Search
This Journal
This Journal
Anywhere
Quick Search in Journals
Enter words / phrases / DOI / ISBN / keywords / authors / etc
Access type:Only show content I have full access toOnly show Open Access
Advanced Search
0 My Cart
Sign in
Institutional Access

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

Research PapersNo Access

Bound states in functional renormalization group

Institute of Physics, Eötvös Loránd University, 1/A Pázmány P. sétány, H-1117 Budapest, Hungary

E-mail Address: jakovac@caesar.elte.hu

Corresponding author.

Search for more papers by this author

and

András Patkós

Institute of Physics, Eötvös Loránd University, 1/A Pázmány P. sétány, H-1117 Budapest, Hungary

E-mail Address: patkos@galaxy.elte.hu

Search for more papers by this author

https://doi.org/10.1142/S0217751X19501549Cited by:8 (Source: Crossref)

Abstract

Equivalence criteria are established for an effective Yukawa-type theory of composite fields representing two-particle fermion bound states with the original “microscopic” theory of interacting fermions based on the spectral decomposition of the 2-to-2 fermion scattering amplitude. Functional renormalization group equations of the effective theory are derived exploiting relations expressing the equivalence. The effect of truncating the spectral decomposition is investigated quantitatively on the example of the nonrelativistic bound states of two oppositely charged fermions.

Keywords:

PACS: 64.60.ae, 42.50.Lc

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. E. E. Salpeter and H. A. Bethe, Phys. Rev. 84, 1232 (1951). https://doi.org/10.1103/PhysRev.84.1232 Crossref, Web of Science, ADS, Google Scholar
2. C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980). Google Scholar
3. P. Maris and C. Roberts, Phys. Rev. C 56, 3369 (1997), arXiv:nucl-th/9708029. https://doi.org/10.1103/PhysRevC.56.3369 Crossref, Web of Science, ADS, Google Scholar
4. P. Maris and P. C. Tandy, Phys. Rev. C 60, 055214 (1999), arXiv:nucl-th/9905056. https://doi.org/10.1103/PhysRevC.60.055214 Crossref, Web of Science, ADS, Google Scholar
5. T. Hilger, C. Popovici, M. Gomez-Rocha and A. Krassnigg, Phys. Rev. D 91, 034013 (2015), arXiv:1409.3205 [hep-ph]. https://doi.org/10.1103/PhysRevD.91.034013 Crossref, Web of Science, ADS, Google Scholar
6. R. Alkofer and L. von Smekal, Phys. Rep. 353, 281 (2001), arXiv:hep-ph/0007355. https://doi.org/10.1016/S0370-1573(01)00010-2 Crossref, Web of Science, ADS, Google Scholar
7. H. Sanchis-Alepuz and R. Williams, J. Phys. Conf. Ser. 631, 012064 (2015), arXiv:1503.05896 [hep-ph]. https://doi.org/10.1088/1742-6596/631/1/012064 Google Scholar
8. G. Eichmann, H. Sanchis-Alepuz, R. Williams, R. Alkofer and C. S. Fischer, Prog. Part. Nucl. Phys. 91, 1 (2016), arXiv:1606.09602 [hep-ph]. https://doi.org/10.1016/j.ppnp.2016.07.001 Crossref, Web of Science, ADS, Google Scholar
9. T. Hilger, M. Gómez-Rocha, A. Krassnigg and W. Lucha, Eur. Phys. J. A 53, 213 (2017), arXiv:1702.06262 [hep-ph]. https://doi.org/10.1140/epja/i2017-12384-4 Crossref, Web of Science, ADS, Google Scholar
10. P. Watson, W. Cassing and P. C. Tandy, Few Body Syst. 35, 129 (2004), arXiv:hep-ph/0406340. https://doi.org/10.1007/s00601-004-0067-x Web of Science, ADS, Google Scholar
11. H. Sanchis-Alepuz and R. Williams, Phys. Lett. 749, 592 (2015), arXiv:1504.07776 [hep-ph]. https://doi.org/10.1016/j.physletb.2015.08.067 Crossref, Web of Science, Google Scholar
12. R. Williams, C. S. Fischer and W. Heupel, Phys. Rev. D 93, 034026 (2016), arXiv:1512.00455 [hep-ph]. https://doi.org/10.1103/PhysRevD.93.034026 Crossref, Web of Science, ADS, Google Scholar
13. C. Wetterich, Phys. Lett. B 301, 90 (1993), arXiv:1710.05815 [hep-th]. https://doi.org/10.1016/0370-2693(93)90726-X Crossref, Web of Science, ADS, Google Scholar
14. T. R. Morris, Int. J. Mod. Phys. A 9, 2411 (1994), arXiv:hep-ph/9308265. https://doi.org/10.1142/S0217751X94000972 Link, Web of Science, ADS, Google Scholar
15. H. Gies, Lect. Notes Phys. 852, 034026 (2012), arXiv:hep-ph/0611146. https://doi.org/10.1007/978-3-642-27320-9˙6 Google Scholar
16. J. Braun, J. Phys. G 39, 033001 (2012), arXiv:1108.4449 [hep-ph]. https://doi.org/10.1088/0954-3899/39/3/033001 Crossref, Web of Science, Google Scholar
17. U. Ellwanger, Z. Phys. C 62, 503 (1994), arXiv:hep-ph/9308260. https://doi.org/10.1007/BF01555911, [,206(1993)]. Crossref, ADS, Google Scholar
18. U. Ellwanger and C. Wetterich, Nucl. Phys. B 423, 137 (1994), arXiv:hep-ph/9402221. https://doi.org/10.1016/0550-3213(94)90568-1 Crossref, Web of Science, ADS, Google Scholar
19. J. P. Blaizot, R. Mendez Galain and N. Wschebor, Phys. Lett. B 632, 571 (2006), arXiv:hep-th/0503103. https://doi.org/10.1016/j.physletb.2005.10.086 Crossref, Web of Science, ADS, Google Scholar
20. F. Benitez, J. P. Blaizot, H. Chate, B. Delamotte, R. Mendez-Galain and N. Wschebor, Phys. Rev. E 85, 026707 (2012), arXiv:1110.2665 [cond-mat.stat-mech]. https://doi.org/10.1103/PhysRevE.85.026707 Crossref, Web of Science, ADS, Google Scholar
21. J.-P. Blaizot, R. Mendez-Galain and N. Wschebor, Phys. Rev. E 74, 051116 (2006), arXiv:hep-th/0512317. https://doi.org/10.1103/PhysRevE.74.051116 Crossref, Web of Science, ADS, Google Scholar
22. J.-P. Blaizot, R. Mendez-Galain and N. Wschebor, Phys. Rev. E 74, 051117 (2006), arXiv:hep-th/0603163. https://doi.org/10.1103/PhysRevE.74.051117 Crossref, Web of Science, ADS, Google Scholar
23. F. Rose, F. Benitez, F. Léonard and B. Delamotte, Phys. Rev. D 93, 125018 (2016), arXiv:1604.05285 [cond-mat.stat-mech]. https://doi.org/10.1103/PhysRevD.93.125018 Crossref, Web of Science, ADS, Google Scholar
24. M. Caselle, M. Hasenbusch, P. Provero and K. Zarembo, Phys. Rev. D 62, 017901 (2000), arXiv:hep-th/0001181. https://doi.org/10.1103/PhysRevD.62.017901 Crossref, Web of Science, ADS, Google Scholar
25. M. Caselle, M. Hasenbusch, P. Provero and K. Zarembo, Nucl. Phys. B 623, 474 (2002), arXiv:hep-th/0103130. https://doi.org/10.1016/S0550-3213(01)00644-7 Crossref, Web of Science, ADS, Google Scholar
26. D. U. Jungnickel and C. Wetterich, Phys. Rev. D 53, 5142 (1996), arXiv:hep-ph/9505267. https://doi.org/10.1103/PhysRevD.53.5142 Crossref, Web of Science, ADS, Google Scholar
27. H. Gies and C. Wetterich, Phys. Rev. D 65, 065001 (2002), arXiv:hep-th/0107221. https://doi.org/10.1103/PhysRevD.65.065001 Crossref, Web of Science, ADS, Google Scholar
28. J. M. Pawlowski, Ann. Phys. 322, 2831 (2007), arXiv:hep-th/0512261. https://doi.org/10.1016/j.aop.2007.01.007 Crossref, Web of Science, ADS, Google Scholar
29. S. Floerchinger and C. Wetterich, Phys. Lett. B 680, 371 (2009), arXiv:0905.0915 [hep-th]. https://doi.org/10.1016/j.physletb.2009.09.014 Crossref, Web of Science, ADS, Google Scholar
30. S. Floerchinger, Eur. Phys. J. C 69, 119 (2010), arXiv:1001.4497 [hep-th]. https://doi.org/10.1140/epjc/s10052-010-1361-z Crossref, Web of Science, ADS, Google Scholar
31. R. Alkofer, A. Maas, W. A. Mian, M. Mitter, J. Paris-Lopez, J. M. Pawlowski and N. Wink, arXiv:1810.07955 [hep-ph]. Google Scholar
32. K. Kamikado, N. Strodthoff, L. von Smekal and J. Wambach, Eur. Phys. J. C 74, 2806 (2014), arXiv:1302.6199 [hep-ph]. https://doi.org/10.1140/epjc/s10052-014-2806-6 Crossref, Web of Science, ADS, Google Scholar
33. R.-A. Tripolt, L. von Smekal and J. Wambach, Phys. Rev. D 90, 074031 (2014), arXiv:1408.3512 [hep-ph]. https://doi.org/10.1103/PhysRevD.90.074031 Crossref, Web of Science, ADS, Google Scholar
34. J. Wambach, R.-A. Tripolt, N. Strodthoff and L. von Smekal, Nucl. Phys. A 928, 156 (2014), arXiv:1404.7312 [hep-ph]. https://doi.org/10.1016/j.nuclphysa.2014.04.027 Crossref, Web of Science, ADS, Google Scholar
35. V. P. Yurov and A. B. Zamolodchikov, Int. J. Mod. Phys. A 5, 3221 (1990). https://doi.org/10.1142/S0217751X9000218X Link, Web of Science, ADS, Google Scholar
36. Z. Bajnok and M. Lajer, J. High Energy Phys. 10, 050 (2016), arXiv:1512.06901 [hep-th]. https://doi.org/10.1007/JHEP10(2016)050 Crossref, Web of Science, ADS, Google Scholar
37. J. Jaeckel and C. Wetterich, Phys. Rev. D 68, 025020 (2003), arXiv:hep-ph/0207094. https://doi.org/10.1103/PhysRevD.68.025020 Crossref, Web of Science, ADS, Google Scholar
38. J. Braun, L. Fister, J. M. Pawlowski and F. Rennecke, Phys. Rev. D 94, 034016 (2016), arXiv:1412.1045 [hep-th]. https://doi.org/10.1103/PhysRevD.94.034016 Crossref, Web of Science, ADS, Google Scholar
39. A. Jakovac and A. Patkos, arXiv:1902.06492 [hep-th]. Google Scholar

Journal cover image

Vol. 34, No. 27

Metrics

Downloaded 27 times

History

Received 3 July 2019

Accepted 10 September 2019

Published: 27 September 2019

Keywords