<p>A search is performed for long-lived particles that decay into final states that include a pair of electrons or a pair of muons. The experimental signature is a distinctive topology consisting of a pair of charged leptons originating from a displaced secondary vertex. Events corresponding to an integrated luminosity of <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>19.6</mml:mn><mml:mtext> </mml:mtext><mml:mo stretchy="false">(</mml:mo><mml:mn>20.5</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:msup><mml:mrow><mml:mi>fb</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> in the electron (muon) channel were collected with the CMS detector at the CERN LHC in proton-proton collisions at <inline-formula><mml:math display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>8</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>TeV</mml:mi></mml:math></inline-formula>. No<mml:math display="inline"></mml:math> significant excess is observed above standard model expectations. Upper limits on the product of the cross section and branching fraction of such a signal are presented as a function of the long-lived particle’s mean proper decay length. The limits are presented in an approximately model-independent way, allowing them to be applied to a wide class of models yielding the above topology. Over much of the investigated parameter space, the limits obtained are the most stringent to date. In the specific case of a model in which a Higgs boson in the mass range <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>125</mml:mn><mml:mi>–</mml:mi><mml:mn>1000</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> decays into a pair of long-lived neutral bosons in the mass range <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>20</mml:mn><mml:mi>–</mml:mi><mml:mn>350</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, each of which can then decay to dileptons, the upper limits obtained are typically in the range 0.2–10 fb for mean proper decay lengths of the long-lived particles in the range 0.01–100 cm. In the case of the lowest Higgs mass considered (<inline-formula><mml:math display="inline"><mml:mrow><mml:mn>125</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), the limits are in the range 2–50 fb. These limits are sensitive to Higgs boson branching fractions as low as <inline-formula><mml:math display="inline"><mml:mn>1</mml:mn><mml:msup><mml:mn>0</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>