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Non-perturbative determinations of $B$-meson decay constants and semi-leptonic form factors

$B$-physics is one of the most promising windows to find new physics in the flavor sector. One key ingredient to these searches are precise theoretical predictions derived from the Standard Model. Focusing at the nonperturbative QCD contributions, we carry out lattice QCD simulations in order to calculate $B$-meson decay constants and semi-leptonic form factors. Combined with experimental measurements our results enable us to determine CKM matrix elements. Here we present $B$ and $B_s$ meson decay constants as well as semi-leptonic form factors including rare decays, CKM or GIM suppressed in the Standard Model. Our results are based on the set of 2+1 flavor domain-wall Iwasaki gauge field configurations generated by the RBC-UKQCD collaboration. Heavy $b$-quarks are simulated using the relativistic heavy quark action.