Renormalization Scheme Research Articles

Higgs boson pair production at NLO in the Powheg approach and the top quark mass uncertainties

We present a new Monte Carlo code for Higgs boson pair production at next-to-leading order in the Powheg-Box Monte Carlo framework. The code is based on analytic results for the two loop virtual corrections which include the full top quark mass dependence. This feature allows to freely assign the value of all input parameters, including the trilinear Higgs boson self coupling, as well as to vary the renormalization scheme employed for the top quark mass. We study the uncertainties due to the top-mass renormalization scheme allowing the trilinear Higgs boson self coupling to vary around its Standard Model value including parton shower effects. Results are presented for both inclusive and differential observables.

Quantum loop effects on the power spectrum and constraints on primordial black holes

We present a detailed exposition on the prospects of the formation of Primordial Black Holes (PBHs) during Slow Roll (SR) to Ultra Slow Roll (USR) sharp transitions in the framework of single-field inflation. We use an effective field theory (EFT) approach in order to keep the analysis model-independent and applicable to both the canonical and non-canonical cases. We show in detail how renormalizing the power spectrum to one loop order in P(X,ϕ) theories severely limits the prospects for PBH formation in a single-field inflationary framework. We demonstrate that for the allowed range of effective sound speed, 1 < cs < 1.17, the consistency of one-loop corrected power spectrum leaves a small window for black hole masses, M PBH∼𝒪(102–103)gm to have sufficient e-foldings, Δ𝒩Total ∼ 𝒪(54–59) for inflation. We confirm that adding an SR regime after USR before the end of inflation does not significantly alter our conclusions. Our findings for sharp transition strictly rule out the possibility of generating large masses of PBHs from all possible models of single field inflation (canonical and non-canonical).Our results are at least valid for the situation where constraints from the loop effects are computed using either Late-Time (LT) or Adiabatic-Wave function(AF) scheme followed by Power Spectrum (PS) renormalization schemes.

Cosmic energy density: particles, fields and the vacuum

We revisit the cosmic evolution of the energy density of a quantized free scalar field and assess under what conditions the particle production and classical field approximations reproduce its correct value. Because the unrenormalized energy-momentum tensor diverges in the ultraviolet, it is necessary to frame our discussion within an appropriate regularization and renormalization scheme. Pauli-Villars avoids some of the drawbacks of adiabatic subtraction and dimensional regularization and is particularly convenient in this context. In some cases, we can predict the evolution of the energy density irrespectively of the quantum state of the field modes. To further illustrate our results we focus however on the in vacuum, the preferred quantum state singled out by inflation, and explore to what extent the latter determines the subsequent evolution of the energy density regardless of the unknown details of reheating. We contrast this discussion with examples of transitions to radiation domination that avoid some of the problems of the one commonly studied in the literature, and point out some instances in which the particle production or the classical field approximations lead to the incorrect energy density. Along the way, we also elaborate on the connection of our analysis to dynamical dark energy models and axion-like dark matter candidates.

Bayesian renormalization

In this note we present a fully information theoretic approach to renormalization inspired by Bayesian statistical inference, which we refer to as Bayesian renormalization. The main insight of Bayesian renormalization is that the Fisher metric defines a correlation length that plays the role of an emergent renormalization group (RG) scale quantifying the distinguishability between nearby points in the space of probability distributions. This RG scale can be interpreted as a proxy for the maximum number of unique observations that can be made about a given system during a statistical inference experiment. The role of the Bayesian renormalization scheme is subsequently to prepare an effective model for a given system up to a precision which is bounded by the aforementioned scale. In applications of Bayesian renormalization to physical systems, the emergent information theoretic scale is naturally identified with the maximum energy that can be probed by current experimental apparatus, and thus Bayesian renormalization coincides with ordinary renormalization. However, Bayesian renormalization is sufficiently general to apply even in circumstances in which an immediate physical scale is absent, and thus provides an ideal approach to renormalization in data science contexts. To this end, we provide insight into how the Bayesian renormalization scheme relates to existing methods for data compression and data generation such as the information bottleneck and the diffusion learning paradigm. We conclude by designing an explicit form of Bayesian renormalization inspired by Wilson’s momentum shell renormalization scheme in quantum field theory. We apply this Bayesian renormalization scheme to a simple neural network and verify the sense in which it organizes the parameters of the model according to a hierarchy of information theoretic importance.

Automated choice for the best renormalization scheme in BSM models

The explorations of models beyond the Standard Model (BSM) naturally involve scans over the unknown BSM parameters. On the other hand, high precision predictions require calculations at the loop-level and thus a renormalization of (some of) the BSM parameters. Often many choices are possible for the renormalization scheme (RS). This concerns the choice of the set of to-be-renormalized parameters out of a larger set of BSM parameters, but can also concern the type of renormalization condition which is chosen for a specific parameter. A given RS can be well suited to yield “stable” and “well behaved” higher-order corrections in one part of the BSM parameter space, but can fail completely in other parts, which may not even be noticed numerically if an isolated parameter point is investigated, or when the higher-order BSM calculations are performed in an automated, not supervised set-up. Consequently, the (automated) exploration of BSM models requires a choice of a good RS before the calculation is performed. We propose a new method with which such a choice can be performed. We demonstrate the feasibility of our new method in the chargino/neutralino sector of the Minimal Supersymmetric Standard Model (MSSM), but stress the general applicability of our method to all types of BSM models.

A variational approach to S1-harmonic maps and applications

We present a renormalization procedure for the Dirichlet Lagrangian for maps from surfaces with or without boundary into S1, whose finite energy critical points are the S1-harmonic maps with isolated singularities. We give some applications of this renormalization scheme in two different frameworks. The first application has to do with the renormalization of the Willmore energy for Lagrangian singular immersions into Kähler-Einstein surfaces while the second application is dealing with frame energies for surfaces immersions into Euclidian spaces.

Probing the weak mixing angle at high energies at the LHC and HL-LHC

Measurements of neutral current Drell-Yan production at large invariant dilepton masses can be used to test the energy scale dependence (running) of the electroweak mixing angle. In this work, we make use of a novel implementation of the full next-to-leading order electroweak radiative corrections to the Drell-Yan process using the MS‾ renormalization scheme for the electroweak mixing angle. The potential of future analyses using proton-proton collisions at s=13.6TeV in the Run 3 and High-Luminosity phases of the LHC is explored. In this way, the Standard Model predictions for the MS‾ running at TeV scales can be probed.

Theoretical concepts and measurement prospects for BSM trilinear couplings: a case study for scalar top quarks

After the possible discovery of new heavy particles at the LHC, it will be crucial to determine the properties and the underlying physics of the new states. In this work, we focus on scalar trilinear couplings, employing as an example the case of the trilinear coupling of scalar partners of the top quark to the Higgs boson. We discuss possible strategies for experimentally determining the scalar top (stop) trilinear coupling parameter, which controls the stop–stop–Higgs interaction, and we demonstrate the impact of different renormalisation prescriptions for this parameter. We find that the best prospects for determining the stop trilinear coupling arise from its quantum effects entering the model prediction for the mass of the SM-like Higgs boson in comparison to the measured value. We point out that the prediction for the Higgs-boson mass has a high sensitivity to the stop trilinear coupling even for heavy masses of the non-standard particles. Regarding the renormalisation of the stop trilinear coupling we identify a renormalisation scheme that is preferred in view of the present level of accuracy and we clarify the source of potentially large logarithms that cannot be resummed with standard renormalisation group methods.

Computer package DIZET v. 6.45

The new version of the DIZET electroweak library is described. Changes and additional code features concerning the previous version are explained. The software allows one to make state-of-the-art theoretical predictions for pseudo-observable quantities, including higher-order radiative corrections. The current version of the DIZET library v. 6.45 incorporates advanced recent results of theoretical calculations. Numerical comparisons with the results of the previous version are performed. Estimates of theoretical uncertainties are discussed. Program summaryProgram Title:DIZET version 6.45CPC Library link to program files:https://doi.org/10.17632/2fr58v92xc.1Code Ocean capsule:https://codeocean.com/capsule/0198682Licensing provisions: GPLv3Programming language: FORTRAN 77/90External routines: AlphaQED http://www-com.physik.hu-berlin.de/~fjeger/software.htmlJournal reference of previous version: Comput. Phys. Commun. 59 (1990) 303Does the new version supersede the previous version?: YesReasons for the new version: Implementation of new options.Summary of revisions: Implemented the complete electroweak two-loop radiative corrections to all the relevant electroweak precision pseudo-observables related to the Z-boson decay. Added support of new library for hadronic contribution to vacuum polarization.Nature of problem: The Z-resonance region is still extremely important for the experimental verification of the Standard Model. The anticipated experimental accuracy on a large variety of observables has to be matched with theory predictions of at least the same level of accuracy to achieve maximum usage of experimental data.Solution method: Theoretical calculations at NNLO in perturbation theory allow to compute higher precision pseudo-observables to verify the Standard Model at high luminosity future colliders. The package includes electroweak two-loop corrections calculated in the on-mass shell renormalization scheme. Pseudo-observables and electroweak form-factors can be calculated in a wide range of input parameters.Additional comments including restrictions and unusual features: The estimate of results at the off-resonance region should be treated with caution as two-loop electroweak corrections were calculated for the Z-resonance peak.

Next-to-leading-order QCD corrections to Higgs production in association with a jet

We compute the next-to-leading-order (NLO) QCD corrections to the Higgs pT distribution in Higgs production in association with a jet via gluon fusion at the LHC, with exact dependence on the mass of the quark circulating in the heavy-quark loops. The NLO corrections are presented including the top-quark mass, and for the first time, the bottom-quark mass as well. Further, besides the on-shell mass scheme, we consider for the first time a running mass renormalisation scheme. The computation is based on amplitudes which are valid for arbitrary heavy-quark masses.

Broken scale invariance and the regularization of a conformal sector in gravity with Wess-Zumino actions

We elaborate on anomaly induced actions of the Wess-Zumino (WZ) form and their relation to the renormalized effective action, which is defined by an ordinary path integral over a conformal sector, in an external gravitational background. In anomaly - induced actions, the issue of scale breaking is usually not addressed, since these actions are obtained only by solving the trace anomaly constraint and are determined by scale invariant functionals. We investigate the changes induced in the structure of such actions once identified in dimensional renormalization (DR) when the ϵ=d−4→0 limit is accompanied by the dimensional reduction (DRed) of the field dependencies. We show that operatorial nonlocal modifications (∼□ϵ) of the counterterms are unnecessary to justify a scale anomaly. In this case, only the ordinary finite subtractions play a critical role in the determination of the scale breaking. This is illustrated for the WZ form of the effective action and its WZ consistency condition, as seen from a renormalization procedure. Logarithmic corrections from finite subtractions are also illustrated in a pure d=4 (cutoff) scheme. The interplay between two renormalization schemes, one based on dimensional regularization (DR) and the second on a cutoff in d=4, illustrates the ambiguities of DR in handling the quantum corrections in a curved background. Therefore, using DR in a curved background, the scale and trace anomalies can both be obtained by counterterms that are Weyl invariant only at d=4.

Conformal renormalization of scalar-tensor theories

We study a conformally coupled scalar-tensor theory with a quartic potential possessing local conformal symmetry up to a boundary term. We show that requiring the restoration of the full local conformal symmetry fixes the counterterms that render the on-shell action finite. The building block of the resulting action is a conformally covariant tensor which is constructed out of the metric and the scalar field and it has the same conformal weight as the Weyl tensor. This allows us to obtain the counterterms for the scalar-tensor sector in a closed form. The finiteness of the conformally complete version of the action is suggestive on the validity of the conformal renormalization prescription. We extend this theory by adding the conformal gravity action and also the Einstein-AdS action written in MacDowell-Mansouri form. Even though the latter breaks the conformal symmetry, we find that the action is still renormalized provided a suitable falloff of the scalar field when considering asymptotically locally anti-de Sitter solutions. Black hole solutions in these theories are studied, for which the Hawking temperature and the partition function to first order in the saddle-point approximation are calculated, providing a concrete example of this renormalization scheme.

Elimination of QCD Renormalization Scale and Scheme Ambiguities

The setting of the renormalization scale (μr) in the perturbative QCD (pQCD) is one of the crucial problems for achieving precise fixed-order pQCD predictions. The conventional prescription is to take its value as the typical momentum transfer Q in a given process, and theoretical uncertainties are then evaluated by varying it over an arbitrary range. The conventional scale-setting procedure introduces arbitrary scheme-and-scale ambiguities in fixed-order pQCD predictions. The principle of maximum conformality (PMC) provides a systematic way to eliminate the renormalization scheme-and-scale ambiguities. The PMC method has rigorous theoretical foundations; it satisfies the renormalization group invariance (RGI) and all of the self-consistency conditions derived from the renormalization group. The PMC has now been successfully applied to many physical processes. In this paper, we summarize recent PMC applications, including event shape observables and heavy quark pair production near the threshold region in e+e− annihilation and top-quark decay at hadronic colliders. In addition, estimating the contributions related to the uncalculated higher-order terms is also summarized. These results show that the major theoretical uncertainties caused by different choices of μr are eliminated, and the improved pQCD predictions are thus obtained, demonstrating the generality and applicability of the PMC.

Dyson–Schwinger equations in minimal subtraction

We compare the solutions of one-scale Dyson–Schwinger equations (DSEs) in the minimal subtraction (MS) scheme to the solutions in kinematic momentum subtraction (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but with a shifted renormalization point, where the shift itself is a function of the coupling. We derive relations between this shift and various renormalization group functions and counterterms in perturbation theory. As concrete examples, we examine three different one-scale Dyson–Schwinger equations: one based on the 1-loop multiedge graph in D=4 dimensions, one for D=6 dimensions, and one for mathematical toy model. For each of the integral kernels, we examine both the linear and nine different non-linear Dyson–Schwinger equations. For the linear cases, we empirically find exact functional forms of the shift between MOM and MS renormalization points. For the non-linear DSEs, the results for the shift suggest a factorially divergent power series. We determine the leading asymptotic growth parameters and find them in agreement with the ones of the anomalous dimension. Finally, we present a tentative exact solution to one of the non-linear DSEs of the toy model.

Revisiting one-loop corrections to the trilinear Higgs boson self-coupling in the inert doublet model

We investigate predictions of the trilinear Higgs self-coupling with radiative corrections in the context of the Inert Doublet Model. The triple Higgs vertex is computed at the one-loop level based on the on-shell renormalization scheme. We calculate its possible deviation from the predictions within the standard model, taking into account all relevant theoretical and experimental constraints, including dark matter searches and the latest bounds on the branching fraction of the Higgs boson decaying to invisible particles. By scanning the model's parameter space, we find that the deviation in the triple Higgs boson self-coupling from standard model expectations can be substantial, exceeding 100% in certain regions of the parameter space.

Holographic imaginary potential of a quark antiquark pair in the presence of gluon condensation

For a moving heavy quark antiquark (QQ) in a quark gluon plasma (QGP), we use gauge/gravity duality to study both real and imaginary parts of the potential ( operatorname{Re}{V}_{Qoverline{Q}} and operatorname{Im}{V}_{Qoverline{Q}} respectively) in a gluon condensate (GC) theory. The complex potential is derived from the Wilson loop by considering the thermal fluctuations of the worldsheet of the Nambu-Goto holographic string. We calculate operatorname{Re}{V}_{Qoverline{Q}} and operatorname{Im}{V}_{Qoverline{Q}} in both cases where the axis of the moving Qoverline{Q} pair is transverse and parallel with respect to its direction of movement in the plasma. Using the renormalization scheme for the operatorname{Re}{V}_{Qoverline{Q}} , we find that the inclusion of GC increases the dissociation length while rapidity has the opposite effect. While for the operatorname{Im}{V}_{Qoverline{Q}} , we observe that by considering the effect of GC, the operatorname{Im}{V}_{Qoverline{Q}} is generated for larger distance thus decreasing quarkonium dissociation, while rapidity has opposite effect. In particular, as the value of GC decreases in the deconfined phase, the operatorname{Im}{V}_{Qoverline{Q}} is generated for smaller distance thus enhancing quarkonium dissociation, and at high temperatures it is nearly not modified by GC, consistent with previous findings of the entropic force.

Nonperturbative renormalization of the supercurrent in N=1 supersymmetric Yang-Mills theory

In this work, we study the nonperturbative renormalization of the supercurrent operator in $\mathcal{N}=1$ supersymmetric Yang-Mills theory, using a gauge-invariant renormalization scheme (GIRS). The proposed prescription addresses successfully the unwanted mixing of the supercurrent with other operators of equal or lower dimension, which respect the same global symmetries. This mixing is introduced by the unavoidable breaking of supersymmetry on the lattice. In GIRS all gauge-noninvariant operators, which mix with the supercurrent, are excluded from the renormalization procedure. The one remaining mixing operator is accessible by numerical simulations. We present results for the renormalization of the supercurrent using GIRS. We also compute at one-loop order the conversion matrix which relates the nonperturbative renormalization factors in GIRS to the reference scheme $\overline{\mathrm{MS}}$.

Precise perturbative predictions from fixed-order calculations

The intrinsic conformality (iCF) is a general property of the renormalizable gauge theory, which ensures the scale invariance of a fixed-order series at each perturbative order. Following the idea of iCF, we suggest a novel single-scale setting approach under the principle of maximum conformality (PMC) with the purpose of removing the conventional renormalization scheme and scale ambiguities. We call this newly suggested single-scale procedure the PMC∞-s approach, in which an overall effective α s , and hence an overall effective scale is achieved by identifying the {β 0} terms at each order. Its resultant conformal series is scale-invariant and satisfies all renormalization group requirements. The PMC∞-s approach is applicable to any perturbatively calculable observable, and its resultant perturbative series provides an accurate basis for estimating the contribution from the unknown higher-order (UHO) terms. Using the Higgs decay into two gluons up to five-loop quantum chromondynamics (QCD) corrections as an example, we show how the PMC∞-s works, and we obtain and . Here the errors are squared averages of those mentioned in the body of the text. The approximation approach (PAA) and the Bayesian approach (BA) have been adopted to estimate the contributions from the UHO terms. We also demonstrate that the PMC∞-s approach is equivalent to our previously suggested single-scale setting approach (PMCs), which also follows from the PMC but treats the {β i } terms from a different point of view. Thus, proper use of the renormalization group equation can provide a solid way to solve the scale-setting problem.

Evanescent operators in one-loop matching computations

Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces — the evanescent operators — can ultimately be removed with a suitable renormalization scheme, resulting in a finite shift of the physical operators. Modern Effective Field Theory matching techniques relying on the method of expansion by regions have to be extended to account for this. After illustrating the importance of these shifts in two specific examples, we compute the finite shifts required to remove all evanescent operators appearing in the one-loop matching of generic ultraviolet theories to the Standard Model Effective Field Theory and elucidate the formalism for generic Effective Field Theory calculations.

Standard model at 200 GeV

The Standard Model can be defined quantitatively by running parameters in a mass-independent renormalization scheme at a fixed reference scale. We provide a set of simple interpolation formulas that give the fundamental Lagrangian parameters in the $\overline{\mathrm{MS}}$ scheme at a renormalization scale of 200 GeV, safely above the top-quark mass and suitable for matching to candidate new physics models at very high mass scales using renormalization group equations. These interpolation formulas take as inputs the on-shell experimental quantities and use the best available calculations in the pure $\overline{\mathrm{MS}}$ scheme. They also serve as an accounting of the parametric uncertainties for the short-distance Standard Model Lagrangian. We also include an interpolating formula for the $W$-boson mass. This paper is based on results obtained with the publicly available computer program smdr.