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Register a new userNear-conformal dynamics in a chirally broken system
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Composite Higgs models must exhibit very different dynamics from quantum chromodynamics (QCD) regardless whether they describe the Higgs boson as a dilatonlike state or a pseudo-Nambu-Goldstone boson. Large separation of scales and large anomalous dimensions are frequently desired by phenomenological models. Mass-split systems are well-suited for composite Higgs models because they are governed by a conformal fixed point in the ultraviolet but are chirally broken in the infrared. In this work we use lattice field theory calculations with domain wall fermions to investigate a system with four light and six heavy flavors. We demonstrate how a nearby conformal fixed point affects the properties of the four light flavors that exhibit chiral symmetry breaking in the infrared. Specifically we describe hyperscaling of dimensionful physical quantities and determine the corresponding anomalous mass dimension. We obtain $y_m=1+gamma^*= 1.47(5)$ suggesting that $N_f=10$ lies inside the conformal window. Comparing the low energy spectrum to predictions of dilaton chiral perturbation theory, we observe excellent agreement which supports the expectation that the 4+6 mass-split system exhibits near-conformal dynamics with a relatively light $0^{++}$ isosinglet scalar.
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The isovector--vector and the isovector--axial-vector current are related by a chiral transformation. These currents can be called chiral partners at the fundamental level. In a world where chiral symmetry was not broken, the corresponding current-current correlators would show the same spectral information. In the real world chiral symmetry is spontaneously broken. A prominent peak -- the rho-meson -- shows up in the vector spectrum (measured in (e^+ e^-)-collisions and tau-decays). On the other hand, in the axial-vector spectrum a broad bump appears -- the a_1-meson (also accessible in tau-decays). It is tempting to call rho and a_1 chiral partners at the hadronic level. Strong indications are brought forward that these ``chiral partners do not only differ in mass but even in their nature: The rho-meson appears dominantly as a quark-antiquark state with small modifications from an attractive pion-pion interaction. The a_1-meson, on the other hand, can be understood as a meson-molecule state mainly formed by the attractive interaction between pion and rho-meson. A key issue here is that the meson-meson interactions are fixed by chiral symmetry breaking. It is demonstrated that one can understand the vector and the axial-vector spectrum very well within this interpretation. It is also shown that the opposite cases, namely rho as a pion-pion molecule or a_1 as a quark-antiquark state lead to less satisfying results. Finally speculations on possible in-medium changes of hadron properties are presented.
We discuss the existence of a conformal phase in SU(N) gauge theories in four dimensions. In this lattice study we explore the model in the bare parameter space, varying the lattice coupling and bare mass. Simulations are carried out with three colors and twelve flavors of dynamical staggered fermions in the fundamental representation. The analysis of the chiral order parameter and the mass spectrum of the theory indicates the restoration of chiral symmetry at zero temperature and the presence of a Coulomb-like phase, depicting a scenario compatible with the existence of an infrared stable fixed point at nonzero coupling. Our analysis supports the conclusion that the onset of the conformal window for QCD-like theories is smaller than Nf=12, before the loss of asymptotic freedom at sixteen and a half flavors. We discuss open questions and future directions.
We propose a novel constraint on the gauge dynamics of strongly interacting gauge theories stemming from the a theorem. The inequality we suggest is used to provide a lower bound on the conformal window of four dimensional gauge theories.
We propose to construct a chirally broken model based on the infrared fixed point of a conformal system by raising the mass of some flavors while keeping the others massless. In the infrared limit the massive fermions decouple and the massless fermions break chiral symmetry. The running coupling of this system walks and the energy range of walking can be tuned by the mass of the heavy flavors. Renormalization group considerations predict that the spectrum of such a system shows hyperscaling. We have studied a model with four light and eight heavy flavors coupled to SU(3) gauge fields and verified the above expectations. We determined the mass of several hadronic states and found that some of them are in the 2-3 TeV range if the scale is set by the pseudoscalar decay constant $F_pi approx 250$ GeV. The $0^{++}$ scalar state behaves very differently from the other hadronic states. In most of our simulations it is nearly degenerate with the pion and we estimate its mass to be less than half of the vector resonance mass.
We suggest the idea, supported by concrete calculations within chiral models, that the critical endpoint of the phase diagram of Quantum Chromodynamics with three colors can be detected, by means of Lattice simulations of grand-canonical ensembles with a chiral chemical potential, $mu_5$, conjugated to chiral charge density. In fact, we show that a continuation of the critical endpoint of the phase diagram of Quantum Chromodynamics at finite chemical potential, $mu$, to a critical end point in the temperature-chiral chemical potential plane, is possible. This study paves the way of the mapping of the phases of Quantum Chromodynamics at finite $mu$, by means of the phases of a fictitious theory in which $mu$ is replaced by $mu_5$.
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