删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

Drell-Yan nuclear modification due to nuclear effects of nPDFs and initial-state parton energy loss

本站小编 Free考研考试/2022-01-01

Li-Hua Song 1,,
, Peng-Qi Wang 1,
, Yin-Jie Zhang 2,
,
Corresponding author: Li-Hua Song, songlh@ncst.edu.cn
1.College of Science, North China University of Science and Technology, Tangshan 063210, China
2.College of Physics Science and Technology, Hebei University, Baoding 071002, China
Received Date:2020-10-26
Available Online:2021-04-15
Abstract:By globally analyzing nuclear Drell-Yan data including all incident energies, the nuclear effects of nuclear parton distribution functions (nPDFs) and initial-state parton energy loss are investigated. Based on the Landau-Pomeranchuk-Migdal (LPM) regime, the calculations are carried out by means of analytic parametrizations of quenching weights derived from the Baier-Dokshitzer-Mueller-Peign$ \acute{e} $-Schiff (BDMPS) formalism and using the new EPPS16 nPDFs. It is found that the results are in good agreement with the data and the role of the energy loss effect in the suppression of Drell-Yan ratios is prominent, especially for low-mass Drell-Yan measurements. The nuclear effects of nPDFs become more obvious with increasing nuclear mass number A, the same as the energy loss effect. By a global fit, the transport coefficient extracted is $ \hat{q} = 0.26\pm0.04 $ GeV2/fm. In addition, to avoid diminishing the QCD NLO correction to the data form of Drell-Yan ratios, separate calculations of the Compton differential cross section ratios $ R_{\rm Fe(W)/C}(x_{\rm F}) $ at 120 GeV are performed, which provides a feasible way to better distinguish the gluon energy loss in Compton scattering. It is found that the role of the initial-state gluon energy loss in the suppression of Compton scattering ratios is not very important and disappears with the increase of $ x_{\rm F} $.

HTML

--> --> -->
I.INTRODUCTION
The nuclear Drell-Yan production of leptons provides an ideal tool to study parton dynamics and nuclear effects in cold nuclear matter. The observed suppression of the nuclear Drell-Yan production ratios ($ R_{A_{1}/A_{2}} $) is generally believed to be induced by the nuclear effects incorporated in nuclear parton distribution functions (nPDFs) and the initial-state parton energy loss [1-3]. Studying the Drell-Yan nuclear modification is conducive to revealing the properties of the radiative energy loss when partons propagate through the nuclear medium, and moreover, may help to better understand the energy loss effect which causes the jet quenching phenomenon observed at RHIC and the LHC [4, 5].
In the past three decades and more, NA3 [6], NA10 [7], E772 [8], E866 [9] and E906 [10] measurements have provided sufficient experimental data to study the suppression of the Drell-Yan differential cross section ratios. Several groups have interpreted the nuclear attenuation in the Drell-Yan process by means of phenomenological models based on energy loss and the nuclear effects of nPDFs [1-3, 11-14]. In Ref. [1], data from E772 and E866 were analyzed, using a very different reference frame and prescription for calculating the shadowing. By disentangling energy loss and shadowing when analyzing experimental data, they extracted the mean quark energy loss per unit path length $ {\rm d}E/{\rm d}z = 2.73 \pm 0.37 \pm 0.5 $ GeV/fm, which is consistent with theoretical expectations including the effects of the inelastic interaction of the incident proton at the surface of the nucleus. Reference [12] analyzed data from E866 and NA3, and extracted the transport coefficient to be $ \hat{q} = 0.24\pm0.18 $ GeV/fm$ ^{2} $ by means of EKS98 nPDFs [15] and the energy loss distribution based on the BDMPS approach, which corresponds to a mean energy loss per unit length $ {\rm d}E/{\rm d}z = 0.20 \pm 0.15 $ GeV/fm for $ L = 5 $ fm and $ A\approx 200 $. By means of EPS08 nPDFs [16], Ref. [14] analyzed data from E866 with the transport coefficient $ \hat{q} = 0.024 $ GeV$ ^{2} $/fm (corresponding to a mean energy loss per unit length $ {\rm d}E/{\rm d}z = 0.20 $ GeV/fm for $ L = 5 $ fm) determined from the nuclear modification of single-inclusive DIS hadron spectra as measured by the HERMES experiment [17]. Because the EKS98 nPDFs [15] and EPS08 nPDFs [16] determine the nuclear shadowing of sea quarks from E866 and E772 nuclear Drell-Yan data, which may be substantially contaminated by energy loss, the initial state energy loss in the Drell-Yan process constrained by the EKS98 or EPS08 nPDFs is underestimated due to an overestimation of the nuclear shadowing correction to the sea quark distribution. So, the conclusions derived from the above two articles (Ref. [12] and Ref. [14]) are analogous.
From the above comments, it can be seen that conclusions about the role of the initial-state energy loss effect on Drell-Yan suppression are dependent on the nPDF sets used in the calculations of the Drell-Yan differential cross section ratios. Like the energy loss effect, the shadowing effect incorporated in nPDFs can also induce the suppression of Drell-Yan ratios. Since the underlying mechanisms driving the in-medium corrections of the nucleon substructure have not been completely understood, the shadowing effect has not been determined reliably. Several sets of nPDFs, such as EKS98 [15], EPS08 [16], EPS09 [18], HKN07 [19] and nDS [20], determine the distributions of the valence quarks at larger momentum fraction and the sea quarks at smaller momentum fraction, by fitting the nuclear Drell-Yan data. This may lead to overestimating the nuclear modification in the sea quark distribution, in view of the role of energy loss in Drell-Yan suppression. Hence, by means of these sets of nPDFs, studies of the nuclear effects of nPDFs and the initial-state energy loss effect in the Drell-Yan process cannot reach a reliable conclusion. Lately, by including data constraints from the new LHC experiments, neutrino DIS measurements and low-mass Drell-Yan data (NA3 [6], NA10 [7] and E615 [21]), the EPPS16 nPDF set [22] has been produced. This significantly extends the kinematic reach of the data constraints and leads to a more reliable modification of the nuclear effects of nPDFs.
The initial-state parton energy loss in the nuclear Drell-Yan process is sensitive to the Landau-Pomeranchuk-Migdal (LPM) regime [23], due to the gluon formation time $ t_{f} $ ($ t_{f}\propto 1/q_{T}^{2} $ as expressed in Ref. [14]) being much smaller than the medium length $ L_{A} $ for large values of $ q_{T} $, which is different from the fully coherent energy loss (FCEL) [24]. Like initial-state (final-state) parton energy loss, FCEL can also induce a significant hadron suppression in hadron-nucleus collisions. In some hadron-nucleus collisions, these two kinds of energy loss effect both exist and it is difficult to distinguish them, such as in the suppression of $ J/\psi $ production. Since FCEL is absent in the nuclear Drell-Yan process, we can clearly probe the initial-state energy loss and constrain the transport coefficient in the cold nuclear medium by means of Drell-Yan measurements. This may help to disentangle the relative contributions of the initial-state (final-state) energy loss and coherent energy loss, when they both exist in some hadron-nucleus collisions.
Up to now, the mechanism of medium-induced parton energy loss has not been understood completely. Due to the lack of reliable determination of the nuclear PDFs and of global analysis for precision data at different incident energies, there is no consensus about the role and the transport coefficient of the initial-state parton energy loss in the nuclear Drell-Yan process. In this work, by means of the new EPPS16 nPDFs [22] and the analytic parametrizations of quenching weights derived from the Baier-Dokshitzer-Mueller-Peign$ \acute{e} $-Schiff (BDMPS) formalism based on the LPM regime [25-27], the Drell-Yan nuclear modification due to the nuclear effects of nPDFs and initial-state quark energy loss will be investigated. To accurately extract the value of the transport coefficient, a global fit will be carried out by including all the incident energy data from the new E906 (120 GeV) to E866 (800 GeV). Furthermore, at next-to-leading order (NLO), the initial-state gluon energy loss rooted in the primary NLO subprocess (Compton scattering) will also be investigated. The theoretical framework is presented in Section II, results and discussion are presented in Section III, and a summary is given in Section IV.
II.MODEL FOR NUCLEAR DRELL-YAN SUPPRESSION
In the nuclear Drell-Yan process, the incident parton undergoes multiple soft collisions accompanied by gluon emission when traveling through the nuclear medium. These radiated gluons carry away some energy $ \epsilon $ of the incident parton with the probability distribution $ D(\epsilon) $. In nuclear Drell-Yan hadron production, as the gluon formation time $ t_{f} $ is much smaller than the medium length $ L_{A} $, the parton energy loss is in the LPM regime [23],
$ \langle\epsilon\rangle_{\rm LPM}\propto\hat{q}L^{2}, $
(1)
where $ \hat{q} $ represents the transport coefficient and L is the length of traversed nuclear matter, which is different from the FCEL regime [24], where
$ \langle\epsilon\rangle_{\rm FCEL}\propto\frac{\sqrt{\hat{q}L}}{M}\cdot E, $
(2)
where M and E represent the mass and energy of the parton respectively. A formalism suitable for describing the LPM energy loss has been presented by Baier, Dokshitzer, Mueller, Peign$ \acute{e} $ and Schiff (BDMPS) [25, 26]. Based on the BDMPS energy loss framework, an analytic parametrization of the probability distribution $ D(\epsilon) $ for LPM initial-state energy loss has been derived by F. Arleo [27]:
$ D(\epsilon) = \frac{1}{\sqrt{2\pi}\sigma(\epsilon/\omega_{c})}\exp\left[-\frac{(\log(\epsilon/\omega_{c})-\mu)^{2}}{2\sigma^{2}}\right], $
(3)
where $ \omega_{c} = \dfrac{1}{2}\hat{q}L^{2} $, $ \mu = -2.55 $ and $ \sigma = 0.57 $.
The energy $ \epsilon $ carried away by radiated gluons results in a change in the incident parton momentum fraction prior to the hard QCD process:
$ x_{1}\rightarrow x'_{1} = x_{1}+\epsilon/E_{\rm beam}, $
(4)
where $ x_{1} $ represents the momentum fraction of the partons in the beam hadron. The model for LPM initial-state energy loss can be expressed as:
$ \frac{{\rm d}^{2}\sigma'_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} = \int_{0}^{(1-x_{1})E_{\rm beam}}{\rm d}\epsilon D(\epsilon)\frac{{\rm d}^{2}\sigma_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}}(x'_{1},x_{2},Q^{2}). $
(5)
Here $ x_{2} $ denotes the momentum fraction of the partons in the target, $ x_{\rm F} = x_{1}-x_{2} $, and the invariant mass of a lepton pair $ Q^{2} = M^{2} = sx_{1}x_{2} $ ($ \sqrt{s} $ is the center of mass energy of the hadronic collision).
The NLO Drell-Yan differential cross section consists of the partonic cross section $ \dfrac{{\rm d}^{2}\sigma^{\rm DY}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} $ from the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $, $ \dfrac{{\rm d}^{2}\sigma^{\rm C}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} $ from the Compton scattering $ qg\rightarrow q\gamma^{*} $, and $ \dfrac{{\rm d}^{2}\sigma^{\rm Ann}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} $ from the annihilation process $ q\bar{q}\rightarrow g\gamma^{*} $, and hence can be given as:
$ \frac{{\rm d}^{2}\sigma_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} = \frac{{\rm d}^{2}\sigma^{\rm DY}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}}+\frac{{\rm d}^{2}\sigma^{\rm C}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}}+\frac{{\rm d}^{2}\sigma^{\rm Ann}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}}, $
(6)
where
$ \frac{{\rm d}^{2}\sigma^{\rm DY(C,Ann)}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} = \int_{x_{1}}^{1}{\rm d}t_{1}\int_{x_{2}}^{1}\frac{{\rm d}^{2}\hat{\sigma}^{\rm DY(C,Ann)}}{{\rm d}x_{\rm F}{\rm d}M^{2}}\hat{Q}^{\rm DY(C,Ann)}(t_{1},t_{2}){\rm d}t_{2}. $
(7)
Here $ t_{1} $ and $ t_{2} $ are the fractions of hadron momenta taken by quarks or gluons. For the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $:
$ \frac{{\rm d}^{2}\hat{\sigma}^{\rm DY}}{{\rm d}x_{\rm F}{\rm d}M^{2}} = \frac{4\pi\alpha^{2}}{9M^{2}s}\frac{1}{x_{1}+x_{2}}\delta(t_{1}-x_{1})\delta(t_{2}-x_{2}), $
(8)
$ \begin{aligned}[b] \hat{Q}^{\rm DY}(t_{1},t_{2}) =& \sum\limits_{f}e_{f}^{2}[q_{f}^{h}(t_{1},Q^{2})\bar{q}_{f}^{A}(t_{2},Q^{2})\\&+\bar{q}_{f}^{h}(t_{1},Q^{2})q_{f}^{A}(t_{2},Q^{2})], \end{aligned}$
(9)
for the Compton scattering $ qg\rightarrow q\gamma^{*} $:
$ \frac{{\rm d}^{2}\hat{\sigma}^{\rm C}}{{\rm d}x_{\rm F}{\rm d}M^{2}} = \frac{3}{16}\times\frac{16\alpha^{2}\alpha_{s}(Q^{2})}{27M^{2}s}\frac{1}{x_{1}+x_{2}}C(x_{1},x_{2},t_{1},t_{2}), $
(10)
$\begin{aligned}[b] \hat{Q}^{\rm C}(t_{1},t_{2}) =& \sum\limits_{f}e_{f}^{2}\{g^{h}(t_{1},Q^{2})[q_{f}^{A}(t_{2},Q^{2})+\bar{q}_{f}^{A}(t_{2},Q^{2})] \\&+g^{A}(t_{2},Q^{2})[q_{f}^{h}(t_{1},Q^{2})+\bar{q}_{f}^{A}(t_{1},Q^{2})]\},\end{aligned} $
(11)
and for the annihilation process $ q\bar{q}\rightarrow g\gamma^{*} $:
$\begin{aligned}[b]\frac{{\rm d}^{2}\hat{\sigma}^{\rm Ann}}{{\rm d}x_{\rm F}{\rm d}M^{2}} = \frac{1}{2}\times\frac{16\alpha^{2}\alpha_{s}(Q^{2})}{27M^{2}s}\frac{1}{x_{1}+x_{2}} Ann(x_{1},x_{2},t_{1},t_{2}), \end{aligned}$
(12)
$ \begin{aligned}[b] \hat{Q}^{\rm Ann}(t_{1},t_{2}) =& \sum\limits_{f}e_{f}^{2}[q_{f}^{h}(t_{1},Q^{2})\bar{q}_{f}^{A}(t_{2},Q^{2})\\&+\bar{q}_{f}^{h}(t_{1},Q^{2})q_{f}^{A}(t_{2},Q^{2})].\end{aligned}$
(13)
In the above formulas, $ q^{h(A)}_{f}(x_{1(2)},Q^{2}) $ refers to the parton distribution function with flavor f in the hadron (nucleus A), $ e_{f} $ denotes the charge of the quark with flavor f, $ \alpha $ represents the fine structure constant, $ \alpha_{s}(Q^{2}) $ is the specific expression of the function, and the complex expressions of functions $ C(x_{1},x_{2},t_{1},t_{2}) $ and $ Ann(x_{1},x_{2},t_{1},t_{2}) $ are shown in Ref. [28]. The partonic density of nucleus A is different from that of a free proton due to the complex nuclear environment, with effects such as EMC suppression, shadowing and anti-shadowing. In this paper, the Drell-Yan nuclear modification due to the nuclear effects of nPDFs is computed with the latest EPPS16 set [22].
In the above energy loss correction model for interpreting the nuclear Drell-Yan suppression, the transport coefficient $ \hat{q} $ is the only parameter. It measures the properties of the initial-state energy loss effect in a cold medium and can be constrained from $ \chi^{2} $ analysis of the fit of the experimental data by calculating the Drell-Yan differential cross section ratio:
$ R_{A_{1}/A_{2}}(x_{\rm F}) = \frac{A_{2}}{A_{1}}\left(\frac{{\rm d}^{2}\sigma'_{h-A1}}{{\rm d}x_{\rm F}{\rm d}M}\bigg/\frac{{\rm d}^{2}\sigma'_{h-A2}}{{\rm d}x_{\rm F}{\rm d}M}\right). $
(14)

III.RESULTS AND DISCUSSION
Firstly, we investigate the nuclear effects of nPDFs on the nuclear Drell-Yan ratio using the EPPS16 nPDFs [22] together with the nCTEQ15 parton density of the proton [29] or the parton distributions of the negative pion [30]. It should be noted that in our calculation the corrections from isospin effects are neglected due to their small influence on the Drell-Yan ratios [2]. The solid lines in Figs. 1, 2, 3, 4, 5 show the next-to-leading order Drell-Yan ratios $ R_{A_{1}/A_{2}} $, and the dashed lines correspond to the leading order calculations ($ q\bar{q}\rightarrow \gamma^{*} $). They are both modified only by the nPDF corrections. It is found that the theoretical results at next-to-leading order and leading order are almost identical for the E906, NA3 and NA10 experiments, and there is a small difference between the two results for the E866 experiments. From the above expressions of $ \dfrac{{\rm d}^{2}\sigma^{\rm DY}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} $ (see Eq. (9)), $ \dfrac{{\rm d}^{2}\sigma^{\rm C}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} $ (see Eq. (11)) and $ \dfrac{{\rm d}^{2}\sigma^{\rm Ann}_{h-A}}{{\rm d}x_{\rm F}{\rm d}M^{2}} $ (see Eq. (13)) in Section II, we can calculate and derive that:
Figure1. E906 nuclear Drell-Yan ratios $ R_{\rm Fe/C}(x_{\rm F}) $ (left) and $ R_{\rm W/C}(x_{\rm F}) $ (right) compared to the theoretical results with EPPS16 nPDFs at next-to-leading order (solid lines), leading order calculation (dashed lines), and considering initial-state quark energy loss from the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $ (dashed-dotted lines).

Figure2. NA3 nuclear Drell-Yan ratios $ R_{\rm H/Pt}(x_{1}) $ (left) and $ R_{\rm H/Pt}(x_{2}) $ (right) compared to the theoretical results with EPPS16 nPDFs at next-to-leading order (solid lines), leading order calculation (dashed lines), and considering initial-state quark energy loss from the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $ (dashed-dotted lines).

Figure3. NA10(140 GeV) nuclear Drell-Yan ratios $ R_{\rm W/D}(x_{1}) $ (left) and $ R_{\rm W/D}(x_{2}) $ (right) compared to the theoretical results with EPPS16 nPDFs at next-to-leading order (solid lines), leading order calculation (dashed lines), and considering initial-state quark energy loss from the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $ (dashed-dotted lines).

Figure4. NA10(286 GeV) nuclear Drell-Yan ratios $ R_{\rm W/D}(x_{1}) $ (left) and $ R_{\rm W/D}(x_{2}) $ (right) compared to the theoretical results with EPPS16 nPDFs at next-to-leading order (solid lines), leading order calculation (dashed lines), and considering initial-state quark energy loss from the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $ (dashed-dotted lines).

Figure5. E866 nuclear Drell-Yan ratios $ R_{\rm Fe/Be}(x_{\rm F}) $ (left) and $ R_{\rm W/Be}(x_{\rm F}) $ (right) compared to the theoretical results with EPPS16 nPDFs at next-to-leading order (solid lines), leading order calculation (dashed lines), and considering initial-state quark energy loss from the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $ (dashed-dotted lines).

$ \begin{aligned}[b]\frac{{\rm d}^{2}\sigma^{\rm DY}_{h-A_{1}}}{{\rm d}x_{\rm F}{\rm d}M^{2}}\bigg/\frac{{\rm d}^{2}\sigma^{\rm DY}_{h-A_{2}}}{{\rm d}x_{\rm F}{\rm d}M^{2}}\approx\frac{{\rm d}^{2}\sigma^{\rm Ann}_{h-A_{1}}}{{\rm d}x_{\rm F}{\rm d}M^{2}}\bigg/\frac{{\rm d}^{2}\sigma^{\rm Ann}_{h-A_{2}}}{{\rm d}x_{\rm F}{\rm d}M^{2}} \approx \frac{{\rm d}^{2}\sigma^{\rm C}_{h-A_{1}}}{{\rm d}x_{\rm F}{\rm d}M^{2}}\bigg/\frac{{\rm d}^{2}\sigma^{\rm C}_{h-A_{2}}}{{\rm d}x_{\rm F}{\rm d}M^{2}}, \end{aligned} $
(15)
in the momentum fraction range where the nuclear effects of gluon distributions are not gigantic. Therefore, the form of the differential cross section ratio given by the nuclear Drell-Yan data actually diminishes the QCD next-to-leading order correction. From Figs. 1, 2, 3, 4, 5 we can also see that there is an obvious deviation between the calculations obtained by only including the EPPS16 nPDFs corrections and the measurements of the E906 (120 GeV), NA3 (150 GeV) and NA10 (140 GeV) experiments at lower incident energies. However, a good fit can be seen between the results and the E866 (800 GeV) and NA10 (286 GeV) measurements with higher beam energies. Further, in Table 1, we compute the $ \chi^{2}/N $ (N is the number of data points) at leading order calculation. Table 1 also shows that the nuclear effects of nPDFs play a more important role in the Drell-Yan nuclear modification with the increase of beam energy.
Exp.data Data points Beam/GeV $\chi^{2}/ndf$
E906($x_{\rm F}$) 12 120 15.07
NA3($x_{1(2)}$) 15 150 7.31
NA10($x_{1(2)}$) 9 140 6.55
NA10($x_{1(2)}$) 15 286 1.43
E866($x_{\rm F}$) 16 800 1.22


Table1.$\chi^{2}/N$ values obtained only with EPPS16 nPDFs [22].

Secondly, we consider the initial-state quark energy loss in nuclear Drell-Yan production. In view of the correction model for initial-state energy loss and the above discussion, the energy loss effect in the Compton scattering and annihilation processes can also be diminished due to the form of the differential cross section ratio given by the nuclear Drell-Yan data. Therefore, in a leading order calculation, only the quark energy loss from the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $ is considered. We calculate the Drell-Yan ratios $ R_{A_{1}/A_{2}} $ using the EPPS16 nPDFs [22] together with the analytic parametrization of quenching weights based on the BDMPS formalism [27] (Eq. (3)). The values of transport coefficient $ \hat{q} $ and $ \chi^{2}/ndf $ extracted from the corresponding experimental data are shown in Table 2. Comparing Table 2 and Table 1 shows that, when considering the initial-state quark energy loss effect, the fitting degree of the calculation results with the experimental data is greatly improved, especially for low incident energy data (E906-120 GeV, NA3-150 GeV and NA10-140 GeV).
Exp.data Data points Momentum fraction $\hat{q}$/(GeV$^{2}$/fm) $\chi^{2}/ndf$
E906($R_{\rm Fe/C}(x_{\rm F})$) 6 $0.22<x_{\rm F}<0.73$ $0.45\pm0.06$ 0.46
E906($R_{\rm W/C}(x_{\rm F})$) 6 $0.22<x_{\rm F}<0.73$ $0.25\pm0.02$ 0.25
Glob fit E906-120 GeV 12 $0.25\pm0.02$ 0.91
NA3($R_{\rm H/Pt}(x_{1})$) 8 $0.25<x_{1}<0.95$ $0.24\pm0.11$ 0.46
NA3($R_{\rm H/Pt}(x_{2})$) 7 $0.074<x_{2}<0.366$ $0.24\pm0.11$ 0.88
Glob fit NA3-150 GeV 15 $0.24\pm0.10$ 0.65
NA10-140 GeV($R_{\rm W/D}(x_{1})$) 5 $0.39<x_{1}<0.82$ $0.35\pm0.02$ 1.13
NA10-140 GeV($R_{\rm W/D}(x_{2})$) 4 $0.163<x_{2}<0.360$ $0.27\pm0.04$ 0.31
Glob fit NA10-140 GeV 9 $0.30\pm0.05$ 0.99
NA10-286 GeV($R_{\rm W/D}(x_{1})$) 9 $0.22<x_{1}<0.83$ $0.19\pm0.11$ 1.45
NA10-286 GeV($R_{\rm W/D}(x_{2})$) 6 $0.125<x_{2}<0.451$ $0.10\pm0.07$ 0.59
Glob fit NA10-286 GeV 15 $0.14\pm0.05$ 1.14
E866($R_{\rm Fe/Be}(x_{\rm F})$) 8 $0.186<x_{\rm F}<0.834$ $0.17\pm0.17$ 0.27
E866($R_{\rm W/Be}(x_{\rm F})$) 8 $0.186<x_{\rm F}<0.834$ $0.39\pm0.10$ 0.46
Glob fit E866-800 GeV 16 $0.36\pm0.10$ 0.41
Global fit 67 $0.26\pm0.04$ 0.82


Table2.$\hat{q}$ and $\chi^{2}/ndf$ values obtained with EPPS16 nPDFs [22] and initial-state quark energy loss.

A plot of $ \chi^2 $ as a function of $ \hat{q} $ for the global fit of all data is given in Fig. 6. From Fig. 6, we can easily and clearly see that the global fit shows the best value is $ \hat{q} = 0.26\pm0.04 $ GeV2/fm ($ \chi^{2}/ndf = 0.82 $), which is a little smaller than the result $ \hat{q} = 0.32\pm0.04 $ GeV2/fm obtained using the HKM nPDFs [31] in our previous work [3]. Since the HKM nPDFs [31] are obtained using only the experimental data for nuclear structure functions, the shadowing effect of the nPDFs on the suppression of Drell-Yan ratios has been reduced in the $ 0.01 < x < 0.3 $ region. In addition, as discussed in Ref. [12], the mean BDMPS energy loss $ \langle\epsilon\rangle $ experienced by the fast parton in the medium is given by:
Figure6. $ \chi^2 $ as a function of $ \hat{q} $ for the global fit of all data.

$ \langle\epsilon\rangle\equiv \int D(\epsilon){\rm d}\epsilon = \frac{1}{2}\alpha C_{R}\omega_{c}, $
(16)
where $ \alpha = \frac{1}{2}, \;C_{R} = \frac{4}{3} $, and the mean quark energy loss per unit path length $ {\rm d}E/{\rm d}z $ is:
$ \frac{{\rm d}E}{{\rm d}Z}\equiv\frac{\langle\epsilon\rangle}{L} = \delta\times\left(\frac{L}{10\;{\rm fm}}\right), $
(17)
where $ \delta $ is a parameter simply related to the transport coefficient $ \hat{q} $ and means the mean BDMPS energy loss per unit path length with $ L = 10 $ fm. It can be derived that the mean BDMPS energy loss per unit path length $ {\rm d}E/{\rm d}z = \dfrac{1}{6}\hat{q}L $. Here the transport coefficient $ \hat{q} = 0.26\pm 0.04 $ GeV$ ^{2} $/fm corresponds to $ \dfrac{{\rm d}E}{{\rm d}Z}\approx1.10\pm0.17 $ GeV/fm for $ L = 5 $fm, which is much bigger than the result $ \dfrac{{\rm d}E}{{\rm d}Z} = 0.20\pm0.15 $ GeV/fm obtained by using EKS98 nPDFs in Ref. [12], the result $ \dfrac{{\rm d}E}{{\rm d}Z} = 0.20 $ GeV/fm obtained by EPS08 nPDFs in Ref. [14], or the result $ \dfrac{{\rm d}E}{{\rm d}Z} = 0.23\pm0.09 $ GeV/fm obtained by EPS09 nPDFs in Ref. [13]. For $ L = 10 $ fm, the transport coefficient $ \hat{q} = 0.26\pm0.04 $ GeV$ ^{2} $/fm corresponds to $ \dfrac{{\rm d}E}{{\rm d}Z}\approx2.20\pm0.34 $ GeV/fm, which is approximately identical to the result $ \dfrac{{\rm d}E}{{\rm d}Z} = 2.73\pm0.37\pm0.5 $ GeV/fm obtained by unambiguously separating shadowing and energy loss in Ref. [1]. This indicates that with the EPPS16 nPDFs, the value of quark energy loss can actually be better constrained from the nuclear Drell-Yan data by avoiding overestimation of the shadowing correction. The reason is that although the fit of the EPPS16 nPDFs includes the nuclear Drell-Yan data, the new data (NA3 [6], NA10 [7] and E615 [21]) increase the variety of the momentum fraction of the target parton from 0.074 to 0.451 with respect to EPS09 and efficiently avoid overestimating the nuclear modification of the sea quark distribution. Furthermore, the fit of the EPPS16 nPDFs includes the data from higher energy LHC proton-lead collisions, which can completely disregard energy loss and provide better constraints for the A dependence of the parton nuclear modifications. For large beam energy nuclear Drell-Yan experiments such as E866 and E772, a large portion of the data is in the range $ x_{2} < 0.05 $, which falls in the region of significant nuclear shadowing. For low beam energy measurements such as NA3, NA10 and E906, a large portion of the data is in the range $ 0.1 <x_{2} < 0.45 $, which falls in the region of only tiny (anti-)shadowing. The nuclear modification of the Drell-Yan process is sensitive to nPDFs mainly due to some kinds of nPDF (such as EPS09, EPS08 and EKS98) determining nuclear shadowing of sea quarks from E866 and E772 nuclear Drell-Yan data, which may be substantially contaminated by energy loss. To minimize the dependence on nPDFs, the nuclear Drell-Yan measurements at lower beam energy should provide better constraints for the initial-state parton energy loss.
With the value of the transport coefficient $ \hat{q} $ displayed in Table 2, the results considering the energy loss effect from the process of the Born diagram $ q\bar{q}\rightarrow \gamma^{*} $ are showed as the dashed-dotted lines in Figs. 1, 2, 3, 4, 5. It is found that the calculations using the EPPS16 nPDFs together with the initial-state quark energy loss effect are in good agreement with the Drell-Yan data, especially for low-mass Drell-Yan measurements (E906-120 GeV, NA3-150 GeV and NA10-140 GeV), and the fitting degree is better than the results acquired using the EPPS16 nPDF and the fully coherent regime $ \hat{q} = 0.07-0.09 $ GeV2/fm extracted from $ J/\psi $ measurements [2]. The role of the incident quark energy loss effect in the suppression of Drell-Yan ratios reduces with increasing beam energy, and becomes more important with increasing nuclear mass number A.
Thirdly, we appraise the role of the initial-state gluon energy loss by means of the primary NLO subprocess (Compton scattering) in Drell-Yan production. At next-to-leading order, the differential cross section of Compton scattering $ qg\rightarrow q\gamma^{*} $ involves the gluon distributions of the incident hadron and the target nucleus, as seen in Eq. (11). This provides an opportunity to explore the initial-state gluon energy loss effect. In order to avoid diminishing the QCD NLO correction to the data form of Drell-Yan ratios and better investigate the gluon energy loss in Compton scattering $ qg\rightarrow q\gamma^{*} $, we separately calculate the Compton differential cross section ratios $ R_{\rm Fe(W)/C}(x_{\rm F}) $ at 120 GeV. The results can be seen in Fig. 7. The dotted lines represent the results without nuclear modification of the gluon distribution of the target nucleus, the solid lines include the gluon nuclear effects, the dashed-dotted lines correspond to the calculations including the initial-state energy loss of the gluon, and the dashed lines include both quark and gluon energy loss. From Fig. 7, it can be seen that the deviation between the dotted lines and the solid lines increases to approximately 2% for $ R_{\rm Fe/C}(x_{\rm F}) $ and 3.5% for $ R_{\rm W/C}(x_{\rm F}) $ at $ x_{\rm F}\approx0.73 $, which indicates that the role of the nuclear effects of gluon distributions in Compton scattering is apparent and becomes more important with the increase of $ x_{\rm F} $ as well as the nuclear mass number A. The deviation between the solid and the dashed-dotted lines is approximately from 1% to 0 with $ x_{\rm F} $ from 0.22 to 0.73, which illustrates that the role of the initial-state gluon energy loss effect in the suppression of Compton scattering ratios is not very important, and reduces with increasing $ x_{\rm F} $. The deviation between the dashed-dotted lines and the dashed lines is approximately from 5% to 19% for $ R_{\rm Fe/C}(x_{\rm F}) $ and from 8% to 29% for $ R_{\rm W/C}(x_{\rm F}) $ with $ x_{\rm F} $ from 0.22 to 0.73, which illustrates that the initial-state quark energy loss effect in Compton scattering becomes more significant with the increase of $ x_{\rm F} $ and nuclear mass number A. It is clear that in the range $ 0.22<x_{\rm F}<0.73 $ at $ E_{\rm beam} = 120 $ GeV, the initial-state quark energy loss is the dominant effect which induces the suppression of Compton scattering ratios, the nuclear effects of the gluon leading to the rise of Compton scattering ratios are obvious, and the initial-state gluon energy loss has an influence on the suppression at small $ x_{\rm F} $. This means that it may be feasible to investigate the initial-state gluon energy loss from a separate calculation of the primary NLO subprocess (Compton scattering) in Drell-Yan production in the small $ x_{\rm F} $ range and at lower incident energy.
Figure7. Differential cross section ratios $ R_{\rm Fe/C}(x_{\rm F}) $ (left) and $ R_{\rm W/C}(x_{\rm F}) $ (right) from the Compton scattering $ qg\rightarrow q\gamma^{*} $. The dotted (solid) lines represent the results without (with) the nuclear modification of the gluon distribution, and the dashed-dotted (dashed) lines correspond to the calculations including the initial-state energy loss of the gluon (quark and gluon).

IV.SUMMARY
By means of the new EPPS16 nPDFs [22] and the analytic parametrizations of quenching weights derived from the BDMPS formalism based on the LPM regime [25-27], the Drell-Yan nuclear modification due to the nuclear effects of nPDFs and initial-state parton energy loss has been investigated, by globally analyzing all the incident energy experimental data (67 points) including E906-120 GeV [10], NA3-150 GeV [6], NA10-140 GeV [7], NA10-286 GeV [7], and E866-800 GeV [9]. It is found that the calculations with the EPPS16 nPDF together with the initial-state energy loss effect are in good agreement with the Drell-Yan data, and that the role of the energy loss effect in the suppression of Drell-Yan ratios is prominent, especially for low-mass Drell-Yan measurements. The nuclear effects of nPDFs become more obvious with increasing nuclear mass number A, the same as the energy loss effect. The value of the transport coefficient extracted by a global fit is $ \hat{q} = 0.26\pm0.04 $ GeV$ ^{2} $/fm ($ \chi^{2}/ndf = 0.82 $).
In addition, to avoid diminishing the QCD NLO correction to the data form of Drell-Yan ratios and better investigate the gluon energy loss in Compton scattering $ qg\rightarrow q\gamma^{*} $, we separately calculate the Compton differential cross section ratios $ R_{\rm Fe(W)/C}(x_{\rm F}) $ at 120 GeV. The calculations indicate that the nuclear effects of gluon distributions leading to the rise of Compton scattering rations are obvious and become more important with the increase of $ x_{\rm F} $ and nuclear mass number A. The role of the initial-state gluon energy loss in the suppression of Compton scattering ratios is not very important and disappears with the increase of $ x_{\rm F} $ and nuclear mass number A. The initial-state quark energy loss effect is the dominant effect which induces the suppression of Compton scattering ratios and becomes more significant with the increase of $ x_{\rm F} $. This mean that it may be feasible to investigate the energy loss of the gluon from a separate calculation of the primary NLO subprocess (Compton scattering) in Drell-Yan production in the small $ x_{\rm F} $ range and at lower incident energy.
闂傚倸鍊搁崐鐑芥嚄閸洖绠犻柟鍓х帛閸嬨倝鏌曟繛鐐珔缂佲偓婢舵劖鐓欓柣鎴炆戦埛鎰版倵濮橆剦鐓奸柡宀嬬秮瀵噣宕掑顒€顬嗛梺璇插绾板秴鐣濋幖浣歌摕婵炴垶菤閺嬪海鈧箍鍎遍幊搴㈡叏鎼淬劍鈷戦弶鐐村椤斿鏌¢崨顖氣枅妤犵偛鍟伴幑鍕偘閳╁喚娼旈梺鍝勵槸閻楀啴寮插☉姘殰闁靛ě鍛紳婵炶揪绲肩划娆撳传閾忓湱纾奸悹鍥皺婢ф洟鏌i敐鍛Щ妞ゎ偅绻勯幑鍕传閸曨喒鍋撻崸妤佲拺闁告繂瀚崒銊╂煕閵娿儺鐓肩€规洩缍侀獮鍥偋閸垹骞楅梻浣虹帛閿氱€殿喖鐖奸獮鏍箛椤掑鍞甸悷婊冪灱閸掓帒鈻庨幘铏К闂侀潧绻堥崐鏍吹閸愵喗鐓冮柛婵嗗閳ь剚鎮傞幆鍐敃閿旇В鎷洪梺鍛婄☉閿曘儲寰勯崟顖涚厱闁圭偓娼欓崫娲煙椤旀枻鑰挎鐐叉喘閹囧醇濮橆厼顏归梻鍌欑閹诧繝骞愰崱娑樼鐟滃秹藟濮樿埖鈷戞慨鐟版搐閻掓椽鏌涢妸銈呭祮妞ゃ垺宀搁、姗€鎮㈡笟顖涢敜闂備礁鎲$粙鎴︽晝閵壯呯闁搞儯鍔婃禍婊堟煙閹佃櫕娅呴柣蹇婃櫆椤ㄣ儵鎮欏顔煎壎濠殿喖锕ュ钘夌暦濡ゅ懏鍋傞幖绮光偓鎵挎垿姊绘担瑙勫仩闁搞劏鍋愭禍鎼侇敂閸惊锕傛煙閹殿喖顣奸柡鍛倐閺屻劑鎮ら崒娑橆伓40%闂傚倸鍊搁崐椋庣矆娴i潻鑰块弶鍫氭櫅閸ㄦ繃銇勯弽顐粶缂佲偓婢舵劖鐓涚€广儱楠搁獮鏍煕閵娿儱鈧綊骞堥妸銉庣喖宕稿Δ鈧幗鐢告煟韫囨挾绠伴悗娑掓櫊楠炲牓濡搁妷搴e枛瀹曞綊顢欓幆褍缂氶梻浣筋嚙缁绘劕霉濮橆厾顩叉い蹇撶墕閽冪喖鏌曟繛鍨姉婵℃彃鐗撻弻褑绠涢敐鍛盎濡炪倕楠忛幏锟�
闂傚倸鍊搁崐宄懊归崶顒婄稏濠㈣泛顑囬々鎻捗归悩宸剰缂佲偓婢跺备鍋撻崗澶婁壕闂侀€炲苯澧伴柛鎺撳笧閹风姴顔忛鍏煎€梻浣规偠閸庮垶宕濆畝鍕剭妞ゆ劏鎳囬弨鑺ャ亜閺冨浂娼$憸鐗堝笒閺勩儵鏌″搴′簵闁绘帒锕ラ妵鍕疀閹捐泛顤€闂佺粯鎸荤粙鎴︹€︾捄銊﹀磯闁绘碍娼欐导鎰版⒑閸濆嫭顥犻柛鐘冲姉閹广垹鈽夊▎蹇曠獮濠碘槅鍨伴幖顐ょ尵瀹ュ棛绡€缁剧増锚婢ф煡鏌熺粙鍨毐闁伙絿鍏橀獮鎺楀箣閺冣偓閺傗偓闂備礁缍婇崑濠囧礈濮橀鏁婇柡鍥╁亹閺€浠嬫煟閹邦剚鈻曢柛銈囧枎閳规垿顢涘鐓庢缂備浇浜崑銈夊春閳ь剚銇勯幒鎴濐仾闁绘挸绻橀弻娑㈠焺閸愮偓鐣堕梺鍝勬4缁插潡鍩€椤掑喚娼愭繛娴嬫櫇缁辩偞绗熼埀顒勫Υ娴g硶妲堥柕蹇娾偓鏂ュ亾閻戣姤鐓冮弶鐐靛椤﹀嘲顭跨憴鍕闁宠鍨块、娆撴儗椤愵偂绨藉瑙勬礋椤㈡﹢鎮╅崗鍝ョ憹闂備礁鎼粙渚€鎮橀幇鐗堝仭闁归潧鍟块悧姘舵⒑閸涘﹥澶勯柛瀣椤㈡牠宕熼鍌滎啎闁诲海鏁告灙鐎涙繈姊虹紒姗嗘當缂佺粯甯掑嵄闁圭増婢樼猾宥夋煕椤愶絿绠樻い鎾存そ濮婅櫣绱掑Ο蹇d邯閹ê顫濈捄铏圭暰闂佹寧绻傞ˇ浼村煕閹烘垯鈧帒顫濋浣规倷婵炲瓨绮嶇换鍫ュ蓟閿涘嫪娌悹鍥ㄥ絻椤鈹戦悙鍙夘棑闁搞劋绮欓獮鍐ㄢ枎閹存柨浜鹃柣銏㈡暩閵嗗﹪鏌$€n偆澧垫慨濠呮缁辨帒螣閾忛€涙闂佽棄鍟存禍鍫曞蓟閻斿吋鍋い鏍ㄧ懃閹牏绱撴担浠嬪摵閻㈩垪鈧剚鍤曟い鏇楀亾闁糕斁鍋撳銈嗗笒鐎氼參宕戦敓鐘崇叆闁哄啫鍊告禍楣冩煛閸℃ḿ鐭岄柟鍙夋倐閹囧醇濠靛牜鍎岄柣搴ゎ潐閹搁娆㈠璺鸿摕婵炴垟鎳囬埀顒婄畵楠炲鈹戦崶鈺佽拫闂傚倷绀侀幉锟犳嚌妤e啫绠犻幖娣妽缁犳帡姊绘担绋挎倯缂佷焦鎸冲鎻掆槈濠ф儳褰洪梻鍌氬€风欢姘跺焵椤掑倸浠滈柤娲诲灡閺呭爼顢涢悙绮规嫼闂佸吋浜介崕閬嶅煕婵傛繂鈹戦悩鍨毄闁稿鍋涘玻鍨枎閹惧疇袝闁诲函缍嗛崰妤呭吹鐏炶娇鏃堟晲閸涱厽娈紓浣哄Х閸犳牠寮婚悢鐓庣畾闁绘鐗滃Λ鍕⒑鐠囪尙绠烘繛鍛礈閹广垹鈹戠€n亜鐎銈嗗姧缁蹭粙寮冲Δ鍐=濞达絾褰冩禍鐐節閵忥絽鐓愰柛鏃€鐗犻幃锟犳偄閸忚偐鍘撻悷婊勭矒瀹曟粌鈻庨幇顏嗙畾婵炲濮撮鍡涙偂閺囥垺鐓冮柛婵嗗閳ь剝顕х叅闁圭虎鍠楅悡娑㈡倶閻愯泛袚闁革綀顫夐妵鍕敃閿濆洨鐣甸梺浼欑悼閸忔ê鐣烽崼鏇炵厸闁告劏鏅滈惁鎺楁⒒閸屾瑦绁扮€规洖鐏氶幈銊╁级閹炽劍妞芥俊鍫曞醇濞戞鐫忛梻浣虹帛閸旀洟骞栭锔藉殝閻熸瑥瀚ㄦ禍婊堟煙閻戞ê鐏ラ柍褜鍓欑紞濠傜暦閹存繍娼ㄩ柍褜鍓熷濠氬即閻旇櫣顔曢悷婊冪Ф閳ь剚鍑归崳锝咁嚕閹惰姤鍋愮紓浣骨氶幏娲⒑閸涘﹦鈽夐柨鏇樺€楃划顓㈠箳閹捐尙绠氬銈嗗姧缁查箖藟閸喍绻嗘い鎰╁灪閸ゅ洭鏌涢埡瀣瘈鐎规洏鍔戦、娆撳箚瑜嶉崣濠囨⒒閸屾瑨鍏岀紒顕呭灦瀹曟繈鏁冮崒姘鳖槶濠电偛妫欓崝鏇犳閻愮鍋撻獮鍨姎妞わ缚鍗抽幃鈥斥枎閹炬潙鈧灚绻涢幋鐐垫喗缂傚倹鑹鹃…鑳檨闁告挾鍠栧濠氭偄閸忕厧鍓梺鍛婄缚閸庡疇鈪靛┑掳鍊楁慨鐑藉磻濞戙垺鐓€闁挎繂妫旂换鍡涙煟閹达絾顥夐幆鐔兼⒑闂堟侗妾у┑鈥虫处缁傚秴鐣¢幍铏杸闂佺粯鍔栧ḿ娆撴倶閿旇姤鍙忓┑鐘插閸も偓濡炪値鍘奸悘婵嬶綖濠婂牆鐒垫い鎺戝瀹撲線鏌涢幇鈺佸闁哄啫鐗嗗婵囥亜閺冨洤袚闁绘繍鍋婇弻锝嗘償閳ュ啿杈呴梺绋款儐閹瑰洭寮诲☉銏犵疀妞ゆ挾鍋涙慨銏犫攽閻愯尙澧㈤柛瀣尵閹广垹鈽夊锝呬壕闁汇垻娅ヨぐ鎺濇晛闁规儳澧庣壕鐣屸偓骞垮劙缁€浣圭妤e啯鈷掑〒姘e亾婵炰匠鍏炬稑螖閸涱厾鏌堥梺鍦檸閸犳牜绮婚悩缁樼厪闊洦娲栧暩闂佸搫妫楅澶愬蓟閳╁啫绶為幖娣灮閵嗗﹪姊虹拠鈥虫珯闁瑰嚖鎷�40%闂傚倸鍊搁崐椋庣矆娴i潻鑰块弶鍫氭櫅閸ㄦ繃銇勯弽顐粶缂佲偓婢舵劖鐓涚€广儱楠搁獮鏍煕閵娿儱鈧綊骞堥妸銉庣喖骞愭惔锝冣偓鎰板级閳哄倻绠炴慨濠呮缁瑩骞愭惔銏″缂傚倷娴囬褏绮旈悷鎵殾闁汇垹鎲¢弲婵嬫煃瑜滈崜鐔凤耿娓氣偓濮婅櫣绱掑Ο鍏煎櫑闂佺娅曢崝妤冨垝閺冨牜鏁嗛柛鏇ㄥ墰閸橆亪姊虹化鏇炲⒉妞ゃ劌鎳樺鎶芥偄閸忚偐鍘甸悗鐟板婢瑰棛绮旈悜妯镐簻闁靛繆鍩楅鍫濈厴闁硅揪绠戦悙濠勬喐濠婂嫬顕遍柛鈩冪⊕閳锋帒霉閿濆懏鍟為柟顖氱墦閺岋絽螖娴h櫣鐓夐悗瑙勬礃缁矂鍩ユ径鎰潊闁炽儱鍘栭幋閿嬩繆閻愵亜鈧牠鎮уΔ鍐煓闁圭偓鐪归埀顒€鎳橀幃婊堟嚍閵夈儰鍖栧┑鐐舵彧缁蹭粙骞楀⿰鍫熸櫖鐎广儱娲ㄧ壕鐓庮熆鐠虹尨鍔熷ù鐘灲濡焦寰勭€n剛鐦堥悷婊冪箲閹便劑骞橀鑲╂焾濡炪倖鐗滈崑娑氱不濮樿埖鐓曠€光偓閳ь剟宕戦悙鐑樺亗闁靛濡囩粻楣冩煙鐎电ǹ鈧垿宕烽娑樹壕婵ê宕。鑲╃磼缂佹ḿ娲撮柟顔瑰墲閹棃鍩ラ崱妤€唯缂傚倸鍊风粈渚€宕愰崫銉х煋鐟滅増甯囬埀顑跨窔瀵挳濮€閻欌偓濞煎﹪姊虹紒妯剁細闁轰焦鐡曢埅锟�9闂傚倸鍊搁崐鐑芥嚄閸洏鈧焦绻濋崶褎妲梺鍝勭▉閸撴瑧绱炲鈧缁樼瑹閳ь剟鍩€椤掑倸浠滈柤娲诲灡閺呭爼顢氶埀顒勫蓟濞戞瑧绡€闁告劏鏅涢埀顒佸姍閺岀喖顢涘顒佹婵犳鍠掗崑鎾绘⒑闂堟稓澧曢柟铏姍钘濇い鎰堕檮閳锋垹绱掗娑欑濠⒀冨级缁绘盯鎳犻鈧弸娑㈡煙椤曞棛绡€闁糕晪绻濆畷銊╊敊鐟欏嫬顏归梻鍌欑閹诧繝骞愰崱娑樼鐟滃秹藟濮樿埖鈷戞慨鐟版搐閻掓椽鏌涢妸鈺€鎲炬鐐村姍閹煎綊顢曢敍鍕暰闂佽瀛╃粙鎺曟懌婵犳鍨遍幐鎶藉箖瀹勬壋鏋庨煫鍥ㄦ惄娴犲ジ姊婚崒姘簽闁搞劏娉涢~蹇涙惞鐟欏嫬鍘归梺鍛婁緱閸ㄤ即鎮у鑸碘拺缂佸娼¢妤冣偓瑙勬处閸撶喎锕㈡担绯曟斀妞ゆ柨顫曟禒婊堟煕鐎n偅宕岄柡宀€鍠栭、娆撳Ω閵夛附鎮欓梺缁樺姇閿曨亪寮诲澶婁紶闁告洦鍋呭▓鏌ユ⒑鐠団€崇伈缂傚秳绀侀~蹇撁洪鍕唶闁硅壈鎻徊鍝勎i崼銉︹拺闁稿繐鍚嬮妵鐔兼煕閵娧勬毈濠碉紕鏁婚獮鍥级鐠侯煉绱查梻浣虹帛閸旀ḿ浜稿▎鎾嶅洭顢曢敂瑙f嫼闂佸憡绻傜€氬嘲危鐟欏嫨浜滈柟瀵稿仧閹冲洨鈧娲樼换鍫濈暦閵娧€鍋撳☉娆嬬細闁告ɑ鎮傞幃妤冩喆閸曨剙闉嶉梺鍛婄箓闁帮絽鐣烽幇鏉课у璺猴功閺屽牓姊洪崜鎻掍簴闁稿孩鐓¢幃锟犲即閻樺啿鏋戦柟鑹版彧缁插潡鎯屽▎鎾跺彄闁搞儯鍔庨埥澶愭煟閹烘垹浠涢柕鍥у楠炲鏁愰崨顓炐ラ梻浣呵圭换鎰板嫉椤掑倹宕叉繛鎴欏灩瀹告繃銇勯幇鈺佺仼妞ゎ剙顦靛铏规嫚閳ュ磭浠┑鈽嗗亜閸熸潙顕i锕€绀冮柍鍝勫€搁鎾剁磽娴e壊鍎撴繛澶嬫礃缁傛帡顢橀姀鈾€鎷绘繛杈剧到閹诧繝宕悙鐑樼厽闁靛⿵濡囬惌瀣煙瀹勭増鍤囨鐐存崌楠炴帒顓奸崪浣诡棥濠电姷鏁搁崑鐘诲箵椤忓棛绀婂〒姘e亾鐎殿喗鐓¢幊鐘活敆閸愩剱锟犳⒑鐟欏嫬鍔跺┑顔哄€濋幃锟犲即閻斿墎绠氶梺闈涚墕鐎氼噣藝閿曞倹鐓欓柛蹇撳悑閸婃劙鏌$仦鐣屝ユい褌绶氶弻娑滅疀閺冨倶鈧帞绱掗鑲╁闁瑰嘲鎳樺畷鐑筋敇瑜庨柨銈夋⒒娴e憡鎯堟繛灞傚姂瀹曚即骞樼拠鑼幋閻庡箍鍎遍ˇ顖滅不閹惰姤鐓欓柟顖滃椤ュ鏌i幒鎴犱粵闁靛洤瀚伴獮瀣攽閸粏妾搁梻浣呵归敃銉ノg€n剛纾介柛灞捐壘閳ь剟顥撶划鍫熺瑹閳ь剙顕i悽鍓叉晢闁逞屽墴閳ユ棃宕橀钘夌檮婵犮垹鍘滈弲婊堟儎椤栨氨鏆︾紒瀣嚦閺冨牆鐒垫い鎺戝暟缁犺姤绻濋悽闈涗哗闁规椿浜炵槐鐐哄焵椤掍胶绠鹃柛婊冨暟缁夘喚鈧娲╃紞渚€宕洪埀顒併亜閹哄秷鍏岀紒鐘荤畺閺岀喓鈧數枪娴狅箓鏌i幘鍗炲姢缂佽鲸甯℃俊鎼佹晜婵劒铏庨梻浣虹《閺備線宕戦幘鎰佹富闁靛牆妫楅悘锕傛倵缁楁稑鎳愰惌鍫澝归悡搴f憼闁绘挾鍠愰妵鍕疀閹炬潙娅ら柣蹇撻獜缁犳捇寮婚悢纰辨晩闁兼亽鍎禒銏ゆ⒑鏉炴壆鍔嶉柛鏃€鐟ラ悾鐑藉醇閺囩偟鍘搁梺绋挎湰缁嬫垿宕濆鈧濠氬磼濞嗘埈妲梺纭咁嚋缁绘繈骞婂┑瀣鐟滃宕戦幘鎰佹僵闁绘挸楠搁埛瀣節绾板纾块柡浣筋嚙閻g兘宕奸弴銊︽櫌闂佺ǹ鏈銊╁Χ閿曞倹鈷掑ù锝呮啞閸熺偤鏌涢弮鈧悧鐐哄Φ閹版澘绀冩い鏃傛櫕閸樻劙姊绘笟鍥у缂佸鏁婚幃陇绠涘☉娆戝幈闂佸疇妫勫Λ妤呯嵁濡ゅ懏鍊垫慨妯煎亾鐎氾拷
相关话题/Drell nuclear modification

闂傚倸鍊搁崐椋庣矆娴h櫣绀婂┑鐘插€寸紓姘辨喐閺冨牄鈧線寮介鐐茶€垮┑锛勫仧缁垶寮悩缁樷拺闂侇偆鍋涢懟顖涙櫠閹绢喗鐓熼柟鍨暙娴滄壆鈧娲栨晶搴ㄥ箲閸曨剚濮滈柡澶嬪閻庢娊姊婚崒娆戠獢闁逞屽墰閸嬫盯鎳熼娑欐珷濞寸厧鐡ㄩ悡鏇㈡煟濡崵鍙€闁告瑥瀚埀顒冾潐濞插繘宕归懞銉ょ箚闁割偅娲栭悙濠囨煏婵炲灝鍔村ù鍏兼礋濮婃椽鎳¢妶鍛€鹃梺鑽ゅ枂閸庢娊鍩€椤掍礁鍤柛娆忓暙椤曪綁骞庨挊澶愬敹闂侀潧顧€婵″洭宕㈤柆宥嗏拺鐟滅増甯掓禍浼存煕閹惧鎳囬柕鍡楀暙閳诲酣骞嬮悩纰夌床闂備礁鎲¢悷锕傛晪閻庤鎸稿Λ娑㈠焵椤掑喚娼愭繛鎻掔箻瀹曟繈骞嬮敃鈧弸渚€鏌熼崜褏甯涢柡鍛倐閺屻劑鎮ら崒娑橆伓闂傚倸鍊搁崐鐑芥倿閿旈敮鍋撶粭娑樻噽閻瑩鏌熸潏楣冩闁稿孩鏌ㄩ埞鎴﹀磼濮橆厼鏆堥梺绋款儑閸犳劗鎹㈠☉銏犵婵炲棗绻掓禒鑲╃磼缂併垹骞愰柛瀣崌濮婅櫣鎷犻弻銉偓妤佺節閳ь剚娼忛妸锕€寮块柣搴ㄦ涧閹芥粍绋夊鍡愪簻闁哄稁鍋勬禒锕傛煟閹惧瓨绀冪紒缁樼洴瀹曞崬螣閸濆嫷娼曞┑鐘媰鐏炶棄顫紓浣虹帛缁诲牓宕洪埀顒併亜閹烘垵顏╃紒鐘劜閵囧嫰寮埀顒勫磿閸愯尙鏆﹂柕澶堝劗閺€浠嬫煟閹邦剙绾фい銉у仱閹粙顢涘⿰鍐ф婵犵鈧磭鍩fい銏℃礋閺佸倿鎮剧仦钘夌闂傚倷鑳舵灙闁哄牜鍓涚划娆撳箻鐠囪尙鐤囬梺绯曞墲閻燂箓宕戦弽銊х闁糕剝蓱鐏忎即鏌i幘瀛樼濞e洤锕、娑樷枎閹烘繂濡抽梻浣呵圭€涒晠宕归崷顓燁潟闁规崘顕х壕鍏兼叏濡搫鎮戝Δ鏃堟⒒娓氣偓閳ь剛鍋涢懟顖涙櫠鐎涙ḿ绠惧ù锝呭暱閸氭ê鈽夊Ο閿嬵潔闂侀潧绻嗛埀顒€鍘栭崙鑺ョ節閻㈤潧孝闁挎洏鍊濋幃褎绻濋崶褏鏌у銈嗗笒鐎氼參鎮¢妷鈺傜厽闁哄洨鍋涢埀顒€婀遍埀顒佺啲閹凤拷