Article

# Experimental Evidence for an Attractive p-ϕ Interaction

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## Abstract

This Letter presents the first experimental evidence of the attractive strong interaction between a proton and a ϕ meson. The result is obtained from two-particle correlations of combined p-ϕ⊕ p[over ¯]-ϕ pairs measured in high-multiplicity pp collisions at sqrt[s]=13 TeV by the ALICE Collaboration. The spin-averaged scattering length and effective range of the p-ϕ interaction are extracted from the fully corrected correlation function employing the Lednický-Lyuboshits approach. In particular, the imaginary part of the scattering length vanishes within uncertainties, indicating that inelastic processes do not play a prominent role for the p-ϕ interaction. These data demonstrate that the interaction is dominated by elastic p-ϕ scattering. Furthermore, an analysis employing phenomenological Gaussian- and Yukawa-type potentials is conducted. Under the assumption of the latter, the N-ϕ coupling constant is found to be g_{N-ϕ}=0.14±0.03(stat)±0.02(syst). This work provides valuable experimental input to accomplish a self-consistent description of the N-ϕ interaction, which is particularly relevant for the more fundamental studies on partial restoration of chiral symmetry in nuclear medium.

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... The scattering length |α φp | ≃ 2.37 was obtained by analyzing the QCD van der Waals potential [13]. And in 2021, the real part of the scattering length of φ-p was found to be 0.85 ± 0.34 fm by pp collision in ALICE Collaboration [16]. Note that these results go beyond the scattering length of the φ-p extracted from the vector meson photoproduction data. ...
... The olive-green triangle is |α φp | ≃ 2.37 fm by QCD van der Waals [13]. The orange diamond is the result of the ALICE Collaboration [16]. |α 2 φp | based on the differential cross section is barely larger than that obtained from the total cross section. ...
... However, two relatively large results clearly go beyond our normal understanding of the scattering length of φ-p. A result from QCD van der Waals [13] is |α φp | ≃ 2.37 fm and a real part of the scattering length of φ-p interaction calculated by ALICE Collaboration [16] from the cross section of the high-multiplicity pp collisions collision is 0.85 ± 0.34 fm. We suppose there should exist different reactions, so these two results are ignored for the time being. ...
Preprint
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In this work, we systematically study the the interaction between of $\phi$ meson and nucleus by analyzing and fitting the cross sections of $\gamma N$$\rightarrow \phi$$N$ ($N$ represent the nucleus) reactions near the threshold. With the help of vector meson dominant model, the distribution of $\phi$-$N$ scattering length as a function of energy is presented, and the results show that there is a slight increase in scattering length with increasing energy. Based on this, the average scattering length of $\phi$-proton is $=0.10\pm0.01$ fm by combining experimental data and theoretical models. Moreover, the average scattering length of $\phi$-deuteron interaction is derived to be $0.014\pm0.002$ fm for the first time. Further, the effect of the momentum transfer $|t_{min}|$ on the $\phi$-$N$ scattering length at the threshold is discussed. The obtained results not only provide important theoretical information for a more comprehensive and accurate study of the $\phi$-$N$ scattering length, but also provide a basis for future experimental measurements of $\phi$ meson production.
... (14) syst. fm [7], an order of magnitude larger than that obtained from the photo-production data by the CLAS Collaboration at JLab [8] combined with the vector meson dominance [9]. ...
... Our a (3/2) 0 is substantially larger in magnitude than the previous calculations of the spin-averaged a 0 using QCD sum rules but is comparable to the spin-averaged a 0 by ALICE Collaboration within the error bar [7]. Also, our r (3/2) eff is about three times smaller than the spinaveraged r eff by ALICE Collaboration. ...
Preprint
First results on the interaction between the $\phi$-meson and the nucleon ($N$) are presented based on the ($2+1$)-flavor lattice QCD simulations with nearly physical quark masses. Using the HAL QCD method, the spacetime correlation of the $N$-$\phi$ system in the spin 3/2 channel is converted into the $N$-$\phi$ scattering phase shift through the interaction potential. The $N$-$\phi$ potential appears to be a combination of a short-range attractive core and a long-range attractive tail. The latter is found to be consistent with the two-pion exchange (TPE) obtained from the interaction between a color-dipole and the nucleon. The resultant scattering length and effective range for $m_{\pi}=$ 146.4 MeV are $a^{(3/2)}_0=-1.43(23)_{\rm stat.}\left(^{+36}_{-06}\right)_{\rm syst.} {\rm fm}$ and $r^{(3/2)}_{\rm eff}=2.36(10)_{\rm stat.}\left(^{+02}_{-48}\right)_{\rm syst.} {\rm fm}$, respectively. The magnitude of the scattering length is shown to have non-trivial dependence of $m_{\pi}$ and is sensitive to the existence of the long-range tail from TPE.
... The situation has drastically changed in recent years, thanks to the novel employment of the femtoscopy technique [37] in pp and p-Pb collisions at the LHC applied to almost all combinations of protons and strange hadrons [38]. The ALICE Collaboration could precisely study the following interactions: pp, pK ± , pΛ, pΛ, pΣ 0 , ΛΛ, ΛΛ, pΞ − , pΩ − and pφ [38][39][40][41][42][43][44][45][46]. Since conventional scattering experiments cannot be performed with D mesons and charm nuclei [47] have not been discovered yet (searches for charm nuclear states are included in the scientific program of the Japan Proton Accelerator Research Complex [48]), the femtoscopy technique can be employed to study the ND and ND interactions. ...
... The resulting correlation function is parametrized by a third-order polynomial in k * ∈ [0, 1.5] GeV/c and is displayed by the green curve in Fig. 1. The observed behavior is determined by meson-meson and baryon-meson mini-jets and residual two-body interactions among the quadruplet, as previously observed [41,45]. ...
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This Letter presents the first measurement of the interaction between charm hadrons and nucleons. The two-particle momentum correlations of $\mathrm{pD^-}$ and $\mathrm{\overline{p}D}^+$ pairs are measured by the ALICE Collaboration in high-multiplicity pp collisions at $\sqrt{s} = 13~\mathrm{TeV}$. The data are compatible with the Coulomb-only interaction hypothesis within (1.1-1.5)$\sigma$. Considering an attractive nucleon(N)$\overline{\mathrm{D}}$ strong interaction, in contrast to most model predictions which suggest an overall repulsive interaction, slightly improves the level of agreement. This measurement allows for the first time an estimation of the 68% confidence level interval for the isospin $\mathrm{I}=0$ inverse scattering length of the $\mathrm{N\overline{D}}$ state ${f_{0,~\mathrm{I}=0}^{-1} \in [-0.4,0.9]~\mathrm{fm^{-1}}}$, assuming negligible interaction for the isospin $\mathrm{I}=1$ channel.
... Recently, the method has been applied to study FSIs of hadrons produced in pp and p-Pb collisions. The large data samples allowed for the precise measurement of correlation functions for multiple hadronic pairs (p-p [25], p-K + and p-K − [26], p-Λ [25], p-Σ 0 [27], Λ-Λ [28], p-Ξ − [29], p-Ω − [30], p-φ [31] and baryon-antibaryon [32]). By using these results, several models for the two-body strong interaction could be validated (for a complete review see Ref. [33]). ...
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We show that the QCD van der Waals attractive potential is strong enough to bind a {phi} meson onto a nucleon inside a nucleus to form a bound state. The direct experimental signature for such an exotic state is proposed in the case of subthreshold {phi} meson photoproduction from nuclear targets. The production rate is estimated and such an experiment is found to be feasible at the Jefferson Laboratory.
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The production of K*(892)^0 and phi(1020) in pp collisions at sqrt(s)=7 TeV was measured by the ALICE experiment at the LHC.The yields and the transverse momentum spectra d^2N/dydpT at midrapidity |y|<0.5 in the range 0<pT<6 GeV/c for K*(892)^0 and 0.4<pT<6 GeV/c for phi(1020) are reported and compared to model predictions. Using the yield of pions, kaons, and Omega baryons measured previously by ALICE at sqrt(s)=7 TeV, the ratios K*/K^-, phi/K*, phi/K^-, phi/\pi^-, and (Omega + anti-Omega)/phi are presented. The values of the K*/K^-, phi/K* and phi/K^- ratios are similar to those found at lower centre-of-mass energies. In contrast, the phi/pi^- ratio, which has been observed to increase with energy, seems to saturate above 200 GeV. The (Omega + anti-Omega)/phi ratio in the pT range 1-5 GeV/c is found to be in good agreement with the prediction of the HIJING/BB v2.0 model with a strong colour field.
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QCD sum rules are evaluated at finite nucleon densities and temperatures to determine the change of mass parameters for the lightest vector mesons ρ, ω and φ in a strongly interacting medium. For conditions relevant for the starting experiments at HADES we find that the in-medium mass shifts of the ρ- and ω-mesons are governed, within the Borel QCD sum rule approach, by the density and temperature dependence of the four-quark condensate. In particular, the variation of the strength of the density dependence of the four-quark condensate reflects directly the decreasing mass of the ρ-meson and can lead to a change of the sign of the ω-meson mass shift as a function of the density. In contrast, the in-medium mass of the φ-meson is directly related to the chiral strange quark condensate which seems correspondingly accessible.
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We investigate the density dependence of the chiral order parameter or quark condensate in nuclear matter using relativistic Brueckner-Hartree-Fock theory. While the leading behavior linear in the density is known to be determined model independently by the pion-nucleon sigma term, we demonstrate that higher order corrections are extremely sensitive to the interpretation of the scalar “σ”-meson and its substructure.
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Based on an effective Lagrangian which combines chiral SU(3) dynamics with vector meson dominance, we have developed a model for the forward vector meson-nucleon scattering amplitudes. We use this as an input to calculate the low energy part of the current-current correlation function in nuclear matter. Its spectrum enters directly in the “left-hand side” of QCD sum rules. For the isovector channel we find a significant enhancement of the in-medium spectral density below the ϱ resonane while the ρ meson mass itself changes only slightly. The situation is different in the isoscalar channel, where the mass and peak position of the ω meson move downward while its width increases less drastically than in the ρ meson case. For the φ meson we find almost no mass shift; the width of the peak broadens moderately. We observe a remarkable degree of consistency with the operator product expansion of QCD sum rules in all three channels. We point out, however, that these results cannot simply be interpreted, as commonly done, in terms of a universal rescaling of vector meson masses in matter.