arXiv subjects

Shan Cheng

Publications and source records attributed to Shan Cheng.

At least 37 records · Page 2Linked to original sources

arXiv2020

The pion light-cone distribution amplitude from the pion electromagnetic form factor

We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor $F_π(Q^2)$ and the integrated modulus of the timelike form factor. For $F_π(Q^2)$, the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients $a_{2,4,6,...}$ (Gegenbauer moments) from this equation, employing the measured pion timelike form factor. For the exploratory fit we use the data of the BaBar collaboration. The results definitely exclude the asymptotic twist-2 distribution amplitude. Also the model with a single $a_2\neq 0$ is disfavoured by the fit. Considering the models with $a_{n>2}\neq 0$, we find that the fitted values of the second and fourth Gegenbauer moments cover the intervals $a_2 (1 \mbox{GeV}) = (0.22 - 0.33) $, $a_4 (1 \mbox{GeV}) = (0.12 - 0.25) $. The higher moments starting from $a_{8}$ are consistent with zero, albeit with large uncertainties. The spacelike pion form factor obtained in two different ways, from the dispersion relation and from the light-cone sum rule, agrees, within uncertainties, with the measurement by the Jefferson Lab $F_π$ collaboration.

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arXiv2020

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

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

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arXiv2019

Pion and Kaon form factors in the perturbative QCD approach

We present the most accurate calculation for the pion and kaon electromagnetic form factors in the framework of perturbative QCD, where the power corrections up to twist-4 of the meson distribution amplitudes and the next-to-leading-order QCD corrections up to subleading power are included. In order to guarantee the gauge invariance of the meson to vacuum matrix element, we take into account both assignments with the lowest Fock state and the high Fock state with an additional valence gluon. Our results confirm the power behaviour of the twist expansion and show the chiral enhancement effect at subleading power in the PQCD approach. We also estimate the $\mathrm{SU(3)}$ asymmetry for the kaon and pion form factors and find that it is smaller than $30 \%$.

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arXiv2019

$Z \to π^+π^-, K^+K^-$: A touchstone of the PQCD approach

We study two rare decays, $Z \to π^+π^-$ and $K^+K^-$, in the perturbative QCD approach up to the next-to-leading order of the strong coupling and the leading power of $1/m_Z$, $m_Z$ being the $Z$ boson mass. The branching ratios $\mathcal{B}(Z\to π^+π^-) = (0.83 \pm 0.02 \pm 0.02 \pm 0.04)\times 10^{-12}$ and $\mathcal{B}(Z\to K^+K^-) = (1.74^{+0.03}_{-0.05} \pm 0.04 \pm 0.02)\times 10^{-12}$ are obtained and can be measured at a tera-$Z$ factory. Because the subleading-power contributions to the branching ratios are negligible, and the leading one does not depend on any free parameter, the two channels can serve as a touchstone for the applicability of the perturbative QCD approach.

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arXiv2019

Dipion light-cone distribution amplitudes and $B \to ππ$ form factors

We suggest to update the expansion coefficients of 2$π$DAs with the distribution amplitudes of light mesons evaluated from lattice QCD, with which we revisit $\overline{B}^0 \to π^+π^0$ transition form factors from light-cone sum rules approach and extend the predictions from the threshold of dipion invariant mass to high energies with including the resonance intervals. We also derive $B^- \to π^0π^0$ transition form factors with the isoscalar dipion final state, serving as the supplement to the isovector ones to complete the set of light-cone sum rules prediction of $B \to ππ$ form factors. Our numerics shows that the lowest resonance gives the dominant contribution to $P-$wave form factors, while the resonance contribution in $S-$wave is not so salient.

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arXiv2018

Rho-pion transition form factors in the $k_T$ factorization formulism revisited

We revisit the evaluations for the spacelike and timelike $ρπ$ transition form factors $F_{ρπ}(Q^2)$ and $G_{ρπ}(Q^2)$ with the inclusion of the the next-to-leading order (NLO) QCD contributions in the framework of the $k_T$ factorization theorem. The infrared divergence is regularized by the transversal momentum carried by external valence quarks, and ultimately absorbed into the meson wave functions. In the region of $ Q^2 \leqslant 2 \, \textrm{GeV}^2 $, where PQCD factorization apporach applicable, the NLO contribution can bring no larger than $ 35\%$ enhancement to the spacelike form factor $F_{ρπ}(Q^2)$. For the timelike form factor derived under the kinematic exchanging symmetry, this contribution is also under control when the momentum transfer squared is large enough. We also prolong our prediction into the small $Q^2$ region by taking the Lattice QCD results into account, and subsequently obtain the coupling $g_{ρπγ} = G_{ρπ}(0)=0.596$.

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arXiv2017

Timelike-helicity $B\to ππ$ form factor from light-cone sum rules with dipion distribution amplitudes

We complete the set of QCD light-cone sum rules for $B\to ππ$ transition form factors, deriving a new sum rule for the timelike-helicity form factor $F_t$ in terms of dipion distribution amplitudes. This sum rule, in the leading twist-2 approximation, is directly related to the pion vector form factor. Employing a relation between $F_t$ and other $B\to ππ$ form factors we obtain also the longitudinal-helicity form factor $F_0$. In this way, all four (axial-)vector $B\to ππ$ form factors are predicted from light-cone sum rules with dipion distribution amplitudes. These results are valid for small dipion masses with large momentum.

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arXiv2017

$B\toππ$ Form Factors from Light-Cone Sum Rules with $B$-meson Distribution Amplitudes

We study $B\toππ$ form factors using QCD light-cone sum rules with $B$-meson distribution amplitudes. These form factors describe the semileptonic decay $B\to ππ\ell\barν_{\ell}$, and constitute an essential input in $B\to ππ\ell^+\ell^-$ and $B\to πππ$ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the $P$-wave $\bar{B}^0\to π^+π^0$ form factors with the time-like pion vector form factor are related to universal $B$-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for $B\to ρ$ form factors in the limit of $ρ$-dominance with zero width, thus providing a systematics for so-far-unaccounted corrections to $B\toρ$ transitions. Using data for the pion vector form factor, we estimate finite width-effects and the contribution of excited $ρ$-resonances to the $B\toππ$ form factors. We find that these contributions amount up to $\sim 20\%$ in the small dipion mass region where they can be effectively regarded as a nonresonant ($P$-wave) background to the $B\toρ$ transition.

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arXiv2017

Revisiting the factorization theorem for $ργ^{*} \to π(ρ)$ at twist 3

We revisit the proof of the perturbative QCD factorization for the exclusive processes $ργ^{\star} \to π(ρ)$ at the two-parton twist-3 level. It is pointed out that the residual collinear divergences observed in the literature, which break the factorization of the above processes at the considered accuracy, are attributed to the improper insertion of the Fierz identity for factorizing the fermion flow. We show that the factorization theorem indeed holds at the two-parton twist-3 level after the mishandling is corrected.

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arXiv2016

The perturbative QCD factorization of $ργ^{\star} \to ρ$

In this paper we firstly demonstrate step by step that the factorization hypothesis is valid at the next-to-leading order (NLO) for the exclusive process $ργ^{\star} \to ρ$ by employing the collinear factorization approach, and then extend this proof to the case of the $k_T$ factorization by taking into account the transversal momentum of the light external quark (anti-quark) lines in the $ρ$ meson. At the NLO level, we then show that the soft divergences from different sub-diagrams will be canceled each other in the quark level, while the remaining collinear divergences can be absorbed into the NLO meson wave functions. The full NLO amplitudes can therefore be factorized as the convolution of the NLO wave functions $ Φ^{(1)}_ρ$ and the infrared-finite leading order (LO) hard kernels $G^0_{X,IJ,kl}$ in the $k_T$ factorization. We also write down the polarized NLO $ρ$ meson wave functions in the form of nonlocal hadron matrix elements with the gauge factor integral path deviating from the light cone. These NLO $ρ$ meson wave functions can be used to calculate the NLO hard corrections to some relevant exclusive processes, such as $B \to ρ$ transition.

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arXiv2015

The $ργ^* \to π(ρ)$ transition form factors in the Perturbative QCD factorization approach

In this paper, we studied the $ργ^* \to π$ and $ργ^*\to ρ$ transition processes and made the calculations for the $ρπ$ transition form factor $Q^4 F_{ρπ}(Q^2)$ and the $ρ$ meson electromagnetic form factors, $F_{\rm LL, LT,TT}(Q^2)$ and $F_{1,2,3}(Q^2)$, by employing the perturbative QCD (PQCD) factorization approach. For the $ργ^* \to π$ transition, we found that the contribution to form factor $Q^4 F_{ρπ}(Q)$ from the term proportional to the distribution amplitude combination $ϕ^T_ρ(x_1)ϕ^P_π(x_2)$ is absolutely dominant, and the PQCD predictions for both the size and the $Q^2$-dependence of this form factor $Q^4 F_{ρπ}(Q^2)$ agree well with those from the extended ADS/QCD models or the light-cone QCD sum rule. For the $ργ^* \to ρ$ transition and in the region of $Q^2\geq 3$ GeV$^2$, further more, we found that the PQCD predictions for the magnitude and their $Q^2$-dependence of the $F_1(Q^2)$ and $F_2(Q^2)$ form factors agree well with those from the QCD sum rule, while the PQCD prediction for $F_3(Q^2)$ is much larger than the one from the QCD sum rule.

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arXiv2015

Time-like pion electromagnetic form factors in $k_{T}$ factorization with the Next-to-leading-order twist-3 contribution

We calculate the time-like pion electromagnetic form factor in the $k_T$ factorization formalism with the inclusion of the next-to-leading-order(NLO) corrections to the leading-twist and sub-leading-twist contributions. It's found that the total NLO correction can enhance (reduce) the magnitude (strong phase) of the leading order form factor by $20\% - 30\%$ ( $< 15^o$) in the considered invariant mass squared $q^2 > 5$ GeV$^2$, and the NLO twist-3 correction play the key role to narrow the gap between the pQCD predictions and the measured values for the time-like pion electromagnetic form factor.

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arXiv2015

The NLO contributions to the scalar pion form factors and the ${\cal O}(α_s^2)$ annihilation corrections to the $B\to ππ$ decays

In this paper, by employing the $k_{T}$ factorization theorem, we made the first calculation for the space-like scalar pion form factor $Q^2 F(Q^2)$ at the leading order (LO) and the next-to-leading order (NLO) level, and then found the time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ by analytic continuation from the space-like one. From the analytical evaluations and the numerical results, we found the following points: (a) the NLO correction to the space-like scalar pion form factor has an opposite sign with the LO one but is very small in magnitude, can produce at most $10\%$ decrease to LO result in the considered $Q^2$ region; (b) the NLO time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ describes the ${\cal O}(α_s^2)$ contribution to the factorizable annihilation diagrams of the considered $B \to ππ$ decays, i.e. the NLO annihilation correction; (c) the NLO part of the form factor $F'^{(1)}_{\rm a,I}$ is very small in size, and is almost independent with the variation of cutoff scale $μ_0$, but this form factor has a large strong phase around $-55^\circ$ and may play an important role in producing large CP violation for $B\to ππ$ decays; and (d) for $B^0 \to π^+π^-$ and $ π^0π^0$ decays, the newly known NLO annihilation correction can produce only a very small enhancement to their branching ratios, less than $3\%$ in magnitude, and therefore we could not interpret the well-known $ππ$-puzzle by the inclusion of this NLO correction to the factorizable annihilation diagrams.

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arXiv2014

The perturbative QCD factorization of $ργ^{\star} \to π$

In this paper, we firstly varify that the factorization hypothesis is valid for the exclusive process $ργ^{\star} \to π$ at the next-to-leading order (NLO) with the collinear factorization approach, and then extend this proof to the case of the $k_T$ factorization approach. We particularly show that at the NLO level, the soft divergences in the full quark level calculation could be canceled completely as for the $πγ^{\star} \to π$ process where only the pseudoscalar $π$ meson involved, and the remaining collinear divergences can be absorbed into the NLO hadron wave functions. The full amplitudes can be factorized as the convolution of the NLO wave functions and the infrared-finite hard kernels with these factorization approaches. We also write out the NLO meson distribution amplitudes in the form of nonlocal matrix elements.

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arXiv2014

The semileptonic decays of $B/B_s$ meson in the perturbative QCD approach: A short review

In this short review, we present the current status about the theoretical and experimental studies for some important semileptonic decays of $B/B_s$ mesons. We firstly gave a brief introduction for the experimental measurements for $B/B_s \to P (l^+l^-, l^-\barν_l, ν\barν)$ decays, the BaBar's $R(D)$ and $R(D^*)$ anomaly, the $P_5^\prime$ deviation for $B^0 \to K^{*0} μ^+ μ^-$ decay. We then made a careful discussion about the evaluations for the relevant form factors in the light-cone QCD sum rule (LCSRs), the heavy quark effective theory, and the perturbative QCD factorization approach. By using the form factors calculated in the perturbative (pQCD) approach, we then calculate and show the pQCD predictions for the decay rates of many semileptonic decays of $B/B_s$ mesons. We also made careful phenomenological analysis for these pQCD predictions and found, in general, the following points: (a) For all the considered $B/B_s$ semileptonic decays, the next-to-leading order (NLO) pQCD predictions for their decay rates agree well with the data and those from other different theoretical methods; (b) For $R(D)$ and $R(D^*)$, the pQCD predictions agree very well with the data, the BaBar's anomaly of $R(D^{(*)})$ are therefore explained successfully in the standard model by employing the pQCD approach; and (c) We defined several new ratios $R_D^{l,τ}$ and $R_{D_s}^{l,τ}$, they may be more sensitive to the QCD dynamics which controls the $B/B_s \to (D^{(*)},D_s^{(*)})$ transitions than the old ratios, we therefore strongly suggest LHCb and the forthcoming Super-B experiments to measure these new ratios.

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arXiv2014

$B\to ππ$ decays and effects of the next-to-leading order contributions

In this paper we perform a systematic study for the three $B \to (π^+π^-,π^+π^0,π^0π^0)$ decays in the perturbative QCD (pQCD) factorization approach with the inclusion of all currently known next-to-leading order (NLO) contributions from various sources. We found that (a) for the CP-averaged decay rates $Br(B^0\to π^+π^-)$ and $Br(B^+\to π^+π^0)$, the NLO pQCD predictions agree with the data within one standard dviation; (b) for $Br(B^0\to π^0π^0)$, however, although the NLO contributions can provide a $\sim 100\%$ enhancement to the leading order (LO) result, it is still not large enough to interpret the data; (c) for the CP-violating asymmetries of $B^0\to π^+π^-$ decay, the central values of the NLO PQCD predictions agree with the data; and (d) we also examined the relative strength of the LO and NLO contributions from different sources.

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arXiv2014

The NLO twist-3 contributions to $B \to π$ form factors in $k_{T}$ factorization

In this paper, we calculate the next-to-leading-order (NLO) twist-3 contribution to the form factors of $B \to π$ transitions by employing the $k_{T}$ factorization theorem. All the infrared divergences regulated by the logarithms $\ln(k_{iT}^{2})$ cancel between those from the quark diagrams and from the effective diagrams for the initial $B$ meson wave function and the final pion meson wave function. An infrared finite NLO hard kernel is therefore obtained, which confirms the application of the $k_{T}$ factorization theorem to $B$ meson semileptonic decays at twist-3 level. From our analytical and numerical evaluations, we find that the NLO twist-3 contributions to the form factors $f^{+,0}(q^2)$ of $B \to π$ transition are similar in size, but have an opposite sign with the NLO twist-2 contribution, which leads to a large cancelation between these two NLO parts. For the case of $f^+(0)$, for example, the $24\%$ NLO twist-2 enhancement to the full LO prediction is largely canceled by the negative ( about $-17\%$ ) NLO twist-3 contribution, leaving a small and stable $7\%$ enhancement to the full LO prediction in the whole range of $0\leq q^2\leq 12$ GeV$^2$. At the full NLO level, the perturbative QCD prediction is $F^{B \to π}(0)=0.269^{+0.054}_{-0.050}$. We also studied the possible effects on the pQCD predictions when different sets of the B meson and pion distribution amplitudes are used in the numerical evaluation.

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arXiv2014

$\bar{B}^0_s \to Kπ,KK$ decays and effects of the next-to-leading order contribution

By employing the perturbative QCD(pQCD) factorization approach, we calculate the branching ratios and CP violating asymmetries of the four $\bar{B}_s^0 \to Kπ$ and $K K $ decays, with the inclusion of all known next-to-leading order (NLO) contributions. We find numerically that (a) the NLO contribution can interfere with the LO part constructively or destructively for different decay modes; (b) the NLO contribution leads to a $22\%$ decrease for $Br(\bar{B}^0_s \to K^+ π^-)$, but $\sim 50\%$ enhancements to other three considered $\bar{B}_s$ decays, and therefore play an important role in interpreting the measured values of the branching ratios; and (c) for both $\bar{B}_s^0 \to K^+ π^-$ and $\bar{B}_s^0 \to K^+K^- $ decays, the NLO pQCD predictions for the direct and mixing induced CP-violating asymmetries agree very well with the measured values in both the sign and the magnitude.

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