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Scale-setting, flavor dependence, and chiral symmetry restoration

Daniele Binosi, Craig D. Roberts, and José Rodríguez-Quintero
Phys. Rev. D 95, 114009 – Published 13 June 2017
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  • INTRODUCTION
  • GAP EQUATION’S KERNEL
  • SCALE SETTING
  • FLAVOR DEPENDENCE OF THE INTERACTION
  • CHIRAL SYMMETRY RESTORATION
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We determine the flavor dependence of the renormalization-group-invariant running interaction through judicious use of both unquenched Dyson-Schwinger equation and lattice results for QCD’s gauge-sector two-point functions. An important step is the introduction of a physical scale setting procedure that enables a realistic expression of the effect of different numbers of active quark flavours on the interaction. Using this running interaction in concert with a well constrained class of dressed–gluon-quark vertices, we estimate the critical number of active lighter-quarks above which dynamical chiral symmetry breaking becomes impossible: nfcr≈9; and hence in whose neighborhood QCD is plausibly a conformal theory.

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    • Received 11 April 2017

    DOI:https://doi.org/10.1103/PhysRevD.95.114009

    © 2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Color confinementNonperturbative effects in field theory
    1. Physical Systems
    GluonsQuarks
    1. Properties
    Chiral symmetryConformal symmetry
    Nuclear PhysicsParticles & Fields

    Authors & Affiliations

    Daniele Binosi1, Craig D. Roberts2, and José Rodríguez-Quintero3,4

    • 1European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione Bruno Kessler Villa Tambosi, Strada delle Tabarelle 286, I-38123 Villazzano (TN), Italy
    • 2Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
    • 3Department of Integrated Sciences; University of Huelva, E-21071 Huelva; Spain
    • 4CAFPE, Universidad de Granada, E-18071 Granada, Spain

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    Issue

    Vol. 95, Iss. 11 — 1 June 2017

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    Images

    • Figure 1
      Figure 1

      Functions characterising the gluon (left panel) and ghost propagators (right panel) obtained from numerical simulations of lQCD with nf=(2,0) and nf=(2,1,1) [42]. Regarding Δ(k2), the curves represent a fit [see Eq. (10)], whereas for the ghost dressing function they depict the solution of the corresponding DSE. For nf=(2,0) we plot both the original lQCD results and the values obtained after rescaling as described in association with Eqs. (12)–(14). Notably, the ghost is hardly affected by rescaling. In the left panel the x-axis scale is linear to the left of the vertical dashed line and logarithmic otherwise, an artifice which enables us to show the appearance of a gluon mass-scale at IR momenta.

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    • Figure 2
      Figure 2

      RGI combinations entering the definition of the gauge-sector quark-gluon interaction kernel, Eqs. (2): LF (left), and d^ (right). Plainly, using the original lQCD output: d^2+1+1(0)≠d^2(0); whereas the two curves almost overlap upon introduction of the rescaling factor in Eq. (13). As in Fig. 1, the vertical dashed line in the right panel marks a change between linear and logarithmic scales for the x-axis.

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    • Figure 3
      Figure 3

      (Left panel) The interaction strength for (2,0) (dot-dashed curve, red) and (2,1,1) [continuous curve, blue] and the corresponding αT [dotted/dashed curves], which, following Eqs. (2b), are obtained as the limiting case for the interaction strength when L(k2)F(k2)≪1. (Right panel) The ratios d^2+1+1/d^2 [continuous curves] and the corresponding ratio of the Taylor coupling [dashed curves] using the original and rescaled (2,0) data.

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    • Figure 4
      Figure 4

      (Left panel) Gap equation RGI interaction kernel (upper curves) for a (2,Nf′) theory with Nf′=0,…,3. The coefficients in Eq. (15) are: a1=1.81−0.292Nf′, b1=9.93+1.79Nf′, b2=1.1−4.96Nf′, b3=22.41+5.61Nf′. The corresponding kernels obtained with lf=0 are also depicted (lower curves). (Right panel) Chiral order parameter in Eq. (20), which exposes the impact on DCSB of adding additional s-quark-like active quarks to the theory. Extrapolating linearly, DCSB is absent in this class of theories for nf=2+Nf′≳9 (nf≳5 in the absence of massless-ghost loops).

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