Measurement of the ratio of prompt <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi></mml:math> production in pp collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>7</mml:mn><mml:mtext> TeV</mml:mtext></mml:math>

The prompt production of charmonium χcand J/ψ states is studied in proton–proton collisions at a centre-of-mass energy of root s=7 TeV at the Large Hadron Collider. The χc and J/ψ mesons are identified through their decays χc→J/ψγ andJ/ψ→μ+μ− using 36 pb−136 pb−1 of data collected by the LHCb detector in 2010. The ratio of the prompt production cross-sections for χc and J/ψ, σ(χc→J/ψγ)/σ(J/ψ), is determined as a function of the J/ψ transverse momentum in the range 2&lt;pT(J/ψ)&lt;15 GeV/c. The results are in excellent agreement with next-to-leading order non-relativistic expectations and show a significant discrepancy compared with the colour singlet model prediction at leading order, especially in the low pT(J/ψ) region.