Symmetric point flavour singlet axial vector current renormalization at two loops
J. A. Gracey
备注：
18 latex pages, 10 figures, anc directory contains txt file with electronic version of the MSbar Green's function for the flavour singlet axial vector current, additional text and references added
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.
We present flavour-symmetric couplings for the OZI-allowed three-meson vertices of effective meson theories, which for the case of the two-meson channels to which the flavour-singlet scalar meson couples, are endowed with a correction factor with respect to the standard formula.
We present data for the axial coupling constant g_A of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g_A based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattic…
We study properties of pseudoscalar flavour-singlet mesons from Wilson twisted mass lattice QCD with Nf=2+1+1 dynamical quark flavors. Results for masses are presented at three values of the lattice spacing and light quark masses corresponding to values of the pion mass from 230 MeV to 500 MeV. We briefly discuss scaling effects and the light and strange quark mass dependence of the eta mass. In addition we present an exploratory study using Osterwalder-Seiler type strange and charm valence quarks. This approach avoids some of the complications of the twisted mass heavy doublet. We present fir…
We investigate the power-suppressed corrections to fragmentation functions in flavour-singlet deep inelastic lepton scattering, to complement the previous results for the non-singlet contribution. Our method is a dispersive approach based on an analysis of Feynman graphs containing massive gluons. As in non-singlet deep inelastic scattering we find that the leading corrections are proportional to 1/Q^2.
We investigate the 1/Q^2 power-suppressed corrections to structure functions in the flavour-singlet channel of deep inelastic lepton scattering arising from renormalon insertions into an initial-state gluon, as obtained using the dispersive approach. The pinch technique is used as a convenient tool in the separation of contributions.
We investigate the power-suppressed corrections to structure functions in flavour singlet deep inelastic lepton scattering, to complement the previous results for the non-singlet contribution. Our method is a dispersive approach based on an analysis of Feynman graphs containing massive gluons; and our results agree with those obtained from leading infrared renormalon contributions. As in non-singlet deep inelastic scattering we find that the leading corrections are proportional to 1/Q^2. We find that the singlet contribution becomes important at small x.
We discuss in detail the extraction of hadronic mixing strengths from lattice studies. We apply this to the mixing of a scalar glueball and a scalar meson in the quenched approximation. We also measure correlations appropriate for flavour-singlet scalar mesons using dynamical quark configurations from UKQCD. This enables us to compare the results from the quenched study of the mixing with the direct determination of the mixed spectrum. Improved methods of evaluating the disconnected quark diagrams are also presented.
We analyze power corrections to flavour singlet deep inelastic scattering structure functions in the framework of the infrared renormalon model. Our calculations, together with previous results for the non-singlet contribution, allow to model the x-dependence of higher twist corrections to F_2, F_L and g_1 in the whole x domain.
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 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…
We argue that eta bound states in nuclei are sensitive to the singlet component in the eta. The bigger the singlet component, the more attraction and the greater the binding. Thus, measurements of eta bound states will yield new information about axial U(1) dynamics and glue in mesons. Eta - etaprime mixing plays an important role in understanding the value of the eta-nucleon scattering length.
We consider the supersymmetric seesaw mechanism induced by the exchange of heavy SU(2)_W triplet states, rather than `right-handed' neutrino singlets, to generate neutrino masses. We show that in this scenario the neutrino flavour structure tested at low-energy in the atmospheric and solar neutrino experiments is directly inherited from the neutrino Yukawa couplings to the triplets. This allows us to predict the ratio of the tau --> mu gamma (or tau --> e gamma) and mu --> e gamma decay rates in terms of the low-energy neutrino parameters. Moreover, once the model is embedded in a grand unifie…
We analytically compute the flavour singlet ${\cal O}(α_s^2 m_b^2/m_t^2)$ radiative corrections to the partial decay rate $Γ(Z\rightarrow b\bar{b})$. These corrections arise from anomalous ``double traingle'' diagrams containing a single $γ_5$ matrix inside each of two closed fermion loops. They represent the next-to-leading term of the asymptotic expansion in the inverse large top mass. As a byproduct of the calculcation we confirm the results of B.Kniehl and J.H.Kühn for the flavour singlet massless corrections \cite{KniKue90} as well as our previous ${\cal O}(α_s^2 m_b^2/M_Z^2)$ result \cit…
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 lightest baryon octet is studied within a covariant and confining Nambu--Jona-Lasinio model. By solving the relativistic Faddeev equations including scalar and axialvector diquarks, we determine the masses and axial charges for ΔS = 0 transitions. For the latter the degree of violation of SU(3) symmetry arising because of the strange spectator quark(s) is found to be up to 10%.
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 singly charged $SU(2)_L$ singlet scalar, with its necessarily flavour violating couplings to leptons, lends itself particularly well for an explanation of the Cabibbo Angle Anomaly and of hints for lepton flavour universality violation in $τ\to μ\bar νν$. In a setup addressing both anomalies, we predict loop-induced effects in $τ\to eγ$ and in $τ\to eμμ$. A recast of ATLAS selectron and smuon searches allows us to derive a coupling-independent lower limit of $\approx 200$ GeV on the mass of the singly charged singlet scalar. At a future $e^+e^-$ collider, dark matter mono-photon searches c…
We present a lattice calculation of the nucleon iso-vector axial and induced pseudoscalar form factors on the CLS ensembles using $N_{\rm f}=2$ dynamical flavours of non-perturbatively $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation…
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.
We study the dark matter phenomenology of scotogenic frameworks through a rather illustrative model extending the Standard Model by scalar and fermionic singlets and doublets. Such a setup is phenomenologically attractive since it provides the radiative generation of neutrino masses, while also including viable candidates for cold dark matter. We employ a Markov Chain Monte Carlo algorithm to explore the associated parameter space in view of numerous constraints stemming from the Higgs mass, the neutrino sector, dark matter, and lepton-flavour violating processes. After a general discussion of…
We show that a simple extension of the Standard Model involving the introduction of vector-like quarks and heavy neutrinos, provides an explanation of the so called B-anomalies in $b\to s\ell\bar\ell$ transitions. Vector-like quarks can explain, in the context of a discrete flavour symmetry, all the relevant characteristics of the Cabibbo-Kobayashi-Maskawa sector. It is in this framework that we study the requirements on the masses of the vector like quarks and the heavy neutrinos leading to viable models with sufficient deviations of lepton flavour universality and which simultaneously avoid …
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）
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.
Using the Closed-Time-Path approach, we perform a systematic leading order calculation of the relaxation rate of flavour correlations of left-handed Standard Model leptons. This quantity is of pivotal relevance for flavoured Leptogenesis in the Early Universe, and we find it to be 5.19*10^-3 T at T=10^7 GeV and 4.83*10^-3 T at T=10^13 GeV. These values apply to the Standard Model with a Higgs-boson mass of 125 GeV. The dependence of the numerical coefficient on the temperature T is due to the renormalisation group running. The leading linear and logarithmic dependencies of the flavour relaxati…
Octet baryon axial, induced pseudoscalar, and pseudoscalar form factors are computed using a symmetry-preserving treatment of a vector$\,\times\,$vector contact interaction (SCI), thereby unifying them with an array of other baryon properties and analogous treatments of semileptonic decays of pseudoscalar mesons. The baryons are treated as quark--plus--interacting-diquark bound states, whose structure is obtained by solving a Poincaré-covariant Faddeev equation. The approach is marked by algebraic simplicity, involves no free parameters, and since it is symmetry preserving, all consequences of…
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.
We discuss the large-x behaviour of the splitting functions P_qg and P_gq and of flavour-singlet coefficient functions, such as the gluon contributions C_2,g and C_L,g to the structure functions F_2,L, in massless perturbative QCD. These quantities are suppressed by one or two powers of 1-x with respect to the 1/(1-x) terms which are the subject of the well-known threshold exponentiation. We show that the double-logarithmic contributions to P_qg, P_gq and C_L at order alpha_s^4 can be predicted from known third-order results and present, as a first step towards a full all-order generalization,…
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.
The U(2)_R x U(2)_L symmetry of QCD with two massless flavours is subject to anomalies which affect correlation functions involving the singlet currents A^0_μor V^0_μ. These are relevant for pion-photon interactions, because - for two flavours - the electromagnetic current contains a singlet piece. We give the effective Lagrangian required for the corresponding low energy analysis to next-to-leading order, without invoking an expansion in the mass of the strange quark. In particular, the Wess-Zumino-Witten term that accounts for the two-flavour anomalies within the effective theory is written …
Motivated by measurements of the flavor singlet axial coupling constant of the nucleon in polarized deep inelastic scattering we study the contribution of instantons to OZI violation in the axial-vector channel. We consider, in particular, the f_1-a_1 meson splitting, the flavor singlet and triplet axial coupling of a constituent quark, and the axial coupling constant of the nucleon. We show that instantons provide a short distance contribution to OZI violating correlation functions which is repulsive in the f_1 meson channel and adds to the flavor singlet three-point function of a constituent…
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.
Low-Scale Leptogenesis from Resonant Thermal Lepton Flavour Coherences
The University of Osaka（大阪大学）；Marietta Blau Institute for Particle Physics, Austrian Academy of Sciences（奥地利科学院玛丽埃塔·布劳粒子物理研究所）；University of Manchester（曼彻斯特大学）
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.
We compare flavour singlet and non-singlet vector mesons from first principles using lattice QCD. With N_f=2 flavours of light quark, this addresses the omega-rho mass difference. Using maximally twisted-mass lattice QCD, we are able for the first time to determine this mass difference precisely and we compare with experiment. We also discuss omega-rho mixing effects arising within QCD through the u-d quark mass difference.
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.
Very recently we proposed a predictive 2 Higgs Doublet Model with $S_{3}$ flavour symmetry that successfully accounts for fermion masses and mixings. In this letter, motivated by the $750$ GeV Higgs diphoton resonance recently reported by the ATLAS and CMS collaborations, we modify this model by adding exotic top partners with electric charge $\frac{5}{3}$ and a electrically charged scalar singlet. These exotic top partners decay into a charged scalar singlet and the SM up type quarks, whereas the charged scalar singlet will mainly decay into SM up and down type quarks. This simple modificatio…
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.
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 the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange structure functions in deep inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top lim…
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 classification of leptonic currents with respect to C-operation requires the separation of elementary particles into the two classes of vector C-even and axial-vector C-odd character. Their nature has been created so that to each type of lepton corresponds a kind of neutrino. Such pairs are united in families of a different C-parity. Unlike the neutrino of a vector type, any C-noninvariant Dirac neutrino must have his Majorana neutrino. They constitute the purely neutrino families. We discuss the nature of a corresponding mechanism responsible for the availability in all types of axial-vecto…
In recent years, evidence for lepton flavour universality violation beyond the Standard Model has been accumulated. In this context, a singly charged $SU(2)_L$ singlet scalar ($ϕ^\pm$) is very interesting, as it can only have flavour off-diagonal couplings to neutrinos and charged leptons, therefore necessarily violating lepton flavour (universality). In fact, it gives a (necessarily constructive) tree-level effect in $\ell\to\ell^\primeνν$ processes, while contributing to charged lepton flavour violating only at the loop-level. Therefore, it can provide a common explanation of the hints for n…
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.
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…
Many studies have been made on extensions of the standard model with $B-L$ gauge symmetry. The addition of three singlet (right-handed) neutrinos renders it anomaly-free. It has always been assumed that the spontaneous breaking of $B-L$ is accomplished by a singlet scalar field carrying two units of $B-L$ charge. This results in a very natural implementation of the Majorana seesaw mechanism for neutrinos. However, there exists in fact another simple anomaly-free solution which allows Dirac or inverse seesaw neutrino masses. We show for the first time these new possibilities and discuss an appl…
We compute the anomalous dimension of the third and fourth moments of the flavour non-singlet twist-2 Wilson and transversity operators at three loops in both the MSbar and RI' schemes. To assist with the extraction of estimates of matrix elements computed using lattice regularization, the finite parts of the Green's function where the operator is inserted in a quark 2-point function are also provided at three loops in both schemes.
We consider the generation of neutrino masses via a singly-charged scalar singlet. Under general assumptions we identify two distinct structures for the neutrino mass matrix. This yields a constraint for the antisymmetric Yukawa coupling of the singly-charged scalar singlet to two left-handed lepton doublets, irrespective of how the breaking of lepton-number conservation is achieved. The constraint disfavours large hierarchies among the Yukawa couplings. We study the implications for the phenomenology of lepton-flavour universality, measurements of the $W$-boson mass, flavour violation in the …
The loop corrections to the couplings of Higgs bosons to quarks and charged leptons are calculated within supersymmetric versions of the Standard Model, extended by a gauge singlet. The effective couplings of the $SU(2)_L$ doublet and singlet Higgs bosons to quarks and leptons, induced by sfermion loops, are derived. Analytic expressions for the case of generic sfermion flavour mixing, including the complete resummation of all chirally-enhanced contributions are presented. These results are important in scenarios in which the mixing between singlet and doublet components of Higgs bosons is sma…
QCD lattice simulations with 2+1 flavours (when two quark flavours are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. Here we discuss an alternative method of tuning the quark masses, in which the singlet quark mass is kept fixed. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavour symmetric line are found, first for the general 1+1+1 flavour case and then for the 2+1 flavour case. This ensures that the kao…
Lattice QCD allows a first-principles study of QCD with the freedom to vary the number and masses of the quarks. I present results on the flavour singlet correlations (this illuminates OZI violating effects) for mesons. Concentrating on the pseudoscalar mesons, the flavour singlet mass splitting ($η$, $η'$ mass splitting) appears naturally. I also present results on an investigation of decay constants for the $η$ and $η'$ ($f_η$) and discuss which quantities may be accessible in future lattice studies. The Witten-Veneziano approach can also be explored by determining the quenched topological s…
We study neutrino masses in the framework of the supersymmetric inverse seesaw model. Different from the non-supersymmetric version a minimal realization with just one pair of singlets is sufficient to explain all neutrino data. We compute the neutrino mass matrix up to 1-loop order and show how neutrino data can be described in terms of the model parameters. We then calculate rates for lepton flavour violating (LFV) processes, such as $μ\to e γ$, and chargino decays to singlet scalar neutrinos. The latter decays are potentially observable at the LHC and show a characteristic decay pattern dic…
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 $…
