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We analyze the effect of scheme transformations in the vicinity of an exact or approximate infrared fixed point in an asymptotically free gauge theory with fermions.
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The latter is the case in QCD and technicolor theories: S. Weinberg, Phys. Rev. D 19
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For a χ \chi GT with requisite fermion content, there is also the alternate possibility that the theory may confine and produce massless composite fermions, as discussed in G. ’t Hooft, Recent Developments in Gauge Theories, Cargése Summer Institute, 1979
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We focus here on an IR zero of the perturbative β \beta function. A nonperturbative zero in β \beta has been discussed in S. J. Brodsky, G. F. de Téramond, and A. Deur, Phys. Rev. D 81
2011
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For recent reviews, see talks in https://latt11.llnl.gov; http://lqcd.fnal.gov/ẽneil/lat-exp-2011; and http://www.kmi.nagoya-u.ac.jp/workshop/SCGT12Mini
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T. A. Ryttov, R. Shrock, Phys. Rev. D 83
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See, e.g., T. Appelquist and J. Terning, Phys. Rev. D 50
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D. D. Dietrich, F. Sannino, and K. Tuominen, Phys. Rev. D 72
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Corrections to this approximation have been discussed, e.g., in T. Appelquist, K. D. Lane, and U. Mahanta, Phys.Rev.Lett. 61
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It is straightforward to generalize our analysis to finite fermion masses in a vectorial gauge theory
Cited in the paper.
One can generalize this to certain STs with f ( a ′ ) f(a^{\prime}) functions that are finite but nonanalytic at a ′ = 0 a^{\prime}=0 , such as f ( a ′ ) = [ 1 + ∑ s = 1 s m a x k s ( a ′ ) s ] [ 1 + κ e − ν / a ′ ] f(a^{\prime})=[1+\sum_{s=1}^{s_{max}}k_{s}(a^{\prime})^{s}][1+\kappa e^{-\nu/a^{\prime}}] , where κ \kappa and ν \nu are (real) constants and ν > 0 \nu>0 . Eqs. ( 7
Cited in the paper.
Hence, if there is an IR zero in the two-loop β α \beta_{\alpha} , at α I R , 2 ℓ \alpha_{IR,2\ell} given by ( 2
Cited in the paper.
See, e.g., S. J. Brodsky and X.-G. Wu, Phys.Rev. D 85
2012
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T. A. Ryttov, R. Shrock, Phys. Rev. D 85
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