dorsal/arxiv
View SchemaTwo-point correlation function with pion in QCD sum rules
| Authors | Hungchong Kim, Su Houng Lee, Makoto Oka |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9811096 |
| URL | https://arxiv.org/abs/nucl-th/9811096 |
| DOI | 10.1103/PhysRevD.60.034007 |
| Journal | Phys.Rev. D60 (1999) 034007 |
Abstract
Within the framework of the conventional QCD sum rules, we study the pion two-point correlation function, $i\int d^4x e^{iq\cdot x} < 0| T J_N(x) {\bar J}_N(0)|\pi(p)>$, beyond the soft-pion limit. We construct sum rules from the three distinct Dirac structures, $i \gamma_5 \notp, i \gamma_5, \gamma_5 \sigma_{\mu \nu} {q^\mu p^\nu}$ 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 $i \gamma_5 \notp$ 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.
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"abstract": "Within the framework of the conventional QCD sum rules, we study the pion\ntwo-point correlation function, $i\\int d^4x e^{iq\\cdot x} \u003c 0| T J_N(x) {\\bar\nJ}_N(0)|\\pi(p)\u003e$, beyond the soft-pion limit. We construct sum rules from the\nthree distinct Dirac structures, $i \\gamma_5 \\notp, i \\gamma_5, \\gamma_5\n\\sigma_{\\mu \\nu} {q^\\mu p^\\nu}$ and study the reliability of each sum rule. The\nsum rule from the third structure is found to be insensitive to the continuum\nthreshold, $S_\\pi$, and contains relatively small contribution from the\nundetermined single pole which we denote as $b$. The sum rule from the $i\n\\gamma_5$ structure is very different even though it contains similar\ncontributions from $S_\\pi$ and $b$ as the ones coming from the $\\gamma_5\n\\sigma_{\\mu \\nu} {q^\\mu p^\\nu}$ structure. On the other hand, the sum rule from\nthe $i \\gamma_5 \\notp$ structure has strong dependence on both $S_\\pi$ and $b$,\nwhich is clearly in constrast with the sum rule for $\\gamma_5 \\sigma_{\\mu \\nu}\n{q^\\mu p^\\nu}$. We identify the source of the sensitivity for each of the sum\nrules by making specific models for higher resonance contributions and discuss\nthe implication.",
"arxiv_id": "nucl-th/9811096",
"authors": [
"Hungchong Kim",
"Su Houng Lee",
"Makoto Oka"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1103/PhysRevD.60.034007",
"journal_ref": "Phys.Rev. D60 (1999) 034007",
"title": "Two-point correlation function with pion in QCD sum rules",
"url": "https://arxiv.org/abs/nucl-th/9811096"
},
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