PMC$_\infty$: Infinite-Order Scale-Setting using the Principle of Maximum Conformality, A Remarkably Efficient Method for Eliminating Renormalization Scale Ambiguities for Perturbative QCD
Leonardo Di Giustino, Stanley J. Brodsky, Sheng-Quan Wang, Xing-Gang Wu
We identify a property of renormalizable SU(N)/U(1) gauge theories, the intrinsic Conformality ($iCF$), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in pQCD: the PMC$_\infty$. This new method reflects the underlying conformal properties displayed by pQCD at NNLO, eliminates the scheme dependence of pQCD predictions and is consistent with the general properties of the PMC (Principle of Maximum Conformality). We introduce a new method to identify conformal and $β$-terms which can be applied either to numerical or to theoretical calculations. We illustrate the PMC$_\infty$ for the thrust and C-parameter distributions in $e^+ e^-$ annihilation and then we show how to apply this new method to general observables in QCD. We point out how the implementation of the PMC$_\infty$ can significantly improve the precision of pQCD predictions; its implementation in multi-loop analysis also simplifies the calculation of higher orders corrections in a general renormalizable gauge theory.
We show results for Thrust and C-parameter in $e^+ e^-$ annihilation to 3 jets obtained using the recently developed new method for eliminating the scale ambiguity and the scheme dependence in pQCD namely the Infinite-Order Scale-Setting method using the Principle of Maximum Conformality (PMC$_\infty$). This method preserves an important underlying property of gauge theories: intrinsic Conformality (iCF). It leads to a remarkably efficient method to eliminate the conventional renormalization scale ambiguity at any order in pQCD. A comparison with Conventional Scale Setting method (CSS) is also…
The {\it Principle of Maximum Conformality} (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs)…
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale $μ$ of the running coupling $α_s(μ^2).$ The purpose of the running coupling in any gauge theory is to sum all terms involving the $β$ function; in fact, when the renormalization scale is set properly, all non-conformal $β\ne 0$ terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with $β=0$. The result…
We present a detailed study on the properties of the free energy density at the high temperature by applying the principle of maximum conformality (PMC) scale-setting method within the effective field theory. The PMC utilizes the renormalization group equation recursively to identify the occurrence and pattern of the non-conformal $\{β_i\}$-terms, and determines the optimal renormalization scale at each order. Our analysis shows that a more accurate free energy density up to $g_s^5$-order level without renormalization scale dependence can be achieved by applying the PMC. We also observe that b…
The Principle of Maximum Conformality (PMC) provides scale-fixed perturbative QCD predictions which are independent of the choice of the renormalization scheme, as well as the choice of the initial renormalization scale. In this article, we will test the PMC by comparing its predictions for the strong coupling α^s_{g_1}(Q), defined from the Bjorken sum rule, with predictions using conventional pQCD scale-setting. The two results are found to be compatible with each other and with the available experimental data. However, the PMC provides a significantly more precise determination, although its…
In any calculation in perturbative Quantum Chromodynamics (QCD) a choice needs to be made for the unphysical renormalisation scale, $μ_R$. The Brodsky-Lepage-Mackenzie/Principle of Maximum Conformality (BLM/PMC) scale-setting procedure is one proposed method for selecting this scale. In this work we identify three ambiguities in the BLM/PMC procedure itself. Their numerical impact is studied using the example of the total cross-section for $t\bar{t}$ production through Next-to-Next-to-Leading Order in QCD. One ambiguity is the arbitrary choice of the value of the highest-order PMC scale. The n…
In the paper, we analyze the $η_c$ decays into light hadrons at the next-to-leading order QCD corrections by applying the principle of maximum conformality (PMC). The relativistic correction at the ${\cal{O}}(α_s v^2)$-order level has been included in the discussion, which gives about $10\%$ contribution to the ratio $R$. The PMC, which satisfies the renormalization group invariance, is designed to obtain a scale-fixed and scheme-independent prediction at any fixed order. To avoid the confusion of treating $n_f$-terms, we transform the usual $\overline{\rm MS}$ pQCD series into the one under t…
The next-to-next-to-leading order (NNLO) pQCD prediction for the $γγ^* \to η_c$ form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BaBar measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BaBar measurements within errors, and the…
We make a detailed study on the properties of the total decay width of Higgs decay channel $H\to gg$ up to $α_s^6$-order QCD corrections by using the newly suggested infinite-order scale-setting approach, which is based on the ideas of both the principle of maximum conformality and the intrinsic conformality. This approach is called as the PMC$_\infty$ approach. By using the PMC$_\infty$ approach, we observe that the conventional renormalization scale ambiguity in perturbative QCD calculation is eliminated and the residual scale dependence due to unknown higher-order terms can also be highly s…
The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium $η_Q$ ($Q$ being $c$ or $b$) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the NNLO decay width still has large conventional renormalization scale dependence due to its weaker pQCD convergence, e.g. about $(^{+4\%}_{-34\%})$ for $η_c$ and $(^{+0.0}_{-9\%})$ for $η_b$, by varying the scale within the range of $[m_Q, 4m_Q]$. The principle of maximum conformality (PMC) provides a systematic way to fix the $α_s$-running behavior of the process…
We present a comprehensive and self-consistent analysis for the thrust distribution by using the Principle of Maximum Conformality (PMC). By absorbing all nonconformal terms into the running coupling using PMC via renormalization group equation, the scale in the running coupling shows the correct physical behavior and the correct number of active flavors is determined. The resulting PMC predictions agree with the precise measurements for both the thrust differential distributions and the thrust mean values. Moreover, we provide a new remarkable way to determine the running of the coupling cons…
In the paper, we study the properties of the $Z$-boson hadronic decay width by using the $\mathcal{O}(α_s^4)$-order quantum chromodynamics (QCD) corrections with the help of the principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent perturbative QCD (pQCD) correction for the $Z$-boson hadronic decay width, which is independent to any choice of renormalization scale. After applying the PMC, a more convergent pQCD series has been obtained; and the contributions from the unknown $\mathcal{O}(α_s^5)$-order…
Under the conventional scale setting, the renormalization scale uncertainty usually constitutes a systematic error for a fixed-order perturbative QCD estimation. The recently suggested principle of maximum conformality (PMC) provides a principle to eliminate such scale ambiguity in a step-by-step way. Using the PMC, all non-conformal terms in perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. In the paper, we make a detailed PMC analysis for both the polarized and the unpolarized cross se…
The renormalization scale uncertainty can be eliminated by the Principle of Maximum Conformality (PMC) in a systematic scheme-independent way. Applying the PMC for the $t\bar{t}$-pair hadroproduction at the NNLO level, we have found that the total cross-sections $σ_{t\bar{t}}$ at both the Tevatron and LHC remain almost unchanged when taking very disparate initial scales $μ^{\rm init}_R$ equal to $m_t$, $10\,m_t$, $20\,m_t$ and $\sqrt{s}$, which is consistent with renormalization group invariance. As an important new application, we apply PMC scale-setting to study the top-quark forward-backwar…
It is conventional to choose a typical momentum transfer of the process as the renormalization scale and take an arbitrary range to estimate the uncertainty in the QCD prediction. However, predictions using this procedure depend on the renormalization scheme, leave a non-convergent renormalon perturbative series, and moreover, one obtains incorrect results when applied to QED processes. In contrast, if one fixes the renormalization scale using the Principle of Maximum Conformality (PMC), all non-conformal $\{β_i\}$-terms in the perturbative expansion series are summed into the running coupling…
The Principle of Maximum Conformality (PMC) provides a systematic and process-independent method to derive renormalization scheme- and scale- independent fixed-order pQCD predictions. In Ref.\cite{pmc3}, we studied the top-quark charge asymmetry at the Tevatron. By applying the PMC, we have shown that the large discrepancies for the top-quark charge asymmetry between the Standard Model estimate and the CDF and D0 data are greatly reduced. In the present paper, with the help of the Bernreuther-Si program, we present a detailed PMC analysis on the top-quark pair production up to next-to-next-to-…
In the paper, we study the $Υ(1S)$ leptonic decay width $Γ(Υ(1S)\to \ell^+\ell^-)$ by using the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct momentum flow of the process, whose value is independent to the choice of the renormalization scale and its prediction thus avoids the conventional renormalization scale ambiguities. Using the known next-to-next-to-next-to-leading order perturbative series together with the PMC single scale-setting approach, we do obtain a renormalization scale independent decay width,…
The principle of maximum conformality (PMC) provides a way to eliminate the conventional renormalization scale ambiguity in a systematic way. By applying the PMC scale setting, all non-conformal terms in perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed prediction at any finite order. In the paper, we make a detailed PMC analysis for the spin-singlet heavy quarkoniums decay (into light hadrons) at the next-to-leading order. After applying the PMC scale setting, the decay widths for all those cases are almost independent of the initial renormalizati…
A complete calculation of the ${\cal O}(α_s^4)$ perturbative QCD corrections to the hadronic decay width of the $Z$-boson has recently been performed by Baikov et al.[1]. In their analysis, Baikov et al. relied on the conventional practice of simply guessing the renormalization scale and taking an arbitrary range to estimate the pQCD uncertainties. This procedure inevitably introduces an arbitrary, scheme-dependent theoretical systematic error in the predictions. In this paper, we show that the renormalization scale uncertainties for hadronic $Z$ decays can be greatly reduced by applying the p…
Using the newly available $α_s^6$-order QCD correction to the Higgs decay channel $H\to gg$, we make a detailed discussion on the perturbative properties of the decay width $Γ(H\to gg)$ by using the principle of maximum conformality (PMC). The PMC provides a way to eliminate the conventional renormalization scheme-and-scale ambiguities, which uses the renormalization group equation to determine the optimal running behavior of the strong coupling constant at each order via a recursive way. Even though there is no ambiguity for setting the renormalization scale, there is residual scale dependenc…
It has been observed that conventional renormalization scheme and scale ambiguities for the pQCD predictions can be eliminated by using the principle of maximum conformality (PMC). However, being the intrinsic nature of any perturbative theory, there are still two types of residual scale dependences due to uncalculated higher-order terms. In the paper, as a step forward of our previous work [Phys.Rev.D {\bf 89},116001(2014)], we reanalyze the electroweak $ρ$ parameter by using the PMC single-scale approach. Using the PMC conformal series and the Pad$\acute{e}$ approximation approach, we observ…
The measured $B_d \to π^0π^0$ branching fraction deviates significantly from conventional QCD predictions, a puzzle which has persisted for more than 10 years. This may be a hint of new physics beyond the Standard Model; however, as we shall show in this paper, the pQCD prediction is highly sensitive to the choice of the renormalization scales which enter the decay amplitude. In the present paper, we show that the renormalization scale uncertainties for $B\to ππ$ can be greatly reduced by applying the Principle of Maximum Conformality (PMC), and more precise predictions for CP-averaged branchi…
We predict the rate for exclusive double-charmonium production in electron-positron annihilation $e^+ e^- \to J/ψ+η_c$ using perturbative quantum chromodynamics and the NRQCD framework for hard, heavy-quarkonium exclusive processes. The cross sections measured at the $B$-factories Belle and Babar at $\sqrt{s}=10.6$ GeV disagree with the pQCD leading-order predictions by an order of magnitude. The predictions at next-to-leading order are, however, very sensitive to the choice of the renormalization scale, resulting in an apparent discrepancy between the theoretical prediction and the data. We s…
In the paper, we study the properties of the top-quark $\overline{\rm MS}$ running mass computed from its on-shell mass by using both the four-loop $\overline{\rm MS}$-on-shell relation and the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct magnitude of the strong running coupling of the perturbative series, its prediction avoids the conventional renormalization scale ambiguity, and thus a more precise pQCD prediction can be achieved. After applying the PMC to the four-loop $\overline{\rm MS}$-on-shell relati…
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC) / Brodsky-Lepage…
The intrinsic conformality 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 intrinsic conformality, 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 as the PMC$_{\infty}$-s approach, in which an overall effective $α_s$, and hence an overall effective scale is achieved by identifying the …
A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-…
The conventional approach to fixed-order perturbative QCD predictions is based on an arbitrary choice of the renormalization scale, together with an arbitrary range. This {\it ad hoc} assignment of the renormalization scale causes the coefficients of the QCD running coupling at each perturbative order to be strongly dependent on the choice of both the renormalization scale and the renormalization scheme. However, such ambiguities are not necessary, since as a basic requirement of renormalization group invariance (RGI), any physical observable must be independent of the choice of both the renor…
We present improved pQCD predictions for Higgs boson hadroproduction at the Large Hadronic Collider (LHC) by applying the Principle of Maximum Conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale $μ_r$ of the QCD coupling $α_s(μ_r)$ is the Higgs m…
A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale $μ_r$. For example, by using the conventional way of setting $μ_r \in [m_t/2,2m_t]$, one obtains the total $t \bar{t}$ production cross-section $σ_{t \bar{t}}$ with the uncertainty $Δσ_{t \bar{t}}/σ_{t \bar{t}}\sim ({}^{+3%}_{-4%})$ at the Tevatron and LHC even for the present NNLO level. The Principle of Maximum Conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. In thi…
The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero $β$-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM c…
We present in detail a new systematic method which can be used to automatically eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions at all orders. We show that all of the nonconformal β-dependent terms in a QCD perturbative series can be readily identified by generalizing the conventional renormalization schemes based on dimensional regularization. We then demonstrate that the nonconformal series of pQCD at any order can be resummed systematically into the scale of the QCD coupling in a unique and unambiguous way due to a special degeneracy of the β-terms…
The predictive power of perturbative QCD (pQCD) depends on two important issues: (1) how to eliminate the renormalization scheme-and-scale ambiguities at fixed order, and (2) how to reliably estimate the contributions of unknown higher-order terms using information from the known pQCD series. The Principle of Maximum Conformality (PMC) satisfies all of the principles of the renormalization group and eliminates the scheme-and-scale ambiguities by the recursive use of the renormalization group equation to determine the scale of the QCD running coupling $α_s$ at each order. Moreover, the resultin…
The D0 collaboration at FermiLab has recently measured the top-quark pair forward-backward asymmetry in $\bar p p \to t \bar{t} X$ reactions as a function of the $t\bar{t} $ invariant mass $M_{t\bar{t}}$. The D0 result for $A_{\rm FB}(M_{t\bar{t}}>650\, {\rm GeV})$ is smaller than $A_{\rm FB}(M_{t\bar{t}})$ obtained for small values of $M_{t\bar{t}}$, which may indicate an "increasing-decreasing" behavior for $A_{\rm FB}(M_{t\bar{t}}>M_{\rm cut})$. This behavior is not explained using conventional renormalization scale-setting, even by a next-to-next-to-leading order (N$^2$LO) QCD calculation …
I discuss a number of novel tests of QCD at the LHC, measurements which can illuminate fundamental features of hadron physics. I also review the "Principle of Maximum Conformality" (PMC) which systematically sets the renormalization scale order-by-order in pQCD, eliminating an unnecessary theoretical uncertainty. The PMC allows LHC experiments to test QCD much more precisely, and the sensitivity of LHC measurements to physics beyond the Standard Model is increased.
In the paper, we present QCD predictions for $η_{c} + γ$ production at an electron-position collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for $e^{+}+e^{-}\toγ+η_{c}$ 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…
The Higgs boson decay channel, $H\toγγ$, is one of the most important channels for probing the properties of the Higgs boson. In the paper, we reanalyze its decay width by using the QCD corrections up to $α_s^4$-order level. The principle of maximum conformality has been adopted to achieve a precise pQCD prediction without conventional renormalization scheme-and-scale ambiguities. By taking the Higgs mass as the one given by the ATLAS and CMS collaborations, i.e. $M_{H}=125.09\pm0.21\pm0.11$ GeV, we obtain $Γ(H\to γγ)|_{\rm LHC}=9.364^{+0.076}_{-0.075}$ KeV.
In the paper, we analyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the $\mathcal{O}(α_s^4)$-order QCD corrections with the help of principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent fixed-order pQCD contribution for GLS sum rule, e.g. $S^{\rm GLS}(Q_0^2=3{\rm GeV}^2)|_{\rm PMC}=2.559^{+0.023}_{-0.024}$, where the error is squared average of those from $Δα_s(M_Z)$, the predicted $\mathcal{O}(α_s^5)$-order terms predicted by using the Padé approximation approach. After applying …
We investigate the theoretical predictions for thrust distribution in the electron positron annihilation to three-jets process at NNLO for different values of the number of flavors, $N_f$. To determine the distribution along the entire renormalization group flow from the highest energies to zero energy we consider the number of flavors near the upper boundary of the conformal window. In this regime of number of flavors the theory develops a perturbative infrared interacting fixed point. We then consider also the QED thrust obtained as the limit $N_c \rightarrow 0$ of the number of colors. In t…
Heavy fermion pair production in $e^+e^-$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the Principle of Maximum Conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are cons…
In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renor…
We study the decay width of the Higgs-boson $H\to gg$ up to order $α_s^5$ under the minimal momentum space subtraction scheme (mMOM-scheme). To improve the accuracy of perturbative QCD prediction, we adopt the principle of maximum conformality (PMC) to set its renormalization scales. A detailed comparison of the total decay width and the separate decay widths at each perturbative order before and after the PMC scale setting is presented. The PMC adopts the renormalization group equation to fix the optimal scales of the process. After the PMC scale setting, the scale-dependence for both the tot…
A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. Two distinct approaches for satisfying the RGI principle have been suggested in the literature. One is the "Principle of Maximum Conformality" (PMC) in which the terms associated with the $β…
The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to $Υ(1S)$ leptonic decay rate $Γ(Υ(1S)\to \ell^+\ell^-)$ has been finished by Beneke {\it et al.} \cite{Beneke:2014qea}. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for $Γ(Υ(1S)\to \ell^+\ell^-)$ by applying the principle of maximum conformality (PMC). The PMC is based on RG-invariance and is designed to solve the pQCD renormalization scheme and scale ambiguities. After applying the PMC, all known-type of $β$-terms at all orders, which are control…
We apply the principle of maximum conformality (PMC) to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron intercept at the next-to-leading logarithmic (NLL) accuracy. The PMC eliminates the conventional renormalization scale ambiguity by absorbing the non-conformal $\{β_i\}$-terms into the running coupling, and a more accurate pQCD estimation can be obtained. After PMC scale setting, the QCD perturbative convergence can be greatly improved due to the elimination of renormalon terms in pQCD series, and the BFKL Pomeron intercept has a weak dependence on the virtuality of the reggeized gluon. For…
The Principle of Maximal Conformality (PMC) provides a rigorous method for eliminating renormalization scheme-and-scale ambiguities for perturbative QCD predictions. The PMC uses the renormalization group equation to fix the $β$-pattern of each order in an arbitrary pQCD approximant, and it then determines the optimal renormalization scale by absorbing all $\{β_{i}\}$ terms into the running coupling at each order. The resulting coefficients of the pQCD series match the scheme-independent conformal series with $β=0$. As in QED, different renormalization scales appear at each order; we call this…
Scheme-independent determination of the QCD running coupling at all scales from jet observables using the principle of maximum conformality and infinite-order scale setting
A key issue in making precise predictions in perturbative QCD is the uncertainty in setting the renormalization scale. If in principle, the entire perturbative series is void of this issue, in practice the perturbative corrections are known up to a certain order of accuracy and scale invariance is only approximated leading to the so-called scheme and scale ambiguities. According to the conventional scale setting (CSS) this problem cannot be avoided and the renormalization scale is set to the typical scale of a process $Q$, and errors are estimated by varying the scale over a range of two $[Q/2…
Novel analysis for the energy-energy correlation in electron-positron annihilation in the perturbative domain
Guizhou Minzu University（贵州民族大学）；Hunan University（湖南大学）；Chongqing University（重庆大学）；University of Insubria（因斯布鲁克大学）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所米兰-比可卡分部）；SLAC National Accelerator Laboratory, Stanford University（斯坦福大学SLAC国家加速器实验室）
