Search for CP violation in the angular distribution of $\Lambda^0_b \rightarrow p \pi^- \pi^+\pi^-$ baryon decays and a proposal for the search of heavy baryon EDM with bent crystal at LHCb

In the past, flavour physics has driven indirect discoveries of new particles through precision measurements of other processes before the actual particles could be produced directly. For example the discovery of the differences in the behaviour of matter and antimatter, CP violation (CPV), has led to the explanation of flavour mixing with three families of quarks; the absence of the decay$K^0_L \rightarrow \mu^+\mu^-$ decay drove the prediction of the $c$quark trough the GIM mechanism; the measurement of the $B^0$ mixing allowed for the prediction of high mass of the $t$quark. The asymmetry between matter and antimatter behaviour is related to the violation of the CP symmetry, where $C$ and $P$ are the charge-conjugation and parity operators. CPV is accommodated in the Standard Model (SM) of particle physics by the Cabibbo-Kobayashi-Maskawa (CKM) mechanism that describes the transitions between up- and down-type quarks, in which quark decays proceed by the emission of a virtual W boson and where the phases of the couplings change sign between quarks and antiquarks. A significant excess of CPV with respect to the theoretical predictions would represent a proof of new physics beyond the SM (BSM). The experiments BaBar and Belle have systematically studied the $B^0$ and $B^{+-}$ mesons. The heavy baryon sector (ie containing the quark quark) still remains largely unexplored. Given the large production of heavy baryons at lhcb, precision measurements have become possible in this field. Moreover, the interest of the scientific community is growing on heavy baryons: the last measurement on $\mid V_{ub}\mid$ in the channel decay $\Lambda^0_b \rightarrow p\mu^- \bar\nu$ and the discovery of the pentaquark in the channel $\Lambda^0_b \rightarrow J/\psi p K^-$ are only few relevant examples. Actually the theory describes very well, within the experimental error, the CPV mechanism so far observed in meson decays. Since in the mesons and baryons decays the quark transitions are the same, the CKM theory predicts CPV also in the baryon sector, which has never been observed so far. It is important to measure CPV also in baryons to check if the mechanisms through which it is generated is the same as mesons. We know that CPV is a key ingredient for baryogenesis, but the CKM mechanism cannot explain it quantitatively. New sources of CPV are necessary to explain baryogenesis. The search for electric dipole moment (EDM) of baryons represents a powerful probe for new sources of CPV and new physics beyond the Standard Model. In particular, it is sensitive to flavour diagonal CPV contributions that are predicted to be minuscule in the SM. The existence of permanent EDMs requires the violation of parity ($P$) and time reversal ($T$) symmetries and thus, relying on the validity of the CPT theorem, the violation of CP symmetry. These measurements are not foreseen in the physics program of the lhcb experiment dedicated to the study of the CP violation of heavy hadron via flavour-changing observables, and require new instrumentation.