Baryons within an effective chiral model with three flavours
Final Report Abstract
Matter is made of molecules, which in turn are composed of atoms. Yet, even atoms are not elementary: there is a small compact atomic nucleus with positive charge, orbited by negatively charged electrons. Electrons have proven to be elementary: as far as we know, they do not possess any internal structure. On the contrary, the nucleus is made of so-called nucleons: positively charged protons and electrically neutral neutrons. The nucleus of a hydrogen atom is the simplest: it consists of one proton (hence, only one electron orbits the proton, in order to provide charge neutrality). Heavier nuclei typically contain more neutrons than protons, since this particular configuration is more stable. Proceeding to even smaller length scales, nucleons themselves are also not elementary, but are made of quarks. A proton is a state made of two up (u) and one down (d) quark, while a neutron is a udd state. The u quark having electric charge +2/3 and the d quark charge −1/3 (in units of the elementary charge e), the electric charges of the nucleons can be described. Moreover, quarks interact with each other via gluons and the corresponding theory is called Quantum Chromodynamics (QCD). In this project we studied properties of protons and nucleons as well as other so-called conventional baryons, i.e., states made of three quarks. In particular, we investigated the following properties: Origin of mass: The mass of an atomic nucleus is by far the largest contribution to the weight of objects. Ultimately, one needs to understand why a nucleon has a mass of approximately 940 MeV (in natural units). In our approach, we used a theoretical model (called the extended Linear Sigma Model, eLSM), in which interactions between the nucleons and other baryons and mesons, which are states made of quark and antiquarks, and so-called glueballs, which are states made entirely of gluons, generate the mass of nucleons and baryons. Extension of the eLSM: Besides the already mentioned u and d quarks, there is also an s (strange) quark. (Further quarks also exist but are much heavier and thus were not studied here). Hence, one can build three-quark baryons which include the s quark as well. In our model, we have included all these baryons by taking into account certain symmetries that appear at the fundamental level of their constituents (the quarks and gluons described by QCD). In particular, we made use of the so-called chiral symmetry, according to which each baryon has a corresponding partner with the same quantum numbers except for parity. For instance, the partner of the nucleon N turns out to be the resonance N (1535). Decays of baryons: The proton is – as far as we know – stable. The neutron has a lifetime of about 10 min, which is extremely long in the realm of baryons. On the other hand, various baryonic resonances live very shortly (10^−22 s). For instance, the resonance N (1535) decays into an N and one pion (the lightest meson, made of u and d quarks and the corresponding anti-quarks) and into an N and one η meson (a meson containing the s and s¯ quark). The latter decay was found to be surprisingly large in experiment and we proposed a mechanism to explain this large value as a result of quantum fluctuations of gluons. Scattering of baryons: Many experiments smash nucleons on nucleons in order to study their properties and to generate new particles. In our theoretical analysis, we investigated neutron-proton scattering. In particular, we showed that a certain scalar dibaryon (a quasi-bound state of a neutron and a proton, a different type of deuteron) exists for a very short time. Its existence is necessary to explain data from neutron-proton collisions. We have also analyzed processes of the type N N → N N X, where X is a certain meson. In particular, an interesting reaction is pp → ppω, where ω is a quark-antiquark object. In conclusion, we developed a model for baryons which allows to study their masses, their decays, and scattering processes. Many other applications of the model can be studied in future work.
Publications
- Role of a four-quark and a glueball state in pion-pion and pion-nucleon scattering
P. Lakaschus, J. L. P. Mauldin, F. Giacosa and D. H. Rischke
- “Is f0(1710) a glueball?”, Phys. Rev. D 90 (2014) no. 11, 114005
S. Janowski, F. Giacosa and D. H. Rischke
(See online at https://doi.org/10.1103/PhysRevD.90.114005) - “Role of scalar dibaryon and f0 (500) in the isovector channel of low-energy neutron-proton scattering”, Phys. Rev. C 94 (2016) no. 4, 044001
W. Deinet, K. Teilab, F. Giacosa and D. H. Rischke
(See online at https://doi.org/10.1103/PhysRevC.94.044001) - “Three-flavor chiral effective model with four baryonic multiplets within the mirror assignment”, Phys. Rev. D 93 (2016) no. 3, 034021
L. Olbrich, M. Zétényi, F. Giacosa and D. H. Rischke
(See online at https://doi.org/10.1103/PhysRevD.93.034021) - “Influence of the axial anomaly on the decay N (1535) → N η ”, Phys. Rev. D 97 (2018) no. 1, 014007
L. Olbrich, M. Zétényi, F. Giacosa and D. H. Rischke
(See online at https://doi.org/10.1103/PhysRevD.97.014007)
