arXiv subjects

Xing-Gang Wu

Publications and source records attributed to Xing-Gang Wu.

At least 163 records · Page 9Linked to original sources

arXiv2015

The Importance of Proper Renormalization Scale-Setting for Testing QCD at Colliders

A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve maximally precise fixed-order predictions for physical observables. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, giving predictions which are independent of the choice of renormalization scheme. The scales of the QCD couplings and the effective number of quark flavors are set order by order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance and all of the the self-consistency conditions derived from the renormalization group......In this brief report, we summarize the results of our recent PMC applications for a number of collider processes, emphasizing their generality and applicability....... These results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing the sensitivity of the colliders to possible new physics beyond the Standard Model.

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arXiv2015

Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting

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 $β$-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the "Principle of Minimum Sensitivity" (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables $R_{e+e-}$ and $Γ(H\to b\bar{b})$ up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: The PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. ......

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arXiv2015

A Possible Solution to the $B\to ππ$ Puzzle Using the Principle of Maximum Conformality

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 branching ratios ${\cal B}(B\toππ)$ can be achieved. Combining the errors in quadrature, we obtain ${\cal B}(B_{d}\to π^0π^0)|_{\rm PMC} = \left(0.98^{+0.44}_{-0.31}\right) \times10^{-6}$ by using the light-front holographic low-energy model for the running coupling. All of the CP-averaged $B\toππ$ branching fractions predicted by the PMC are consistent with the Particle Data Group average values and the recent Belle data. Thus, the PMC provides a possible solution for the $B_d \to π^0π^0$ puzzle.

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arXiv2015

BCVEGPY2.2: A Newly Upgraded Version for Hadronic Production of the Meson $B_c$ and Its Excited States

A newly upgraded version of the BCVEGPY, a generator for hadronic production of the meson $B_c$ and its excited states, is available. In comparison with the previous one [C.H. Chang, J.X. Wang and X.G. Wu, Comput. Phys. Commun. {\bf 175}, 624 (2006)], the new version is to apply an improved hit-and-miss technology to generating the un-weighted events much more efficiently under various simulation environments. The codes for production of $2S$-wave $B_c$ states are also given here.

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arXiv2015

Renormalization group improved pQCD prediction for $Υ(1S)$ leptonic decay

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 controlled by the RG-equation, are resummed to determine optimal renormalization scale for its strong running coupling at each order. We then achieve a more convergent pQCD series, a scheme- independent and more accurate pQCD prediction for $Υ(1S)$ leptonic decay, i.e. $Γ_{Υ(1S) \to e^+ e^-}|_{\rm PMC} = 1.270^{+0.137}_{-0.187}$ keV, where the uncertainty is the squared average of the mentioned pQCD errors. This RG-improved pQCD prediction agrees with the experimental measurement within errors.

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arXiv2015

Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale

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 correspondence \mbox{(PMC-I)}; the other, more recent, method \mbox{(PMC-II)} uses the ${\cal R}_δ$-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio $R_{e^+ e^-}$ and the Higgs partial width $Γ(H\to b\bar{b})$. Both methods lead to the same resummed (`conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group $\{β_i\}$-terms in the pQCD expansion are taken into account. We also show that {\it special degeneracy relations}, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

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arXiv2015

Setting the Renormalization Scale in pQCD: Comparisons of the Principle of Maximum Conformality with the Sequential Extended Brodsky-Lepage-Mackenzie Approach

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-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all-orders. In this paper we discuss two distinct methods. One is based on the "Principle of Maximum Conformality" (PMC), which provides a systematic all-orders method to eliminate the scale- and scheme- ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the "sequential extended BLM" (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the $β_0$-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low-orders......

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arXiv2015

Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops

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-Mackenzie (BLM) scale-setting method, all non-conformal $\{β_i\}$ terms in the perturbative expansion series can be summed into the running coupling, and the resulting scale-fixed predictions are independent of the renormalization scheme. Different schemes lead to different effective PMC/BLM scales, but the final results are scheme independent. Conversely, from the requirement of scheme independence, one not only can obtain scheme-independent commensurate scale relations among different observables, but also determine the scale displacements among the PMC/BLM scales which are derived under different schemes. In principle, the PMC/BLM scales can be fixed order-by-order, and as a useful reference, we present a systematic and scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit application for determining the scale setting of $R_{e^{+}e^-}(Q)$ up to four loops is presented. By using the world average $α^{\bar{MS}}_s(M_Z) =0.1184 \pm 0.0007$, we obtain the asymptotic scale for the 't Hooft associated with the $\bar{MS}$ scheme, $Λ^{'tH}_{\bar{MS}}= 245^{+9}_{-10}$ MeV, and the asymptotic scale for the conventional $\bar{MS}$ scheme, $Λ_{\bar{MS}}= 213^{+19}_{-8}$ MeV.

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arXiv2015

General Properties on Applying the Principle of Minimum Sensitivity to High-order Perturbative QCD Predictions

As one of the key components of perturbative QCD theory, it is helpful to find a systematic and reliable way to set the renormalization scale for a high-energy process. The conventional treatment is to take a typical momentum as the renormalization scale, which assigns an arbitrary range and an arbitrary systematic error to pQCD predictions, leading to the well-known renormalization scheme and scale ambiguities. As a practical solution for such scale setting problem, the "Principle of Minimum Sensitivity" (PMS), has been proposed in the literature. The PMS suggests to determine an optimal scale for the pQCD approximant of an observable by requiring its slope over the scheme and scale changes to vanish. In the paper, we present a detailed discussion on general properties of PMS by utilizing three quantities $R_{e^+e^-}$, $R_τ$ and $Γ(H\rightarrow b\bar{b})$ up to four-loop QCD corrections. After applying the PMS, the accuracy of pQCD prediction, the pQCD convergence, the pQCD predictive power and etc., have been discussed. Furthermore, we compare PMS with another fundamental scale setting approach, i.e. the Principle of Maximum Conformality (PMC)... Our results show that PMS does provide a practical way to set the effective scale for high-energy process, and the PMS prediction agrees with the PMC one by including enough high-order QCD corrections, both of which shall be more accurate than the prediction under the conventional scale setting. However, the PMS pQCD convergence is an accidental, which usually fails to achieve a correct prediction of unknown high-order contributions with next-to-leading order QCD correction only, i.e. it is always far from the "true" values predicted by including more high-order contributions.

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arXiv2015

$B\to ρ$ transition form factors within the QCD light-cone sum rules and the $ρ$-meson leading-twist distribution amplitude

The QCD light-cone sum rules (LCSR) provides an effective way for dealing with the heavy-to-light transition form factors (TFFs), whose non-perturbative dynamics are parameterized into the light-meson's light-cone distribution amplitudes (LCDAs) with various twist structures. By taking the chiral correlator as the starting point, we calculate the LCSRs for the $B\toρ$ TFFs up to twist-4 accuracy. As for the TFFs at the large recoil region, we observe that the twist-2 transverse DA $ϕ_{2;ρ}^\bot$ provides the dominant contribution, while the contributions from the remaining twist-3 and twist-4 terms are $δ^2$-suppressed. Thus, our present improved LCSRs provides a good platform for testing the $ϕ_{2;ρ}^\bot$ behavior. For the purpose, we suggest a convenient WH-model for the $ρ$-meson leading-twist wavefunction, in which the parameter $B_{2;ρ}^\bot\sim a^\bot_2$ dominantly controls its longitudinal distribution. Typically, its DA $ϕ_{2;ρ}^\bot$ is CZ-like as $B_{2;ρ}^\bot\simeq-0.20$, which changes to be asymptotic-like as $B_{2;ρ}^\bot\simeq0.00$. By varying $B_{2;ρ}^\bot\in[-0.20,0.20]$, we present a detailed comparison of the LCSR estimation for the $B\toρ$ TFFs with those of pQCD and Lattice QCD predictions. Furthermore, by using the extrapolated TFFs, we estimate the CKM-matrix element $|V_{\rm ub}|$ with the help of two $B\toρ$ semi-leptonic decays. The predicted value for $|V_{\rm ub}|$ increases with the increment of $B_{2;ρ}^\bot$, i.e. we have $\Vub=(2.91\pm0.19)\times 10^{-3}$ for $B_{2;ρ}^\bot=-0.20$ and $\Vub=(3.11\pm0.19)\times 10^{-3}$ for $B_{2;ρ}^\bot=0.00$. If using the BABAR prediction as a criteria, we observe that $B^{\perp}_{2;ρ}\in[-0.2,0.10]$, which indicates that the $ρ$-meson DA $ϕ_{2;ρ}^\bot$ prefers a single-peak behavior rather than a double-humped behavior.

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arXiv2014

Photoproduction of doubly heavy baryon at the ILC

In the present paper, we make a detailed study on the doubly heavy baryon photoproduction in the future $e^+e^-$ International Linear Collider (ILC). The baryons $Ξ_{cc}$, $Ξ_{bc}$, and $Ξ_{bb}$ are produced via the channel $γγ\to Ξ_{QQ'} +\bar{Q'} +\bar{Q}$, where $Q$ and $Q'$ stand for heavy $c$ or $b$ quark, respectively. As for the $Ξ_{QQ'}$-baryon production, it shall first generate a $(QQ')[n]$-diquark and then form the final baryon via fragmentation, where $[n]$ stands for the color- and spin- configurations for the $(QQ')$-diquark states. According to the non-relativistic QCD theory, four diquark configurations shall provide sizable contributions to the baryon production, e.g., $[n]$ equals $[^3S_1]_{\bar{\textbf{3}}}$, $[^1S_0]_{\textbf{6}}$, $[^3S_1]_{\textbf{6}}$, or $[^1S_0]_{\bar{\textbf{3}}}$, respectively. We adopt the improved helicity amplitude approach for the hard scattering amplitude to improve the calculation efficiency. Total and differential cross sections of those channels, as well as the theoretical uncertainties, are presented. We show that sizable amounts of baryon events can be generated at the ILC, i.e., about $2.0\times 10^{6}$ $Ξ_{cc}$, $2.2\times 10^{5}$ $Ξ_{bc}$, as well as $3.0\times 10^{3}\;Ξ_{bb}$ events are to be generated in one operation year for $\sqrt{S}=500$ GeV and ${\cal L}\simeq 10^{36}$cm$^{-2}$s$^{-1}$.

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arXiv2014

Application of the Principle of Maximum Conformality to the Top-Quark Charge Asymmetry at the LHC

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-leading order level at the LHC. After applying PMC scale setting, the pQCD prediction for the top-quark charge asymmetry at the LHC has very small scale uncertainty; e.g., $A_{\rm C}|_{\rm 7 TeV;PMC} =\left(1.15^{+0.01}_{-0.03}\right)\%$, $A_{\rm C}|_{\rm 8 TeV;PMC} =\left(1.03^{+0.01}_{+0.00}\right)\%$, and $A_{\rm C}|_{\rm 14 TeV;PMC} =\left(0.62^{+0.00}_{-0.02}\right)\%$. The corresponding predictions using conventional scale setting are: $A_{\rm C}|_{\rm 7 TeV;Conv.} =\left(1.23^{+0.14}_{-0.14}\right)\%$, $A_{\rm C}|_{\rm 8 TeV;Conv.} =\left(1.11^{+0.17}_{-0.13}\right)\%$, and $A_{\rm C}|_{\rm 14 TeV;Conv.} =\left(0.67^{+0.05}_{-0.05}\right)\%$. In these predictions, the scale errors are predicted by varying the initial renormalization and factorization scales in the ranges $μ^{\rm init}_r\in[m_t/2,2m_t]$ and $μ_f\in[m_t/2,2m_t]$. The PMC predictions are also in better agreement with the available ATLAS and CMS data. In addition, we have calculated the top-quark charge asymmetry assuming several typical cuts on the top-pair invariant mass $M_{t\bar{t}}$. For example, assuming $M_{t\bar{t}}>0.5 ~ {\rm TeV}$ and $μ_f=μ^{\rm init}_r =m_t$, we obtain $A_{\rm C}|_{\rm 7 TeV;PMC}=2.67\%$, $A_{\rm C}|_{\rm 8 TeV;PMC}=2.39\%$, and $A_{\rm C}|_{\rm 14 TeV;PMC}=1.28\%$.

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arXiv2014

Photoproduction of the heavy quarkonium at the ILC

We study the photoproduction of the heavy quarkonium at the future International Linear Collider (ILC) within the nonrelativistic QCD theory. We focus on the production channel via the subprocess $γγ\to |[Q\bar{Q'}]_{\bf 1}(n)>+Q'+\bar{Q}$, where $Q$ and $Q'$ stand for heavy $c$- or $b$-quark, respectively. $|[Q\bar{Q'}]_{\bf 1}(n)>$ stands for color-singlet $S$-wave quarkonium, i.e., $η_{c}(|[c\bar{c}]_{\bf 1}(^1S_0)>)$, $J/ψ(|[c\bar{c}]_{\bf 1}(^3S_1)>)$, $B_{c}(|[c\bar{b}]_{\bf 1}(^1S_0)>)$, $B^*_{c}(|[c\bar{b}]_{\bf 1}(^3S_1)>)$, $η_{b}(|[b\bar{b}]_{\bf 1}(^1S_0)>)$, and $Υ(|[b\bar{b}]_{\bf 1}(^3S_1)>)$, respectively. To improve the calculation efficiency, we adopt the improved helicity amplitude approach to deal with the difficulty of calculating the expressions for the yields when the quark masses cannot be neglected. Total and differential photoproduction cross sections, together with their uncertainties, have been presented. It is noted that sizable amount of $|c\bar{c}>$-charmonium and $|c\bar{b}>$-quarkonium events can be generated at the ILC. More specifically, we predict $(2.8^{+1.0}_{-0.7})\times 10^{6}$ $η_c$, $(5.4^{+1.9}_{-1.3})\times 10^{6}$ $J/ψ$, $(8.3^{+2.2}_{-1.8})\times 10^{4}$ $B_c$, $(4.3^{+1.1}_{-0.9})\times 10^{5}$ $B_c^*$, $(9.0^{+1.7}_{-1.4})\times 10^{3}$ $η_b$, and $(1.6\pm0.3)\times 10^{4}$ $Υ$ events to be generated in one operation year at the ILC under the condition of $\sqrt{S}=500$ GeV and ${\cal L}\simeq 10^{36}$cm$^{-2}$s$^{-1}$.

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arXiv2014

The $ρ$-meson longitudinal leading-twist distribution amplitude

In the present paper, we suggest a convenient model for the vector $ρ$-meson longitudinal leading-twist distribution amplitude $ϕ_{2;ρ}^\|$, whose distribution is controlled by a single parameter $B^\|_{2;ρ}$. By choosing proper chiral current in the correlator, we obtain new light-cone sum rules (LCSR) for the $B\toρ$ TFFs $A_1$, $A_2$ and $V$, in which the $δ^1$-order $ϕ_{2;ρ}^\|$ provides dominant contributions. Then we make a detailed discussion on the $ϕ_{2;ρ}^\|$ properties via those $B\toρ$ TFFs. A proper choice of $B^\|_{2;ρ}$ can make all the TFFs agree with the lattice QCD predictions. A prediction of $|V_{\rm ub}|$ has also been presented by using the extrapolated TFFs, which indicates that a larger $B^{\|}_{2;ρ}$ leads to a larger $|V_{\rm ub}|$. To compare with the BABAR data on $|V_{\rm ub}|$, the longitudinal leading-twist DA $ϕ_{2;ρ}^\|$ prefers a doubly-humped behavior.

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arXiv2014

Heavy Pseudoscalar Leading-Twist Distribution Amplitudes within QCD Theory in Background Fields

In this paper, we study the leading-twist distribution amplitude (DA) of the heavy pseudoscalars (HPs), such as $η_c$, $η_b$ and $B_c$, within the QCD theory in the background fields. New sum rules up to dimension-six condensates for both the HP decay constants and their leading-twist DA moments are presented. From the sum rules for the HP decay constants, we obtain $f_{η_c} = 453 \pm 4 \textrm{MeV}$, $f_{B_c} = 498 \pm 14 \textrm{MeV}$, and $f_{η_b} = 811 \pm 34 \textrm{MeV}$. Basing on the sum rules for the HPs' leading-twist DA moments, we construct a new model for the $η_c$, $η_b$ and $B_c$ leading-twist DAs. Our present HP DA model can also be adaptable for the light pseudo-scalar DAs, such as the pion and kaon DAs. Thus, it shall be applicable for a wide range of QCD exclusive processes. As an application, we apply the $η_c$ leading-twist DA to calculate the $B_c \to η_c$ transition form factor $f_+^{B_c \to η_c}(q^2)$. At the maximum recoil region, we obtain $f_+^{B_c \to η_c}(0) = 0.612^{+0.053}_{-0.052}$. After further extrapolating the TFF $f_+^{B_c \to η_c}(q^2)$ to its allowable $q^2$ region, we predict the branching ratio for the semi-leptonic decay $B_c \to η_c l ν$. We obtain ${\cal B}(B_c \to η_c l ν)=\left(7.70^{+1.65}_{-1.48}\right) \times 10^{-3}$ for massless leptons, which is consistent with the LCSRs estimation obtained in the literature.

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arXiv2014

QCD corrections to the $B_c$ to charmonia semi-leptonic decays

We present a detailed analysis on the $B_c$ meson semi-leptonic decays, $B_c \to η_c (J/ψ) \ell ν$, up to next-to-leading order (NLO) QCD correction. We adopt the principle of maximum conformality (PMC) to set the renormalization scales for those decays. After applying the PMC scale setting, we determine the optimal renormalization scale for the $B_c\toη_c(J/ψ)$ transition form factors (TFFs). Because of the same $\{β_0\}$-terms, the optimal PMC scales at the NLO level are the same for all those TFFs, i.e. $μ_r^{\rm PMC} \approx 0.8{\rm GeV}$. We adopt a strong coupling model from the massive perturbation theory (MPT) to achieve a reliable pQCD estimation in this low energy region. Furthermore, we adopt a monopole form as an extrapolation for the $B_c\toη_c(J/ψ)$ TFFs to all their allowable $q^2$ region. Then, we predict $Γ_{B_c \to η_c \ell ν}(\ell=e,μ) =(71.53^{+11.27}_{-8.90})\times 10^{-15} {\rm GeV}$, $Γ_{B_c \to η_c τν}=(27.14^{+5.93}_{-4.33})\times 10^{-15} {\rm GeV}$, $Γ_{B_c \to J/ψ\ell ν}(\ell=e,μ) =(106.31^{+18.59}_{-14.01}) \times 10^{-15} {\rm GeV}$, $Γ_{B_c \to J/ψτν} =(28.25^{+6.02}_{-4.35})\times 10^{-15} {\rm GeV}$, where the uncertainties are squared averages of all the mentioned error sources. We show that the present prediction of the production cross section times branching ratio for $B^+_c\to J/ψ\ell^+ v$ relative to that for $B^+ \to J/ψK^+$, i.e. $\Re(J/ψ\ell^+ ν)$, is in a better agreement with CDF measurements than the previous predictions.

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arXiv2014

Reanalysis of the Higher Order Perturbative QCD corrections to Hadronic $Z$ Decays using the Principle of Maximum Conformality

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 principle of maximum conformality (PMC), a rigorous extension of the BLM method. The PMC prediction is independent of the choice of renormalization scheme; i.e., it respects renormalization group invariance, and thus it provides an optimal and theoretically rigorous method for setting the renormalization scale. We show that the convergence of the pQCD prediction for the $Z$ hadronic width is greatly improved using the PMC since the divergent renormalon series does not appear. The magnitude of the high-order corrections quickly approach a steady point. The PMC predictions also have the property that any residual dependence on the choice of initial scale is highly suppressed, even for low-order predictions. Thus, one obtains optimal fixed-order predictions for the $Z$-boson hadronic decay rates thus enabling high precision tests of the Standard Model.

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arXiv2014

The QCD improved electroweak parameter $ρ$

In the present paper, we make a detailed analysis for the QCD corrections to the electroweak $ρ$ parameter by applying the principle of maximum conformality (PMC). As a comparison, we show that under the conventional scale setting, we have $Δρ|_{\rm N^3LO} = \left(8.257^{+0.045}_{-0.012}\right) \times10^{-3}$ by varying the scale $μ_{r}\in[M_{t}/2$, $2M_{t}]$. By defining a ratio, $ΔR=Δρ/3X_t-1$, which shows the relative importance of the QCD corrections, it is found that its scale error is $\sim \pm9 \%$ at the two-loop level, which changes to $\sim\pm4\%$ at the three-loop level and $\sim \pm 2.5\%$ at the four-loop level, respectively. These facts well explain why the conventional scale uncertainty constitutes an important error for estimating the $ρ$ parameter. On the other hand, by applying the PMC scale setting, the four-loop estimation $Δρ|_{\rm N^3LO}$ shall be almost fixed to $8.228\times10^{-3}$, which indicates that the conventional scale error has been eliminated. We observe the pQCD convergence for the $ρ$ parameter has also been greatly improved due to the elimination of the divergent renormalon terms. As applications of the present QCD improved $ρ$ parameter, we show the shifts of the $W$-boson mass and the effective leptonic weak-mixing angle due to $Δρ$ can be reduced to $δM_{W}|_{\rm N^3LO} =0.7$ MeV and $δ\sin^2θ_{\rm eff}|_{\rm N^3LO}=-0.4\times10^{-5}$.

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