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 current of the Standard Model, due to the trace anomaly, is mediated, in each gauge invariant sector, by effective massless scalar degrees of freedom. We derive the Ward and Slavnov-Taylor identities characterizing the vertex. Our analysis includes the contributions from the improvements of the scalar sector, induced by a conformally coupled Higgs sector in curved space.
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.
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.
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.
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.
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.
We elaborate on the structure of the graviton-gauge-gauge vertex in the electroweak theory, obtained by the insertion of the complete energy-momentum tensor ($T$) on 2-point functions of neutral gauge currents ($VV'$). The vertex defines the leading contribution to the effective action which accounts for the conformal anomaly and related interaction between the Standard Model and gravity. The energy momentum tensor is derived from the curved spacetime Lagrangian in the linearized gravitational limit, and with the inclusion of the term of improvement of a conformally coupled Higgs sector. As in…
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.
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…
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…
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.
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 point out that vector boson fusion (VBF) at the Large Hadron Collider (LHC) can lead to useful signals for charginos and neutralinos in supersymmetric scenarios where these particles are almost invisible. The proposed signals are just two forward jets with missing transverse energy. It is shown that in this way one can put by far the strongest constraint on the parameter space of a theory with anomaly mediated supersymmetry breaking (AMSB) at the LHC. In addition, scenarios where the lightest neutralinos and charginos are Higgsino-like can give signals of the above type.
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…
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…
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 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.
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 $\bar{C}_{q,g}$.
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…
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.
We inquire if the total decay rate of neutral vector mesons can contain relevant off-shell contributions from the triangle anomaly. The answer seems to be affirmative for the case of J/Psi, and as a byproduct we get estimates of the decay width for neutral pions.
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…
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…
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 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 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…
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 investigate effects of the axial anomaly term with a chiral-diquark coupling on the phase diagram within a two-plus-one-flavor Nambu-Jona-Lasinio (NJL) model under the charge-neutrality and $β$-equilibrium constraints. We find that when such constraints are imposed, the new anomaly term plays a quite similar role as the vector interaction does on the phase diagram, which the present authors clarified in a previous work. Thus, there appear several types of phase structures with multiple critical points at low temperature $T$, although the phase diagrams with intermediate-$T$ critical point(s…
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…
We report on effects of the q-$\bar{\rm q}$ vector interaction and/or the U(1)$_A$-anomaly-induced chiral-diquark coupling on the charge-neutral quark matter in $β$-equilibrium. We show that when the vector coupling is absent, there can appear a cross-over region sandwiched by two critical points in the intermediate temperature ($T$) region, while the phase transition in the low-$T$ region including zero temperature keeps being first order until the strength of the anomaly term is increased to have a critical value. On the other hand, when the vector coupling is also present, there appears a c…
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
Università del Salento（萨伦托大学）；INFN Sezione di Lecce（意大利国家核物理研究所莱切分部）；National Center for HPC, Big Data and Quantum Computing（高性能计算、大数据与量子计算国家中心）；CNR Nanotec（意大利国家研究委员会纳米技术研究所）；Institute of Physics, Academia Sinica（中央研究院物理学研究所）
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.
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…
We study the QCD vacuum structure under the influence of an electromagnetic field with a nonzero second Lorentz invariant $I_2=\vec{E}\cdot{\vec B}$. We show that the presence of $I_2$ can induce neutral pion ($π^0$) condensation in the QCD vacuum through the electromagnetic triangle anomaly. Within the frameworks of chiral perturbation theory at leading small-momenta expansion as well as the Nambu--Jona-Lasinio model at leading $1/N_c$ expansion, we quantify the dependence of the $π^0$ condensate on $I_2$. The stability of the $π^0$-condensed vacuum against the Schwinger charged pair producti…
We investigate decay and production of neutral pions in strong magnetic fields. In the presence of strong magnetic fields, transition between a neutral pion and a virtual photon becomes possible through the triangle diagram relevant for the chiral anomaly. We find that the decay mode of a neutral pion into two photons cannot persist in the dominant mode in strong magnetic fields, and that decay into a dilepton instead dominates over the other modes. We also investigate the effects of magnetic fields on prompt virtual photons created in ultrarelativistic heavy-ion collisions. There is no anisot…
We investigate how the anticipated neutral current rate from $SNO$ will sharpen our understanding of the solar neutrino anomaly. Quantitative analyses are performed with representative values of this rate in the expected range of $0.8 - 1.2$. This would provide a $5 - 10 σ$ signal for $ν_e$ transition into a state containing an active neutrino component. Assuming this state to be purely active one can estimate both the $^8B$ neutrino flux and the $ν_e$ survival probability to a much higher precision than currently possible. Finally the measured value of the $NC$ rate will have profound implica…
Zhejiang Ocean University（浙江海洋大学）；University of Science and Technology of China（中国科学技术大学）；Shandong University（山东大学）；Joint Institute for Nuclear Research（苏联联合核研究所）；NRC Kurchatov Institute（库尔恰托夫国家研究中心）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）
An anomaly-free $U(1)'$ effective Lagrangian as the most common new physics beyond the standard model is proposed to survey the maximal parameter space constrained by electroweak precise measurements at the LEP and direct detection in dilepton decay channel at the LHC at $\sqrt{s}=7$ TeV. By the global fit of effective couplings of $Z$ boson to the SM fermions, $Δ_{11},Δ_{21},g_2Δ_{31}$ related to mixings and $r$ related to $U(1)'$ charge assignment are bounded. The allowed areas are plotted in the not only $r$-$g_2$ but also $m_{Z'}$-$g_2$ planes, which show that a sub-TeV $Z'$ is still permi…
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.
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.
We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider models with a gauged $U(1)$ flavor symmetry with one flavon and two Higgs doublets and three right-handed SM singlets to provide three model examples based on different physical assumptions. The models we study are: anomaly-free with no SM neutral heavy chiral fermions, anomaly-free with SM neutral heavy chiral fermions, and supersymmetric …
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…
The QCD Trace Anomaly in Pion Gravitational Form Factors with Sudakov Resummation
Dipartimento di Matematica e Fisica, Università del Salento（萨伦托大学数学与物理系）；INFN Sezione di Lecce（意大利国家核物理研究所莱切分部）；National Centre for HPC, Big Data and Quantum Computing（高性能计算、大数据与量子计算国家中心）；CNR Nanotec（意大利国家研究委员会纳米技术研究所）
