arXiv subjects

Cai-Dian Lü

Publications and source records attributed to Cai-Dian Lü.

At least 19 recordsLinked to original sources

arXiv2026

Complete Access to Leading-Twist $Λ$-Baryon Light-Cone Distribution Amplitudes from Lattice QCD

We report the first complete lattice-QCD determination of the leading-twist light-cone distribution amplitudes (LCDAs) of the $Λ$ baryon, obtained as full two-dimensional functions of the valence-quark momentum fractions. The calculation employs large-momentum effective theory to relate the light-cone amplitudes to equal-time nonlocal three-quark matrix elements of boosted $Λ$ baryons. Controlled physical extrapolations to the continuum, physical pion mass, and infinite momentum, together with hybrid renormalization, large-$λ$ extrapolation, and perturbative matching, yield the three leading-twist LCDAs $V$, $A$, and $T$. Using the lattice-determined LCDAs in place of the asymptotic form, we find an $\mathcal{O}(10\%)$ shift in the $Λ$ electromagnetic form factor at perturbative scales, demonstrating that the full two-dimensional LCDAs, rather than only their asymptotic shapes or lowest moments, are required for precision baryonic phenomenology. This work, together with the companion paper [1] detailing the baryon-LaMET framework, provides the first complete multi-dimensional $x$-dependent baryon LCDAs from first principles and establishes a benchmark for lattice access to multi-dimensional baryon structure.

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arXiv2026

Baryon Light-Cone Distribution Amplitudes from Lattice QCD: Formalism, Renormalization, Extrapolation, and Matching

Baryon light-cone distribution amplitudes (LCDAs) are inherently multidimensional objects parametrized by two independent longitudinal momentum fractions, making their first-principles determination substantially more challenging than that of meson LCDAs. We present a systematic large-momentum effective theory (LaMET) framework for determining baryon leading-twist LCDAs from lattice QCD. The framework covers the complete path from equal-time three-quark quasi-distribution amplitudes to physical baryon LCDAs. We formulate the leading-twist $V$, $A$, and $T$ quasi-DAs and analyze their spin-flavor and coordinate-space symmetries, including antisymmetric amplitudes with vanishing local limits. We develop a hybrid renormalization prescription on the $(z_1,z_2)$ plane, introduce a newly developed large-$λ$ extrapolation strategy based on the asymptotic large-distance behavior of Euclidean correlators, and derive the corresponding one-loop LaMET matching relation in the hybrid renormalization scheme. As a demonstration, we apply the complete analysis pipeline to the $Λ$-baryon $A$-structure quasi-DAs using seven $2+1$--flavor lattice ensembles, and use this amplitude to examine the impact of large-distance extrapolation, perturbative matching, and extrapolation to the continuum, physical-pion-mass, and infinite-momentum limits, together with the associated systematic uncertainties. This work provides the formalism, renormalization, extrapolation, and matching infrastructure for first-principles determinations of $x$-dependent baryon LCDAs.

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arXiv2026

Determination of $B$-meson distribution amplitudes from $B\to π,K,D$ transition form factors

Recent work on $B \to π$, $K$ and $B\to D$ form factors from lattice QCD and light-cone sum rules has made it possible to constrain the inverse moment $λ_B$ of the $B$-meson light-cone distribution amplitudes by performing a global fit of $B\to π,K,D$ form factors. We have compiled the $B\to π,K,D$ form factors calculated by the HPQCD, MILC, and RBC/UKQCD collaborations in the large $q^2$ region. By employing an three-parameter ansatz of the $B$-meson light-cone distribution amplitudes, we express the $B\to π,K,D$ form factors at $q^2=0$ that are calculated from light-cone sum rules, in terms of the inverse moment $λ_B$ of the leading-twist $B$-meson light-cone distribution amplitude. In the $B \to π\ell ν$ channel, we also include the available $q^2$-binned experimental data from the BaBar, Belle, and Belle~II collaborations. Using the Bourrely-Caprini-Lellouch parametrization, we perform a global fit and obtain $λ_B=217(19)_{-17}^{+82}$~MeV and $|V_{\text{ub}}|=3.68(13)_{-1}^{+0}\times10^{-3}$. The second uncertainty is obtained by constraining $λ_B>200$ MeV and varying the inverse logarithmic moments $\hatσ_1\in[-0.7,0.7]$ and $\hatσ_2\in[-6,6]$, which represents the model-dependent uncertainty from the $B$-meson light-cone distribution amplitudes. When taking into account $λ_B$ and $\hatσ_1$ as fitting parameters simultaneously, the intervals of our preditions are $λ_B=[208, 324]$~MeV and $\hatσ_1=[-0.7, 0.27]$.

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arXiv2026

Continuum-Limit HQET LCDAs from Lattice QCD for Tightening B Decay Uncertainties

Heavy meson HQET light-cone distribution amplitudes (LCDAs) are critical for precision predictions of $B$ meson weak decays, but currently are one of dominant theoretical uncertainties that obscure interpretations of $B$ anomalies and CP-violating measurements. Building on the established HQLaMET framework, supplemented by lattice QCD calculations of the OPE moments, we present a precise lattice QCD calculation of HQET LCDAs by employing multi-ensemble simulations for continuum and physical pion mass extrapolation, quantifying comprehensive systematic errors, and validating results through OPE moment cross-validation. Details of the lattice calculations are provided in a companion paper \cite{HeavymesonDA_long_paper}. Our final results for key inverse moments (at $μ=1$ GeV) are $λ_B=0.340(20)$ GeV and $σ_B^{(1)}=1.685(63)$, with the total uncertainty reduced by a factor of three relative to the previous analysis. These results can greatly reduce the uncertainty in the $B \to K^*$ form factors in the large-recoil region. This work resolves the long-standing bottleneck in first-principles predictions of heavy meson LCDAs, advancing precision flavor physics to new frontiers.

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arXiv2026

Determination of heavy meson light-cone distribution amplitudes: theoretical framework and lattice simulations

We present a first-principles determination of heavy meson light-cone distribution amplitudes (LCDAs) from lattice QCD in the continuum limit, improving substantially on our previous pioneering study. Within the heavy-quark large-momentum effective theory (HQLaMET) framework, supplemented by lattice QCD calculations of the OPE moments, we analyze six ensembles with lattice spacings ranging from $a=0.0519-0.1053$\,fm and pion masses from $m_π=135.5-317.2$\,MeV, thereby enabling controlled continuum, chiral, and infinite-momentum extrapolations to the physical point. Momentum-smeared sources, hypercubic-smeared Wilson lines, and optimized interpolating operators are adopted to significantly improved signals for the nonlocal correlators. Within a unified framework, we determine both QCD LCDAs and HQET LCDAs. Our resulting QCD LCDAs of $D$ meson peak at $y\approx 0.2-0.3$, with total uncertainties below $30\%$ for $0.1<y<0.9$. The leading-twist HQET LCDA is constructed using a peak-and-tail factorization, in which the nonperturbative peak region is obtained from lattice QCD and the perturbative tail is incorporated from HQET, with the two regions combined through a model-independent Laguerre-polynomial parametrization. At $μ=1$\,GeV, we obtain the inverse moment of HQET LCDA $λ_B=0.340(20)$\,GeV and first inverse-logarithmic moment $σ_B^{(1)}=1.685(63)$, consistent with experimental constraints and phenomenological determinations. Direct lattice calculations based on operator product expansion provide a nontrivial cross-check of the LaMET results. Final results and phenomenological impact of these results are presented in a companion paper~\cite{HeavymesonDA_short_paper}. Our results remove the single-lattice-spacing limitation of the previous study, and provide a robust determinations of heavy meson LCDAs in both QCD and HQET for next-generation heavy flavor physics.

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arXiv2025

Next-to-Next-to-Leading-Order Corrections to the $B \to π$ Form Factors from Light-Cone Sum Rules

By incorporating the available leading-power results at $\mathcal{O}(α_s)$ and next-to-leading-power corrections at tree level, we improve the precision of the theoretical predictions for $B\toπ$ form factors to the $\mathcal{O}(α_s^2β_0)$ level in the large-recoil region using the light-cone sum rule approach with $B$-meson light-cone distribution amplitudes. We find that the QCD corrections at $\mathcal{O}(α_s^2β_0)$ contribute approximately $+6.1\%$ compared to the tree-level result. Combining the light-cone sum rule predictions in the large-recoil region, lattice QCD results in the small-recoil region, we perform a combined fit for the $B\toπ$ form factors across the full kinematic range. Utilizing these form factors, we calculate the branching ratios, lepton-flavor-universality ratio $R_π$, forward-backward asymmetry $\mathcal{A}_{\rm FB}$, flat term $\mathcal{F}_{\rm H}$ and polarization asymmetry $\mathcal{A}_{\rm λ_\ell}$ of $B\toπμ\barν_μ$ and $B\toπτ\barν_τ$ decays. Using the experimentally measured $q^2$-binned differential branching ratios of $B\toπμ\barν_μ$ decay as input, employing the Bourrely-Caprini-Lellouch parametrization, we extract the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}| = 3.73(14) \times 10^{-3}$.

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arXiv2025

New horizon in particle physics: first observation of CP violation in baryon decays

Recently, the LHCb Collaboration achieved the observation of CP violation (CPV) in baryon decays through the process of $Λ_b^0\to pK^-π^+π^-$, reporting an asymmetry of $(2.45\pm0.46\pm0.10)\%$ with a significance of 5.2$σ$. This marks a breakthrough and a milestone in particle physics, six decades after the first observation of CPV in mesons. It will be helpful to understand the matter-antimatter asymmetry in the universe. In addition to the global CPV, local CPV is also observed by LHCb in the low mass region of $m_{pπ^+π^-}<2.7$GeV as $(5.4\pm0.9\pm0.1)\%$ with a significance of 6.0$σ$. Intriguingly, this measurement aligns well with a theoretical prediction of $(5.6-5.9)\%$ based on a CPV dynamics using the data of $Nπ\to pπ^+π^-$ scatterings. Since baryons contain one more quark than mesons, the dynamics of baryon decays are significantly different from those of mesons. Therefore, the first observation of baryon CPV by LHCb opens a new horizon in the studies of dynamics of the strong interaction.

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arXiv2025

SCET sum rules for $Λ_b \to Λ\ell^+\ell^-$, $Λγ$ decays

We construct light-cone sum rules for various types of effective form factors in the $Λ_b \to Λ\ell^+\ell^-$ and $Λ_b \to Λγ$ decays by analyzing vacuum-to-$Λ_b$ (or $γ^\ast$-to-$Λ_b$) correlation functions with the light $Λ$-baryon interpolating current. These form factors, defined via hadronic matrix elements within soft-collinear effective theory (SCET), enter the next-to-leading-power QCD factorization formulas for large-recoil transitions. Implementing the perturbative matching from $\text{SCET}_\text{I}$ to heavy quark effective theory, we determine the hard-collinear functions at next-to-leading-order accuracy. Based on light-cone sum rule predictions for the $Λ_b \to Λ$ form factors, we compute the $q^2$-dependent differential branching fraction, forward-backward asymmetry and dilepton longitudinal polarization fraction for $Λ_b \to Λ\ell^+\ell^-$ decay, as well as the branching fraction for $Λ_b \to Λγ$ decay.

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arXiv2025

A realistic method to access heavy meson light-cone distribution amplitudes from first-principle

Lightcone distribution amplitudes (LCDAs) of heavy meson within heavy quark effective theory (HQET) are crucial for predicting physical observables in $B$ decays, but unfortunately there is no first-principle result due to severe challenges. After analyzing these challenges, we propose a realistic method to determine heavy meson LCDA. We utilize equal-time correlations and incorporate a dynamic quark field for a fast moving heavy quark. To verify this method, we make use of lattice QCD simulation on a lattice ensemble with spacing $a = 0.05187$\,fm. The preliminary findings for HQET LCDAs qualitatively align with phenomenological models, and the fitted result for the first inverse moment $λ_B^{-1}$ is consistent with the experimentally constrain from $B \to γ\ellν_\ell$. We explore how our findings can reduce model uncertainties in predictions of heavy-to-light form factors at large recoil. These results demonstrate the promise of our method in providing first-principle predictions for heavy meson LCDAs.

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arXiv2025

Heavy meson lightcone distribution amplitudes from Lattice QCD

Lightcone distribution amplitudes (LCDAs) within the framework of heavy quark effective theory (HQET) play a crucial role in the theoretical description of weak decays of heavy bottom mesons. However, the first-principle determination of HQET LCDAs faces significant theoretical challenges. In this presentation, we introduce a practical approach to address these obstacles. This makes sequential use of effective field theories. Leveraging the newly-generated lattice ensembles, we present a pioneering lattice calculation, offering new insights into LCDAs for heavy mesons. Additionally, we discuss the impact of these results on the heavy-to-light form factors and briefly give potential future directions in this field.

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arXiv2025

Study of rare top quark decays into a jet plus a charged pseudo-scalar meson

The semi-inclusive decay processes of a top quark into a charged pseudo-scalar meson and a jet are studied within the framework of QCD factorization. The leading power of the decay matrix elements can be factorized into heavy-to-light quark transition current and a hadron matrix element up to next-to-leading order QCD corrections. We calculate one-loop virtual corrections together with real gluon emission corrections at the αs order. The numerical results of the branching ratios are presented for the sum of two-body and three-body decays. We also study the energy cut-off dependence of the gluon jet. These processes are hopeful to be detected in the near future experiments, which can serve as probes for new physics.

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arXiv2025

Calculation of heavy meson light-cone distribution amplitudes from lattice QCD

We develop an approach for calculating heavy quark effective theory (HQET) light-cone distribution amplitudes (LCDAs) by employing a sequential effective theory methodology. The theoretical foundation of the framework is established, elucidating how the quasi distribution amplitudes (quasi DAs) with three scales can be utilized to compute HQET LCDAs. We provide theoretical support for this approach by demonstrating the rationale behind devising a hierarchical ordering for the three involved scales, discussing the factorization at each step, clarifying the underlying reason for obtaining HQET LCDAs in the final phase, and addressing potential theoretical challenges. The lattice QCD simulation aspect is explored in detail, and the computations of quasi DAs are presented. We employ three fitting strategies to handle contributions from excited states and extract the bare matrix elements. For renormalization purposes, we apply hybrid renormalization schemes at short and long distance separations. To mitigate long-distance perturbations, we perform an extrapolation in $λ= z\cdot P^z$ and assess the stability against various parameters. After two-step matching, our results for HQET LCDAs are found in agreement with existing model parametrizations. The potential phenomenological implications of the results are discussed, shedding light on how these findings could impact our understanding of the strong interaction dynamics and physics beyond the standard model. It should be noted, however, that systematic uncertainties have not been accounted for yet.

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arXiv2024

Invisible and Semi-invisible Decays of Bottom Baryons

The similar densities of dark matter and baryons in the universe imply that they might arise from the same ultraviolet model. The B-Mesogenesis, which assumes dark matter is charged under the baryon number, attempts to simultaneously explain the origin of baryon asymmetry and dark matter in the universe. In particular, the B-Mesogenesis might induce bottom-baryon decays into invisible or semi-invisible final states, which provide a distinctive signal for probing this scenario. In this work, we systematically study the invisible decays of bottom baryons into dark matters, and semi-invisible decays of bottom baryons into a meson or a photon together with a dark matter particle. In particular, the fully invisible decay can explore the stable particles in B-Mesogenesis. Some QCD-based frameworks are used to calculate the hadronic matrix elements under the B-Mesogenesis model. We estimate the constraints on the Wilson coefficients or the product of some new physics couplings with the Wilson coefficients by the semi-invisible and invisible decays of bottom baryons at future colliders.

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arXiv2024

$Λ_{b}\rightarrow P \ell$ factorization in QCD

We calculate the form factors for the baryon number violation processes of a heavy-flavor baryon decaying into a pseudoscalar meson and a lepton. In the framework of the Standard Model effective field theory, the leptoquark operators at the bottom quark scale, whose matrix elements define the form factors, are derived by integrating out the high energy physics. Under the QCD factorization approach, the form factors of the baryon number violation processes at leading power can be factorized into the convolution of the long-distance hadron wave functions as well as the short-distance hard and jet functions representing the hard scale and hard-collinear scale effects, separately. Based on measurements of the baryon number violation processes by LHCb, we further impose constraints on the new physics constants of leptoquark operators.

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arXiv2023

Next-to-leading order QCD corrections to the form factors of $B$ to scalar meson decays

We calculate the next-to-leading order QCD corrections to $B$ to scalar meson form factors from QCD light-cone sum rules with $B$ meson light-cone distribution amplitudes. We demonstrate that the $B$ meson-to-vacuum correlation functions can be factorized into the convolution of short-distance coefficients and light-cone distribution amplitudes at the one-loop level and find that only $ϕ_B^+(ω,μ)$ contributes to the form factors. We then employ the $z$-parameterization combined with constraints from strong coupling constants to reconstruct the $q^2$ dependence of the form factors in the whole kinematic allowed regions. Due to the large cancellations between the hard functions and the jet functions, the next-to-leading order results show a modest increase of approximately 5\% compared to the leading order results. Based on the results of form factors, we predict the branching ratios of semi-leptonic $B\to S\ell\barν_\ell$ and $B\to Sν_\ell\barν_\ell$ processes, as well as several angular observables, such as forward-backward asymmetries, "flat terms" and lepton polarization asymmetries. We compare these results with calculations from other methods. Experimental verification of these results is required in future experiments.

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arXiv2022

Charmless two-body $B$ meson decays in perturbative QCD factorization approach

The perturbative QCD (PQCD) approach based on $k_T$ factorization has made a great achievement for the QCD calculation of the hadronic B decays. Regulating the endpoint divergence by the transverse momentum of quarks in the propagators, one can do the perturbation calculation for kinds of diagrams including the annihilation type diagrams. In this paper, we review the current status of PQCD factorization calculation of two-body charmless $B\to PP, PV, VV$ decays up to the next-to-leading order (NLO) QCD corrections. two new power suppressed terms in decaying amplitudes are also taken into account. By using the universal input (non-perturbative) parameters, we collected the branching ratios and ${\bf CP}$ asymmetry parameters for all the charmless two body $B$ decays, calculated in the PQCD approach up to the NLO, including some power suppressed terms in decaying amplitudes. The results are compared with the ones from QCD factorization approach, soft-collinear effective theory approach and the current experimental measurements. For most considered B meson decays, the PQCD results for branching ratios agree well with other approaches and the experimental data. The PQCD predictions for the ${\bf CP}$ asymmetry parameters for many of the decay channels do not agree with other approaches, but have a better agreement with the experimental data. The longstanding $K π$ puzzle about the pattern of the direct CP asymmetries of the penguin-dominated $B \to K π$ decays can be understood after the inclusion of the NLO contributions in PQCD. The NLO corrections and power suppressed terms play an important role in the color suppressed and pure annihilation type $B$ decay modes. These rare decays are more sensitive to different types of corrections, providing opportunity to examine the factorization approach with the more precise experimental measurements.

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arXiv2022

Scrutinizing New Physics in Semi-leptonic $B_{c}\rightarrow J/ψτν$ Decay

We perform a global analysis of the $b\to cτν$ data using the recent lattice results on the $B_c\to J/ψ$ vector and axial-vector form factors. To explore the effects from the tensor operator of new physics beyond the standard model, we determine the tensor form factors by using the non-relativistic QCD (NRQCD) relations between tensor and (axial-)vector form factors. Based on the lattice+NRQCD form factors, we fit the Wilson coefficients and the new physics couplings in $R_2$, $S_1$ and $U_1$ leptoquark models by including the recently measured $R(Λ_c)$ and imposing the relaxed constraint $\mathcal B(B_c\to J/ψ)<30\%$ in light of the recent studies on LEP1 data and $B_c$ lifetime. We give predictions for the experimental observables including $R(J/ψ)$, $P_τ(J/ψ)$, $F_L(J/ψ)$ and $\mathcal A_{FB}(J/ψ)$ as well as their $q^2$ distribution in new physics scenarios/models. Our results suggest that the longitudinal $τ$ polarization fraction $P_τ(J/ψ)$ and the forward-backward asymmetry $\mathcal A_{FB}(J/ψ)$ are useful for testing the $R_2$ leptoquark model.

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arXiv2022

Strange quark mass effect in $B_s \to γγ,γ\ell\bar{\ell}$ decays

In this paper we investigate the next-to-leading power contribution to the $B_s \to γγ$ and $B_s \to γ\ell\bar{\ell}$ decays from the strange quark mass effect with the dispersion approach which is QCD inspired and more predictive. We have presented the analytic expression of the quark mass contribution in the $B_s \to γγ$ and $B_s \to γ\ell\bar{\ell}$ decays, together with a new term that is missed in the previous study. The numerical results of the strange quark mass contribution to the $B_s \to γγ$ decay is about 6% relative to the total branching ratio, while it is relatively small in the $B_s \to γ\ell\bar{\ell}$ decay due to the large resonance contribuiton

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