We accomplish for the first time the next-to-leading-order QCD computations of the leading-twist contributions to the Dirac nucleon form factors by applying the hard-collinear factorization theorem rigorously. Our predictions for these baryon form factors indicate that the one-loop perturbative corrections to the hard-gluon-exchange contributions are numerically substantial for a wide range of momentum transfers. Including further the soft nonfactorizable contributions, we then perform the state-of-the-art analysis of the Dirac nucleon form factors, allowing for the most robust determinations of the nucleon distribution amplitudes from the comparison with the experimental data.

China

Yong-Kang Huang

Bo-Xuan Shi

Yu-Ming Wang

Xue-Chen Zhao

Next-to-Leading-Order QCD Predictions for the Nucleon Form Factors

We accomplish for the first time the two-loop computation of the leading-twist contribution to the pion form factor by employing the effective field theory formalism rigorously. The next-to-next-to-leading-order hard function is determined by evaluating the appropriate five-point QCD amplitude with the modern multiloop technique and by implementing the ultraviolet renormalization and infrared subtractions in the presence of evanescent operators. The yielding two-loop correction to this fundamental quantity turns out to be numerically significant at experimentally accessible momentum transfers. We further demonstrate that the newly computed two-loop QCD correction is highly beneficial for an improved determination of the leading-twist pion distribution amplitude.

Hong Kong

Germany

Yao Ji

Jian Wang

Ye-Fan Wang

Hui-Xin Yu

Next-to-Next-to-Leading-Order QCD Prediction for the Pion Form Factor

The production of heavy-quark (HQ) jets is a new area that addresses the mass effect of jet quenching in heavy-ion physics. This paper presents a theoretical study of HQ jet yield suppression in Pb+Pb collisions at the Large Hadron Collider (LHC) and focuses on the energy loss of HQ jets produced by different mechanisms. The $\textit{p+p}$ baseline is provided by the generator simulation of high-energy reactions of particles (SHERPA), and the jet-medium interactions are described by the SHELL transport model, which considers the elastic and inelastic partonic energy loss in the quark-gluon plasma (QGP). In $\textit{p+p}$ collisions, our numerical results indicate that the HQ jets from gluon splitting ( $ g \rightarrow Q $ -jet) are the dominant contribution at high $ p_T $ , displaying more dispersive structures than the HQ-initiated ( $ Q \rightarrow Q $ -jet). In nucleus-nucleus collisions, our calculations were consistent with the inclusive and b-jet $ R_{AA} $ recently measured by the ATLAS collaboration, revealing a remarkable manifestation of the mass effect of jet energy loss. As a result of the dispersive substructure, the $ g \rightarrow Q $ -jet loses more energy than the $ Q \rightarrow Q $ -jet in the QGP. Due to the significant contribution of $ g \rightarrow c $ -jet, the $ R_{AA} $ of $\textit{c}$-jet is comparable or even smaller than that of inclusive jet. To experimentally distinguish the $ g \rightarrow Q $ -jet and $ Q \rightarrow Q $ -jet, we propose event selection strategies based on their topological features and test their performances. By isolating the $ c \rightarrow c $ -jet, $ b \rightarrow b $ -jet, and the jets initiated by heavy quarks, we predicted that the order of their $ R_{AA} $ are in line with the mass hierarchy of energy loss. Future measurements on the $ R_{AA} $ of $ Q \rightarrow Q $ -jet and $ g \rightarrow Q $ -jet will provide a unique opportunity for testing the flavor/mass dependence of energy loss at the jet level.

Sa Wang

Shuang Li

Yao Li

Ben-Wei Zhang

Enke Wang

Probing the mass effect of heavy quark jets in high-energy nuclear collisions * Supported by the MajorProject of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008, 2023A1515011460), and the National Natural Science Foundation of China (11935007, 12035007, 12247127, 12375137). Sa Wang is supported by the Open Foundation of Key Laboratory of Quark and Lepton Physics (MOE) (QLPL2023P01) and the Talent Scientific Star-up Foundation of the China Three Gorges University, China (CTGU) (2024RCKJ013)

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

We accomplish for the first time the next-to-leading-order computation of the weak annihilation contribution to the electroweak penguin decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mrow><mo stretchy="false">{</mo><mi>K</mi><mo>,</mo><mi>π</mi><mo stretchy="false">}</mo></mrow><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, which is an essential missing piece of the complete QCD correction to the matrix elements of hadronic operators in the weak effective Hamiltonian. Both the hard functions and the jet functions in the perturbative factorization formulas from the short-distance fluctuations at the two distinct scales <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mrow><msub><mi>m</mi><mi>b</mi></msub><mi mathvariant="normal">Λ</mi></mrow></msqrt></math> are determined at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">)</mo></math>. We then demonstrate that the one-loop weak annihilation correction can bring about the noticeable impacts on theory predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries and the isospin asymmetry in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decays.

Yue-Long Shen

Chao Wang

Next-to-Leading-Order Weak-Annihilation Correction to Rare <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi><mo stretchy="false">→</mo><mo stretchy="false">{</mo><mi>K</mi><mo>,</mo><mi>π</mi><mo stretchy="false">}</mo><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> Decays

We determine for the first time the renormalization-group equation for the three-particle <math><mi>B</mi></math>-meson soft function dictating the nonperturbative strong interaction dynamics of the long-distance penguin contributions to the double radiative <math><mi>B</mi></math>-meson decays. The distinctive feature of the ultraviolet renormalization of this fundamental soft function consists in the pattern of mixing positive into negative support for an arbitrary initial condition. The exact solution to this integrodifferential evolution equation is then derived with the Laplace transform technique, allowing for the model-independent extraction of the asymptotic behavior at large and small partonic momenta.

Renormalization-Group Evolution for the Three-Particle <math><mi>B</mi></math>-Meson Soft Function

We compute for the first time the next-to-leading-order QCD corrections to the <math><msub><mover><mi>B</mi><mo>¯</mo></mover><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub><mo>→</mo><msubsup><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></math> form factors at large hadronic recoil. Both the charm-quark-mass- and the strange-quark-mass- dependent pieces can generate the leading-power contributions to these form factors. Including further various power-suppressed contributions, we perform the combined fits of the considered form factors to both our large-recoil theory predictions and the lattice QCD results, thus improving upon the previous determinations of the lepton-flavor-universality ratios <math><mi>R</mi><mo>(</mo><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mo>)</mo></math> significantly.

Bo-Yan Cui

Shedding new light on <math><mi>R</mi><mo>(</mo><msubsup><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><mo>)</mo></math> and <math><mo>|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo></math> from semileptonic <math><msub><mover><mi>B</mi><mo>¯</mo></mover><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub><mo>→</mo><msubsup><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><mo>ℓ</mo><msub><mover><mi>ν</mi><mo>¯</mo></mover><mo>ℓ</mo></msub></math> decays

We compute for the first time the long-distance penguin contribution to the double radiative <math><mi>B</mi></math>-meson decays by applying the perturbative factorization theorem. The numerically dominant penguin amplitude arises from the soft-gluon radiation off the light up-quark loop rather than the counterpart charm-loop effect. Importantly, the long-distance up-quark penguin contribution brings about the substantial cancellation of the known factorizable power correction, thus enabling <math><msub><mi>B</mi><mrow><mi>d</mi><mo>,</mo><mi>s</mi></mrow></msub><mo>→</mo><mi>γ</mi><mi>γ</mi></math> to become new benchmark probes of physics beyond the standard model.

Qin Qin

Deciphering the Long-Distance Penguin Contribution to <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>d</mi><mo>,</mo><mi>s</mi></mrow></msub><mo>→</mo><mi>γ</mi><mi>γ</mi></mrow></math> Decays

We identify a novel leading-power contribution to the pure weak annihilation non-leptonic B-meson decay amplitudes, which arises from the hard-collinear gluon exchange between the light quark of the bottom meson and the final-state active partons. This interesting observation is naturally expected to shed new light on deciphering rapidity divergences in the convolution integrals of the soft-collinear factorization formulae. Subsequently we explore an intriguing enhancement mechanism due to the penguin contractions of the current-current operators from the weak effective Hamiltonian, which yields the significant impacts on the CP violating observables.

Cai-Dian Lü

Shedding new light on weak annihilation -meson Decays

We improve QCD calculations of the semileptonic B d,s → π, K decay form factors at large hadronic recoil by implementing the next-to-leading-logarithmic resummation for the obtained leading-power light-cone sum rules in the soft-collinear effective theory (SCET) framework and by computing for the first time the non-vanishing spectator-quark mass correction dictating the SU(3)-flavour symmetry breaking effects between these fundamental quantities at the one-loop accuracy. Additionally, we endeavour to investigate a variety of the subleading-power contributions to these heavy-to-light form factors at <math> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>s</mi> <mn>0</mn> </msubsup> </mfenced> </math> $$ \mathcal{O}\left({\alpha}_s^0\right) $$ with the same methodology, by including the higher-order terms in the heavy-quark expansion of the hard-collinear quark propagator, by evaluating the desired effective matrix element of the next-to-leading-order term in the SCETI representation of the weak transition current, by taking into account the off-light-cone contributions of the two-body heavy-quark effective theory (HQET) matrix elements as well as the three-particle higher-twist corrections from the subleading bottom-meson light-cone distribution amplitudes (LCDAs), and by computing the twist-five and twist-six four-body higher-twist effects with the aid of the factorization approximation. Having at our disposal the SCET sum rules for the exclusive B-meson decay form factors under discussion, we further explore in detail numerical implications of the newly computed subleading-power corrections by employing the three-parameter model for both the leading-twist and higher-twist B-meson distribution amplitudes. Taking advantage of the customary Bourrely-Caprini-Lellouch (BCL) parametrization for the complete set of the semileptonic B d,s → π, K form factors, we then determine the correlated numerical results for the interesting series coefficients, by carrying out the simultaneous fit of the exclusive B-meson decay form factors to both the achieved SCET sum rule predictions at small momentum transfer (q 2) and the available lattice QCD results at large momentum transfer. Subsequently, we perform a comprehensive phenomenological analysis of the full angular observables, the lepton-flavour university ratios and the lepton polarization asymmetries for the flavour-changing charged- current <math> <mi>B</mi> <mo>→</mo> <mi>π</mi> <mi>ℓ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>ℓ</mi> </msub> </math> $$ B\to \pi \ell {\overline{\nu}}_{\ell } $$ and <math> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <mi>K</mi> <mi>ℓ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>ℓ</mi> </msub> </math> $$ {B}_s\to K\ell {\overline{\nu}}_{\ell } $$ decays (with ℓ = μ, τ) together with the differential q 2-distribution for the exclusive rare <math> <mi>B</mi> <mo>→</mo> <mi>K</mi> <msub> <mi>ν</mi> <mi>ℓ</mi> </msub> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>ℓ</mi> </msub> </math> $$ B\to K{\nu}_{\ell }{\overline{\nu}}_{\ell } $$ decays in the Standard Model.