We discuss whether the bound nature of multiquark states in quark models could benefit from relativistic effects on the kinetic energy operator. For mesons and baryons, relativistic corrections to the kinetic energy lead to lower energies, and thus call for a retuning of the parameters of the model. For multiquark states, as well as their respective thresholds, a comparison is made of the results obtained with nonrelativistic and relativistic kinetic energy. It is found that the binding energy is lower in the relativistic case. In particular, <math><mi>Q</mi><mi>Q</mi><mover><mi>q</mi><mo>¯</mo></mover><mover><mi>q</mi><mo>¯</mo></mover></math> tetraquarks with double heavy flavor become stable for a larger ratio of the heavy to light quark masses; the all-heavy tetraquarks <math><mi>Q</mi><mi>Q</mi><mover><mi>Q</mi><mo>¯</mo></mover><mover><mi>Q</mi><mo>¯</mo></mover></math> that are not stable in standard nonrelativistic quark models remain unstable when a relativistic form of kinetic energy is adopted.

France

Jean-Marc Richard

Spain

Alfredo Valcarce

Javier Vijande

Effect of relativistic kinematics on the stability of multiquarks

The hadronic weak decays of <math><msub><mi>Λ</mi><mi>c</mi></msub></math> are studied in the framework of a constituent quark model. With the combined analysis of the Cabbibo-favored processes, <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>→</mo><mi>Λ</mi><msup><mi>π</mi><mo>+</mo></msup></math>, <math><msup><mi>Σ</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math>, and <math><msup><mi>Σ</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>, we confirm that the nonfactorizable transition mechanisms play a crucial role in the understanding of their compatible branching ratios. We emphasize that the SU(3) flavor symmetry breaking effects, which is generally at the order of 1–2%, can be amplified by the destructive interferences among the pole terms in the diagrams with internal conversion. Some contributions are sensitive to the spatial distribution of the scalar-isoscalar light-quark sector in the <math><msub><mi>Λ</mi><mi>c</mi></msub></math>, and its overlap with the light quarks in the final state hyperon. Namely, a compact diquark configuration is disfavored.

China

Peng-Yu Niu

Qian Wang

Qiang Zhao

Hadronic weak decays of <math><msub><mi>Λ</mi><mi>c</mi></msub></math> in the quark model

We explore the possibility of very heavy dibaryons with three charm quarks and three beauty quarks, <math><mi>b</mi><mi>b</mi><mi>b</mi><mi>c</mi><mi>c</mi><mi>c</mi></math>, using a constituent model which should lead to the correct solution in the limit of hadrons made of heavy quarks. The six-body problem is treated rigorously, in particular taking into account the orbital, color, and spin mixed-symmetry components of the wave function. Unlike a recent claim based on lattice QCD, no bound state is found below the lowest dissociation threshold.

Very Heavy Flavored Dibaryons

With the imminent construction of the Deep Underground Neutrino Experiment (DUNE) and Hyper-Kamiokande, nucleon decay searches as a means to constrain beyond standard model extensions are once again at the forefront of fundamental physics. Abundant neutrons within these large experimental volumes, along with future high-intensity neutron beams such as the European Spallation Source, offer a powerful, high-precision portal onto this physics through searches for <math><mi>B</mi></math> and <math><mi>B</mi><mo>−</mo><mi>L</mi></math> violating processes such as neutron-antineutron transformations (<math><mi>n</mi><mo>→</mo><mover><mi>n</mi><mo>¯</mo></mover></math>), a key prediction of compelling theories of baryogenesis. With this in mind, this paper discusses a novel and self-consistent intranuclear simulation of this process within <math><mrow><mmultiscripts><mrow><mi>Ar</mi></mrow><mprescripts></mprescripts><mrow><mn>18</mn></mrow><mrow><mn>40</mn></mrow></mmultiscripts></mrow></math>, which plays the role of both detector and target within the DUNE’s gigantic liquid argon time projection chambers. An accurate and independent simulation of the resulting intranuclear annihilation respecting important physical correlations and cascade dynamics for this large nucleus is necessary to understand the viability of such rare searches when contrasted against background sources such as atmospheric neutrinos. Recent theoretical improvements to our model, such as the first calculations of the <math><mrow><mmultiscripts><mrow><mi>Ar</mi></mrow><mprescripts></mprescripts><mrow><mn>18</mn></mrow><mrow><mn>40</mn></mrow></mmultiscripts></mrow></math> intranuclear radial annihilation probability distribution and the inclusion of a realistic <math><mover><mi>n</mi><mo>¯</mo></mover><mi>A</mi></math> potential, are discussed. A Monte Carlo simulation comparison to another publicly available <math><mi>n</mi><mo>→</mo><mover><mi>n</mi><mo>¯</mo></mover></math> generator within GENIE is shown in some detail. The first calculation of <math><mrow><mmultiscripts><mrow><mi>Ar</mi></mrow><mprescripts></mprescripts><mrow><mn>18</mn></mrow><mrow><mn>40</mn></mrow></mmultiscripts></mrow></math>’s <math><mi>n</mi><mo>→</mo><mover><mi>n</mi><mo>¯</mo></mover></math>-intranuclear suppression factor, an important quantity for future searches at the DUNE, is also completed, finding <math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>R</mi></mrow><mrow><mi>Ar</mi></mrow></msubsup><mo>∼</mo><mn>5.6</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>22</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>.

United States

Joshua L. Barrow

Russia

Elena S. Golubeva

Eduard Paryev

Progress and simulations for intranuclear neutron-antineutron transformations in <math><mrow><mmultiscripts><mrow><mi>Ar</mi></mrow><mprescripts></mprescripts><mrow><mn>18</mn></mrow><mrow><mn>40</mn></mrow></mmultiscripts></mrow></math>

We present the first full-fledged study of the flavor-exotic isoscalar <math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>≡</mo><mi>b</mi><mi>b</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> tetraquark with spin and parity <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup></math>. We report accurate solutions of the four-body problem in a quark model, characterizing the structure of the state as a function of the ratio <math><msub><mrow><mi>M</mi></mrow><mrow><mi>Q</mi></mrow></msub><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>q</mi></mrow></msub></math> of the heavy to light quark masses. For such a standard constituent model, <math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math> lies approximately 150 MeV below the strong decay threshold <math><msup><mrow><mi>B</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mover><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></math> and 105 MeV below the electromagnetic decay threshold <math><msup><mrow><mi>B</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mi>γ</mi></math>. We evaluate the lifetime of <math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math>, identifying the promising decay modes where the tetraquark might be looked for in future experiments. Its total decay width is <math><mi>Γ</mi><mo>≈</mo><mn>87</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>15</mn></mrow></msup></math> GeV and therefore its lifetime τ≈ 7.6 ps. The promising final states are <math><msup><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>−</mo></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>+</mo></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup><mspace width="0.2em"></mspace><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>ℓ</mi></mrow></msub></math> and <math><msup><mrow><mover><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mn>0</mn></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup><mspace width="0.2em"></mspace><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>ℓ</mi></mrow></msub></math> among the semileptonic decays, and <math><msup><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>−</mo></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>+</mo></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><msup><mrow><mover><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mn>0</mn></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></mrow><mrow><mo>−</mo></mrow></msup></math>, and <math><msup><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>−</mo></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mo>+</mo></mrow></msup><mspace width="0.2em"></mspace><msup><mrow><mi>ρ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> among the nonleptonic ones. The semileptonic decay to the isoscalar <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math> tetraquark <math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math> is also relevant but it is not found to be dominant. There is a broad consensus about the existence of this tetraquark, and its detection will validate our understanding of the low-energy realizations of Quantum Chromodynamics (QCD) in the multiquark sector.

E. Hernández

J. Vijande

A. Valcarce

Spectroscopy, lifetime and decay modes of the Tetraquark

We use a constituent model to analyze the stability of pentaquark <math><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>q</mi><mi>q</mi><mi>q</mi><mi>q</mi></math> configurations with a heavy antiquark <math><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> or <math><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>, and four light quarks <math><mi>u</mi><mi>u</mi><mi>d</mi><mi>s</mi></math>, <math><mi>d</mi><mi>d</mi><mi>s</mi><mi>u</mi></math> or <math><mi>s</mi><mi>s</mi><mi>u</mi><mi>d</mi></math>. The interplay between chromoelectric and chromomagnetic effects is not favorable, and, as a consequence, no bound state is found below the lowest dissociation threshold.

Pentaquarks with anticharm or beauty revisited

We discuss the adequate treatment of the three- and four-body dynamics for the quark model picture of double-charm baryons and tetraquarks. We stress that the variational and Born-Oppenheimer approximations give energies very close to the exact ones, while the diquark approximation might be somewhat misleading. The Hall-Post inequalities also provide very useful lower bounds that exclude the possibility of stable tetraquarks for some mass ratios and some color wave functions.

Few-body quark dynamics for doubly heavy baryons and tetraquarks

We analyze the stability of self-gravitating systems which dynamics is investigated using the collisionless Boltzmann equation, and the modified Poisson equation of Eddington-inspired Born–Infield gravity. These equations provide a description of the Jeans paradigm used to determine the critical scale above which such systems collapse. At equilibrium, the systems are described using the time-independent Maxwell–Boltzmann distribution function $$f_0(v)$$ <math><mrow><msub><mi>f</mi><mn>0</mn></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math> . Considering small perturbations to this equilibrium state, we obtain a modified dispersion relation, and we find a new characteristic scale length. Our results indicate that the dynamics of self-gravitating astrophysical systems can be fully addressed in the Eddington-inspired Born–Infeld gravity. The latter modifies the Jeans instability in high densities environments, while its effects become negligible in star formation regions.

Ivan Martino

Italy

Antonio Capolupo

Kinetic theory of Jean instability in Eddington-inspired Born–Infeld gravity

We perform a numerical study of the four-dimensional spin-2 Kaluza-Klein spectrum of supersymmetric AdS 4 × S 2 ℬ 4 $$ {\mathrm{AdS}}_4\times {S}^2\left({\mathrm{\mathcal{B}}}_4\right) $$ vacua and show that they do not exhibit scale separation. Our methods are generally applicable to similar problems where the compactification geometry is not known analytically, hence an analytic treatment of the spectrum of Kaluza-Klein masses is not available.

Robin Terrisse

Dimitrios Tsimpis

On the spin-2 Kaluza-Klein spectrum of AdS 4 × S 2 ℬ 4 $$ {\mathrm{AdS}}_4\times {S}^2\left({\mathrm{\mathcal{B}}}_4\right) $$

The isovector partners of the &lt;math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mn&gt;3872&lt;/mn&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/math&gt; , recently found at BES III, Belle and CLEO-c were predicted in a simple model based on the chromomagnetic interaction among quarks. The extension to the hidden-beauty sector is discussed.