Renormalization Scheme Research Articles

One-loop corrections to the two-body decays of the charged Higgs bosons in the real and complex NMSSM

We evaluate the full next-to-leading order supersymmetric (SUSY) electroweak and SUSY-QCD corrections to the on-shell two-body decays of the charged Higgs bosons in the framework of the next-to-minimal supersymmetric extension of the Standard Model (NMSSM) allowing also for CP violation. We furthermore provide the possibility to choose between different renormalization schemes in the electroweakino and the squark and slepton sectors. Our corrections are implemented in the code NMSSMCALCEW and thus complete the one-loop corrections of the charged Higgs boson decays which so far only included the state-of-the-art QCD corrections and the resummed SUSY-electroweak and SUSY-QCD corrections. We investigate the impact of the NLO corrections including the newly computed higher-order corrections for each decay mode in a wide range of the parameter space that is allowed by the theoretical and experimental constraints as well as the effect of CP violation and the dependence on the choice of the renormalization scheme. The new version of NMSSMCALCEW is made publicly available.

Gauge-invariant renormalization of the gluino-glue operator

We study the Gluino-Glue operator in the context of Supersymmetric N=1 Yang-Mills (SYM) theory. This composite operator is gauge invariant, and it is directly connected to light bound states of the theory; its renormalization is very important as a necessary step for the study of low-lying bound states via numerical simulations. We make use of a Gauge-Invariant Renormalization Scheme (GIRS). This requires the calculation of the Green's function of a product of two Gluino-Glue operators, situated at distinct space-time points. Within this scheme, the mixing with non-gauge invariant operators which have the same quantum numbers is inconsequential. We compute the one-loop conversion factor relating the GIRS scheme to MS‾. This conversion factor can be used in order to convert to MS‾ Green's functions which are obtained via lattice simulations and are renormalized nonperturbatively in GIRS.

Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit Δ degrees of freedom

We compute various nucleon polarizabilities in chiral perturbation theory implementing the $\Delta$-full ($\Delta$-less) approach up to order $\epsilon^3 + q^4$ ($q^4$) in the small-scale (chiral) expansion. The calculation is carried out using the covariant formulation of $\chi$PT by utilizing the extended on-mass shell renormalization scheme. Except for the spin-independent dipole polarizabilities used to fix the values of certain low-energy constants, our results for the nucleon polarizabilities are pure predictions. We compare our calculations with available experimental data and other theoretical results. The importance of the explicit treatment of the $\Delta$ degree of freedom in the effective field theory description of the nucleon polarizabilities is analyzed. We also study the convergence of the $1/m$ expansion and analyze the efficiency of the heavy-baryon approach for the nucleon polarizabilities.

Finite Z-Less Integral Expressions for β-Functions in the MS4 Scheme

The generalized minimal subtraction scheme for ultraviolet renormalization (Kuznetsov and Tkachov, 1988) is fine-tuned with applications in mind. The resulting $\text{MS}^4$ scheme obviates extraneous regularizations and renders momentum integrands integrable by subtracting troublesome asymptotic terms in a physically correct fashion due to the use of special minimal subtraction operators defined congruously with the physically natural Polchinski cutoffs. A direct derivation of the Callan-Symanzik equations avoids divergent renormalization factors or counterterms, and automatically yields explicit exact finite integral expressions for renormalization group functions.

Mixed EW-QCD leading fermionic three-loop corrections at mathcal{O} (\u03b1s\u03b12) to electroweak precision observables

Measurements of electroweak precision observables at future electron-position colliders, such as the CEPC, FCC-ee, and ILC, will be sensitive to physics at multi-TeV scales. To achieve this sensitivity, precise predictions for the Standard Model expectations of these observables are needed, including corrections at the three- and four-loop level. In this article, results are presented for the calculation of a subset of three-loop mixed electroweak-QCD corrections, stemming from diagrams with a gluon exchange and two closed fermion loops. The numerical impact of these corrections is illustrated for a number of applications: the prediction of the W-boson mass from the Fermi constant, the effective weak mixing angle, and the partial and total widths of the Z boson. Two alternative renormalization schemes for the top-quark mass are considered, on-shell and overline{mathrm{MS}} .

Galilean-invariant effective field theory for the X(3872) at next-to-leading order

XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the $X(3872)$ resonance. To simplify calculations beyond leading order, we introduce a new formulation of XEFT with a dynamical field for a pair of charm mesons in the resonant channel. We simplify the renormalization of XEFT by introducing a new renormalization scheme that involves the subtraction of amplitudes at the complex $D^{*0} \bar D^0$ threshold. The new formulation and the new renormalization scheme are illustrated by calculating the complex pole energy of $X$ and the $D^{*0} \bar D^0$ scattering amplitude to next-to-leading order using Galilean-invariant XEFT.

Self-dualities and renormalization dependence of the phase diagram in 3d O(N) vector models

In the classically unbroken phase, 3d O(N) symmetric ϕ4 vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by κ) and for any N. It is shown that for κ = κ∗ the two fixed points merge and then, for κ < κ∗, they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the N = 1 ϕ4 theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d O(N) models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-product of our analysis, we show how the non-perturbative mass gap at large N in 2d can be seen as the analytic continuation of the perturbative one in the classically unbroken phase.

Diphoton decay of the higgs from the Epstein\u2013Glaser viewpoint

We revisit a nearly 10-year old controversy on the diphoton decay of the Higgs particle. To a large extent, the controversy turned around the respective merits of the regularization techniques employed. The novel aspect of our approach is that no regularization techniques are brought to bear: we work within the Bogoliubov–Epstein–Glaser scheme of renormalization by extension of distributions. Solving the problem actually required an expansion of this method’s toolkit, furnished in the paper.

Optimal corrector estimates on percolation cluster

We prove optimal quantitative estimates on the first-order correctors on supercritical percolation clusters: we show that they are bounded in dimension larger than 3 and have logarithmic growth in dimension 2 in the sense of stretched exponential moments. The main ingredients are a renormalization scheme of the supercritical percolation cluster, following the works of Pisztora (Probab. Theory Related Fields 104 (1996) 427–466); large-scale regularity estimates developed by Armstrong and the author in (Comm. Pure Appl. Math. 71 (2018) 1717–1849); and a nonlinear concentration inequality of the Efron–Stein type which is used to transfer quantitative information from the environment to the correctors.

Renormalization mass scale and scheme dependence in the perturbative contribution to inclusive semi-leptonic b decays

We examine the perturbative calculation of the inclusive semi-leptonic decay rate Γ for the b quark, using mass-independent renormalization. To finite order of perturbation theory the series for Γ will depend on the unphysical renormalization scale parameter μ and on the particular choice of mass-independent renormalization scheme; these dependencies will only be removed after summing the series to all orders. In this paper we show that all explicit μ-dependence of Γ, through powers of ln(μ), can be summed by using the renormalization group equation. We then find that this explicit μ-dependence can be combined together with the implicit μ-dependence of Γ (through powers of both the running coupling a(μ) and the running b quark mass m(μ)) to yield a μ-independent perturbative expansion for γ in terms of a(μ) and m(μ) both evaluated at a renormalization scheme independent mass scale [Formula: see text] which is fixed in terms of either the “[Formula: see text] mass” [Formula: see text] of the b quark or its pole mass mpole. At finite order the resulting perturbative expansion retains a degree of arbitrariness associated with the particular choice of mass-independent renormalization scheme. We use the coefficients ci and gi of the perturbative expansions of the renormalization group functions β(a) and γ(a), associated with a(μ) and m(μ) respectively, to characterize the remaining renormalization scheme arbitrariness of Γ. We further show that all terms in the expansion of Γ can be written in terms of the ci and gi coefficients and a set of renormalization scheme independent parameters τi. A second set of renormalization scheme independent parameters σi is shown to play a very similar role in the perturbative expansion of mpole in terms of m(μ) and a(μ). We illustrate our approach by a perturbative computation of Γ using the [Formula: see text] renormalization scheme. Two other particular mass independent renormalization schemes are briefly considered.

A hybrid renormalization scheme for quasi light-front correlations in large-momentum effective theory

In large-momentum effective theory (LaMET), calculating parton physics starts from calculating coordinate-space-z correlation functions h˜(z,a,Pz) in a hadron of momentum Pz in lattice QCD. Such correlation functions involve both linear and logarithmic divergences in lattice spacing a, and thus need to be properly renormalized. We introduce a hybrid renormalization procedure to match these lattice correlations to those in the continuum MS‾ scheme, without introducing extra non-perturbative effects at large z. We analyze the effect of O(ΛQCD) ambiguity in the Wilson line self-energy subtraction involved in this hybrid scheme. To obtain the momentum-space distributions, we recommend to extrapolate the lattice data to the asymptotic z-region using the generic properties of the coordinate space correlations at moderate and large Pz, respectively.

PQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables?

We investigate a large class of perturbative QCD (pQCD) renormalization schemes whose beta functions β(a) are meromorphic functions of the running coupling and give finite positive value of the coupling a(Q 2) in the infrared regime (‘freezing’), a(Q 2) → a 0 for Q 2 → 0. Such couplings automatically have no singularities on the positive axis of the squared momenta Q 2 ( ≡ − q 2). Explicit integration of the renormalization group equation (RGE) leads to the implicit (inverted) solution for the coupling, of the form . An analysis of this solution leads us to an algebraic algorithm for the search of the Landau singularities of a(Q 2) on the first Riemann sheet of the complex Q 2-plane, i.e., poles and branching points (with cuts) outside the negative semiaxis. We present specific representative examples of the use of such algorithm, and compare the found Landau singularities with those seen after the 2-dimensional numerical integration of the RGE in the entire first Riemann sheet, where the latter approach is numerically demanding and may not always be precise. The specific examples suggest that the presented algebraic approach is useful to find out whether the running pQCD coupling has Landau singularities and, if yes, where precisely these singularities are.

Strong CP violation in spin-1/2 singly charmed baryons

We report on the calculation of the CP-violating form factor F3 and the corresponding electric dipole moment for charmed baryons in the spin-1/2 sector generated by the QCD θ-term. We work in the framework of covariant baryon chiral perturbation theory within the extended-on-mass-shell renormalization scheme up to next-to-leading order in the chiral expansion.

Scale-fixed predictions for \u03b3 + \u03b7c production in electron-positron collisions at NNLO in perturbative QCD

In the paper, we present QCD predictions for γ + ηc production at an electron-positron collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for e+ + e− → γ + ηc using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the e+e− center-of-mass collision energy sqrt{s} . The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal β contributions into the QCD coupling αs(Q2). The renormalization group equation then sets the value of αs for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a renormalization scale-and-scheme independent prediction, σ|NNLO,PMC ≃ 41.18 fb for sqrt{s} =10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large K factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the Padé approximation approach, we predict σ|NNNLO,PMC+Pade ≃ 18.99 fb, which is consistent with the recent BELLE measurement {sigma}^{mathrm{obs}}={16.58}_{-9.93}^{+10.51} fb at sqrt{s} ≃ 10.6 GeV. This procedure also provides a first estimate of the NNNLO contribution.

Nonminimal gradient flows in QCD-like theories

The Yang-Mills gradient flow for QCD-like theories is generalized by including a fermionic matter term in the gauge field flow equation. We combine this with two different flow equations for the fermionic degrees of freedom. The solutions for the different gradient flow setups are used in the perturbative computations of the vacuum expectation value of the Yang-Mills Lagrangian density and the field renormalization factor of the evolved fermions up to next-to-leading order in the coupling. We find a one-parameter family of flow systems for which there exists a renormalization scheme in which the evolved fermion anomalous dimension vanishes to all orders in perturbation theory. The fermion number dependence of different flows is studied and applications to lattice studies are anticipated.

The symmetry group of Feynman diagrams and consistency of the BPHZ renormalization scheme * *Supported by the National Natural Science Foundation of China (11805152, 10575080, 11947301), the Natural Science Basic Research Program of Shaanxi Province (2019JQ-107), and Shaanxi Key Laboratory for Theoretical Physics Frontiers in China

We study the relation between the symmetry group of a Feynman diagram and its reduced diagrams. We then prove that the counterterms in the BPHZ renormalization scheme are consistent with adding counterterms to the interaction Hamiltonian in all cases, including that of Feynman diagrams with symmetry factors.

Hyperasymptotic approximation to the plaquette and determination of the gluon condensate

We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. Subleading effects are also considered. The perturbative series is regulated using the principal value prescription for its Borel integral. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: {leftlangle {G}^2rightrangle}_{mathrm{PV}}left({n}_f=0right)=3.15(18){r}_0^{-4} .

Renormalized entanglement entropy and curvature invariants

Renormalized entanglement entropy can be defined using the replica trick for any choice of renormalization scheme; renormalized entanglement entropy in holographic settings is expressed in terms of renormalized areas of extremal surfaces. In this paper we show how holographic renormalized entanglement entropy can be expressed in terms of the Euler invariant of the surface and renormalized curvature invariants. For a spherical entangling region in an odd-dimensional CFT, the renormalized entanglement entropy is proportional to the Euler invariant of the holographic entangling surface, with the coefficient of proportionality capturing the (renormalized) F quantity. Variations of the entanglement entropy can be expressed elegantly in terms of renormalized curvature invariants, facilitating general proofs of the first law of entanglement.

One-loop RG improvement of the screened massive expansion in the Landau gauge

The RG improvement of the screened massive expansion is studied at one loop in two renormalization schemes, the momentum subtraction (MOM) scheme and the screened momentum subtraction (SMOM) scheme. The respective Taylor-scheme running couplings are shown not to develop a Landau pole, provided that the initial value of the coupling is sufficiently small. The improved ghost and gluon propagators are found to behave as expected, displaying dynamical mass generation for the gluons and the standard UV limit of ordinary perturbation theory. In the MOM scheme, when optimized by a matching with the fixed-coupling framework, the approach proves to be a powerful method for obtaining propagators which are in excellent agreement with the lattice data already at one loop. After optimization, the gluon mass parameter is left as the only free parameter of the theory and is shown to play the same role of the ordinary perturbative QCD scale $\Lambda_{\text{QCD}}$.

Emergence of N-Body Tunable Interactions in Universal Few-Atom Systems

A three-atom molecule AAB, formed by two identical bosons A and a distinct one B, is studied by considering coupled channels close to a Feshbach resonance. It is assumed that the subsystems AB and AA have, respectively, one and two channels, where, in this case, AA has open and closed channels separated by an energy gap. The induced three-body interaction appearing in the single channel description is derived using the Feshbach projection operators for the open and closed channels. An effective three-body interaction is revealed in the limit where the trap setup is tuned to vanishing scattering lengths . The corresponding homogeneous coupled Faddeev integral equations are derived in the unitarity limit. The s-wave transition matrix for the AA subsystem is obtained with a zero-range potential by a subtractive renormalization scheme with the introduction of two finite parameters, besides the energy gap. The effect of the coupling between the channels in the coupled equations is identified with the energy gap, which essentially provides an ultraviolet scale that competes with the van der Waals radius - this sets the short-range physics of the system in the open channel. The competition occurring at short distances exemplifies the violation of the ``van der Waals universality" for narrow Feshbach resonances in cold atomic setups. In this sense, the active role of the energy gap drives the short-range three-body physics.