Essence of the vacuum quark condensate

Preprint number: CP3-Origins-2010-18
Authors: Stanley J. Brodsky (SLAC, Stanford and CP3-Origins), Craig D. Roberts (Argonne National Laboratory and Peking University), Robert Shrock (Stony Brook University), and Peter C. Tandy (Kent State University)
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We show that the chiral-limit vacuum quark condensate is qualitatively equivalent to the pseudoscalar meson leptonic decay constant in the sense that they are both obtained as the chiral-limit value of well-defined gauge-invariant hadron-to-vacuum transition amplitudes that possess a spectral representation in terms of the current-quark mass. Thus, whereas it might sometimes be convenient to imagine otherwise, neither is essentially a constant mass-scale that fills all spacetime. This means, in particular, that the quark condensate can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions.