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While reducing the tensor integrals to scalar integrals all that we use are Lorentz covariance and the physical interpretation of the result. Thus I think that the Pa-Ve Reduction of Tensor integrals is purely a mathematical result and does not depend on the undelying theory.

Am I missing something? Are they really dependent?

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    $\begingroup$ Tip: Consider to add references for readability. $\endgroup$
    – Qmechanic ♦
    Commented Jun 27, 2017 at 16:56

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I don't know if this is weird or not to answer one's own question but here it goes: the Passarino-Veltmann Decomposition aims at expressing the tensor loop integral using the Lorentz covariant quantities in the integral.

As such in a general Lorentz Covariant Theory the decomposition rules will change depending on the Physical Lorentz Covariant Quantities involved, but the algorithm of reduction remains the same.

If the theory however is not Lorentz Covariant(NRQCD or similar effective theories) then the entire construct fails.

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