A comprehensive revisit of the &rho; meson with improved Monte-Carlo based QCD sum rules

Qi-Nan Wang; Zhu-Feng Zhang; T. G. Steele; Hong-Ying Jin; Zhuo-Ran Huang

doi:10.1088/1674-1137/41/7/074107

Chinese Physics C> 2017, Vol. 41> Issue(7) : 074107 DOI: 10.1088/1674-1137/41/7/074107

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

1.
Physics Department, Ningbo University, Zhejiang 315211, China
2.
Physics Department, Ningbo University, Zhejiang 315211, China
3.
Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E2, Canada
4.
Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E2, Canada
5.
Zhejiang Institute of Modern Physics, Zhejiang University, Zhejiang 310027, China
6.
Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E2, Canada
7.
Zhejiang Institute of Modern Physics, Zhejiang University, Zhejiang 310027, China

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Abstract：
We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hölder-inequality-determined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function. In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters (the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of α_s corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.
- QCD sum rules ,
- H ,
- lder inequality ,
- phenomenological spectral function ,
- s corrections to dimension-4 operators

References

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[34]	K. G. Chetyrkin, V. P. Spiridonov, and S. G. Gorishnii, Phys. Lett. B, 160: 149 (1985)
[35]	H. Y. Jin and J. G. Korner, Phys. Rev. D, 64: 074002 (2001) [hep-ph/0003202]
[36]	H. Y. Jin, J. G. Korner, and T. G. Steele, Phys. Rev. D, 67: 014025 (2003) [hep-ph/0211304]
[37]	L. F. Abbott, Nucl. Phys. B, 185: 189 (1981)
[38]	S. Narison and E. de Rafael, Phys. Lett. B, 103: 57 (1981)
[39]	R. E. Cutkosky, J. Math. Phys., 1: 429 (1960)
[40]	A. K. Das, V. S. Mathur, and P. Panigrahi, Phys. Rev. D, 35: 2178 (1987)
[41]	C. A. Dominguez and N. Paver, Z. Phys. C, 31: 591 (1986)
[42]	L. Martinovic, Phys. Rev. D, 41: 1709 (1990)
[43]	L. Martinovic, Phys. Rev. D, 44: 220 (1991)
[44]	E. F. Beckenbach, R. Bellman,Inequalities (Berlin: Springer, 1961)
[45]	S. K. Berberian,Measure and Integration (New York: MacMillan, 1965)
[46]	Y. Chung, H. G. Dosch, M. Kremer, and D. Schall, Z. Phys. C, 25: 151 (1984)
[47]	S. Narison, Phys. Lett. B, 361: 121 (1995) [hep-ph/9504334]
[48]	S. Narison, Phys. Lett. B, 673: 30 (2009) [arXiv:0901.3823 [hep-ph]]
[49]	E. V. Shuryak, Rev. Mod. Phys., 65: 1 (1993)
[50]	J. Gasser and U. G. Meissner, Nucl. Phys. B, 357: 90 (1991)

References

[1]	M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B, 147: 448 (1979)
[2]	M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B, 147: 385 (1979)
[3]	L. J. Reinders, H. Rubinstein, and S. Yazaki, Phys. Rept., 127: 1 (1985)
[4]	S. Narison, Nucl. Phys. Proc. Suppl., 207-208: 315 (2010) [arXiv:1010.1959 [hep-ph]]
[5]	S. Narison, Nucl. Part. Phys. Proc., 258-259: 189 (2015) [arXiv:1409.8148 [hep-ph]]
[6]	S. Narison, Phys. Lett. B, 738: 346 (2014) [arXiv:1401.3689 [hep-ph]]
[7]	S. Narison, Nucl. Part. Phys. Proc., 270-272: 143 (2016) [arXiv:1511.05903 [hep-ph]]
[8]	R. Albuquerque, S. Narison, A. Rabemananjara, and D. Rabetiarivony, Int. J. Mod. Phys. A, 31(17): 1650093 (2016) [arXiv:1604.05566 [hep-ph]]
[9]	Z. R. Huang, H. Y. Jin, T. G. Steele, and Z. F. Zhang, Phys. Rev. D, 94(5): 054037 (2016) [arXiv:1608.03028 [hep-ph]]
[10]	R. Albuquerque, S. Narison, F. Fanomezana, A. Rabemananjara, D. Rabetiarivony, and G. Randriamanatrika, Int. J. Mod. Phys. A, 31(36): 1650196 (2016) [arXiv:1609.03351 [hep-ph]]
[11]	Z. R. Huang, W. Chen, T. G. Steele, Z. F. Zhang, and H. Y. Jin, Phys. Rev. D, 95(7): 076017 (2017) [arXiv:1610.02081[hep-ph]]
[12]	R. Shankar, Phys. Rev. D, 15: 755 (1977)
[13]	R. D. Matheus and S. Narison, Nucl. Phys. Proc. Suppl., 152: 236 (2006) [hep-ph/0412063]
[14]	S. Narison, Phys. Lett. B, 675: 319 (2009) [arXiv:0903.2266 [hep-ph]]
[15]	D. B. Leinweber, Annals Phys., 254: 328 (1997) [nucl-th/9510051]
[16]	F. X. Lee, D. B. Leinweber, and X.-M. Jin, Phys. Rev. D, 55: 4066 (1997) [nucl-th/9611011]
[17]	F. X. Lee, Phys. Rev. C, 57: 322 (1998) [hep-ph/9707332]
[18]	F. X. Lee, Phys. Lett. B, 419: 14 (1998) [hep-ph/9707411]
[19]	G. Erkol and M. Oka, Nucl. Phys. A, 801: 142 (2008) [arXiv:0801.0783 [nucl-th]]
[20]	L. Wang and F. X. Lee, Phys. Rev. D, 78: 013003 (2008) [arXiv:0804.1779 [hep-ph]]
[21]	Z. F. Zhang, H. Y. Jin, and T. G. Steele, Chin. Phys. Lett., 31: 051201 (2014) [arXiv:1312.5432 [hep-ph]]
[22]	Z. R. Huang, H. Y. Jin, and Z. F. Zhang, JHEP, 1504: 004 (2015) [arXiv:1411.2224 [hep-ph]]
[23]	M. Benmerrouche, G. Orlandini, and T. G. Steele, Phys. Lett. B, 356: 573 (1995) [hep-ph/9507304]
[24]	T. G. Steele, S. Alavian, and J. Kwan, Phys. Lett. B, 392: 189 (1997) [hep-ph/9701267]
[25]	T. G. Steele, K. Kostuik, and J. Kwan, Phys. Lett. B, 451: 201 (1999) [hep-ph/9812497]
[26]	F. Shi, T. G. Steele, V. Elias, K. B. Sprague, Y. Xue, and A. H. Fariborz, Nucl. Phys. A, 671: 416 (2000) [hep-ph/9909475]
[27]	R. T. Kleiv, T. G. Steele, A. Zhang, and I. Blokland, Phys. Rev. D, 87(12): 125018 (2013) [arXiv:1304.7816 [hep-ph]]
[28]	W. Chen, H. X. Chen, X. Liu, T. G. Steele, and S. L. Zhu, arXiv:1605.01647 [hep-ph]
[29]	C. Patrignani et al (Particle Data Group Collaboration), Chin. Phys. C, 40(10): 100001 (2016)
[30]	S. Leupold, W. Peters, and U. Mosel, Nucl. Phys. A, 628: 311 (1998) [nucl-th/9708016]
[31]	S. H. Lee, K. Morita, and M. Nielsen, Phys. Rev. D, 78: 076001 (2008) [arXiv:0808.3168 [hep-ph]]
[32]	L. R. Surguladze and F. V. Tkachov, Nucl. Phys. B, 331: 35 (1990)
[33]	V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Fortsch. Phys., 32: 585 (1984)
[34]	K. G. Chetyrkin, V. P. Spiridonov, and S. G. Gorishnii, Phys. Lett. B, 160: 149 (1985)
[35]	H. Y. Jin and J. G. Korner, Phys. Rev. D, 64: 074002 (2001) [hep-ph/0003202]
[36]	H. Y. Jin, J. G. Korner, and T. G. Steele, Phys. Rev. D, 67: 014025 (2003) [hep-ph/0211304]
[37]	L. F. Abbott, Nucl. Phys. B, 185: 189 (1981)
[38]	S. Narison and E. de Rafael, Phys. Lett. B, 103: 57 (1981)
[39]	R. E. Cutkosky, J. Math. Phys., 1: 429 (1960)
[40]	A. K. Das, V. S. Mathur, and P. Panigrahi, Phys. Rev. D, 35: 2178 (1987)
[41]	C. A. Dominguez and N. Paver, Z. Phys. C, 31: 591 (1986)
[42]	L. Martinovic, Phys. Rev. D, 41: 1709 (1990)
[43]	L. Martinovic, Phys. Rev. D, 44: 220 (1991)
[44]	E. F. Beckenbach, R. Bellman,Inequalities (Berlin: Springer, 1961)
[45]	S. K. Berberian,Measure and Integration (New York: MacMillan, 1965)
[46]	Y. Chung, H. G. Dosch, M. Kremer, and D. Schall, Z. Phys. C, 25: 151 (1984)
[47]	S. Narison, Phys. Lett. B, 361: 121 (1995) [hep-ph/9504334]
[48]	S. Narison, Phys. Lett. B, 673: 30 (2009) [arXiv:0901.3823 [hep-ph]]
[49]	E. V. Shuryak, Rev. Mod. Phys., 65: 1 (1993)
[50]	J. Gasser and U. G. Meissner, Nucl. Phys. B, 357: 90 (1991)

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Qi-Nan Wang, Zhu-Feng Zhang, T. G. Steele, Hong-Ying Jin and Zhuo-Ran Huang. A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules[J]. Chinese Physics C, 2017, 41(7): 074107. doi: 10.1088/1674-1137/41/7/074107

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Received: 2017-03-01

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Supported by NSFC (11175153, 11205093, 11347020), Open Foundation of the Most Important Subjects of Zhejiang Province, and K. C. Wong Magna Fund in Ningbo University, TGS is Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Z. F. Zhang and Z. R. Huang are Grateful to the University of Saskatchewan for its Warm Hospitality

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沈阳化工大学材料科学与工程学院沈阳 110142

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

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A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

Corresponding author: Zhu-Feng Zhang,

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