Published 18 May, 2021
  • Received 15 December 2020
  • Accepted 23 April 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation