Trace anomaly and dynamical quark mass

Effective pion mass term and the trace anomaly

Recently, we developed an effective theory of pions and a light dilatonic meson for gauge theories with spontaneously broken chiral symmetry that are close to the conformal window. The pion mass term in this effective theory depends on an exponent $y$. We derive the transformation properties under dilatations of the renormalized fermion mass, and use this to rederive $y=3-γ_m^*$, where $γ_m^*$ is fixed-point value of the mass anomalous dimension at the sill of the conformal window. This value for $y$ is consistent with the trace anomaly of the underlying near-conformal gauge theory.

Lattice energy sum rules and the trace anomaly

We show that the additional contribution to the Michael lattice energy sum rule for the static quark-antiquark potential, pointed out recently, can be identified with the contribution to the field energy arising from the trace anomaly of the energy momentum tensor. We also exlicitely exhibit the anomalous contribution to the field energy in the sum rule for the glueball mass obtained recently by Michael.

来自格点QCD的迹反常形状因子

Trace anomaly form factors from lattice QCD

本文利用格点QCD计算π介子和核子胶子迹反常形状因子、半径及空间分布，并通过轻质量区变号行为解释手征极限下迹反常对π介子质量贡献趋零。

可约基重整化引发的关于QCD迹反常物理学的误解

Misconceptions About the Physics of the QCD Trace Anomaly from Renormalization in a Reducible Basis

该研究指出近期提出的可约基重整化方法否定了QCD迹反常的三项公认核心特征，由此引发了对核子质量起源、内部作用力等反常相关核子物理的误解。

On trace anomaly in 2+1 flavor QCD

We report on recent progress by the HotQCD collaboration in studying the trace anomaly at non-zero temperature in 2+1 flavor QCD on lattices with the temporal extent N_tau=4, 6, 8, 10 and 12 using the highly improved staggered quark (HISQ) action as well as the asqtad action. We discuss the dependence of our lattice results on the scale setting procedure and compare them with hadron resonance gas (HRG) calculations as well as to resummed perturbative results.

Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem

We demonstrate the existence of an anomaly-induced inhomogeneous phase in a class of vector-like gauge theories without sign problem, thus disproving the long-standing conjecture that the absence of sign problem precludes spontaneous breaking of translational invariance. The presence of the phase in the two-color modification of quantum chromodynamics can be tested by an independent nonperturbative evaluation of the neutral pion decay constant as a function of external magnetic field. Our results provide a benchmark for future lattice studies of inhomogeneous phases in dense quark matter.

Renormalization group, trace anomaly and Feynman-Hellmann theorem

We show that the logarithmic derivative of the gauge coupling on the hadronic mass and the cosmological constant term of a gauge theory are related to the gluon condensate of the hadron and the vacuum respectively. These relations are akin to Feynman-Hellmann relations whose derivation for the case at hand are complicated by the construction of the gauge theory Hamiltonian. We bypass this problem by using a renormalisation group equation for composite operators and the trace anomaly. The relations serve as possible definitions of the gluon condensates themselves which are plagued in direct app…

Effective holographic models for QCD: glueball spectrum and trace anomaly

We investigate effective holographic models for QCD arising from five dimensional Dilaton-Gravity. The models are characterized by a dilaton with a mass term in the UV, dual to a CFT deformation by a relevant operator, and quadratic in the IR. The UV constraint leads to the explicit breaking of conformal symmetry whereas the IR constraint guarantees linear confinement. We propose semi-analytic interpolations between the UV and the IR and obtain a spectrum for scalar and tensor glueballs consistent with lattice QCD data. We use the glueball spectrum as a physical constraint to find the evolutio…

核子质量：迹异常和σ项

Nucleon mass: trace anomaly and $σ$-terms

本文探讨了核子质量的起源，通过迹异常和σ项分析了胶子场及希格斯机制对核子质量的影响。

Anomaly Matching and Low Energy Theories at High Matter Density

I provide new arguments supporting the validity of the t'Hooft anomaly conditions at non zero quark chemical potential. These constraints strengthen the quark-hadron continuity scenario. Finally I review the 2SC effective Lagrangian for color superconductivity.

有效自由度、迹异常和类似c定理的条件在强子共振气体模型中

Effective degrees of freedom, trace anomaly and c-theorem like condition in the hadron resonance gas model

研究了有效自由度与迹异常的关系，提出类似c定理的条件，探讨了排除体积效应下的极限温度，发现第一条件给出的极限温度高于格点QCD计算的相变温度，第二条件则与之前研究一致。

Transport Coefficient to Trace Anomaly in the Clustering of Color Sources Approach

From our previously obtained shear viscosity to entropy density ratio ($η/s$) in the framework of clustering of color sources (Color String Percolation Model: CSPM), we calculate the jet quenching parameter $\hat {q}$ and trace anomaly $Δ= (\varepsilon -3\it p)/T^{4}$ as a function of temperature. It is shown that the scaled $\hat {q}/T^{3}$ is in agreement with the recent JET Collaboration estimates. The inverse of $η/s$ is found to represent $Δ$. The results for $Δ$ are in excellent agreement with Lattice Quantum Chromo Dynamics (LQCD) simulations. From the trace anomaly and energy density $…

On the continuum limit of the lattice chiral anomaly trace relation

Different aspects concerning the rigorous definition of the traces and determinants of the operators involved in a procedure ---proposed by Neuberger and others--- for avoiding fermion doublers on the lattice, are considered. A result of the analysis is that it seems unclear that the consequences derived from the independent treatment of the traces of the two operators contributing to the index relation on the lattice, as carried out in recent manuscripts, can be given rigorous mathematical footing, in particular, that these treatments can commute with the continuum limit ---the lattice regula…