Abstract
We study the triviality and hierarchy problem of a Z 2-invariant Yukawa system with massless fermions and a real scalar field, serving as a toy model for the standard-model Higgs sector. Using the functional RG, we look for UV stable fixed points which could render the system asymptotically safe. Whether a balancing of fermionic and bosonic contributions in the RG flow induces such a fixed point depends on the algebraic structure and the degrees of freedom of the system. Within the region of parameter space which can be controlled by a nonperturbative next-to-leading order derivative expansion of the effective action, we find no non-Gaußian fixed point in the case of one or more fermion flavors. The fermion-boson balancing can still be demonstrated within a model system with a small fractional flavor number in the symmetry-broken regime. The UV behavior of this small-N f system is controlled by a conformal Higgs expectation value. The system has only two physical parameters, implying that the Higgs mass can be predicted. It also naturally explains the heavy mass of the top quark, since there are no RG trajectories connecting the UV fixed point with light top masses.
Similar content being viewed by others
References
K.G. Wilson, J.B. Kogut, Phys. Rep. 12, 75 (1974)
M. Luscher, P. Weisz, Nucl. Phys. B 295, 65 (1988)
M. Luscher, P. Weisz, Nucl. Phys. B 318, 705 (1989)
A. Hasenfratz, K. Jansen, C.B. Lang, T. Neuhaus, H. Yoneyama, Phys. Lett. B 199, 531 (1987)
U.M. Heller, H. Neuberger, P.M. Vranas, Nucl. Phys. B 399, 271 (1993). arXiv:hep-lat/9207024
D.J.E. Callaway, Phys. Rep. 167, 241 (1988)
O.J. Rosten, arXiv:0808.0082 [hep-th]
L.D. Landau, in Niels Bohr and the Development of Physics, ed. by W. Pauli (Pergamon, London, 1955)
M. Gell-Mann, F.E. Low, Phys. Rev. 95, 1300 (1954)
M. Goeckeler, R. Horsley, V. Linke, P. Rakow, G. Schierholz, H. Stuben, Phys. Rev. Lett. 80, 4119 (1998)
M. Goeckeler, R. Horsley, V. Linke, P. Rakow, G. Schierholz, H. Stuben, Nucl. Phys. Proc. Suppl. 63, 694 (1998)
H. Gies, J. Jaeckel, Phys. Rev. Lett. 93, 110405 (2004). arXiv:hep-ph/0405183
N. Cabibbo, L. Maiani, G. Parisi, R. Petronzio, Nucl. Phys. B 158, 295 (1979)
L. Maiani, G. Parisi, R. Petronzio, Nucl. Phys. B 136, 115 (1978)
J. Kuti, L. Lin, Y. Shen, Phys. Rev. Lett. 61, 678 (1988)
T. Hambye, K. Riesselmann, Phys. Rev. D 55, 7255 (1997). arXiv:hep-ph/9610272
Z. Fodor, K. Holland, J. Kuti, D. Nogradi, C. Schroeder, PoS LAT2007, 056 (2007). arXiv:0710.3151 [hep-lat]
P. Gerhold, K. Jansen, J. Kallarackal, arXiv:0810.4447 [hep-lat]
F.J. Yndurain, in Ann Arbor 1991, Proceedings, Gauge theories—past and future, 337–353
S. Weinberg, in C76-07-23.1 HUTP-76/160, Erice Subnucl. Phys., 1 (1976)
R. Percacci, arXiv:0709.3851 [hep-th]
B. Rosenstein, B.J. Warr, S.H. Park, Phys. Rev. Lett. 62, 1433 (1989)
K. Gawedzki, A. Kupiainen, Phys. Rev. Lett. 55, 363 (1985)
C. de Calan, P.A. Faria da Veiga, J. Magnen, R. Seneor, Phys. Rev. Lett. 66, 3233 (1991)
A. Codello, R. Percacci, arXiv:0810.0715 [hep-th]
M. Reuter, Phys. Rev. D 57, 971 (1998). arXiv:hep-th/9605030
O. Lauscher, M. Reuter, Phys. Rev. D 65, 025013 (2002). arXiv:hep-th/0108040
O. Lauscher, M. Reuter, Class. Quantum Gravity 19, 483 (2002). arXiv:hep-th/0110021
W. Souma, Prog. Theor. Phys. 102, 181 (1999). arXiv:hep-th/9907027
P. Forgacs, M. Niedermaier, arXiv:hep-th/0207028
R. Percacci, D. Perini, Phys. Rev. D 67, 081503 (2003). arXiv:hep-th/0207033
A. Codello, R. Percacci, C. Rahmede, Int. J. Mod. Phys. A 23, 143 (2008). arXiv:0705.1769 [hep-th]
R. Percacci, D. Perini, Phys. Rev. D 68, 044018 (2003). arXiv:hep-th/0304222
H. Gies, Phys. Rev. D 68, 085015 (2003). arXiv:hep-th/0305208
H. Gies, J. Jaeckel, C. Wetterich, Phys. Rev. D 69, 105008 (2004). arXiv:hep-ph/0312034
J.M. Schwindt, C. Wetterich, arXiv:0812.4223 [hep-th]
S. Bornholdt, C. Wetterich, Phys. Lett. B 282(3–4), 399 (1992)
C. Wetterich, Phys. Lett. B 301, 90 (1993)
K. Aoki, Int. J. Mod. Phys. B 14, 1249 (2000)
J. Berges, N. Tetradis, C. Wetterich, Phys. Rep. 363, 223 (2002)
D.F. Litim, J.M. Pawlowski, in The Exact Renormalization Group, ed. by Krasnitz, et al. (World Scientific, Singapore, 1999), p. 168
J. Polonyi, Cent. Eur. J. Phys. 1, 1 (2004)
J.M. Pawlowski, Ann. Phys. 322, 2831 (2007). arXiv:hep-th/0512261
H. Gies, arXiv:hep-ph/0611146
B. Delamotte, arXiv:cond-mat/0702365
H. Gies, C. Gneiting, in preparation
C. Gneiting, Diploma thesis, Heidelberg (2005)
L. Rosa, P. Vitale, C. Wetterich, Phys. Rev. Lett. 86, 958 (2001). arXiv:hep-th/0007093
F. Hofling, C. Nowak, C. Wetterich, Phys. Rev. B 66, 205111 (2002). arXiv:cond-mat/0203588
D.F. Litim, Phys. Lett. B 486, 92 (2000). hep-th/0005245
D.F. Litim, Phys. Rev. D 64, 105007 (2001). hep-th/0103195
D.U. Jungnickel, C. Wetterich, Phys. Rev. D 53, 5142 (1996). arXiv:hep-ph/9505267
B.J. Schaefer, H.J. Pirner, Nucl. Phys. A 660, 439 (1999). arXiv:nucl-th/9903003
H. Gies, C. Wetterich, Phys. Rev. D 65, 065001 (2002). arXiv:hep-th/0107221
H. Gies, C. Wetterich, Phys. Rev. D 69, 025001 (2004). arXiv:hep-th/0209183
J. Braun, arXiv:0810.1727 [hep-ph]
M.C. Birse, B. Krippa, J.A. McGovern, N.R. Walet, Phys. Lett. B 605, 287 (2005). arXiv:hep-ph/0406249
S. Diehl, H. Gies, J.M. Pawlowski, C. Wetterich, Phys. Rev. A 76, 053627 (2007). arXiv:cond-mat/0703366
S. Diehl, H. Gies, J.M. Pawlowski, C. Wetterich, Phys. Rev. A 76, 21602 (2007). arXiv:cond-mat/0701198 (Rap. Comm.)
S. Floerchinger, M. Scherer, S. Diehl, C. Wetterich, arXiv:0808.0150 [cond-mat.supr-con]
K. Halpern, K. Huang, Phys. Rev. D 53, 3252 (1996). arXiv:hep-th/9510240
K. Halpern, K. Huang, Phys. Rev. Lett. 74, 3526 (1995). arXiv:hep-th/9406199
H. Gies, Phys. Rev. D 63, 065011 (2001). arXiv:hep-th/0009041
T.R. Morris, Nucl. Phys. B 458, 477 (1996). arXiv:hep-th/9508017
V.A. Miransky, M. Tanabashi, K. Yamawaki, Mod. Phys. Lett. A 4, 1043 (1989)
V.A. Miransky, M. Tanabashi, K. Yamawaki, Phys. Lett. B 221, 177 (1989)
W.A. Bardeen, C.N. Leung, S.T. Love, Phys. Rev. Lett. 56, 1230 (1986)
J. Zinn-Justin, Nucl. Phys. B 367, 105 (1991)
A. Hasenfratz, P. Hasenfratz, K. Jansen, J. Kuti, Y. Shen, Nucl. Phys. B 365, 79 (1991)
M.B. Halpern, W. Siegel, Phys. Rev. D 16, 2486 (1977)
H. Gies, J. Sanchez-Guillen, R.A. Vazquez, J. High Energy Phys. 0508, 067 (2005). arXiv:hep-th/0505275
J. Smit, Nucl. Phys. Proc. Suppl. 17, 3 (1990)
J. Shigemitsu, Nucl. Phys. Proc. Suppl. 20, 515 (1991)
K. Jansen, Phys. Rep. 273, 1 (1996). arXiv:hep-lat/9410018
I.H. Lee, J. Shigemitsu, R.E. Shrock, Nucl. Phys. B 334, 265 (1990)
I.H. Lee, J. Shigemitsu, R.E. Shrock, Nucl. Phys. B 330, 225 (1990)
R.E. Shrock, in Quantum Fields on the Computer, ed. by M. Creutz (ed.) (World Scientific, Singapore, 1992), pp. 150–210
P. Gerhold, K. Jansen, J. High Energy Phys. 0710, 001 (2007). arXiv:0707.3849 [hep-lat]
P. Gerhold, K. Jansen, J. High Energy Phys. 0709, 041 (2007). arXiv:0705.2539 [hep-lat]
K. Jansen, J. Kuti, C. Liu, Phys. Lett. B 309, 119 (1993). arXiv:hep-lat/9305003
K. Jansen, J. Kuti, C. Liu, Phys. Lett. B 309, 127 (1993). arXiv:hep-lat/9305004
H. Gies, S. Rechenberger, M.M. Scherer, arXiv:0907.0327 [hep-th]
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gies, H., Scherer, M.M. Asymptotic safety of simple Yukawa systems. Eur. Phys. J. C 66, 387–402 (2010). https://doi.org/10.1140/epjc/s10052-010-1256-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjc/s10052-010-1256-z