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Xing-Gang Wu

Publications and source records attributed to Xing-Gang Wu.

At least 109 records · Page 6Linked to original sources
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

PMC$_\infty$: Infinite-Order Scale-Setting using the Principle of Maximum Conformality, A Remarkably Efficient Method for Eliminating Renormalization Scale Ambiguities for Perturbative QCD

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.

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arXiv2020

Determination of the top-quark $\overline{\rm MS}$ running mass via its perturbative relation to the on-shell mass with the help of principle of maximum conformality

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 relation and taking the top-quark on-shell mass $M_t=172.9\pm0.4$ GeV as an input, we obtain the renormalization scale-invariant $\overline{\rm MS}$ running mass at the scale $m_t$, e.g., $m_t(m_t)\simeq 162.6\pm 0.4$ GeV, in which the error is the squared average of those from $Δα_s(M_Z)$, $ΔM_t$, and the approximate error from the uncalculated five-loop terms predicted by using the Padé approximation approach.

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arXiv2020

Average speed and its powers $v^n$ of a heavy quark in quarkonia

The typical velocity of a heavy quark in a quarkonium is a widely used quantity, in this paper, based on the relativistic Bethe-Salpeter equation method, we calculate the average values ${\overline{|\boldsymbol{q}|^n}}$ and $ \overline{|\boldsymbol{v}|^n}\equiv v^n$ of a heavy quark in a $S$ wave or $P$ wave quarkonium rest frame, where $\boldsymbol{q}$ and $\boldsymbol{v}$ are the three dimensional momentum and velocity, $n=1,2,3,4$. For a charm quark in $J/ψ$, we obtained $v_{J/ψ}=0.46$, $v^2_{J/ψ}=0.26$, $v^3_{J/ψ}=0.18$, and $v^4_{J/ψ}=0.14$, for a bottom quark in $Υ(1S)$, $v_{Υ(1S)}=0.24$, $v^2_{Υ(1S)}=0.072$, $v^3_{Υ(1S)}=0.025$, and $v^4_{Υ(1S)}=0.010$. The values indicate that ${v^n} >{v^{n_1}}\cdot{v^{n_2}}$, where $n_1+n_2=n$, which is correct for all the charmonia and bottomonia. Our results also show the poor convergence if we make the {speed} expansion in charmonium system, but good for bottomonium. Based on the $v^n$ values and the following obtained relations $v^n_{4S} > v^n_{3S}> v^n_{2S}>v^n_{1S}$, $v^n_{4P} > v^n_{3P}> v^n_{2P}>v^n_{1P}$ and $v^n_{mP}>v^n_{mS}$ ($n,m=1,2,3,4$), we conclude that highly excited quarkonia have larger relativistic corrections than those of the corresponding low excited and ground states, and there are large relativistic corrections in charmonium system.

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arXiv2020

The production of the doubly charmed baryon in deeply inelastic $ep$ scattering at the Large Hadron Electron Collider

In this paper, we carry out a detailed study on the production of the doubly charmed baryon in deeply inelastic $ep$ scattering (DIS) for $Q^2\in[2, 100]~\textrm{GeV}^2$, at the Large Hadron Electron Collider (LHeC) with $E_e=60(140)$ GeV and $E_p=7000$ GeV. To exclude the contributions from the diffractive productions and the $b$ hadron decays, we impose the kinematic cuts $0.3 1~\textrm{GeV}^2$ in the center-of-mass (CM) frame of $γ^{*}p$. Based on the designed LHeC luminosity, by detecting the decay channel $Ξ^{+}_{cc}(Ξ^{++}_{cc}) \to Λ_c^{+}$ with the subsequent decay $Λ_c^{+} \to pK^{-}π^{+}$, we predict that about 1880 (2700) $Ξ^{+}_{cc}$ events and 3750 (5400) $Ξ^{++}_{cc}$ events can be accumulated per year, which signifies the prospect of observing them via the DIS at the forthcoming LHeC. In addition, we also predict the distributions of a rich variety of physical observables in the laboratory frame and the $γ^{*}p$ CM frame, including $Q^2$, $p_t^{2}$, $Y$(rapidity), $p_t^{\star2}$, $Y^{\star}$, $W$, and $z$ distributions, respectively, which can provide helpful references for studying the doubly charmed baryon. In conclusion, we think that in addition to the LHC, the LHeC is also a helpful platform for studying the properties of the doubly charmed baryon.

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arXiv2020

Revisiting the Heavy Vector Quarkonium Leptonic Widths

We revisit the heavy quarkonium leptonic decays $ψ(nS) \to \ell^+\ell^-$ and $Υ(nS) \to \ell^+\ell^-$ using the Bethe-Salpeter method. The emphasis is on the relativistic correction. For the $ψ(1S-5S)$ decays, the relativistic effects are $22^{+3}_{-2}\%$, $34^{+5}_{-5}\%$, $41^{+6}_{-6}\%$, $52^{+11}_{-13}\%$ and $62^{+14}_{-12}\%$, respectively. For the $Υ(1S-5S)$ decays, the relativistic effects are $14^{+1}_{-2}\%$, $23^{+0}_{-3}\%$, $20^{+8}_{-2}\%$, $21^{+6}_{-7}\%$ and $28^{+2}_{-7}\%$, respectively. Thus, the relativistic corrections are large and important in heavy quarkonium leptonic decays, especially for the highly excited charmonium. Our results for $Υ(nS) \to \ell^+\ell^-$ are consistent with the experimental data.

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arXiv2020

The heavy quarkonium inclusive decays using the principle of maximum conformality

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, which satisfies the requirements of renormalization group invariance and eliminates the conventional renormalization scheme and scale ambiguities. Using the PMC single-scale method, we show that the resultant PMC conformal series is renormalization scale independent, and the precision of the $η_Q$ inclusive decay width can be greatly improved. Taking the relativistic correction $\mathcal{O}(α_{s}v^2)$ into consideration, the ratios of the $η_{Q}$ decays to light hadrons or $γγ$ are: $R^{\rm NNLO}_{η_c}|_{\rm{PMC}}=(3.93^{+0.26}_{-0.24})\times10^3$ and $R^{\rm NNLO}_{η_b}|_{\rm{PMC}}=(22.85^{+0.90}_{-0.87})\times10^3$, respectively. Here the errors are for $Δα_s(M_Z) = \pm0.0011$. As a step forward, by applying the Pad$\acute{e}$ approximation approach (PAA) over the PMC conformal series, we obtain approximate NNNLO predictions for those two ratios, e.g. $R^{\rm NNNLO}_{η_c}|_{\rm{PAA+PMC}} =(5.66^{+0.65}_{-0.55})\times10^3$ and $R^{\rm NNNLO}_{η_b}|_{\rm{PAA+PMC}}=(26.02^{+1.24}_{-1.17})\times10^3$. The $R^{\rm NNNLO}_{η_c}|_{\rm{PAA+PMC}}$ ratio agrees with the latest PDG value $R_{η_c}^{\rm{exp}}=(5.3_{-1.4}^{+2.4})\times10^3$, indicating the necessity of a strict calculation of NNNLO terms.

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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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arXiv2020

Next-to-leading order QCD corrections to the production of $B_c$ and $B_c^*$ through $W^+$-boson decays

In this paper, we calculate the total decay widths for the $W^+$-boson decays, $W^+ \to B_c+b+\bar{s}+X$ and $W^+ \to B^*_c+b+\bar{s}+X$, up to next-to-leading order (NLO) accuracy within the framework of the nonrelativistic QCD theory. Both the fixed-order and the fragmentation approaches are adopted to do the calculation. Differential decay widths $dΓ/dz$ and $dΓ/ds_1$ are also given. We find that the NLO corrections are significant in those two $W^+$ decay channels. Our numerical results show that at the LHC, there are about $7.03\times 10^4$ $B_c$-meson events and $5.10\times 10^4$ $B^*_c$-meson events to be produced via the $W^+$-boson decays per operation year.

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arXiv2020

The $D\to ρ$ semileptonic and radiative decays within the light-cone sum rules

The measured branching ratio of the $D$ meson semileptonic decay $D \to ρe^+ ν_e$, which is based on the $0.82~{\rm fb^{-1}}$ CLEO data taken at the peak of $ψ(3770)$ resonance, disagrees with the traditional SVZ sum rules analysis by about three times. In the paper, we show that this discrepancy can be eliminated by applying the QCD light-cone sum rules (LCSR) approach to calculate the $D\to ρ$ transition form factors $A_{1,2}(q^2)$ and $V(q^2)$. After extrapolating the LCSR predictions of these TFFs to whole $q^2$-region, we obtain $1/|V_{\rm cd}|^2 \times Γ(D \to ρe ν_e) =(55.45^{+13.34}_{-9.41})\times 10^{-15}~{\rm GeV}$. Using the CKM matrix element and the $D^0(D^+)$ lifetime from the Particle Data Group, we obtain ${\cal B} (D^0\to ρ^- e^+ ν_e) = (1.749^{+0.421}_{-0.297}\pm 0.006)\times 10^{-3}$ and ${\cal B} (D^+ \to ρ^0 e^+ ν_e) = (2.217^{+0.534}_{-0.376}\pm 0.015)\times 10^{-3}$, which agree with the CLEO measurements within errors. We also calculate the branching ratios of the two $D$ meson radiative processes and obtain ${\cal B}(D^0\to ρ^0 γ)= (1.744^{+0.598}_{-0.704})\times 10^{-5}$ and ${\cal B}(D^+ \to ρ^+ γ) = (5.034^{+0.939}_{-0.958})\times 10^{-5}$, which also agree with the Belle measurements within errors. Thus we think the LCSR approach is applicable for dealing with the $D$ meson decays.

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arXiv2019

The QCD NLO fragmentation functions for $c$ or $\bar{b}$ quark to $B_c$ or $B_c^*$ meson and their application

The fragmentation functions for $c$ or $\bar{b}$ quark to $B_c$ or $B_c^*$ meson are derived up to QCD next-to-leading order (NLO). They are further computed numerically and presented in figures precisely. In order to reach a higher accuracy, we have also tried properly to apply them to estimating the $B_c$ and $B_c^*$ production at a $Z$-factory (an $e^+e^-$ collider running at the energy of the $Z$-boson pole).

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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 $B\to π\ellν_\ell$ semileptonic decay within the LCSR approach under heavy quark effective field theory

The heavy quark effective field theory (HQEFT) provides an effective way to deal with the heavy meson decays. In the paper, we adopt two different correlators to derive the light-cone sum rules of the $B \to π$ transition form factors (TFFs) within the framework of HQEFT. We label those two LCSR results as LCSR-${\cal U}$ and LCSR-${\cal R}$, which are for conventional correlator and right-handed correlator, respectively. We observe that the correlation parameter $|ρ_{\rm RU}|$ for the branching ratio ${\cal B}(B \to πl ν_{l})$ is $\sim 0.85$, implying the consistency of the LCSRs under different correlators. Moreover, we obtain $|V_{\rm ub}|_{{\rm LCSR}-{\cal U}}=(3.45^{+0.28}_{-0.20}\pm{0.13}_{\rm{exp}})\times10^{-3}$ and $|V_{\rm ub}|_{{\rm LCSR}-{\cal R}} =(3.38^{+0.22}_{-0.16} \pm{0.12}_{\rm{exp}})\times10^{-3}$. We then obtain $\mathcal{R}_π|_{{\rm LCSR}-{\cal U}}=0.68^{+0.10}_{-0.09}$ and $\mathcal{R}_π|_{{\rm LCSR}-{\cal R}}=0.65^{+0.13}_{-0.11}$, both of them agree with the Lattice QCD predictions. Thus the HQEFT provides a useful framework for studying the $B$ meson decays. Moreover, by using right-handed correlator, the twist-2 terms shall dominant the TFF $f^+(q^2)$, which approaches over $\sim97\%$ contribution in the whole $q^2$-region; and the large twist-3 uncertainty for the conventional correlator is greatly suppressed. One can thus adopt the LCSR-${\cal R}$ prediction to test the properties of the various models for the pion twist-2 distribution amplitudes.

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arXiv2019

Impacts of the intrinsic charm content of the proton on the $Ξ_{cc}$ hadroproduction at a fixed target experiment at the LHC

In the present paper, we present detailed discussions on the hadronic production of $Ξ_{cc}$ at a fixed target experiment at the LHC (After@LHC). The charm quarks in hadron could be either extrinsic or intrinsic. By using the BHPS model as the intrinsic charm distribution function in proton, we observe that even if by setting the proportion of finding the intrinsic charm in a proton as $A_{\rm in}=1\%$, total cross sections for the $g+c$ and $c+c$ production mechanisms shall be enhanced by nearly two times. Thus the number of $Ξ_{cc}$ events to be generated at the After@LHC can be greatly enhanced. Since the total cross sections and differential distributions for the $Ξ_{cc}$ production at the After@LHC are sensitive to the value of $A_{\rm in}$, the After@LHC could be a good platform for testing the idea of intrinsic charm.

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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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