(Q
合集下载
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
0
0 1 d ( p ! V X ) = @ 81 G(x; t) + X q(x; t) + q(x; t)]A d ( q ! V q) : dtdx 16 dt f
(2)
In ref. 1] some arguments are presented in a favor that, at HERA energies and at jtj 2 2 a deviation from this simple picture ( the possibility to connect t? channel gluons with the di erent partons in proton ) does not exceed 15% for the events, in which the invariant 2 mass of the products of photon's disintegration is not too large, MX ?t. In Born approximation (two{gluon exchange in the t? channel) the process of light vector meson production on quark (Q2)q ! V q was considered in detail earlier 13]. In the next section we obtain the results for this process in LLA. In the closing section the comparison of results of LLA and Born approximation will be done, we also estimate the possibility to study BFKL pomeron in this reaction at HERA. In Appendix we will discuss the approximate method for the calculation of amplitudes in LLA based on the result of 14] for the amplitude of quark-quark scattering.
transfer the elastic process p ! V p was considered in refs. 7, 8, 9, 10, 11]. The interest to inelastic process (1) relates with the possibility to study BFKL pomeron in the modern experiments at ep collaider HERA in the wide range of parameters s; jtj; Q2. The process (1) in the same kinematics was considered in ref. 1], where for the description of transition of quark's pair to the meson, consisted of heavy quarks ( V = J= ; ), the non{relativistic approximation was used. The process of light mesons production needs to be considered separately, since here the non{relativistic approximation is not applicable. It is necessary to take into account the nontrivial longitudinal motion of quarks in a light meson in accordance with the standard leading twist approach to the hard exclusive processes, see 2, 16]. Besides, there is a substantial di erence in the polarization state of the meson produced in reaction (1). For heavy mesons production there is an approximate helisity conservation, the helisity of meson coincides with the helisity of initial photon M = = 1, . 12]. In contrast, the light mesons, as the consequence of a helisity conservation at each vertex in the hiral limit of QCD, are produced in a state with helisity M = 0, irrespective of helisity state of initial photon. The amplitudes of production of light and heavy mesons have the di erent structure, compare eqs. (9,12) and (13,14). The results for amplitude of J= production process cannot be directly (by substitution mJ= ! m ) transferred to light meson production. Therefore, the conclusion of ref. 1] (which is based on this substitution), about a larger yield at jtj >> m2 of heavy vector V mesons than that of the lighter ones, seems to us as arbitrary one. At su ciently large momentum transfer (?t >> 2 ) the cross section of process (1) QCD may be represented as a product of 'hard scattering' cross section and parton distribution functions in a proton, see Fig. 1,
Abstract
This paper deals with the di ractive production of light vector mesons (V = 0; !; ) in gamma (Q2)p interactions p!VX ; (1) where the meson V and the hadrons X to that the proton dissociates are divided by the large rapidity gap. Q2 is the virtuality of photon. We will consider the process (1) in the region of large momentum transfers, jtj >> 2 , and su ciently large centre-of-mass QCD energies, s >> jtj; Q2. The rst condition justi es the using of perturbative QCD to the description of the process (1). We reason that the transferred momentum is large enough, therefore a hadron (VDM) nature of photon will be neglected below. The second condition suggests the necessity of perturbative series summation, since parameter s ln s can be not small. We will discuss both the di ractive photoproduction (process (1) at Q2 = 0) and the di ractive production of mesons in the deep inelastic scattering at arbitrary relation between Q2 and jtj. Process (1) has the vacuum quantum numbers in the t? channel. The summation of leading logarithms ( s ln (s)) in the vacuum channel leads to the famous BFKL equation, that describes the perturbative ('hard') QCD pomeron in the leading log approximation (LLA), see refs. 3, 4, 5, 6]. Using the solution of BFKL equation, we will obtain the asymptotic behaviour of the cross section of the process considered at s ! 1 and nonzero value of momentum transfer. 1
Di ractive light vector meson production at large momentum transfers
D.Yu. Ivanov Institute of Mathematics, 630090 Novosibirsk, Russia
The di ractive process (Q2)p ! V + X (where V = 0; !; are the vector mesons, consisted of light quarks, X represents the hadrons to that a proton dissociates) is studied. We consider the region of large momentum transfers, jtj >> 2 , QCD and large energies, s. In the leading log approximation of perturbative QCD ( using BFKL equation ) the asymptotic behaviour of the cross section in the limit s ! 1; s >> jtj; Q2 is obtained. We compare the results derived from BFKL equation with that obtained in the lowest order of QCD (two{gluon exchange in the t- channel). The possibility to investigate these reactions at HERA is discussed.
0 1 d ( p ! V X ) = @ 81 G(x; t) + X q(x; t) + q(x; t)]A d ( q ! V q) : dtdx 16 dt f
(2)
In ref. 1] some arguments are presented in a favor that, at HERA energies and at jtj 2 2 a deviation from this simple picture ( the possibility to connect t? channel gluons with the di erent partons in proton ) does not exceed 15% for the events, in which the invariant 2 mass of the products of photon's disintegration is not too large, MX ?t. In Born approximation (two{gluon exchange in the t? channel) the process of light vector meson production on quark (Q2)q ! V q was considered in detail earlier 13]. In the next section we obtain the results for this process in LLA. In the closing section the comparison of results of LLA and Born approximation will be done, we also estimate the possibility to study BFKL pomeron in this reaction at HERA. In Appendix we will discuss the approximate method for the calculation of amplitudes in LLA based on the result of 14] for the amplitude of quark-quark scattering.
transfer the elastic process p ! V p was considered in refs. 7, 8, 9, 10, 11]. The interest to inelastic process (1) relates with the possibility to study BFKL pomeron in the modern experiments at ep collaider HERA in the wide range of parameters s; jtj; Q2. The process (1) in the same kinematics was considered in ref. 1], where for the description of transition of quark's pair to the meson, consisted of heavy quarks ( V = J= ; ), the non{relativistic approximation was used. The process of light mesons production needs to be considered separately, since here the non{relativistic approximation is not applicable. It is necessary to take into account the nontrivial longitudinal motion of quarks in a light meson in accordance with the standard leading twist approach to the hard exclusive processes, see 2, 16]. Besides, there is a substantial di erence in the polarization state of the meson produced in reaction (1). For heavy mesons production there is an approximate helisity conservation, the helisity of meson coincides with the helisity of initial photon M = = 1, . 12]. In contrast, the light mesons, as the consequence of a helisity conservation at each vertex in the hiral limit of QCD, are produced in a state with helisity M = 0, irrespective of helisity state of initial photon. The amplitudes of production of light and heavy mesons have the di erent structure, compare eqs. (9,12) and (13,14). The results for amplitude of J= production process cannot be directly (by substitution mJ= ! m ) transferred to light meson production. Therefore, the conclusion of ref. 1] (which is based on this substitution), about a larger yield at jtj >> m2 of heavy vector V mesons than that of the lighter ones, seems to us as arbitrary one. At su ciently large momentum transfer (?t >> 2 ) the cross section of process (1) QCD may be represented as a product of 'hard scattering' cross section and parton distribution functions in a proton, see Fig. 1,
Abstract
This paper deals with the di ractive production of light vector mesons (V = 0; !; ) in gamma (Q2)p interactions p!VX ; (1) where the meson V and the hadrons X to that the proton dissociates are divided by the large rapidity gap. Q2 is the virtuality of photon. We will consider the process (1) in the region of large momentum transfers, jtj >> 2 , and su ciently large centre-of-mass QCD energies, s >> jtj; Q2. The rst condition justi es the using of perturbative QCD to the description of the process (1). We reason that the transferred momentum is large enough, therefore a hadron (VDM) nature of photon will be neglected below. The second condition suggests the necessity of perturbative series summation, since parameter s ln s can be not small. We will discuss both the di ractive photoproduction (process (1) at Q2 = 0) and the di ractive production of mesons in the deep inelastic scattering at arbitrary relation between Q2 and jtj. Process (1) has the vacuum quantum numbers in the t? channel. The summation of leading logarithms ( s ln (s)) in the vacuum channel leads to the famous BFKL equation, that describes the perturbative ('hard') QCD pomeron in the leading log approximation (LLA), see refs. 3, 4, 5, 6]. Using the solution of BFKL equation, we will obtain the asymptotic behaviour of the cross section of the process considered at s ! 1 and nonzero value of momentum transfer. 1
Di ractive light vector meson production at large momentum transfers
D.Yu. Ivanov Institute of Mathematics, 630090 Novosibirsk, Russia
The di ractive process (Q2)p ! V + X (where V = 0; !; are the vector mesons, consisted of light quarks, X represents the hadrons to that a proton dissociates) is studied. We consider the region of large momentum transfers, jtj >> 2 , QCD and large energies, s. In the leading log approximation of perturbative QCD ( using BFKL equation ) the asymptotic behaviour of the cross section in the limit s ! 1; s >> jtj; Q2 is obtained. We compare the results derived from BFKL equation with that obtained in the lowest order of QCD (two{gluon exchange in the t- channel). The possibility to investigate these reactions at HERA is discussed.