Study of charmonium-nucleon interaction in lattice QCD

Abstract

Abstract. We report preliminary results for charmonium-nucleon potential V ccN (r) from quenched lattice QCD, which is calculated from the equal-time Bethe-Salpeter amplitude through the effective Schrödinger equation. Our simulations are performed at a lattice cutoff of 1/a=2.0 GeV in a spatial volume of (3 fm) 3 with the nonperturbatively O(a) improved Wilson action for the light quarks and a relativistic heavy quark action for the charm quark. We have found that the potential V ccN (r) is weakly attractive at short distance and exponentially screened at long distance.Keywords: Lattice QCD, Hadron-hadron interaction PACS: 11.15. Ha, The heavy quarkonium state such as the charmonium (cc) state does not share the same quark flavor with the nucleon (N). This suggests that the heavy quarkoniumnucleon interaction is mainly induced by the genuine QCD effect of multi-gluon exchange [1,2]. As an analog of the van der Waals force, two-gluon exchange contribution gives a weakly attractive, but long-ranged interaction between the heavy quarkonium state and the nucleon. However, the validity of the calculation based on the perturbative theory is questionable for QCD where the nature of the strong coupling appears in the long distance region.The cc-N scattering at low energies has been studied from first principles of QCD. The s-wave J/ψ-N scattering length is about 0.1 fm by using QCD sum rules [4] and 0.71±0.48 fm (0.70±0.66 fm for η c -N) by lattice QCD [5], while it is estimated as large as 0.25 fm from the gluonic van der Waals interaction [1]. All studies suggest that the cc-N interaction is weakly attractive. This indicates that the possibility of the formation of charmonium bound to nuclei is enhanced. In 1991, Brodsky et al. had argued that the cc-nucleus (A) bound system may be realized for the mass number A ≥ 3 if the attraction between the charmonium and the nucleon is sufficiently strong [3]. Therefore, precise information on the cc-N potential V ccN (r) is indispensable for exploring nuclear-bound charmonium state like η c -3 He or J/ψ-3 He bound state in few body calculations [6].We recall a recent great success of the N-N potential from lattice QCD [7]. In this new approach, the potential between hadrons can be calculated from the equal-time BetheSalpeter (BS) amplitude through the effective Schrödinger equation. Thus, the direct measurement of the cc-N potential is now feasible by using lattice QCD. It should be very important to give a firm theoretical prediction about nuclear-bound charmonium, which is possibly investigated by experiments at J-PARC and GSI.The method utilized here to calculate the hadron-hadron potential in lattice QCD is based on the same idea originally applied for the N-N potential [7,8]. We first calculate arXiv:1007.1515v1 [hep-lat]

Lüscher’s finite size method with twisted boundary conditions: An application to theJ/ψ−ϕsystem to search for a narrow resonance

“…An effective description for the interaction between the J/ψ and φ may be given by the soft Pomeron exchange, which carries the quantum number of the vacuum [51]. In this sense, the difference of boundaries between dynamical quarks and valence quarks in this study would be negligibly small since the mass of the Pomeron is typically of the order of 500−600 MeV, which is, phenomenologically, a good agreement with what is observed through the charmonium-nucleon potential [34,52]. Scattering phase shifts as a function of the twoparticle energy E. Open symbols are calculated through the approximated formula (44), where the P -wave mixing is ignored, for data taken with two types of twist angle vectors, θ = (0, 0, θ) and (θ, θ, θ).…”

“…As a consequence, even-l and odd-l partial waves would be mixed together under twisted boundary conditions in the range of 0 < |θ| < π. The possibility of such unwanted mixing is simply ignored in early exploratory works with twisted boundary conditions [28,34]. Recently, the same pathological issue is properly addressed in the derivation of Rummukainen-Gottlieb's formula (or, equivalently, Lüscher's finite size formula in a moving frame) for the case of two particles with different masses [30][31][32][33], where the symmetry of the system is reduced to the same little groups C nv .…”

“…Therefore, for the quarkonium states, the twisted boundary condition trick does not seems to be applicable. However, we can practically choose θ q f = θq f as partially twisted boundary conditions to construct the meson interpolating operator [34]. A price to pay is that, by construction, a disconnected diagram contribution in quarkonium two-point functions is inevitably spoiled.…”

Potential description of charmonium and charmed-strange mesons from lattice QCD

“…This is an application based on the approach originally used for the hadron-hadron potential, which is defined through the equal-time BS amplitude [24][25][26][27][28][29][30][31][32][33]. More details of determination of the interquark potential are given in Ref.…”

Hidden charm molecules in finite volume

“…There exist other resonances far more difficult to get with this approach like the a 1 (1260), which was also attempted in [14] (see also its determination using finite volume calculations with effective field theory in [16]). Scalar mesons have also been searched for with this method [17][18][19][20] and gradually some calculations are being performed for systems in the charm sector [21][22][23][24][25][26][27]. From another field theoretical perspective, finite volume calculations have also been devoted to this sector in [27][28][29].…”