Two-point correlation function with pion in QCD sum rules

Abstract

Within the framework of the conventional QCD sum rules, we study the pion two-point correlation function, $i\int d^{4}x{e}^{iq\cdot x}<0|T{J}_N(x){\bar{J}}_N(0)|\pi (p)>$, beyond the soft-pion limit. We construct sum rules from the three distinct Dirac structures, $i γ_5 \notp, i γ_5, γ_5 σ_{μν} {q^μp^ν}$ and study the reliability of each sum rule. The sum rule from the third structure is found to be insensitive to the continuum threshold, $S_{\pi }$, and contains relatively small contribution from the undetermined single pole which we denote as $b$. The sum rule from the $i{\gamma }_5$ structure is very different even though it contains similar contributions from $S_{\pi }$ and $b$ as the ones coming from the ${\gamma }_5{\sigma }_{\mu \nu }{q}^{\mu }{p}^{\nu }$ structure. On the other hand, the sum rule from the $i γ_5 \notp$ structure has strong dependence on both $S_{\pi }$ and $b$, which is clearly in constrast with the sum rule for ${\gamma }_5{\sigma }_{\mu \nu }{q}^{\mu }{p}^{\nu }$. We identify the source of the sensitivity for each of the sum rules by making specific models for higher resonance contributions and discuss the implication.

slightly revised. version accepted for publication in Physical Review D

References in corpus (1)

• Chirality and Reliability of Baryon QCD Sum Rules

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