arXiv subjects

Feng-Kun Guo

Publications and source records attributed to Feng-Kun Guo.

At least 19 recordsLinked to original sources

arXiv2026

Precise determination of the properties of $X(3872)$ and of its isovector partner $W_{c1}$

We perform a simultaneous fit to BESIII data on $e^+e^-\to γ(D^0{\bar{D}^{0}}π^0/J/ψπ^+π^-)$ and LHCb data on $B^+\to K^+(J/ψπ^+π^-)$ to precisely determine the properties of the $X(3872)$, with full consideration of three-body effects from $D^*\to Dπ$ decay, respecting both analyticity and unitarity. The $X(3872)$ is determined to be a quasi-bound state with a significance of $2.7\,σ$, representing the most precise determination to date. Its pole is located at $\left(-160^{+57}_{-74}-125^{+23}_{-38}\,i\right) \rm keV$, relative to the nominal $D^0\bar{D}^{*0}$ threshold. Moreover, we confirm the presence of an isovector partner state, $W_{c1}$. It is found as a virtual state at $\left(3.1\pm0.7+ 1.3^{+1.9}_{-0.6}\,i\right)\ \rm MeV$ relative to the $D^+ D^{*-}$ threshold on an unphysical Riemann sheet, strongly supporting a molecular nature of both $X(3872)$ and $W_{c1}$. As a highly nontrivial prediction we show that the $W_{c1}$ leads to nontrivial lineshapes around 3.88 GeV in $B^0\to K^0 X(3872)\to K^0 D^0\bar D^0π^0$ and $K^0J/ψπ^+π^-$ -- thus the scheme presented here can be tested further by improved measurements.

hep-ph↗

arXiv2026

QCD $θ$-vacuum energy and axion properties

At low energies, the strong interaction is governed by the Goldstone bosons associated with the spontaneous chiral symmetry breaking, which can be systematically described by chiral perturbation theory. In this paper, we apply this theory to study the $θ$-vacuum energy density and hence the QCD axion potential up to next-to-leading order with $N$ non-degenerate quark masses. By setting $N=3$, we then derive the axion mass, self-coupling, topological susceptibility and the normalized fourth cumulant both analytically and numerically, taking the strong isospin breaking effects into account. In addition, the model-independent part of the axion-photon coupling, which is important for axion search experiments, is also extracted from the chiral Lagrangian supplemented with the anomalous terms up to $\mathcal{O}(p^6)$.

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arXiv2026

Precision Sum Rule for Nucleon Isovector Polarizabilities and the Proton-Neutron Mass Difference

The precision of the electromagnetic proton-neutron mass difference $δm_\mathrm{QED}$ extracted from the Cottingham formula hinges on a subtraction function whose low-energy normalization $\bar S(0)$ is fixed by the isovector combination of the proton and neutron polarizabilities, $(α_{E1}-β_{M1})^{p-n}$. We derive a dispersive sum rule for this combination in terms of $s$-channel photoabsorption cross sections and the product of $t$-channel $γγ\toπη/K\bar K_{I_t=1}$ and $πη/K\bar K_{I_t=1}\to N\bar N$ amplitudes, without invoking Reggeon dominance. Combining empirical pion-photoproduction multipoles with coupled-channel Muskhelishvili--Omnès representations of the scalar-isovector $πη/K\bar K$ amplitudes, we obtain $(α_{E1}-β_{M1})^{p-n}=-2.26(73)\times10^{-4}\,\mathrm{fm}^3$, fixing its sign and reducing the uncertainty by a factor of 4 compared with the previously known value. This result yields $\bar S(0)=-1.76(61)\,\mathrm{GeV}^{-2}$, leading to $δm_\mathrm{QED}=0.71^{+0.03}_{-0.06}\,\mathrm{MeV}$, substantially more precise than previous Cottingham determinations. The negative $\bar S(0)$ also provides a stringent low-energy test of Reggeon dominance in the subtraction function.

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arXiv2026

Vector charmonium(-like) states in the energy range of 4.1-4.6 GeV

The spectrum of vector charmonium(-like) states in the 4.1\dash4.6~GeV energy region exhibits a long-standing tension between inclusive and exclusive measurements. While the inclusive $R$-value indicates only conventional vector charmonia such as $ψ(4160)$ and $ψ(4415)$, exclusive $e^+e^-$ cross sections reveal additional structures whose parameters strongly depend on the observed final states when fitted with Breit--Wigner functions. This puzzling pattern suggests that coupled-channel and threshold effects play an essential role. In this work, we develop a unified coupled-channel framework for the $1^{--}$ resonances in this energy region. The framework incorporates the $S$-wave open-charm channels $D\bar{D}_1$, $D^*\bar{D}_1$, and $D^*\bar{D}_2^*$ constrained by heavy-quark spin symmetry, optional bare poles associated with $ψ(4160)$ and $ψ(4415)$, and final-state interactions in the $Z_c$ channels. We perform simultaneous fits to the BESIII cross sections for $e^+e^-\to J/ψπ^+π^-$, $h_cπ^+π^-$, $D\bar{D}^*π$, $D^*\bar{D}^*π$, $J/ψη$, and $χ_{c0}ω$, together with invariant-mass distributions exhibiting the $Z_c(3900)$ and $Z_c(4020)$ structures. The benchmark models differ in the number of bare seed states and the fitting strategy. We show that even the purely dynamical scheme without bare charmonia captures the gross features of the analyzed distributions. The inclusion of bare compact states improves the fit quality but does not change the conclusion that the measured line shapes can be understood in terms of strong coupled-channel effects with dynamically generated poles. We also discuss possible heavy-quark spin partners of the exotic $1^{--}$ states.

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arXiv2026

Amplitude structure of $3\to 3$ scattering in a Mandelstam variable representation

We construct a dispersive representation of the relativistic $3\to 3$ scattering amplitude for three identical spinless particles in the $S$-wave. The two-particle subenergy, instead of the total energy, is used as the dispersive variable. This choice keeps the physical dispersive contour free of the kinematical cuts that complicate total-energy dispersion relations. By separating discontinuities across the two-particle subenergy cuts from that across the three-body cut, we derive a linear integral equation with one-particle exchange as the driving term. We further show that the solution satisfies three-body unitarity as a consequence of two-body unitarity, analyticity, and crossing symmetry. For pair-wise interactions, this representation can be rewritten into the form used for isobar-spectator scattering. Finally, we give prescriptions for contour deformation and the subtraction of poles in the two-body subsystem amplitudes, which continue the amplitude onto adjacent unphysical Riemann sheets and thus provide direct access to the analytic structure relevant for three-body resonance poles.

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arXiv2026

Amplified Isospin Breaking from Coupled-Channel Dynamics Near Threshold

We identify the dynamical origin of amplified isospin breaking in near-threshold states. Using a pole-residue-based measure defined directly from the pole couplings, rather than from decay observables that are also affected by different final-state kinematics, we show that threshold proximity of the pole alone is insufficient: large isospin breaking requires a sizable interaction in the companion isospin channel. Applied to the $X(3872)$, the observed large isospin breaking points to a nearby partner pole, $W_{c1}$, as predicted in previous studies. In addition, we find that the $W_{c1}$ pole, which predominantly affects the line shapes near the charged threshold in the physical case, does not evolve into the pure $I=1$ eigenstate in the isospin limit; instead, that eigenstate is continuously connected to a more distant shadow pole.

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arXiv2026

A femtoscopic tale of two $C$-parities: the $Z_c(3900)$ and the isovector partner of the $X(3872)$

Understanding the nature of the exotic $Z_c(3900)$ and $Z_{cs}(3985)$ states, and searching for the predicted isovector partner $W_{c1}$ of the $X(3872)$, remain central challenges in exotic-hadron spectroscopy. We investigate the femtoscopic correlation functions (CFs) of the $D^{(\ast)0}D_{(s)}^{(\ast)-}$ systems. Since these charm-meson--antimeson pairs are not $G$-parity eigenstates, their CFs contain contributions from both the $C$-odd and $C$-even sectors, providing direct access to the dynamics underlying the $Z_c$, $Z_{cs}$, and the predicted isovector exotic $W_{c1}$. Within a heavy-quark-spin-symmetric coupled-channel framework, we show that the $C$-even admixture enhances the low-momentum CFs by more than $2.5σ$ in the vicinity of their thresholds. Free from Coulomb distortions and accessible in high-multiplicity $pp$ collisions at the LHC, these channels offer the first direct femtoscopic probe of the isovector $C$-even sector and of the elusive $W_{c1}$ state.

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arXiv2026

Low-energy scattering of the $J/ψπ$ and $J/ψK$ system

We investigate the low-energy interactions between the charmonium state $J/ψ$ and the light pseudoscalar mesons ($π$ and $K$) within the framework of dispersion relations. We demonstrate that the symmetry-breaking terms in the chiral Lagrangian induce mixing between the bare charmonium fields, necessitating a diagonalization procedure to correctly identify the physical $J/ψ$ and $ψ'$ states. Using the resulting diagonalized Lagrangian, we construct the crossed-channel amplitudes for $J/ψJ/ψ\to {\cal P}\bar{\cal P}$ and incorporate the $ππ$ and $K\bar{K}$ rescattering effects through dispersion relations. This framework is used consistently both in the phenomenological extraction of the transition parameters from $ψ' \to J/ψππ$ and in the continuation of the crossed amplitudes to the near-threshold $J/ψ{\cal P}~({\cal P}=π,K)$ region. As a result, we determine both the scattering lengths and the effective ranges. We obtain the upper-bound estimates $a_{J/ψπ}\lesssim -0.0037$~fm and $a_{J/ψK}\lesssim -0.049$~fm, where the negative sign indicates an attractive interaction without a bound state in our convention. Our results show that the $J/ψK$ interaction is moderately enhanced relative to the pion channel, driven by explicit chiral symmetry breaking. Furthermore, a quantitative comparison of the coupled-channel mechanism, where $J/ψπ$ and $J/ψK$ couple to open-charm channels, reveals that both $J/ψπ$ and $J/ψK$ scatterings are predominantly governed by the soft-gluon exchange mechanism.

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arXiv2026

Low-energy $DD$ scattering in lattice QCD

We present the first lattice QCD calculation of single-channel $DD$ scattering with quantum numbers $I(J^P)=1(0^+)$ and $0(1^-)$. The calculation is performed on the $2+1$ flavor Wilson-Clover ensembles with a lattice spacing $a\simeq 0.077$ fm and two different pion masses, $m_π\simeq207$ and $305$ MeV. The scattering parameters are determined using the Lüscher's finite volume method. Our results indicate a weak repulsive interaction in the $1(0^+)$ channel and a slightly attractive interaction in the $0(1^-)$ channel. The $S$-wave isovector $DD$ scattering length and effective range, extrapolated to the physical pion mass, are $(-0.25\pm0.08\pm 0.12)$ fm and $(-5.7\pm4.5\pm 1.7)$ fm, respectively.

hep-lat↗

arXiv2026

Novel method for determining the light quark mass ratio using $η'\toηππ$ decays

We propose a novel approach for extracting symmetry breaking effects from symmetry conserving three-body decays. The method is based on mapping the Dalitz plot to a unit disk, and the difference of the disk distributions of two related decays isolates purely symmetry breaking effects. We demonstrate this method by extracting the fundamental parameter $Q$, an isospin breaking ratio of light quark masses defined as $Q^2\equiv (m_s^2-\hat m^2)/(m_d^2-m_u^2)$ with $\hat m$ the average of up and down quark masses, from the decays $η'\toηπ^+π^-$ and $η'\toηπ^0π^0$. With the Dalitz plot distributions for these two decays reported by BESIII, we illustrate the method and obtain $Q=22.5\pm1.0$, which is consistent with previous determinations and has a comparable uncertainty. With the full BESIII data set, which is eight times larger than the one used here, a more precise determination of $Q$ should become possible. This promising and novel method can be generalized to other three-body decays to extract symmetry breaking effects.

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arXiv2026

Three-body unitary determination of the $f_1(1285)$ and $f_1(1420)$ pole positions

We study the $I^G(J^{PC})=0^+(1^{++})$ $K\bar Kπ$ system in an infinite-volume three-body unitary framework, focusing on the pole content of the region of the $f_1(1285)$ and $f_1(1420)$ resonances. The coupled $πa_0$-$K\bar K^*$ amplitude is constructed in the spectator-isobar representation, where the one-particle-exchange interaction required by three-body unitarity automatically incorporates the triangle-singularity mechanism. The short-range three-body interaction is constrained by fitting the $0^+(1^{++})$ component of the BESIII $K^0_SK^0_Sπ^0$ invariant-mass distribution in the $J/ψ\toγ(K^0_SK^0_Sπ^0)$ decay. Analytically continuing the fitted amplitude to the relevant unphysical Riemann sheets, we find two robust poles: \begin{align} \sqrt{s_{f_1(1285)}}&= \left(1277\pm2\pm1\right) -i\left(12\pm1\pm0\right)\text{MeV}\,,\notag\\ \sqrt{s_{f_1(1420)}}&= \left(1435\pm2\pm7\right) -i\left(40\pm2\pm1\right)\text{MeV}\,.\notag \end{align} The pole trajectories indicate that the $f_1(1285)$ originates from dressing a bare state introduced in the potential. In contrast, the $f_1(1420)$ is predominantly dynamically generated, and a single-channel analysis traces it to an $S$-wave $K\bar K^*$ quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. We also find an additional pole deeper in the complex plane in the best-fit amplitude on the same Riemann sheet as the $f_1(1285)$. This additional pole is generated by the $P$-wave $πa_0$ contact interaction alone. It has a sizable cutoff and two-body-input dependence, and leaves little visible imprint on the physical lineshape. Finally, we provide a detailed and pedagogical appendix on how three-body cuts affect the solution of the integral equation.

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arXiv2026

Threshold cusp effects to measure masses of radiatively decaying hadrons: The $B_{s0}^*$ mass from the $Υϕ$ spectrum

Hadrons that decay predominantly into final states containing photons are notoriously difficult to detect at hadron colliders. Prominent examples are the yet-unobserved $B_{s0}^*$ and $B_{s1}$, the bottom partners of the $D_{s0}^*(2317)$ and $D_{s1}(2460)$, which are expected to exhibit exotic properties deviating from the conventional quark-model predictions of $\bar b s$ mesons. We propose a general, model-independent method to overcome this problem: when the target hadron has an attractive $S$-wave interaction with a companion hadron of precisely known mass, the line shape of a suitable final state develops a cusp at the pair threshold, or a peak just below it if the attraction binds, so that subtracting the companion mass returns the target mass, up to the binding energy in the latter case. As a proof of concept, a leading-order particle-dimer calculation of the $D\bar D_s K$ three-body system reproduces the $X(4274)$ structure in the LHCb $J/ψϕ$ distribution extracted from $B\to K J/ψϕ$, as a $D_{s0}^*\bar D_s$ threshold cusp driven by a nearby virtual-state pole, yielding $m_{D_{s0}^*}=(2322\pm6)$ MeV in agreement with its measured value and favoring $J^{PC}=0^{-+}$ for the $X(4274)$. Transferring the elastic three-body interaction to the bottom sector, we predict an analogous structure at the $B_{s0}^*\bar B_s$ threshold near $11.09$ GeV, making the $Υϕ$ invariant-mass distribution at the LHC a clean probe of the $B_{s0}^*$ mass.

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arXiv2026

Pion axioproduction revisited

In this work, we extend the analysis of the pion axioproduction, $aN \to π{N}$, to include the impact of the Roper resonance $N^*(1440)$ together the previously studied $Δ(1232)$ resonance. Our theoretical framework is chiral perturbation theory with explicit resonance fields to account for their respective impacts. We find that the Roper resonance also leads to an enhancement of the cross section within its energy range for various axion models.

hep-ph↗

arXiv2026

Effective Range Expansion with the Left-Hand Cut: Higher Order Improvements

A model-independent parameterization of the low-energy scattering amplitude that incorporates the left-hand cut from one-particle exchange, an extension of the conventional effective-range expansion (ERE), was recently proposed and successfully applied to the low-energy $DD^*$ system [Phys. Rev. Lett. 135, 011903 (2025)]. While the original formulation is based on a nonrelativistic approximation and is thus limited to a [1,1] approximant for self-consistency, we extend the framework by explicitly including the higher-order terms up to $\mathcal{O}(k^6)$. We systematically investigate the reliability and robustness of the generalized ERE by incorporating relativistic kinematic effects. In addition, we develop a relativistic version of the ERE that accounts for lhc contributions. These results affirm the generalized ERE as a robust and systematically improvable framework for near-threshold scattering processes, providing both analytical and numerical reliability for applications in two-body scattering problems with a particle exchange.

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arXiv2026

Determination of the $Z_c(3900)$ and the $Z_{cs}(3985)$ states from joint analysis of experimental and lattice data

We present a unified analysis of the $Z_c(3900)$ and $Z_{cs}(3985)$ states considering both experimental and lattice data. The study simultaneously includes the processes $e^+e^- \rightarrow J/ψπ^+π^-, J/ψK^+ K^-, D^0 D^{\ast-} π^+, (D^{\ast 0} D_s^{-}+D^0 D_s^{\ast -}) K^+$, together with finite-volume energy levels from recent lattice QCD simulations. Open-charm meson loops with triangle singularities, the $J/ψπ(J/ψ\bar{K})$-$\bar{D}D^*(\bar{D}D^*_s)$ coupled-channel interactions, and the $ππ$-$K\bar K$ final-state interaction are all taken into account. We find that pole contributions associated with the $Z_c(3900)$ and $Z_{cs}(3985)$ are indispensable for describing the data. The successful joint description of the experimental and lattice data supports the interpretation that the $Z_c(3900)$ and $Z_{cs}(3985)$ are SU(3) flavor partners within the same octet multiplet and indicates that both are resonance states. The extracted pole masses and half-widths of the $Z_c(3900)$ and the $Z_{cs}(3985)$ are $(3879.6 \pm 4.8)$ MeV and $(32.2 \pm 4.7)$ MeV, and $(3976.9 \pm 5.1)$ MeV and $(28.8 \pm 5.9)$ MeV, respectively. The ratios of the $Z_c(Z_{cs})$ couplings to the $D\bar D^*(D_s\bar{D}^\ast+D\bar{D}_s^\ast)$ and $J/ψπ(J/ψK)$ channels are also determined. A compositeness analysis indicates that, although the $D\bar D^* (D_s\bar{D}^\ast+D\bar{D}_s^\ast)$ component in the $Z_c(3900) (Z_{cs}(3985))$ state is sizable, additional components are still needed to form these exotic states.

hep-ph↗

arXiv2026

Dispersive analysis of the $J/ψ\toπ^0 γ^\ast$ transition form factor with $ρ$-$ω$ mixing effects

Motivated by the discrepancies noted recently between the theoretical predictions of the electromagnetic $J/ψ\to π^0 γ^*$ transition form factor and the BESIII data, we reanalyze this transition form factor using the dispersive Khuri-Treiman equations, with final-state interactions in both the direct channel and the crossed channels properly considered. This improved framework incorporates $ρ$-$ω$ mixing effects. The effect of four-pion states is evaluated through a dispersively improved vector-meson-dominance model. From this information, we propose a two-parameter fit that provides an excellent description of the BESIII data over the broad energy range from 0 to 2.8GeV. We demonstrate that the $ρπ^0$ decay mode of the $J/ψ$ is dominated by strong interaction, while the $ωπ^0$ mode is dominated by one-photon exchange. From this, we extract the relative phase between the strong and the one-virtual-photon (electromagnetic) modes in hadronic decays of $J/ψ$ as $(62 \pm 21)^{\circ}$. This could provide useful information in understanding the long-standing $ρπ$ puzzle in $J/ψ$ decays.

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arXiv2026

What can we learn from the radiative decays of the $D_{s1}(2460)$ meson?

We study the radiative decays $D_{s1}(2460)\toγD^{*}_{s0}(2317)$ and $D_{s1}(2460)\to γD^0K^+/γD^+K^0$ and argue that their simultaneous experimental measurement, or at least a constraint on the ratio of the corresponding branching fractions, can allow one to probe the nature of the $D^{*}_{s0}(2317)$ and $D_{s1}(2460)$ mesons.

hep-ph↗

arXiv2026

Neutrinoless double-beta decay of the $Δ^-$ resonance

The subprocess $nn\to ppe^-e^-$ is a key ingredient in the interpretation of nuclear neutrinoless double-beta decay. Intermediate $Δ$ resonances may provide additional enhancements to this transition. We take a first step toward a $Δ$-full description of $nn\to ppe^-e^-$ by investigating the neutrinoless double-beta decay $Δ^- \to p e^-e^-$ in the framework of chiral effective field theory. We systematically derive the long-range contribution from light-Majorana-neutrino exchange through loop diagrams and incorporate the short-range part through counterterms required by renormalization. We predict the pion-mass dependence of the decay amplitude in the kinematic configuration with collinear electrons. Furthermore, to facilitate lattice-QCD matching, we calculate the decay amplitude in the degenerate $Δ$-nucleon mass limit and provide the corresponding long-range prediction.

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