arXiv subjects

Jian-Ming Shen

Publications and source records attributed to Jian-Ming Shen.

At least 37 records · Page 2Linked to original sources

arXiv2021

Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders

In the paper, we make a detailed study on the generalized Crewther Relation (GCR) between the Adler function ($D$) and the Gross-Llewellyn Smith sum rules coefficient ($C^{\rm GLS}$) by using the newly suggested single-scale approach of the principle of maximum conformality (PMC). The resultant GCR is scheme-independent, whose residual scale dependence due to unknown higher-order terms are highly suppressed. Thus a precise test of QCD theory without renormalization scheme and scale ambiguities can be achieved by comparing with the data. Moreover, a demonstration of the scheme independence of commensurate scale relation up to all orders has been presented. And as the first time, the Pade approximation approach has been adopted for estimating the unknown $5_{\rm th}$-loop contributions from the known four-loop perturbative series.

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arXiv2021

$Z$-boson hadronic decay width up to $\mathcal{O}(α_s^4)$-order QCD corrections using the single-scale approach of the principle of maximum conformality

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 terms are highly suppressed, e.g. conservatively, we have $ΔΓ_{\rm Z}^{\rm had}|^{{\cal O}(α_s^5)}_{\rm PMC}\simeq \pm 0.004$ MeV. In combination with the known electro-weak (EW) corrections, QED corrections, EW-QCD mixed corrections, and QED-QCD mixed corrections, our final prediction of the hadronic $Z$ decay width is $Γ_{\rm Z}^{\rm had}=1744.439^{+1.390}_{-1.433}$ MeV, which agrees with the PDG global fit of experimental measurements, $1744.4\pm 2.0$ MeV.

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arXiv2020

Revisiting the Bottom Quark Forward-Backward Asymmetry $A_{\rm {FB}}$ in Electron-Positron Collisions

The bottom quark forward-backward asymmetry $A_{\rm{FB}}$ is a key observable in electron-positron collisions at the $Z^{0}$ peak. In this paper, we employ the Principle of Maximum Conformality (PMC) to fix the $α_s$-running behavior of the next-to-next-to-leading order QCD corrections to $A_{\rm{FB}}$. The resulting PMC scale for this $A_{\rm{FB}}$ is an order of magnitude smaller than the conventional choice $μ_r=M_Z$. This scale has the physically reasonable behavior and reflects the virtuality of its QCD dynamics, which is independent to the choice of renormalization scale. Our analyses show that the effective momentum flow for the bottom quark forward-backward asymmetry should be $μ_r\ll M_Z$ other than the conventionally suggested $μ_r=M_Z$. Moreover, the convergence of perturbative QCD series for $A_{\rm{FB}}$ is greatly improved using the PMC. Our prediction for the bare bottom quark forward-backward asymmetry is refined to be $A^{0,b}_{\rm FB}=0.1004\pm0.0016$, which diminishes the well known tension between the experimental determination for this (pseudo) observable and the respective Standard Model fit to $2.1σ$.

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arXiv2020

Renormalization Scale Setting for Heavy Quark Pair Production in $e^+e^-$ Annihilation near the Threshold Region

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 consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass $m_f$, which enters the hard virtual corrections, and the other scale is of order $ v\,m_f$, where $v$ is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated.

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arXiv2020

$\bar{B}_s \to f_0(980)$ form factors and the width effect from light-cone sum rules

In this paper we calculate the $\bar{B}_s \to f_0(980)$ form factors from light-cone sum rules with $B$ meson DAs. With adopting the quark-antiquark configuration of light scalar mesons,the high twist two-particle and the three-particle contributions are found to be $\sim 25\%$ individual, and totally they give about $50\%$ correction to certain form factors in the considered energy regions. We further explore the light-cone sum rules approach to study the $S-$wave $\bar{B}_s \to KK$ form factors,the $f_0+f'_0+f''_0$ resonance model is proposed and the result shows that the background effect from $f'_0+f''_0$ accounts $\sim 5\%$. As a by-product, we extract the strong coupling $|g_{f_0 KK }| = 1.08^{+0.05}_{-0.14}$ GeV with taking the $\bar{B}_s \to f_0(980)$ form factors calculated previous under the narrow width approximation.

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arXiv2020

Gauge dependence of the perturbative QCD predictions under the momentum space subtraction scheme

The momentum space subtraction (MOM) scheme is one of the most frequently used renormalization schemes in perturbative QCD (pQCD) theory. In the paper, we make a detailed discussion on the gauge dependence of the pQCD prediction under the MOM scheme. Conventionally, there is renormalization scale ambiguity for the fixed-order pQCD predictions, which assigns an arbitrary range and an arbitrary error for the fixed-order pQCD prediction. The principle of maximum conformality (PMC) adopts the renormalization group equation to determine the magnitude of the coupling constant and hence determines an effective momentum flow of the process, which is independent to the choice of renormalization scale. There is thus no renormalization scale ambiguity in PMC predictions. To concentrate our attention on the MOM gauge dependence, we first apply the PMC to deal with the pQCD series. We adopt the Higgs boson decay width, $Γ(H\to gg)$, up to five-loop QCD contributions as an example to show how the gauge dependence behaves before and after applying the PMC. It is found that the Higgs decay width $Γ(H\to gg)$ depends very weakly on the choices of the MOM schemes, being consistent with the renormalization group invariance. It is found that the gauge dependence of $Γ(H\to gg)$ under the $\rm{MOMgg}$ scheme is less than $\pm1\%$, which is the smallest gauge dependence among all the mentioned MOM schemes.

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arXiv2019

Novel Method for the Precise Determination of the QCD Running Coupling from Event Shapes Distributions in Electron-Positron Annihilation

We present a novel method for precisely determining the running QCD coupling constant $α_s(Q^2)$ over a wide range of $Q^2$ from event shapes for electron-positron annihilation measured at a single annihilation energy $\sqrt{s}$. The renormalization scale $Q^2$ of the running coupling depends dynamically on the virtuality of the underlying quark and gluon subprocess and thus the specific kinematics of each event. The determination of the renormalization scale for event shape distributions is obtained by using the Principle of Maximum Conformality (PMC), a rigorous scale-setting method for gauge theories which satisfies all the requirements of Renormalization Group Invariance, including renormalization-scheme independence and consistency with Abelian theory in the $N_C \to 0$ limit. In this paper we apply the PMC to two classic event shapes measured in $e^+ e^-$ annihilation: the thrust ($T$) and C-parameter ($C$). The PMC renormalization scale depends differentially on the values of $T$ and $C$. The application of PMC scale-setting determines the running coupling $α_s(Q^2)$ to high precision over a wide range of $Q^2$ from $10$ to $250~\rm{GeV}^2$ from measurements of the event shape distributions at the $Z^0$ peak. The extrapolation of the running coupling using pQCD evolution gives the value $α_s(M^2_Z)=0.1185\pm0.0012$ from the thrust, and $α_s(M^2_Z)=0.1193^{+0.0021}_{-0.0019}$ from the C-parameter in the $\bar{\rm{MS}}$ scheme. These determinations of $α_s(M^2_Z)$ are consistent with the world average and are more precise than the values obtained from analyses of event shapes currently used in the world average. The highly-consistent results for the $T$ and $C$ event-shape distributions provide an additional verification of the applicability of the PMC to pQCD.

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arXiv2019

The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality

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 renormalization scheme and the renormalization scale. In fact, if one uses the {\it Principle of Maximum Conformality} (PMC) to fix the renormalization scale, the coefficients of the pQCD series match the series of conformal theory, and they are thus scheme independent. It has been found that the elimination of the scale and scheme ambiguities at all orders relies heavily on how precisely we know the analytic form of the QCD running coupling $α_s$. In this review, we summarize the known properties of the QCD running coupling and its recent progresses, especially for its behavior within the asymptotic region. We also summarize the current progress on the PMC and some of its typical applications, showing to what degree the conventional renormalization scheme-and-scale ambiguities can be eliminated after applying the PMC. We also compare the PA approach for the conventional scale-dependent pQCD series and the PMC scale-independent conformal series. We observe that by using the conformal series, the PA approach can provide a more reliable estimate of the magnitude of the uncalculated terms. And if the conformal series for an observable has been calculated up to $n_{\rm th}$-order level, then the $[N/M]=[0/n-1]$-type PA series provides an important estimate for the higher-order terms.

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arXiv2019

The $Υ(1S)$ leptonic decay using the principle of maximum conformality

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, $Γ_{Υ(1S) \to e^+ e^-} = 1.262^{+0.195}_{-0.175}$ keV, where the error is squared average of those from $α_s(M_{Z})=0.1181\pm0.0011$, $m_b=4.93\pm0.03$ GeV and the choices of factorization scales within $\pm 10\%$ of their central values. To compare with the result under conventional scale-setting approach, this decay width agrees with the experimental value within errors, indicating the importance of a proper scale-setting approach.

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arXiv2019

Extending the Predictive Power of Perturbative QCD

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 resulting PMC predictions are independent of the choice of the renormalization scheme, satisfying the key principle of renormalization group invariance. In this letter, we show that by using the conformal series derived using the PMC single-scale procedure, in combination with the Padé Approximation Approach (PAA), one can achieve quantitatively useful estimates for the unknown higher-order terms from the known perturbative series. We illustrate this procedure for three hadronic observables $R_{e^+e^-}$, $R_τ$, and $Γ(H \to b \bar{b})$ which are each known to 4 loops in pQCD. We show that if the PMC prediction for the conformal series for an observable (of leading order $α_s^p$) has been determined at order $α^n_s$, then the $[N/M]=[0/n-p]$ Padé series provides quantitatively useful predictions for the higher-order terms. We also show that the PMC + PAA predictions agree at all orders with the fundamental, scheme-independent Generalized Crewther relations which connect observables, such as deep inelastic neutrino-nucleon scattering, to hadronic $e^+e^-$ annihilation. Thus, by using the combination of the PMC series and the Padé method, the predictive power of pQCD theory can be greatly improved.

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arXiv2018

Properties of the decay $H\toγγ$ using the approximate $α_s^4$-corrections and the principle of maximum conformality

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.

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arXiv2018

Reanalysis of the Higgs-boson decay $H \to gg$ up to $α_s^6$-order level using the principle of maximum conformality

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 dependence for the PMC predictions due to unknown high-order terms. Using the $α_s^6$-order terms, the somewhat larger residual renormalization scale dependence at the $α_s^5$-order level observed in our previous work can be greatly suppressed, which shows $Γ(H\to gg)\rm{|_{ PMC }} =337.9 \pm1.7_{-0.1}^{+0.9}\pm1.9$ KeV, where the first error is caused by the Higgs mass uncertainty $ΔM_{H}=0.24$ GeV, the second one is the residual scale dependence by varying the initial choice of scale within the region of $\left[{M_H}/{2},4 M_H\right]$, and the third one is the conservative prediction of unknown high-order contributions.

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arXiv2018

A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling

As a basic requirement of the renormalization group invariance, any physical observable must be independent of the choice of both the renormalization scheme and the initial renormalization scale. In this paper, we show that by using the newly suggested $C$-scheme coupling, one can obtain a demonstration that the {\it Principle of Maximum Conformality} prediction is scheme-independent to all-orders for any renormalization schemes, thus satisfying all of the conditions of the renormalization group invariance. We illustrate these features for the non-singlet Adler function and for $τ$ decay to $ν+$ hadrons at the four-loop level.

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arXiv2018

Properties of the Free Energy Density Using the Principle of Maximum Conformality

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 by using a smaller factorization scale around the effective parameter $m_E$, the PMC prediction shall be consistent with the Lattice QCD prediction derived at the low temperature.

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arXiv2017

Reconsideration of the QCD corrections to the $η_c$ decays into light hadrons using the principle of maximum conformality

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 the minimal momentum space subtraction scheme. To compare with the prediction under conventional scale setting, $R_{\rm{Conv,mMOM}-r}= \left(4.12^{+0.30}_{-0.28}\right)\times10^3$, after applying the PMC, we obtain $R_{\rm PMC,mMOM-r}=\left(6.09^{+0.62}_{-0.55}\right) \times10^3$, where the errors are squared averages of the ones caused by $m_c$ and $Λ_{\rm mMOM}$. The PMC prediction agrees with the recent PDG value within errors, i.e. $R^{\rm exp}=\left(6.3\pm0.5\right)\times10^3$. Thus we think the mismatching of the prediction under conventional scale-setting with the data is due to improper choice of scale, which however can be solved by using the PMC.

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arXiv2017

The Generalized Scheme-Independent Crewther Relation in QCD

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD process. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived for conformal theory, provides a remarkable connection between two observables when the $β$ function vanishes. The "Generalized Crewther Relation" relates these two observables for physical QCD with nonzero $β$ function; specifically, it connects the non-singlet Adler function ($D^{\rm ns}$) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering ($C_{\rm Bjp}$) at leading twist. A scheme-dependent $Δ_{\rm CSB}$-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. ...... Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $\widehatα_d(Q)= \sum_{i\geq1} \widehatα^{i}_{g_1}(Q_i)$, at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.

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arXiv2017

Implications of the Principle of Maximum Conformality for the QCD Strong Coupling

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 domain of applicability (Q \gtrsim 1.5 GeV) does not extend to as small values of momentum transfer as that of a conventional pQCD analysis (Q \gtrsim 1 GeV). We suggest that the PMC range of applicability could be improved by a modified intermediate scheme choice or using a single effective PMC scale.

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arXiv2017

Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting

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 the multi-scale approach. In this paper, we present a novel single-scale approach for the PMC, in which a single effective scale is constructed to eliminate all non-conformal $β$-terms up to a given order simultaneously. The PMC single-scale approach inherits the main features of the multi-scale approach; for example, its predictions are scheme-independent, and the pQCD convergence is greatly improved due to the elimination of divergent renormalon terms. As an application of the single-scale approach, we investigate the $e^+e^-$ annihilation cross-section ratio $R_{e^+e^-}$ and the Higgs decay-width $Γ(H \to b \bar{b})$, including four-loop QCD contributions. The resulting predictions are nearly identical to the multi-scale predictions for both the total and differential contributions. Thus in many cases, the PMC single-scale approach PMC-s, which requires a simpler analysis, could be adopted as a reliable substitution for the PMC multi-scale approach for setting the renormalization scale for high-energy processes, particularly when one does not need detailed information at each order. The elimination of the renormalization scale uncertainty increases the precision of tests of the Standard Model at the LHC.

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