We provide the $\bar{\mathrm{MS}}$ factor of the renormalization constant of the singlet axial-current operator in dimensional regularization at $\mathcal{O}(α_s^5)$ in perturbative Quantum Chromodynamics (QCD). The result is obtained from a formula derived using the Adler-Bell-Jackiw equation in terms of renormalized operators. The required input consists of the complete four-loop results for operator renormalization constants obtained by explicit diagrammatic computation in a previous publication.
A careful and complete discussion is given of the renormalization of the singlet axial anomaly equation in a vector-like nonabelian gauge theory such as QCD regularized by ordinary dimensional regularization. Pseudotensorial structures are treated with the 't Hooft-Veltman prescription. A general framework for calculations is developed, and subsequently verified by explicit computations through two loops. This is followed by a discussion of the matrix elements obtained.
We provide the renormalization constants of the axial current operators, both singlet and non-singlet, in dimensional regularization up to four-loop order in QCD, determined using the off-shell Ward-Takahashi identity for an axial current with a non-anticommuting $γ_5$. A possible application of the result for the singlet axial current operator is the extraction of the non-decoupling mass logarithms in the axial quark form factors.
We compute the three-loop corrections to the quark axial vector form factor in massless QCD, focusing on the pure-singlet contributions where the axial vector current couples to a closed quark loop. Employing the Larin prescription for $γ_5$, we discuss the UV renormalization of the form factor. The infrared singularity structure of the resulting singlet axial-vector form factor is explained from infrared factorization, defining a finite remainder function.
The value of the proton singlet axial constant is estimated. It has been shown that the axial anomaly plays a crucial role in this calculation. Obtained result is sufficiently suppressed in comparison with the naively expected one. The magnitude of the strange quark contribution for the proton state is also computed approximately.
We have analyzed axial-vector current-current correlation functions between one-nucleon states to calculate the singlet axial-vector coupling constant of the nucleon. The octet-octet and the octet-singlet current correlators, investigated in this work, do not require any use of instanton effects. The QCD and hadronic parameters used for the evaluation of correlators have been varied by (10 - 20)%. The value of the singlet axial-vector coupling constant of the nucleon obtained from this analysis is consistent with its current determination from experiments and QCD theory.
In chiral models with SU(3) group structure, strange form factors of baryon octet are evaluated by constructing their sum rules to yield theoretical predictions comparable to the recent experimental data of SAMPLE Collaboration. We also study sum rules for the flavor singlet axial currents for the EMC experiment in a modified quark model.
The renormalization constant $Z_J$ of the flavor-singlet axial-vector current with a non-anticommuting $γ_5$ in dimensional regularization is determined to order $α_s^3$ in QCD with massless quarks. The result is obtained by computing the matrix elements of the operators appearing in the axial-anomaly equation $\big[\partial_μ J^μ_{5} \big]_{R} = \frac{α_s}{4 π}\, n_f\, {\displaystyle \mathrm{T}_{F}} \, \big[F \tilde{F} \big]_{R}$ between the vacuum and a state of two (off-shell) gluons to 4-loop order. Furthermore, through this computation, the conjectured equality between the $\overline{\mat…
The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff $Ł$ and the boundary conditions for the relevant couplings. The physical theory is obtained at $Ł=0$. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point $Ł=Ł_0\to\infty$ but at the physical value $Ł=0$. As an illustration, we compute the triangle axial anomalies.
The recent suggestion of a vanishing flavor-singlet axial charge of nucleon due to a nontrivial vacuum structure is further amplified. A perturbative QCD discussion, applicable for the heavy quark contributions, relates it to the physics of the decoupling theorem. It is also shown that $g_{A}^{0}\simeq 0$ leads to a negative $η'$-meson-quark coupling, which has been found to be compatible with the chiral quark model phenomenology.
We analyze the singlet axial form factor of the proton for small momentum transferred in the framework of QCD sum rules using the interpolating nucleon current which explicitly accounts for the gluonic degrees of freedom. As a result we come to the quantitative description of the singlet axial constant: G_A(0)=0.2. The bilocal power corrections play the most important role in the analysis.
The renormalization constant $Z_J$ of the flavor-singlet axial-vector current with a non-anticommuting $γ_5$ in dimensional regularization is determined to order $α_s^3$ in QCD with massless quarks. In addition, the equality between the $\overline{\mathrm{MS}}$ renormalization constant $Z_{F\tilde{F}}$ associated with the operator $\big[F \tilde{F} \big]_{R}$ and that of $α_s$ is verified explicitly to hold true at 4-loop order.
The transition in quantum chromodynamics (QCD) from hadronic matter to the quark-gluon plasma (QGP) at high temperatures and/or net-baryon densities is associated with the restoration of chiral symmetry and can be investigated in the laboratory via heavy-ion collisions. We study this chiral transition within the functional renormalization group (FRG) approach applied to the two-flavor version of the extended Linear Sigma Model (eLSM). The eLSM is an effective model for the strong interaction and features besides scalar and pseudoscalar degrees of freedom also vector and axial- vector mesons. W…
The $SU(2)_A \times U(2)_V$-symmetric chiral linear sigma model in the presence of the axial anomaly is studied in the local-potential approximation of the Functional Renormalization Group (FRG). The renormalization group (RG) flow is investigated in a truncation which reproduces recent results for the $U(2)_A \times U(2)_V$-symmetric model in the limit of vanishing axial anomaly strength. We search for the conjectured O(4) fixed point in the presence of the $U(1)_A$ anomaly and analyze its stability properties.
To accomodate recent RHIC data on eta prime multiplicity, we propose a minimal modification of the Witten-Veneziano relation at high temperature. This renders a significant drop of eta prime mass at high temperature signaling a restoration of the U(1)A, and the Goldstone character of etaprime.
The prescription for the $γ_5$-matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.
We perform a full next-to-leading analysis of the the available experimental data on the polarized structure function g_1 of the nucleon, and give a precise determination of its singlet axial charge together with a thorough assessment of the theoretical uncertainties. We find that the data are now sufficient to separately determine first moments of the polarized quark and gluon distributions, and show in particular that the gluon contribution is large and positive.
The non-renormalization theorem of chiral vertices and the generalized non-renormalization theorem of the photon self energy are derived in SQED on the basis of algebraic renormalization. For this purpose the gauge coupling is extended to an external superfield. This extension already provides detailed insight into the divergence structure. Moreover, using the local supercoupling together with an additional external vector multiplet that couples to the axial current, the model becomes complete in the sense of multiplicative renormalization, with two important implications. First, a Slavnov--Ta…
The interplay of mesonic fluctuations with an axial $U(1)_A$-symmetry breaking and resulting effects on the location of a possibly existing critical endpoint in the QCD phase diagram are investigated in a framework of the functional renormalization group within a $N_f = 2 + 1$ flavor quark-meson model truncation. The axial $U(1)_A$-symmetry breaking is imposed by a mesonic Kobayashi-Maskawa-'t Hooft determinant. The quark mass sensitivity of the chiral phase transition with and without the $U(1)_A$-symmetry breaking is studied.
We calculate the two loop correction to the quark 2-point function with the non-zero momentum insertion of the flavour singlet axial vector current at the fully symmetric subtraction point for massless quarks in the modified minimal subtraction (MSbar) scheme. The Larin method is used to handle $γ^5$ within dimensional regularization at this loop order ensuring that the effect of the chiral anomaly is properly included within the construction.
Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. We show that the presence of this surface term first discovered several years ago allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. This has relevance to what is referred to as the ``proton spin problem" on the one hand and to the Cheshire-Cat phenomenon in hadron structure on the other. We show that when calculated to the leading or…
We present a method to estimate the matrix element of the singlet axial current within a polarized proton state using lattice QCD. The method relies on using the Adler-Bell-Jackiw anomaly and gives the desired result in the chiral limit. We show that this method fails in the quenched approximation. For heavy quarks one does not expect much difference between simulations including dynamical quarks and those done in the quenched approximation. For that reason we explore numerical methods on an existing set of quenched configurations. The data obtained in this exploratory study show a poor statis…
It is well known that the effect of top quark loop corrections in the axial part of quark form factors (FF) does not decouple in the large top mass or low energy limit due to the presence of the axial-anomaly type diagrams. The top-loop induced singlet-type contribution should be included in addition to the purely massless result for quark FFs when applied to physics in the low energy region, both for the non-decoupling mass logarithms and for an appropriate renormalization scale dependence. In this work, we have numerically computed the so-called singlet contribution to quark FFs with the exa…
The gluonic contributions to the conventional PCAC formulas due to flavor singlet axial anomaly have been instrumental in explaining the mass of the $η^{\prime}$ and providing a plausible explanation for solving the spin crisis. We show that they also play an important role in the description of photo- and electroproduction of vector mesons at low energy and high momentum transfers. We calculate the contributions of this type to $ϕ$ meson electromagnetic production in a model, which contains also a soft pomeron, and find agreement with recent CLAS data.
We match the electroweak chiral Lagrangian with two singlet scalars to the next-to-minimal composite Higgs model with $ SO(6)/SO(5) $ coset structure and extract the scalar divergences to one loop. Assuming the additional scalar to be heavy, we integrate it out and perform a matching to the well-established electroweak chiral Lagrangian with one light Higgs.
Correlators of singlet and octet axial currents, as well as anomaly and pseudoscalar densities have been studied using QCD sum rules. Several of these sum rules are used to determine the couplings f^8_eta, f^0_eta, f^8_etaprime and f^0_etaprime. We find mutually consistent values which are also in agreement with phenomenological values obtained from data on various decay and production rates. While most of the sum rules studied by us are independent of the contributions of direct instantons and screening correction, the singlet-singlet current correlator and the anomaly-anomaly correlator impr…
The renormalization of softly broken SQED is related to the one of supersymmetric QED by using the construction with a local gauge supercoupling and by taking into account softly broken anomalous axial U(1) symmetry. From this extended model one obtains the non-renormalization theorems of SQED and the counterterms of the soft breaking parameters as functions of the supersymmetric counterterms. Due to the Adler-Bardeen anomaly of the axial current an invariant regularization scheme does not exist, and therefore the $β$-functions of soft breaking parameters are derived from an algebraic construc…
The strange and flavor-singlet axial form factors of the nucleon from lattice QCD
Helmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz（美因茨亥姆霍兹研究所）；GSI Helmholtzzentrum für Schwerionenforschung（GSI重离子研究中心）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）；Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn（波恩大学辐射与核物理亥姆霍兹研究所）
We have calculated the axial-vector form factors of the low lying octet baryons ($N$, $Σ$, $Ξ$ and $Λ$) in the chiral constituent quark model ($χ$CQM). In particular, we have studied the implications of chiral symmetry breaking and SU(3) symmetry breaking for the singlet ($g^0_{A}$) and non-singlet ($g^3_{A}$ and $g^8_{A}$) axial-vector coupling constants expressed as combinations of the spin polarizations at zero momentum transfer. The conventional dipole form of parametrization has been used to analyse the $Q^2$ dependence of the axial-vector form factors ($G^0_{A}(Q^2)$, $G^3_{A}(Q^2)$ and …
Splitting functions govern the scale evolution of parton distribution functions. Through a Mellin transformation, they are related to anomalous dimensions of twist-two operators in the operator product expansion. We study off-shell operator matrix element, where the physical operators mix under renormalization with other gauge-variant operators of the same quantum numbers. We devise a new method to systematically extract the Feynman rules resulting from those operators without knowing the operators themselves. As a first application of the new approach, we independently reproduce the well-know…
The observed small value of the first moment of the polarized nucleon spin structure function $g_1$ may be interpreted, in the Veneziano--Shore approach, as a suppression of the first moment $χ^\prime(0)$ of the QCD topological susceptibility. I give an extension of the Witten--Veneziano argument for the $U(1)$ problem, which yields the $O(1/N)$ correction to the $N = \infty$ relation $χ^\prime(0)/F^2_0 = 1$ (where $F_0$ is the $η^\prime$ axial vector coupling).The correction, although negative, seems too small to account for the data. I further argue that the $(η,η^\prime)\rightarrowγγ$ and $…
The framework of the electroweak chiral Lagrangian with a light Higgs is extended by an additional scalar and then generalized to N scalars in the Higgs sector. Divergences from scalar fluctuations are renormalized up to one loop using the background field method. The results are crosschecked against the case of one scalar. A subset of the divergences is demonstrated and crosschecked diagrammatically. Together with the complete one-loop renormalization of the electroweak chiral theory with one light Higgs conducted previously, this constitutes a renormalization framework of any pure scalar ext…
We investigate the nucleon's transverse spin-dependent structure function g_2(x, Q^2) in the framework of the operator product expansion and the renormalization group. We construct the complete set of the twist-3 operators for the flavor singlet channel, and give the relations among them. We develop an efficient, covariant approach to derive the anomalous dimension matrix of the twist-3 singlet operators by computing the off-shell Green's functions. As an application, we investigate the Q^2-evolution of g_2(x, Q^{2}) for the lowest moment case, and discuss its experimental implication.
We introduce a new method for calculating the mixing matrix for non-singlet quark operators including total derivatives, based solely on their renormalization structure in the chiral limit. As input, the method requires the well-known forward anomalous dimensions, which determine the evolution of parton distribution functions, and a calculation of the matrix elements of operators without total derivatives. Assuming a large number of quark flavors $n_f$, we are able to calculate the mixing matrix to fifth order in the strong coupling $α_s$ in the $\overline{\mbox{MS}}$-scheme.
The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large-N_c limit, where N_c is the number of colors. Loop graphs with octet and decuplet intermediate states cancel to various orders in N_c as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. These cancellations are explicitly shown for the general case of N_f flavors of light quarks. In particular, a new generic cancellation is identified in the renormalization of the baryon axial vector current at one-loop order. A comparison with conventional heavy baryon chiral…
Non-conserved composite operators like the quark axial current have divergent matrix elements therefore must be renormalized. We explore how this can be done in quark model calculations where the systematic procedure of dimensional regularization and minimal subtraction is not applicable. We propose a most natural and convenient regularization scheme of cutting the intermediate quark states over which we sum in loop diagram calculations at a certain energy. We show that this scheme works perfectly for the quark axial current and we obtain the quark spin contribution to the proton spin: $Δ_u=0.…
Conformal symmetry-based relations between concrete perturbative QED and QCD approximations for the Bjorken, the Ellis-Jaffe sum rules of polarized lepton- nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector channels are derived. They result from the application of the operator product expansion to three triangle Green functions, constructed from the non-singlet axial-vector, and two vector currents, the singlet axial-vector and two non-singlet vector currents and the non-singlet axial-vect…
We use the BLM procedure to eliminate the renormalization scale ambiguity in the evolution equation for the non-singlet deep-inelastic structure function $F_2^{\text NS}(x,Q).$ The scale of the QCD coupling in the $\overline{\text{MS}}$ scheme has the form $Q^*(x) = Q (1-x)^{1/2} / x~f(x) $, where $x$ is the Bjorken variable and $f(x)$ is a smoothly varying function bounded between 0.30 to 0.45. Equivalently, the evolution of the $n$th moment of the structure function should contain an effective $Λ_{\text{QCD}}$ pattern, with $Λ_n \sim n^{1/2}$. This variation of $Λ_n$ agrees with experimental…
The correlator of singlet axial-vector and vector currents in the external electromagnetic field is studied within the instanton liquid model of QCD vacuum. In the chiral limit we calculate the longitudinal w_L^0 and transversal w_T^0 with respect to axial-vector index invariant amplitudes at arbitrary momentum transfer q. It is demonstrated how the anomalous longitudinal part of the correlator is renormalized at low momenta due to the presence of the U_A(1) anomaly.
The value of the nucleon's flavour-singlet axial-charge extracted from polarised deep inelastic scattering is sensitive to the value of the octet axial-charge g_A^8 which is usually taken from an analysis of hyperon beta-decays within the framework of SU(3) symmetry, namely 0.58 \pm 0.03. Using the Cloudy Bag model we find that the value of g_A^8 is reduced by as much as 20% below the usual phenomenological value. This increases the value of the flavour singlet axial charge (g_A^0|_inv) derived from deep inelastic data and significantly reduces the difference between it and g_A^8.
We derive a QCD sum rule for the flavour-singlet axial coupling constant $g_A^{(0)}$ from a two point correlation function of flavour-singlet axial vector currents in a one-nucleon state. In evaluating the correlation function by an operator product expansion we take into account the terms up to dimension 6. This correlation function receives an additional two-loop diagram which comes from an (anti-)instanton. If we do not include it, $g_A^{(0)}$ is estimated to be 0.8. However, the additional diagram due to instantons contributes negatively and reduces $g_A^{(0)}$ towards the experimental val…
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme. We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments. A unique feature of our calculation is the prediction of a non-vanishing form factor $C_3^A(Q^2)$. Moreover, our results show a surprising sensitivity to the coupling constant $\texttt{g}_1$ of the leading-order Lagrangian…
We combine Witten's renormalization group with the matching conditions of Bernreuther and Wetzel to calculate at next-to-leading order the complete heavy-quark contribution to the neutral-current axial-charge measurable in neutrino-proton elastic scattering. Our results are manifestly renormalization group invariant.
We calculate non-singlet quark operator matrix elements of deep-inelastic scattering in the chiral limit including operators with total derivatives. This extends previous calculations with zero-momentum transfer through the operator vertex which provides the well-known anomalous dimensions for the evolution of parton distributions, as well as calculations in off-forward kinematics utilizing conformal symmetry. Non-vanishing momentum-flow through the operator vertex leads to mixing with total derivative operators under renormalization. In the limit of a large number of quark flavors $n_f$ and f…
In this work we present first results on vector and axial-vector meson spectral functions as obtained by applying the non-perturbative functional renormalization group approach to an effective low-energy theory motivated by the gauged linear sigma model. By using a recently proposed analytic continuation method, we study the in-medium behavior of the spectral functions of the $ρ$ and $a_1$ mesons in different regimes of the phase diagram. In particular, we demonstrate explicitly how these spectral functions degenerate at high temperatures as well as at large chemical potentials, as a consequen…
Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity we consider the Abelian axial anomaly in two dimensions. At finite lattice spacing and with gauge interactions, the axial anomaly arises from non-conservation of the flavor-singlet current. Similar non-conservation also leads to the axial ano…
A method for calculating coefficient functions of the operator product expansion, which was previously derived for the non-singlet case, is generalized for the singlet coefficient functions. The resulting formula defines coefficient functions entirely in terms of corresponding singlet composite operators without applying to elementary (quark and gluon) fields. Both "diagonal" and "non-diagonal" gluon coefficient functions in the product expansion of two electromagnetic currents are calculated in QCD. Their renormalization properties are studied.
Renormalization of the axial vector currents due to Goldstone loops is studied in a simple extension of Manohar - Georgi chiral quark model which incorporates $U(1)_A$ anomaly effects. The polarized strage quark sea in the polarized nucleon results from different renormalization of the flavor singlet and octet currents and is in reasonable agreement with the experiment.
We illustrate that both of massless pseudoscalar meson fields and constitutent quark fields are dynamical field degrees of freedom in energy region between chiral symmetry spontaneously broken scale and quark confinement scale. This physical configuration yields a renormalization running axial coupling constant $g_{_A}(μ)$. The one-loop renormalization prediction $g_{_A}(μ=m_{_N})=0.75$ and $g_{_A}(μ=m_π)=0.96$ agree with $β$ decay of neutron and $π^0\toγγ$ respectively. We also calculate $ρ^\pm\toγπ$ and $ω\toγπ$ decays up to the next to leading order of $N_c^{-1}$ expansion and including all…
The recent experimental results on deep inelastic polarized lepton scattering off proton, deuteron and $^{3}$He together with polari% zed neutron $β$-decay data are analyzed. It is shown that the problem of Ellis-Jaffe and Bjorken sum rules deficiency and the neutron paradox could be solved simultaneously by assuming the small right handed current (RHC) admixture in the weak interaction Lagrangian. The possible RHC impact on pion-nucleon $σ$-term and Gamow-Teller sum rule for $(p,n)$ nuclear reactions is pointed out.
Proton spin is investigated in chiral effective field theory through an examination of the singlet axial charge, $a_0$, and the two non-singlet axial charges, $a_3$ and $a_8$. Finite-range regularization is considered as it provides an effective model for estimating the role of disconnected sea-quark loop contributions to baryon observables. Baryon octet and decuplet intermediate states are included to enrich the spin and flavour structure of the nucleon, redistributing spin under the constraints of chiral symmetry. In this context, the proton spin puzzle is well understood with the calculatio…
In this article, we construct both the color singlet-singlet type and octet-octet type currents to interpolate the $X(3872)$, $Z_c(3900)$, $Z_b(10610)$, and calculate the vacuum condensates up to dimension-10 in the operator product expansion. Then we study the axial-vector hidden charmed and hidden bottom molecular states with the QCD sum rules, explore the energy scale dependence of the QCD sum rules for the heavy molecular states in details, and use the formula $μ=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_Q)^2}$ with the effective masses ${\mathbb{M}}_Q$ to determine the energy scales. The numerical…
We discuss renormalization effects on neutrino masses and mixing angles in a supersymmetric string-inspired SU(4) X SU(2)_L X SU(2)_R X U(1)_X model, with matter in fundamental and antisymmetric tensor representations and singlet Higgs fields charged under the anomalous U(1)_X family symmetry. The quark, lepton and neutrino Yukawa matrices are distinguished by different Clebsch-Gordan coefficients. The presence of a second U(1)_X breaking singlet with fractional charge allows a more realistic, hierarchical light neutrino mass spectrum with bi-large mixing. By numerical investigation we find a …
The baryon axial vector current is computed at one-loop order in large-N_c baryon chiral perturbation theory, where N_c is the number of colors. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference and SU(3) flavor symmetry breaking are accounted for. As expected, large-N_c cancellations between different one-loop graphs are observed as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. Fitting our analytical formulas against experimental data on baryon semileptonic decay…
The concept of effective field theory leads in a natural way to a construction principle for phenomenological sensible models known under the name of the Cheshire Cat Principle. We review its formulation in the chiral bag scenario and discuss its realization for the flavor singlet axial charge. Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. The presence of this surface term allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for th…
