Tevatron上重夸克偶素产生的相对论修正
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摘要
在过去的几年里重夸克偶素在高能散射中的产生被大家认为是一个有趣的话题。人们也做了很多有价值的实验,他们中的一些揭露的以往夸克模型的严重不足。
在理论上已取得的进展是重夸克产生过程中的短程部分和束缚态的长程部分的分解。色单态模型已经被基于有效场理论的非相对论量子色动力学(NRQCD)的色八重态理论所取代,色八重态机制更加完整和严谨。但是色八重态机制也存在着一些问题。所以人们考虑QCD修正或相对论修正。本文在NRQCD框架下计算了Tevetron上产生的J /ψ色八重态的相对论修正。短程系数通过QCD与NRQCD在g + g→J/ψ+g子过程中匹配得到。长程部分与实验数据拟合得出。在部分子分布函数CTEQ6L下,我们计算了Tevatron上p + p→J/ψ+g过程, 1S 0[8]态和3S 1[8]态领头阶和相对论修正的散射截面。
本文发现3S 1[8]相对论修正对于散射截面大小的影响不大可以忽略。我们计算的结果对解决Tevetron上J /ψ的超额产生问题有所帮助。
The production of heavy quarkonium states at high-energy colliders has been the subject of considerable interest during the past few years. A wealth of new experimental results has become available, some of which revealed dramatic shortcomings of earlier quarkonium models.
In theory progress has been made on the factorisation between the short-distance physics of heavy-quark creation and the long-distance physics of bound state formation. The colour-singlet model has been superseded by a consistent and rigorous framework, based on the use of non-relativistic QCD (NRQCD)an effective field theory that includes the so-called colour-octet mechanisms。But colour-octet mechanisms also have some problem,somebody consider QCD correctionor relativistic corrections.
In this paper Relativistic corrections to the colour-octet J /ψhadroproduction at the Tevatron are calculated in nonrelativistic QCD (NRQCD). The short distance coefficients are obtainedby matching full QCD with NRQCD results for the subprocess g + g→J/ψ+g.The long distance matrix elements are fited with experiment data.Using the CTEQ6 parton distribution functions, we calculate the LO production cross sections and relativistic corrections for the process p + p→J/ψ+g at the Tevatron of 1S 0[8]and 3S 1[8] We find that the enhancement of relativistic corrections to the cross sections is tiny and negligiable, This effect is due to the bigness of the correction to short distance coefficients These results indicate that relativistic corrections can help to resolve the problem of for J /ψexceeding productionat at Tevatron.
在理论上已取得的进展是重夸克产生过程中的短程部分和束缚态的长程部分的分解。色单态模型已经被基于有效场理论的非相对论量子色动力学(NRQCD)的色八重态理论所取代,色八重态机制更加完整和严谨。但是色八重态机制也存在着一些问题。所以人们考虑QCD修正或相对论修正。本文在NRQCD框架下计算了Tevetron上产生的J /ψ色八重态的相对论修正。短程系数通过QCD与NRQCD在g + g→J/ψ+g子过程中匹配得到。长程部分与实验数据拟合得出。在部分子分布函数CTEQ6L下,我们计算了Tevatron上p + p→J/ψ+g过程, 1S 0[8]态和3S 1[8]态领头阶和相对论修正的散射截面。
本文发现3S 1[8]相对论修正对于散射截面大小的影响不大可以忽略。我们计算的结果对解决Tevetron上J /ψ的超额产生问题有所帮助。
The production of heavy quarkonium states at high-energy colliders has been the subject of considerable interest during the past few years. A wealth of new experimental results has become available, some of which revealed dramatic shortcomings of earlier quarkonium models.
In theory progress has been made on the factorisation between the short-distance physics of heavy-quark creation and the long-distance physics of bound state formation. The colour-singlet model has been superseded by a consistent and rigorous framework, based on the use of non-relativistic QCD (NRQCD)an effective field theory that includes the so-called colour-octet mechanisms。But colour-octet mechanisms also have some problem,somebody consider QCD correctionor relativistic corrections.
In this paper Relativistic corrections to the colour-octet J /ψhadroproduction at the Tevatron are calculated in nonrelativistic QCD (NRQCD). The short distance coefficients are obtainedby matching full QCD with NRQCD results for the subprocess g + g→J/ψ+g.The long distance matrix elements are fited with experiment data.Using the CTEQ6 parton distribution functions, we calculate the LO production cross sections and relativistic corrections for the process p + p→J/ψ+g at the Tevatron of 1S 0[8]and 3S 1[8] We find that the enhancement of relativistic corrections to the cross sections is tiny and negligiable, This effect is due to the bigness of the correction to short distance coefficients These results indicate that relativistic corrections can help to resolve the problem of for J /ψexceeding productionat at Tevatron.
引文
[1]高崇寿曾谨严言.粒子物理与核物理讲座.北京:高等教育出版社,1990:1～40.
[2]章乃深，粒子物理学。科学技术出版社。
[3]李政道粒子物理和量子场论.上海:上海科学技术出版社,2006.
[4]褚圣麟原子物理学.北京:高等教育出版社,1980.
[5]李锡培《实验的数学处理》，科学出版社，1983,268-276
[6] J.J.Aubert et al.(E598 Collaboration),Phys.Rev.Lett. 33(1974)1404
[7] J.E.Augustin et al.(SLAC-SP-017 Collaboration), Phys.Rev.Lett. 33(1974)1406
[8] S.W.Herb et al., Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-NucleusCollisions Phys.Rev.Lett. 39(1977)252
[9] F.Abe et al.(CDF Collaboration), Observation of Top Quark Production in p p Collisions withthe Collider Detector at Fermilab, Phys.Rev.Lett. 74(1995)2626
[10] S.Abachi et al.,(D0 Collaboration), Observation of the Top Quark Phys.Rev.Lett. 74 (1995)2632
[11] B.Cassen and E.U.Condon, Rotational Phase Transition and Melting in a Two-DimensionalHard-Cyclic-Tetramer System Phys. Rev. Lett. 50, 846–849 (1983)
[12] M.Gell-Mann, Nuovo Cim, Supp Random-Alloy splitting of Cu levels in GaAs1-xPx Phys. Rev.Lett. 54, 848–848 (1985) Phys. Rev. Lett 54 (1956)848
[13] K.Nishijima, Progress in Theoretical Physics 13 (1955)285
[14] Y.Ne’eman,Nucl.Phys. Derivation of strong interactions from a gauge invariance26(1961)222
[15] M. Kramer, Quarkonium production at high-energy colliders, Prog. Part. Nuci. Phys,2001,47：141～201, hep-ph/0106120
[16] G. P. Lepage, L. Magnea, C. Nakhleh, U. Magnea and K. Hornbostel, Improved NRQCD forheavy-quark physicsPhys.Rev. D46 (1992) 4052 [hep-lat/9205007]
[17] M.Beneke and I.Z.Rothstein.Hadro-production of quarknia in fixed target experiments. Phys.Rev.D，1996，54：2005～2016
[18] G. T. Bodwin, E. Braaten, and G. P. Lepage, Rigorous QCD analysis of inclusiveannihilationand production of heavy quarkonium, Phys. Rev. D51 (1995) 1125-1171
[19] T Bodwin.Recent Results on Quarkonium Production and Decay.arxiv:hep-ph/0212203,2002:1～5
[20] Eric Braaten,Yu-Qi Chen.Dimensional regularization in quatkonium calculations.Phys RevD55,1997:2693～2707
[21] H.-W.Huang, K.-T.Chao.The cancellation of infrared divergences in the hadronic annihilationdecay of heavy quarkonium. Phys. Rev. D，1997，55：244～248
[22] P. L. Cho and M. B. Wise. Spin symmetry predictions for heavy quarkonia alignment. Phys.Lett. B，1995，346(129):1～10.
[23] M. Beneke and I. Z. Rothstein, Phys. Lett. B372 (1996) 157 [hep-ph/9509375];erratum ibid.D54 (1997) 7082.
[24] T. Affolder et al. [CDF Collaboration], Measurement of J/ψandψ(2S) Polarization in pp Collisions at√s = 1.8TeV Phys. Rev. Lett. 85 (2000) 2886 [hepex/0004027].
[25] E Braaten,T.C. Yuan.Gluon Fragmentation into Heavy Quarkonium.Phys. Rev. Lett. 71,1993:1673
[26] ]E.Braaten, K.Cheung ,T..C.Yuan. Z0 decay into charmoniun via charm quark fragmentation.Phys. Rev. D 48,1993:4230
[27] R. AITCHISO《GAUGE THEORIES IN PARTICLE PHYSICS》.31～35
[28] J. Campbell, F. Maltoni and F. Tramontano, QCD Corrections to J/ψandΥProduction atHadron Colliders Phys. Rev. Lett. 98, 252002 (2007).
[29] B. Gong and J. X. Wang, Next-to-Leading-Order QCD Corrections to J/ψPolarization atTevatron and LHC EnergiesPhys. Rev. Lett. 100, 232001 (2008) (arXiv:0802.3727); Phys. Rev. D78, 074011 (2008)
[30] Ying Fan,_ Yan-Qing Ma,? and Kuang-Ta Chao Relativistic Correction to J/ψProduction atHadron Colliders PhysRevD.79.114009
[31] G.T. Bodwin, D. Kang and J. Lee, Phys. Rev.D74, 014014 (2006); Phys. Rev. D74, 114028(2006).
[32] Z. G. He, Y. Fan and K. T. Chao, Potential-model calculation of an order-v2 nonrelativisticQCD matrix element Phys. Rev. D 75, 074011 (2007) [arXiv:hep-ph/0702239].
[33] Geoffrey T. Bodwin and Andrea Petrelli, Order-v4 corrections to S-wave quarkonium decayPhys. Rev. D 66, 094011 (2002).
[34] C. Amsler et al. [Particle Data Group], Measurement of the J= meson and b-hadron productioncross sections in p_p collisionsPhys. Lett. B 667, 1 (2008).
[2]章乃深，粒子物理学。科学技术出版社。
[3]李政道粒子物理和量子场论.上海:上海科学技术出版社,2006.
[4]褚圣麟原子物理学.北京:高等教育出版社,1980.
[5]李锡培《实验的数学处理》，科学出版社，1983,268-276
[6] J.J.Aubert et al.(E598 Collaboration),Phys.Rev.Lett. 33(1974)1404
[7] J.E.Augustin et al.(SLAC-SP-017 Collaboration), Phys.Rev.Lett. 33(1974)1406
[8] S.W.Herb et al., Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-NucleusCollisions Phys.Rev.Lett. 39(1977)252
[9] F.Abe et al.(CDF Collaboration), Observation of Top Quark Production in p p Collisions withthe Collider Detector at Fermilab, Phys.Rev.Lett. 74(1995)2626
[10] S.Abachi et al.,(D0 Collaboration), Observation of the Top Quark Phys.Rev.Lett. 74 (1995)2632
[11] B.Cassen and E.U.Condon, Rotational Phase Transition and Melting in a Two-DimensionalHard-Cyclic-Tetramer System Phys. Rev. Lett. 50, 846–849 (1983)
[12] M.Gell-Mann, Nuovo Cim, Supp Random-Alloy splitting of Cu levels in GaAs1-xPx Phys. Rev.Lett. 54, 848–848 (1985) Phys. Rev. Lett 54 (1956)848
[13] K.Nishijima, Progress in Theoretical Physics 13 (1955)285
[14] Y.Ne’eman,Nucl.Phys. Derivation of strong interactions from a gauge invariance26(1961)222
[15] M. Kramer, Quarkonium production at high-energy colliders, Prog. Part. Nuci. Phys,2001,47：141～201, hep-ph/0106120
[16] G. P. Lepage, L. Magnea, C. Nakhleh, U. Magnea and K. Hornbostel, Improved NRQCD forheavy-quark physicsPhys.Rev. D46 (1992) 4052 [hep-lat/9205007]
[17] M.Beneke and I.Z.Rothstein.Hadro-production of quarknia in fixed target experiments. Phys.Rev.D，1996，54：2005～2016
[18] G. T. Bodwin, E. Braaten, and G. P. Lepage, Rigorous QCD analysis of inclusiveannihilationand production of heavy quarkonium, Phys. Rev. D51 (1995) 1125-1171
[19] T Bodwin.Recent Results on Quarkonium Production and Decay.arxiv:hep-ph/0212203,2002:1～5
[20] Eric Braaten,Yu-Qi Chen.Dimensional regularization in quatkonium calculations.Phys RevD55,1997:2693～2707
[21] H.-W.Huang, K.-T.Chao.The cancellation of infrared divergences in the hadronic annihilationdecay of heavy quarkonium. Phys. Rev. D，1997，55：244～248
[22] P. L. Cho and M. B. Wise. Spin symmetry predictions for heavy quarkonia alignment. Phys.Lett. B，1995，346(129):1～10.
[23] M. Beneke and I. Z. Rothstein, Phys. Lett. B372 (1996) 157 [hep-ph/9509375];erratum ibid.D54 (1997) 7082.
[24] T. Affolder et al. [CDF Collaboration], Measurement of J/ψandψ(2S) Polarization in pp Collisions at√s = 1.8TeV Phys. Rev. Lett. 85 (2000) 2886 [hepex/0004027].
[25] E Braaten,T.C. Yuan.Gluon Fragmentation into Heavy Quarkonium.Phys. Rev. Lett. 71,1993:1673
[26] ]E.Braaten, K.Cheung ,T..C.Yuan. Z0 decay into charmoniun via charm quark fragmentation.Phys. Rev. D 48,1993:4230
[27] R. AITCHISO《GAUGE THEORIES IN PARTICLE PHYSICS》.31～35
[28] J. Campbell, F. Maltoni and F. Tramontano, QCD Corrections to J/ψandΥProduction atHadron Colliders Phys. Rev. Lett. 98, 252002 (2007).
[29] B. Gong and J. X. Wang, Next-to-Leading-Order QCD Corrections to J/ψPolarization atTevatron and LHC EnergiesPhys. Rev. Lett. 100, 232001 (2008) (arXiv:0802.3727); Phys. Rev. D78, 074011 (2008)
[30] Ying Fan,_ Yan-Qing Ma,? and Kuang-Ta Chao Relativistic Correction to J/ψProduction atHadron Colliders PhysRevD.79.114009
[31] G.T. Bodwin, D. Kang and J. Lee, Phys. Rev.D74, 014014 (2006); Phys. Rev. D74, 114028(2006).
[32] Z. G. He, Y. Fan and K. T. Chao, Potential-model calculation of an order-v2 nonrelativisticQCD matrix element Phys. Rev. D 75, 074011 (2007) [arXiv:hep-ph/0702239].
[33] Geoffrey T. Bodwin and Andrea Petrelli, Order-v4 corrections to S-wave quarkonium decayPhys. Rev. D 66, 094011 (2002).
[34] C. Amsler et al. [Particle Data Group], Measurement of the J= meson and b-hadron productioncross sections in p_p collisionsPhys. Lett. B 667, 1 (2008).