[논문 리뷰] Doubly Charmed Tetraquark $T^+_{cc}$ from Lattice QCD near Physical Point

Y. Lyu, Sinya Aoki외 4명|PubMed|2023. 02. 09.

Quantum Chromodynamics and Particle Interactions참고 문헌 56인용 수 7

한 줄 요약

Lattice QCD study of D*D scattering in the I=0, S-wave channel finds a near-threshold virtual state at m_pi=146 MeV, which evolves toward a loosely bound state at the physical point, with implications for the D0D0π+ spectrum measured by LHCb.

ABSTRACT

The doubly charmed tetraquark T_{cc}^{+} recently discovered by the LHCb Collaboration is studied on the basis of (2+1)-flavor lattice QCD simulations of the D^{*}D system with nearly physical pion mass m_{π}=146 MeV. The interaction of D^{*}D in the isoscalar and S-wave channel, derived from the hadronic spacetime correlation by the HAL QCD method, is attractive for all distances and leads to a near-threshold virtual state with a pole position E_{pole}=-59(_{-99}^{+53})(_{-67}^{+2}) keV and a large scattering length 1/a_{0}=0.05(5)(_{-2}^{+2}) fm^{-1}. The virtual state is shown to evolve into a loosely bound state as m_{π} decreases to its physical value by using a potential modified to m_{π}=135 MeV based on the pion-exchange interaction. Such a potential is found to give a semiquantitative description of the LHCb data on the D^{0}D^{0}π^{+} mass spectrum. Future study is necessary to perform physical-point simulations with the isospin-breaking and open three-body-channel effects taken into account.

연구 동기 및 목표

• Investigate the D*D interaction in the I=0, S-wave channel using (2+1)-flavor lattice QCD near the physical point.
• Extract the D*D potential from HAL QCD and analyze its implications for near-threshold states.
• Connect lattice results to experimental D0D0π+ spectra and assess evolution toward the physical point.

제안 방법

• Compute hadronic spacetime correlation R(r,t) for D* and D with wall-type sources and Coulomb gauge fixing.
• Extract the HAL QCD potential V(r) from the derivative expansion of the normalized correlation function.
• Solve the Schrödinger equation with the extracted potential in infinite volume to obtain phase shifts, scattering length, and pole positions.
• Fit V(r) with multi-Gaussian forms and test long-range behavior including pion-exchange contributions.
• Estimate the evolution of the near-threshold state by modifying m_pi to 135 MeV and comparing with LHCb D0D0π+ data.

실험 결과

연구 질문

• RQ1 Does the D*D interaction in the I=0, S-wave channel exhibit attraction at all distances near the physical point?
• RQ2 Is there a near-threshold pole (virtual or bound state) for D*D, and how does its nature evolve toward the physical pion mass?
• RQ3 Can the lattice-derived D*D potential semi-quantitatively describe the LHCb D0D0π+ mass spectrum?
• RQ4 What is the impact of long-range forces (pion exchange) on the D*D interaction and the near-threshold state?

주요 결과

m_pi (MeV)	1/a0 (fm^-1)	r_eff (fm)	kappa_pole (MeV)	E_pole (keV)
146.4	0.05(5)^{+2}_{-2}	1.12(3)^{+3}_{-8}	-8(8)^{+3}_{-5}	-59^{+53}_{-99}{}^{+2}_{-67}
135.0	-0.03(4)		+5(8)	-45^{+41}_{-78}

• The D*D potential in the I=0, S-wave channel is attractive for all distances.
• At m_pi = 146.4 MeV, the system has a near-threshold virtual state with pole position E_pole = -59^{+53}_{-99} (stat)^{+2}_{-67} (syst) keV and a large scattering length 1/a0 = 0.05(5)^{+2}_{-2} fm^{-1}.
• The effective range is r_eff = 1.12(3)^{+3}_{-8} fm at m_pi = 146.4 MeV.
• Modifying the potential to m_pi = 135.0 MeV yields a loosely bound state with E_pole ≈ -45^{+41}_{-78} keV, indicating evolution toward binding at the physical point.
• A potential-based analysis describes the D0D0π+ mass spectrum from LHCb reasonably well, supporting a near-threshold interpretation.
• The long-range part of the potential is consistent with two-pion exchange (TPE) effects, while single-pion exchange (OPE) is not clearly visible in the lattice data.