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The first evidence of spin alignment of vector mesons (K*0 and ϕ) in heavy-ion collisions at the Large Hadron Collider (LHC) is reported. The spin density matrix element ρ00 is measured at midrapidity (|y|< 0.5) in Pb-Pb collisions at a center-of-mass energy (√sNN) of 2.76 TeV
with the ALICE detector. ρ00 values are found to be less than 1/3 (1/3 implies no spin alignment) at low transverse momentum (pT<2 GeV/c) for K*0 and ϕ at a level of 3σ and 2σ, respectively. No significant spin alignment is observed for the K0S meson (spin = 0) in Pb-Pb collisions and for the vector mesons in pp collisions. The measured spin alignment is unexpectedly large but qualitatively consistent with the expectation from models which attribute it to a polarization of quarks in the presence of angular momentum in heavy-ion collisions and a subsequent hadronization by the process of recombination.