Multiparticle production and initial quasi-temperature from proton induced carbon collisions at p Lab =31 GeV/ c
aa r X i v : . [ h e p - ph ] D ec Multiparticle production and initial quasi-temperature from protoninduced carbon collisions at p Lab = 31
GeV/ c Pei-Pin Yang ∗ , Mai-Ying Duan , † , Fu-Hu Liu , ‡ , Raghunath Sahoo , § Institute of Theoretical Physics and Department of Physics andState Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, Shanxi 030006, China Discipline of Physics, School of Basic Sciences, Indian Institute of Technology Indore, Simrol, Indore 453552, India
Abstract:
The momentum spectra of charged pions ( π + and π − ) and kaons ( K + and K − ), as well as protons( p ), produced in the beam protons induced collisions in a 90-cm-long graphite target [proton-carbon ( p -C) collisions]at the beam momentum p Lab = 31 GeV/ c are studied in the framework of a multisource thermal model by usingBoltzmann distribution and Monte Carlo method. The theoretical model results are approximately in agreementwith the experimental data measured by the NA61/SHINE Collaboration. The related free parameters (effectivetemperature, rapidity shifts, and fraction of non-leading protons) and derived quantities (average transverse mo-mentum and initial quasi-temperature) under given experimental conditions are obtained. It is shown that theconsidered free parameters and derived quantities to be strongly dependent on emission angle over a range from 0to 380 mrad and weakly dependent on longitudinal position (graphite target thickness) over a range from 0 to 90 cm. Keywords:
Momentum spectra, effective temperature, rapidity shift, average transverse momentum, initialquasi-temperature
PACS:
High energy (relativistic) nucleus-nucleus (heavyion) collisions with nearly zero impact parameter (cen-tral collisions) are believed to form Quark-Gluon Plasma(QGP) or quark matter [1, 2, 3] in the laboratory. Highenergy nucleus-nucleus collisions with large impact pa-rameter are not expected to form QGP due to low par-ticle multiplicity yielding lower energy density and tem-perature [4]. Small collision systems such as proton-nucleus and proton-proton collisions at high energy, pro-duce usually low multiplicity, which are not expectedto form QGP, but are useful to study the multiparticleproduction processes. However, a few of proton-nucleusand proton-proton collisions at the LHC energies canproduce high multiplicity due to nearly zero “impactparameter”, which are possibly expected to form QGP,where the concept “impact parameter” or “centrality”used in nuclear collisions are used in proton-proton colli-sions [5]. Degree of collectivity, long-range correlations,strangeness enhancement etc., which are considered asQGP-like signatures, are recently observed in these highmultiplicity events [6, 7, 8].Assuming nucleus-nucleus collisions as a mere super- position of proton-proton collisions in the absence ofany nuclear effects, usually one considers proton-protoncollisions as the baseline measurements. On the otherhand, proton-nucleus collisions [9, 10, 11, 12, 13] serveas studying the initial state effects and making a bridgebetween proton-proton [14, 15, 16, 17, 18] to nucleus-nucleus collisions [19, 20, 21, 22, 23] while studying themultiparticle production processes, though fewer parti-cles are produced in proton-nucleus collisions than innucleus-nucleus collisions.There are different types of models or theories be-ing introduced in the studies of high energy colli-sions [24, 25]. Among these models or theories, differentversions of thermal and statistical models [26, 27, 28, 29]characterize some of the aspects of high-energy nuclearcollisions, while there are many other aspects that arestudied by other approaches. As a basic concept, tem-perature is ineluctable to be used in analyses. In fact,not only the “temperature is surely one of the cen-tral concepts in thermodynamics and statistical me-chanics” [30], but also it is very important due to itsextremely wide applications in experimental measure-ments and theoretical studies in subatomic physics, es- ∗ E-mail: [email protected] † E-mail: [email protected] ‡ Corresponding author. E-mail: [email protected]; [email protected] § E-mail: [email protected]; [email protected] p -C) collisions] at thebeam momentum p Lab = 31 GeV/ c measured by theNA61/SHINE Collaboration [32] at the Super ProtonSynchrotron (SPS), the European Organisation for Nu-clear Research or the European Laboratory for ParticlePhysics (CERN).The remainder of this paper is structured as follows.The formalism and method are shortly described in Sec-tion 2. Results and discussion are given in Section 3.In Section 4, we summarize our main observations andconclusions. According to the multisource thermal model [31], itis assumed that there are many local emission sources tobe formed in high energy collisions due to different ex-citation degrees, rapidity shifts, reaction mechanisms,impact parameters (or centralities). In the transverseplane, the local emission sources with the same excita-tion degree form a (large) emission source. In the ra-pidity space, the local emission sources with the samerapidity shift form a (large) emission source. In therest frame of an emission source with a determined ex-citation degree, the particles are assumed to be emittedisotropically.In the rest frame of a given emission source, let T denote the temperature parameter. The particles withrest mass m produced in the rest frame of the emissionsource are assumed to have the simplest Boltzmann dis-tribution of momenta p ′ [33]. That is f p ′ ( p ′ ) = Cp ′ exp − p p ′ + m T ! , (1)where C is the normalization constant which is relatedto T . As a probability density function, Eq. (1) is nat-urally normalized to 1.If we need to consider multiple sources, we can use asuperposition of different equations with different tem-peratures and fractions. We have f p ′ ( p ′ ) = X j k j C j p ′ exp − p p ′ + m T j ! , (2) where k j , C j , and T j are the fraction, normalizationconstant, and temperature for the j -th source or compo-nent. The average temperature obtained from Eq. (2)is T = P j k j T j / P j k j = P j k j T j due to P j k j = 1.The derived parameter T is the weighted average overvarious components, but not the simple weighted sum.It should be noted that T or T j is not the “real”temperature of the emission source, but the effectivetemperature due to the fact that the flow effect is notexcluded in the momentum spectrum. The “real” tem-perature is generally smaller than the effective temper-ature which contains the contribution of collective ra-dial flow effect. To disengage the thermal motion andcollective flow effect, one may use different methodssuch as the blast-wave model [34, 35] or any alterna-tive method [36, 37]. As an example, we shall discussshortly the results of the blast-wave model in section 3.The contribution of spin being small, is not includedin Eq. (1). The effect of chemical potential ( µ ) isnot included in Eq. (1) as well, due to the fact that µ affects only the normalization, but not the trend, ofthe spectrum if the spin effect is neglected. Our previ-ous work [38] shows that the spin effect together with µ ≫ m or µ ≪ m is so small ( < µ ≈ m causes an obviouseffect, which is not the case in this paper.In the Monte Carlo method [39, 40], let R , , , de-note random numbers distributed evenly in [0 , p ′ which satisfies Eq. (1) orone of the components in Eq. (2), we can perform thesolution of Z p ′ f p ′ ( p ′′ ) dp ′′ < R < Z p ′ + δp ′ f p ′ ( p ′′ ) dp ′′ , (3)where δp ′ denotes a small shift relative to p ′ .Under the assumption of isotropic emission in therest frame of emission source, the emission angle θ ′ ofthe considered particle has the probability density func-tion: f θ ′ ( θ ′ ) = 12 sin θ ′ (4)which is a half sine distribution in [0 , π ], and the azimuth φ ′ obeys the probability density function f φ ′ ( φ ′ ) =1 / (2 π ) which is an even distribution in [0 , π ] [41]. Inthe Monte Carlo method, θ ′ satisfies θ ′ = 2 arcsin (cid:16)p R (cid:17) (5)which is the solution of R θ ′ (1 /
2) sin θ ′′ dθ ′′ = R .2onsidering p ′ and θ ′ obtained from Eqs. (3) and(5), we have the transverse momentum p ′ T to be p ′ T = p ′ sin θ ′ , (6)the longitudinal momentum p ′ z to be p ′ z = p ′ cos θ ′ , (7)the energy E ′ to be E ′ = q p ′ + m , (8)and the rapidity y ′ to be y ′ ≡
12 ln (cid:18) E ′ + p ′ z E ′ − p ′ z (cid:19) . (9)In the center-of-mass reference frame or the labo-ratory reference frame, the rapidity of the consideredemission source is assumed to be y x in the rapidityspace. Then, the rapidity of the considered particle inthe center-of-mass or laboratory reference frame is y = y ′ + y x (10)due to the additivity of rapidity. Multiple emissionsources are assumed to distribute evenly in the rapid-ity range [ y min , y max ], where y min and y max are theminimum and maximum rapidity shifts of the multiplesources. In the Monte Carlo method, y x = ( y max − y min ) R + y min . (11)In particular, comparing with small mass particles,protons exhibit large effect of leading particles whichare assumed to distribute evenly in the rapidity range[ y L min , y L max ], where y L min and y L max are the mini-mum and maximum rapidity shifts of the leading pro-tons. We have y x = ( y L max − y L min ) R + y L min . (12)The fraction of the non-leading (leading) protons in to-tal protons is assumed to be k (1 − k ). The effects ofleading pions and kaons are small and can be neglectedin this paper.In the center-of-mass or laboratory reference frame,the transverse momentum p T is p T = p ′ T , (13)the longitudinal momentum p z is p z = q p T + m sinh y, (14) the momentum p is p = q p T + p z , (15)and the emission angle θ is θ = arctan (cid:18) p T p z (cid:19) . (16)The whole calculation is performed by the MonteCarlo method, though only random numbers are usedfor the numerical calculation. To compare the theo-retical model results with the experimental momentumspectra in a given θ range, we analyze the momentumdistribution of particles which are in the given θ range.It should be noted that another experimental selection,i.e. the longitudinal position z [32], is not regarded asthe selected condition in the theoretical model work dueto the fact that z is only a reflection of target thicknessin a 90-cm-long graphite target. From z = 0 to z = 90cm, the beam momentum slightly decreases, which is ne-glected in this paper. In the calculation using randomnumbers, the energy-momentum conservation was de-manded at each step. The results violating the energy-momentum conservation are not considered for our dis-cussions.It should be noticed that the Boltzmann distribu-tion, Eq. (1), can be used to describe low momentumspectra in the source’s rest frame or low transverse mo-mentum spectra after analytic derivation [41] or viathe Monte Carlo method, Eqs. (3), (5), and (6). Inthe case of considering high momentum spectra in thesource’s rest frame or high transverse momentum spec-tra, one may use possibly the multi-component Boltz-mann distribution, Eq. (2). This paper treats multiplesources moving directly in a rapidity range, [ y min , y max ]or [ y L min , y L max ], which results in high momentum inlaboratory reference frame. However, in the rest frameof each source, the total momentum and transverse mo-mentum are small. As a consequence, Eq. (1) is validin all momentum range, after the transformation fromsource’s rest frame to laboratory reference frame. Figures 1 and 2 present the momentum spectra,(1 /N pot ) d n/dpdθ , of charged pions ( π + and π − ) pro-duced in p -C collisions at 31 GeV/ c in the laboratory ref-erence frame respectively, where N pot denotes the num-ber of protons on target and n denotes the number ofparticles. Panels (a)–(c), (d)–(f), (g)–(i), (j)–(l), (m)–(o), and (p)–(q) represent the spectra for z = 0–18, 18–36, 36–54, 54–72, 72–90, and 90 cm, respectively. Forclarity, spectra in different θ ranges are scaled by adding3 z=0 −
18 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (a) π + z=0 −
18 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (b) z=0 −
18 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (c) z=18 −
36 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (d) z=18 −
36 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (e) z=18 −
36 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (f) z=36 −
54 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (g) ((r ad * G e V / c ) − ) . z=36 −
54 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (h) z=36 −
54 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (i) z=54 −
72 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (j) . ( / N po t ) d n / dpd θ z=54 −
72 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (k) z=54 −
72 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (l) z=72 −
90 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (m) z=72 −
90 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (n) z=72 −
90 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (o) z=90 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (p) z=90 cm θ (mrad) −
140 +0.5 −
180 +0.6 −
220 +0.7 −
260 +0.8 −
300 +0.9 (q) p (GeV/c)
Fig. 1. Momentum spectra of π + produced in p -C collisions at 31 GeV/ c . Panels (a)–(c), (d)–(f), (g)–(i), (j)–(l), (m)–(o),and (p)–(q) represent the spectra for z = 0–18, 18–36, 36–54, 54–72, 72–90, and 90 cm, respectively. The symbols representthe experimental data [32]. The curves are our results fitted by the multisource thermal model due to Eq. (1) and MonteCarlo method. To show clearly, different spectra are scaled by adding different amounts marked in the panels. z=0 −
18 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (a) π − z=0 −
18 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (b) z=0 −
18 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (c) z=18 −
36 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (d) z=18 −
36 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (e) z=18 −
36 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (f) z=36 −
54 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (g) ((r ad * G e V / c ) − ) . z=36 −
54 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (h) z=36 −
54 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (i) z=54 −
72 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (j) . ( / N po t ) d n / dpd θ z=54 −
72 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (k) z=54 −
72 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (l) z=72 −
90 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (m) z=72 −
90 cm θ (mrad) −
120 +0.5 −
140 +0.6 −
160 +0.7 −
180 +0.8 −
200 +0.9 (n) z=72 −
90 cm θ (mrad) −
220 +1.0 −
260 +1.1 −
300 +1.2 −
340 +1.3 −
380 +1.4 (o) z=90 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
80 +0.3 −
100 +0.4 (p) z=90 cm θ (mrad) −
140 +0.5 −
180 +0.6 −
220 +0.7 −
260 +0.8 −
300 +0.9 (q) p (GeV/c)
Fig. 2. Same as Fig. 1, but showing the spectra of π − . (a) θ =20 −
40 mrad π + z (cm) −
18 +0.0 −
36 +0.025 −
54 +0.05 −
72 +0.075 −
90 +0.1
90 +0.125 ((r ad * G e V / c ) − ) . (b) θ =100 −
140 mrad π + z (cm) −
18 +0.05 −
36 +0.125 −
54 +0.1 −
72 +0.075 −
90 +0.025
90 +0.0 (c) θ =20 −
40 mrad π − z (cm) −
18 +0.0 −
36 +0.025 −
54 +0.05 −
72 +0.075 −
90 +0.1
90 +0.125 p (Ge ( / N po t ) d n / dpd θ (d) θ =100 −
140 mrad π − z (cm) −
18 +0.05 −
36 +0.125 −
54 +0.1 −
72 +0.075 −
90 +0.025
90 +0.0
V/c) . Fig. 3. Same as Fig. 1, but showing the spectra of (a)–(b) π + and (c)–(d) π − in (a)–(c) θ =20–40 mrad and (b)–(d) θ =100–140 mrad in six z ranges. different numbers (marked in the panels) are representedby different symbols, which are the experimental datameasured by the NA61/SHINE Collaboration [32]. Thecurves are our results fitted by the multisource thermalmodel using to Eq. (1) and Monte Carlo method. Thevalues of free parameters ( T , y max and y min ), normaliza-tion constant ( N ), χ , and number of degree of freedom(ndof) corresponding to the fits for the spectra of π + and π − are listed in Tables A1 and A2 in the appendix,respectively. In two cases, ndof in the fittings are nega-tive which appear in the tables with “ − ” signs and thecorresponding curves are for eye guiding only. One cansee that the theoretical model results are approximatelyin agreement with the NA61/SHINE experimental dataof π + and π − .Figure 3 presents the momentum spectra of (a)–(b) π + and (c)–(d) π − in (a)–(c) θ = 20–40 mrad and (b)–(d) θ = 100–140 mrad in six z ranges with differentscaled amounts shown in the panels. The symbols rep-resent the experimental data [32]. The curves are ourresults fitted by the model. The values of T , y max , y min , N , χ , and ndof corresponding to the fits for the spec-tra of π + and π − are listed in Table A3 in the appendix.One can see again that the theoretical model results areapproximately in agreement with the experimental dataof π + and π − .Similar to Figs. 1 and 2, Figs. 4 and 5 show themomentum spectra of positively and negatively chargedkaons ( K + and K − ) produced in p -C collisions at 31GeV/ c respectively. Panels (a), (b), (c), (d), (e), and(f) represent the spectra for z = 0–18, 18–36, 36–54,54–72, 72–90, and 90 cm, respectively. The values of T , y max , y min , N , χ , and ndof corresponding to thefits for the spectra of K + and K − are listed in TablesA4 and A5 respectively in the appendix. One can seethat the theoretical model results are approximately inagreement with the experimental data of K + and K − .Similar to Fig. 1, Fig. 6 shows the momentum spec-tra of p emitted in p -C collisions at 31 GeV/ c . Pan-els (a)–(b), (c)–(d), (e)–(f), (g)–(h), (i)–(j), and (k)–(l)represent the spectra for z = 0–18, 18–36, 36–54, 54–72, 72–90, and 90 cm, respectively. The values of T , k ,6 z=0 −
18 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (a) Κ + ((r ad * G e V / c ) − ) . z=18 −
36 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (b) z=36 −
54 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (c) z=54 −
72 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (d) . ( / N po t ) d n / dpd θ z=72 −
90 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (e) p (GeV/c) z=90 cm θ (mrad) −
60 +0.0 −
120 +0.025 (f)
Fig. 4. Same as Fig. 1, but showing the spectra of K + . Panels (a), (b), (c), (d), (e), and (f) represent the spectra for z = 0–18, 18–36, 36–54, 54–72, 72–90, and 90 cm, respectively. z=0 −
18 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (a) Κ − ((r ad * G e V / c ) − ) . z=18 −
36 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (b) z=36 −
54 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (c) z=54 −
72 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (d) . ( / N po t ) d n / dpd θ z=72 −
90 cm θ (mrad) −
60 +0.0 −
120 +0.05 −
180 +0.1 −
280 +0.15 (e) p (GeV/c) z=90 cm θ (mrad) −
60 +0.0 −
120 +0.025 (f)
Fig. 5. Same as Fig. 1, but showing the spectra of K − . Panels (a), (b), (c), (d), (e), and (f) represent the spectra for z = 0–18, 18–36, 36–54, 54–72, 72–90, and 90 cm, respectively. y max , y min , y L max , y L min , N , χ , and ndof correspond-ing to the fits for the spectra are listed in Table A6 in the appendix. In a few cases, ndof are negative whichappear in the table in terms of “ − ” and the correspond-7 z=0 −
18 cm θ (mrad) −
20 +0.0 −
40 +0.05 −
60 +0.1 −
100 +0.15 −
140 +0.2 (a) p z=0 −
18 cm θ (mrad) −
180 +0.3 −
220 +0.4 −
260 +0.5 −
300 +0.6 −
380 +0.7 (b) z=18 −
36 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
100 +0.3 −
140 +0.4 (c) z=18 −
36 cm θ (mrad) −
180 +0.5 −
220 +0.6 −
260 +0.7 −
300 +0.8 −
380 +0.9 (d) ((r ad * G e V / c ) − ) . z=36 −
54 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
100 +0.3 −
140 +0.4 (e) z=36 −
54 cm θ (mrad) −
180 +0.5 −
220 +0.6 −
260 +0.7 −
300 +0.8 −
380 +0.9 (f) z=54 −
72 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
100 +0.3 −
140 +0.4 (g) . ( / N po t ) d n / dpd θ z=54 −
72 cm θ (mrad) −
180 +0.5 −
220 +0.6 −
260 +0.7 −
300 +0.8 −
380 +0.9 (h) z=72 −
90 cm θ (mrad) −
20 +0.0 −
40 +0.1 −
60 +0.2 −
100 +0.3 −
140 +0.4 (i) z=72 −
90 cm θ (mrad) −
180 +0.5 −
220 +0.6 −
260 +0.7 −
300 +0.8 −
380 +0.9 (j) z=90 cm θ (mrad) −
20 +0.0 −
40 +0.15 −
60 +0.25 −
100 +0.35 (k) p (GeV/c) z=90 cm (l) θ (mrad) −
140 +0.4 −
180 +0.45 −
220 +0.5
Fig. 6. Same as Fig. 1, but showing the spectra of p . Panels (a)–(b), (c)–(d), (e)–(f), (g)–(h), (i)–(j), and (k)–(l) representthe spectra for z = 0–18, 18–36, 36–54, 54–72, 72–90, and 90 cm, respectively. ing curves are just for eye guiding only. It should benoted that the contributions of leading protons have tobe considered in the spectra. One can see that the the-oretical model results are approximately in agreementwith the experimental data.We notice from Tables A1–A6 that different T fora range of z and its dependence with θ or y are ob-served, but the development of the model in our previ- ous work [42] concludes that T is independent of y . Wewould like to explain here that this paper treats T asdifferential function of θ or y , which is more detailed.While, our previous work treats T as integral or meanquantity over y . As for which case should be used, itdepends on experimental data.We now analyze the dependences of free parameterson θ and z . Figures 7 and 8 show respectively the depen-8 .10.20.30.40 100 200 300 400 z (cm) − − − − − (a) π + T ( G e V ) z (cm) − − − − − (b) π − z (cm) − − − − − (c) K + z (cm) − − − − − (d) K − z (cm) − − − − − (e) p θ (mrad), z (cm) θ (mrad) π + − − π − − − (f) Fig. 7. Dependence of T on (a)–(e) θ , which are extracted from the data samples within different z ranges for π + , π − , K + , K − , and p respectively, and on (f) z , which are extracted from the data samples within different θ ranges for π + and π − . z (cm) − − − − − (a) π + ∆ y z (cm) − − − − − (b) π − z (cm) − − − − − (c) K + z (cm) − − − − − (d) K − z (cm) − − − − − (e) p θ (mrad), z (cm) θ (mrad) π + − − π − − − (f) Fig. 8. Same as Fig. 7, but showing the dependence of ∆ y . Large ∆ y (= y L max − y L min >
1) in panel (e) represent mainlythe rapidity shifts for leading protons. dences of T and ∆ y (= y max − y min ) on (a)–(e) θ , whichare extracted from the data samples within different z ranges for π + , π − , K + , K − , and p respectively, and on(f) z , which are extracted from the data samples within different θ ranges for π + and π − , where we use ∆ y todenote the difference between y max and y min to avoidtrivialness in using both y max and y min . In particular,in Fig. 8(e), the results with ∆ y > .10.20.30.40 25 50 75 100 (a) π + T ( G e V ) π − (b) K + (c) K − (d) p (e) z (cm) θ (mrad)(a)(b): (c)(d): − − − − − − − − − (e): − − − − − − − − − − − − − − − − − − − − Fig. 9. Dependence of T on z , which are extracted from the data samples within different θ ranges for (a) π + , (b) π − , (c) K + , (d) K − , and (e) p . (a) π + ∆ y π − (b) K + (c) K − (d) p (e) z (cm) θ (mrad)(a)(b): (c)(d): − − − − − − − − − (e): − − − − − − − − − − − − − − − − − − − − Fig. 10. Same as Fig. 9, but showing the dependence of ∆ y . Large ∆ y (= y L max − y L min >
1) in panel (e) represent mainlythe rapidity shifts for leading protons. ing protons and obtained by y L max − y L min . One can seethat, for π ± and K ± , T and ∆ y decrease slightly withthe increase of θ , and do not change obviously with theincrease of z . The obtained T (∆ y ) values for negative and positive pions or kaons seem to be very similar aswe expect. The data for antiproton ( p ) are not availablein ref. [32], which forbids in making a comparison for p and p in this paper. In fact, the situation for p is more10 .30.40.50.60.70.80.90 100 200 300 400 z (cm) − − − − − p (a) θ (mrad) k θ (mrad) − − − − − − − − − − p (b) z (cm) k Fig. 11. Dependences of k on (a) θ and (b) z , which are extracted from the data samples within different z and θ ranges,respectively. z (cm) − − − − − (a) π + < p T > ( G e V / c ) z (cm) − − − − − (b) π − z (cm) − − − − − (c) K + z (cm) − − − − − (d) K − z (cm) − − − − − (e) p θ (mrad), z (cm) θ (mrad) π + − − π − − − (f) Fig. 12. Dependence of h p T i on (a)–(e) θ , which are extracted from the data samples within different z ranges for π + , π − , K + , K − , and p respectively, and on (f) z , which are extracted from the data samples within different θ ranges for π + and π − . complex due to the effect of leading protons.The dependences of T and ∆ y on θ for the produc-tions of π ± and K ± can be explained by the effect of cas-cade collisions in the target and by the nuclear stoppingof the target. The cascade collisions can cause larger θ and more energy loss and then lower T . The nuclear stopping can cause smaller ∆ y . Combining with cas-cade collisions and nuclear stopping, one can obtain low T and small ∆ y at large θ for the productions of π ± and K ± . Because of the effect of leading particles, the situa-tion for the emissions of p is more complex, which showsdifferent trends from those of π ± and K ± . Meanwhile,11 .20.40.60 100 200 300 400 z (cm) − − − − − (a) π + T i ( G e V / c ) z (cm) − − − − − (b) π − z (cm) − − − − − (c) K + z (cm) − − − − − (d) K − z (cm) − − − − − (e) p θ (mrad), z (cm) θ (mrad) π + − − π − − − (f) Fig. 13. Same as Fig. 12, but showing the dependence of T i . (a) π + < p T > ( G e V / c ) π − (b) K + (c) K − (d) p (e) z (cm) θ (mrad)(a)(b): (c)(d): − − − − − − − − − (e): − − − − − − − − − − − − − − − − − − − − Fig. 14. Dependence of h p T i on z , which are extracted from the data samples within different θ ranges for (a) π + , (b) π − ,(c) K + , (d) K − , and (e) p . the flow effect can cause larger T , which is related tomore complex mechanism. The dependences of T and ∆ y on z , which are ex-tracted from the data samples within different θ ranges12 .10.20.30.40 25 50 75 100 (a) π + T i ( G e V ) π − (b) K + (c) K − (d) p (e) z (cm) θ (mrad)(a)(b): (c)(d): − − − − − − − − − (e): − − − − − − − − − − − − − − − − − − − − Fig. 15. Same as Fig. 14, but showing the dependence of T i . β T (c) T ( G e V ) π + K + p Fig. 16. Relation between T and β T from the blast-wave model. The symbols represent the results from the spectra ofpositive particles. for (a) π + , (b) π − , (c) K + , (d) K − , and (e) p , are givenin Figs. 9 and 10 respectively. In particular, large ∆ y (= y L max − y L min >
1) in Fig. 10(e) represent mainlythe rapidity shifts of leading protons. In principle, thereis no obvious increase or decrease in T and ∆ y with theincrease of z , but some statistical fluctuations in fewcases. This result is natural due to the fact that z isnot the main factor in a 90-cm-long graphite target. Itis expected that T and ∆ y will decrease with the in-crease of z in a very long graphite target in which theenergy loss of the beam protons has to be considered. The NA61/SHINE experimental data analyzed in thispaper are not obtained from a long graphite target andhence it is not necessary to consider the energy loss ofthe beam protons.Figure 11 displays the dependences of fraction k ofnon-leading protons on (a) θ and (b) z , which are ex-tracted from the data samples within different z and θ ranges, respectively. One can see that there is no ob-vious change in the dependence of k on θ , but somestatistical fluctuations. There is a slight increase in thedependence of k on z with the increase of z , which can13e explained by more energy loss of the beam protonsat larger z . This energy loss is small in a not too large z range, which does not affect obviously other free param-eters such as T and ∆ y due to their less sensitivity atthe energy in the z range considered in this paper. It isnatural that the larger (fewer) fraction k (1 − k ) of pro-tons appears as non-leading (leading) particles at lowerenergy or larger z . Indeed, the fraction is mainly deter-mined by the collision energy, and the leading protonsare considerable at the SPS. In fact, the leading protonsare those existed in the projectile with high momentumand small emission angle, but not the produced protons.With the increase of collision energy up to dozens ofGeV and above at which meson-dominated final statesappear [43], k will increase due to the increase of accom-panied produced protons. With the decrease of collisionenergy down to several GeV and below at which baryon-dominated final states appear [43], k will also increasedue to the increase of target stopping which causes thedecrease of leading protons.Figures 12 and 13 show respectively the dependencesof average p T ( h p T i ) and T i on (a)–(e) θ , which are ex-tracted from the data samples within different z rangesfor π + , π − , K + , K − , and p respectively, and on (f) z ,which are extracted from the data samples within dif-ferent θ ranges for π + and π − , where T i denotes theinitial quasi-temperature which is given by the root-mean-square p T ( p h p T i ) over √ p h p T i /
2) accordingto the color string percolation model [44, 45, 46]. Itshould be noted that p h p T i / p h p T i / h p T i and T i on z are presented in Figs. 14 and 15respectively, which are extracted from the data sampleswithin different θ ranges. One can see that, for pionsand kaons, there are increases in h p T i and T i when θ increases. The situation is complex for protons due tothe effect of leading protons which have high momentaand result in high h p T i and T i at small θ . The producedprotons which are non-leading should have similar trendin h p T i and T i as those for pions and kaons. As a com-bination, the final protons are the sum of leading andproduced protons. There is no obvious change in h p T i and T i when z increases due to not too large energy lossin a 90-cm-long graphite target.We would like to point out that there are dif-ferent definitions [47] for leading particles in exper-iments. There are at least four production mecha-nisms [48, 49] for leading protons in electron induceddeep-inelastic scattering on proton. Among these mech- anisms, at HERA energy, diffractive deep-inelastic scat-tering [50, 51] in which 72% of leading protons havemomentum being larger than 0.9 p Lab occupy about26% [48] of leading protons, which are not enough tocover all leading protons. In particular, for leadingprotons with momenta being (0.5–0.98) p Lab , a largefraction (77%) comes from non-diffractive deep-inelasticscatterings. In proton-proton and proton-nucleus colli-sions at the considered energy of this paper, the frac-tion of diffractive process is about 20% [52] in inelasticevents, which is only a half of the fraction of leadingprotons. Even in nucleus-nucleus collisions, the effect ofleading protons in forward rapidity region is also obvi-ous [42, 53, 54, 55], which also reflects in high momen-tum region and is not only from diffractive process.Naturally, there are other additional arguments toexplain the behavior of Figs. 12 and 13 for the protoncase. In fact, there are multiple or cascade secondaryscatterings among produced particles and target nucle-ons. As low mass particles, the emission angles of pionsand kaons increase obviously after multiple scatterings.This results in large h p T i and T i due to large θ for pi-ons and kaons. Contrary to this, the emission angles ofprotons increase in smaller amount after multiple scat-terings due to higher mass of protons compared to pionsand kaons. This results in small h p T i and T i due to small θ for protons. However, non-negligible leading protonswhich have high momenta and smaller angles do not ex-perience much multiple scatterings, which renders large h p T i and T i at small θ . As a competitive result, protonspresent different case from pions and kaons.One can see naturally the coincident trend for h p T i and T i in different θ and z ranges. Due to the flow ef-fect not being excluded, the trend of T is inconsistentwith that of T i . As an all-around result, the effects oftransverse and longitudinal flows are complex. The floweffect can obviously affect T , which is model dependent.The flow effect also affects h p T i and T i which are alsomodel dependent. Therefore, we mention here that T is not a “real” temperature, but the effective tempera-ture. In our opinion, the temperature and flow velocityshould be independent of models, which is usually notthe case more often, as some formalisms are used to ex-tract the radial flow and the real/thermal temperature,which estimate the real temperature of the system beingdependent of models.The experimental data cannot be clearly distin-guished into two parts: One part is the contribution ofthermal motion, which reflects the “real” temperatureat the kinetic freeze-out. The other part is the contri-bution of the collective flow. The current blast-wavemodel [34, 35] treats the thermal motion and flow effectby using the kinetic freeze-out temperature and trans-14erse flow velocity, respectively. After fitting the spectrawith ndof > p T coverage as widely as pos-sible ( p T = 0–3 GeV/ c ), our study using the blast-wavemodel with flow profile parameter being 2 can obtainsimilar fit results as the curves in Figs. 1–6. To pro-trude the fit results of thermal model, the fit resultsof blast-wave model are not displayed in these figures.The relation between T and β T for different cases fromthe spectra of positive particles are plotted in Fig. 16,where the circles, squares, and triangles represent theresults from π + , K + , and p spectra, respectively. Onecan see considerable flow-like effect in p -C collisions at31 GeV/ c , which shows a positive correlation between T and β T . The kinetic freeze-out temperature T is aboutfrom 0.080 to 0.135 GeV. The corresponding transverseflow velocity β T is about from 0 .
21 to 0 . c . Massiveparticles such as p correspond to larger T and smaller β T comparing to π + at the same or similar θ , which is inagreement with hydrodynamic type behavior. The flow-like effect observed in this work is slightly less than theflow velocity (0 . c in peripheral and 0 . c in central gold-gold collisions) obtained from the yield ratio of p/π in asimple afterburner model [56]. The difference is due tothe fact that lower energy small system with minimum-bias sample is studied in this paper. In some cases, theresults on kinetic freeze-out temperature or transverseflow velocity obtained from different models are not al-ways harmonious [36, 37].It should be noted that there is entanglement in de-termining T and β T . For a give p T spectrum, T and β T are negatively correlated, which means an increasein T should result in a decrease of β T . But for a setof p T spectra, after determining T and β T for each p T spectrum, the correlation between T and β T is possi-bly positive or negative, which depends on the choicesof flow profile function and p T coverage. If the correla-tion is negative, one may increase T and decrease β T by changing the flow profile function and p T coverage,and obtain possibly positive correlation. If the correla-tion is positive, one may decrease T and increase β T bychanging the flow profile function and p T coverage, andobtain possibly negative correlation. Unlike experimen-tal papers, where one finds a single T and a common β T by fitting the blast-wave model to the bulk part of the p T spectra (in a very narrow coverage which is particledependent and much less than 3 GeV/ c ) by performinga simultaneous fitting to the identified particle spectrausing a changeable n (from 0 to 4.3) [57], here we haveconsidered a differential freeze-out scenario and have re-stricted uniformly the fitting up to 3 GeV/ c for differentparticles and have used always n = 2. The value of T ( β T ) in positive correlation is larger (less) than that innegative correlation. Positive correlation means high ex- citation and quick expansion, while negative correlationmeans longer lifetime (lower excitation) and quicker ex-pansion. In our opinion, although both positive and neg-ative correlations are available, one needs other methodto check which one is suitable. In fact, positive corre-lation in Fig. 16 is in agreement with the alternativemethod used in our previous works [36, 37].We would rather like to use h p T i directly in the de-termination of kinetic freeze-out temperature and trans-verse flow velocity. For example, the contribution of oneparticipant in each binary collision in the Erlang distri-bution is h p T i / k . Then, the kinetic freeze-out temperature is k h p T i /
2, and the transverse flowvelocity is (1 − k ) h p T i / m γ , where γ is the meanLorentz factor of the considered particles in the restframe of emission source. If we take k ≈ . θ , the obtained kinetic freeze-out temperature(0.05 GeV for pion emission and 0.10 GeV for protonemission) are in agreement with those from the blast-wave model [34, 35], and transverse flow velocity (0 . c for pion emission and 0 . c for proton emission) are qual-itatively in agreement with those from the blast-wavemodel [34, 35] and the afterburner model [50]. Thetreatment of h p T i / h p T i / T and β T , whichshows positive correlation between T and β T . The pos-itive correlation in Fig. 16 is also in agreement with thetreatment of h p T i / χ /ndof, making the description unphysical,though the corresponding curves could be used as eyeguiding only. We summarize here our main observations and con-clusions.15a) The momentum spectra of π + , π − , K + , K − ,and p produced in p -C collisions at 31 GeV/ c are an-alyzed in the framework of multisource thermal modelby using the Boltzmann distribution and Monte Carlomethod. The results are approximately in agreementwith the experimental data in various emission angle, θ ,ranges and longitudinal positions, z , measured by theNA61/SHINE Collaboration at the SPS.(b) The effective temperature T and rapidity shifts∆ y from the spectra under given experimental condi-tions which limit various θ and z ranges are obtained.For π ± and K ± , T and ∆ y decrease slightly with theincrease of θ , and do not change obviously with the in-crease of z . The situation for p is more complex due tothe effect of leading protons. There is no obvious changein T and ∆ y when z increases due to not too large en-ergy loss in a not too long graphite target. Both T and∆ y depend on models. In particular, T contains thecontribution of flow effect, which is not ideal to describethe excitation degree of emission source.(c) The fraction k (1 − k ) of non-leading (leading)protons in total protons from the spectra in various θ and z ranges are obtained. There is no obvious changein the dependence of k (1 − k ) on θ , but some statisti-cal fluctuations. There is a slight increase (decrease) inthe dependence of k (1 − k ) on z with the increase of z due to more energy loss of the beam protons in thetarget at larger z . The effect of leading protons cannotbe neglected at the SPS energies. It is expected that k (1 − k ) will be larger (smaller) at both lower ( ≤ severalGeV) and higher energies ( ≥ dozens of GeV).(d) The average transverse momentum h p T i and ini-tial quasi-temperature T i from the spectra in various θ and z ranges are obtained. For π ± and K ± , there areincreases in h p T i and T i when θ increases. The situa-tion for p is complex due to the effect of leading protons.There is no obvious change in h p T i and T i when z in-creases due to not too large energy loss in a not too longgraphite target. Both h p T i and T i are model dependentdue to the fact that they are obtained from the modelwhich fits the data.(e) The behaviors of effective temperature, rapidityshifts, fraction of non-leading (leading) protons, averagetransverse momentum, and initial quasi-temperatureobtained from the fits of multisource thermal model tothe NA61/SHINE data can be explained in terms ofcascade collisions in the target, stopping power of thetarget, energy loss of the beam protons in the target,and so on. This paper provides a new evidence for theeffectiveness of the multisource thermal model, thoughthere is no connection with a possible formation of aQuark-Gluon Plasma due to small system being consid-ered. Data Availability
The data used to support the findings of this studyare included within the article and are cited at relevantplaces within the text as references.
Compliance with Ethical Standards
The authors declare that they are in compliance withethical standards regarding the content of this paper.
Conflict of Interest
The authors declare that there are no conflicts ofinterest regarding the publication of this paper.
Acknowledgments
Communications from Debasish Das are highly ac-knowledged. Authors P.P.Y., M.Y.D., and F.H.L. ac-knowledge the financial supports from the NationalNatural Science Foundation of China under GrantNos. 11575103 and 11847311, the Shanxi ProvincialInnovative Foundation for Graduate Education GrantNo. 2019SY053, the Scientific and Technological In-novation Programs of Higher Education Institutions inShanxi (STIP) under Grant No. 201802017, the ShanxiProvincial Natural Science Foundation under GrantNo. 201701D121005, and the Fund for Shanxi “1331Project” Key Subjects Construction. Author R.S. ac-knowledges the financial supports from ALICE ProjectNo. SR/MF/PS-01/2014-IITI(G) of Department of Sci-ence & Technology, Government of India. The fundingagencies have no role in the design of the study; in thecollection, analysis, or interpretation of the data; in thewriting of the manuscript, or in the decision to publishthe results.
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Advances in High Energy Physics , vol. 2016,Article ID 4149352, 2016. ppendix: The tables for parameters Table A1. Values of T , y max , y min , N , χ , and ndof corresponding to the curves in Fig. 1 in which different data are measured in different θ and z ranges. In the table, z is in the units of cm, and θ is not listed, which appears in Fig. 1. In one case, ndof is negative which appears interms of “ − ” and the corresponding curve is just for eye guiding purpose. Figure T (GeV) y max y min N × . χ . ± .
005 2 . ± .
02 1 . ± .
02 0 . ± .
010 22/2Fig. 1(a) 0 . ± .
004 3 . ± .
05 1 . ± .
06 0 . ± .
020 42/120 ≤ z<
18 0 . ± .
006 2 . ± .
04 1 . ± .
03 2 . ± .
100 93/120 . ± .
003 2 . ± .
04 1 . ± .
03 6 . ± .
200 87/90 . ± .
005 2 . ± .
04 1 . ± .
03 11 . ± .
400 85/90 . ± .
004 2 . ± .
03 0 . ± .
04 14 . ± .
300 60/9Fig. 1(b) 0 . ± .
003 2 . ± .
04 0 . ± .
02 16 . ± .
340 15/90 ≤ z<
18 0 . ± .
003 2 . ± .
03 0 . ± .
02 17 . ± .
260 16/60 . ± .
002 2 . ± .
03 0 . ± .
03 19 . ± .
300 37/60 . ± .
002 1 . ± .
02 0 . ± .
02 18 . ± .
340 57/60 . ± .
001 1 . ± .
02 0 . ± .
02 17 . ± .
200 70/6Fig. 1(c) 0 . ± .
002 2 . ± .
06 0 . ± .
04 31 . ± .
720 35/30 ≤ z<
18 0 . ± .
003 1 . ± .
03 0 . ± .
02 25 . ± .
560 28/20 . ± .
004 2 . ± .
08 0 . ± .
05 26 . ± .
800 12/10 . ± .
004 2 . ± .
04 0 . ± .
10 25 . ± .
200 2/ − . ± .
010 2 . ± .
02 1 . ± .
01 0 . ± .
020 49/3Fig. 1(d) 0 . ± .
004 2 . ± .
02 1 . ± .
04 5 . ± .
080 48/1218 ≤ z<
36 0 . ± .
003 2 . ± .
04 1 . ± .
03 17 . ± .
400 76/120 . ± .
004 2 . ± .
03 1 . ± .
02 28 . ± .
000 90/90 . ± .
004 2 . ± .
03 1 . ± .
02 31 . ± .
400 67/90 . ± .
005 1 . ± .
04 0 . ± .
03 31 . ± .
800 70/9Fig. 1(e) 0 . ± .
004 2 . ± .
03 0 . ± .
05 30 . ± .
400 29/918 ≤ z<
36 0 . ± .
005 2 . ± .
02 0 . ± .
02 28 . ± .
600 3/60 . ± .
002 1 . ± .
04 0 . ± .
05 25 . ± .
400 19/60 . ± .
001 1 . ± .
02 0 . ± .
01 24 . ± .
200 50/60 . ± .
002 1 . ± .
03 0 . ± .
02 22 . ± .
400 64/6Fig. 1(f) 0 . ± .
001 1 . ± .
02 0 . ± .
02 38 . ± .
800 44/318 ≤ z<
36 0 . ± .
002 1 . ± .
03 0 . ± .
03 33 . ± .
800 22/20 . ± .
002 1 . ± .
03 0 . ± .
02 30 . ± .
800 6/10 . ± .
003 0 . ± .
02 0 . ± .
03 31 . ± .
600 7/00 . ± .
002 2 . ± .
02 1 . ± .
02 1 . ± .
030 38/3Fig. 1(g) 0 . ± .
003 2 . ± .
01 1 . ± .
02 10 . ± .
200 108/1236 ≤ z<
54 0 . ± .
003 2 . ± .
05 1 . ± .
03 23 . ± .
400 85/120 . ± .
005 2 . ± .
03 0 . ± .
03 21 . ± .
600 60/90 . ± .
003 2 . ± .
02 0 . ± .
02 27 . ± .
400 69/90 . ± .
002 1 . ± .
02 0 . ± .
03 26 . ± .
600 42/9Fig. 1(h) 0 . ± .
003 2 . ± .
02 0 . ± .
03 26 . ± .
400 29/936 ≤ z<
54 0 . ± .
003 2 . ± .
04 0 . ± .
05 22 . ± .
400 13/60 . ± .
005 1 . ± .
03 0 . ± .
02 21 . ± .
600 40/60 . ± .
002 1 . ± .
03 0 . ± .
04 19 . ± .
500 44/60 . ± .
002 1 . ± .
07 0 . ± .
05 17 . ± .
300 97/6Fig. 1(i) 0 . ± .
002 1 . ± .
03 0 . ± .
04 32 . ± .
800 37/336 ≤ z<
54 0 . ± .
003 1 . ± .
05 0 . ± .
04 23 . ± .
600 5/20 . ± .
005 1 . ± .
05 0 . ± .
04 26 . ± .
800 6/10 . ± .
005 0 . ± .
07 0 . ± .
05 21 . ± .
600 22/10 . ± .
004 2 . ± .
02 0 . ± .
04 1 . ± .
040 66/3Fig. 1(j) 0 . ± .
001 2 . ± .
02 1 . ± .
02 11 . ± .
200 145/1254 ≤ z<
72 0 . ± .
003 2 . ± .
03 1 . ± .
02 18 . ± .
400 81/120 . ± .
005 2 . ± .
03 0 . ± .
03 21 . ± .
500 60/90 . ± .
004 2 . ± .
03 0 . ± .
02 21 . ± .
400 72/90 . ± .
005 1 . ± .
02 0 . ± .
03 19 . ± .
300 76/9Fig. 1(k) 0 . ± .
002 2 . ± .
02 0 . ± .
03 19 . ± .
400 36/954 ≤ z<
72 0 . ± .
004 2 . ± .
04 0 . ± .
03 16 . ± .
400 13/60 . ± .
001 1 . ± .
01 0 . ± .
01 14 . ± .
200 87/60 . ± .
001 1 . ± .
03 0 . ± .
02 15 . ± .
300 35/60 . ± .
001 1 . ± .
05 0 . ± .
03 14 . ± .
200 94/6Fig. 1(l) 0 . ± .
002 2 . ± .
02 0 . ± .
02 26 . ± .
400 22/354 ≤ z<
72 0 . ± .
002 1 . ± .
03 0 . ± .
03 23 . ± .
400 5/20 . ± .
002 1 . ± .
04 0 . ± .
03 20 . ± .
240 8/10 . ± .
001 0 . ± .
02 0 . ± .
01 17 . ± .
280 16/10 . ± .
005 2 . ± .
03 1 . ± .
03 1 . ± .
020 49/3Fig. 1(m) 0 . ± .
003 2 . ± .
02 1 . ± .
03 10 . ± .
300 56/1272 ≤ z<
90 0 . ± .
002 2 . ± .
03 1 . ± .
03 13 . ± .
400 67/120 . ± .
004 2 . ± .
02 0 . ± .
03 15 . ± .
300 52/90 . ± .
003 2 . ± .
03 0 . ± .
03 15 . ± .
400 66/90 . ± .
003 1 . ± .
02 0 . ± .
02 15 . ± .
300 64/9Fig. 1(n) 0 . ± .
003 2 . ± .
02 0 . ± .
03 14 . ± .
400 73/972 ≤ z<
90 0 . ± .
004 2 . ± .
03 0 . ± .
03 12 . ± .
300 9/60 . ± .
003 1 . ± .
03 0 . ± .
02 11 . ± .
200 14/60 . ± .
003 1 . ± .
05 0 . ± .
03 11 . ± .
200 36/60 . ± .
005 1 . ± .
04 0 . ± .
05 11 . ± .
200 66/6Fig. 1(o) 0 . ± .
002 2 . ± .
03 0 . ± .
03 18 . ± .
400 35/372 ≤ z<
90 0 . ± .
002 1 . ± .
02 0 . ± .
02 18 . ± .
200 13/20 . ± .
002 1 . ± .
06 0 . ± .
02 14 . ± .
400 3/10 . ± .
003 0 . ± .
04 0 . ± .
03 14 . ± .
400 19/10 . ± .
001 2 . ± .
01 1 . ± .
01 16 . ± .
200 46/3Fig. 1(p) 0 . ± .
003 2 . ± .
02 1 . ± .
03 20 . ± .
200 97/12 z =90 0 . ± .
005 2 . ± .
03 1 . ± .
03 16 . ± .
200 88/120 . ± .
004 2 . ± .
02 0 . ± .
03 13 . ± .
300 50/90 . ± .
002 2 . ± .
01 0 . ± .
02 10 . ± .
200 104/90 . ± .
003 1 . ± .
02 0 . ± .
02 14 . ± .
400 83/9Fig. 1(q) 0 . ± .
003 1 . ± .
03 0 . ± .
02 8 . ± .
400 64/6 z =90 0 . ± .
002 1 . ± .
03 0 . ± .
02 7 . ± .
120 118/60 . ± .
002 1 . ± .
02 0 . ± .
03 4 . ± .
240 71/30 . ± .
003 1 . ± .
03 0 . ± .
02 3 . ± .
200 29/2 able A2. Values of T , y max , y min , N , χ , and ndof corresponding to the curves in Fig. 2 in which different data are measured in different θ and z ranges. In the table, z is in the units of cm, and θ is not listed, which appears in Fig. 2. In one case, ndof is negative which appears interms of “ − ” and the corresponding curve is just for eye guiding only. Figure T (GeV) y max y min N × . χ . ± .
005 2 . ± .
02 1 . ± .
02 0 . ± .
002 33/2Fig. 2(a) 0 . ± .
004 3 . ± .
03 1 . ± .
03 0 . ± .
020 116/120 ≤ z<
18 0 . ± .
004 2 . ± .
02 1 . ± .
03 1 . ± .
060 71/120 . ± .
003 2 . ± .
04 0 . ± .
03 4 . ± .
100 88/90 . ± .
003 2 . ± .
02 0 . ± .
04 8 . ± .
120 18/90 . ± .
004 1 . ± .
02 0 . ± .
02 11 . ± .
200 33/9Fig. 2(b) 0 . ± .
002 2 . ± .
05 0 . ± .
03 13 . ± .
200 18/90 ≤ z<
18 0 . ± .
004 2 . ± .
03 0 . ± .
03 14 . ± .
300 27/60 . ± .
003 1 . ± .
02 0 . ± .
03 14 . ± .
300 50/60 . ± .
003 1 . ± .
02 0 . ± .
04 15 . ± .
300 37/60 . ± .
030 1 . ± .
03 0 . ± .
02 15 . ± .
200 39/6Fig. 2(c) 0 . ± .
002 2 . ± .
04 0 . ± .
03 27 . ± .
400 28/30 ≤ z<
18 0 . ± .
002 1 . ± .
04 0 . ± .
03 23 . ± .
400 38/20 . ± .
003 1 . ± .
02 0 . ± .
02 21 . ± .
400 12/10 . ± .
003 0 . ± .
02 0 . ± .
03 30 . ± .
400 2/ − . ± .
004 2 . ± .
03 0 . ± .
03 0 . ± .
020 57/3Fig. 2(d) 0 . ± .
002 3 . ± .
02 1 . ± .
03 3 . ± .
140 73/1218 ≤ z<
36 0 . ± .
003 2 . ± .
02 1 . ± .
02 11 . ± .
200 84/120 . ± .
003 2 . ± .
03 0 . ± .
03 19 . ± .
300 69/90 . ± .
002 2 . ± .
01 0 . ± .
02 24 . ± .
400 9/90 . ± .
002 1 . ± .
02 0 . ± .
02 25 . ± .
300 57/9Fig. 2(e) 0 . ± .
004 2 . ± .
01 0 . ± .
03 25 . ± .
200 64/918 ≤ z<
36 0 . ± .
003 2 . ± .
03 0 . ± .
05 24 . ± .
300 21/60 . ± .
005 1 . ± .
03 0 . ± .
02 22 . ± .
300 30/60 . ± .
002 1 . ± .
01 0 . ± .
05 21 . ± .
400 55/60 . ± .
004 1 . ± .
02 0 . ± .
03 19 . ± .
200 84/6Fig. 2(f) 0 . ± .
003 2 . ± .
04 0 . ± .
03 35 . ± .
600 28/318 ≤ z<
36 0 . ± .
002 1 . ± .
05 0 . ± .
03 31 . ± .
600 52/20 . ± .
003 1 . ± .
02 0 . ± .
02 28 . ± .
600 7/10 . ± .
005 1 . ± .
02 1 . ± .
03 23 . ± .
600 176/00 . ± .
004 2 . ± .
03 0 . ± .
03 0 . ± .
020 36/3Fig. 2(g) 0 . ± .
003 3 . ± .
03 1 . ± .
04 7 . ± .
159 95/1236 ≤ z<
54 0 . ± .
003 2 . ± .
03 0 . ± .
02 16 . ± .
360 79/120 . ± .
002 2 . ± .
03 0 . ± .
03 19 . ± .
300 58/90 . ± .
002 2 . ± .
02 0 . ± .
03 20 . ± .
400 33/90 . ± .
003 1 . ± .
02 0 . ± .
02 22 . ± .
400 48/9Fig. 2(h) 0 . ± .
002 2 . ± .
03 0 . ± .
03 20 . ± .
360 63/936 ≤ z<
54 0 . ± .
002 2 . ± .
03 0 . ± .
03 20 . ± .
300 25/60 . ± .
004 1 . ± .
04 0 . ± .
03 17 . ± .
200 9/60 . ± .
002 1 . ± .
01 0 . ± .
02 18 . ± .
300 41/60 . ± .
002 1 . ± .
01 0 . ± .
01 16 . ± .
200 74/6Fig. 2(i) 0 . ± .
002 2 . ± .
01 0 . ± .
02 31 . ± .
640 30/336 ≤ z<
54 0 . ± .
002 1 . ± .
02 0 . ± .
02 24 . ± .
400 47/20 . ± .
002 1 . ± .
02 0 . ± .
03 23 . ± .
600 9/10 . ± .
003 1 . ± .
02 0 . ± .
01 19 . ± .
400 8/00 . ± .
004 2 . ± .
03 0 . ± .
03 0 . ± .
020 41/3Fig. 2(j) 0 . ± .
003 3 . ± .
02 1 . ± .
03 7 . ± .
200 65/1254 ≤ z<
72 0 . ± .
004 2 . ± .
02 0 . ± .
02 13 . ± .
200 61/120 . ± .
003 2 . ± .
01 0 . ± .
03 15 . ± .
200 60/90 . ± .
003 2 . ± .
02 0 . ± .
03 16 . ± .
240 13/90 . ± .
004 1 . ± .
02 0 . ± .
02 16 . ± .
240 50/9Fig. 2(k) 0 . ± .
002 2 . ± .
02 0 . ± .
03 15 . ± .
200 70/954 ≤ z<
72 0 . ± .
003 2 . ± .
03 0 . ± .
02 15 . ± .
200 28/60 . ± .
004 1 . ± .
02 0 . ± .
03 13 . ± .
200 48/60 . ± .
003 1 . ± .
03 0 . ± .
02 14 . ± .
200 25/60 . ± .
004 1 . ± .
03 0 . ± .
03 12 . ± .
100 66/6Fig. 2(l) 0 . ± .
002 2 . ± .
02 0 . ± .
02 23 . ± .
400 31/354 ≤ z<
72 0 . ± .
002 1 . ± .
03 0 . ± .
04 19 . ± .
400 44/20 . ± .
002 1 . ± .
03 0 . ± .
02 15 . ± .
400 16/10 . ± .
003 2 . ± .
02 0 . ± .
02 15 . ± .
400 26/10 . ± .
002 2 . ± .
03 0 . ± .
02 1 . ± .
020 43/3Fig. 2(m) 0 . ± .
003 3 . ± .
03 1 . ± .
03 6 . ± .
240 73/1272 ≤ z<
90 0 . ± .
002 2 . ± .
02 0 . ± .
03 9 . ± .
200 88/120 . ± .
002 2 . ± .
03 0 . ± .
03 11 . ± .
200 86/90 . ± .
002 2 . ± .
02 0 . ± .
02 12 . ± .
200 23/90 . ± .
003 1 . ± .
02 0 . ± .
02 12 . ± .
200 51/9Fig. 2(n) 0 . ± .
002 1 . ± .
03 0 . ± .
03 11 . ± .
200 33/972 ≤ z<
90 0 . ± .
003 2 . ± .
02 0 . ± .
03 11 . ± .
200 7/60 . ± .
003 1 . ± .
02 0 . ± .
02 11 . ± .
200 45/60 . ± .
003 1 . ± .
02 0 . ± .
03 11 . ± .
200 41/60 . ± .
003 1 . ± .
03 0 . ± .
04 10 . ± .
200 50/6Fig. 2(o) 0 . ± .
003 2 . ± .
04 0 . ± .
03 18 . ± .
400 23/372 ≤ z<
90 0 . ± .
004 1 . ± .
04 0 . ± .
05 15 . ± .
400 30/20 . ± .
004 1 . ± .
03 0 . ± .
03 12 . ± .
600 15/10 . ± .
002 2 . ± .
04 0 . ± .
04 11 . ± .
400 19/10 . ± .
006 2 . ± .
04 0 . ± .
01 9 . ± .
200 47/3Fig. 2(p) 0 . ± .
002 3 . ± .
02 1 . ± .
02 14 . ± .
140 18/12 z =90 0 . ± .
003 2 . ± .
03 0 . ± .
03 11 . ± .
200 70/120 . ± .
002 2 . ± .
02 0 . ± .
03 10 . ± .
160 66/90 . ± .
003 2 . ± .
02 0 . ± .
02 8 . ± .
200 64/90 . ± .
004 1 . ± .
01 0 . ± .
02 12 . ± .
400 91/9Fig. 2(q) 0 . ± .
004 1 . ± .
02 0 . ± .
02 8 . ± .
400 30/6 z =90 0 . ± .
002 1 . ± .
03 0 . ± .
03 5 . ± .
320 37/60 . ± .
005 1 . ± .
01 0 . ± .
03 4 . ± .
120 13/30 . ± .
003 1 . ± .
03 0 . ± .
04 3 . ± .
040 34/2 able A3. Values of T , y max , y min , N , χ , and ndof corresponding to the curves in Fig. 3 in which different data are measured in different z and θ ranges. In the table, θ is in the units of mrad, and z is not listed, which appears in Fig. 3. Figure T (GeV) y max y min N × . χ . ± .
004 1 . ± .
02 1 . ± .
02 1 . ± .
040 48/120 . ± .
004 1 . ± .
03 1 . ± .
02 6 . ± .
100 57/12Fig. 3(a) 0 . ± .
004 1 . ± .
02 1 . ± .
02 10 . ± .
200 95/1220 ≤ θ<
40 0 . ± .
003 2 . ± .
01 1 . ± .
02 11 . ± .
240 55/120 . ± .
005 2 . ± .
02 1 . ± .
02 8 . ± .
240 68/120 . ± .
001 2 . ± .
01 1 . ± .
02 19 . ± .
400 231/120 . ± .
004 2 . ± .
03 0 . ± .
02 30 . ± .
400 30/90 . ± .
003 1 . ± .
02 0 . ± .
02 58 . ± .
600 19/9Fig. 3(b) 0 . ± .
002 1 . ± .
03 0 . ± .
02 46 . ± .
600 11/9100 ≤ θ<
140 0 . ± .
003 1 . ± .
02 0 . ± .
02 34 . ± .
800 17/90 . ± .
004 1 . ± .
03 0 . ± .
02 26 . ± .
600 20/90 . ± .
003 1 . ± .
02 0 . ± .
02 12 . ± .
400 37/90 . ± .
005 1 . ± .
02 0 . ± .
03 1 . ± .
020 57/120 . ± .
004 1 . ± .
03 0 . ± .
03 4 . ± .
200 16/12Fig. 3(c) 0 . ± .
004 1 . ± .
03 0 . ± .
02 7 . ± .
160 52/1220 ≤ θ<
40 0 . ± .
005 2 . ± .
03 0 . ± .
03 7 . ± .
200 23/120 . ± .
004 1 . ± .
02 0 . ± .
02 5 . ± .
100 26/120 . ± .
005 2 . ± .
02 0 . ± .
02 12 . ± .
200 40/120 . ± .
002 2 . ± .
02 0 . ± .
02 24 . ± .
480 17/90 . ± .
005 1 . ± .
02 0 . ± .
02 48 . ± .
800 15/9Fig. 3(d) 0 . ± .
004 1 . ± .
02 0 . ± .
02 40 . ± .
600 36/9100 ≤ θ<
140 0 . ± .
004 1 . ± .
02 0 . ± .
02 30 . ± .
800 11/90 . ± .
002 1 . ± .
02 0 . ± .
02 23 . ± .
520 27/90 . ± .
002 1 . ± .
02 0 . ± .
02 10 . ± .
520 36/9
Table A4. Values of T , y max , y min , N , χ , and ndof corresponding to the curves in Fig. 4 in which different data are measured in different θ and z ranges. In the table, z is in the units of cm, and θ is not listed, which appears in Fig. 4. Figure T (GeV) y max y min N × . χ . ± .
003 2 . ± .
03 1 . ± .
03 0 . ± .
012 18/2Fig. 4(a) 0 . ± .
003 1 . ± .
02 1 . ± .
03 3 . ± .
120 30/20 ≤ z<
18 0 . ± .
003 1 . ± .
03 1 . ± .
03 4 . ± .
180 24/20 . ± .
004 1 . ± .
02 0 . ± .
03 6 . ± .
300 31/20 . ± .
003 2 . ± .
03 1 . ± .
03 2 . ± .
060 8/2Fig. 4(b) 0 . ± .
003 2 . ± .
03 1 . ± .
02 9 . ± .
300 26/218 ≤ z<
36 0 . ± .
004 1 . ± .
02 0 . ± .
01 8 . ± .
180 27/20 . ± .
004 1 . ± .
02 0 . ± .
03 8 . ± .
100 25/20 . ± .
004 1 . ± .
02 1 . ± .
02 3 . ± .
060 47/4Fig. 4(c) 0 . ± .
004 1 . ± .
04 1 . ± .
03 7 . ± .
180 39/236 ≤ z<
54 0 . ± .
004 1 . ± .
04 1 . ± .
03 6 . ± .
240 21/20 . ± .
004 1 . ± .
03 0 . ± .
04 7 . ± .
500 14/20 . ± .
005 2 . ± .
03 1 . ± .
02 4 . ± .
180 38/4Fig. 4(d) 0 . ± .
003 1 . ± .
03 1 . ± .
03 5 . ± .
300 18/254 ≤ z<
72 0 . ± .
005 1 . ± .
03 0 . ± .
06 4 . ± .
180 13/20 . ± .
002 1 . ± .
01 1 . ± .
01 5 . ± .
200 38/20 . ± .
004 2 . ± .
03 1 . ± .
03 3 . ± .
120 14/4Fig. 4(e) 0 . ± .
004 1 . ± .
03 1 . ± .
03 4 . ± .
120 32/272 ≤ z<
90 0 . ± .
003 1 . ± .
03 1 . ± .
03 3 . ± .
120 17/20 . ± .
004 1 . ± .
03 0 . ± .
04 4 . ± .
150 22/2Fig. 4(f) 0 . ± .
003 2 . ± .
03 1 . ± .
03 6 . ± .
120 10/5 z =90 0 . ± .
006 1 . ± .
03 1 . ± .
02 3 . ± .
060 36/2
Table A5. Values of T , y max , y min , N , χ , and ndof corresponding to the curves in Fig. 5 in which different data are measured in different θ and z ranges. In the table, z is in the units of cm, and θ is not listed, which appears in Fig. 5. Figure T (GeV) y max y min N × . χ . ± .
005 1 . ± .
03 1 . ± .
03 0 . ± .
006 27/2Fig. 5(a) 0 . ± .
005 1 . ± .
03 1 . ± .
02 1 . ± .
060 18/20 ≤ z<
18 0 . ± .
003 1 . ± .
01 1 . ± .
01 1 . ± .
060 67/20 . ± .
005 1 . ± .
04 0 . ± .
02 2 . ± .
100 19/20 . ± .
005 1 . ± .
03 1 . ± .
03 0 . ± .
060 39/2Fig. 5(b) 0 . ± .
003 1 . ± .
03 1 . ± .
03 3 . ± .
120 72/218 ≤ z<
36 0 . ± .
003 1 . ± .
02 0 . ± .
01 2 . ± .
090 18/20 . ± .
003 0 . ± .
02 0 . ± .
02 3 . ± .
150 25/20 . ± .
005 1 . ± .
02 1 . ± .
01 1 . ± .
030 33/4Fig. 5(c) 0 . ± .
003 1 . ± .
03 1 . ± .
03 3 . ± .
150 18/236 ≤ z<
54 0 . ± .
003 1 . ± .
03 1 . ± .
03 2 . ± .
090 18/20 . ± .
003 1 . ± .
03 0 . ± .
01 2 . ± .
100 29/20 . ± .
010 1 . ± .
07 1 . ± .
05 1 . ± .
060 67/4Fig. 5(d) 0 . ± .
004 1 . ± .
03 1 . ± .
03 2 . ± .
060 21/254 ≤ z<
72 0 . ± .
005 1 . ± .
03 1 . ± .
03 2 . ± .
090 17/20 . ± .
002 1 . ± .
02 0 . ± .
02 2 . ± .
100 55/20 . ± .
004 1 . ± .
03 1 . ± .
02 0 . ± .
060 39/4Fig. 5(e) 0 . ± .
004 2 . ± .
04 0 . ± .
04 1 . ± .
060 10/272 ≤ z<
90 0 . ± .
004 1 . ± .
03 1 . ± .
02 1 . ± .
060 5/20 . ± .
004 0 . ± .
03 0 . ± .
02 1 . ± .
100 23/2Fig. 5(f) 0 . ± .
003 2 . ± .
02 1 . ± .
02 1 . ± .
060 36/5 z =90 0 . ± .
004 1 . ± .
04 1 . ± .
03 1 . ± .
060 39/2 able A6. Values of T , k , y max , y min , y L max , y L min , N , χ , and ndof corresponding to the curves in Fig. 6 in which different data aremeasured in different θ and z ranges. In the table, z is in the units of cm, and θ is not listed, which appears in Fig. 6. In a few cases, ndof arenegative which appear in terms of “ − ” and the corresponding curves are just for eye guiding only.Figure T (GeV) k y max y min y L max y L min N ( × . χ /ndof0 . ± .
004 0 . ± .
01 1 . ± .
05 1 . ± .
10 4 . ± .
07 3 . ± .
08 2 . ± .
200 10/ − Fig. 6(a) 0 . ± .
004 0 . ± .
02 1 . ± .
10 1 . ± .
10 3 . ± .
10 2 . ± .
10 1 . ± .
020 118/90 ≤ z<
18 0 . ± .
005 0 . ± .
02 1 . ± .
08 1 . ± .
10 3 . ± .
10 2 . ± .
08 2 . ± .
100 86/70 . ± .
003 0 . ± .
01 1 . ± .
07 1 . ± .
06 3 . ± .
05 2 . ± .
05 7 . ± .
160 202/60 . ± .
005 0 . ± .
01 1 . ± .
05 0 . ± .
05 3 . ± .
08 2 . ± .
05 10 . ± .
400 128/60 . ± .
003 0 . ± .
01 0 . ± .
02 0 . ± .
02 3 . ± .
08 1 . ± .
05 11 . ± .
400 50/3Fig. 6(b) 0 . ± .
004 0 . ± .
02 0 . ± .
03 0 . ± .
03 2 . ± .
07 0 . ± .
10 13 . ± .
400 57/30 ≤ z<
18 0 . ± .
004 0 . ± .
02 0 . ± .
03 0 . ± .
03 3 . ± .
10 0 . ± .
20 13 . ± .
400 57/ − . ± .
005 0 . ± .
02 0 . ± .
05 0 . ± .
05 3 . ± .
12 1 . ± .
10 12 . ± .
800 28/ − . ± .
010 0 . ± .
02 0 . ± .
05 0 . ± .
05 3 . ± .
10 1 . ± .
05 27 . ± .
800 5/ − . ± .
010 0 . ± .
02 1 . ± .
10 1 . ± .
10 4 . ± .
10 3 . ± .
05 8 . ± .
400 9/ − Fig. 6(c) 0 . ± .
006 0 . ± .
02 1 . ± .
20 1 . ± .
20 3 . ± .
03 2 . ± .
03 7 . ± .
300 117/918 ≤ z<
36 0 . ± .
003 0 . ± .
01 1 . ± .
05 1 . ± .
06 3 . ± .
05 2 . ± .
03 14 . ± .
400 42/70 . ± .
006 0 . ± .
02 1 . ± .
02 1 . ± .
03 3 . ± .
03 2 . ± .
01 28 . ± .
800 171/60 . ± .
005 0 . ± .
02 1 . ± .
03 0 . ± .
03 3 . ± .
05 2 . ± .
05 22 . ± .
480 118/70 . ± .
003 0 . ± .
01 1 . ± .
03 0 . ± .
03 3 . ± .
04 1 . ± .
04 20 . ± .
600 40/3Fig. 6(d) 0 . ± .
003 0 . ± .
01 0 . ± .
03 0 . ± .
03 2 . ± .
05 0 . ± .
05 20 . ± .
600 50/318 ≤ z<
36 0 . ± .
003 0 . ± .
03 0 . ± .
04 0 . ± .
04 3 . ± .
10 0 . ± .
05 19 . ± .
400 18/ − . ± .
002 0 . ± .
02 0 . ± .
02 0 . ± .
02 3 . ± .
30 1 . ± .
08 19 . ± .
400 18/ − . ± .
006 0 . ± .
01 0 . ± .
03 0 . ± .
02 3 . ± .
06 1 . ± .
02 47 . ± .
800 6/ − . ± .
005 0 . ± .
01 1 . ± .
05 1 . ± .
06 4 . ± .
06 3 . ± .
05 18 . ± .
400 11/ − Fig. 6(e) 0 . ± .
004 0 . ± .
01 1 . ± .
15 1 . ± .
15 3 . ± .
02 2 . ± .
03 15 . ± .
300 94/936 ≤ z<
54 0 . ± .
005 0 . ± .
01 1 . ± .
08 1 . ± .
10 3 . ± .
05 2 . ± .
03 22 . ± .
600 35/70 . ± .
004 0 . ± .
01 1 . ± .
01 1 . ± .
03 3 . ± .
03 2 . ± .
01 28 . ± .
400 173/60 . ± .
003 0 . ± .
02 1 . ± .
02 0 . ± .
02 3 . ± .
02 2 . ± .
02 20 . ± .
400 118/60 . ± .
002 0 . ± .
01 1 . ± .
02 0 . ± .
02 4 . ± .
03 1 . ± .
02 19 . ± .
400 42/3Fig. 6(f) 0 . ± .
004 0 . ± .
02 0 . ± .
02 0 . ± .
02 2 . ± .
02 0 . ± .
03 18 . ± .
400 48/336 ≤ z<
54 0 . ± .
001 0 . ± .
02 0 . ± .
03 0 . ± .
03 3 . ± .
20 0 . ± .
08 17 . ± .
400 23/ − . ± .
005 0 . ± .
01 0 . ± .
04 0 . ± .
04 3 . ± .
20 1 . ± .
10 16 . ± .
400 12/ − . ± .
004 0 . ± .
01 0 . ± .
03 0 . ± .
03 3 . ± .
15 1 . ± .
02 37 . ± .
960 7/ − . ± .
004 0 . ± .
01 1 . ± .
20 1 . ± .
20 4 . ± .
05 3 . ± .
05 24 . ± .
500 13/ − Fig. 6(g) 0 . ± .
003 0 . ± .
01 1 . ± .
03 1 . ± .
15 3 . ± .
02 2 . ± .
03 19 . ± .
240 32/954 ≤ z<
72 0 . ± .
005 0 . ± .
01 1 . ± .
10 1 . ± .
10 3 . ± .
06 2 . ± .
05 18 . ± .
200 31/70 . ± .
002 0 . ± .
01 1 . ± .
01 1 . ± .
01 3 . ± .
03 2 . ± .
01 23 . ± .
400 174/60 . ± .
003 0 . ± .
01 1 . ± .
02 0 . ± .
02 3 . ± .
03 2 . ± .
03 17 . ± .
400 129/60 . ± .
003 0 . ± .
02 0 . ± .
02 0 . ± .
03 4 . ± .
10 0 . ± .
03 15 . ± .
400 32/3Fig. 6(h) 0 . ± .
005 0 . ± .
01 0 . ± .
03 0 . ± .
03 3 . ± .
05 1 . ± .
05 14 . ± .
400 66/354 ≤ z<
72 0 . ± .
003 0 . ± .
02 0 . ± .
03 0 . ± .
03 3 . ± .
20 0 . ± .
02 14 . ± .
400 9/ − . ± .
004 0 . ± .
02 0 . ± .
05 0 . ± .
05 3 . ± .
10 1 . ± .
05 13 . ± .
400 16/ − . ± .
003 0 . ± .
01 0 . ± .
03 0 . ± .
03 3 . ± .
07 1 . ± .
03 29 . ± .
960 37/ − . ± .
004 0 . ± .
01 1 . ± .
03 1 . ± .
05 4 . ± .
10 3 . ± .
10 26 . ± .
600 6/ − Fig. 6(i) 0 . ± .
003 0 . ± .
01 1 . ± .
10 1 . ± .
15 3 . ± .
03 2 . ± .
03 17 . ± .
280 33/972 ≤ z<
90 0 . ± .
004 0 . ± .
01 1 . ± .
03 1 . ± .
02 3 . ± .
03 2 . ± .
03 13 . ± .
240 19/70 . ± .
004 0 . ± .
01 1 . ± .
03 0 . ± .
03 3 . ± .
02 1 . ± .
03 18 . ± .
480 99/60 . ± .
004 0 . ± .
01 1 . ± .
03 0 . ± .
02 3 . ± .
03 0 . ± .
03 13 . ± .
520 133/60 . ± .
005 0 . ± .
01 0 . ± .
04 0 . ± .
05 4 . ± .
04 0 . ± .
05 12 . ± .
520 8/3Fig. 6(j) 0 . ± .
001 0 . ± .
01 0 . ± .
02 0 . ± .
01 3 . ± .
02 1 . ± .
03 11 . ± .
480 51/372 ≤ z<
90 0 . ± .
002 0 . ± .
02 0 . ± .
01 0 . ± .
01 3 . ± .
15 0 . ± .
05 11 . ± .
320 10/ − . ± .
006 0 . ± .
03 0 . ± .
03 0 . ± .
03 3 . ± .
15 1 . ± .
06 10 . ± .
400 25/ − . ± .
003 0 . ± .
01 0 . ± .
02 0 . ± .
03 3 . ± .
20 1 . ± .
05 20 . ± .
400 56/ − . ± .
010 0 . ± .
02 1 . ± .
10 1 . ± .
04 4 . ± .
15 3 . ± .
15 193 . ± .
460 44/1Fig. 6(k) 0 . ± .
005 0 . ± .
01 1 . ± .
10 1 . ± .
10 3 . ± .
01 2 . ± .
03 36 . ± .
460 186/9 z =90 0 . ± .
002 0 . ± .
01 1 . ± .
03 1 . ± .
02 3 . ± .
04 2 . ± .
03 15 . ± .
500 192/90 . ± .
004 0 . ± .
01 1 . ± .
03 0 . ± .
05 3 . ± .
07 1 . ± .
06 14 . ± .
400 104/6Fig. 6(l) 0 . ± .
005 0 . ± .
01 1 . ± .
03 0 . ± .
02 3 . ± .
12 1 . ± .
03 6 . ± .
200 146/6 z =90 0 . ± .
004 0 . ± .
01 0 . ± .
05 0 . ± .
03 2 . ± .
02 0 . ± .
04 4 . ± .
200 30/10 . ± .
001 0 . ± .
01 0 . ± .
03 0 . ± .
02 3 . ± .
02 1 . ± .
04 3 . ± .
200 51/1200 51/1