arXiv subjects

Jian-Ming Shen

Publications and source records attributed to Jian-Ming Shen.

46 records · Page 3Linked to original sources

arXiv2016

The Higgs-Boson Decay $H\to gg$ to Order $α_s^5$ under the mMOM-Scheme

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 total and the separate decay widths are greatly suppressed, and the convergence of perturbative QCD series is improved. By taking the Higgs mass $M_H=125.09\pm 0.21\pm 0.11$ GeV, as recently given by the ATLAS and CMS collaborations, we predict $Γ(H\to gg)|_{\rm mMOM, PMC} = 339.1\pm 1.7^{+4.0}_{-2.4}$ keV, where the first error is for Higgs mass and the second error is the residual scale dependence by varying the initial scale $μ_r\in[M_H/2,4M_H]$.

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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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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

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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arXiv2014

An analysis of $H \to γγ$ up to three-loop QCD corrections

The principle of maximum conformality (PMC) provides a convenient way for setting the optimal renormalization scales for high-energy processes, which can eliminate the conventional renormalization scale error via an order-by-order manner. At present, we make a detailed PMC analysis on the Higgs decay $H\rightarrow γγ$ up to three-loop QCD corrections. As an important point of deriving reliable PMC estimation, it is noted that only those $\{β_i\}$-terms that rightly determine the running behavior of coupling constant via the renormalization group equation should be absorbed into the coupling constant, and those $\{β_i\}$-terms that pertain to the quark mass renormalization and etc. should be kept as a separate. To avoid confusion of separating and absorbing different types of $\{β_i\}$-terms into the coupling constant, we first transform the decay width in terms of top quark $\overline{\rm MS}$ mass into that of on-shell mass and then apply the PMC scale setting. After applying PMC scale setting, the final estimation is conformal and is scheme-independent and scale-independent. Up to three-loop QCD corrections, we obtain a PMC scale $μ^{\rm PMC}_{r}=242.3$ GeV $\sim 2M_H$, which is optimal and highly independent of any choice of initial scale. Thus, we obtain a more accurate scale-independent prediction by taking the Higgs mass as the same as that of ATLAS and CMS measurements, i.e., $Γ(H\rightarrow γγ)|_{\rm ATLAS}=9.504^{+0.226}_{-0.252}$ keV and $Γ(H\rightarrow γγ)|_{\rm CMS}=9.568^{+0.195}_{-0.191}$ keV, where the error is caused by the measured Higgs mass, i.e. the Higgs mass $M_{H}$ is taken as $125.5\pm0.2^{+0.5}_{-0.6}$ GeV for ATLAS and $125.7\pm0.3\pm0.3$ GeV for CMS, respectively.

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arXiv2014

The Higgs boson inclusive decay channels $H \to b\bar{b}$ and $H \to gg$ up to four-loop level

The principle of maximum conformality (PMC) has been suggested to eliminate the renormalization scheme and renormalization scale uncertainties, which are unavoidable for the conventional scale setting and are usually important errors for theoretical estimations. In this paper, by applying PMC scale setting, we analyze two important inclusive Standard Model Higgs decay channels, $H\rightarrow b\bar{b}$ and $H\rightarrow gg$, up to four-loop and three-loop levels accordingly. After PMC scale setting, it is found that the conventional scale uncertainty for these two channels can be eliminated to a high degree. There is small residual initial scale dependence for the Higgs decay widths due to unknown higher-order $\{β_i\}$-terms. Up to four-loop level, we obtain $Γ(H\rightarrow b\bar{b}) = 2.389\pm0.073 \pm0.041$ MeV and up to three-loop level, we obtain $Γ(H\rightarrow gg) = 0.373\pm0.030$ MeV, where the first error is caused by varying $M_H=126\pm4$ GeV and the second error for $H\to b\bar{b}$ is caused by varying the $\overline{\rm MS}$-running mass $m_b(m_b)=4.18\pm0.03$ GeV. Taking $H\to b\bar{b}$ as an example, we present a comparison of three BLM-based scale setting approaches, e.g. the PMC-I approach based on the PMC-BLM correspondence, the $R_δ$-scheme and the seBLM approach, all of which are designed to provide effective ways to identify non-conformal $\{β_i\}$-series at each perturbative order. At four-loop level, all those approaches lead to good pQCD convergence, they have almost the same pQCD series, and their predictions are almost independent on the initial renormalization scale. In this sense, those approaches are equivalent to each other.

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arXiv2013

Next-to-leading order QCD corrections for the charmonium production via the channel $e^+ e^- \to H(|c\bar{c}\rangle) + γ$ round the $Z^0$ peak

In our previous work [2], it has been found that sizable charmonium events via the channel $e^+e^- \to γ^*/Z^0 \to H(|c\bar{c}\rangle) +γ$ can be produced at the suggested super $Z$ factory, where $H(|c\bar{c}\rangle)$ represents the dominant color-singlet $S$-wave and $P$-wave charmonium states $J/ψ$, $η_c$, $h_c$ and $χ_{cJ}$ ($J=0, 1, 2$), respectively. As an important step forward, in the present paper, we present a next-to-leading order (NLO) QCD analysis within the framework of nonrelativistic QCD. In different to the case of $B$ factory in which the single charmonium production is dominated by the channel via a virtual photon, at the super $Z$ factory, its cross-section is dominated by the channel via a $Z^0$ boson. Estimations up to NLO level are done at both the $B$ factory and the super $Z$ factory experimental conditions. We observe that the NLO distributions have the same shapes as those of LO distributions, but their differences are sizable. This indicates that a NLO calculation is necessary and important to achieve a more accurate estimation. Due to $Z^0$ boson resonance effect, at the super $Z$ factory with a high luminosity up to $10^{36}{\rm cm}^{-2}{\rm s}^{-1}$, when summing all the color-singlet states' contribution together, one may observe about $8.0\times10^{4}$ charmonium events via the channel $e^+e^-\to Z^0 \to H(|c\bar{c}\rangle)+γ$ in one operation year. Then, such super $Z$ factory could provide another useful platform to study the charmonium properties, even for the higher charmonium states.

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arXiv2013

Exclusive charmonium production from $e^+ e^-$ annihilation round the $Z^0$ peak

We make a comparative and comprehensive study on the charmonium exclusive productions at the $e^+e^-$ collider with the collision energy either round the $Z^0$-boson mass for a super $Z$ factory or equals to 10.6 GeV for the $B$ factories as Belle and BABAR. We study the total cross sections for the charmonium production via the exclusive processes $e^+e^- \to γ^*/Z^0 \to H_{1}+H_{2}$ and $e^+e^- \to γ^*/Z^0 \to H_{1} +γ$, where $H_{1}$ and $H_{2}$ represent the dominant color-singlet $S$-wave and $P$-wave charmonium states respectively. Total cross sections versus the $e^+e^-$ collision energy $\sqrt{s}$, together with their uncertainties, are presented, which clearly show the relative importance of these channels. At the $B$ factory, the production channels via the virtual $γ^*$ propagator are dominant over the channels via the $Z^0$ propagator by about four orders. While, at the super $Z$ factory, due to the $Z^0$-boson resonance effect, the $Z^0$ boson channels shall provide sizable or even dominant contributions in comparison to the channels via the $γ^*$ propagator. Sizable exclusive charmonium events can be produced at the super $Z$ factory with high luminocity up to $10^{36}{\rm cm}^{-2}{\rm s}^{-1}$, especially for the channel of $e^+e^- \to Z^0 \to H_{1} +γ$, e.g. by taking $m_c=1.50\pm0.20$ GeV, we shall have $(5.0^{+0.8}_{-0.6})\times10^4$ $J/ψ$, $(7.5^{+1.1}_{-0.9})\times10^3$ $η_c$, $(6.2^{+3.3}_{-1.9})\times10^3$ $h_{c}$, $(3.1^{+1.7}_{-0.9})\times10^2$ $χ_{c0}$, $(2.2^{+1.0}_{-0.4})\times10^3$ $χ_{c1}$, and $(7.7^{+4.1}_{-2.4})\times10^2$ $χ_{c2}$ events by one operation year. Thus, in addition to the $B$ factories as BABAR and Belle, such a super $Z$ factory shall provide another useful platform for studying the heavy quarkonium properties and for testing QCD theories.

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arXiv2013

Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy

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 example, by taking the Fried-Yennie gauge, we obtain $ω_{\rm MOM}^{\rm PMC}(Q^{2},0)\in [0.149,0.176]$ for $Q^2\in[1,100]\;{\rm GeV}^2$. This is a good property to apply to the high-energy phenomenology. Further more, to compare with the data, it is found that the physical ${\rm MOM}$-scheme is more reliable than the $\overline{\rm MS}$-scheme. The ${\rm MOM}$-scheme is gauge dependent, which can also be greatly suppressed after PMC scale setting. We discuss the MOM-scheme gauge dependence for the Pomeron intercept by adopting three gauges, i.e. the Landau gauge, the Feynman gauge and the Fried-Yennie gauge, and we obtain $ω_{\rm MOM}^{\rm PMC}(Q^{2}=15\;{\rm GeV}^2,0) = 0.166^{+0.010}_{-0.017}$; i.e. about $10\%$ gauge dependence is observed. We apply the BFKL Pomeron intercept to the photon-photon collision process, and compare the theoretical predictions with the data from the OPAL and L3 experiments.

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arXiv2013

$J/ψ+χ_{cJ}$ Production at the $B$ Factories under the Principle of Maximum Conformality

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 sections for the double charmonium production process, $e^{+} + e^{-} \to J/ ψ(ψ') + χ_{cJ}$ with $(J=0,1,2)$. The running behavior for the coupling constant, governed by the PMC scales, are determined exactly for the specific processes. We compare our predictions with the measurements at the $B$ factories, BABAR and Belle, and the theoretical estimations obtained in the literature. Because the non-conformal terms are different for various polarized and unpolarized cross sections, the PMC scales of these cross sections are different in principle. It is found that all the PMC scales are almost independent of the initial choice of renormalization scale. Thus, the large renormalization scale uncertainty usually adopted in the literature up to $sim40%$ at the NLO level, obtained from the conventional scale setting, for both the polarized and the unpolarized cross sections are greatly suppressed. It is found that the charmonium production is dominated by J=0 channel. After PMC scale setting, we obtain $σ(J/ψ+χ_{c0}) = 12.25^{+3.70}_{-3.13}$ fb and $σ(ψ'+χ_{c0}) =5.23^{+1.56}_{-1.32}$ fb,......

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