One-pion Exchange Research Articles

Toward the quark mass dependence of Tcc+ from lattice QCD

The DD* scattering phase shifts in the Tcc+=ccu¯d¯ channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to mπ≃280 MeV. The phase shifts are analyzed employing two approaches: effective range expansion and Lippmann-Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrized by contact terms and a slight repulsion at long range mediated by one-pion exchange with mπ>mD*−mD. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for mc close to the physical value. They turn into a pair of virtual states at the largest mc studied. With further increasing mc, one virtual pole representing Tcc+ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the Tcc+ pole is briefly discussed using the data on DD* scattering from other lattice collaborations. Published by the American Physical Society 2024

Solving the left-hand cut problem in lattice QCD: Tcc(3875)+ from finite volume energy levels

We discuss a novel effective-field-theory-based approach for extracting two-body scattering information from finite volume energies, serving as an alternative to Lüscher’s method. By explicitly incorporating one-pion exchange, we overcome the challenging left-hand cut problem in Lüscher’s method and can handle finite volume energy levels both below and above the left-hand cut. Applied to the lattice data for DD* scattering at a pion mass of 280 MeV, as an illustrative example, our results reveal the significant impact of the one-pion exchange on P-wave and S-wave phase shifts. The pole position of the Tcc(3875)+ state, extracted from the finite-volume energy levels at this pion mass while taking into account left-hand cut effects, range corrections and partial-wave mixing, is consistent with a near-threshold resonance. This study demonstrates, for the first time, that two-body scattering information can be reliably extracted from lattice spectra including the left-hand cut. Published by the American Physical Society 2024

Cut structures and an observable singularity in the three-body threshold dynamics: The Tcc+ case

The three-body threshold effect, the distinctive and intriguing nonperturbative dynamics in the low-energy hadron-hadron scattering, has acquired compelling significance in the wake of the recent observation of the double-charm tetraquark Tcc+. This dynamics is characterized by the emergence of singular points and branch cuts within the interaction potential, occurring when the on-shell condition of the mediated particle is satisfied. The presence of these potential singularities indicates that the system is no longer Hermitian and also poses intractable challenges in obtaining exact solutions for dynamical scattering amplitudes. In this work, we develop a complex scaled Lippmann-Schwinger equation as an operation of analytical continuation of the T matrix to resolve this problem. Through a practical application to the DD*→DD* process, we reveal complicated cut structures of the three-body threshold dynamics in the complex plane, primarily stemming from the one-pion exchange. Notably, our methodology succeeds in reproducing the Tcc+ structure, in alignment with the quasibound pole derived from the complex scaling method within the Schrödinger equation framework. More remarkably, after solving the on-shell T matrix on the positive real axis of momentum plane, we find an extra new structure in the DD* mass spectrum, which arises from a right-hand cut at a physical pion mass and should be observable in lattice QCD simulations and future high-energy experiments. Published by the American Physical Society 2024

Long-range S -wave DD* interaction in covariant chiral effective field theory

Motivated by the recent lattice QCD study of the DD* interaction at unphysical quark masses, we perform a theoretical study of the DD* interaction in covariant chiral effective field theory. In particular, we calculate the relevant leading-order two-pion exchange contributions. The results compare favorably with the lattice QCD results, supporting the conclusion that the intermediate-range DD* interaction is dominated by two-pion exchanges and the one-pion exchange contribution is absent. At a quantitative level, the covariant chiral perturbation theory results agree better with the lattice QCD results than their nonrelativistic counterparts, showing the relevance of relativistic corrections in the charm sector. Published by the American Physical Society 2024

Doubly heavy tetraquarks including one-pion exchange potential

Spectrum of the doubly heavy tetraquarks is studied in a constituent quark model including one-pion exchange (OPE) potential. Central and tensor forces induced by OPE between two light quarks are considered. Our results show that I(JP)=0(1+) compact bound states are shifted up because of the repulsive central force between q¯q¯. This effect possibly leads to the small binding energy in Tcc. In addition, a I(JP)=1(1+) resonant state is reported with E=10641MeV,Γ=15MeV and E=10640 MeV,Γ=15 MeV, without and with including OPE potential, respectively. The repulsive central force and attractive tensor force almost cancel with each other and leave a small energy difference when OPE potential is included.

Role of Left-Hand Cut Contributions on Pole Extractions from Lattice Data: Case Study for T_{cc}(3875)^{+}.

We discuss recent lattice data for the T_{cc}(3875)^{+} state to stress, for the first time, a potentially strong impact of left-hand cuts from the one-pion exchange on the pole extraction for near-threshold exotic states. In particular, if the left-hand cut is located close to the two-particle threshold, which happens naturally in the DD^{*} system for the pion mass exceeding its physical value, the effective-range expansion is valid only in a very limited energy range up to the cut and as such is of little use to reliably extract the poles. Then, an accurate extraction of the pole locations requires the one-pion exchange to be implemented explicitly into the scattering amplitudes. Our findings are general and potentially relevant for a wide class of hadronic near-threshold states.

Amplitudes of 3H, 3He Two-Particle Photo-Breakup in Non-Local QED Approach

Three-nucleon systems are essential for the investigation of many-body forces in nuclear physics. Well-grounded parametrization of their vertex functions with further application for the calculation of cross-sections in nonlocal QED approach provides the ground for investigation of the variety of multi-particle systems. In present paper we describe the process of parametrization of two-particle photo-breakup amplitudes of three-nucleon systems (3H, 3He). We provide the general description of the wave function construction for three-nucleon systems as well as the parametrization of their vertex functions accounting two- and three-nucleon interactions based on meson exchange current formalism. In our calculations we account first and second order one-pion exchange terms and the term related to the exchange of ω and ρ mesons. The three-nucleon interaction potential is given as a sum of attraction (two-pion exchange) term andappropriate repulsive part. Based on the variational ”Urbana + Model VII” amplitudes we provide the results for energy dependence of differential cross-section of 3He(γ, p)d reaction at proton angle θ = 90◦ from the threshold up to Eγ = 40 MeV and compare theoretical predictions with the available experimental data. The investigation is also provided for angular cross-section distributions at high photon energies (Eγ = 305 ± 5 MeV; 365 ± 5 MeV; 450 ± 10 MeV and 675 ± 50 MeV). Correct description of 3H, 3He photo-disintegration processes in a unified approach based on the gauge nature of the electromagnetic field implies application of this model for other multi-particle systems.

Performance evaluation of LHCf-ATLAS ZDC joint measurement using proton beam

Measurements of forward neutrons in pp collisions will allow us to investigate π-p cross-section via one-pion exchange process, which are important for air shower development. However, the precision of these measurements is limited by the energy resolution of the LHCf detectors. To improve it, a joint measurement with the ATLAS ZDC was planned. In 2021, a beam test was conducted to evaluate the performance of the joint measurement of the LHCf-Arm1 and ZDC detectors using proton beams of 350 GeV at SPS. Combining the LHCf data with the ZDC data, we confirmed that the energy resolution improved from about 40% to 21.4%.

Renormalization of one-pion exchange in higher partial waves in chiral effective field theory for antinucleon-nucleon system* *Supported by the Doctoral Fund Project of Nanfang College, Guangzhou (2020BQ03)

The renormalization of the iterated one-pion exchange (OPE) has been studied in chiral effective field theory (χEFT) for the antinucleon-nucleon () scattering in some partial waves (Phys. Rev. C 105, 054005 (2022)). In this paper, we go further for the other higher partial waves but with total angular momenta . Contact interactions are represented by a complex spherical well in the coordinate space. Changing the radius of the spherical well means changing the cutoff. We check the cutoff dependence of the phase shifts, inelasticities, and mixing angles for the partial waves and show that contact interactions are needed at leading order in channels where the singular tensor potentials of OPE are attractive. The results are compared with the energy-dependent partial-wave analysis of scattering data. Comparisons between our conclusions and applications of χEFT to the nucleon-nucleon system are also discussed.

Dibaryon resonances and short-range NN interaction* *The work has been partially supported by RFBR, grants Nos. 19-02-00011 and 19-02-00014. M.N.P. also appreciates support from the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”

The dibaryon concept for nuclear force is presented, assuming that the attraction between nucleons at medium distances is mainly due to the s-channel exchange of an intermediate six-quark (dibaryon) state. To construct the respective NN interaction model, a microscopic six-quark description of the NN system is used, in which symmetry aspects play a special role. It is shown that the NN interaction in all important partial waves can be described by the superposition of long-range t-channel one-pion exchange and s-channel exchange by an intermediate dibaryon. The model developed in this study provides a good description of both elastic phase shifts and inelasticities of NN scattering in all S, P, D, and F partial waves at energies from zero to 600–800 MeV and even higher. The parameters of the intermediate six-quark states, corresponding to the best fit of NN scattering data, are found to be consistent with the parameters of the known dibaryon resonances in those NN partial configurations, where their existence has been experimentally confirmed. Predictions for new dibaryon states are given as well.

Two-pion exchange as a leading-order contribution in chiral effective field theory

Pion exchange is the central ingredient to nucleon-nucleon interactions used in nuclear structure calculations, and one pion exchange (OPE) enters at leading order in chiral effective field theory. In the $^{2S+1}L_J={^1S_0}$ partial wave, however, OPE and a contact term needed for proper renormalization fail to produce the qualitative, and quantitative, features of the scattering phase shifts. Cutoff variation also revealed a surprisingly low breakdown momentum of about 330 MeV in this partial wave. Here we show that potentials consisting of OPE, two pion exchange (TPE), and a single contact address these problems and yield accurate and renormalization group (RG) invariant phase shifts in the $^1S_0$ partial wave. We demonstrate that a leading-order potential with TPE can be systematically improved by adding a contact quadratic in momenta. For momentum cutoffs below about 500 MeV, the removal of relevant physics from TPE loops needs to be compensated by additional contacts to keep RG invariance. Inclusion of the $\Delta$ isobar degree of freedom in the potential does not change the strong contributions of TPE.

Contribution of the Weinberg-type operator to atomic and nuclear electric dipole moments

The contribution of the CP violating three-gluon Weinberg operator, frac{1}{3!}w{f}^{abc}{epsilon}^{nu rho alpha beta}{G}_{mu nu}^a{G}_{alpha beta}^b{G}_{rho}^{cmu} , to the atomic and nuclear EDMs is estimated using QCD sum rules. After calculating the transition matrix element between the pion and the vacuum through the Weinberg operator, we obtain the long-range CP-odd nuclear force by determining the isovector CP-odd pion-nucleon vertex, using chiral perturbation theory at NLO. The EDMs of 199Hg, 129Xe, and 225Ra atoms, as well as those of 2H and 3He nuclei are finally given including comprehensive uncertainty analysis. While the leading contribution of the 199Hg EDM is given by the intrinsic nucleon EDM, that of 129Xe atom may be dominated by the one-pion exchange CP-odd nuclear force generated by the Weinberg operator. From current experimental data of the 199Hg atomic EDM, we obtain an upper limit on the Weinberg operator magnitude of |w| < 4 × 10−10GeV−2 if we assume that it is the only source of CP violation at the scale μ = 1 TeV.

Renormalization of one-pion exchange in chiral effective field theory for antinucleon-nucleon scattering

The renormalization of iterated one-pion exchange (OPE) is studied in chiral effective field theory $(\ensuremath{\chi}\mathrm{EFT})$ for the antinucleon-nucleon $(\overline{N}N)$ system. The OPE potential is cut off at a certain distance and contact interactions are represented by a complex spherical well with the same radius. We investigate the dependence on the cutoff radius of the phase shifts, inelasticities, and mixing angles for the low partial waves in $\overline{N}N$ scattering. We show that renormalization requires additional contact interactions compared to the expectation based on naive dimensional analysis. Results after renormalization are compared with the state-of-the-art energy-dependent partial-wave analysis of $\overline{N}N$ data. We compare our conclusions with applications of $\ensuremath{\chi}\mathrm{EFT}$ to the nucleon-nucleon system.

Molecular interpretation of the LHCb pentaquarks from an analysis of J/ψp spectrum

A coupled-channel approach including the ΛcD¯(*) and ηcp channels in addition to the Σc(*)D¯(*) and J/ψp channels, as required by unitarity and heavy quark spin symmetry (HQSS), is applied to the hidden-charm pentaquark Pc states, i.e., Pc(4312), Pc(4440) and Pc(4457), discovered by LHCb Collaboration. It is demonstrated that to obtain cutoff independent results, the one-pion exchange potential in the multichannel systems is to be supplemented with next-leading order counter terms responsible for the S-wave-to-D-wave transitions. We show that the experimental data for the J/ψp mass distributions are fully in line with the ΣcD¯ and ΣcD¯* hadronic molecular interpretation of the Pc(4312) and Pc(4440)/Pc(4457), respectively. A narrow Σc*D¯ molecule around 4.38 GeV is required by the HQSS with the evidence for its existence seen in the J/ψp spectrum. Moreover, we predict the line shapes for the elastic and inelastic channels.

Coupled-channel effects of the Σc(*)D¯(*)−Λc(2595)D¯ system and molecular nature of the Pc pentaquark states from one-boson exchange model

The effects of the $\Sigma_c\bar{D}^*$-$\Lambda_{c}(2595)\bar{D}$ coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, $P_c(4440)$ and $P_c(4457)$, are reinvestigated. Both the pion and $\rho$-meson exchanges are considered for the $\Sigma_c\bar{D}^*$-$\Lambda_{c}(2595)\bar{D}$ coupled-channel dynamics. It is found that the role of the $\Lambda_{c}(2595)\bar{D}$ channel in the descriptions of the $P_c(4440)$ and $P_c(4457)$ states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance $\delta(\vec{r})$ term of the one-pion exchange (OPE) keep failing to reproduce the $P_c(4440)$ and $P_c(4457)$ states simultaneously. The OPE potential with the full $\delta(\vec{r})$ term results in a too large mass splitting for the $J^P=1/2^-$ and $3/2^-$ $\Sigma_c\bar{D}^*$ bound states with total isospin $I=1/2$. The OBE model with only the OPE $\delta(\vec{r})$ term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the $\delta(\vec r)$ potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the $\delta(\vec r)$ potential and find that the masses of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ can be reproduced simultaneously with the $\delta(\vec r)$ term in the OBE model reduced by about 80\%. While two different spin assignments are possible to produce their masses, in the preferred description, the spin parities of the $P_c(4440)$ and $P_c(4457)$ are $3/2^-$ and $1/2^-$, respectively.

Two-particle scattering from finite-volume quantization conditions using the plane wave basis

We propose an alternative approach to Lüscher’s formula for extracting two-body scattering phase shifts from finite volume spectra with no reliance on the partial wave expansion. We use an effective-field-theory-based Hamiltonian method in the plane wave basis and decompose the corresponding matrix elements of operators into irreducible representations of the relevant point groups. The proposed approach allows one to benefit from the knowledge of the long-range interaction and avoids complications from partial wave mixing in a finite volume. We consider spin-singlet channels in the two-nucleon system and pion-pion scattering in the ρ-meson channel in the rest and moving frames to illustrate the method for non-relativistic and relativistic systems, respectively. For the two-nucleon system, the long-range interaction due to the one-pion exchange is found to make the single-channel Lüscher formula unreliable at the physical pion mass. For S-wave dominated states, the single-channel Lüscher method suffers from significant finite-volume artifacts for a L = 3 fm box, but it works well for boxes with L > 5 fm. However, for P-wave dominated states, significant partial wave mixing effects prevent the application of the single-channel Lüscher formula regardless of the box size (except for the near-threshold region). Using a toy model to generate synthetic data for finite-volume energies, we show that our effective-field-theory-based approach in the plane wave basis is capable of a reliable extraction of the phase shifts. For pion-pion scattering, we employ a phenomenological model to fit lattice QCD results at the physical pion mass. The extracted P-wave phase shifts are found to be in a good agreement with the experimental results.

Revisiting the nature of the Pc pentaquarks

The nature of the three narrow hidden-charm pentaquark Pc states, i.e., Pc(4312), Pc(4440) and Pc(4457), is under intense discussion since their discovery from the updated analysis of the process {Lambda}_b^0to J/psi {pK}^{-} by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124, 072001 (2020)], in which the Pc states are treated as {Sigma}_c^{left(ast right)}{overline{D}}^{left(ast right)} molecules, by including the {Lambda}_c{overline{D}}^{left(ast right)} and ηcp as explicit inelastic channels in addition to the J/ψp, as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., {Sigma}_c^{left(ast right)}{overline{D}}^{left(ast right)} , and inelastic channels and without the {Lambda}_c{overline{D}}^{left(ast right)} interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the {Lambda}_c{overline{D}}^{left(ast right)} interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S-wave-to-D-wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/ψp invariant mass distribution are consistent with the interpretation of the Pc(4312) and Pc(4440)/Pc(4457) as {Lambda}_coverline{D} and {Sigma}_c{overline{D}}^{ast } hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, Pc(4380), identified as a {Sigma}_c^{ast}overline{D} molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the Pc(4440) and Pc(4457) being JP = 3/2− and 1/2−, respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the Pc(4440) and the Pc(4457) in the {Sigma}_c^{left(ast right)}overline{D} and ηcp mass distributions from {Lambda}_b^0to {Sigma}_c^{left(ast right)}overline{D}{K}^{-} and {Lambda}_b^0to {eta}_c{pK}^{-} will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the {Lambda}_c{overline{D}}^{left(ast right)} final states.

Magnetars and axion-like particles: probes with the hard X-ray spectrum

Quiescent hard X-ray and soft gamma-ray emission from neutron stars constitute a promising frontier to explore axion-like-particles (ALPs). ALP production in the core peaks at energies of a few keV to a few hundreds of keV; subsequently, the ALPs escape and convert to photons in the magnetosphere. The emissivity goes as ∼ T 6 while the conversion probability is enhanced for large magnetic fields, making magnetars, with their high core temperatures and strong magnetic fields, ideal targets for probing ALPs. We compute the energy spectrum of photons resulting from conversion of ALPs in the magnetosphere and then compare it against hard X-ray data from NuSTAR, INTEGRAL, and XMM-Newton for a set of eight magnetars for which such data exists. Upper limits are placed on the product of the ALP-nucleon and ALP-photon couplings. For the production in the core, we perform a calculation of the ALP emissivity in degenerate nuclear matter modeled by a relativistic mean field theory. The reduction of the emissivity due to improvements to the one-pion exchange approximation is incorporated, as is the suppression of the emissivity due to proton superfluidity in the neutron star core. A range of core temperatures is considered, corresponding to different models of the steady heat transfer from the core to the stellar surface. For the subsequent conversion, we solve the coupled differential equations mixing ALPs and photons in the magnetosphere. The conversion occurs due to a competition between the dipolar magnetic field and the photon refractive index induced by the external magnetic field. Semi-analytic expressions are provided alongside the full numerical results. We also present an analysis of the uncertainty on the axion limits we derive due to the uncertainties in the magnetar masses, nuclear matter equation of state, and the proton superfluid critical temperature.

The short-range correlation of asymmetric nucleonic matter at finite temperature: The LOCV approach

The short-range correlation of the asymmetric nucleonic matter (ASM) is perused at finite temperature in the lowest order constrained variational (LOCV) method. It is observed that, by increasing the temperature, the LOCV ASM static non-central distribution functions become weak. For small inter-particle distances, a universal behavior is found for the LOCV ASM state-dependent density distributions. Using the expectation value of the one-pion exchange part of the AV18 interaction, the scaling factor of the pion absorption cross section (the number of quasideuterons), for the different proton to neutron ratios R, is also estimated in the LOCV formalism. It is shown that, by increasing (decreasing) the ratio R (the temperature), the number of quasideuterons grows. Considering the scaling factor, the Bethe-Levinger (BL) factor for the ASM is also investigated. It is demonstrated that, at the saturation density and temperature 20 MeV, the BL factor for the ASM with R=1(0.5) becomes 4.3 (4.5).

Measurement of beam asymmetry for π−Δ++ photoproduction on the proton at Eγ=8.5GeV

We report a measurement of the $\pi^-$ photoproduction beam asymmetry for the reaction $\vec{\gamma} p \rightarrow \pi^- \Delta^{++}$ using data from the GlueX experiment in the photon beam energy range 8.2--8.8 GeV. The asymmetry $\Sigma$ is measured as a function of four-momentum transfer $t$ to the $\Delta^{++}$ and compared to phenomenological models. We find that $\Sigma$ varies as a function of $t$: negative at smaller values and positive at higher values of $|t|$. The reaction can be described theoretically by $t$-channel particle exchange requiring pseudoscalar, vector, and tensor intermediaries. In particular, this reaction requires charge exchange, allowing us to probe pion exchange and the significance of higher-order corrections to one-pion exchange at low momentum transfer. Constraining production mechanisms of conventional mesons may aid in the search for and study of unconventional mesons. This is the first measurement of the process at this energy.