We evaluate discovery prospects for photophobic axion-like particles (ALPs) in the $\textit{WWjj}$ final state at the High-Luminosity LHC (HL-LHC; $\sqrt{s}=14\ {\rm{TeV}}$ , ${\cal{L}}=3\ {\rm{ab}}^{-1}$ ). In the photophobic limit ( $g_{a\gamma\gamma}=0$ ), ALPs couple to electroweak gauge bosons and are produced in association with two jets ( $ pp\to jj\ a $ ) via both $\textit{s}$-channel electroweak exchange and vector boson fusion (VBF)–like topologies, followed by $a\to W^+W^-$ decay. We target the different-flavour dilepton mode $W^+W^- \to e^\pm\mu^\mp\nu \bar{\nu}$ with two jets and moderate missing transverse momentum. The analysis employs a two-step strategy: initial preselection that defines the signal-like final state, followed by a multivariate analysis (MVA) trained on dijet and dileptonic-$\textit{WW}$ kinematics from both the $\textit{s}$-channel and VBF-like production mechanisms to separate signal from background; the MVA threshold is optimized independently at each $m_a$ . We present 2$\textit{σ}$ and 5$\textit{σ}$ discovery sensitivities for the ALP–$\textit{W}$ coupling $g_{aWW}$ across the 170–4000 GeV mass range. For $260\ {\rm{GeV}}\le m_a\le1500\ {\rm{GeV}}$ , the 2$\textit{σ}$ (5$\textit{σ}$) sensitivity is approximately flat around $ 0.61(0.76)\ {\rm{TeV}}^{-1}$ . At large masses/couplings, the mapping between an experimental rate and a single EFT parameter $g_{aWW}$ can become UV sensitive, and we treat the extreme high-mass/high-coupling corner as an extrapolation; therefore, we also report model-independent discovery thresholds for the fiducial quantity $ \sigma(pp\to jj\ a)\times\rm{Br}(a\to W^+W^-) $ over the same mass range to enable reinterpretation for other models. These results indicate that the $WWjj$ topology offers competitive and complementary sensitivity to heavy photophobic ALPs at the HL-LHC.

China

Jiaojiao Feng

Ying-nan Mao

Kechen Wang

Discovery prospects for photophobic axion-like particles in the $\textit{WWjj}$ final state at the High-Luminosity LHC * Jiaojiao Feng and Kechen Wang are supported by the National Natural Science Foundation of China (11905162), the Excellent Young Talents Program of the Wuhan University of Technology (40122102, 40122103) and the research program of the Wuhan University of Technology (2020IB024, 104972025KFYjc0101). Ying-nan Mao is supported by the National Natural Science Foundation of China (12205227). The simulation and analysis work of this article was completed with the computational cluster provided by the Theoretical Physics Group at the Department of Physics, School of Physics and Mechanics, Wuhan University of Technology

Xuan-Heng Zhang

Sheng-Qi Zhang

Cong-Feng Qiao

Erratum: The spectra of $$p\bar{\Lambda }$$ and $$p\bar{\Sigma }$$ hexaquark states

To understand the nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2075</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2085</mn><mo stretchy="false">)</mo></math> observed by the BESIII Collaboration in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> system, we systematically investigate the possibility that these states are compact hexaquark with triquark-antitriquark configurations for the first time. Within the framework of QCD sum rules, the mass spectrum and decay constants of such hexaquark states with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>−</mo></msup><mo>,</mo><msup><mn>0</mn><mo>+</mo></msup><mo>,</mo><msup><mn>1</mn><mo>−</mo></msup><mo>,</mo><msup><mn>1</mn><mo>+</mo></msup></math> are studied. Consequently, six independent and nondegenerate hexaquark candidates are obtained, among which two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>−</mo></msup></math> states exhibit masses consistent with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2075</mn><mo stretchy="false">)</mo></math>, while the two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> states differ markedly from the mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2075</mn><mo stretchy="false">)</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2085</mn><mo stretchy="false">)</mo></math>. The remaining two states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mo>−</mo></msup></math> may serve as predictions for potential compact hexaquark configurations. Furthermore, the possible decay modes of these hexaquark states are analyzed, which could be the experimental signatures for their identification.

Spectrum of light hexaquark states in a triquark-antitriquark configuration

Dimuonium (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>) is one of the pure QED bound systems of leptons, together with positronium and ditauonium. The former had been observed in an experiment in 1951 [M. Deutsch, <a href="http://dx.doi.org/10.1103/PhysRev.82.455">Phys. Rev. 82, 455 (1951)</a>], while the search for dimuonium and ditauonium (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math>) are still in vain. The ditauonium is thought to be hard to measure due to its short life time, whereas the dimuonium is very likely to be observed in current running experiments. We calculate in this work the para and ortho dimuonium production in photon-photon collision at the next-to-leading order (NLO) in QED. To handle the Coulomb divergence within the bound system, the nonrelativistic QED description is adopted for consistency. The results indicate that the NLO corrections are negative for both para and ortho states, at the normal order of perturbative QED corrections. The measurement of the dimuonium in the Belle II experiment, especially at the forthcoming facility of STCF, is tenable.

Qi-Ming Feng

Si-Mao Guo

Qi-Wei Hu

Qi-Ming Qiu

Yu-Jie Tian

Bai-Rong Zhang

Hao Zhang

Bo-Ting Zhou

NLO corrections to dimuonium production in photon-photon collision

The quarkonium production in association with a heavy-quark pair of the same flavor was found to play an important role in various production schemes and provide a distinctive signature that could be studied in experiment. Within the nonrelativistic QCD framework, we perform the first complete calculation of the hadroproduction process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mi>g</mi><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> at the next-to-leading order (NLO) in the expansion of strong coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>. The result tells us that the NLO corrections substantially enhance the color-singlet yield and alter the predicted polarization patterns and, hence, lead to a better agreement with experimental data across the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi>T</mi></msub></math> spectrum. In contrast to charm-quark fragmentation, the fixed-order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> associated production channel displays a markedly different kinematic behavior. While the inclusion of this process greatly reduces the discrepancy between color-singlet theoretical prediction and experimental measurement, a residual gap of approximately 1 order of magnitude still remains.

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> polarization and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi>T</mi></msub></math> distribution in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> associated hadroproduction at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>5</mn></msubsup><mo stretchy="false">)</mo></math>

We analyzed two-loop planar contributions to a three-body form factor at next-to-leading power in the high-energy limit, where the masses of the external particles are much smaller than their energies. Calculations were performed by exploiting differential equations for the expansion coefficients, both to facilitate linear relations among them and to derive their analytic expressions. The results are expressed in terms of generalized polylogarithms involving a few simple symbol letters. Our method can readily be applied to calculations of non-planar contributions as well. Our results provide crucial information for establishing sub-leading factorization theorems for massive scattering amplitudes in the high-energy limit.

Yishuai Guo

Zhi-Feng Liu

Mingming Lu

Tianya Xia

Li-Lin Yang

A three-body form factor at sub-leading power in the high-energy limit: planar contributions * Supported in part by the National Natural Science Foundation of China Sunder (12375097, 12347103) and the Fundamental Research Funds for the Central Universities. Zhi-Feng Liu was supported by the China Postdoctoral Science Foundation (2023M733123, 2023TQ0282) and the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation

Motivated by the recent observation of the $$J^P = 1^+$$ resonance $\textit{X}$(2085) in the $$p\bar{\Lambda }$$ system by the BESIII collaboration, we study the molecular states of $$p\bar{\Lambda }$$ and $$p\bar{\Sigma }$$ with baryon-antibaryon structures within the framework of the QCD sum rules. Non-perturbative contributions up to dimension 13 in quark operator expansion (OPE) are considered. Our calculation results indicate the possible existence of six $$p\bar{\Lambda }$$ and $$p\bar{\Sigma }$$ molecular states with quantum numbers $$J^{P}=0^{-}, 0^{+}, 1^{-}$$ , which do not support $\textit{X}$(2085), or at least not its main component, being a $$p\bar{\Lambda }$$ or $$p\bar{\Sigma }$$ molecular state. Additionally, the previously observed state $\textit{X}$(2075) also lies in the vicinity of $$p\bar{\Lambda }$$ and $$p\bar{\Sigma }$$ molecular states, and its inner structure might not be entirely transparent, rather possibly a mixture of tetraquark and hexaquark states. The possible decay modes of the concerned states are analyzed.

The spectra of $$p\bar{\Lambda }$$ and $$p\bar{\Sigma }$$ hexaquark states

Within the framework of nonrelativistic quantum chromodynamics, this study examines the electroproduction processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo>+</mo><mi>p</mi><mo stretchy="false">→</mo><mi>e</mi><mo>+</mo><msub><mi>B</mi><mi>c</mi></msub><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi>b</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo>+</mo><mi>p</mi><mo stretchy="false">→</mo><mi>e</mi><mo>+</mo><msub><mi>B</mi><mi>s</mi></msub><mo>+</mo><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi>b</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo>+</mo><mi>p</mi><mo stretchy="false">→</mo><mi>e</mi><mo>+</mo><msub><mi>D</mi><mi>s</mi></msub><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi>s</mi></math> at lepton-hadron colliders. The differential cross sections in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>cos</mi><mi>θ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>p</mi><mi>T</mi><mn>2</mn></msubsup></math> at HERA are presented. Comparisons with fragmentation contributions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> production are made. The results indicate that the detection of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> is possible at the EIC, whereas not feasible at HERA. The cross sections of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>s</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> production are significant at HERA, though they are notably quark mass and renormalization scale dependent.

Li-Ping Sun

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>s</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> production at lepton-hadron colliders

Inspired by the experimental measurement of the charmed hadronic state X(6900), we calculate the mass spectra of tetraquark hybrid states with configuration of $$[8_{c}]_{Q\bar{Q}} \otimes [8_{c}]_{G} \otimes [8_{c}]_{Q\bar{Q}}$$ in color, by virtue of QCD sum rules. The two feasible types of currents with quantum numbers $$J^{PC} = 0^{++}$$ and $$0^{-+}$$ are investigated, in which the contributions from operators up to dimension six are taken into account in operator product expansion (OPE). In the end, we find that, in charm sector, the tetracharm hybrid states with quantum number $$0^{++}$$ has a mass of about $$6.98^{+0.16}_{-0.14} \, \text {GeV}$$ , while $$0^{-+}$$ state mass is about $$7.26^{+0.16}_{-0.15} \, \text {GeV}$$ . The results overlap with the experimental observations, suggesting potential tetracharm hybrid interpretations. In bottom sector, calculation shows that the masses of tetrabottom hybrid states with quantum numbers $$0^{++}$$ and $$0^{-+}$$ are $$19.30^{+0.16}_{-0.17} \, \text {GeV}$$ and $$19.50^{+0.17}_{-0.17} \, \text {GeV}$$ , respectively, which are left for future experimental confirmation.

Chun-Meng Tang

Chun-Gui Duan

Liang Tang

A novel configuration of gluonic tetraquark state

In this paper, we investigate the Higgs boson decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo stretchy="false">→</mo><mi>f</mi><mover accent="true"><mi>f</mi><mo stretchy="false">¯</mo></mover><mi>Z</mi><mo stretchy="false">→</mo><mi>f</mi><mover accent="true"><mi>f</mi><mo stretchy="false">¯</mo></mover><msup><mi>μ</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math> denotes any light fermions, at the next-to-leading order (NLO) accuracy. The calculation is performed within the framework of single-pole approximation, in which the contributions of different polarization states of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson are considered separately. Numerical results show that, by taking appropriate cut, the nonresonant background is negligible, and the NLO corrections are 1%–4% of the LO contributions. We also find that the inclusion of NLO corrections can greatly reduce the dependence on the electroweak coupling scheme, and enhance the prediction reliability. We formulate a method for the extraction of the pseudo-observable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Γ</mi><mrow><mi>H</mi><mo stretchy="false">→</mo><mi>f</mi><mi>f</mi><mi>Z</mi></mrow></msup></math> from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi><mover accent="true"><mi>f</mi><mo stretchy="false">¯</mo></mover><msup><mi>μ</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> signal.

Zi-Qiang Chen

Higgs boson decays to a fermion pair and a polarized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson at NLO accuracy