arXiv subjects

Xing-Gang Wu

Publications and source records attributed to Xing-Gang Wu.

At least 145 records · Page 8Linked to original sources

arXiv2018

The asymmetries of the $B \to K^* μ^+ μ^-$ decay and the search of new physics beyond the Standard Model

In this paper, we compute the forward-backward asymmetry and the isospin asymmetry of the $B \to K^* μ^+ μ^-$ decay. The $B \to K^*$ transition form factors (TFFs) are key components of the decay. To achieve a more accurate QCD prediction, we adopt a chiral correlator for calculating the QCD light-cone sum rules for those TFFs with the purpose of suppressing the uncertain high-twist distribution amplitudes. Our predictions show that the asymmetries under the Standard Model and the Minimal Supersymmetric Standard Model with minimal flavor violation are close in shape for $q^2 \ge 6~{\rm GeV}^2$ and are consistent with the Belle, LHCb and CDF data within errors. When $q^2 < 2~{\rm GeV}^2$, their predictions behave quite differently. Thus a careful study on the $B \to K^* μ^+ μ^-$ decay within small $q^2$-region could be helpful for searching new physics beyond the Standard Model. As a further application, we also apply the $B \to K^*$ TFFs to the branching ratio and longitudinal polarization fraction of the $B\to K^*ν\barν$ decay within different models.

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arXiv2018

The longitudinal leading-twist distribution amplitude of $J/ψ$ meson within background field theory

We make a detailed study on the $J/ψ$ meson longitudinal leading-twist distribution amplitude $ϕ_{2;J/ψ}^\|$ by using the QCD sum rules within the background field theory. By keeping all the non-perturbative condensates up to dimension-six, we obtain accurate QCD sum rules for the moments $\langleξ_{n;J/ψ}^\|\rangle$. The first three ones are $\langleξ_{2;J/ψ}^\|\rangle=0.083(12)$, $\langleξ_{4;J/ψ}^\|\rangle=0.015(5)$ and $\langleξ_{6;J/ψ}^\|\rangle=0.003(2)$, leading to a single peaked behavior for $ϕ_{2;J/ψ}^\|$ which is sharper than the previous ones around the region of $x\sim0.5$. As an application, we adopt the QCD light-cone sum rules to calculate the $B_c$ meson semileptonic decay $B_c^+ \to J/ψ\ell^+ ν_\ell$. We obtain $Γ(B_c^+ \to J/ψ\ell^+ ν_\ell) = (89.67^{+24.76}_{-19.06}) \times 10^{-15}~{\rm GeV}$ and $\Re(J/ψ\ell^+ ν_\ell) = 0.217^{+0.069}_{-0.057}$, which agree with the next-to-leading order pQCD prediction and the new CDF measurement within errors.

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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

Uncertainties of the $B\to D$ transition form factor from the $D$-Meson Leading-Twist Distribution Amplitude

The $B\to D$ transition form factor (TFF) $f^{B\to D}_+(q^2)$ is determined mainly by the $D$-meson leading-twist distribution amplitude (DA) , $ϕ_{2;D}$, if the proper chiral current correlation function is adopted within the light-cone QCD sum rules. It is therefore significant to make a comprehensive study of DA $ϕ_{2;D}$ and its impact on $f^{B\to D}_+(q^2)$. In this paper, we calculate the moments of $ϕ_{2;D}$ with the QCD sum rules under the framework of the background field theory. New sum rules for the leading-twist DA moments $\left<ξ^n\right>_D$ up to fourth order and up to dimension-six condensates are presented. At the scale $μ= 2 \rm GeV$, the values of the first four moments are: $\left<ξ^1\right>_D = -0.418^{+0.021}_{-0.022}$, $\left<ξ^2\right>_D = 0.289^{+0.023}_{-0.022}$, $\left<ξ^3\right>_D = -0.178 \pm 0.010$ and $\left<ξ^4\right>_D = 0.142^{+0.013}_{-0.012}$. Basing on the values of $\left<ξ^n\right>_D(n=1,2,3,4)$, a better model of $ϕ_{2;D}$ is constructed. Applying this model for the TFF $f^{B\to D}_+(q^2)$ under the light cone sum rules, we obtain $f^{B\to D}_+(0) = 0.673^{+0.038}_{-0.041}$ and $f^{B\to D}_+(q^2_{\rm max}) = 1.124^{+0.053}_{-0.058}$. The uncertainty of $f^{B\to D}_+(q^2)$ from $ϕ_{2;D}$ is estimated and we find its impact should be taken into account, especially in low and central energy region. The branching ratio $\mathcal{B}(B\to Dl\barν_l)$ is calculated, which is consistent with experimental data.

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arXiv2017

Photoproduction of the $B_c^{(*)}$ Meson at the LHeC

We make a detailed study on the photoproduction mechanism of the doubly heavy flavored $B_c^{(*)}$ meson at the purposed Large Hadron Electron Collider (LHeC) within the framework of nonrelativistic QCD. In addition to the photoproduction mechanism via the gluon-induced channel $γ+ g \to B_c^{(*)} + b + \bar{c}$, the extrinsic heavy quark mechanism via the two channels $γ+ c \to B_c^{(*)} + b $ and $γ+ \bar{b} \to B_c^{(*)} + \bar{c}$ has also been studied. Those two extrinsic channels are generally suppressed by the heavy quark distribution functions in proton, which however provide significant contributions in low and intermediate $p_T$ region. A detailed comparison of those channels together with the theoretical uncertainties has been presented. By summing up all the mentioned photoproduction channels, we observe that about $(1.04^{+0.90}_{-0.53})\times 10^{5}$ $B_c$ and $(4.86^{+3.72}_{-2.30})\times 10^{5}$ $B_c^*$ events can be generated at the LHeC in one operation year with the proton-electron collision energy $\sqrt{S}=1.30$ TeV and the luminosity ${\mathcal L}\simeq 10^{33}$ ${\rm cm}^{-2} {\rm s}^{-1}$. Here the errors are for $m_c=1.50\pm0.20$ GeV and $m_b=4.9\pm0.40$ GeV. Thus, in addition to the hadronic experiments, the LHeC shall provide another helpful platform for studying the $B_c^{(*)}$ meson properties, especially to test the extrinsic heavy quark mechanism.

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arXiv2017

Photoproduction of doubly heavy baryon at the LHeC

The photoproduction of doubly heavy baryon, $Ξ_{cc}$, $Ξ_{bc}$ and $Ξ_{bb}$, is predicted within the nonrelativistic QCD at the Large Hadron Electron Collider (LHeC). The $Ξ_{QQ'}$ production via the photon-gluon fusing channel $γ+ g \to \langle{QQ'}\rangle[n] +\bar{Q} +\bar{Q'}$ and the extrinsic heavy quark channel $γ+ Q \to \langle{QQ'}\rangle[n]+\bar{Q'}$ have been considered, where $Q$ or $Q'$ stand for heavy $c$ or $b$ quark and $\langle{QQ'}\rangle[n]$ stands for a $QQ'$ diquark with given spin- and color- configurations $[n]$. The diquark shall fragmentate into $Ξ_{QQ'}$ baryon with high probability. For $Ξ_{cc}$ and $Ξ_{bb}$ production, $[n]$ equals $[^1S_0]_{\textbf{6}}$ (in configurations spin-singlet $^1S_0$-wave and color-sextuplet $\textbf{6}$) or $[^3S_1]_{\bar{\textbf{3}}}$ (in configurations spin-triplet $^3S_1$-wave and color-antitriplet $\bar{\textbf{3}}$) and for $Ξ_{bc}$ production, $[n]$ equals $[^1S_0]_{\bar{\textbf{3}}}$, $[^1S_0]_{\textbf{6}}$, $[^3S_1]_{\bar{\textbf{3}}}$ or $[^3S_1]_{\textbf{6}}$. A detailed comparison of those channels and configurations on total and differential cross sections, together with their uncertainties, is presented. We find the dominate contributions for $Ξ_{QQ'}$ production are from extrinsic heavy quark channel and for $[^3S_1]_{\bar{\textbf{3}}}$ configuration; While other diquark states can also provide sizable contributions to the $Ξ_{QQ'}$ production. As a combination of all the mentioned channels and configurations and by taking $m_c=1.80\pm0.10$ GeV and $m_b=5.1\pm0.20$ GeV, we observe that $(6.70^{+1.40}_{-1.10})\times 10^{3}$ $Ξ_{bb}$, $(8.81^{+3.08}_{-2.20})\times 10^{6}$ $Ξ_{cc}$ and $(4.63^{+1.21}_{-0.92})\times 10^{5}$ $Ξ_{bc}$ events can be generated at the LHeC in one operation year.

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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

Reconsideration of the $B \to K^*$ Transition Form Factors within the QCD Light-Cone Sum Rules

In this paper, we study the $B \to K^*$ transition form factors (TFFs) within the QCD light-cone sum rules (LCSR) approach. Two correlators, i.e. the usual one and the right-handed one, are adopted in the LCSR calculation. The resultant LCSRs for the $B \to K^*$ TFFs are arranged according to the twist structure of the $K^*$-meson light-cone distribution amplitudes (LCDAs), whose twist-2, twist-3 and twist-4 terms behave quite differently by using different correlators. We observe that the twist-4 LCDAs, though generally small, shall have sizable contributions to the TFFs $A_{1/2}$, $V$ and $T_1$, thus the twist-4 terms should be kept for a sound prediction. We also observe that even though different choices of the correlator lead to different LCSRs with different twist contributions, the large correlation coefficients for most of the TFFs indicate that the LCSRs for different correlators are close to each order, not only for their values at the large recoil point $q^2=0$ but also for their ascending trends in whole $q^2$-region. Such a high degree of correlation is confirmed by their application to the branching fraction of the semi-leptonic decay $B \to K^* μ^+ μ^-$. Thus, a proper choice of correlator may inversely provide a chance for probing uncertain LCDAs, i.e. the contributions from those LCDAs can be amplified to a certain degree via a proper choice of correlator, thus amplifying the sensitivity of the TFFs, and hence their related observables, to those LCDAs.

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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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arXiv2016

The $ρ$-meson longitudinal leading-twist distribution amplitude within QCD background field theory

We revisit the $ρ$-meson longitudinal leading-twist distribution amplitude (DA) $ϕ_{2;ρ}^\|$ by using the QCD sum rules approach within the background field theory. To improve the accuracy of the sum rules for its moments $\langleξ_{n;ρ}^\|\rangle$, we include the next-to-leading order QCD correction to the perturbative part and keep all non-perturbative condensates up to dimension-six consistently within the background field theory. The first two moments read $\langle ξ_{2;ρ}^\| \rangle|_{1{\rm GeV}} = 0.241(28)$ and $\langle ξ_{4;ρ}^\| \rangle|_{1{\rm GeV}} = 0.109(10)$, indicating a double humped behavior for $ϕ_{2;ρ}^\|$ at small energy scale. As an application, we apply them to the $B\to ρ$ transition form factors within the QCD light-cone sum rules, which are key components for the decay width $Γ(B\to ρ\ell ν_\ell)$. To compare with the world-average of $Γ(B\to ρ\ell ν_\ell)$ issued by Particle Data Group, we predict $|V_{\rm ub}| = 3.19^{+0.65}_{-0.62}$, which agrees with the BABAR and Omnès parameterization prediction within errors.

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arXiv2016

Application of the Principle of Maximum Conformality to the Hadroproduction of the Higgs Boson at the LHC

We present improved pQCD predictions for Higgs boson hadroproduction at the Large Hadronic Collider (LHC) by applying the Principle of Maximum Conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale $μ_r$ of the QCD coupling $α_s(μ_r)$ is the Higgs mass, and then to vary this choice over the range $1/2 m_H < μ_r < 2 m_H $ in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the non-conformal $β$ terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where pQCD series has large higher order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this \mbox{\it ad hoc} choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading order RG resummed pQCD predictions for Higgs boson hadroproduction which are renormalization-scheme independent and have minimal sensitivity to the choice of the initial renormalization scale. Taking $m_H=125$ GeV, the PMC predictions for the $p p \to H X$ Higgs inclusive hadroproduction cross-sections for various LHC center-of-mass energies and the fiducial cross section $σ_{\rm fid}(pp\to H\toγγ)$ are presented...... The PMC predictions show better agreement with the ATLAS measurements than the LHC-XS predictions which are based on conventional renormalization scale-setting.

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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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arXiv2016

Heavy Pseudoscalar Twist-3 Distribution Amplitudes within QCD Theory in Background Fields

In this paper, we study the properties of the twist-3 distribution amplitude (DA) of the heavy pseudo-scalars such as $η_c$, $B_c$ and $η_b$. New sum rules for the twist-3 DA moments $\left<ξ^n_P\right>_{\rm HP}$ and $\left<ξ^n_σ\right>_{\rm HP}$ up to sixth orders and up to dimension-six condensates are deduced under the framework of the background field theory. Based on the sum rules for the twist-3 DA moments, we construct a new model for the two twist-3 DAs of the heavy pseudo-scalar with the help of the Brodsky-Huang-Lepage prescription. Furthermore, we apply them to the $B_c\toη_c$ transition form factor ($f^{B_c\toη_c}_+(q^2)$) within the light-cone sum rules approach, and the results are comparable with other approaches. It has been found that the twist-3 DAs $ϕ^P_{3;η_c}$ and $ϕ^σ_{3;η_c}$ are important for a reliable prediction of $f^{B_c\toη_c}_+(q^2)$. For example, at the maximum recoil region, we have $f^{B_c\toη_c}_+(0) = 0.674 \pm 0.066$, in which those two twist-3 terms provide $\sim33\%$ and $\sim22\%$ contributions. Also we calculate the branching ratio of the semi-leptonic decay $B_c \toη_c lν$ as $Br(B_c \toη_c lν) = \left( 9.31^{+2.27}_{-2.01} \right) \times 10^{-3}$.

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arXiv2015

Predictions for the Top-Quark Forward-Backward Asymmetry at High Invariant Pair Mass Using the Principle of Maximum Conformality

The D0 collaboration at FermiLab has recently measured the top-quark pair forward-backward asymmetry in $\bar p p \to t \bar{t} X$ reactions as a function of the $t\bar{t} $ invariant mass $M_{t\bar{t}}$. The D0 result for $A_{\rm FB}(M_{t\bar{t}}>650\, {\rm GeV})$ is smaller than $A_{\rm FB}(M_{t\bar{t}})$ obtained for small values of $M_{t\bar{t}}$, which may indicate an "increasing-decreasing" behavior for $A_{\rm FB}(M_{t\bar{t}}>M_{\rm cut})$. This behavior is not explained using conventional renormalization scale-setting, even by a next-to-next-to-leading order (N$^2$LO) QCD calculation -- one predicts a monotonically increasing behavior. In the conventional scale-setting method, one simply guesses a single renormalization scale $μ_r$ for the argument of the QCD running coupling and then varies it over an arbitrary range. However, the conventional method has inherent difficulties. ...... In contrast, if one fixes the scale using the Principle of Maximum Conformality (PMC), the resulting pQCD predictions are renormalization-scheme independent since all of the scheme-dependent $\{β_i\}$-terms in the QCD perturbative series are resummed into the QCD running couplings at each order. ...... In this paper we show that if one applies the PMC to determine the top versus anti-top quark forward-backward asymmetry by properly using the pQCD predictions up to N$^2$LO level, one obtains the predictions without renormalization scheme or scale ambiguities. ...... In addition, the PMC prediction for $A_{\rm FB}(M_{t\bar{t}}> M_{\rm cut})$ shows an "increasing-decreasing" behavior for increasing values of $M_{\rm cut}$ which is not observed in the NLO and N$^2$LO predictions for $A_{\rm FB}(M_{t\bar{t}}> M_{\rm cut})$ with conventional scale-setting. This behavior could be tested by the future more precise measurements at the LHC.

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arXiv2015

$B\to K^$ Transition Form Factors and the Semi-leptonic Decay $B \to K^ μ^+ μ^-$

We present a detailed calculation on the $B\to K^*$ transition form factors (TFFs), $A_{0,1,2}$, $V$ and $T_{1,2,3}$, within the QCD light-cone sum rules (LCSR). To suppress the contributions from high-twist light-cone distribution amplitudes, we adopt a right-handed chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leading-twist distribution amplitude $ϕ_{2;K^*}^\bot$ provides over $90\%$ contribution, thus those TFFs provide good platforms for testing the property of $ϕ_{2;K^*}^\bot$. We suggest a model for $ϕ_{2;K^*}^\bot$, in which two parameters $B_{2;K^*}^\bot$ and $C_{2;K^*}^\bot$ dominantly control its longitudinal distribution. With a proper choice of $B_{2;K^*}^\bot$ and $C_{2;K^*}^\bot$, our predictions on $B\to K^*$ TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the $B$-meson rare decay $B \to K^* μ^+ μ^-$. The predicted differential branching fraction $d{\cal B}/dq^2(B\to K^{*}μ^+μ^-)$ is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable $q^2$-region, we get the branching fraction, ${\cal B}(B\to K^*μ^+μ^-) = \left(1.088^{+0.261}_{-0.205} \right)\times 10^{-6}$, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of $ϕ_{2;K^*}^\bot$.

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arXiv2015

The longitudinal and transverse distributions of the pion wavefunction from the present experimental data on the pion-photon transition form factor

It is noted that the low-energy behavior of the pion-photon transition form factor $F_{πγ}(Q^2)$ is sensitive to the transverse distribution of the pion wavefunction, and its high-energy behavior is sensitive to the longitudinal one. Thus a careful study on $F_{πγ}(Q^2)$ can provide helpful information on the pion wavefunction precisely. In this paper, we present a combined analysis of the data on $F_{πγ}(Q^2)$ reported by the CELLO, the CLEO, the BABAR and the BELLE collaborations. It is performed by using the method of least squares. By using the combined measurements of BELLE and CLEO Collaborations, the pion wavefunction longitudinal and transverse behavior can be fixed to a certain degree, i.e. we obtain $β\in [0.691,0.757] \rm GeV$ and $B \in [0.00,0.235]$ for $P_{χ^2} \geq 90\%$, where $β$ and $B$ are two parameters of a convenient pion wavefunction model whose distribution amplitude can mimic the various longitudinal behavior under proper choice of parameters. We observe that the CELLO, CLEO and BELLE data are consistent with each other, all of which prefers the asymptotic-like distribution amplitude; while the BABAR data prefers a more broad distribution amplitude, such as the CZ-like one.

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arXiv2015

The prompt $J/ψ$ production in Association with a $c\bar{c}$ Pair within the Framework of Non-relativistic QCD via photon-photon collision at the International Linear Collider

We present a systematical study on the prompt $J/ψ$ production in association with a $c\bar{c}$ pair via the process, $γγ\to H(c\bar{c}) +c+\bar{c}$, within the framework of non-relativistic QCD at the future high-energy $e^{+}e^{-}$ collider - International Linear Collider (ILC), including both direct and feed-down contributions. For direct $J/ψ$ production, the states with color-octet channels, especially the $^3P_J^{[8]}$ and $^1S_0^{[8]}$ ones, provide dominant contribution to the production cross-section, which are about fifty-two times over that of the color-singlet one. This is clearly shown by the transverse momentum ($p_t$) and rapidity distributions. The feed-down contribution from $ψ'$ and $χ_{cJ}$ ($J=0,1,2$) is sizable, which is about $20\%$ to the total prompt cross-section. Besides the yields, we also calculate the $J/ψ$ polarization parameter $λ$. In small $p_t$ region, the polarization of the prompt $J/ψ$ is longitudinal due to large contributions through the $^3P_J^{[8]}$ channel, and becomes transverse in high $p_t$ region due to $^3S_1^{[8]}$ channel. Thus the $J/ψ$ production via photon-photon collisions at the ILC shall provide a useful platform for testing the color-octet mechanism.

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