arXiv subjects

Tao Zhong

Publications and source records attributed to Tao Zhong.

At least 91 records · Page 5Linked to original sources

arXiv2022

The ratio $\mathcal{R}(D_s)$ for $B_s \to D_s \ellν_\ell$ by using the QCD light-cone sum rules within the framework of heavy quark effective field theory

In the paper, we study the $B_s\to D_s$ transition form factors by using the light-cone sum rules within the framework of heavy quark effective field theory. We adopt a chiral current correlation function to do the calculation, the resultant transition form factors $f_+^{B_s\to D_s}(q^2)$ and $f_0^{B_s\to D_s}(q^2)$ are dominated by the contribution of $D_s$-meson leading-twist distribution amplitude, while the contributions from less certain $D_s$-meson twist-3 distribution amplitudes are greatly suppressed. At the largest recoil point, we obtain $f_{+,0}^{B_s \to D_s}(0)=0.533^{+0.112}_{-0.094}$. By further extrapolating the transition form factors into all the physically allowable $q^2$ region with the help of the $z$-series parametrization approach, we calculate the branching fractions $\mathcal{B}(B_s \to D_s \ell^\prime ν_{\ell^\prime})$ with $(\ell^\prime= e,μ)$ and $\mathcal{B}(B_s \to D_s τν_τ)$, which gives $\mathcal{R}(D_s)=0.334\pm 0.017$.

hep-ph↗

arXiv2022

Investigating the ratio of CKM matrix elements $|V_{ub}|/|V_{cb}|$ from semileptonic decay $B_s^0\to K^-μ^+ν_μ$ and kaon twist-2 distribution amplitude

In this paper, we calculate the ratio of Cabibbo-Kobayashi-Maskawa matrix elements, $|V_{ub}|/|V_{cb}|$, based on the semileptonic decay $B_s^0\to K^-μ^+ν_μ$. Its key component, the $B_s\to K$ transition form factor $f^{B_s\to K}_+(q^2)$, is studied within the QCD light-cone sum rules approach by using a chiral correlator. The derived $f^{B_s\to K}_+(q^2)$ is dominated by the leading-twist part, and to improve its precision, we construct a new model for the kaon leading-twist distribution amplitude $ϕ_{2;K}(x,μ)$, whose parameters are fixed by using the least squares method with the help of the moments calculated by using the QCD sum rules within the background field theory. The first four moments at the initial scale $μ_0 = 1~{\rm GeV}$ are, $\langle ξ^1\rangle _{2;K} = -0.0438^{+0.0053}_{-0.0075}$, $\langle ξ^2\rangle _{2;K} = 0.262 \pm 0.010$, $\langle ξ^3\rangle _{2;K} = -0.0210^{+0.0024}_{-0.0035}$ and $\langle ξ^4\rangle _{2;K} = 0.132 \pm 0.006$, respectively. And their corresponding Gegenbauer moments are, $a^{2;K}_1 = -0.0731^{+0.0089}_{-0.0124}$, $a^{2;K}_2 = 0.182^{+0.029}_{-0.030}$, $a^{2;K}_3 = -0.0114^{+0.0008}_{-0.0016}$ and $a^{2;K}_4 = 0.041^{-0.003}_{+0.005}$, respectively. At the large recoil region, we obtain $f^{B_s\to K} _+ (0) = 0.270^{+0.022}_{-0.030}$. By extrapolating $f^{B_s\to K}_+(q^2)$ to all the physical allowable region, we obtain a $|V_{ub}|$-independent decay width for the semileptonic decay $B_s^0\to K^-μ^+ν_μ$, $5.626^{+1.271}_{-0.864} \times 10^{-12}\ {\rm GeV}$, which then leads to $|V_{ub}|/|V_{cb}| = 0.072\pm0.005$.

hep-ph↗

arXiv2021

$η^{(\prime)}$-meson twist-2 distribution amplitude within QCD sum rule approach and its application to the semi-leptonic decay $ D_s^+ \toη^{(\prime)}\ell^+ ν_\ell$

In this paper, we make a detailed discussion on the $η$ and $η'$-meson leading-twist light-cone distribution amplitude $ϕ_{2;η^{(\prime)}}(u,μ)$ by using QCD sum rules approach under the background field theory. Taking both the non-perturbative condensates up to dimension-six and NLO QCD corrections to the perturbative part, its first three moments $\langleξ^n_{2;η^{(\prime)}}\rangle|_{μ_0} $ with $n = (2,4,6)$ at initial scale $μ_0 = 1$ GeV can be determined. e.g. $\langleξ_{2;η}^2\rangle|_{μ_0} =0.231_{-0.013}^{+0.010}$, $\langleξ_{2;η}^4 \rangle|_{μ_0} =0.109_{-0.007}^{+0.007}$, and $\langleξ_{2;η}^6 \rangle|_{μ_0} =0.066_{-0.006}^{+0.006}$ for $η$-meson, $\langleξ_{2;η'}^2\rangle|_{μ_0} =0.211_{-0.017}^{+0.015}$, $\langleξ_{2;η'}^4 \rangle|_{μ_0} =0.093_{-0.009}^{+0.009}$, and $\langleξ_{2;η'}^6 \rangle|_{μ_0} =0.054_{-0.008}^{+0.008}$ for $η'$-meson. Next, we calculate $D_s\toη^{(\prime)}$ TFFs $f^{η^{(\prime)}}_+(q^2)$ within QCD light-cone sum rules approach up to NLO level. The values at large recoil region are $f^η_+(0) = 0.476_{-0.036}^{+0.040}$ and $f^{η'}_+(0) = 0.544_{-0.042}^{+0.046}$. After extrapolating TFFs to the allowable physical regions within the series expansion, we obtain the branching fractions of the semi-leptonic decay, i.e. $D_s^+\toη^{(\prime)}\ell^+ ν_\ell$, i.e. ${\cal B}(D_s^+\toη^{(\prime)} e^+ν_e)=2.346_{-0.331}^{+0.418}(0.792_{-0.118}^{+0.141})\times10^{-2}$ and ${\cal B}(D_s^+\toη^{(\prime)} μ^+ν_μ)=2.320_{-0.327}^{+0.413}(0.773_{-0.115}^{+0.138})\times10^{-2}$ for $\ell = (e, μ)$ channels respectively. And in addition to that, the mixing angle for $η-η'$ with $φ$ and ratio for the different decay channels ${\cal R}_{η'/η}^\ell$ are given, which show good agreement with the recent BESIII measurements.

hep-ph↗

arXiv2021

An improved light-cone harmonic oscillator model for the pionic leading-twist distribution amplitude

In this paper, we study the pion leading-twist distribution amplitude $ϕ_{2;π}(x,μ)$ by improving the traditional light-cone harmonic oscillator model within the reconstruction of the function $φ_{2;π}(x)$. In order to constraining the model parameters, we calculate its moments $\langleξ^n\rangle_{2;π}|_μ$ in the framework of QCD background field theory sum rule (BFTSR) up to $10^{\rm th}$ order. Considering the fact that the sum rule of the $0^{\rm th}$ moment $\langleξ^0\rangle_{2;π}|_μ$ cannot be normalized, we suggest a more reasonable sum rule formula for $\langleξ^n\rangle_{2;π}|_μ$. Then, we obtain the values of $\langleξ^n\rangle_{2;π}|_{μ_0}$ with $n=(2,4,6,8,10)$ at the initial scale $μ_0 = 1~{\rm GeV}$. The first two moments are: $\langle ξ^2\rangle_{2;π}|_{μ_0} = 0.271 \pm 0.013$, $\langleξ^4\rangle_{2;π}|_{μ_0} = 0.138 \pm 0.010$; and the corresponding Gegenbauer moments are $a^{2;π}_2(μ_0) = 0.206 \pm 0.038$, $a^{2;π}_4(μ_0) = 0.047 \pm 0.011$, respectively. After fitting the moments $\langleξ^n\rangle_{2;π}|_μ$, we obtained the appropriate model parameters by using the least square method. The resultant behavior for twist-2 pion DA is more closely to the AdS/QCD and lattice result, but is narrower than that by Dyson-Schwinger equation. Furthermore, we calculate the pion-photon transition form factors (TFF) and $B\toπ$ TFF within light-cone sum rule approach, which are conform with experimental and theoretical results.

hep-ph↗

arXiv2021

The $D_s$-meson leading-twist distribution amplitude within the QCD sum rules and its application to the $B_s \to D_s$ transition form factor

We make a detailed study on the $D_s$ meson leading-twist LCDA $ϕ_{2;D_s}$ by using the QCD sum rules within the framework of the background field theory. To improve the precision, its moments $\langle ξ^n\rangle _{2;D_s}$ are calculated up to dimension-six condensates. At the scale $μ= 2{\rm GeV}$, we obtain: $\langle ξ^1\rangle _{2;D_s}= -0.261^{+0.020}_{-0.020}$, $\langle ξ^2\rangle _{2;D_s} = 0.184^{+0.012}_{-0.012}$, $\langle ξ^3\rangle _{2;D_s} = -0.111 ^{+0.007}_{-0.012}$ and $\langle ξ^4\rangle _{2;D_s} = 0.075^{+0.005}_{-0.005}$. Using those moments, the $ϕ_{2;D_s}$ is then constructed by using the light-cone harmonic oscillator model. As an application, we calculate the transition form factor $f^{B_s\to D_s}_+(q^2)$ within the light-cone sum rules (LCSR) approach by using a right-handed chiral current, in which the terms involving $ϕ_{2;D_s}$ dominates the LCSR. It is noted that the extrapolated $f^{B_s\to D_s}_+(q^2)$ agrees with the Lattice QCD prediction. After extrapolating the transition form factor to the physically allowable $q^2$-region, we calculate the branching ratio and the CKM matrix element, which give $\mathcal{B}(\bar B_s^0 \to D_s^+ \ellν_\ell) = (2.03^{+0.35}_{-0.49}) \times 10^{-2}$ and $|V_{cb}|=(40.00_{-4.08}^{+4.93})\times 10^{-3}$.

hep-ph↗

arXiv2020

Human Segmentation with Dynamic LiDAR Data

Consecutive LiDAR scans compose dynamic 3D sequences, which contain more abundant information than a single frame. Similar to the development history of image and video perception, dynamic 3D sequence perception starts to come into sight after inspiring research on static 3D data perception. This work proposes a spatio-temporal neural network for human segmentation with the dynamic LiDAR point clouds. It takes a sequence of depth images as input. It has a two-branch structure, i.e., the spatial segmentation branch and the temporal velocity estimation branch. The velocity estimation branch is designed to capture motion cues from the input sequence and then propagates them to the other branch. So that the segmentation branch segments humans according to both spatial and temporal features. These two branches are jointly learned on a generated dynamic point cloud dataset for human recognition. Our works fill in the blank of dynamic point cloud perception with the spherical representation of point cloud and achieves high accuracy. The experiments indicate that the introduction of temporal feature benefits the segmentation of dynamic point cloud.

cs.CV↗

arXiv2020

Branching fractions and polarizations of $D\to V(ω,ρ, K^*) \ell ν_\ell$ within QCD LCSR

In this paper, we make a detailed study about the $D\to V$ helicity form factors (HFFs) within the framework of QCD light-cone sum rule (LCSR) up to twist-4 accuracy. After extrapolating the LCSR predictions of HFFs to the whole physical $q^2$-region, we get the longitudinal, transverse and total $|V_{cq}|$-independent decay widths of semileptonic decay $D\to V\ell^+ν_\ell$. Meanwhile, the branching fractions of these decays are also obtained by using the $D^0(D^+)$-meson lifetime, which agree well with the BES-III results within errors. As a further step, we also investigate the differential and mean predictions for charged lepton (vector meson) polarization in the final state $P_{\rm L,T}^\ell$ ($F_{\rm L,T}^\ell$), the forward-backward asymmetry ${\cal A}_{\rm FB}^\ell$, and the lepton-side convexity parameters ${\cal C}_{\rm F}^\ell$. Our predictions are consistent with Covariant Confining Quark Model results within the errors. Thus, we think the LCSR approach for HFFs is applicable for dealing with the $D$-meson semileptonic decays.

hep-ph↗

arXiv2020

Multi-Site Infant Brain Segmentation Algorithms: The iSeg-2019 Challenge

To better understand early brain growth patterns in health and disorder, it is critical to accurately segment infant brain magnetic resonance (MR) images into white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). Deep learning-based methods have achieved state-of-the-art performance; however, one of major limitations is that the learning-based methods may suffer from the multi-site issue, that is, the models trained on a dataset from one site may not be applicable to the datasets acquired from other sites with different imaging protocols/scanners. To promote methodological development in the community, iSeg-2019 challenge (http://iseg2019.web.unc.edu) provides a set of 6-month infant subjects from multiple sites with different protocols/scanners for the participating methods. Training/validation subjects are from UNC (MAP) and testing subjects are from UNC/UMN (BCP), Stanford University, and Emory University. By the time of writing, there are 30 automatic segmentation methods participating in iSeg-2019. We review the 8 top-ranked teams by detailing their pipelines/implementations, presenting experimental results and evaluating performance in terms of the whole brain, regions of interest, and gyral landmark curves. We also discuss their limitations and possible future directions for the multi-site issue. We hope that the multi-site dataset in iSeg-2019 and this review article will attract more researchers on the multi-site issue.

eess.IV↗

arXiv2018

The Ratio $\mathcal{R}(D)$ and the $D$-meson Distribution Amplitude

In this paper, we calculate the $B\to D$ transition form factors (TFFs) within the light-cone sum rules (LCSR) and predict the ratio $\mathcal{R}(D)$. More accurate $D$-meson distribution amplitudes (DAs) are essential to get a more accurate theoretical prediction. We construct a new model for the twist-3 DAs $ϕ^p_{3;D}$ and $ϕ^σ_{3;D}$ based on the QCD sum rules under the background field theory for their moments as we have done for constructing the leading-twist DA $ϕ_{2;D}$. As an application, we observe that the twist-3 contributions are sizable in whole $q^2$-region. Taking the twist-2 and twist-3 DAs into consideration, we obtain $f^{B\to D}_{+,0}(0) = 0.659^{+0.029}_{-0.032}$. As a combination of the Lattice QCD and the QCD LCSR predictions on the TFFs $f^{B\to D}_{+,0}(q^2)$, we predict $\mathcal{R}(D) = 0.320^{+0.018}_{-0.021}$, which improves is about $1.5σ$ deviation from the HFAG average of the Belle and BABAR data. At present the data are still of large errors, and we need further accurate measurements of the experiment to confirm whether there is signal of new physics from the ratio $\mathcal{R}(D)$.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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 $Br(B_c \toη_c lν) = \left( 9.31^{+2.27}_{-2.01} \right) \times 10^{-3}$.

hep-ph↗

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 $ϕ_{2;K^*}^\bot$.

hep-ph↗

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.

hep-ph↗

arXiv2014

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

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

hep-ph↗

arXiv2014

Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory

We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex $(z\cdot \tensor{D})^n$ of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain $\left<ξ^2\right>|_{\rm 1\;GeV} = 0.338 \pm 0.032$, $\left<ξ^4\right>|_{\rm 1\;GeV} = 0.211 \pm 0.030$ and $\left<ξ^6\right>|_{\rm 1\;GeV} = 0.163 \pm 0.030$. It is shown that the dimension-six condensates shall provide sizable contributions to the pion DA moments. We show that the first Gegenbauer moment of the pion leading-twist DA is $a^π_2|_{\rm 1\;GeV} = 0.403 \pm 0.093$, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.

hep-ph↗