Study of the decay $B^0 \to \chi_{c1} K^+ \pi^-$ and search of exotic resonances at LHCb

In 2008 the Belle Collaboration reported the observation of two charged resonance-like structures in the ${\chi_c}_1 \pi^-$ mass spectrum produced in the decay $B^0 \to {\chi_c}_1 K^+ \pi^-$. These were labelled as $Z_1(4050)^-$ and $Z_2(4250)^-$. Alternatively, a single wider resonance hypothesis was also pursued by Belle, and labelled as $Z(4150)^-$. The fact that these are charged states would be a clear sample, if they really exist, of four quark bound systems; for this reason this observation has given rise to a great deal of interest. In 2012 the BABAR Collaboration has searched for these resonances in the channels $B^{0,+} \to {\chi_c}_1 K^{+,0} \pi^-$ and did not find any evidence of them. In this thesis a search for these claimed exotic charmonium-like states $Z_1(4050)^-$ and $Z_2(4250)^-$ is presented, in the decay $B^0 \to {\chi_c}_1 K^+ \pi^-$, where ${\chi_c}_1 \to J/\psi \gamma$ and $J/\psi \to \mu^+ \mu^-$. Charged conjugate are implied throughout the whole thesis. The analysis is performed using data collected with the LHCb detector at the $p-p$ Large Hadron Collider operating at a center-of-mass energy of $7$ and $8 \, TeV$. The data sample consists of the LHCb full statistics from years 2011-2012 data taking, corresponding to an integrated luminosity of $3 \, {fb}^{-1}$. LHCb has more than twice the Belle and BABAR cumulative $B^0 \to {\chi_c}_1 K \pi^-$ signal events. Hence it is the right environment to clarify the existence of exotic states in the ${\chi_c}_1 \pi^-$ system. The analysis strategy adopted in this thesis is inspired to what BABAR did in. The BABAR approach, unlike the Belle one, is model independent and its philosophy could be shortly summarized saying that any exotic explanation should not be given as long as a reasonable explanation of the data can be found in terms of traditional effects, namely if the data can be explained only in terms of the relatively well known resonances in the $K^+\pi^-$ system. In the BABAR analysis, first a representation is given of the $K^+\pi^-$ mass and angular distribution structures dominating the final state in terms of their expected angular-momentum intensity contributions. Then the reflection of each $K^+\pi^-$ component into the ${\chi_c}_1 \pi^-$ mass distribution is investigated in order to establish if any additional signal is needed or not. BABAR conclusion is that, in the limit of their statistical significance, no additional states are required in the ${\chi_c}_1 \pi^-$ spectrum to explain the data. The reflections of the known resonances in the system $K^+\pi^-$ are sufficient, and there are no needs for introducing any exotic $Z$.