ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
SINGLE-SPIN ASYMMETRY OF INCLUSIVE 7 PRODUCTION IN p}p
INTERACTIONS AT 200 GeV/c
© 2004 Yu. V. Kharlov, D. A. Morozov, S. B. Nurushev, A. N. Vasiliev
Institute for High Energy Physics, Protvino, Russia Received September 17, 2003
From the data of Fermilab polarization experiment E704 the analyzing power AN of inclusively produced photons was extracted. It is small, of the order of 2—4%. The analyzing power of "leading" photons (the fastest in п0 ^ 77 decay) is twice higher than AN assuming a definite model for xF dependence of AN. The Monte Carlo simulation is performed in order to see effects at higher statistics than in E704 experiment. This simulation showed that the process of the inclusive photons may be used as a basis for future polarimetry at polarized colliders. The example of one local photon polarimeter at RHIC is discussed.
INTRODUCTION
The powerfully polarized RHIC becomes available for spin physics study in the highest ever reached beam energy range (50 < yfs < 500 GeV) [1]. One of the important problems in making RHIC as an efficient tool is to build a local polarimeter for measuring the beam polarization at the interaction region. There are several proposals to use for such a goal the inclusive neutral pion polarimeter [2—4]. But space limitation and several other experimental conditions may require a polarimeter placement long away from the interaction point. In this case the inclusive photon production becomes attractive and it was proposed in paper [5]. Due to an absence of experimentaldata on ayn(xf,pT), the authors of [5] used the phe-nomenological model forestimation of AYN(xf,pT). In the present paper we aim to reconstruct AYN(x1F,p'Yr) from the Fermilab polarization experiment E704 [6, 7] making use of experimental data and the Monte Carlo simulation. The consistency of two such approaches is also considered.
This paper is organized in the following way. Section 1 is dedicated to analysis of experimental data in E704 and offers the extracted asymmetries ayn(x1F,p'T). Section 2 describes a simulation procedure by the Monte Carlo technique and presents the estimated values of AYN(xf,pT). In Section 3 one discusses a photon polarimeter in E704 environment at 200 GeV. Section 4 presents the estimates of parameters for one inclusive photon polarimeter which is under test at RHIC [8]. In Conclusion the main results of our study are summarized.
1. EXTRACTION OF AYN(xFp) FROM E704 DATA
In the previous papers [6, 7] the analyzing power for inclusive n0 production AnN (xf,pT) in the reaction
p\ + p ^ n0 + X, (1)
was extracted at 200-GeV/c initial momentum by detecting both photons from n0 decay. In the present paper we have a goal to perform an extraction of the photon analyzing power AYN (xF,pT) in reaction
p\ + p ^ Y + X,
in various conditions.
First of all, one needs to know the analyzing power of all inclusively produced photons. A shower in the calorimeter which is well fitted by the electromagnetic shower shape is accepted as a photon. To select the electromagnetic shower, we follow the criterium developed in [9] (see also [10]). Table 1 contains the reconstructed analyzing power AYN(xf,pT) for such photons at threshold pT = 0.5 GeV/c. Analyzing power is defined as a relative difference of the cross sections with different beam polarization. Figure 1a shows small but nonzero asymmetries of the order of 2—4% at xf = 0.3—0.5. False asymmetry is determined similarly to the analyzing power but the event samples are not correlated with the beam polarization. These uncorrelated samples can be defined in different ways: (i) on the base of the same statistics which was used for AYN (xF,pT) estimates mixing all directions of the beam polarizations, (ii) using the unpolarized beam and (iii) for a whole statistics. All cases give us the value of false asymmetry of the
An, % 10
5
0
-5
-10b
SINGLE-SPIN ASYMMETRY OF INCLUSIVE y PRODUCTION An, % AN, %
10
5 0 -5 -10b
b
P
10
5 0 -5 -10
-ff
1.0 0
Xp
0.5
1.0 0
Xp
0.5
1.0
Xp
Fig. 1. The analyzing power in E704 experiment for (a) all inclusively produced photons, (b) "raw" neutral pions, (c) "leading" photons. The inner error bars are the statistical uncertainties, and the outer error bars are the statistical and systematic uncertainties added in quadrature.
order of 1% in average and it has been added as systematic error in Fig. 1. There is an indication that the inclusively produced photons might have small but nonzero analyzing power AYN. The statistics of E704 is poor for making an unambiguous statement.
Keeping in mind that the reaction (1) has AN much higher than estimated above A1N for inclusively produced photons we decided to restrict sources of photon pairs to the mass region 0.07 < mYY < < 0.2 GeV/c2. Not being able to identify decay photon from n0, we called such source of photon pairs as "raw" n0's. The analyzing power of such "raw" neutral pions is presented in Table 2 and Fig. 1b. The false asymmetries calculated in a similar way as in Fig 1a give 1% values as well. Asymmetry ANN(xF,Pt) in this case is a little bit higher than in Fig. 1a for Ayn(xF,pT) but approximately twice smaller than for true n0. Such a difference can be ex-
plained by an unpolarized combinatorial background which was estimated strictly in [7].
To improve the situation, we selected the leading photons (i.e., the photons with a higher energy) for each n0 decay. The corresponding analyzing powers for "leading" photons are presented in Table 3 and in Fig. 1 c. Again, the systematic errors connected with false asymmetry are of the order of 1%. Analyzing power of leading photons is approximately twice higher than that of inclusive photons (see Tables 1 and 3 in xF intervals 0.2—0.3 and 0.3—0.4).
So somehow our expectation is justified. The conclusions from analysis of E704 data are the following:
the inclusively produced photons have an asymmetry of the order of 2% at xF = 0.35 and about 4% at xF = 0.45;
the leading photons have an analyzing power of the order of 4% at xF = 0.35;
c
Table 1. The analyzing power of reaction pj + p — j + X at 200 GeV/c
Xp AN, %
0.0-0.1 -1.0 ±0.4
0.1-0.2 -0.7 ±0.4
0.2-0.3 0.8 ±0.5
0.3-0.4 2.4 ±0.8
0.4-0.5 4.6 ± 1.7
0.5-0.6 2.9 ± 3.1
0.6-1.0 -4.9 ±4.8
Table 2. The analyzing power of reaction pj + p — — "raw" n0 + X at 200 GeV/c
Xp AN, %
0.0-0.1 —1.6 ± 0.5
0.1-0.2 —1.0 ± 0.4
0.2-0.3 0.3 ±0.4
0.3-0.4 1.1 ± 0.7
0.4-0.5 2.1 ±0.9
0.5-0.6 4.7 ± 1.4
0.6-0.8 7.1 ±2.2
An, %
15
10
AYN (xp) for leading photon at the decay n0
YY
0.2 0.4 0.6
0.8
1.0
Xp
Fig. 2. The asymmetry parameters AN for inclusive n0 production by 200-GeV polarized protons. Points: • — experimental values, à — Monte Carlo results.
the asymmetry of photons is smaller than the asymmetry of n0 (approximately in 2—3 times) but in the case of photons one can work at smaller xp.
The statistics of E704 experiment are scarce for more detailed analysis. For this reason, in the following sections we will describe a Monte Carlo simulation procedure which we made in order to see asymmetries at much higher statistics.
2. SIMULATION OF A SINGLE-SPIN ASYMMETRY BASED ON THE E704 DATA
In E704 experiment the single-spin asymmetry of n0 mesons in the reaction pfp — n°X was studied. We simulated a n0 production with the single-spin asymmetry defined by the experimental measurements [6, 7]. Expecting that the decay photons (from n0 — yy) have nonzero asymmetry, we have analyzed the following dependencies:
Table 3. The analyzing power of reaction p^ + p ing" y + X at 200 GeV/c
"lead-
Xp AN, %
0.0-0.1 -0.9 ±0.4
0.1-0.2 -0.7 ±0.3
0.2-0.3 1.4 ±0.5
0.3-0.4 4.6 ± 1.2
0.4-1.0 0.7 ± 3.1
(it means that xp of this photon is the highest in n0 decay) for every n0 having nonzero asymmetry ("useful" pion [5]),
Ayn (xF) for all photons produced by 'pfp interaction versus cuts in pT: 0.3, 0.4, 0.5, 0.6, and 0.7 GeV/c.
2.1. Event-Generation Algorithm
In E704 experiment the following results for single-spin n0 asymmetry were obtained (see Fig. 2 (circles)) [6].
The following algorithm was built for generation of such events for the reactions p^p — aX at E(p^) = = 200 GeV, where
n
'useful'
Y from "useful"
Y from all sources.
n
(2)
1. Minimum-bias pp events are generated by PYTHIA-5.72 [11]. The decay n0 — yy is forbidden.
2. Assuming that AN(xF) depends on xF linearly (from Fig. 2):
An = b + cx, (3)
the factors b and c are determined: b = —0.082 ± ± 0.032, c = 0.341 ± 0.070 with x2/ndf = 1.76/2.
3. For each generated "useful" n0 meson (in correspondence with Fig. 2) the AN0 (xF) value was assigned according to relation (3). The other n0's have been left in the events without asymmetry.
4. The azimuthal angle of n0 was generated by the following dependence of the n0 yield:
I (xf ,pt ) = I0(xf ,pt )[1 + An (xf,pt )P cos 4>\,
(4)
where I is invariant cross section of n0 production, I0 is the same cross section for unpolarized beam, Pb = 0.456 is beam polarization in E704.
5. All n0 decays are allowed.
After proceeding through this algorithm we have the same set of events as in E704 with only difference that polarization asymmetry (spin | and j) is converted to azimuthal asymmetry (left—right), and we assume zero asymmetry in all other channels of Y production in the p^p interaction.
5
0
0
a
—-
MEPHA^ OH3HKA TOM 67 № 7 2004
x 103 12
x 104
8
x 104 6
ID 100
Entries 1352478
Mean 179.9
RMS 104.9
0.2 0.4 0.6 0.8 1.0
Xf
ID 101
Entries 1352478
Mean 0.5007
RMS 0.1482
Ö, deg
ID 103
Entries 1352478
Mean 0.7456
RMS 0.1366
4
pT, GeV/c
Fig. 3. The distributions of "useful" n0 mesons on (a) the azimuthal angle 0, (b) the polar angle 0, (c) xF, and (d) pr.
2.2. An Approach to Estimate the Asymmetry
The asymmetry of inclusively produced particle a (see (2)) in the interaction of interest was calculated in the following way.
With fixed value of xf the asymmetry AN (pT) is determined f
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