Anomaly Term Research Articles

Quark and Glue Components of the Proton Spin from Lattice Calculation

The status of lattice calculations of the quark spin, the quark orbital angular momentum, the glue angular momentum and glue spin in the nucleon is summarized. The quark spin calculation is recently carried out from the anomalous Ward identity with chiral fermions and is found to be small mainly due to the large negative anomaly term which is believed to be the source of the ‘proton spin crisis’. We also present the first calculation of the glue spin at finite nucleon momenta.

Scalar Hint from the Diboson Excess?

In view of the recent diboson resonant excesses reported by both ATLAS and CMS Collaborations, we suggest that a new weak singlet pseudoscalar particle η(WZ) may decay into two weak bosons while being produced in gluon fusion at the LHC. The couplings to the gauge bosons can arise from a Wess-Zumino-Witten anomaly term and thus we study an effective model based on the anomaly term as a well motivated phenomenological model. In models where the pseudoscalar particle arises as a composite state, the coefficients of the anomalous couplings can be related to the fermion components of the underlying dynamics. We provide an example to test the feasibility of the idea.

Basis invariant description of chemical equilibrium with implications for a recent axionic leptogenesis model

We provide a systematic treatment of chemical equilibrium in the presence of a specific type of time dependent background. The type of time dependent background we consider appears, for example, in recently proposed axion/Majoron leptogenesis models [1,2]. In describing the chemical equilibrium we use quantities which are invariant under redefinition of fermion phases (we refer to this redefinition as a change of basis for short), and therefore it is a basis invariant treatment. The change of the anomaly terms due to the change of the path integral measure [3,4] under a basis change is taken into account. We find it is useful to go back and forth between different bases, and there are insights which can be more easily obtained in one basis rather than another. A toy model is provided to illustrate the ideas. For the axion leptogenesis model [1], our result suggests that at $T > 10^{13}$ GeV , when sphaleron processes decouple, and $\Gamma_{B+L} << H < \Gamma_L$ (where $H$ is the Hubble parameter at temperature $T$ and $\Gamma_L$ is the $\Delta L = 2$ lepton number violating interaction rate), the amount of $B-L$ created is controlled by the smallness of the sphaleron interaction rate, $\Gamma_{B+L}$. Therefore it is not as efficient as described. In addition, we notice an interesting modification of gauge boson dispersion relations at subleading order.

Low-energy photon production in neutrino neutral-current interactions

The search for $\nu_\mu \to \nu_e$ oscillations by the MiniBooNE Collaboration at Fermilab has revealed a low-energy signal which could be due either to electrons produced by $\nu_e$ or photons produced by the interaction of the weak neutral current on the target nucleus. One contribution to the latter is a Wess-Zumino-Witten anomaly leading to a term in the Lagrangian proportional to $\epsilon^{\mu \nu \kappa \lambda} Z_\mu \omega_\nu F_{\kappa \lambda}$. This term is normalized with the help of the known rates for the processes $f_1 \to \rho \gamma$ and $\tau \to \nu_\tau a_1$. A rate of about 1/4 of that employed in several previous estimates is obtained. As the anomaly term had already been found to play a subdominant role in photon production (e.g., in comparison with $\Delta$ excitation and decay), the present estimate reduces its strength even further.

The dilaton Wess–Zumino action in six dimensions from Weyl gauging: local anomalies and trace relations

We extend a previous analysis on the derivation of the dilaton Wess–Zumino (WZ) action in d = 4, based on the method of Weyl gauging, to six dimensions. As in the previous case, we discuss the structure of the same action in dimensional regularization using six-dimensional Weyl invariants, extracting the dilaton interactions in the most general scheme, with the inclusion of the local anomaly terms. As an application, we present the WZ action for the (2,0) tensor multiplet, which has been investigated in the past in the context of the AdS7/CFT6 holographic anomaly matching. We then extend to d = 6 the investigation of fully traced correlation functions of energy–momentum tensor’s, formerly presented in d = 4, showing that their hierarchy is functionally related only to the first six correlators. We give the explicit expressions of these in the most general scheme, up to rank-4.

Domain walls and vortices in chiral symmetry breaking

We study domain walls and vortices in chiral symmetry breaking in a QCD-like theory with N flavors in the chiral limit. If the axial anomaly is absent, there exist stable Abelian axial vortices winding around the spontaneously broken U(1)_A symmetry and non-Abelian axial vortices winding around both the U(1)_A and non-Abelian SU(N) chiral symmetries. In the presence of the axial anomaly term, metastable domain walls are present and Abelian axial vortices must be attached by N domain walls, forming domain wall junctions. We show that a domain wall junction decays into N non-Abelian vortices attached by domain walls, implying its metastability. We also show that domain walls decay through the quantum tunneling by creating a hole bounded by a closed non-Abelian vortex.

QED effective action for an O(2)×O(3) symmetric field in the full mass range

An interesting class of background field configurations in QED are the O(2)×O(3) symmetric fields. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial but amenable to numerical calculation, for both scalar and spinor QED. Here we use the recently developed "partial-wave-cutoff method" for a numerical analysis of both effective actions in the full mass range. In particular, at large mass we are able to match the asymptotic behavior of the physically renormalized effective action against the leading two mass levels of the inverse mass (or heat kernel) expansion. At small mass we obtain good numerical results even in the massless case for the appropriately (unphysically) renormalized effective action after the removal of the chiral anomaly term through a small radial cutoff factor. In particular, we show that the effective action after this removal remains finite in the massless limit, which also provides indirect support for M. Fry's hypothesis that the QED effective action in this limit is dominated by the chiral anomaly term.

Full mass range analysis of the QED effective action for anO(2)×O(3)symmetric field

An interesting class of background field configurations in quantum electrodynamics (QED) are the O(2)xO(3) symmetric fields, originally introduced by S.L. Adler in 1972. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial, but amenable to numerical calculation. Here, we use the recently developed "partial-wave-cutoff method" for a full mass range numerical analysis of the effective action for the "standard" O(2)xO(3) symmetric field, modified by a radial suppression factor. At large mass, we are able to match the asymptotics of the physically renormalized effective action against the leading two mass levels of the inverse mass expansion. For small masses, with a suitable choice of the renormalization scheme we obtain stable numerical results even in the massless limit. We analyze the N - point functions in this background and show that, even in the absence of the radial suppression factor, the two-point contribution to the effective action is the only obstacle to taking its massless limit. The standard O(2)xO(3) background leads to a chiral anomaly term in the effective action, and both our perturbative and nonperturbative results strongly suggest that the small-mass asymptotic behavior of the effective action is, after the subtraction of the two-point contribution, dominated by this anomaly term as the only source of a logarithmic mass dependence. This confirms a conjecture by M. Fry.

CHIRAL ANOMALY OF MASSLESS FERMION AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL

In this paper, using the imaginary-time temperature field theory, we discuss the possible modification of chiral anomaly of a massless fermion in (3+1)-dimensional QED (QED4) when the temperature and chemical potential effects are included. It is found that the chiral anomaly is independent of the temperature and chemical potential. Meanwhile, we also introduce the chemical potential corresponding to chiral charge, and find that it will induce a Chern–Simons-like term, which has similar C transformation properties (and opposite P transformation property) to the corresponding Chern–Simons term in (2+1)-dimensional QED (QED3). More importantly, we find that when the chemical potential corresponding to the fermion number is space-dependent, it will induce an extra anomaly term. It is expected that this can yield new physical effects.

Meson Vacuum Phenomenology in a Three-flavor Linear Sigma Model with (Axial-)Vector Mesons: Investigation of the U$(1)_A$ Anomaly Term

Zero temperature properties of an (axial-) vector meson extended linear sigma model are discussed, concerning on the possible different realizations of the axial anomaly term. The different anomaly terms are compared with each other on the basis of a chi^2 minimalization process. It is found that there is no essential difference among the different realizations. This means that any of them can be equally used from phenomenological point of view.

Batalin-Vilkovisky Formalism in Perturbative Algebraic Quantum Field Theory

On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum field theory. The crucial technical ingredient is a proof that the renormalized time-ordered product is equivalent to the pointwise product of classical field theory. The renormalized Batalin-Vilkovisky algebra is then the classical algebra but written in terms of the time-ordered product, together with an operator which replaces the ill defined graded Laplacian of the unrenormalized theory. We identify it with the anomaly term of the anomalous Master Ward Identity of Brennecke and D\"utsch. Contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps.

On renormalization group flows and the a-theorem in 6d

We study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p^6 in the low energy limit of n-point scattering amplitudes of the dilaton for n > 3. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p^6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4. Given the confirmation in two distinct models, we attempt to use dispersion relations to prove that the anomaly flow is positive in general. Unfortunately the 4-point matrix element of the Euler anomaly is proportional to stu and vanishes for forward scattering. Thus the optical theorem cannot be applied to show positivity. Instead the anomaly flow is given by a dispersion sum rule in which the integrand does not have definite sign. It may be possible to base a proof of the a-theorem on the analyticity and unitarity properties of the 6-point function, but our preliminary study reveals some difficulties.

Axial Anomaly, Mismatched Fermi Surfaces and Vector Interaction in Dense Neutral Quark Matter

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 $\beta$-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 crossover region in the low-$T$ area including zero temperature with a new critical point, as was first demonstrated by Kitazawa et al and the present authors without and with the charge-neutral condition, respectively. We remark that the possible chromomagnetic instability is suppressed and can be even completely absent owing to the enhanced diquark coupling due to the anomaly term and/or by the vector interaction.

Killing spinors for the bosonic string and Kaluza–Klein theory with scalar potentials

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza–Klein theory can be gauged so that the Killing spinors are charged under the Kaluza–Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories.

DeWitt-Virasoro Construction in Tensor Representations

We generalize the DeWitt-Virasoro (DWV) construction of arXiv:0912.3987 [hep-th] to tensor representations of higher ranks. A rank-ntensor state, which is by itself coordinate invariant, is expanded in terms of position eigenstates that transform as tensors of the same rank. The representation of the momentum operator in these basis states is then obtained by generalizing DeWitt's argument (1952). Such a representation is written in terms of certain bivector of parallel displacement and its covariant derivatives. With this machinery at hand we find tensor representations of the DWV generators defined in the previous work. The results differ from those in spin-zero representation by additional terms involving the spin connection. However, we show that the DWV algebra found earlier as a scalar expectation value remains the same, as required by consistency, as all the additional contributions conspire to cancel in various ways. In particular, vanishing of the anomaly term requires the same condition of Ricci-flatness for the background.

Effect of r averaging on chiral anomaly in lattice QCD with Wilson fermion: finite volume and cutoff effects

We demonstrate the effectiveness of averaging over the Wilson parameter r (which has been proposed earlier) in removing the cutoff effects of naive Wilson fermions in both the anomaly term and the pseudoscalar density term in the flavor singlet axial Ward identity at O(g^2) involving slowly varying background gauge fields. We show that it is the physical fermion contribution which is largely influenced by the r averaging. We have studied the possible interplay between finite size and cutoff effects by investigating in detail naive, O(a) improved and OStm Wilson fermion cases for a range of volumes and lattice fermion mass (am). For naive Wilson fermions r averaging is shown to remove the effects of the interplay. We have shown that for the pseudoscalar density term to O (g^2) the lattice result differs from the continuum result by exhibiting considerable am dependence which appears to be a manifestation of cutoff effects with naive Wilson fermion. The pseudoscalar density term to O(g^2) is shown to be almost independent of am when r-averaging is performed.

Roles of axial anomaly on neutral quark matter with color superconducting phase

We investigate the effects of the axial-anomaly term with a chiral-diquark coupling on the phase diagram within a two-plus-one-flavor Nambu-Jona-Lasinio model under the charge-neutrality and $\ensuremath{\beta}$-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) are never realized without these constraints even within the same model Lagrangian. This drastic change is attributed to an enhanced interplay between the chiral and diquark condensates due to the anomaly term at finite temperature; the $u\mathrm{\text{\ensuremath{-}}}d$ diquark coupling is strengthened by the relatively large chiral condensate of the strange quark through the anomaly term, which in turn definitely leads to the abnormal behavior of the diquark condensate at finite $T$, inherent to the asymmetric quark matter. We note that the critical point from which the crossover region extends to zero temperature appears only when the strength of the vector interaction is larger than a critical value. We also show that the chromomagnetic instability of the neutral asymmetric homogenous two-flavor color-superconducting phase is suppressed and can be even completely cured by the enhanced diquark coupling due to the anomaly term and/or by the vector interaction.

Discrimination of low missing energy look-alikes at the LHC

The problem of discriminating possible scenarios of TeV scale new physics with large missing energy signature at the Large Hadron Collider (LHC) has received some attention in the recent past. We consider the complementary, and yet unexplored, case of theories predicting much softer missing energy spectra. As there is enough scope for such models to fake each other by having similar final states at the LHC, we have outlined a systematic method based on a combination of different kinematic features which can be used to distinguish among different possibilities. These features often trace back to the underlying mass spectrum and the spins of the new particles present in these models. As examples of "low missing energy look-alikes", we consider Supersymmetry with R-parity violation, Universal Extra Dimensions with both KK-parity conserved and KK-parity violated and the Littlest Higgs model with T-parity violated by the Wess-Zumino-Witten anomaly term. Through detailed Monte Carlo analysis of the four and higher lepton final states predicted by these models, we show that the models in their minimal forms may be distinguished at the LHC, while non-minimal variations can always leave scope for further confusion. We find that, for strongly interacting new particle mass-scale ~600 GeV (1 TeV), the simplest versions of the different theories can be discriminated at the LHC running at sqrt{s}=14 TeV within an integrated luminosity of 5 (30) fb^{-1}.

Black holes in gravity with conformal anomaly and logarithmic term in black hole entropy

We present a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly. The solutions have two branches, one is asymptotically flat and the other asymptotically de Sitter. We study thermodynamic properties of the black hole solutions and find that there exists a logarithmic correction to the well-known Bekenstein-Hawking area entropy. The logarithmic term might come from non-local terms in the effective action of gravity theories. The appearance of the logarithmic term in the gravity side is quite important in the sense that with this term one is able to compare black hole entropy up to the subleading order, in the gravity side and in the microscopic statistical interpretation side.

Orbital Oscillator Commutation Relations and Mass Shifting for Superstring

In this work we extend the results obtained in [5] on mass shifting for bosonic string to the case of superstring. The modified anomaly terms of superstring superalgebras are shown and the corresponding BRST charge is used.