Renormalization Scale Dependence Research Articles

QCD corrections at subleading power for inclusive nonleptonic b→cu¯d decays

In this paper we compute the next-to-leading order (NLO) QCD corrections for the inclusive nonleptonic decay rates of B hadrons at subleading power of the heavy quark expansion. In particular, we discuss the coefficient of the chromomagnetic moment parameter μG, which has a large uncertainty at leading order due to its dependence on the renormalization scale. We find that the renormalization-scale dependence of this coefficient is significantly reduced, thereby reducing the theoretical uncertainty of the coefficient and, consequently, the rates. The sign of the coefficient becomes stable, and we estimate that the NLO corrections will increase the decay rates by around 2%. Published by the American Physical Society 2024

First-order electroweak phase transition at finite density

We study the Electroweak phase transition with the Standard Model effective field theory at finite temperature and finite density. Utilizing the dimensional reduction approach, we construct the tree dimensional thermal effective field theory at finite density and investigate the phase transition dynamics. We evaluate how the results depend on the renormalization scale and the chemical potential. Our results show that, with the tree dimensional thermal effective potential at 2-loop level, we can effectively reduce the theoretical uncertainty in the calculations of the phase transition parameters due to the renormalization scale dependence, and the new physics scale is restricted to be Λ ≲ (770 − 800) GeV by the baryon number washout avoidance condition. Meanwhile, the presence of the chemical potential would affect the phase transition parameter and make the constraints from the baryon number washout avoidance condition more strict, especially for weaker first-order phase transition scenarios at higher new physics scales.

Reanalysis of the top-quark pair production via the e+e− annihilation near the threshold region up to N3LO QCD corrections

In this paper, we present an improved analysis of the top-quark pair production via the process e+e−→γ⁎→tt¯ near the threshold region up to next-to-next-to-next-to-leading order (N3LO) QCD corrections. Near the threshold region, the top-quark velocity v tends to zero, leading to Coulomb singularity. To achieve a reasonable prediction in the threshold region, we reconstruct the analytical expression for the Coulomb-terms up to N3LO accuracy by using the PSLQ algorithm, whose numerical values agree well with the previous N3LO-level calculations. It is found that the N3LO series still has sizable renormalization scale dependence, and to improve the precision of the series, we apply the Principle of Maximum Conformality to eliminate such scale dependence. After that, the Coulomb part is resummed into a Sommerfeld-Gamow-Sakharov factor, which finally leads to a much more reasonable behavior near the threshold region.

Renormalization group improvement for thermally resummed effective potential

We propose a novel method for renormalization group improvement of thermally resummed effective potential. In our method, β-functions are temperature dependent as a consequence of the divergence structure in resummed perturbation theory. In contrast to the ordinary MS¯ scheme, the renormalization group invariance of the resummed finite-temperature effective potential holds order by order, which significantly mitigates a notorious renormalization scale dependence of phase transition quantities such as a critical temperature even at the one-loop order. We also devise a tractable method that enables one to incorporate temperature-dependent higher-order corrections by fully exploiting the renormalization group invariance. Published by the American Physical Society 2024

Precise determination of the top-quark on-shell mass via its scale- invariant perturbative relation to the top-quark mass * *Supported in part by the National Natural Science Foundation of China (12247129, 12175025, 12347101) and the Graduate Research and Innovation Foundation of Chongqing, China (ydstd1912)

The principle of maximum conformality (PMC) provides a systematic approach to solve the conventional renormalization scheme and scale ambiguities. Scale-fixed predictions of physical observables using the PMC are independent of the choice of renormalization scheme – a key requirement for renormalization group invariance. In this paper, we derive new degeneracy relations based on the renormalization group equations that involve both the usual β-function and the quark mass anomalous dimension -function. These new degeneracy relations enable improved PMC scale-setting procedures for correct magnitudes of the strong coupling constant and -running quark mass to be determined simultaneously. By using these improved PMC scale-setting procedures, the renormalization scale dependence of the -on-shell quark mass relation can be eliminated systematically. Consequently, the top-quark on-shell (or ) mass can be determined without conventional renormalization scale ambiguity. Taking the top-quark mass GeV as the input, we obtain GeV. Here, the uncertainties arise from errors combined with those from and the approximate uncertainty resulting from the uncalculated five-loop terms predicted through the Padé approximation approach.

Perturbative effective field theory expansions for cosmological phase transitions

Guided by previous non-perturbative lattice simulations of a two-step electroweak phase transition, we reformulate the perturbative analysis of equilibrium thermodynamics for generic cosmological phase transitions in terms of effective field theory (EFT) expansions. Based on thermal scale hierarchies, we argue that the scale of many interesting phase transitions is in-between the soft and ultrasoft energy scales, which have been the focus of studies utilising high-temperature dimensional reduction. The corresponding EFT expansions provide a handle to control the perturbative expansion, and allow us to avoid spurious infrared divergences, imaginary parts, gauge dependence and renormalisation scale dependence that have plagued previous studies. As a direct application, we present a novel approach to two-step electroweak phase transitions, by constructing separate effective descriptions for two consecutive transitions. Our approach provides simple expressions for effective potentials separately in different phases, a numerically inexpensive method to determine thermodynamics, and significantly improves agreement with the non-perturbative lattice simulations.

Scale dependence of non-factorizable virtual corrections to Higgs boson production in weak boson fusion

The renormalization-scale dependence of the non-factorizable virtual corrections to Higgs boson production in weak boson fusion at next-to-next-to-leading order in perturbative QCD is unusually strong, due to the peculiar nature of these corrections. To address this problem, we compute the three-loop non-factorizable contribution to this process which accounts for the running of the strong coupling constant, and show that it stabilizes the theoretical prediction.

Stop comparing resummation methods

I argue that the consistency of any resummation method can be established if the method follows a power counting derived from a hierarchy of scales. I.e. whether it encodes a top-down effective field theory. This resolves much confusion over which resummation method to use once an approximation scheme is settled on. And if no hierarchy of scales exists, you should be wary about resumming. I give evidence from the study of phase transitions in thermal field theory, where adopting a consistent power-counting scheme and performing a strict perturbative expansion dissolves many common problems of such studies: gauge dependence, strong renormalization scale dependence, the Goldstone boson catastrophe, IR divergences, imaginary potentials, mirages (illusory barriers), perturbative breakdown, and linear terms.

Formula omitted] corrections to J/ψ + χc0,1,2 production at B factories

We compute the O(αs2) corrections to the exclusive channels e+e−→J/ψ+χcJ (J=0,1,2) at s=10.58 GeV within the nonrelativistic QCD (NRQCD) factorization framework. The validity of NRQCD factorization at O(αs2) has been confirmed for these double-charmonium exclusive production processes. We analyze the impact of the O(αs2) corrections on the polarized and unpolarized cross sections, as well as the J/ψ angular distributions, which largely reduce the renormalization scale dependence but increase the O(αs) NRQCD predictions to some extent for χc0,1. With high numerical accuracy, our predictions for σ(J/ψ+χc1,2) through O(αs2) are compatible with the upper limit of the Belle measurement. Although the theoretical prediction for σ(J/ψ+χc0) is consistent with both Belle and BaBar measurements within uncertainties, there still exists serious tension between the predicted and the measured profiles for the J/ψ angular distribution. Regarding the bright observation prospect of the e+e−→J/ψ+χc1,2 channels in Belle 2 experiment, it is interesting to compare the future measurements with our NRQCD predictions. The more accurate measurement of e+e−→J/ψ+χ0 at Belle 2 will also help to clarify the long-standing puzzle of J/ψ angular distribution.

An off-shell Wilson loop

It is well-known that on-shell maximally helicity-violating gluon scattering amplitudes in planar maximally supersymmetric Yang-Mills theory are dual to a bosonic Wilson loop on a null-polygonal contour. The light-like nature of the intervals is a reflection of the mass-shell condition for massless gluons involved in scattering. Presently, we introduce a Wilson loop prototype on a piece-wise curvilinear contour that can be interpreted in the T-dual language to correspond to nonvanishing gluon off-shellness. We analyze it first for four sites at one loop and demonstrate that it coincides with the four-gluon amplitude on the Coulomb branch. Encouraged by this fact, we move on to the two-loop order. To simplify our considerations, we only focus on the Sudakov asymptotics of the Wilson loop, when the off-shellness goes to zero. The latter serves as a regulator of short-distance divergences around the perimeter of the loop, i.e., divergences when gluons are integrated over a small vicinity of the Wilson loop cusps. It does not however regulate conventional ultraviolet divergences of interior closed loops. This unavoidably introduces a renormalization scale dependence and thus scheme dependence into the problem. With a choice of the scale setting and a finite renormalization, we observe exponentiation of the double logarithmic scaling of the Wilson loop with the accompanying exponent being given by the so-called hexagon anomalous dimension, which recently made its debut in the origin limit of six-leg gluon amplitudes. This is contrary to the expectation for the octagon anomalous dimension to rather emerge from our analysis suggesting that the current object encodes physics different from the Coulomb branch scattering amplitudes.

How arbitrary are perturbative calculations of the electroweak phase transition?

We investigate the extent to which perturbative calculations of the electroweak phase transition are arbitrary and uncertain, owing to their gauge, renormalisation scale and scheme dependence, as well as treatments of the Goldstone catastrophe and daisy diagrams. Using the complete parameter space of the Standard Model extended by a real scalar singlet with a ℤ2 symmetry as a test, we explore the properties of the electroweak phase transition in general Rξ and covariant gauges, OS and overline{textrm{MS}} renormalisation schemes, and for common treatments of the Goldstone catastrophe and daisy diagrams. Reassuringly, we find that different renormalisation schemes and different treatments of the Goldstone catastrophe and daisy diagrams typically lead to only modest changes in predictions for the critical temperature and strength of the phase transition. On the other hand, the gauge and renormalisation scale dependence may be significant, and often impact the existence of the phase transition altogether.

Higher-Order QCD Corrections to ϒ Decay into Double Charmonia

In this Letter, we study the exclusive decay of ϒ into J/ψ in association with η_{c} (χ_{c0,1,2}). The decay widths for different helicity configurations are evaluated up to QCD next-to-leading order within the nonrelativistic QCD framework. We find that the QCD corrections notably mitigate the renormalization scale dependence of the decay widths for all the processes. The branching fraction of ϒ→J/ψ+χ_{c1} is obtained as 3.73_{-2.06-1.19}^{+5.10+0.10}×10^{-6}, which agrees well with the Belle measurement, i.e., Br(ϒ→J/ψ+χ_{c1})=(3.90±1.21±0.23)×10^{-6}. For the other processes, our results of the branching fractions are compatible with the upper limits given by the Belle experiments, except for ϒ(2S)→J/ψ+χ_{c1}, where some tension exists between theory and experiment. Having the polarized decay widths, we study the J/ψ polarization, which turns out to be independent of any nonperturbative parameters. Further, according to our calculation, it is promising to measure all the processes at Super B factory thanks to the high luminosity.

Decay of the charged Higgs boson and the top quark in two-Higgs-doublet model at NNLO in QCD

We present numerical calculations of the partial width of the charged Higgs boson decay into a top quark, H− → overline{t} + b + X, and the partial width of the top quark decay into a light charged Higgs boson t → H+ + b + X at next-to-next-to-leading order (NNLO) in QCD, based on a factorization formula of the jet mass. The NNLO corrections significantly reduce the renormalization scale dependence of the partial decay width in both cases. We show relative size of the NNLO corrections for different charged Higgs boson masses and for different renormalization scales. The NNLO corrections are about 16% (1%) of the leading order widths for the charged Higgs boson mass of 200 GeV (2000 GeV), while it is quite small for the top quark decay. Our analyses are independent of the detailed structure of the Yukawa couplings, and can be applied to various new physics models, as demonstrated by the decay branching ratio in different types of the two-Higgs-doublet models.

Achieving Effective Renormalization Scale and Scheme Independence via the Principle of Observable Effective Matching

In this work, we explicate a new approach for eliminating renormalization scale and scheme (RSS) dependence in observables. We develop this approach by matching RSS-dependent observables (such as cross-sections and decay rates) to a theory which is independent of both these forms of dependencies. We term the fundamental basis behind this approach as the principle of observable effective matching (POEM), which entails matching of a scale- and scheme-dependent observable with the fully physical scale (PS) and dynamical scale-dependent theory at loop orders at which RSS independence is guaranteed. This is aimed toward achieving so-called “effective” RSS-independent expressions as the resulting dynamical dependence is derived from a particular order in RSS-dependent perturbation theory. With this matching at a PS at which the coupling (and masses) is experimentally determined at this scale, we obtain an “effective theoretical observable (ETO)”, a finite-order RSS-independent version of the RSS-dependent observable. We illustrate our approach with a study of the cross-section ratio Re+e− for e+e− → hadrons, which is demonstrated to achieve scale and scheme independence utilizing the three- and four-loop order MS̄ scheme expression in QCD perturbation theory via matching at both one-loop and two-loop orders for obtaining the ETO. With two-loop matching, we obtain an ETO prediction of 311Re+e−eff=1.052431−0.0006+0.0006 at Q = 31.6GeV, which is in excellent agreement with the experimental value of 311Re+e−exp=1.0527−0.005+0.005. Given its new conceptual basis, ease of use, and performance, we contend that POEM be explored in its application for obtaining ETOs for predicting RSS-independent observables across domains of high-energy theory and phenomenology as well as other areas of fundamental and applied physics, such as cosmology and statistical and condensed matter physics.

The complete singlet contribution to the massless quark form factor at three loops in QCD

It is well known that the effect of top quark loop corrections in the axial part of quark form factors (FF) does not decouple in the large top mass or low energy limit due to the presence of the axial-anomaly type diagrams. The top-loop induced singlet-type contribution should be included in addition to the purely massless result for quark FFs when applied to physics in the low energy region, both for the non-decoupling mass logarithms and for an appropriate renormalization scale dependence. In this work, we have numerically computed the so-called singlet contribution to quark FFs with the exact top quark mass dependence over the full kinematic range. We discuss in detail the renormalization formulae of the individual subsets of the singlet contribution to an axial quark FF with a particular flavor, as well as the renormalization group equations that govern their individual scale dependence. Finally we have extracted the 3-loop Wilson coefficient in the low energy effective Lagrangian, renormalized in a mathrm{non}hbox{-} overline{mathrm{MS}} scheme and constructed to encode the leading large mass approximation of our exact results for singlet quark FFs. We have also examined the accuracy of the approximation in the low energy region.

Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium

Within the framework of nonrelativistic QCD (NRQCD) factorization, we calculate the next-to-leading-order (NLO) perturbative corrections to the radiative decay Υ → ηc(χcJ) + γ. Both the helicity amplitudes and the helicity decay widths are obtained. It is the first computation for the processes involving both bottomonium and charmonium at two-loop accuracy. By employing the Cheng-Wu theorem, we are able to convert most of complex-valued master integrals (MIs) into real-valued MIs, which makes the numerical integration much efficient. Our results indicate the mathcal{O}left({alpha}_sright) corrections are moderate for ηc and χc2 production, and are quite marginal for χc0 and χc1 production. It is impressive to note the NLO corrections considerably reduce the renormalization scale dependence in both the decay widths and the branching fractions for χcJ, and slightly improve that for ηc. With the NRQCD matrix elements evaluated via the Buchmüller-Tye potential model, we find the decay width for ηc production is one-order-of-magnitude larger than χcJ production, which may provide a good opportunity to search for Υ → ηc + γ in experiment. In addition, the decay width for χc1 production is several times larger than those for χc0,2. Finally, we find the NLO NRQCD prediction for the branching fraction of Υ → χc1 + γ is only half of the lower bound of the experimental data measured recently by Belle. Moreover, there exists serious contradiction between theory and experiment for Υ → ηc + γ. The discrepancies between theory and experiment deserve further research efforts.

Renormalization group optimized λϕ4 pressure at next-to-next-to-leading order

We investigate the renormalization group optimized perturbation theory (RGOPT) at the next-to-next-to-leading order (NNLO) for the thermal scalar field theory. From comparing three thus available successive RGOPT orders, we illustrate the efficient resummation and very good apparent convergence properties of the method. In particular, the remnant renormalization scale dependence of thermodynamical quantities is drastically improved as compared to both standard perturbative expansions and other related resummation methods, such as the screened perturbation theory. Our present results thus constitute a useful first NNLO illustration in view of NNLO applications of this approach to the more involved thermal QCD.

Soft Interactions in Cold Quark Matter.

Accurate knowledge of the thermodynamic properties of zero-temperature, high-density quark matter plays an integral role in attempts to constrain the behavior of the dense QCD matter found inside neutron-star cores, irrespective of the phase realized inside the stars. In this Letter, we consider the weak-coupling expansion of the dense QCD equation of state and compute the next-to-next-to-next-to-leading-order contribution arising from the non-Abelian interactions among long-wavelength, dynamically screened gluonic fields. Accounting for these interactions requires an all-loop resummation, which can be performed using hard-thermal-loop (HTL) kinematic approximations. Concretely, we perform a full two-loop computation using the HTL effective theory, valid for the long-wavelength, or soft, modes. We find that the soft sector is well behaved within cold quark matter, contrary to the case encountered at high temperatures, and find that the new contribution decreases the renormalization-scale dependence of the equation of state at high density.

Two-loop mathcal{O} ((\u03b1t + \u03b1\u03bb + \u03b1\u03ba)2) corrections to the Higgs boson masses in the CP-violating NMSSM

We present our computation of the mathcal{O} ((αt + αλ + ακ)2) two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum. We choose a mixed overline{mathrm{DR}} -on-shell (OS) renormalisation scheme for the Higgs sector and apply both overline{mathrm{DR}} and OS renormalisation in the top/stop sector. For the treatment of the infrared divergences we apply and compare three different regularisation methods: the introduction of a regulator mass, the application of a small momentum expansion, and the inclusion of the full momentum dependence. Our new corrections have been implemented in the Fortran code NMSSMCALC that computes the Higgs mass spectrum of the CP-conserving and CP-violating NMSSM as well as the Higgs boson decays including the state-of-the-art higher-order corrections. Our numerical analysis shows that the newly computed corrections increase with rising λ and κ, remaining overall below about 3% compared to our previously computed mathcal{O} (αt(αt + αs)) corrections, in the region compatible with perturbativity below the GUT scale. The renormalisation scheme and scale dependence is of typical two-loop order. The impact of the CP-violating phases in the new corrections is small. We furthermore show that the Goldstone Boson Catastrophe due to the infrared divergences can be treated in a numerically efficient way by introducing a regulator mass that approximates the momentum-dependent results best for squared mass values in the permille range of the squared renormalisation scale. Our results mark another step forward in the program of increasing the precision in the NMSSM Higgs boson observables.

Renormalization group improved pressure for hot and dense quark matter

We apply the renormalization group optimized perturbation theory (RGOPT) to evaluate the quark contribution to the QCD pressure at finite temperatures and baryonic densities, at next-to-leading order (NLO). Our results are compared to NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a nonperturbative approximation, exhibiting a drastically better remnant renormalization scale dependence than pQCD, thanks to built-in renormalization group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed quark contributions the purely perturbative NLO glue contribution, our results show a remarkable agreement with ab initio lattice simulation data for temperatures $0.25 \lesssim T \lesssim 1 \, {\rm GeV}$, with a remnant scale dependence drastically reduced as compared to HTLpt.