Bao-dong Sun, Ze-hao Sun, Jian Zhou
We compute trace anomaly contribution to hydrogen atom mass, which turns out to be related to the part of the Lamb shift. This finding might shed new light on our understandings of the mass structure of QCD bound states, such as, proton.
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The trace anomaly is relevant to the renormalisation of the unpolarised parton distributions. The role of the trace anomaly in F_2 is compared with the axial anomaly in g_1.
Systematic investigation of trace anomaly contribution in nucleon mass
本文基于矢量介子主导模型，首次利用矢量介子光生数据提取中子迹反常贡献，通过对比分析质子与中子的结果揭示了其内部结构相似性，并详细探讨了影响提取的主要因素，为理解核子质量来源和未来精确提取提供了理论基础与探索。
We examine the contribution of W boson loops to the amplitude of the process H --> γγwithin the dispersion relation approach, taking up an issue raised in this context recently. We show that the non-vanishing limit of the relevant formfactor for mW --> 0 is due to a finite subtraction induced by the value of the corresponding trace anomaly. The argument can be truned around and one thus arrives at a dispersive ("infrared") derivation of the trace anomaly.
We show that, in dimensional reguralization in the minimal subtraction scheme, the QCD trace anomaly can be unambiguously decomposed into two parts coming from the renormalized quark and gluon energy momentum tensors. We carry out this decomposition at the two-loop level. The result can be used to constrain the renormalization group properties of the nucleon's twist-four gravitational form factor $\bar{C}_{q,g}$.
One-loop electron mass and QED trace anomaly
本文探讨了静止系中作为能动量迹矩阵元的电子质量，阐明其单圈图与教科书质量重整化图的联系，并解析及图解证明两者计算结果一致。
The trace anomaly term in the low energy chiral Lagrangian is established by deriving a low energy theorem for $γγ\rightarrow π^0π^0$ scattering. It contributes to $σ(γγ\rightarrow π^0π^0)$ in the same order as the previously computed pion loop contribution. The coherent sum of the two contributions explains the shape of the measured cross section, while the magnitude is determined by the anomalous dimension of the quark mass operator.
The trace anomaly of gluodynamics on the lattice shows clear fingerprints of a dimension two condensate above the phase transition. The condensate manifests itself through even powers of the inverse temperature while the total perturbative contribution corresponds to a mild temperature dependence and turns out to be compatible with zero within errors. We try several resummation methods based on a renormalization group improvement. The trace anomaly data are analyzed and compared with other determinations of the dimension two condensate based on the Polyakov loop and the heavy qq free energy, y…
Finding out universal conditions describing the freeze-out parameters was a subject of various phenomenological studies. In the present work, we introduce a new condition based on constant trace anomaly (or interaction measure) calculated in the hadron resonance gas (HRG) model. Various extensions to the {\it ideal} HRG which are conjectured to take into consideration different types of interactions have been analysed. When comparing HRG thermodynamics to that of lattice quantum chromodynamics, we conclude that the hard-core radii are practically irrelevant, especially when HRG includes all re…
The dimension two gluon condensate has been used previously within a simple phenomenological model to describe power corrections from available lattice data for the renormalized Polyakov loop and the heavy quark-antiquark free energy in the deconfined phase of QCD (hep-ph/0505215,hep-ph/0702055). The QCD trace anomaly of gluodynamics also shows unequivocal inverse temperature power corrections which may be encoded as dimension two gluon condensate. We analyze lattice data of the trace anomaly and compare with other determinations of the condensate from previous references, yielding roughly sim…
The trace anomalous energy contribution to the proton mass is a very important topic in non-perturbative QCD and hadron physics. In experiments, it is under the hot discussions on how to measure the trace anomalous energy.The QCD interpretation of proton trace anomaly is still not clear.To connect the theory with the experiment,we extract the trace anomaly by analyzing the near-threshold photo-production data of $ϕ$ and J/$ψ$ vector mesons. Based on the vector-meson-dominance model and QCD Van der Waals representation, we find that the percentage of trace anomaly in the proton mass ranges from…
In the scalar $ϕ^4$ field model the dispersive approach to the trace anomaly is proposed. It is shown that it is impossible to get dispersion representation for all formfactors so that preserve both the translation and dilatation Ward identities. Subtractions which preserve energy-momentum conservation violate the classical trace Ward--Takahashi identity and give rise to an anomalous contribution to the matrix element of stress tensor $θ_μ^ν$. This contribution coincides with one-loop $β$-function in accordance with previous analyses based on RG technique.
We build the electromagnetic trace anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four quark content. In the leading order of this framework, we study the decays into two photons of the lowest isosinglet scalar mesons. We find that the direct inclusion of underlying mixing among two- and four-quark components in the trace anomaly term is essential in order for the model prediction to agree with the available experimental data on decay width of $f_0(980)$ to two photons. Consequently, this sets a low…
The QED trace anomaly is calculated at one-loop level based on the loop regularization method which is realized in 4-dimensional spacetime and preserves gauge symmetry and Poincare symmetry in spite of the introduction of two mass scales, namely the ultraviolet (UV) cut-off $M_c$ and infrared (IR) cut-off $μ_s$. It is shown that the dilation Ward identity which relates the three-point diagrams with the vacuum polarization diagrams gets the standard form of trace anomaly through quantum corrections in taking the consistent limit $M_c\to \infty$ and $μ_s = 0$ which recovers the original integral…
The Pion Gravitational Form Factors and the Trace Anomaly in QCD Factorization
利用QCD因子化研究π介子引力形状因子，重点分析非阿贝尔TJJ顶点产生的迹反常成分，通过与格点QCD数据比较揭示反常在形状因子中的抵消与主导作用。
The interaction of QCD and electroweak sector with gravity is characterized by the generation of a massless pole in a specific form factor present in the 1-loop effective action. We briefly illustrate how to single out this behaviour in perturbation theory, by taking as an example the $TJJ$ vertex, with $T$ denoting the energy momentum tensor of the Standard Model. The breaking of scale invariance, due to the trace anomaly, is then related to the appearance of a local degree of freedom in the effective action, which is of dilaton type.
The trace anomaly of the energy-momentum tensor is usually quoted in the form which is proportional to the beta function of the theory. However, there are in general many definitions of gauge couplings depending on renormalization schemes, and hence many beta functions. In particular, N=1 supersymmetric pure Yang-Mills has the holomorphic gauge coupling whose beta function is one-loop exact, and the canonical gauge coupling whose beta function is given by the Novikov-Shifman-Vainshtein-Zakharov beta function. In this paper, we study which beta function should appear in the trace anomaly in N=1…
We present a simple derivation of the one-loop trace anomaly in spinor QED through dispersion relations, avoiding completely any ultraviolet regularization. The anomaly can be expressed as a convergent sum rule for the imaginary part of a relevant formfactor. In the massless limit, the imaginary part produces a delta-function singularity at zero external momentum squared. Such a treatment reveals an "infrared face" of the trace anomaly, in striking similarity with the well-known case of the axial anomaly.
In this paper we consider non-minimal couplings of the Standard Model fermions to the vector (trace) and axial vector (pseudo-trace) components of the torsion tensor. We then evaluate the contributions of these vector and axial vector components to the muon anomaly and use the recent precision measurement of the muon anomaly to derive constraints on the torsion parameters.
Concerning the trace anomaly in field theory a nonvanishing vacuum energy breaks the scale symmetry as well, in addition to the usual beta function dependent term, requiring a unit operator in the trace anomaly. This additional term is also necessary in quantum chromodynamics (QCD) to cancel the inherent ambiguity in the gluon condensate. The inseparability of the gluon condensate effect from the perturbative contribution to the vacuum energy renders it impossible to isolate the gluon condensate effect on the cosmological constant.
The QCD Trace Anomaly in Pion Gravitational Form Factors with Sudakov Resummation
本文在微扰QCD框架下研究π介子引力形状因子，通过包含QCD迹反常的$TJJ$关联函数和Sudakov重求和，揭示了反常在不同形状因子中的层级作用，并识别出β函数控制的短距离机械结构贡献。
We report on the computation of the effective actions describing the interaction of gravity both for an abelian and a non-abelian gauge theory, mediated by the trace anomaly.
In the quantum chromodynamics, the mass source of the proton is decomposed into four parts by the energy momentum tensor : quark energy term, gluon energy term, quark mass term and trace anomaly term. And the trace anomaly term is the most crucial contribution for studying the internal structure of the proton. In this work, under the definition of the vector meson dominant model, the trace anomaly contribution of the proton is extracted from the experimental datas of light vector mesons $ρ$, $ω$ and $ϕ$ photoproduction at the near-threshold, which are ($1.15\pm0.08$)$\%$, ($2.70\pm0.04$)$\%$ a…
We review briefly some well known facts about trace anomaly and then concentrate on its 'infrared' manifestation. Among other things we show by means of dispersion relations that dilatations and translations are conflicting symmetries. We discuss the occurrence of some subtraction constants in convergent dispersion relations and illustrate it on the decay process of Higgs to two photons in the electroweak theory.
We discuss an interpretation that a peak in the sound velocity in neutron star matter, as suggested by the observational data, signifies strongly-coupled conformal matter. The normalized trace anomaly is a dimensionless measure of conformality leading to the derivative and the non-derivative contributions to the sound velocity. We find that the peak in the sound velocity is attributed to the derivative contribution from the trace anomaly that steeply approaches the conformal limit. Smooth continuity to the behavior of high-density QCD implies that the matter part of the trace anomaly may be po…
We extend a previous computation of the TJJ correlator, involving the energy-momentum tensor of an abelian gauge theory and two vector currents, to the case of mixed axial-vector/vector currents. The study is performed in analogy to the case of the $AVV$ vertex for the chiral anomaly. We derive the general structure of the anomalous Ward identities and provide explicit tests of their consistency using Dimensional Reduction. Mixed massive correlators of the form $TJ_V J_A$ are shown to vanish both by Ward identities and by C-invariance. The result is characterized by the appearance of massless …
We find an exact coordinate transformation rule from the $AdS_5$ Schwarzschild black hole in the Poincare and the global patch to the Fefferman-Graham coordinate system. Using these results, we evaluate the corresponding holographic stress tensor and trace anomaly of the boundary theory as a function of the radial coordinate. Following the AdS/CFT correspondence, we reinterpret the radial coordinate dependence of the trace anomaly as the Wilsonian renormalization group(RG) flow of the boundary theory.
The recently claimed anomaly in the measurement of the 21 cm hydrogen absorption signal by EDGES at $z\sim 17$, if cosmological, requires the existence of new physics. The possible attempts to resolve the anomaly rely on either (i) cooling the hydrogen gas via new dark matter-hydrogen interactions or (ii) modifying the soft photon background beyond the standard CMB one, as possibly suggested also by the ARCADE~2 excess. We argue that solutions belonging to the first class are generally in tension with cosmological dark matter probes once simple dark sector models are considered. Therefore, we …
Hydrogen energy levels from the anomalous energy-momentum QED trace
本文通过计算QED能量-动量张量迹的单圈矩阵元得到氢原子能级，建立与兰姆位移图的联系，论证反常迹项不应单独加入哈密顿量，并展示迹反常的实现。
Quantum chromodynamics (QCD) claims that the major source of the nucleon invariant mass is not the Higgs mechanism but the trace anomaly in QCD energy momentum tensor. Although experimental and theoretical results support such conclusion, a direct demonstration is still absent. We present the first Lattice QCD calculation of the quark and gluon trace anomaly contributions to the hadron masses, using the overlap fermion on the 2+1 flavor dynamical Domain wall quark ensemble at $m_π=340$ MeV and lattice spacing $a=$0.1105 fm. The result shows that the gluon trace anomaly contributes to most of t…
In this brief report we compare the predictions of a recent next-to-next-to-leading order hard-thermal-loop perturbation theory (HTLpt) calculation of the QCD trace anomaly to available lattice data. We focus on the trace anomaly scaled by T^2 in two cases: N_f=0 and N_f=3. When using the canonical value of mu = 2 pi T for the renormalization scale, we find that for Yang-Mills theory (N_f=0) agreement between HTLpt and lattice data for the T^2-scaled trace anomaly begins at temperatures on the order of 8 T_c while when including quarks (N_f=3) agreement begins already at temperatures above 2 T…
A New Gravitational Action For The Trace Anomaly
针对广义相对论结合现有迹反常作用量不自洽的问题，提出将其拓展为保留GR迹反常方程的标量-张量理论，引入低于普朗克标度的新质量标度管控高维项，所得理论保持二阶运动方程，特定近似下退化为共形Gallileon。
We explore trace-anomaly driven inflation in modified gravity. It is explicitly shown that in $T^2$ teleparallel gravity, the de Sitter inflation can occur, although quasi de Sitter inflation happens in $R^2$ gravity. Furthermore, we investigate the influence of the trace anomaly on inflation. It is found that in $f(T)$ gravity, the de Sitter inflation can end because it becomes unstable due to the trace anomaly, whereas also in higher derivative gravity, the de Sitter inflation can be realized and it will be over thanks to the trace anomaly for smaller parameter regions in comparison with tho…
Exact relations between the QCD thermal pressure and the trace anomaly are derived. These are used, first, to prove the equivalence of the thermodynamic and the hydrodynamic pressure in equilibrium in the presence of the trace anomaly, closing a gap in previous arguments. Second, in the temporal axial gauge a formula is derived which expresses the thermal pressure in terms of a Dyson-resummed two-point function. This overcomes the infrared problems encountered in the conventional perturbation-theory approach.
We consider deconfined matter in SU(N) gauge theory as an ideal gas of transversely polarized quasi-particle modes having a temperature-dependent mass m(T). Just above the transition temperature, the mass is assumed to be determined by the critical behavior of the energy density and the screening length in the medium. At high temperature, it becomes proportional to T as the only remaining scale. The resulting (trace anomaly based) interaction measure Delta=(e - 3P)/T^4 and energy density are found to agree well with finite temperature SU(3) lattice calculations.
In the QCD energy-momentum tensor $T^{μν}$, the terms that contribute to physical matrix elements are expressed as the sum of the gauge-invariant quark part and gluon part. Each part undergoes the renormalization due to the interactions among quarks and gluons, although the total tensor $T^{μν}$ is not renormalized thanks to conservation of energy and momentum. We show that, through the renormalization, each of the quark and gluon parts of $T^{μν}$ receives a definite amount of anomalous trace contribution, such that their sum reproduces the well-known QCD trace anomaly. We provide a procedure…
We investigated the origin of the RI'/MOM quark mass under the Landau gauge at the non-perturbative scale, using the chiral fermion with different quark masses and lattice spacings. Our result confirms that such a mass is non-vanishing based on the linear extrapolation to the chiral and continuum limit, and shows that such a mass comes from the spontaneous chiral symmetry breaking induced by the near zero modes with the eigenvalue $λ<{\cal O}(5m_q)$, and is proportional to the quark matrix element of the trace anomaly at least down to $\sim $1.3 GeV.
Within the framework of the recently proposed Taylor-Lagrange regularization scheme - which leads to finite elementary amplitudes in $4$-dimensional space-time with no additional dimensionful scales - we show that the trace of the energy-momentum tensor does not show any anomalous contribution even though quantum corrections are considered. Moreover, since the only renormalization we can think of within this scheme is a finite renormalization of the bare parameters to give the physical ones, the canonical dimension of quantum fields is also preserved by the use of this regularization scheme.
Five dimensional dilaton models are considered as possible holographic duals of the pure gauge QCD vacuum. In the framework of these models, the QCD trace anomaly equation is considered. Each quantity appearing in that equation is computed by holographic means. Two exact solutions for different dilaton potentials corresponding to perturbative and non-perturbative beta-functions are studied. It is shown that in the perturbative case, where the beta-function is the QCD one at leading order, the resulting space is not asymptotically AdS. In the non-perturbative case, the model considered presents…
We discuss the derivation of the trace anomaly using a non-local effective action at one loop. This provides a simple and instructive form and emphasizes infrared physics. We then use this example to explore several of the properties of non-local actions, including displaying the action for the full non-local energy-momentum tensor. As an application, we show that the long-distance corrections at one loop lead to quantum violations of some classical consequences of the equivalence principle, for example producing a frequency dependence of the gravitational bending of light.
Weakly-Coupled Trace Anomaly Action for Gravity
本研究提出通过抵消项实现迹反常的定域微分同胚不变引力量子有效作用量，指出其低能强耦合问题，引入带自发破缺标度不变性的新扇区解决该问题，并通过三类反常的有效作用量附录佐证相关形式关联。
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.
It is known that the trace anomaly in the QCD energy-momentum tensor $T^{μν}$ can be attributed to the anomalies for each of the gauge-invariant quark part and gluon part of $T^{μν}$, and their explicit three-loop formulas have been derived in the $\overline{\rm MS}$ scheme in the dimensional regularization. The matrix elements of this quark/gluon decomposition of the QCD trace anomaly allow us to derive the QCD constraints on the hadron's gravitational form factors, in particular, on the twist-four gravitational form factor, $\bar{C}_{q,g}$. Using the three-loop quark/gluon trace anomaly form…
We present a complete study of the one graviton-two neutral gauge bosons vertex at 1-loop level in the electroweak theory. This vertex provides the leading contribution to the interaction between the Standard Model and gravity, mediated by the trace anomaly, at first order in the inverse Planck mass and at second order in the electroweak expansion. At the same time, these corrections are significant for precision studies of models with low scale gravity at the LHC. We show, in analogy with previous results in the QED and QCD cases, that the anomalous interaction between gravity and the gauge c…
We propose an effective chiral Lagrangian with a chiral scalar introduced as a dilaton associated with broken conformal symmetry and responsible for the trace anomaly in QCD and discuss the properties of hadronic matter at high density and temperature. As the "dilaton limit" is taken, which drives a system from nuclear matter density to near chiral restoration density, a linear sigma model emerges from the highly non-linear structure. A striking prediction is that as the dilaton limit is approached, the omega-nucleon interaction gets strongly suppressed at high density. This is shown to be a f…
Non-relativistic trace anomaly and equation of state in dense fermionic matter
本研究针对带三体相互作用的一维三分量费米子系统，用G矩阵方法推导高密度区基态物态方程解析形式，阐明迹反常的产生机制，结果与量子蒙特卡洛数据相符，可为致密星强子-夸克渡越物理提供参考。
The thermodynamical properties of a pure Yang-Mills theory SU(N) is described by a gas of gluonic quasiparticles with temperature dependent mass $m(T)$ and a bag function $B(T).$ The analytic behavior of $m(T)$ and the pressure $p$ at high $T$ are derived and constraints on the parameters defining $B(T)$ are discussed. The trace anomaly $θ=ρ-3p$ is evaluated in the high $T$ domain: it is dominated by a quadratic behavior $θ=nKT^{2},$ where $n=2(N^{2}-1)$ is the number of degrees of freedom and $K$ is an integration constant which does not depend on the bag function $B(T)$. This is a general re…
Trace anomaly and interior curvature of neutron stars in energy-momentum squared gravity
研究能动量平方引力中中子星内部迹反常与曲率的关系，发现迹反常仍能组织内部几何，但随耦合强度分裂，扩展了GR热力学-几何对应。
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。
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。
Trace Anomaly of Cold Dense Matter Constrained by Collective Flow
通过中间能重离子碰撞中的集体流观测，首次提取出冷密集物质的迹异常，证实了重离子碰撞与中子星观测对宏观性质的一致性。
From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomophic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In part…
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。
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…
Holography for the Trace Anomaly Action
本文证明大$N_c$共形场论产生的迹反常作用量可通过全息Randall-Sundrum双膜理论实现紫外完备化，radion作为自发破缺共形对称性的低能残余，并探讨了次领头$N_c$项的弱耦合推导及其强耦合行为。
In the QCD energy-momentum tensor $T^{μν}$, the terms that contribute to physical matrix elements are expressed as the sum of the gauge-invariant quark part and gluon part. Each part undergoes the renormalization due to the interactions among quarks and gluons, although the total tensor $T^{μν}$ is not renormalized thanks to the conservation of energy and momentum. Recently it has been shown that, through the renormalization, each of the quark and gluon parts of $T^{μν}$ receives a definite amount of anomalous trace contribution, such that their sum reproduces the well-known QCD trace anomaly,…
Model-independent results on parity violation in the trace anomaly
针对自由外尔费米子迹反常是否存在宇称破坏的学界争议，研究通过路径积分方法及维数正则化相容理论分析，证明庞特里亚金项不存在，指出三类反常的有限性阻止了反常宇称破坏，给出模型无关结论。
Mass formulas for the light-vector mesons written in terms of the gluon condensate i.e., the trace anomaly in quantum chromodynamics (QCD), are derived on the basis of finite energy QCD sum rules. We utilize sum rules with $s^n$ and $s^{n+1/2}$ weights, which relate the energy-weighted spectral sums to the vacuum expectation values of certain commutation relations. After evaluating the commutation relations, the sum rules with $s^n$ weights are reduced to the familiar ones obtained from the operator product expansion (OPE). On the other hand, the sum rules with $s^{n+1/2}$ weights cannot be de…
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…
Trace anomaly, effective degrees of freedom, and chemical potential effects near the QCD crossover
本文提出一种紧凑的分析方法，结合多组分范德瓦尔型描述与温度依赖的有效自由度，以描述超密集的强子物质。通过引入温度依赖的退化度和有效化学势，自然再现轨异常及其在临界区的峰值结构。
Trace Anomaly of Weyl Fermions via the Path Integral
本文用路径积分正则化方法计算了引力背景中自由 Weyl 费米子的迹反常，发现其为 Dirac 费米子的一半，并证明 Pontryagin 密度项为零，澄清了文献中的争议。
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