L.R. Dai

J. Song

E. Oset

Erratum to “Evolution of genuine states to molecular ones: The <italic>T</italic> <inf><italic>cc</italic></inf>(3875) case&#8221; [Phys. Lett. B 846 (2023) 138200]

When we impose discrete symmetries in the standard model we have Dai-Freed global anomalies. However, interestingly if we introduce three right-handed neutrinos we can have an anomaly-free discrete Z 4 gauge symmetry. This Z 4 symmetry should be spontaneously broken down to the Z 2 symmetry to generate the heavy Majorana masses for the right-handed neutrinos. We show that this symmetry breaking naturally generates topological inflation, which is consistent with the CMB observations at present and predicts a significant tensor mode with scalar-tensor ratio r &gt; 0.03. The right-handed neutrinos play an important role in reheating processes. The reheating temperature is as high as ∼ 108 GeV, and non-thermal leptogenesis successfully takes place.

Japan

Masahiro Kawasaki

China

Tsutomu Yanagida

Dai-Freed anomaly in the standard model and topological inflation

We address the issue of the compositeness of hadronic states and demonstrate that starting with a genuine state of nonmolecular nature, but which couples to some meson-meson component to be observable in that channel, if that state is blamed for a bound state appearing below the meson-meson threshold it gets dressed with a meson cloud and it becomes pure molecular in the limit case of zero binding. We discuss the issue of the scales, and see that if the genuine state has a mass very close to threshold, the theorem holds, but the molecular probability goes to unity in a very narrow range of energies close to threshold. The conclusion is that the value of the binding does not determine the compositeness of a state. However, in such extreme cases we see that the scattering length gets progressively smaller and the effective range grows indefinitely. In other words, the binding energy does not determine the compositeness of a state, but the additional information of the scattering length and effective range can provide an answer. We also show that the consideration of a direct attractive interaction between the mesons in addition to having a genuine component, increases the compositeness of the state. Explicit calculations are done for the <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mn>3875</mn><mo>)</mo></math> state, but are easily generalized to any hadronic system.

Spain

Evolution of genuine states to molecular ones: The (3875) Case

We have chosen the <math><msup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo><mo>+</mo></mrow></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></math> reaction in order to observe the <math><mi>I</mi><mo>=</mo><mn>0</mn><mo>,</mo><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> (<math><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub></math>) partner state of the <math><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>2866</mn><mo>)</mo></math> stemming from the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup></math> molecular picture. The reaction proceeds via external emission in the most favored Cabibbo decay mode and one observes the <math><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub></math> state as a very strong peak versus the background in the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></math> spectrum. The branching ratio for <math><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub></math> production in this reaction is estimated of the order of <math><mn>4</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. The method used, applied to the <math><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math> reaction, produces a ratio of signal to background in the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math> spectrum in very good agreement with the LHCb experiment that observed the <math><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>2866</mn><mo>)</mo></math>.

R. Molina

The Reaction to Detect the = 0, = 1 Partner of the (2866)

Anomalies can be elegantly analyzed by means of the Dai-Freed theorem. In this framework it is natural to consider a refinement of traditional anomaly cancellation conditions, which sometimes leads to nontrivial extra constraints in the fermion spectrum. We analyze these more refined anomaly cancellation conditions in a variety of theories of physical interest, including the Standard Model and the SU(5) and Spin(10) GUTs, which we find to be anomaly free. Turning to discrete symmetries, we find that baryon triality has a ℤ9 anomaly that only cancels if the number of generations is a multiple of 3. Assuming the existence of certain anomaly-free ℤ4 symmetry we relate the fact that there are 16 fermions per generation of the Standard model — including right-handed neutrinos — to anomalies under time-reversal of boundary states in four-dimensional topological superconductors. A similar relation exists for the MSSM, only this time involving the number of gauginos and Higgsinos, and it is non-trivially, and remarkably, satisfied for the SU(3) × SU(2) × U(1) gauge group with two Higgs doublets. We relate the constraints we find to the well-known Ibañez-Ross ones, and discuss the dependence on UV data of the construction. Finally, we comment on the (non-)existence of K-theoretic θ angles in four dimensions.

United Kingdom

Germany

Iñaki García-Etxebarria

Belgium

Netherlands

Miguel Montero

Dai-Freed anomalies in particle physics

We study the Bc-→π-J/ψω and Bc-→π-D∗D¯∗ reactions and show that they are related by the presence of two resonances, the X (3940) and X (3930), that are of molecular nature and couple most strongly to D∗D¯∗ , but also to J/ψω . Because of that, in the J/ψω mass distribution we find a cusp with large strength at the D∗D¯∗ threshold and predict the ratio of strengths between the peak of the cusp and the maximum of the D∗D¯∗ distribution close to D∗D¯∗ threshold, which are distinct features of the molecular nature of these two resonances.

Brazil

J.M. Dias

Disclosing D∗D¯∗ molecular states in the Bc-→π-J/ψω decay

We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter. This is done by studying a massive fermion. The key role is played by the wave function of the ground state in the Hilbert space of the fermion in the large mass limit. The ground state takes values in the determinant line bundle and has nontrivial Berry phases which characterize the low energy topological phases.

Kazuya Yonekura

Dai-Freed theorem and topological phases of matter

We study the B0 decay to D0D¯0K0 based on the chiral unitary approach, which generates the X(3720) resonance, and we make predictions for the D0D¯0 invariant mass distribution. From the shape of the distribution, the existence of the resonance below threshold could be induced. We also predict the rate of production of the X(3720) resonance to the D0D¯0 mass distribution with no free parameters.