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V tem delu teoretično študiramo resonanco $Z_{b}$, opaženo leta 2011 v detektorju Belle, ki izkazuje tetrakvarkovsko strukturo. Sistem analiziramo s kvantno kromodinamiko na mreži, saj gre za močno interagirajoč sistem v neperturbativnem režimu. Iz razpadnih produktov resonance je mogoče sklepati na kvarkovsko strukturo $bar{b} b bar{d} u$. Zaradi ogromne razlike mas med kvarki uporabimo Born-Oppenheimerjev približek, kjer težja kvarka $bar{b}$ in $b$ v prvem koraku privzamemo za statična. Možna stanja, s katerimi opišemo tetrakvark $Z_{b}$, razvrstimo v dva tipa. Prvemu ustreza par interagirajočih mezonov $B$ in $bar{B}^{*}$, drugemu pa interagirajoča botomonij $Upsilon$ in pion s tremi najnižjimi vrednostmi gibalne količine, ki so v skladu s simetrijo sistema. Stanja z neničelno gibalno količino piona moramo vključiti v analizo, saj ta še vedno ležijo pod vrednostjo resonanc $Z_{b}$. Do sedaj tega ni vsebovala še nobena študija. Z izbranimi operatorji numerično izračunamo korelacijske funkcije, iz katerih izluščimo lastne energije sistema kot funkcijo razdalje med težkima kvarkoma. Za interpretacijo energijskega spektra izračunamo lastne energije neinteragirajoče verzije originalnega sistema. Po primerjavi ustreznih lastnih energij opazimo očitno odstopanje v kanalu $Bbar{B}^{*}$, kjer je za majhne razdalje med mezonoma $B$ znaten privlačen potencial. Izluščen potencial nato uporabimo za reševanje Schr"odingerjeve enačbe za mezona v težiščnem sistemu. Preučimo stanja, ki jih takšen potencial dopušča, ter skušamo rezultate povezati z izmerjenio resonanco $Z_{b}$. In this thesis we study the resonance $Z_{b}$, observed in 2011 at Belle detector, with exotic quark structure. We analyse the system using quantum chromodynamics on lattice, since the system considered is governed by the strong interaction in nonperturbative regime. From decay channels of $Z_{b}$, it is possible to deduce that the valence quark structure is $bar{b} b bar{d} u$. A large difference in mass of the valence quarks allows us to use Born-Oppenheimer approximation, where in the first step of the calculation the two heavier quarks $bar{b}$ and $b$ are treated as static. Possible states, that we use to describe $Z_{b}$, are classified into two types. The first set resembles two interacting mesons, $B$ and $bar{B}^{*}$. The second one describes bottomonium $Upsilon$ and a pion with three different smallest values of momenta, that are allowed by the symmetry of the system. States with non-zero pion momenta need to be included, since some of them still lie below or close to the threshold of the $Z_{b}$ resonance. Up to this point no theoretical study has included those states in their analysis. After chossing the operators we compute the correlation function, from which we extract the eigen energies as a function of separation of the two heavy quarks. To make any physical conclusion based of the spectrum, we compute eigenenergies of a non-interacting version of the original system. After comparing the two, we observe a large deviation in the channel $B bar{B}^{*}$, where for small separations between the two mesons there appears a large binding potential. The extracted potential is then used to solve the Schr"odinger equation for mesons in the center of mass system. We analyse the states, that are allowed by the potential, and try to connect those with the experimentally observed resonance $Z_{b}$.