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We report the first measurement of the fraction of J=ψ mesons coming from B-meson decay (FB→J=ψ ) in p þ p collisions at ffiffi s p ¼ 510 GeV. The measurement is performed using the forward silicon vertex detector and central vertex detector at PHENIX, which provide precise tracking and distance-of-closestapproach determinations, enabling the statistical separation of J=ψ due to B-meson decays from prompt J=ψ. The measured value of FB→J=ψ is 8.1% 2.3%ðstatÞ 1.9%ðsystÞ for J=ψ with transverse momenta 0 < pT < 5 GeV=c and rapidity 1.2 < jyj < 2.2. The measured fraction FB→J=ψ at PHENIX is compared to values measured by other experiments at higher center of mass energies and to fixed-order-next-toleading-logarithm and color-evaporation-model predictions. The bb¯ cross section per unit rapidity [dσ=dyðpp → bb¯Þ] extracted from the obtained FB→J=ψ and the PHENIX inclusive J=ψ cross section measured at 200 GeV scaled with color-evaporation-model calculations, at the mean B hadron rapidity y ¼ 1.7 in 510 GeV p þ p collisions, is 3.63+1.92 −1.70 μb. It is consistent with the fixed-order-next-toleading-logarithm calculations. D

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