We obtain the s- and p-wave low-energy scattering parameters for n$^{3}$H elastic scattering and the position of the $^{4}$H <math><msup><mrow><mi>J</mi></mrow><mrow><mi>π</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math> resonance using the pionless effective field theory at leading order. Results are extracted with three numerical techniques: confining the system in a harmonic oscillator trap, solving the Faddeev-Yakubovsky equations in configuration space, and using an effective two-body cluster approach. The renormalization of the theory for the relevant amplitudes is assessed in a cutoff-regulator range between <math><mn>1</mn><mspace width="0.2em"></mspace><msup><mrow><mtext>fm</mtext></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> and <math><mn>10</mn><mspace width="0.2em"></mspace><msup><mrow><mtext>fm</mtext></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>.Most remarkably, we find a cutoff-stable/RG-invariant resonance in the $^{4}$H <math><msup><mrow><mi>J</mi></mrow><mrow><mi>π</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math> system. This p-wave resonance is a universal consequence of a shallow two-body state and the introduction of a three-body s-wave scale set by the triton binding energy. The stabilization of a resonant state in a few-fermion system through pure contact interactions has a significant consequence for the powercounting of the pionless theory. Specifically, it suggests the appearance of similar resonant states also in larger nuclei, like 16-oxygen, in which the theory's leading order does not predict stable states. Those resonances would provide a starting state to be moved to the correct physical position by the perturbative insertion of sub-leading orders, possibly resolving the discrepancy between data and contact EFT.

France

Lorenzo Contessi

Israel

Martin Schäfer

India

United Kingdom

United States

Johannes Kirscher

Rimantas Lazauskas

Jaume Carbonell

Emergence of H = 1 Resonance in Contact Theories

Energy levels are investigated for two charged particles possessing an attractive, momentum-independent, zero-range interaction in a uniform magnetic field. A transcendental equation governs the spectrum, which is characterized by a collective Landau-level quantum number incorporating both center-of-mass and relative degrees of freedom. Results are obtained for a system of one charged and one neutral particle, with the interaction chosen to produce a bound state in vanishing magnetic field. Beyond deriving the weak-field expansion of the energy levels, we focus on non-perturbative aspects. In the strong-field limit, or equivalently for a system in the unitary limit, a single bound level with universal binding energy exists. By contrast, excited states are resonances that disappear into the continuum as the magnetic field is raised beyond critical values. A hyperbola is derived that approximates the number of bound levels as a function of the field strength remarkably well.

Brian C. Tiburzi

Two particles with zero-range interaction in a magnetic field

The <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> resonance has been conjectured to be a <math><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> charm meson-antimeson two-body molecule. Meanwhile, there is no experimental evidence for larger, few-body compounds of multiple charm meson-antimeson pairs which would resemble larger molecules or nuclei. Here, we investigate such multimeson states to the extent of what can be deduced theoretically from essentials of the interaction between uncharged <math><msup><mi>D</mi><mn>0</mn></msup></math> and <math><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> mesons. From a molecular <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>, we predict a <math><mn>4</mn><mi>X</mi></math> (<math><msup><mn>4</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>) octamer with a binding energy <math><msub><mi>B</mi><mrow><mn>4</mn><mi>X</mi></mrow></msub><mo>&gt;</mo><mn>2.08</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, assuming a <math><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mn>0</mn></msup></math> system close to the unitary limit [as suggested by the mass of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>]. If we consider heavy-quark spin symmetry explicitly, the <math><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> (<math><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>) system is close to unitarity, too. In this case, we predict a bound <math><mn>3</mn><mi>X</mi></math> (<math><msup><mn>3</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>) hexamer with <math><msub><mi>B</mi><mrow><mn>3</mn><mi>X</mi></mrow></msub><mo>&gt;</mo><mn>2.29</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and a more deeply bound <math><mn>4</mn><mi>X</mi></math> octamer with <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mn>4</mn><mi>X</mi></mrow></msub><mo>&gt;</mo><mn>11.21</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. These results exemplify with hadronic molecules a more general phenomenon of equal-mass two-species Bose systems composed of equal number of either type: the emergence of unbound four- and six-boson clusters in the limit of a short-range two-body interaction which acts only between bosons of different species. Finally, we also study the conditions under which a <math><mn>2</mn><mi>X</mi></math> (<math><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>) tetramer might form.

China

Manuel Pavon Valderrama

Triple-<math><mi>X</mi></math> and beyond: Hadronic systems of three and more <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>