Anomalous Operators Research Articles

Structure of holographic BCFT correlators from geodesics

We compute correlation functions, specifically 1-point and 2-point functions, in holographic boundary conformal field theory (BCFT) using geodesic approximation. The holographic model consists of a massive scalar field coupled to a Karch-Randall brane -- a rigid boundary in the bulk AdS space. Geodesic approximation requires the inclusion of paths reflecting off of this brane, which we show in detail. For the 1-point function, we find agreement between geodesic approximation and the harder $\Delta$-exact calculation, and we give a novel derivation of boundary entropy using the result. For the 2-point function, we find a factorization phase transition and a mysterious set of anomalous boundary-localized BCFT operators. We also discuss some puzzles concerning these operators.

Gauging anomalous unitary operators

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as $C$ and $\mathit{CP}$, for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.

2, 12, 117, 1959, 45171, 1170086, \u2026: a Hilbert series for the QCD chiral Lagrangian

We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the mathfrak{su}(n) Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order p8, as well as enumeration of CP-even, CP-odd, C-odd, and P-odd terms beginning from order p6. The method is extendable to very high orders, and we present results up to order p16.(The title sequence is the number of independent C-even and P-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions p2, p4, p6, …)

From the signature theorem to anomaly cancellation

We survey the Hirzebruch signature theorem as a special case of the Atiyah–Singer index theorem. The family version of the Atiyah–Singer index theorem in the form of the Riemann–Roch–Grothendieck–Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of elliptic curves. The RRGQ formula allows us to determine a generalized cohomology class on the base of the elliptic fibration that is known in physics as (a measure of) the local and global anomaly. Combining several anomalous operators allows us to cancel the local anomaly on a Jacobian elliptic surface, a construction that is based on the construction of the Poincaré line bundle over an elliptic surface.

Black holes, heavy states, phase shift and anomalous dimensions

We compute the phase shift of a highly energetic particle traveling in the background of an asymptotically AdS black hole. In the dual CFT, the phase shift is related to a four point function in the Regge limit. The black hole mass is translated to the ratio between the conformal dimension of a heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power measures the number of stress tensors appearing in the intermediate channel. We compute the leading term in the phase shift in a holographic CFT of arbitrary dimensionality using Conformal Regge Theory and observe complete agreement with the gravity result. In a two-dimensional CFT with a large central charge the heavy-heavy-light-light Virasoro vacuum block reproduces the gravity phase shift to all orders in the expansion parameter. We show that the leading order phase shift is related to the anomalous dimensions of certain double trace operators and verify this agreement using known results for the latter. We also perform a separate gravity calculation of these anomalous dimensions to second order in the expansion parameter and compare with the phase shift expansion.

Pinning down electroweak dipole operators of the top quark

We consider hadronic top quark pair production and pair production in association with a photon or a $Z$ boson to probe electroweak dipole couplings in $t\bar{b}W$, $t\bar{t}\gamma$ and $t\bar{t}Z$ interactions. We demonstrate how measurements of these processes at the 13 TeV LHC can be combined to disentangle and constrain anomalous dipole operators. The construction of cross section ratios allows us to significantly reduce various uncertainties and exploit orthogonal sensitivity between the $t\bar{t}\gamma$ and $t\bar{t}Z$ couplings. In addition, we show that angular correlations in $t\bar{t}$ production can be used to constrain the remaining $t\bar{b}W$ dipole operator. Our approach yields excellent sensitivity to the anomalous couplings and can be a further step towards precise and direct measurements of the top quark electroweak interactions.

Observation of top quark pairs produced in association with a vector boson in pp collisions at s = 8 $$ \sqrt{s}=8 $$ TeV

Measurements of the cross sections for top quark pairs produced in association with a W or Z boson are presented, using 8 TeV pp collision data corresponding to an integrated luminosity of 19.5 inverse femtobarns, collected by the CMS experiment at the LHC. Final states are selected in which the associated W boson decays to a charged lepton and a neutrino or the Z boson decays to two charged leptons. Signal events are identified by matching reconstructed objects in the detector to specific final state particles from ttW or ttZ decays. The ttW cross section is measured to be 382 +117 -102 fb with a significance of 4.8 standard deviations from the background-only hypothesis. The ttZ cross section is measured to be 242 +65 -55 fb with a significance of 6.4 standard deviations from the background-only hypothesis. These measurements are used to set bounds on five anomalous dimension-six operators that would affect the ttW and ttZ cross sections.

Front propagation in reaction-diffusion systems with anomalous diffusion

A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that combines fractional diffusion and regular diffusion. The reaction kinetics corresponds to a Fisher-Kolmogorov nonlinearity. The numerical method is based on a finite-difference operator splitting algorithm with an explicit Euler step for the time advance of the reaction kinetics, and a Crank-Nicholson semi-implicit time step for the transport operator. The anomalous diffusion operators are discretized using an upwind, flux-conserving, Grunwald-Letnikov finite-difference scheme applied to the regularized fractional derivatives. With fractional diffusion of order $\alpha$, fronts exhibit exponential acceleration, $a_L(t) \sim e^{\gamma t/\alpha}$, and develop algebraic decaying tails, $\phi \sim 1/x^{\alpha}$. In the case of tempered fractional diffusion, this phenomenology prevails in the intermediate asymptotic regime $\left(\chi t \right)^{1/\alpha} \ll x \ll 1/\lambda$, where $1/\lambda$ is the scale of the tempering. Outside this regime, i.e. for $x > 1/\lambda$, the tail exhibits the tempered decay $\phi \sim e^{-\lambda x}/x^{\alpha+1}$, and the front velocity approaches the terminal speed $v_*= \left(\gamma-\lambda^\alpha \chi\right)/ \lambda$. Of particular interest is the study of the interplay of regular and fractional diffusion. It is shown that the main role of regular diffusion is to delay the onset of front acceleration. In particular, the crossover time, $t_c$, to transition to the accelerated fractional regime exhibits a logarithmic scaling of the form $t_c \sim \log \left(\chi_d/\chi_f\right)$ where $\chi_d$ and $\chi_f$ are the regular and fractional diffusivities.

Constraints on anomalous color dipole operators from Higgs boson production at the LHC

Physics beyond the standard model (SM) can be parameterized with an effective Lagrangian that respects the symmetries of the standard model and contains many operators of dimension six. We consider the subset of these operators that is responsible for flavor diagonal anomalous color magnetic (CMDM) and electric (CEDM) dipole couplings between quarks and gluons. Invariance of these operators under the SM implies that they contribute to Higgs boson production at the LHC and we study the corresponding constraints that can be placed on them. For the case of the top-quark we first review constraints from top-quark pair production and decay, and then compare them to what can be achieved by studying $t\bar{t}h$ production. We also constrain the corresponding couplings for $b$-quarks and light quarks by studying $pp \to b\bar{b}h$ and $pp \to hX$ respectively.

A new twist on top quark spin correlations

Top-antitop pairs produced at hadron colliders are largely unpolarized, but their spins are highly correlated. The structure of these correlations varies significantly over top production phase space, allowing very detailed tests of the Standard Model. Here, we explore top quark spin correlation measurement from a general perspective, highlighting the role of azimuthal decay angles. By taking differences and sums of these angles about the top-antitop production axis, the presence of spin correlations can be seen as sinusoidal modulations resulting from the interference of different helicity channels. At the LHC, these modulations exhibit nontrivial evolution from near-threshold production into the boosted regime, where they become sensitive to almost the entire QCD correlation effect for centrally produced tops. We demonstrate that this form of spin correlation measurement is very robust under full kinematic reconstruction, and should already be observable with high significance using the current LHC data set. We also illustrate some novel ways that new physics can alter the azimuthal distributions. In particular, we estimate the power of our proposed measurements in probing for anomalous color-dipole operators, as well as for broad resonances with parity-violating couplings. Using these methods, the 2012 run of the LHC may be capable of setting simultaneous limits on the top quark’s anomalous chromomagnetic and chromoelectric dipole moments at the level of 3 × 10−18 cm (0.03/m t ).

Unique continuation property for the anomalous diffusion and its application

The unique continuation for anomalous diffusion operators with fractional time derivative of order 1/2 is proved by deriving Carleman estimates for the operators. By applying operators which have a negative sign in front of the diffusion terms of anomalous diffusion operators, the anomalous diffusion operators are transformed to parabolic operators of order 4 in the space variables. The Carleman estimates are derived for these transformed operators considered as semi-elliptic operators. The usual Calderón uniqueness argument for semi-elliptic operators does not work due to the singularities in factors of the factorization of their principal parts. In order to have smooth factorizations of the operators, we took into account the lower order terms of the operators.

Constraints on the anomalous tensor operators fromB→ phiK*, ηK* and ηKdecays

We investigate whether the anomalous tensor operators with the Lorentz structure $\sigma_{\mu\nu} (1+\gamma_{5})\otimes \sigma^{\mu\nu}(1+\gamma_{5})$, which could provide a simple resolution to the polarization anomaly observed in $B\to \phi K^{\ast}$ decays, could also provide a coherent resolution to the large ${\cal B}(B\to \eta K^{\ast})$ and survive bounds from $B\to\eta K$ decays. Parameter spaces satisfying all these experimental data are obtained, and found to be dominated by the color-octet tensor operator contribution. Constraints for the equivalent solution with $(1+\gamma_{5})\otimes(1+\gamma_{5})$ operators are also derived and found to be dominated by the color-singlet one. With the constrained parameter spaces, we finally give predictions for $B_{s}\to \phi \phi$ decay, which could be tested at the Fermilab Tevatron and the LHC-b experiments.

New Higgs couplings ate+e−and hadronic colliders

We examine the potentiality of both CERN LEP and Fermilab Tevatron colliders to establish bounds on new couplings involving the bosonic sector of the standard model. We pay particular attention to the anomalous Higgs interactions with $\gamma$, $W^{\pm}$ and $Z^0$. A combined exclusion plot for the coefficients of different anomalous operators is presented. The sensitivity that can be achieved at the Next Linear Collider and at the upgraded Tevatron is briefly discussed.

Probing anomalous top quark interactions at the Fermilab Tevatron collider

We study the effects of dimension-six operators contributing to the $\mathrm{gt}\overline{t}$ vertex in top quark pair production at the Fermilab Tevatron collider. We derive both the limits from run 1 data and the potential bounds from future runs (runs 2 and 3). Although the current constraints are not very strong, the future runs are quite effective in probing these operators. We investigate the possibility of disentangling different operators with the $t\overline{t}$ invariant mass distribution and the top quark polarization asymmetry. We also study the effects of a different set of operators contributing to single top quark production via the $\mathrm{Wt}\overline{b}$ coupling. We derive the current and potential future bounds on these anomalous operators and find that the upgraded Fermilab Tevatron collider can improve the existing constraints from ${R}_{b}$ for one of the operators.

AnomalousW+W−tt¯couplings at thee+e−linear collider

We study production of t{bar t} via W{sup +}W{sup {minus}} fusion, including the initial state radiation background at the proposed Linear Collider (an e{sup +}e{sup {minus}} collider with {radical} (S) =1.5 TeV) in the context of a standard model (SM) without a Higgs boson, i.e., a nonlinear SU(2){sub L}{times}U(1){sub Y} chiral Lagrangian, including dimension five W{sup +}W{sup {minus}}t{bar t}interactions. Deviation from the SM total cross section can be used to constrain the coefficients of these operators to an order of 0.2 (divided by the cutoff scale {Lambda}=3.1 TeV) with a 95{percent} C.L. However, there are three ways in which this sensitivity can be improved by a factor of two. First, by studying the deviation of the t{bar t} kinematics from what is predicted by the SM; second, by polarizing the collider electron beam; and third, by studying the polarization of the produced top quarks. In this way, we show that it is also possible to attempt to disentangle the contributions from different anomalous operators, isolating the form of new physics contributions. {copyright} {ital 1998} {ital The American Physical Society}

Probing anomalous Wtb coupling via single top production at TeV energy γe colliders

Results of complete tree level calculations of the single top production reaction γe → vīb at the Next Linear Collider, including the contribution of anomalous operators to the Wtb coupling are presented. The sensitivity for probing the structure of the Wtb coupling in a model independent way is analyzed and found to be significantly higher than for comparable measurements at the Tevatron.

Top quark interactions and the search for new physics

We give a complete set of 19 independent effective dimension 5 interactions involving the top and bottom quarks with the electroweak gauge bosons within the context of the chiral Lagrangian. The anomalous operators contribute to the leading energy power E^3 of the V_L V_L -> t\bar t or t\bar b amplitudes. We also show the top quark production rates at the LHC and the LC via V_L V_L fusion processes. If no anomalous production rate is found, then these coefficients can be bound (based on the naive dimensional analysis) to be of order 10^{-2} or 10^{-1}. This is about an order of magnitude more stringent than the bounds for the next-to-leading order bosonic operators commonly studied in V_L V_L -> V_L V_L scatterings. The effect on a CP-odd observable is also briefly discussed.

The nucleon anomalous magnetic moment and meson exchange current operators

Abstract The anomalous magnetic moment term in the nucleon electromagnetic current operator leads to an important correction to the pion and ϱ -meson exchange current operators. The additional term is essential for quantitative predictions of the backward deuteron electrodisintegration cross section and the magnetic form factors of the trinucleons.

Massless limits, anomalous dimensions from the renormalization group, and the Callan-Symanzik equations forgφ4+fφ6theory

The renormalization-group and Callan-Symanzik equations for gphi/sup 4/ + fphi/sup 6/ theory are obtained by using the technique of differential vertex operations in a normal-product algorithm. The Lagrangian constructed by the addition of all possible counterterms obtained from power-counting arguments contains two over-subtracted terms, in contrast to the usual Lagrangians containing only mass-type over-subtractions. The solutions of partial-differential equations are discussed in detail, which contain as a particular case the saddle-point solution implying the nonexistence of an anomalous dimension, while the usual fixed-point solution mimics the situation of the coupling-constant-dependent engineering dimension of fields. The massless limits are also considered, which involve the strong-coupling limit (g ..-->.. infinity) of the theory not encountered in other scalar field theories. By some means or other one can ascertain the m ..-->.. 0 limit of GAMMA/sup N/(x/sub 1/,x/sub 2/,x/sub 3/,...,x/sub n/); yet the massless limits of GAMMA (N/sub 1/(phi/sup 2/),x/sub 1/,...,x/sub n/) and GAMMA (N/sub 2/(phi/sup 4/),x/sub 1/,...,x/sub n/) require higher-order partial-differential equations. This peculiarity regarding the anomalous dimension and composite operators all seems to stem from the masslike dimension of g. In this connection the functional forms of the group equations are also derived, which are nothing but the generalizations of themore » equations obtained by Migdal.« less

On anomalous conversion coefficients of dipole transitions

General aspects of the problem of anomalous nuclear-structure-dependent contributions to the internal-conversion process are considered in conjunction with highly retarded electric or magnetic dipole transitions. Formulas for an elementary theory of anomalous internal conversion for E1 transitions are given. Selection rules for the relevant nuclear matrix elements are given in the quantu, numbers appropriate to spheroidally deformed nuclei (K, N, n z, Λ, ⩞) . Similar selection rules for M1 transtions are given on the basis of the anomalous operators previously derived by Church and Weneser. The experimental data on dipole conversion coefficients of retarded transitions for odd-mass spheroidal nuclei are surveyed. It is noted that where retardation is ascribable to K-forbiddenness (up to retardation from the single-proton rate by a factor of 10 9) no detectable anomalies are found, but where transitions are allowed by K-selection rules detectable conversion-coefficient anomalies may generally be found at retardations greater than 10 5 to 10 6 and are not found at lesser retardation. There are some exceptions to this general rule, though. From the present meager data the utility of selection rules in the asymptotic quantum numbers, N, n z , Λ and Σ, for anomalous -conversion matrix elements may be open to question, although their utility in qualitatively explaining retardation of the radiative transitions is very evident. The simple E1 theory is applied in an attempt to explain quantitatively the very anomalous 85-keV transition in Pa 231. Values of the two parameters in the simple theoretical expressions can be found to explain all three L-subshell conversion coefficients. The magnitude of one parameter, the nuclear matrix element 〈 r 3 Y 1〉, is consistent with estimates from the single-particle model. However, the magnitude required of the other parameter is such as to suggest that in the intranuclear process terms of higher order in the electromagnetic field than treated here may be of importance.