Nuclear Modification Factor for Charged Pions and Protons at Forward Rapidity in Central Au+Au Collisions at 200 GeV

We present spectra of charged pions and protons in 0-10% central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV at mid-rapidity ($y=0$) and forward pseudorapidity ($\eta=2.2$) measured with the BRAHMS experiment at RHIC. The spectra are compared to spectra from p+p collisions at the same energy scaled by the number of binary collisions. The resulting nuclear modification factors for central Au+Au collisions at both $y=0$ and $\eta=2.2$ exhibit suppression for charged pions but not for (anti-)protons at intermediate $p_T$. The $\bar{p}/\pi^-$ ratios have been measured up to $p_T\sim 3$ GeV/$c$ at the two rapidities and the results indicate that a significant fraction of the charged hadrons produced at intermediate $p_T$ range are (anti-)protons at both mid-rapidity and $\eta = 2.2$.


Introduction
One of the reasons for studying heavy-ion collisions at high energies is to search for the predicted Quark-Gluon Plasma (QGP), a deconfined state of quarks and gluons, and to investigate the properties of this state of matter at extremely high energy densities.High p T hadrons, primarily produced from the fragmentation of the hard-scattered partons, are considered a good probe of the QGP [1,2,3].Due to induced gluon radiation, hard-scattered partons will suffer a larger energy loss in a hot dense medium of color charges than in color neutral matter.This results in fewer charged hadrons produced at moderate to high p T ; the hadrons are said to be suppressed.Indeed, all four experiments at RHIC have observed that high p T inclusive hadron yields in central Au+Au collisions are suppressed as compared to p+p and d+Au interactions at mid-rapidity [4,5,6,7].However, it was also discovered that the yields of protons and anti-protons at intermediate p T (1.5-4.5 GeV/c) are comparable to those of pions and not suppressed at mid-rapidity as compared to elementary nucleon-nucleon collisions [5,8].These experimental results have motivated several suggestions on how hadrons are produced at intermediate p T [9,10,11,12], such as the possibility that boosted quarks from a collectively expanding QGP recombine to form the final-state hadrons [10,11,12].Among the interesting results from the BRAHMS experiment is that at forward pseudorapidity η = 2.2 inclusive negatively charged hadrons are suppressed in both central Au+Au and minimum-bias d+Au collisions [4,13].This raises the possibility that initial-state effects such as gluon saturation may also influence hadron production at intermediate p T [14,15,16].
To explore the effect of the nuclear medium on intermediate p T particle production, we present in this paper the invariant p T spectra of charged pions and protons measured by the BRAHMS experiment at RHIC up to 3 GeV/c in central Au+Au collisions at √ s N N = 200 GeV at both mid-rapidity and forward pseudorapidity η = 2.2.The spectra are then compared to reference data from p+p collisions at the same energy scaled by the number of binary collisions N bin by using the nuclear modification factor: where d 2 N AA /dp T dy is the differential yield per event in the nucleus-nucleus (A+A) collision, and σ pp inel and d 2 σ pp inel /dp T dy are the total and differential cross section for inelastic p+p collisions, respectively.

Experiment and data analysis
The BRAHMS experiment [17] consists of event characterization detectors and two independent magnetic spectrometers, the mid-rapidity spectrometer (MRS) and the Forward Spectrometer (FS), both of which can be rotated in the horizontal plane around the beam direction.For the present studies the MRS was positioned at 90 degrees and the FS at 12 degrees with respect to the beam direction.Collision centrality is determined from the charged particle multiplicity measured by multiplicity detectors as described in [18].The trajectories of charged particles are reconstructed in the tracking devices (time projection chambers and drift chambers).The resulting straight-line track segments in two detectors located on either side of a magnet are then matched and the particle momentum is determined from the deflection of the track in the magnetic field.The intrinsic momentum resolution of the spectrometers at maximum magnetic field setting is δp/p = 0.0077p for the MRS and δp/p = 0.0008p for the FS [13], where p is written in units of GeV/c.In the MRS charged particles are identified using a time-of-flight wall (TOFW), whereas in the FS a time-of-flight wall (H2) and a ring imaging Cherenkov (RICH) detector are used for particle identification (PID).To identify charged pions and protons using time-of-flight detectors, 2σ standard deviation PID cuts in the derived m 2 and momentum space are imposed for each species.With a timing resolution of σ TOFW ∼ 80 ps in the Au+Au runs, protons and pions can be well separated from kaons up to momenta 3.2 GeV/c and 2.0 GeV/c, respectively.For pions above 2 GeV/c, an asymmetric PID cut is applied, i.e. the region where the pion and kaon 2σ cuts overlap is excluded for PID, and the pion yield in the region is obtained by assuming a symmetric PID distribution about the mean pion mass squared value.This allows the pion p T spectrum to be extended to 3 GeV/c, at which point the kaon contamination of pions is estimated to be less than 5% and is accounted for in the systematic errors.For the FS PID in the present analysis, H2 is used only for the low momentum data.With a timing resolution of σ H2 ∼ 90 ps, protons and pions can be identified up to 7.1 GeV/c and 4.2 GeV/c, respectively with a 2σ separation.Above 7.1 GeV/c, an asymmetric PID cut is applied and the proton yields in the overlap region are estimated by assuming a symmetric PID distribution about the mean proton mass squared value.Between 7.9 GeV/c and 9 GeV/c, the Cherenkov threshold for protons, the RICH detector is used to determine the kaon contamination of the proton spectrum.At 9 GeV/c the contamination of protons by kaons is estimated to be less than 6%.Above 9 GeV/c, protons are identified by using the RICH to veto pions and kaons.To identify pions, the RICH is directly used to separated pions from kaons well from momentum of 2.5 GeV/c up to 20 GeV/c.The invariant differential yields 1 2π p T dηdp T at forward rapidity) were constructed for each spectrometer setting.As discussed in [19] the differential yields were corrected for geometrical acceptance, tracking and PID inefficiencies, in-flight decay of pions, the effect of absorption and multiple scattering.The pion contamination by hyperon (Λ) and neutral K 0 S decays were investigated in [20] and found to be less than 5% in the MRS and 7% in the FS, respectively.The contribution to proton spectra by the Λ decays was estimated with a GEANT [21] simulation where an exponential distribution in p T with inverse slope taken from the PHENIX and STAR measurements [22,23] for both (anti-)protons and (anti-)lambdas was generated for several spectrometer settings.By taking the ratio of Λ( Λ) to p(p) yields of 0.89 (0.95) [22] in 0-10% central Au+Au and 0.45 (0.55) [23] in p+p collisions at √ s N N = 200 GeV and assuming a constant behavior in the rapidity interval |y| ≤ 2.2 as indicated by HIJING model [24], it is found that the fraction of protons originating from Λ( Λ) decays is at a maximum value around 35-40% in central Au+Au and 27-30% in p+p collisions and decreases with p T .In the following correction for feed-down from the (anti-)lambda decays has been applied, whereas the contamination of pions due to weak decays has not been corrected but is accounted for in the systematic errors.

Particle spectra
The top row of Figure 1 shows the p T spectra of charged pions (left panel) and protons (right panel) at mid-rapidity in 0-10% central Au+Au and p+p The systematic errors are estimated to be less than 15% for pions and 18% for (anti-)protons.For the reference spectrum the systematic error is estimated to be less than 19%.For clarity, some spectra are scaled vertically as quoted.Bottom row: p T spectra for π − and p at forward rapidity η = 2.2 in 0-10% central Au+Au and p+p collisions at √ s N N = 200 GeV.The systematic errors are estimated to be 14% for pions and 17% for anti-protons.collisions at √ s N N = 200 GeV.Also shown in the left panel of the figure is the measured spectrum of (π + + π − )/2 in p+p collisions, where pions can only be identified up to 1.5 GeV/c with TOFW for 2003 p+p runs.We thus constructed a reference spectrum shown as a solid line by dividing the neutral pion spectrum in p+p collisions measured by PHENIX [25] by the spectrum from PYTHIA simulation [26] at the same rapidity range and then multiplying the results by the (π + + π − )/2 spectrum from PYTHIA.The spectra of (anti-)protons in p+p collisions are measured by the BRAHMS spectrometer but to a smaller p T coverage compared to those in Au+Au collisions due to a worse TOF resolution in the p+p runs.The spectra have been corrected for the trigger inefficiency [13] and fitted with an exponential function as shown in solid lines with the rapidity density and the inverse slope parameter of 0.101 ± 0.004 (0.098 ± 0.004) and 0.304 ± 0.005 (0.285 ± 0.005 GeV) for proton (antiproton), respectively.The error bars are statistical only.The systematic errors in the measured spectra, which come from the uncertainties in the momentum determination, the time-of-flight measurements and ring radius reconstruction procedures, and the uncertainties in the corrections estimations, are estimated to be less than 15% for pions and 18% for (anti-)protons.The systematic error in the reconstructed reference spectrum for charged pions is estimated to be less than 19%.
The bottom row of Figure 1 shows the p T spectra for π − (left panel) and p (right panel) at forward rapidity η = 2.2 in 0-10% central Au+Au and p+p collisions at √ s N N = 200 GeV.Solid lines are curves fit to the π − and p spectra in p+p collisions.The spectra are constructed in terms of d 2 N/dp T dη because the rapidity coverages of the FS at 12 degrees for pions and protons are different, making a comparison of anti-proton to pion yields difficult.In addition, since the Jacobian effect is largest at mid-rapidity and gets rather small at larger rapidities at intermediate p T range as we focused on in this paper, we expect the conclusions drawn from the spectra expressed in terms of d 2 N/dp T dη should be the same as from those of d 2 N/dp T dy.

Nuclear modification factor
In Figure 2  Similar to the unidentified charged hadrons [4] at both mid-rapidity and forward rapidity, R AuAu for charged pions increases monotonically up to ∼ 1.5 GeV/c and levels off at a value below unity above 1.5 GeV/c indicating that charged pions yields are suppressed with respect to p+p collisions at intermediate p T .Furthermore, the π − yields at forward rapidity show a similar or even stronger suppression, indicating that nuclear effects other than parton energy loss (jet quenching) might be contributing to the strong suppression.The suppression at midrapidity around p T ∼ 2 GeV/c is smaller (about 30%) than the suppression that has been reported for neutral pions [27] and which is seen at forward rapidity.This difference can -to a large extent -be attributed to the construction of the reference spectrum and has been accounted for by the systematical error for π − at mid-rapidity.Another interesting feature shown in the figure is that the anti-proton yields at both mid-rapidity and η = 2.2 are not suppressed at p T > 1.5 GeV/c.In the present ratios, most systematic errors cancel out.Remaining systematic errors arising from PID efficiencies, acceptance corrections, corrections for nuclear interactions with detector etc. are estimated to be less than 12% at both y = 0 and η = 2.2.Also shown in the figure are the corresponding ratios for p+p collisions at √ s N N = 200 GeV.There is a clear increase of the p/π − ratios at intermediate p T in central Au+Au collisions relative to the level seen in p+p collisions (see also [8,28]).This enhancement is most likely due to the interplay of several final-state effects and possibly a new hadronization mechanism other than parton fragmentation.Calculations based on a parton recombination scenario [12] with a collective flow at the partonic level appear to be able to qualitatively describe the data at mid-rapidity.

Summary
In summary, the BRAHMS measurements demonstrate a significant suppression of charged pions at intermediate p T at both mid-rapidity and forward rapidity for 0-10% central Au+Au collisions at √ s N N = 200 GeV.Such a strong suppression is believed to be caused primarily by the parton losing energy when traversing the partonic (i.e.characterized by color degrees of freedom) medium created in central Au+Au collisions.The strong π − suppression at forward rapidity suggests that the hot dense partonic medium may also exist in the forward rapidity region and that there might be other nuclear effects such as gluon saturation contributing to the suppression.However, the suppression is not observed for (anti-)protons at intermediate p T at either mid-rapidity or forward pseudorapidity η = 2.2.p/π − ratios in central Au+Au show an enhancement of (anti-)proton production relative to the p+p collisions at intermediate p T .All these observations are consistent with a picture where a dense strongly interacting partonic matter with a strong collective flow is most likely formed in central Au+Au collisions over a large rapidity range which results in the strong suppression of charged pion yields and boosts the protons to higher transverse momentum.

Fig. 1 .
Fig. 1.Top row: p T spectra of charged pions (left panel) and protons (right panel) at mid-rapidity in 0-10% central Au+Au and p+p collisions at √ s N N = 200 GeV.The error bars are statistical only.The systematic errors are estimated to be less than 15% for pions and 18% for (anti-)protons.For the reference spectrum the systematic error is estimated to be less than 19%.For clarity, some spectra are scaled vertically as quoted.Bottom row: p T spectra for π − and p at forward rapidity η = 2.2 in 0-10% central Au+Au and p+p collisions at √ s N N = 200 GeV.The systematic errors are estimated to be 14% for pions and 17% for anti-protons.

Fig. 2 .
Fig. 2. Nuclear modification factors for π − and p measured for 0-10% central Au+Au collisions at √ s N N = 200 GeV at mid-rapidity (left panel) and η = 2.2 (right panel).Error bars represent statistical errors; the systematic errors are indicated by horizontal lines.The dotted and dashed lines indicate the expectations of participant scaling and binary scaling, respectively.The shaded bars represent the systematic errors associated with the determination of these quantities.Systematic errors other than the uncertainties in N bin determinations are estimated to be 20% except for π − at mid-rapidity, where they are around 24%.

Fig. 3 .Figure 3
Fig. 3. p/π − ratios at both mid-rapidity and η = 2.2 for 0-10% central Au+Au collisions at √ s N N = 200 GeV.The error bars show the statistical errors only.The systematic errors are estimated to be less than 12% at both y = 0 and η = 2.2.The corresponding ratios in p + p collisions at √ s N N = 200 GeV are sketched as solid line and dotted line, respectively.