The beyond-the-standard-model scenario presented in this work is motivated by the observations of neutrino masses, the anomalous magnetic moments of the electron and muon, and dark matter in the Universe. We explain these observations by extending the standard model with two generations of vector-like fermions and an inert scalar doublet, all of which are odd under a $Z_2$ symmetry. The light neutrino masses and mixings are generated radiatively while maintaining consistency with bounds on lepton flavor violation. Loop diagrams featuring the same fields also explain the anomalous magnetic moments. Similarly, the correct dark matter relic abundance is reproduced without conflicting with direct detection constraints, or those from big bang nucleosynthesis or cosmic microwave background observations. Finally, prospective signatures at the LHC are discussed.

India

Vandana Sahdev

Neutrino masses, anomalous magnetic moments and dark matter with vector-like fermions and an inert scalar doublet * V.S. acknowledges the support from research grant no. CRG/2018/004889 of the SERB, India; T.R. Seshadri for providing resources during the initial stages of the work; and Brajesh Choudhary for providing access to computers bought under the aegis of Grant No. SR-MF/PS-0212014-DUB (G) of the DST (India)

We present an investigation of the $ K^*(1680) $ state in its strong decays into two-body final states within the flux-tube model and quark pair creation model. Since charge conjugation parity is not conserved in the strange sector, the conventional $ q\bar{q} $ states with $ J^{P(C)}=1^{-(-)} $ can mix with the lowest hybrid states with $ J^{P(C)}=1^{-(+)} $ . Our analysis of the $ K^*(1680) $ two-body strong decays indicates that the decay pattern of $ K^*(1680) $ cannot be explained by the conventional $ q\bar{q} $ scenario. Moreover, there is strong evidence for the $ q\bar{q} $ -hybrid mixing mechanism in the strange sector. The phenomenological consequences of such mixing are also discussed. Our study can provide guidance for future searches for hybrid multiplets in experiments at BESIII, LHCb, and Belle II.

China

Samee Ullah

Ye Cao

Ming-Xiao Duan

Hai-Bing Fu

Qiang Zhao

Nature of ${K^*(1680)}$ and ${q\bar{q}}$ -hybrid mixing as the $\textit{SU}$(3) partner of ${\eta_{1}(1855)}$ in the strange sector * Supported in part by the National Natural Science Foundation of China (12235018, 12265010, 12505098), and the Project of Guizhou Provincial Department of Science and Technology (MS[2025]219, CXTD[2025]030, ZD[2026]168, QN[2025]178), and the project of Guizhou Normal University (GZNUD[2025]05)

Uncovering physical laws from experimental data is a fundamental goal of theoretical physics. In this work, we apply the spline-based, interpretable Kolmogorov–Arnold Network (KAN) to investigate the algebraic structure underlying the baryon octet and decuplet mass spectra. Within a symbolic regression framework and without imposing theoretical priors, KAN recovers a symbolic representation equivalent to the classical Gell-Mann–Okubo mass relations, which can be transformed into the standard form through algebraic rearrangement. Compared with conventional fitting approaches, this method achieves comparable predictive accuracy while providing substantially improved interpretability and analytical transparency. Our results demonstrate the potential of KAN as a powerful tool for symbolic discovery in hadron physics and for bridging data-driven modeling with fundamental physical laws.

Jian-Yao He

Italy

Xun Chen

Xiao-Yan Zhu

Wen Luo

Discovering the Gell-Mann–Okubo formula with Kolmogorov-Arnold networks * Supported by the National Natural Science Foundation of China (NSFC) (12405154) and the European Union – Next Generation EU through research grant (P2022Z4P4B), ''SOPHYA - Sustainable Optimised PHYsics Algorithms: fundamental physics to build an advanced society'', under the PRIN 2022 PNRR program of the Italian Ministero dell'Università e Ricerca (MUR)

The rare exclusive decay of the Higgs boson, $ H \to J/\psi + \gamma $ , is a crucial channel for assessing the Yukawa coupling of the charm quark. In this article, we examine this process up to the next-to-next-to-leading order (NNLO) in QCD utilizing the Principle of Maximum Conformality (PMC). The PMC offers a systematic approach to eliminate renormalization scale uncertainties by resumming non-conformal $\textit{β}$ contributions into the QCD running coupling through the renormalization group equation (RGE). A PMC scale of $ Q_\star = 3.29\ {\rm{GeV}} $ is obtained, which reflects the low virtuality of the underlying QCD dynamics in the $ H \to J/\psi + \gamma $ process. Notably, this is an order of magnitude smaller than the scale estimated using the conventional method, $\textit{i.e.}$, $ \mu_r = m_H/2 $ . By removing the non-conformal $ \{\beta_i\} $ -terms from the perturbative QCD (pQCD) series, we observe that the PMC NLO QCD correction term is significantly enhanced, while the PMC NNLO QCD correction is suppressed. This indicates improved convergence of the pQCD series up to NNLO. Finally, we calculate the decay width $ \Gamma(H \to J/\psi + \gamma) = $ $ 14.183^{+0.249}_{-0.347} \pm 0.022 $ eV, where the first uncertainty arises from the factorization scale $ \mu_\Lambda \in [1, 2]\ {\rm{GeV}} $ , and the second is due to the estimation of unknown higher-order terms using the Pad $ \acute{e} $ approximant approach. The corresponding branching fraction is $ {\cal{B}}(H \to J/\psi + \gamma) = 3.485_{-0.161}^{+0.152} \times 10^{-6} $ .

Wen-Yuan Li

Ting Sun

Sheng-Quan Wang

Jian-Ming Shen

Hua Zhou

Xing-Gang Wu

Leonardo Di Giustino

Analysis of $\textit{H}$ → $\textit{J}$/$\textit{ψ}$ + $\textit{γ}$ up to Next-to-Next-to-Leading order QCD corrections * Supported in part by the Natural Science Foundation of China (12265011, 12175025, 12347101); the Project of Guizhou Provincial Department of Science and Technology (YQK[2023]016, ZK[2023]141, CXTD[2025]030); the Hunan Provincial Natural Science Foundation (2024JJ3004); the YueLuShan Center for Industrial Innovation (2024YCII0118), and the Natural Science Foundation of Sichuan Province (2024NSFSC1367)

This work presents a comprehensive analysis of polarization transfer in the decays of $\chi_{cJ}$ ( $J=0,1,2$ ) into octet baryon-antibaryon pairs in polarized electron-positron collisions. Using the spin density matrix formalism, we trace the polarization from the initial beams through the production chain $e^+e^- \to \psi(2S) \to \gamma \chi_{cJ}$ to the final-state baryon-antibaryon system. The helicity amplitude analysis for $\chi_{c1} \to B\bar{B}$ confirms the universal angular distribution parameter $\alpha = -1/3$ , as dictated by the charge-conjugation helicity selection rule. For $\chi_{c2}$ decays, $\textit{α}$ and the transverse polarization depend on two independent amplitudes, and our quark-model calculations agree with existing data. We demonstrate that the longitudinal beam polarization $P_z$ modifies the spin observables for $\chi_{c1}$ and $\chi_{c2}$ . This offers new experimental handles at future polarized facilities, such as the Super $\textit{τ}$-Charm Facility (STCF), to test decay mechanisms and explore baryonic spin entanglement as a quantum information resource.

Cai-Ying Pang

Rong-Gang Ping

Dai-Hui Wei

Polarization analysis of χ$_{cJ}$ decay into octet baryonic pairs * Supported by the National Natural Science Foundation of China (NSFC) (12575112, 12465015)

The triangle singularity interpretation of the $a_1(1420)$ observed by the COMPASS Collaboration has been widely accepted. In this work, we investigate the triangle mechanism in the decay $B^0 \to D^- \pi^+ a_0(980)(\pi^0 \eta)$ , where the $a_0(980)$ is treated as a dynamically generated state. The $\bar{K}^{*0}$ - $K^+$ - $K^-$ triangle loop originates from the decay $B^0 \to D^- K^+ \bar{K}^{*0}$ , which has been observed by the Belle Collaboration, followed by the subsequent decay $\bar{K}^{*0} \to K^- \pi^+$ . The triangle amplitude develops a pronounced peak around 1420 MeV, which is reflected in the invariant mass spectrum of the $\pi a_0(980)$ system. The differential decay width is calculated and exhibits a narrow peak around $980~\mathrm{MeV}$ in the $\pi^0 \eta$ invariant mass distribution. Furthermore, the invariant mass distribution of the $\pi^+ \pi^0 \eta$ system shows a clear peak around $1420~\mathrm{MeV}$ , which further confirms the triangle singularity explanation of the $a_1(1420)$ . We expect that the proposed $B^0$ decay mode could provide a potential platform for further exploring the triangle-singularity nature of the $a_1(1420)$ and could be tested in future experiments such as LHCb, BESIII, and Belle II.

Wei Wang

Dazhuang He

Xuan Luo

The role of triangle singularity in the $ {B^0 \to D^- \pi^+ a_0(980)(\pi^0 \eta)}$ decay * Dazhuang He is supported by the Heze University doctoral fund project (010008002039037). Xuan Luo is supported by the National Natural Science Foundation of China (12205002)

The observation of the associated production of an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">ϒ</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></mrow></mrow></math> meson with a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson and a measurement of the ratio of its fiducial cross section to the fiducial cross section of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson are presented. Both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></mrow></math> meson and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson are identified via decays into a pair of opposite-sign muons. The analysis is based on proton-proton (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math>) collision data at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> collected with the CMS detector in 2016–2018 and corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>138</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. Using the production of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson decaying into four muons as a normalization channel, the ratio of the fiducial cross sections <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>σ</mi><mo stretchy="false">[</mo><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>Z</mi><mo>+</mo><mrow><mi mathvariant="normal">ϒ</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">]</mo></mrow><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>Z</mi><mo stretchy="false">→</mo><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mrow><mi mathvariant="normal">ϒ</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">→</mo><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow><mo stretchy="false">]</mo></mrow></mrow></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>σ</mi><mo stretchy="false">(</mo><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>Z</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>Z</mi><mo stretchy="false">→</mo><mrow><mn>4</mn><mi>μ</mi></mrow><mo stretchy="false">)</mo></mrow></mrow></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">R</mi></mrow><mrow><mi>Z</mi><mo>+</mo><mrow><mi mathvariant="normal">ϒ</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></mrow></mrow></mrow></msub><mo>=</mo><mo stretchy="false">[</mo><mn>21.1</mn><mo>±</mo><mn>5.5</mn><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mo>±</mo><mn>0.6</mn><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">]</mo><mrow><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></mrow></math>, where stat and syst denote the statistical and systematic uncertainties, respectively. The result is used to extract the effective double-parton scattering cross section <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>eff</mi></mrow></msub><mo>=</mo><mrow><msubsup><mrow><mn>13.0</mn></mrow><mrow><mo>−</mo><mn>3.4</mn></mrow><mrow><mo>+</mo><mn>7.7</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>mb</mi></mrow></mrow></math>. In addition, for the first time, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><mi>eff</mi></msub></math> is measured in bins of the transverse momentum of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></mrow></math> meson or of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson.

Armenia

A. Hayrapetyan

V. Makarenko

A. Tumasyan

Austria

W. Adam

J.W. Andrejkovic

L. Benato

T. Bergauer

M. Dragicevic

C. Giordano

P.S. Hussain

M. Jeitler

N. Krammer

A. Li

D. Liko

M. Matthewman

I. Mikulec

J. Schieck

R. Schöfbeck

D. Schwarz

M. Shooshtari

M. Sonawane

W. Waltenberger

C.E. Wulz

Belgium

T. Janssen

H. Kwon

D. Ocampo Henao

T. Van Laer

P. Van Mechelen

J. Bierkens

N. Breugelmans

J. D’Hondt

S. Dansana

A. De Moor

M. Delcourt

F. Heyen

Y. Hong

P. Kashko

S. Lowette

I. Makarenko

D. Müller

J. Song

S. Tavernier

M. Tytgat

G.P. Van Onsem

S. Van Putte

D. Vannerom

B. Bilin

B. Clerbaux

A.K. Das

I. De Bruyn

G. De Lentdecker

H. Evard

L. Favart

P. Gianneios

A. Khalilzadeh

F.A. Khan

A. Malara

M.A. Shahzad

L. Thomas

M. Vanden Bemden

C. Vander Velde

P. Vanlaer

F. Zhang

M. De Coen

D. Dobur

G. Gokbulut

J. Knolle

L. Lambrecht

D. Marckx

K. Skovpen

N. Van Den Bossche

J. van der Linden

J. Vandenbroeck

L. Wezenbeek

S. Bein

A. Benecke

A. Bethani

G. Bruno

A. Cappati

J. De Favereau De Jeneret

C. Delaere

A. Giammanco

A.O. Guzel

V. Lemaitre

J. Lidrych

P. Malek

P. Mastrapasqua

S. Turkcapar

Brazil

G.A. Alves

M. Barroso Ferreira Filho

E. Coelho

C. Hensel

T. Menezes De Oliveira

C. Mora Herrera

P. Rebello Teles

M. Soeiro

E.J. Tonelli Manganote

A. Vilela Pereira

W.L. Aldá Júnior

H. Brandao Malbouisson

Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo><mo>+</mo><mi>Z</mi></math> Associated Production and Measurement of the Effective Double-Parton Scattering Cross Section in Proton-Proton Collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>

We demonstrate that at finite density and sufficiently high temperatures, phase-quenched (PQ) lattice simulations combined with perturbation theory provide a new precision approach to determining the thermodynamics of QCD across a wide arc of the phase diagram where the strong coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> remains small. In this regime, nonperturbative pairing effects in the PQ theory are parametrically suppressed, so that the difference between the PQ and full QCD pressures becomes a small perturbative correction. We compute this correction up to and including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mrow><mn>7</mn><mo>/</mo><mn>2</mn></mrow></msubsup><mo stretchy="false">)</mo></math> using electrostatic QCD together with a novel numerical method to compute four-loop sum-integrals. This enables the determination of the perturbative QCD pressure with precision beyond the current state of the art while including nonperturbative pure-gluonic contributions from the lattice.

United States

Tyler Gorda

Finland

Pablo Navarrete

Risto Paatelainen

Leon Sandbote

Switzerland

Kaapo Seppänen

New approach to determine the thermodynamics of deconfined matter to high accuracy

We present the first paleodetector dark-matter sensitivity analysis based on a calorimetric readout, in which the number of stable lattice vacancies produced by each nuclear recoil is used as a per-event observable complementary to the track length. Using full-cascade srim simulations in olivine, we compute the expected sensitivity for a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>100</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">g</mi><mo>·</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>Gyr</mi></mrow></math> exposure. We find that a vacancy-only readout reaches a sensitivity envelope very similar to that of state-of-the-art track-only analyses. The combination of the two observables provides an event-by-event proxy for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi><mo stretchy="false">|</mo></math> and hence for the recoiling nuclear species. Since the neutron-nucleus cross section is approximately flat in nuclear mass while the dark-matter–nucleus cross section scales as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>A</mi><mn>2</mn></msup></math>, this discrimination suppresses the dominant neutron background by more than an order of magnitude at moderate dark-matter masses. The combined-analysis sensitivity reaches spin-independent dark-matter–nucleon cross sections of order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>48</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mn>2</mn></msup></math> at weakly interacting massive particle masses of a few tens of GeV, comparable to future direct-detection experiments. A two-stage readout combining selective-plane illumination microscopy with scanning electron microscopy is identified as a path to making a 100 g-scale analysis plausible.

S.C. Hedges

P. Huber

Calorimetric approach to paleodetection of dark matter

We present a further theoretical study of the orbital <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave bottom-charmed baryon within the framework of nonrelativistic QCD, considering both the direct photoproduction channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>γ</mi><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow></msub><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> and the resolved photoproduction channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>g</mi><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow></msub><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math>. At future linear colliders, ILC and CLIC, the initial photons can be emitted from the laser backscattering and then the parton gluon can be emitted from the photon. The formation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow></msub></math> can be modeled in two steps: a compact diquark state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><mi>b</mi><mi>c</mi><mo stretchy="false">⟩</mo><mo stretchy="false">[</mo><mi>n</mi><mo stretchy="false">]</mo></math> is formed first and subsequently captures a light quark from the vacuum to hadronize into the baryon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow></msub></math>. The color and spin quantum number [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>] of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><mi>b</mi><mi>c</mi><mo stretchy="false">⟩</mo></math> diquark can be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">[</mo><mrow><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub></mrow><msub><mrow><mo stretchy="false">]</mo></mrow><mrow><mover accent="true"><mrow><mn mathvariant="bold">3</mn></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>/</mo><mn mathvariant="bold">6</mn></mrow></msub></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mrow><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow><mrow><mn>0</mn></mrow></msub></mrow><msub><mo stretchy="false">]</mo><mrow><mover accent="true"><mn mathvariant="bold">3</mn><mo stretchy="false">¯</mo></mover><mo>/</mo><mn mathvariant="bold">6</mn></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mrow><msub><mrow><mmultiscripts><mrow><mi>P</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub></mrow><msub><mo stretchy="false">]</mo><mrow><mover accent="true"><mn mathvariant="bold">3</mn><mo stretchy="false">¯</mo></mover><mo>/</mo><mn mathvariant="bold">6</mn></mrow></msub></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><msub><mrow><mmultiscripts><mrow><mi>P</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mi>J</mi></msub><msub><mo stretchy="false">]</mo><mrow><mover accent="true"><mn mathvariant="bold">3</mn><mo stretchy="false">¯</mo></mover><mo>/</mo><mn mathvariant="bold">6</mn></mrow></msub></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2. Using three benchmark collision energies and an illustrative integrated luminosity, we analyze the cross sections, differential distributions, and the estimated produced events of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow></msub></math> baryon. For the conservative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn mathvariant="bold">6</mn></msub><mo>=</mo><mn>0</mn></math> baseline, the combined <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave contribution amounts to approximately 8% of the combined <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave rate at three considered collision energies and is therefore non-negligible.

Juan-Juan Niu

Hong-Hao Ma

Investigation of the photoproduction of bottom-charmed baryons within NRQCD