# Gluon Shadowing Effects onJ/ψ and Υ Production in p+Pb Collisions at sNN=115 GeV and Pb+p Collisions at sNN=72 GeV at AFTER@LHC

Authors: R. Vogt
Journal: Advances in High Energy Physics
 (2015)

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## Abstract

We explore the effects of shadowing on inclusiveJ/ψ and Υ(1S) production at AFTER@LHC. We also present the rates as a function of pT and rapidity for p+Pb and Pb+p collisions in the proposed AFTER@LHC rapidity acceptance.


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## Body

## 1. Introduction

The AFTER@LHC quarkonium program has the unique opportunity to study quarkonium production at large momentum fractions,x, in the target region [1]. The most favorable configuration for high rates at large x for the nucleus is a proton beam from the LHC on a heavy nuclear target. In this case, the nucleon-nucleon center of mass energy is more than half that of the RHIC collider, sNN=115 GeV, for the top LHC proton beam energy of 7 TeV. However, the fixed-target configuration is an advantage because of the higher intensity on target. The longer LHC proton runs give a luminosity over a 107 s LHC “year.” On a 1 cm thick Pb target, with p+Pb collisions, L=16A μb−1 s−1. When a lead beam is extracted, the run time is shorter and an LHC Pb “year” is 106 s. The lower Z/A ratio also results in a lower center of mass energy of sNN=72 GeV for the top lead beam energy of 2.76 TeV. On a liquid H2 target, for Pb+p collisions, L=8APb mb−1 s−1 per centimeter target length so that a 1 m target gives a luminosity of L=800APb mb−1 s−1 [1].Here, we will consider the inclusiveJ/ψ and Υ(1S) rates in p+Pb collisions at sNN=115 GeV and Pb+p collisions at sNN=72 GeV. The results are presented as a function of rapidity, y, and transverse momentum, pT, of the quarkonium state. We choose to present the pT results in a 0.5-unit wide rapidity bin in the backward region of the center of mass of the collision, -2.5<ycms<-2.0 for sNN=115 GeV and -1.9<ycms<-1.4 for sNN=72 GeV. This is a region that has been virtually unexplored in previous quarkonium production measurements but, as we will show, can be studied by AFTER@LHC with relatively high statistics in most cases.Our calculations are done in the next-to-leading order (NLO) color evaporation model (CEM) [2] and employ the EPS09 NLO parameterization [3] of the effects of modification of the parton distribution functions in the nucleus, referred to here as “shadowing.” Since this set also provides an uncertainty band, the results are representative of the range of shadowing parameterizations produced by other groups.We also present the nuclear suppression factor ratios,RpPb for p+Pb collisions and RPbp for Pb+p collisions. These quantities are the ratio of the per nucleon cross sections in p+Pb (Pb+p) collisions relative to the same cross section in p+p collisions at the same center of mass energy. These ratios are also given as a function of pT and y.In Section2, we will show the EPS09 NLO shadowing parameterizations at the appropriate factorization scale for J/ψ and Υ production as a function of x with emphasis on the appropriate x regions for the AFTER@LHC kinematics. We present the ratios and rates obtained with the EPS09 NLO parameterization in Section 3. We conclude with some final remarks in Section 4.


## 2. Shadowing Parameterization

Our calculations employ the EPS09 shadowing parameterization [3]. At NLO, it is based on the CTEQ6M proton parton densities (PDFs) [4, 5]. In our calculations of quarkonium production [6, 7], we use the CT10 [8] proton PDFs with the EPS09 NLO parameterization. As long as both calculations are at NLO, the choice of proton PDFs used to calculate quarkonium production does not affect the shape or magnitude of the nuclear suppression factors [9].One possibility for the AFTER@LHC experiment is to use the LHCb detector, either as is, with2<ylab<5, or an improved LHCb (LHCb+), with 1<ylab<5.In the fixed-target kinematics of AFTER@LHC, with a 7 TeV proton beam, the rapidity range isΔy=4.8, corresponding to a center of mass rapidity coverage of -2.8<ycms<0.2 for LHCb or -3.8<ycms<0.2 for LHCb+ in p+Pb collisions at sNN=115 GeV. In this case, the Pb nucleus is the target. If x1 refers to the momentum fraction probed in the proton beam and x2 is the momentum fraction probed in the lead target, in these kinematics, the negative rapidity means that x2 is large, x2>0.1. This x2 range has not been explored since early nuclear deep-inelastic scattering (nDIS) measurements, such as the European Muon Collaboration [10, 11] and SLAC [12], and has never been explored by gluon-dominated processes such as quarkonium production. AFTER@LHC would be the first experiment to probe these kinematics since most fixed-target configurations studying quarkonium have placed the detectors downstream where x1>x2, as the CERN SPS [13, 14] and the Fermilab Tevatron [15]. The only quarkonium experiment to measure part of this backward large x2 region was HERA-B with its foils placed around the edges of the proton beam at HERA [16].On the other hand, with a 2.76 TeV lead beam, the rapidity range isΔy=4.3, corresponding to a center of mass rapidity coverage of -2.3<ycms<0.7 for LHCb or -3.3<ycms<0.7 for LHCb+ in Pb+p collisions at sNN=72 GeV. In this case, the proton is the target, with x2, and the lead beam is assigned as x1. Thus, the nuclear momentum fractions probed are moderate, x1~0.01. This x region has been well studied in nDIS experiments but, again, not for final states dominated by initial-state gluons.Global fits to the nuclear parton densities (nPDFs), such as EPS09, typically include nuclear deep-inelastic scattering data (F2 in l+A and dF2/dln⁡Q2), Drell-Yan data, and, more recently, RHIC data such as π0 production [3]. The range over which DGLAP evolution can be applied (Q2>1 GeV2) for fixed-target nDIS limits the minimum x values probed. In addition, such analyses do not take into account the possibility of any other cold nuclear matter effects so that the possibility of an effect such as initial-state energy loss in matter by quarks in Drell-Yan dilepton production is folded in with the global analysis of nuclear shadowing. Quarkonium production is particularly subject to other cold nuclear matter effects such as energy loss in matter, breakup of the quarkonium state by nucleons (nuclear absorption), and interactions with comoving hadrons; see, for example, [17] for a discussion. Regarding the purposes of this paper, we focus only on the expected effects of shadowing.Figure1 shows the EPS09 NLO gluon shadowing parameterization as a function of momentum fraction, x. The scales at which the results are shown correspond to those used in the CEM for J/ψ (Figures 1(a) and 1(c)) and Υ (Figures 1(b) and 1(d)) production. Along with the central set, denoted by the solid curves, the dotted curves display the uncertainty band. EPS09 obtains 30 additional sets of shadowing ratios by varying each of the 15 parameters within one standard deviation of the mean. The differences are added in quadrature to produce the uncertainty band in the shadowing ratio Sg. (We note that the uncertainties in the corresponding LO set are larger while the central shadowing effect is greater at LO than at NLO. For more details concerning this set as well as differences between other available nPDF sets, see [9].)Figure 1
The EPS09 NLO shadowing ratios forJ/ψ (a, c) and Υ(1S) (b, d) production. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band. (a, b) are on a linear scale to emphasize the large x region, while (c, d) are on a logarithmic scale to expand the low x region. The approximate kinematic area of interest is indicated by the vertical line in each case.
(a)
(b)
(c)
(d)The vertical blue line in Figure1 shows the average x value for the final quarkonium states at each energy, p+Pb on top and Pb+p on the bottom. This is obtained by estimating the average x value from the simpler 2→1 kinematics of the LO CEM with x1,2=(2m/sNN)exp⁡(±y) and replacing m by mT=m2+pT2 with pT2=0.5(pTQ2+pTQ¯2). The x value from the LO CEM represents a lower limit on x relative to the actual 2→2 and 2→3 kinematics of the LO and NLO contributions to the full NLO CEM calculation. The average center of mass rapidity, 〈ycms〉, shown in Figure 1 is the approximate midpoint of our chosen rapidity interval in each case. The average pT of ~2 GeV is near the peak of the pT distributions. These values should not be thought of as having the most weight in the actual calculations which integrate over the rapidity interval for the pT distributions and all pT for the rapidity distributions. Indeed, since the rapidity distributions are steeply falling, the preponderance of the rate comes from the upper end of the range in each case. Thus, the vertical lines represent an estimate of the lower bound on the x range at the given value of pT.Thep+Pb kinematics emphasize high x in the nucleus (Figures 1(a) and 1(b)) and thus explore an x range rarely probed, especially by gluon-dominated processes. It is partly in the “EMC” region of the x range and also moves into the regime of “Fermi motion.” See a discussion of how the various x regions are parameterized by Eskola and collaborators in [18, 19]. Given the shortage of direct gluon-induced data in the global analyses, the gluon shadowing ratios are constrained by the momentum sum rule. The gluon shadowing ratios shown in Figures 1(a) and 1(b) are plotted on a linear scale to highlight the large x region. Here, the scale dependence is very weak, illustrated by the similarities in the results for the two quarkonium scales shown, while the uncertainties in the nPDF extraction are the largest. AFTER@LHC measurements could help narrow this uncertainty range.On the other hand, thePb+p kinematics are in an x region where quark-dominated processes, as in nDIS, are well measured and the uncertainties can be expected to be relatively small, see Figures 1(c) and 1(d).


## 3. Cold Nuclear Matter Effects and Quarkonium Production Rates

There are other possible cold matter effects onJ/ψ production in addition to those of shadowing: breakup of the quarkonium state due to inelastic interactions with nucleons (absorption) or produced hadrons (comovers) and energy loss in cold matter.The quarkonium absorption cross section at midrapidity was seen to decrease with center of mass energy in [20], independent of whether shadowing effects were included or not. It was also seen that incorporating shadowing into the extraction of the absorption cross section required a larger effective cross section [20]. Extrapolating from the results of [20] to the energy range of AFTER@LHC, we can expect an effective absorption cross section of a few millibarns at midrapidity. Away from midrapidity, the effective absorption cross section was seen to rise at forward Feynman x, xF [20], which could be attributed to energy loss in matter [21, 22]. When a similar analysis was extended to the RHIC collider geometry, the effective absorption cross section was also seen to increase in the backward region [23]. Such behavior could be attributed to the quarkonium state being fully formed inside the nucleus. The p+Pb kinematics of AFTER@LHC would be an ideal environment to study absorption in the target if other observables such as direct photon production can also probe shadowing effects to disentangle the two.The shadowing results shown here are obtained in the color evaporation model (CEM) [24, 25] at next-to-leading order in the total cross section [2]. In the CEM, the quarkonium production cross section is some fraction, FC, of all QQ¯ pairs below the HH¯ threshold where H is the lowest mass heavy-flavor hadron: (1)σCCEMs=FC∑i,j∫4m24mH2ds∫dx1dx2fipx1,μF2·fjpx2,μF2σ^ijs^,μF2,μR2,where ij=qq¯ or gg and σ^ij(s^) are the ij→QQ¯ subprocess cross section. The normalization factor FC is fit to the forward (integrated over xF>0) J/ψ cross-sectional data and the combined Υ(nS) state data at midrapidity. We use the code of [26] with the mass cut implemented.The same values of the central charm quark mass and scale parameters are employed as those found for open charm,mc=1.27±0.09 GeV, μF/mc=2.10-0.85+2.55, and μR/mc=1.60-0.12+0.11 [6]. The normalization FC is obtained for the central set, (mc,μF/mc,μR/mc)=(1.27GeV,2.1,1.6). The calculations for the extent of the mass and scale uncertainties are multiplied by the same value of FC to obtain the extent of the J/ψ uncertainty band [6]. These values reproduce the energy dependence of J/ψ production from fixed target to collider energies. The resulting rapidity and pT distributions also agree with the p+p data from RHIC and the LHC at s=200 GeV and 7 TeV, respectively [6].We calculateΥ production in the same manner, with the central result obtained for (mb,μF/mb,μR/mb)=(4.65GeV,1.4,1.1) [7]. We have also found good agreement with s and pT distributions from previous measurements [7]. Unfortunately, the uncertainties from RHIC measurements are rather large and few data are available on the shape of the Υ rapidity distributions.To obtain the quarkoniumpT distributions at low pT, intrinsic transverse momentum, kT, smearing for quarkonium is included in the initial-state parton densities [27]. Since the MNR code cancels divergences numerically, instead of slowing the calculations by adding more integrations, the kT kick is added in the final, rather than the initial, state [26]. The Gaussian function gp(kT)=π〈kT2〉p-1exp(-kT2/〈kT2〉p) [28] multiplies the parton distribution functions for both hadrons, assuming that x and kT dependencies in the initial partons completely factorize. If factorization applies, it does not matter whether the kT dependence appears in the initial or final state if the kick is not too large. The effect of the intrinsic kT on the shape of the J/ψpT distribution can be expected to decrease as s increases because the average pT of the J/ψ also increases with energy. However, the value of 〈kT2〉 may increase with s. We can check the energy dependence of 〈kT2〉 by the shape of the J/ψpT distributions at central and forward rapidity at RHIC. We find that 〈kT2〉=1+(1/12)ln⁡(s/20)≈1.19 GeV2 at s=200 GeV agrees well with the J/ψpT distributions [6]. All the calculations are NLO in the total cross section and assume that the intrinsic kT broadening is the same in p+p as in p+Pb. While the broadening is expected to increase in collisions with nuclei as projectile, target, or both, the agreement of the J/ψp+Pb ratio RpPb(pT) with the LHC data is better without any additional broadening [9]. Therefore, we do not change the value here.


### 3.1.J/ψ and Υ(1S) Production in p+Pb Collisions at sNN=115 GeV

In this section, the results forJ/ψ and Υ shadowing in p+Pb collisions at sNN=115 GeV are presented. Figure 2 shows the results for J/ψ while Figure 3 shows the Υ results. In both cases, the left-hand side shows the ratios RpPb as a function of y (Figures 2(a) and 3(a)) and pT in the rapidity range -2.5<ycms<-2 (Figures 2(c) and 3(c)). The rates to dileptons in the rapidity acceptance, assuming a lead target, are shown in Figures 2(b), 2(d), 3(b), and 3(d).Figure 2
The predictedJ/ψ shadowing ratios (a, c) and rates (b, d) as a function of center of mass rapidity (a, b) and pT (c, d) for p+Pb collisions at sNN=115 GeV. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band.
(a)
(b)
(c)
(d)Figure 3
The predictedΥ(1S) shadowing ratios (a, c) and rates (b, d) as a function of center of mass rapidity (a, b) and pT (c, d) for p+Pb collisions at sNN=115 GeV. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band.
(a)
(b)
(c)
(d)In the kinematics of this configuration, the largex2 in the nucleus puts the peak for Fermi motion at the most negative rapidities. (The full center of mass rapidity range for J/ψ’s produced at this energy is |ycms|=ln(s/m)<3.8 for the mass and scale parameters appropriate for the CEM calculation.) The EMC region is in the J/ψ rapidity acceptance. There is a steep drop in RpPb(ycms) as ycms decreases from −2 to −2.5, changing the central value of RpPb(ycms) by ~30% over the range. The decrease into the EMC region is more apparent as a function of pT where the region is expanded for pT<10 GeV. The large uncertainty in this x range, as emphasized in Figures 1(a) and 1(b), is enhanced here.The rates as a function of rapidity forJ/ψ and Υ(1S) decays to lepton pairs are shown in Table 1. While the rates are shown for the entire rapidity range, the broad LHCb+ center of mass rapidity acceptance ends at ycms~1. The rates are given in the bins of Δycms=0.5 with the value of ycms at the center of the bin shown in Table 1. The rates include the branching ratios to lepton pairs.Table 1
The rates per 0.5-unit rapidity forJ/ψ and ϒ(1S) in the two scenarios discussed in the text. The values are given for the EPS09 NLO central set.
System
y
c
m
s
N
(
J
/
ψ
→
l
+
l
-
)
N
(
ϒ
(
1
S
)
→
l
+
l
-
)
p + Pb  sNN=115 GeV
-
3.75
2.32 × 105
—
-
3.25
1.67 × 107
—
-
2.75
9.56 × 107
—
-
2.25
2.69 × 108
8.68 × 103
-
1.75
5.50 × 108
1.10 × 105
-
1.25
8.88 × 108
3.56 × 105
-
0.75
1.11 × 109
6.81 × 105
-
0.25
1.14 × 109
9.33 × 105
0.25
1.02 × 109
9.47 × 105
0.75
8.36 × 108
6.96 × 105
1.25
6.10 × 108
3.85 × 105
1.75
3.86 × 108
1.39 × 105
2.25
2.10 × 108
1.15 × 104
2.75
9.25 × 107
—
3.25
2.04 × 107
—
3.75
2.13 × 105
—
Pb +p sNN=72 GeV
-
3.25
1.54 × 103
—
-
2.75
1.05 × 105
—
-
2.25
4.36 × 105
—
-
1.75
9.67 × 105
5.36 × 101
-
1.25
1.78 × 106
5.10 × 102
-
0.75
2.79 × 106
1.20 × 103
-
0.25
3.72 × 106
1.66 × 103
0.25
4.15 × 106
1.59 × 103
0.75
3.64 × 106
1.03 × 103
1.25
2.42 × 106
3.78 × 102
1.75
1.24 × 106
3.77 × 101
2.25
4.58 × 105
—
2.75
8.68 × 104
—
3.25
1.55 × 103
—TheJ/ψ rates in p+Pb collisions are very high. The rate is BdN/dy~2.7×108 in the chosen backward rapidity bin of -2.5<ycms<-2; see Figure 2(b). The cross section is rather high since sNN is above the region where the production cross section is still increasing steeply with sNN. In addition, the J/ψ production range in rapidity is fully within the AFTER@LHC acceptance.Finally, even though the rates fall off quickly withpT, more than 100 events can be collected at pT~9.5 GeV; see Figure 2(d) and the upper part of Table 2, which is likely enough to determine where RpPb(pT) lies within the EPS09 band.Table 2
ThepT-dependent rates per 1 GeV pT  bin for J/ψ and ϒ(1S) in the two scenarios discussed in the text. The values are given for the EPS09 NLO central set.
System
p
T (GeV)
N
(
J
/
ψ
→
l
+
l
-
)
N
(
ϒ
(
1
S
)
→
l
+
l
-
)
p + Pb  sNN=115 GeV
0.5
3.83 × 107
1.06 × 103
1.5
6.62 × 107
1.79 × 103
2.5
2.83 × 107
1.04 × 103
3.5
6.69 × 106
3.40 × 102
4.5
9.78 × 105
7.93 × 101
5.5
2.03 × 105
1.84 × 101
6.5
2.96 × 104
4.64 × 100
7.5
6.20 × 103
1.62 × 100
8.5
1.12 × 103
3.40 × 10-1
9.5
2.60 × 102
6.51 × 10-2
10.5
3.96 × 101
1.03 × 10-2
Pb +p  sNN=72 GeV
0.5
1.38 × 105
1.39 × 101
1.5
2.36 × 105
2.26 × 101
2.5
1.33 × 105
1.20 × 101
3.5
3.90 × 104
3.39 × 100
4.5
7.69 × 103
7.44 × 10-1
5.5
1.16 × 103
1.71 × 10-1
6.5
2.11 × 102
4.69 × 10-2
7.5
4.15 × 101
1.28 × 10-2
8.5
8.62 × 100
3.25 × 10-3
9.5
1.89 × 100
6.72 × 10-4
10.5
3.39 × 10-1
1.65 × 10-4TheΥ(1S) rates, shown in Figure 3, are significantly lower. At this energy, the production cross section is still increasing rapidly so that the available phase space for Υ production is |ycms|<2.9 in the CEM calculation. Thus, the AFTER@LHC acceptance is just inside the lower end of this range and the rate for Υ production in this region is relatively low. While the rates over all phase space can be quite high, with nearly 106 events at midrapidity, there are less than 104 events in the region -2.5<ycms<-2; see Table 1 and Figure 3(d).As shown in Table2, the Υ states that are produced in the AFTER@LHC acceptance are primarily at low pT, pT≤3 GeV. Indeed, there are fewer than 10 events per year for pT>6 GeV so that any division into pT bins for pT>5 GeV is unlikely to be feasible.The AFTER@LHC rapidity bin is in the EMC region and touching on the Fermi motion region atycms~-2.5, as seen on Figure 3(a). The pT-dependent ratio reflects the large uncertainty of the EMC region and is almost independent of pT until pT~9 GeV in the EPS09 parameterization where it increases sharply. The low rate will make it difficult to study this interesting region in detail.


### 3.2.J/ψ and Υ(1S) Production in Pb+p Collisions at sNN=72 GeV

In this section, the results forJ/ψ and Υ shadowing in Pb+p collisions at sNN=72 GeV are presented. Figure 4 shows the results for J/ψ while Figure 5 shows the Υ results. In both cases, Figures 5(a) and 5(c) shows the ratios RPbp as a function of ycms (Figure 5(a)) and pT in the -1.9<ycms<-1.4 rapidity bin (Figure 5(c)). The rates to dileptons in the rapidity acceptance, assuming a 1 m long liquid hydrogen target, are shown in Figures 4(b), 4(d), 5(b), and 5(d)and in the bottom parts of Tables 1 and 2. The lower cross sections at this reduced energy still result in rather high rates for the long liquid hydrogen target, at least at midrapidity.Figure 4
The predictedJ/ψ shadowing ratios (a, c) and rates (b, d) as a function of center of mass rapidity (a, b) and pT (c, d) for Pb+p collisions at sNN=72 GeV. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band.
(a)
(b)
(c)
(d)Figure 5
The predictedΥ(1S) shadowing ratios (a, c) and rates (b, d) as a function of center of mass rapidity (a, b) and pT (c, d) for Pb+p collisions at sNN=72 GeV. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band.
(a)
(b)
(c)
(d)In these kinematics, the rapidity bin-1.9<ycms<-1.4 now corresponds to the more typical fixed-target kinematics with the lead nucleus at the lower x1. Here, the ratio RPbp(ycms) is reversed. The x range for the J/ψ is in the higher x end of the shadowing region while the Υ is just entering the antishadowing region; recall Figure 1.The antishadowing peak forJ/ψ in Figure 4(a) is actually just at forward rapidity instead of being in the ycms<0 region. (The full center of mass rapidity range for J/ψ production at this energy is |ycms|<3.3.) Within the chosen rapidity bin, the pT-dependent ratio has the largest uncertainty at the low pT where there is still some shadowing. However, at pT>5 GeV, the x values move somewhat into the antishadowing region (Figure 4(c)).TheJ/ψ rates for this system are still high; see the lower half of Table 1. Thanks to the length of the H2 target, for the lead beam, the pT-integrated rates in this configuration are still on the order of 106 in the AFTER@LHC acceptance. The pT-dependent rates show that the statistics become poor for the J/ψ at pT>7 GeV. The rates at this energy are helped somewhat since there is antishadowing for pT>8 GeV while there is strong shadowing at sNN=115 GeV; see Figure 2.The situation withΥ(1S) is similar; see Figure 5 and Table 1. (The rapidity range for Υ production is |ycms|<2.4 so that again the AFTER@LHC acceptance is on the edge of the Υ range.) The shadowing (or antishadowing) effect is on the order of a few percent. While there are a few thousand Υ in a year at midrapidity, the rate in the AFTER@LHC acceptance is rather low, under 100 per year, as shown in Figures 5(b) and 5(d) and in Table 2. Indeed, there is effectively no rate for the Υ rate for pT>4 GeV.


## 3.1.J/ψ and Υ(1S) Production in p+Pb Collisions at sNN=115 GeV

In this section, the results forJ/ψ and Υ shadowing in p+Pb collisions at sNN=115 GeV are presented. Figure 2 shows the results for J/ψ while Figure 3 shows the Υ results. In both cases, the left-hand side shows the ratios RpPb as a function of y (Figures 2(a) and 3(a)) and pT in the rapidity range -2.5<ycms<-2 (Figures 2(c) and 3(c)). The rates to dileptons in the rapidity acceptance, assuming a lead target, are shown in Figures 2(b), 2(d), 3(b), and 3(d).Figure 2
The predictedJ/ψ shadowing ratios (a, c) and rates (b, d) as a function of center of mass rapidity (a, b) and pT (c, d) for p+Pb collisions at sNN=115 GeV. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band.
(a)
(b)
(c)
(d)Figure 3
The predictedΥ(1S) shadowing ratios (a, c) and rates (b, d) as a function of center of mass rapidity (a, b) and pT (c, d) for p+Pb collisions at sNN=115 GeV. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band.
(a)
(b)
(c)
(d)In the kinematics of this configuration, the largex2 in the nucleus puts the peak for Fermi motion at the most negative rapidities. (The full center of mass rapidity range for J/ψ’s produced at this energy is |ycms|=ln(s/m)<3.8 for the mass and scale parameters appropriate for the CEM calculation.) The EMC region is in the J/ψ rapidity acceptance. There is a steep drop in RpPb(ycms) as ycms decreases from −2 to −2.5, changing the central value of RpPb(ycms) by ~30% over the range. The decrease into the EMC region is more apparent as a function of pT where the region is expanded for pT<10 GeV. The large uncertainty in this x range, as emphasized in Figures 1(a) and 1(b), is enhanced here.The rates as a function of rapidity forJ/ψ and Υ(1S) decays to lepton pairs are shown in Table 1. While the rates are shown for the entire rapidity range, the broad LHCb+ center of mass rapidity acceptance ends at ycms~1. The rates are given in the bins of Δycms=0.5 with the value of ycms at the center of the bin shown in Table 1. The rates include the branching ratios to lepton pairs.Table 1
The rates per 0.5-unit rapidity forJ/ψ and ϒ(1S) in the two scenarios discussed in the text. The values are given for the EPS09 NLO central set.
System
y
c
m
s
N
(
J
/
ψ
→
l
+
l
-
)
N
(
ϒ
(
1
S
)
→
l
+
l
-
)
p + Pb  sNN=115 GeV
-
3.75
2.32 × 105
—
-
3.25
1.67 × 107
—
-
2.75
9.56 × 107
—
-
2.25
2.69 × 108
8.68 × 103
-
1.75
5.50 × 108
1.10 × 105
-
1.25
8.88 × 108
3.56 × 105
-
0.75
1.11 × 109
6.81 × 105
-
0.25
1.14 × 109
9.33 × 105
0.25
1.02 × 109
9.47 × 105
0.75
8.36 × 108
6.96 × 105
1.25
6.10 × 108
3.85 × 105
1.75
3.86 × 108
1.39 × 105
2.25
2.10 × 108
1.15 × 104
2.75
9.25 × 107
—
3.25
2.04 × 107
—
3.75
2.13 × 105
—
Pb +p sNN=72 GeV
-
3.25
1.54 × 103
—
-
2.75
1.05 × 105
—
-
2.25
4.36 × 105
—
-
1.75
9.67 × 105
5.36 × 101
-
1.25
1.78 × 106
5.10 × 102
-
0.75
2.79 × 106
1.20 × 103
-
0.25
3.72 × 106
1.66 × 103
0.25
4.15 × 106
1.59 × 103
0.75
3.64 × 106
1.03 × 103
1.25
2.42 × 106
3.78 × 102
1.75
1.24 × 106
3.77 × 101
2.25
4.58 × 105
—
2.75
8.68 × 104
—
3.25
1.55 × 103
—TheJ/ψ rates in p+Pb collisions are very high. The rate is BdN/dy~2.7×108 in the chosen backward rapidity bin of -2.5<ycms<-2; see Figure 2(b). The cross section is rather high since sNN is above the region where the production cross section is still increasing steeply with sNN. In addition, the J/ψ production range in rapidity is fully within the AFTER@LHC acceptance.Finally, even though the rates fall off quickly withpT, more than 100 events can be collected at pT~9.5 GeV; see Figure 2(d) and the upper part of Table 2, which is likely enough to determine where RpPb(pT) lies within the EPS09 band.Table 2
ThepT-dependent rates per 1 GeV pT  bin for J/ψ and ϒ(1S) in the two scenarios discussed in the text. The values are given for the EPS09 NLO central set.
System
p
T (GeV)
N
(
J
/
ψ
→
l
+
l
-
)
N
(
ϒ
(
1
S
)
→
l
+
l
-
)
p + Pb  sNN=115 GeV
0.5
3.83 × 107
1.06 × 103
1.5
6.62 × 107
1.79 × 103
2.5
2.83 × 107
1.04 × 103
3.5
6.69 × 106
3.40 × 102
4.5
9.78 × 105
7.93 × 101
5.5
2.03 × 105
1.84 × 101
6.5
2.96 × 104
4.64 × 100
7.5
6.20 × 103
1.62 × 100
8.5
1.12 × 103
3.40 × 10-1
9.5
2.60 × 102
6.51 × 10-2
10.5
3.96 × 101
1.03 × 10-2
Pb +p  sNN=72 GeV
0.5
1.38 × 105
1.39 × 101
1.5
2.36 × 105
2.26 × 101
2.5
1.33 × 105
1.20 × 101
3.5
3.90 × 104
3.39 × 100
4.5
7.69 × 103
7.44 × 10-1
5.5
1.16 × 103
1.71 × 10-1
6.5
2.11 × 102
4.69 × 10-2
7.5
4.15 × 101
1.28 × 10-2
8.5
8.62 × 100
3.25 × 10-3
9.5
1.89 × 100
6.72 × 10-4
10.5
3.39 × 10-1
1.65 × 10-4TheΥ(1S) rates, shown in Figure 3, are significantly lower. At this energy, the production cross section is still increasing rapidly so that the available phase space for Υ production is |ycms|<2.9 in the CEM calculation. Thus, the AFTER@LHC acceptance is just inside the lower end of this range and the rate for Υ production in this region is relatively low. While the rates over all phase space can be quite high, with nearly 106 events at midrapidity, there are less than 104 events in the region -2.5<ycms<-2; see Table 1 and Figure 3(d).As shown in Table2, the Υ states that are produced in the AFTER@LHC acceptance are primarily at low pT, pT≤3 GeV. Indeed, there are fewer than 10 events per year for pT>6 GeV so that any division into pT bins for pT>5 GeV is unlikely to be feasible.The AFTER@LHC rapidity bin is in the EMC region and touching on the Fermi motion region atycms~-2.5, as seen on Figure 3(a). The pT-dependent ratio reflects the large uncertainty of the EMC region and is almost independent of pT until pT~9 GeV in the EPS09 parameterization where it increases sharply. The low rate will make it difficult to study this interesting region in detail.


## 3.2.J/ψ and Υ(1S) Production in Pb+p Collisions at sNN=72 GeV

In this section, the results forJ/ψ and Υ shadowing in Pb+p collisions at sNN=72 GeV are presented. Figure 4 shows the results for J/ψ while Figure 5 shows the Υ results. In both cases, Figures 5(a) and 5(c) shows the ratios RPbp as a function of ycms (Figure 5(a)) and pT in the -1.9<ycms<-1.4 rapidity bin (Figure 5(c)). The rates to dileptons in the rapidity acceptance, assuming a 1 m long liquid hydrogen target, are shown in Figures 4(b), 4(d), 5(b), and 5(d)and in the bottom parts of Tables 1 and 2. The lower cross sections at this reduced energy still result in rather high rates for the long liquid hydrogen target, at least at midrapidity.Figure 4
The predictedJ/ψ shadowing ratios (a, c) and rates (b, d) as a function of center of mass rapidity (a, b) and pT (c, d) for Pb+p collisions at sNN=72 GeV. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band.
(a)
(b)
(c)
(d)Figure 5
The predictedΥ(1S) shadowing ratios (a, c) and rates (b, d) as a function of center of mass rapidity (a, b) and pT (c, d) for Pb+p collisions at sNN=72 GeV. The solid curve in each plot is the central EPS09 NLO result, while the dotted curves outline the shadowing uncertainty band.
(a)
(b)
(c)
(d)In these kinematics, the rapidity bin-1.9<ycms<-1.4 now corresponds to the more typical fixed-target kinematics with the lead nucleus at the lower x1. Here, the ratio RPbp(ycms) is reversed. The x range for the J/ψ is in the higher x end of the shadowing region while the Υ is just entering the antishadowing region; recall Figure 1.The antishadowing peak forJ/ψ in Figure 4(a) is actually just at forward rapidity instead of being in the ycms<0 region. (The full center of mass rapidity range for J/ψ production at this energy is |ycms|<3.3.) Within the chosen rapidity bin, the pT-dependent ratio has the largest uncertainty at the low pT where there is still some shadowing. However, at pT>5 GeV, the x values move somewhat into the antishadowing region (Figure 4(c)).TheJ/ψ rates for this system are still high; see the lower half of Table 1. Thanks to the length of the H2 target, for the lead beam, the pT-integrated rates in this configuration are still on the order of 106 in the AFTER@LHC acceptance. The pT-dependent rates show that the statistics become poor for the J/ψ at pT>7 GeV. The rates at this energy are helped somewhat since there is antishadowing for pT>8 GeV while there is strong shadowing at sNN=115 GeV; see Figure 2.The situation withΥ(1S) is similar; see Figure 5 and Table 1. (The rapidity range for Υ production is |ycms|<2.4 so that again the AFTER@LHC acceptance is on the edge of the Υ range.) The shadowing (or antishadowing) effect is on the order of a few percent. While there are a few thousand Υ in a year at midrapidity, the rate in the AFTER@LHC acceptance is rather low, under 100 per year, as shown in Figures 5(b) and 5(d) and in Table 2. Indeed, there is effectively no rate for the Υ rate for pT>4 GeV.


## 4. Conclusions

We have only presented a bare minimum of the rates for the breadth of quarkonium studies possible at AFTER@LHC. The fixed-target configuration, especially for long runs with the dedicated proton beam, allows detailed measurements with a range of nuclear targets. We have only shown the Pb results here because the larger nuclear mass number produces what is expected to be the maximum effect due to shadowing.The largex region available for nuclear targets in the AFTER@LHC kinematics with a proton beam has the unique capability to make unprecedented studies of this heretofore unexplored range. The AFTER@LHC measurements would bridge the gap between the dedicated fixed-target experiments in the range 17.2≤sNN≤41 GeV and the d+Au and the upcoming p+A collider experiments at RHIC, albeit in an x range never before studied.In the AFTER@LHC configuration with a Pb beam, the rates are smaller, though still significant, and the more conventionalx range is probed.



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