Partial Wave Research Articles

Development of the Time-Independent Methods for the Cl + H2/F + HD Reaction Using Hyper-Spherical Coordinates Including (Full) Spin-Orbit Characteristics.

Recently, a combined study of high-resolution molecular crossed beam experiment and accurate full-dimensional time-dependent theory, including full spin-orbit characteristics on the effect of electronic spin and orbital angular momenta in the F + HD reaction, was reported by some of us, focusing on the partial wave resonance phenomenon (Science 2021, 371, 936-940). It revealed that the time-dependent theory could explain all of the details observed in the high-resolution experiment. Here, we develop two time-independent close-coupling methods using hyperspherical coordinates, including the two-state model, where only a part of the spin-orbit characteristics is considered, and the six-state model, where the full spin-orbit characteristics is considered. With these two newly developed theoretical models and the adiabatic theoretical model, the detailed reaction dynamics of the F + HD (v = 0, j = 0) reaction and the Cl + H2 (v = 0, j = 0) reaction are investigated and compared. Some of the results are compared with the time-dependent quantum wave packet theory and the experimental observations, and good agreements have been obtained, which suggests the validity of the pure-procession approximation in the six-state model using different theoretical methods. This work demonstrates the ability of the reactive scattering theory including full spin-orbit characteristics for describing the reactions of a halogen atom plus hydrogen molecule and its isotopologues.

Quantum dynamics of the P(2D) + H2 (X1[formula omitted]) → PH (X3Σ-) + H(2S) reaction

The title reaction is thought to be important for the astronomical PO formation, which may contribute to the generation of bioavailable H3PO3. Using quasi-classical trajectory (QCT) method, the state-specified (v = 0, j = 0) rate constant of this reaction was calculated. The comparison with previous temperature-averaged QCT rate constant shows that the effect of ro-vibrational excitation is relatively small below 2000 K. Then, the time-dependent wave packet (TDWP) method was applied to investigate the quantum reaction mechanisms, obtaining the state-specified (v = 0, j = 0) reaction probability, integral cross sections and rate constants. The number of partial waves and the integral interval of collision energy considered were rigorously tested to ensure the convergence of the TDWP rate constant below 2000 K. The TDWP rate constant agrees better to the latest experimental results at 291 to 685 K than those from the two QCT calculations. Also, the TDWP calculations can produce relatively reliable rate constants at 700 to 2000 K, where the Arrhenius formula fitted by experimental results ignores the temperature dependence of the activation energy. The calculated rate constants are helpful for modelling the phosphorus chemistry and determining the abundances of the P-bearing species in interstellar media (ISM).

De-projecting the EFThedron

The space of Wilson coefficients of EFT that can be UV completed into consistent theories was recently shown to be described analytically by a positive geometry, termed the EFThedron. However, this geometry, as well as complementary numerical methods of semi-definite programming, have so far focused on the positivity of the partial wave expansion, which allows bounding only ratios of couplings. In this paper we describe how the unitarity upper bound of the partial waves can be incorporated. This new problem can be formulated in terms of the well known L-moment problem, which we generalize and solve from a geometrical perspective. We find the non-projective generalization of the EFThedron has an infinite number of non-linear facets, which in some cases have remarkably simple descriptions. We use these results to derive bounds on single couplings, finding that the leading derivative operators are bounded by unity, when normalized by the cut-off scale and loop factors. For general operators of mass dimension 2k we find the upper bound is heavily suppressed at large k, with an 1/k fall-off.

Production of Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document} in B nonleptonic decays

In 2021, a new charm-strange meson, Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document}, was discovered, which is believed to be the Ds+(21S0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_s^+(2^1S_0)$$\\end{document}. However, its low mass and wide width are challenged by theoretical results. Given the small branching ratio of the current production channel, resulting in a small number of events and large errors, we suggest searching for the Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document} in the B meson nonleptonic decays, Bq→Dq(∗)Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_q\\rightarrow D^{(*)}_qD_{s0}(2590)^+$$\\end{document} (q=u,d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q=u,d$$\\end{document}), followed by Ds0(2590)+→D∗K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+\\rightarrow D^*K$$\\end{document}. We find that Br(Bq→Dq(∗)Ds0(2590)+)×Br(Ds0(2590)+→D∗K)=(2.16∼2.82)×10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Br(B_q\\rightarrow D^{(*)}_qD_{s0}(2590)^+)\ imes Br(D_{s0}(2590)^+\\rightarrow D^{*}K)=(2.16\\sim 2.82)\ imes 10^{-3}$$\\end{document} is very large, and the result is not sensitive to the mass of Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document}. Due to the large branching ratio, numerous Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document} events are expected. This study is based on the framework of the instantaneous Bethe–Salpeter equation, and the relativistic wave functions used for mesons contain different partial waves. The contributions of the different partial waves are also studied.

Quantum Dynamics of O(3P)+HBr→OH+Br Reaction: Integral Cross Sections and Rate Constants and their Initial State Dependence.

The integral cross sections (ICSs) and rate constants (RCs) for the title reaction are calculated by means of accurate quantum wave packet method employing the recent ab initio potential energy surface developed by Peterson and co-workers. Hundreds of partial wave contributions (up to J=150) are calculated explicitly taking Coriolis coupling into account. The ICSs are found to increase monotonically with energy and their energy dependences are smooth except in the energy range below the potential energy barrier, where several resonance peaks are observed. The temperature dependences of the RCs obey in general the Arrhenius law. These behaviors manifest the dominance of abstract mechanism. Initial rotational state (ji) excitations are found to greatly enhance the reactivity starting from ji=4, while exhibiting a complicated dependence for ji<4. From Boltzmann average of the initial state specified RCs (for ji=0-15) we obtained thermal RCs which are in reasonable agreement with available experimental results.

Determination of Spin-Parity Quantum Numbers of X(2370) as 0^{-+} from J/ψ→γK_{S}^{0}K_{S}^{0}η^{'}.

Based on (10087±44)×10^{6} J/ψ events collected with the BESIII detector, a partial wave analysis of the decay J/ψ→γK_{S}^{0}K_{S}^{0}η^{'} is performed. The mass and width of the X(2370) are measured to be 2395±11(stat)_{-94}^{+26}(syst) MeV/c^{2} and 188_{-17}^{+18}(stat)_{-33}^{+124}(syst) MeV, respectively. The corresponding product branching fraction is B[J/ψ→γX(2370)]×B[X(2370)→f_{0}(980)η^{'}]×B[f_{0}(980)→K_{S}^{0}K_{S}^{0}]=(1.31±0.22(stat)_{-0.84}^{+2.85}(syst))×10^{-5}. The statistical significance of the X(2370) is greater than 11.7σ and the spin parity is determined to be 0^{-+} for the first time. The measured mass and spin parity of the X(2370) are consistent with the predictions of the lightest pseudoscalar glueball.

Black hole perturbation theory meets CFT2 : Kerr-Compton amplitudes from Nekrasov-Shatashvili functions

We present a novel study of Kerr Compton amplitudes in a partial wave basis in terms of the Nekrasov-Shatashvili (NS) function of the confluent Heun equation (CHE). Remarkably, NS-functions enjoy analytic properties and symmetries that are naturally inherited by the Compton amplitudes. Based on this, we characterize the analytic dependence of the Compton phase shift in the Kerr spin parameter and provide a direct comparison to the standard post-Minkowskian (PM) perturbative approach within general relativity (GR). We also analyze the universal large frequency behavior of the relevant characteristic exponent of the CHE—also known as the renormalized angular momentum—and find agreement with numerical computations. Moreover, we discuss the analytic continuation in the harmonics quantum number ℓ of the partial wave, and show that the limit to the physical integer values commutes with the PM expansion of the observables. Finally, we obtain the contributions to the tree-level, point-particle, gravitational Compton amplitude in a covariant basis through O(aBH8), without the need to take the superextremal limit for Kerr spin. Published by the American Physical Society 2024

Partial dam-break wave characteristics due to partial gate opening

Understanding how to predict the characteristic height of a dam-break wave is crucial for effective risk management in dam-break scenarios. This study introduces an experimental framework to simulate partial dam-break waves triggered by partial gate openings. We conducted numerous experiments to explore how different factors, including water-level differences (hi), reservoir widths (L), dam-break openings (e), and submerged depths (hw) influence the characteristic heights of the main-wave peak (h1c), subwave peak (h2c), and main-wave trough (h1t). Our analysis led to the development of an equation for predicting h1c. Furthermore, we compared the partial dam-break wave profile with the theoretical profile of a solitary wave, identifying optimal conditions for solitary wave generation and examining the velocity characteristics of partial dam-break waves. The results reveal that: (1) h1c, h2c, and h1t have positive correlations with hi and L, but negative correlations with e and hw; (2) notably, the main-wave pre-peak profile aligns more closely with the solitary wave theory; and (3) the solitary wave theory accurately predicts the main-wave peak velocity. This study enhances our understanding of wave characteristic evolution during partial dam-breaks and can be used for validation in numerical simulations.

Incoherent non-Hermitian skin effect in photonic quantum walks

The non-Hermitian skin effect describes the concentration of an extensive number of eigenstates near the boundaries of certain dissipative systems. This phenomenon has raised a huge interest in different areas of physics, including photonics, deeply expanding our understanding of non-Hermitian systems and opening up new avenues in both fundamental and applied aspects of topological phenomena. The skin effect has been associated to a nontrivial point-gap spectral topology and has been experimentally demonstrated in a variety of synthetic matter systems, including photonic lattices. In most of physical models exhibiting the non-Hermitian skin effect full or partial wave coherence is generally assumed. Here we push the concept of skin effect into the fully incoherent regime and show that rather generally (but not universally) the non-Hermitian skin effect persists under dephasing dynamics. The results are illustrated by considering incoherent light dynamics in non-Hermitian photonic quantum walks.

Finite series approach for the calculation of beam shape coefficients in ultrasonic and other acoustic scattering

Partial wave expansions with spherical wave functions are usually employed to describe complex velocity potentials or pressure fields in ultrasonic and acoustic scattering by spherical particles. The expansion coefficients – known as the beam shape coefficients (BSCs) – can be calculated using different approaches which have been largely unexplored in the acoustical literature. Here, we formally present the Finite Series method for the evaluation of BSCs of ultrasonic and acoustic arbitrary-shaped beams. Such a series, which relies on Neumann expansion theorem, is an alternative to quadratures whenever analytical solutions cannot be obtained from direct integration over polar and azimuthal spherical angles. As examples of application, we consider the calculation of BSCs of Bessel, Laguerre–Gauss and Gaussian beams under on-axis configuration, including a discussion on a modified version of the finite series method recently presented in the context of optical fields.

Analytical and experimental analysis of guided waves in an aluminum plate under bending load

Although guided waves offer great potential for monitoring various structures, interpreting signals from piezoelectric sensors remains a challenging task. One main reason is the significant influence of environmental conditions on the wave propagation. A lot of research has already been done on the influence of temperature effects and recently more attention has been shifted towards loads. While previous publications have mainly focused on uni- or bi-directional loads, this publication expands the developed models to include bending loads.After reviewing the analytical basis of acoustoelasticity, the derived equations are expanded to nonhomogeneous elastic bending loads using the partial wave method. The analysis is completed using recent results developed by C. Hakoda and C. J. Lissenden (2018) [1], that gave more physical insight in the propagation of guided waves in various frequency-bands.The focus of the experimental analysis is around the fundamental S0- and A0-Modes of Lamb waves. To validate the analytical results an aluminum plate is instrumented using piezoelectric transducers and loaded with varying bending loads. The experimental results are in good agreement with the analytical theory and demonstrate the influence of bending prestress on guided wave propagation. Based on these results an innovative measurement method for bending loads is developed, that is robust to small temperature changes.

Imaging Resonance Effects in C + H2 Collisions Using a Zeeman Decelerator.

An intriguing phenomenon in molecular collisions is the occurrence of scattering resonances, which originate from bound and quasi-bound states supported by the interaction potential at low collision energies. The resonance effects in the scattering behavior are extraordinarily sensitive to the interaction potential, and their observation provides one of the most stringent tests for theoretical models. We present high-resolution measurements of state-resolved angular scattering distributions for inelastic collisions between Zeeman-decelerated C(3P1) atoms and para-H2 molecules at collision energies ranging from 77 cm-1 down to 0.5 cm-1. Rapid variations in the angular distributions were observed, which can be attributed to the consecutive reduction of contributing partial waves and effects of scattering resonances. The measurements showed excellent agreement with distributions predicted by ab initio quantum scattering calculations. However, discrepancies were found at specific collision energies, which most likely originate from an incorrectly predicted quasi-bound state. These observations provide exciting prospects for further high-precision and low-energy investigations of scattering processes that involve paramagnetic species.

Single-particle spectroscopies of p-wave and d-wave interacting Bose gases in normal phase

Motivated by experiments with interacting quantum gases across high partial wave resonance, we investigate the thermodynamic properties and single-particle spectra of Bose gases in normal phase for different interaction strengths for both p- and d-wave interactions. The equation of state, contact density, momentum distributions and self-energies of single-particle Green’s functions are obtained in the spirit of ladder diagram approximations. The radio-frequency (RF) spectrum, as an important experimental approach for detecting Feshbach molecules or the interaction effect, is calculated at different temperatures. A reversed temperature dependence on the Bose–Einstein condensation side and Bardeen–Cooper–Schrieffer side is identified for both p- and d-wave interactions. An estimate for the signal of RF spectra under typical experimental conditions is also provided.

Study of excited Ξ states in ψ(3686)→K−ΛΞ¯++c.c.

Based on a sample of (448.1±2.9)×106 ψ(3686) events collected with the BESIII detector at BEPCII, the decays of ψ(3686)→K−ΛΞ¯++c.c. with Ξ¯+→Λ¯π+, Λ¯→p¯π+ are studied. We investigate the two excited resonances, Ξ(1690)− and Ξ(1820)−, which are each observed with large significance (≫10σ) in the K−Λ invariant mass distributions. A partial wave analysis is performed, and the spin-parities of Ξ(1690)− and Ξ(1820)− are measured to be 12− and 32−, respectively. The masses, widths, and product branching fractions of Ξ(1690)− and Ξ(1820)− are also measured. Published by the American Physical Society 2024

A Linear Theory for Periodic Convectively Forced Gravity Waves near a Coastline

Abstract This study presents a simple 2D linear analytical model aimed at investigating gravity waves forced by temporally periodic convection near a coastline. This investigation encompasses two distinct convective heating scenarios: deep convective heating and stratiform heating/cooling. Our model explores the intricate behavior of gravity waves in proximity to a time-dependent convective source and examines their propagation characteristics across diverse atmospheric conditions. Close to the convective source, gravity waves demonstrate nearly horizontal propagation with vertically aligned phase lines. The velocity of their propagation primarily depends on the vertical scale of the convective heating. The presence of a tropopause further extends their horizontal reach through partial wave ducting between the surface and the tropopause. However, the horizontal scale of the convective heating also plays a crucial role in determining the horizontal wavelength, and consequently, affecting the horizontal propagation speed of the gravity waves. If the heating horizontal scale is small compared to the horizontal scale of free waves at the forcing frequency, the heating vertical scale determines the vertical wavelength and thus the horizontal wavelength. However, if the heating horizontal scale is large, the horizontal wavelength determined by the heating vertical scale has little energy, so that the horizontal wavelength is mainly determined by the heating horizontal scale. Moreover, longer periods of convective heating and stronger background winds contribute to an increased downstream propagation distance of the gravity waves away from the source. Additionally, inertia-gravity waves generated by diurnal convection can propagate horizontally over greater distances at a higher latitude but become confined or trapped at latitudes exceeding 30°.

Early screening of colorectal cancer using feature engineering with artificial intelligence-enhanced analysis of nanoscale chromatin modifications

Colonoscopy is accurate but inefficient for colorectal cancer (CRC) prevention due to the low (~ 7 to 8%) prevalence of target lesions, advanced adenomas. We leveraged rectal mucosa to identify patients who harbor CRC field carcinogenesis by evaluating chromatin 3D architecture. Supranucleosomal disordered chromatin chains (~ 5 to 20 nm, ~1 kbp) fold into chromatin packing domains (~ 100 to 200 nm, ~ 100 to 1000 kbp). In turn, the fractal-like conformation of DNA within chromatin domains and the folding of the genome into packing domains has been shown to influence multiple facets of gene transcription, including the transcriptional plasticity of cancer cells. We deployed an optical spectroscopic nanosensing technique, chromatin-sensitive partial wave spectroscopic microscopy (csPWS), to evaluate the packing density scaling D of the chromatin chain conformation within packing domains from rectal mucosa in 256 patients with varying degrees of progression to colorectal cancer. We found average packing scaling D of chromatin domains was elevated in tumor cells, histologically normal-appearing cells 4 cm proximal to the tumor, and histologically normal-appearing rectal mucosa compared to cells from control patients (p < 0.001). Nuclear D had a robust correlation with the model of 5-year risk of CRC with r2 = 0.94. Furthermore, rectal D was evaluated as a screening biomarker for patients with advanced adenomas presenting an AUC of 0.85 and 85% sensitivity and specificity. artificial intelligence-enhanced csPWS improved diagnostic performance with AUC = 0.90. Considering the low sensitivity of existing CRC tests, including liquid biopsies, to early-stage cancers our work highlights the potential of chromatin biomarkers of field carcinogenesis in detecting early, significant precancerous colon lesions.

Capping the positivity cone: dimension-8 Higgs operators in the SMEFT

SMEFT Wilson coefficients are subject to various positivity bounds in order to be consistent with the fundamental principles of S-matrix. Previous bounds on dimension-8 SMEFT operators have been obtained using the positivity part of UV partial wave unitarity and form a (projective) convex cone. We derive a set of linear UV unitarity conditions that go beyond positivity and are easy to implement in an optimization scheme with dispersion relations in a multi-field EFT. Using Higgs scattering as an example, we demonstrate how to obtain closed bounds in the space of the three relevant dimension-8 coefficients, making use of the UV unitarity conditions as well as so-called null constraints that arise from full crossing symmetry. Specifically, we show that they are bounded by inequalities schematically going like C <O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document} ((4π)2). We compare the newly obtained upper bounds with the traditional perturbative unitarity bounds from within the EFT, and discuss some phenomenological implications of the two-sided positivity bounds in the context of experimental probes of Vector Boson Scattering.

Bootstrapping high-energy observables

In this paper, we set up the numerical S-matrix bootstrap by using the crossing symmetric dispersion relation (CSDR) to write down Roy equations for the partial waves. As a motivation behind examining the local version of the CSDR, we derive a new crossing symmetric, 3-channels-plus-contact-terms representation of the Virasoro-Shapiro amplitude in string theory that converges everywhere except at the poles. We then focus on gapped theories and give novel analytic and semi-analytic derivations of several bounds on low-energy data. We examine the high-energy behaviour of the experimentally measurable rho-parameter, introduced by Khuri and Kinoshita and defined as the ratio of the real to the imaginary part of the amplitude in the forward limit. Contrary to expectations, we find numerical evidence that there could be multiple changes in the sign of this ratio before it asymptotes at high energies. We compare our approach with other existing numerical methods and find agreement, with improvement in convergence.

Semirelativistic study of the semileptonic decays of Bq mesons to orbital excited heavy tensors

Based on the method of solving the complete Salpeter equation, we study the semileptonic decays of a 0− heavy meson to 1P, 2P, or 3P heavy-tensor mesons, Bq→(c¯q)(nP)ℓ+νℓ (q=u,d,s,c;n=1,2,3). The obtained branching ratio of B(B→D2⋆(2460)ℓ+νℓ) agrees with the experimental data. We predict B(Bs0→Ds2⋆−(1P)ℓ+νℓ)=3.76×10−3 and B(Bc+→χc2(1P)ℓ+νℓ)=1.82×10−3. The branching ratios of decays to 2P and 3P final states are found to be very small. The ratios R(D¯2⋆0)=0.045, R(Ds2⋆)=0.048 and R(χc2)=0.059 are also obtained. This study focuses on the contribution of relativistic corrections. The wave function of the pseudoscalar includes nonrelativistic S-wave and relativistic P-wave. While for a tensor, it contains nonrelativistic P-wave and relativistic P-, D-, and F-waves in its wave function. We find the individual contributions of relativistic partial waves are significant in the decay B→D2⋆(2460)ℓ+νℓ, but the overall contribution of the relativistic effect is 24.4%, which is small due to cancellation. Similarly, for the decay Bs0→Ds2⋆−(1P)ℓ+νℓ, the contribution of the relativistic effect is 28.8%. While for Bc+→χc2(1P)ℓ+νℓ, the individual contributions of relativistic partial waves and the overall relativistic correction are both small, the later of which is 22.1%. Published by the American Physical Society 2024

Arbitrary multi-directional acoustic beam emission from a cylindrical metasurface with grafted topological charge

Directional sound beam emission from compact devices is highly desirable in many practical acoustic applications. Here, we present an approach for the efficient control of arbitrary multi-directional emission through a grafted metasurface that is designed by cutting and stitching two cylindrical phase-gradient metasurfaces carrying two opposite topological charges. The grafted metasurface provides a compact and robust platform for diverse multi-directional beam emission, whose beam number and azimuthal angles are precisely controlled by the topological charge. The underlying mechanism contributes to the wave interference of two opposite partial vortex waves. This scheme was verified by simulation and experimental results. Our work provides a design methodology for directional sound beam emission devices and may be useful for applications such as acoustic imaging, beam steering, and vortex detection.