Scaling properties of the mean multiplicity and pseudorapidity density in $e^{-}+e^{+}$, $e^{\pm}$+p, p($\bar{\mathrm{p}}$)+p, p+A and A+A(B) collisions

0.39 MB·

by  Roy A. Lacey

Scaling properties of the mean multiplicity and pseudorapidity density
in e− +e+, e±+p, p(p¯)+p, p+A and A+A(B) collisions
Roy A. Lacey,1,2,∗ Peifeng Liu,1,2 Niseem Magdy,1 M.Csan´ad,1,3
B. Schweid,1,2 N. N. Ajitanand,1 J. Alexander,1 and R. Pak4
1Department of Chemistry, Stony Brook University, Stony Brook, NY, 11794-3400, USA
2Dept. of Physics, Stony Brook University, Stony Brook, NY, 11794, USA
3Eotvos University, Department of Atomic Physics, H-1117 Budapest, Hungary
4Brookhaven National Laboratory, Upton, New York 11973, USA
(Dated: January 29, 2016)
The pseudorapidity density (dNch/dη) for p(p¯)+p, p+A and A+A(B) collisions, and the mean
6 multiplicity Nch for e−+e+, e±+p, and p(p¯)+p collisions, are studied for an inclusive range
h i
1 of beam energies (√s). Characteristic scaling patterns are observed for both dNch/dη and Nch ,
h i
0 consistentwithathermalparticleproductionmechanismforthebulkofthesoftparticlesproduced
2 inallofthesesystems. Theyalsovalidateanessentialroleforquarkparticipantsinthesecollisions.
n Thescaled valuesfor dNch/dη and hNchi areobservedtofactorize intocontributionswhichdepend
a onlog(√s) andthenumberofnucleon orquarkparticipant pairsNpp. Quantification of thesecon-
J tributions give expressions which serve to systematize dNch/dη and hNchi measurements spanning
nearly four orders of magnitude in √s, and topredict theirvalues as a function of √s and Npp.
8
2
PACSnumbers: 25.75.Dw

]
x
Measurements of particle yields and kinematic distri- anisotropic flow in A+A collisions, has been observed in
e
- butions in electron-positron (e−+e+), electron-proton p+p and p+Pb collisions at the LHC [15–18], and in
l
c (e±+p),proton-proton(p(p¯)+p),proton-nucleus(p+A) d+Au and He+Au collisions at RHIC [19, 20]. Qualita-
u and nucleus-nucleus (A+A(B)) collisions, are essential tiveconsistencywiththesedatahasalsobeenachievedin
n
forcharacterizingtheglobalpropertiesofthesecollisions, initial attempts to describe the amplitudes of these cor-
[
and to developa goodunderstanding of the mehanism/s relations hydrodynamically [19–21]. Thus, an important

2 for particle production [1–9]. The p+p measurements open question is whether equilibrium dynamics, linked
v
also provide crucialreference data for studies of nuclear- toacommonunderlyingparticleproductionmechanism,
1
medium effects in A+A(B) and p+A collisions, as well dominates for these systems?
0
0 as improved constraints to differentiate between particle In this work, we use the available dNch/dη measure-
6 production models and to fine-tune event generators. ments for p+p, p+A and A+A(B) collisions, as well as
0 the N measurementsfore−+e+,e±+p,andp(p¯)+p
. Particle production in A+A(B) collisions, is fre- h chi
1 quently described with thermodynamic and hydrody- collisions to search for scaling patterns which could sig-
0 nal such an underlying particle production mechanism.
namical models which utilize macroscopic variables such
6
as temperature and entropy as model ingredients. This
1
Our scaling analysis employs the macroscopic entropy
: contrastswiththemicroscopicphenomenology(involving
v (S) ansatz
ladders of perturbative gluons, classical random gauge
i
X fields or strings, and parton hadronization) often used S (TR)3 const., (1)
r to characterize the soft collisions which account for the ∼ ∼
a bulkoftheparticlesproducedine−+e+,e±+p,p(p¯)+p to capture the underlying physics ofparticle production,
and p+A collisions [10–14]. The associatedmechanisms, where T is the temperature, R is a characteristicsize re-
commonly classified as single-diffractive (SD) dissocia- lated to the volume, and dN /dη and N are both
ch ch
tion, double-diffractive (DD) dissociation and inelastic proportional to S. A further simplificatihon, Nip1p/3 R,
non-diffractive (ND) scattering in p(p¯)+p collisions [1], ∝
can be used to relate the number of participant pairs
typically do not emphasize temperature and entropy as
N , to the initial volume. These pairs can be spec-
pp
model elements.
ified as colliding participant pairs (e.g. N = 1 for
pp
Despite this predilection to use different theoretical e−+e+, e±+p and p(p¯)+p collisions), nucleon partici-
model frameworks for p(p¯)+p, p+A and A+A(B) colli- pantpairs(N )or quarkparticipantpairs(N ). For
npp qpp
sions, it is well known that similar chargedparticle mul- p+p,p+AandA+A(B)collisions,MonteCarloGlauber
tiplicity(N )andpseudorapiditydensity(dN /dη)are (MC-Glauber) calculations [31–36], were performed for
ch ch
obtained in p(p¯)+p, and peripheral A+A(B) and p+A several collision centralities at each beam energy to ob-
collisions. Moreover, an azimuthal long-range (pseudo- tainN andN . Ineachofthesecalculations,asub-
npp qpp
rapidity difference ∆η 4) two-particle angular corre- setN =2N (N =2N )ofthenucleons(quarks)
np npp qp qpp
| | ≥
lation, akin to the “ridge” which results from collective become participants in each collision by undergoing an
2
(cid:2)(cid:20)(cid:6) (cid:2)(cid:17)(cid:6) (cid:2)(cid:10)(cid:6)
(cid:4)(cid:18)(cid:18)(cid:1)(cid:4)(cid:19) (cid:2)(cid:1)(cid:4)(cid:1)(cid:5)(cid:6)(cid:3)
(cid:13)(cid:2)(cid:13)(cid:6)(cid:1)(cid:18)(cid:1)(cid:13) (cid:9)(cid:13)(cid:13)(cid:1)(cid:21)(cid:1)(cid:7) (cid:3) (cid:16)
(cid:2)(cid:1)(cid:4)(cid:1)(cid:5)(cid:6)(cid:8)
(cid:16)(cid:8) (cid:4)(cid:1)(cid:18)(cid:1)(cid:13) (cid:7)
(cid:14)(cid:8)
(cid:14) (cid:14)
(cid:7)(cid:12)
(cid:6)
(cid:13)
(cid:11) (cid:13)
(cid:10) (cid:9)
(cid:9)
(cid:15)(cid:8) (cid:12)(cid:10)(cid:11)
(cid:9)
(cid:2)
(cid:15)
(cid:7)(cid:8)
(cid:8) (cid:7)
(cid:7) (cid:7)(cid:8) (cid:7)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8) (cid:7) (cid:7)(cid:8) (cid:7)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8) (cid:7) (cid:7)(cid:8) (cid:7)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8)
s (cid:2)(cid:3)(cid:4)(cid:5)(cid:6) s (cid:2)(cid:3)(cid:4)(cid:5)(cid:6) (cid:2) s (cid:2)(cid:3)(cid:4)(cid:5)(cid:6)
n
FIG. 1. (a) Nch vs. √s for e−+e+ [22], p(p¯)+p [23–27] and e±+p [28–30] collisions; (b) [ Nch /Npp]1/3 vs. √s;
h i h i
(c) [ Nch /Npp]1/3 vs. κn√s for theκn valuesindicated. The curvesare drawn to guide theeye.
h i
initialinelasticN+N(q+q)interaction. TheN+N(q+q) production.
cross sections used in these calculations were obtained
Figure 1(c) validates this leading particle effect. It
from the data systematics reported in Ref. [37].
shows that the disparate magnitudes of [ N /N ]1/3
ch pp
Equation 1 suggests similar characteristic patterns for h i
vs. √s for e−+e+, p(p¯)+p and e±+p collisions (cf.
[(dN /dη)/N ]1/3 and [ N /N ]1/3 as a function of
ch pp h chi pp Fig. 1(b)) scale to a single curve for [ Nch /Npp]1/3 vs.
centrality and √s for all collision systems. We use this h i
κ √s where κ =1, κ 1/2 and κ 1/6. The values
n 1 2 3
scaling ansatz in conjunction with the wealth of mea- ∼ ∼
forκ validate the importantroleofquarkparticipants
2,3
surements spanning several orders of magnitude in √s,
in p(p¯)+p and e±+p collisions. A fit to the data in
to search for, and study these predicted patterns.
Fig. 1(c) gives the expression
The N measurements for e−+e+, e±+p, and
ch
h i
p(p¯)+p collisions are shown in Fig. 1(a). They indi-
cate a nonlinear increase with log(√s), with N > 3
N > N at each value of √s. h Icnhieceon- hNchi=(cid:2)bhNchi+mhNchilog(κn√s)(cid:3) , (2)
ch pp ch ep
h i h i b =1.22 0.01, m =0.775 0.006,
trast, Fig. 1(b) shows a linear increase of [ Nch /Npp]1/3 hNchi ± hNchi ±
h i
(N =1)withlog(√s),suggestingalinearincreaseofT
pp
with log(√s). Fig. 1(b) also indicates comparable slopes
which can be used to predict N as a function of √s,
for [ N /N ]1/3 vs. log(√s) for e−+e+, e±+p, and h chi
h chi pp for e−+e+, e±+p, and p(p¯)+p collisions.
p(p¯)+p collisions, albeit with different magnitudes for
[hNchi/Npp]1/3. This similarity is compatible with the Figures2(a)and3(a)showdNch/dη|η≈0measurements
notion of an effective energy E in p(p¯)+p and e±+p for inelastic (INE)andnon-single-diffractive(NSD) p+p
eff
collisions, available for particle production [49–52]. The collisions (respectively) for beam energies spanning the
remainingenergyisassociatedwiththeleadingparticle/s range √sNN 15GeV - 13TeV; they indicate a
∼
which emerge at small angles with respect to the beam monotonic increase of dNch/dη η≈0 with √sNN similar
|
direction - the so-called leading particle effect [53]. In a to that observed for Nch in Fig. 1(a). Figs. 2(b)
h i
constituentquarkpicture[54],onlyafractionoftheavail- and 3(b), by contrast, confirms the expected linear
able quarks in p(p¯)+p and e±+p collisions, contribute growthof[(dNch/dη η≈0)/Nnpp]1/3 withlog(√sNN). The
|
to E . Thus, √s κ √s κ √s (κ =1) would open points and dotted curves in these figures, af-
eff ee ≈ 2 pp ≈ 3 ep 1
beexpectedtogivesimilarvaluesforE [55]andhence, firm the expected trend for the √s dependence of
eff
comparable hNchi values in e−+e+, p(p¯)+p and e±+p [(dNch/dη|η≈0)/Nqpp]1/3. Here,thechangeinmagnitude
collisions. Here, κ are scale factors that are related to largely reflects the difference in the proportionality con-
2,3
thenumberofquarkparticipantsandhence,thefraction stants for N and N (i.e., N1/3 R). The fits,
npp qpp pp
∝
of the available c.m energy which contribute to particle indicated by the dashed curves in Figs. 2(b) and 3(b),
3
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(cid:14)(cid:17)(cid:21)(cid:18)(cid:17)(cid:15)(cid:19)(cid:22)(cid:14)(cid:16)(cid:1)(cid:20) (cid:10)(cid:10)(cid:28)(cid:28)(cid:28)(cid:28)(cid:1)(cid:1)’’(cid:1)(cid:1)(cid:10)(cid:10)(cid:30)((cid:28)(cid:28)(cid:28)(cid:28) (cid:14)(cid:17)(cid:14)(cid:18)(cid:21)(cid:15)(cid:19)(cid:22)(cid:14)(cid:16)(cid:1)(cid:20) (cid:10)(cid:10)(cid:26)(cid:26)(cid:26)(cid:26)(cid:1)(cid:1)(cid:28)(cid:28)(cid:1)(cid:1)(cid:10)(cid:10)(cid:29)(cid:30)(cid:26)(cid:26)(cid:26)(cid:26)
(cid:23)(cid:24)(cid:25)(cid:26)(cid:25)(cid:16) (cid:23)(cid:17)(cid:7)
(cid:19)(cid:16)(cid:27) (cid:23)(cid:17)(cid:24) (cid:8)
(cid:13) (cid:10)(cid:17)(cid:18)(cid:1) & (cid:7)(cid:4)(cid:8)(cid:6)(cid:28) (cid:13) (cid:27) (cid:7)(cid:4)(cid:6)(cid:5)(cid:26)(cid:26)
(cid:2)(cid:10)(cid:11)(cid:9) (cid:2)(cid:3)(cid:4)(cid:5)(cid:28) (cid:2)(cid:10)(cid:11)(cid:9) (cid:2)(cid:3)(cid:4)(cid:9)
(cid:9) (cid:9) (cid:9) (cid:10)(cid:11)
(cid:10)(cid:11) (cid:9)
(cid:12) (cid:7) (cid:2)(cid:9) (cid:12) (cid:7) (cid:25)(cid:2)
%
(cid:8) (cid:8) (cid:8) (cid:8)
(cid:7)(cid:8) (cid:7)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8)(cid:8) (cid:7)(cid:8) (cid:7)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8) (cid:7)(cid:8)(cid:8)(cid:8)(cid:8)
s (cid:2)(cid:3)(cid:4)(cid:5)(cid:6) s (cid:2)(cid:3)(cid:4)(cid:5)(cid:6)
NN NN
FIG. 2. (a) dNch/dηη≈0 vs. √sNN and (b) FIG. 3. (a) dNch/dηη≈0 vs. √sNN and (b)
| |
[(dNch/dη)/Npp]1/3vs. √sNN,forp+pinelasticmeasurements [(dNch/dη)/Nnpp]1/3 vs. √sNN, for p+p NSD measure-
from CMS [38], ALICE [39–41], UA5 [42], PHOBOS [43], ments from CMS [45], ALICE [40], CDF [46], UA1 [47] and
ISR [25] and NAL Bubble Chamber [44]. The error bars UA5 [42]. The error bars include the available systematic
include systematic uncertainties, when available. The curves uncertainties. The curves in panel (b) represent fits to the
in panel(b) represent fitsto thedata (see text). data (see text).
(cid:17)(cid:18)(cid:19)(cid:17)(cid:18)(cid:1)(cid:20)(cid:1)(cid:5)(cid:21)(cid:9)(cid:13)(cid:1)(cid:1)(cid:22)(cid:23)(cid:24)(cid:1) (cid:15)(cid:30)(cid:31) (cid:15)(cid:18)(cid:31) (cid:15)"(cid:31) (cid:5)(cid:16)(cid:13)
(cid:25)(cid:26)(cid:19)(cid:25)(cid:26)(cid:1)(cid:20)(cid:1)(cid:5)(cid:13)(cid:13)(cid:1)(cid:1)(cid:22)(cid:23)(cid:24)(cid:1)
(cid:27)(cid:26)(cid:19)(cid:25)(cid:26)(cid:1)(cid:20)(cid:1)(cid:5)(cid:13)(cid:13)(cid:1)(cid:1)(cid:22)(cid:23)(cid:24)(cid:1)
(cid:5)(cid:16)(cid:8) (cid:27)(cid:26)(cid:19)(cid:27)(cid:26)(cid:1)(cid:20)(cid:1)(cid:5)(cid:13)(cid:13)(cid:1)(cid:1)(cid:22)(cid:23)(cid:24)(cid:1)
(cid:4)(cid:16)!
(cid:28)(cid:1)(cid:19)(cid:1)(cid:28)(cid:1)(cid:1)(cid:1)(cid:20)(cid:1)(cid:4)(cid:29)(cid:6)(cid:1)(cid:1)(cid:22)(cid:23)(cid:24)(cid:1)
(cid:25)(cid:26)(cid:19)(cid:25)(cid:26)(cid:1)(cid:20)(cid:1)(cid:9)(cid:5)(cid:16)(cid:7)(cid:1)(cid:22)(cid:23)(cid:24)
(cid:25)(cid:26)(cid:19)(cid:25)(cid:26)(cid:1)(cid:20)(cid:1)(cid:5)(cid:21)(cid:16)(cid:13)(cid:1)(cid:22)(cid:23)(cid:24) (cid:4)(cid:16)(cid:9)
(cid:5)(cid:6)(cid:7)(cid:9) (cid:25)(cid:3)(cid:1)(cid:26)(cid:19)(cid:19)(cid:1)(cid:17)(cid:25)(cid:18)(cid:26)(cid:1)(cid:1)(cid:20)(cid:20)(cid:1)(cid:1)(cid:8)(cid:21)(cid:13)(cid:16)(cid:21)(cid:5)(cid:13)(cid:13)(cid:1)(cid:1)(cid:22)(cid:1)(cid:22)(cid:23)(cid:23)(cid:24)(cid:24)(cid:1) (cid:5)(cid:6)(cid:7)(cid:9)
(cid:2)(cid:3)(cid:3) (cid:5)(cid:16)(cid:13) (cid:4)(cid:16)(cid:7) (cid:3)(cid:3)
(cid:3) (cid:3)
(cid:4)(cid:6) (cid:4)(cid:6)
(cid:8) (cid:4)(cid:16)(cid:5) (cid:8)
(cid:10) (cid:10)
(cid:11)(cid:12) (cid:11)(cid:12)
(cid:10) (cid:4)(cid:16)(cid:8) (cid:4)(cid:16)(cid:13) (cid:10)
(cid:15) (cid:15)
(cid:14) (cid:14)
(cid:13)(cid:16)!
(cid:13)(cid:16)(cid:9)
(cid:4)(cid:16)(cid:13)
(cid:13)(cid:16)(cid:7)
(cid:4)(cid:13) (cid:4)(cid:13)(cid:13) (cid:4)(cid:13)(cid:13)(cid:13) (cid:4) (cid:5) (cid:6) (cid:7) (cid:8) (cid:9) (cid:5) (cid:7) (cid:9) !
(cid:10)(cid:11)(cid:12)(cid:10)(cid:8) (cid:2)(cid:3) (cid:4)(cid:5)(cid:6)(cid:7) (cid:2)(cid:3) (cid:4)(cid:5)(cid:6)(cid:7)
(cid:2)(cid:3)(cid:3) (cid:3)(cid:3)
FIG.4. (a) [(dNch/dη||η|=0.5)/Nnpp]1/3 vs. dNch/dη;(b)[(dNch/dη||η|=0.5)/Nnpp]1/3 vs. Nn1p/p3;(c) [(dNch/dη||η|=0.5)/Nqpp]1/3
vs. Nq1p/p3. Results are shown for several systems and √sNN values as indicated. The data are obtained from Refs. [4–9, 48].
The curvesare drawn to guide theeye.
3
dN /dη =[b +m log(√s )] ,
give the expressions ch NSD NSD NSD NN
| (4)
b =0.747 0.022, m =0.267 0.007,
NSD NSD
± ±
forthemid-pseudorapiditydensityforINEandNSDp+p
collisions. Here,itisnoteworthythattherecentinelastic
3
dNch/dη|INE =[bINE+mINElog(√sNN)] , (3) p+p measurements at √sNN =13TeV by the CMS [38]
b =0.826 0.008, m =0.220 0.004, and ALICE [41] collaborations are in very good agree-
INE INE
± ±
4
mentwiththescalingpredictionshowninFig.2(b). The (cid:22) (cid:23) (cid:22)(cid:13)(cid:23) (cid:5)(cid:21)(cid:4)
(cid:11) (cid:12)(cid:13)(cid:14)(cid:12)(cid:13)(cid:1)(cid:15)(cid:1)(cid:5)(cid:11)(cid:7)(cid:4)(cid:1)(cid:1)(cid:16)(cid:17)(cid:18)(cid:1)
data trendsin Figs.1(c), 2(b) and3(b)alsosuggestthat (cid:19)(cid:20)(cid:14)(cid:19)(cid:20)(cid:1)(cid:15)(cid:1)(cid:5)(cid:4)(cid:4)(cid:1)(cid:1)(cid:1)(cid:16)(cid:17)(cid:18)(cid:1) (cid:3)(cid:14)(cid:3)(cid:1)(cid:27)(cid:30)(cid:31)
the mean transverse momentum ( p T) for the par- (cid:19)(cid:20)(cid:14)(cid:19)(cid:20)(cid:1)(cid:15)(cid:1)(cid:11)(cid:21)(cid:11)(cid:4)(cid:1)(cid:1)(cid:16)(cid:17)(cid:18)(cid:1) (cid:19)(cid:14)(cid:19)(cid:22)(cid:29)(cid:23)
h Ti∝ (cid:7) (cid:5)(cid:6)(cid:7)
ticles emitted in these collisions, increase as log(√s). (cid:24)(cid:21)(cid:10) (cid:9)(cid:3)
sioTnhsearsecsaulimngmaprriozpederitnieFsigfo.r4pw+hAereainlldustAr+atAiv(eBp)loctoslloi-f (cid:6)(cid:3)(cid:3)(cid:2)(cid:3)(cid:3)(cid:10) (cid:8)(cid:4)(cid:6)(cid:3)(cid:8)(cid:3)
[(dNch/dη |η|=0.5)/Nnpp]1/3 vs. dNch/dη and Nn1p/p3, and (cid:3)(cid:8)(cid:6) (cid:24)(cid:21)(cid:4) (cid:27)(cid:28)(cid:26)
[(dNch/dη||η|=0.5)/Nqpp]1/3 vs. Nq1p/p3 are shown. Analo- (cid:25)(cid:22)(cid:26)
| (cid:9)
gous plots were obtained for other collision systems and
(cid:4)(cid:21)(cid:10)
beam energies. Figs. 4(a) and 4(b) show that, irrespec-
(cid:5)
tive of the collision system, [(dNch/dη |η|=0.5)/Nnpp]1/3 (cid:4) (cid:5) (cid:6) (cid:7) (cid:24)(cid:4) (cid:24)(cid:4)(cid:4) (cid:24)(cid:4)(cid:4)(cid:4) (cid:24)(cid:4)(cid:4)(cid:4)(cid:4)
increases as log(dNch/dη) (Nn1p/p3), sugge|sting that T has (cid:2)(cid:3)(cid:2)(cid:3)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7) sNN (cid:22)(cid:16)(cid:17)(cid:18)(cid:23)
a logarithmic (linear) dependence on the pseudorapidity
density (size) at a given value of √sNN; note the slope FIG. 5. (a) Nqp/Nnpp vs. Nn1p/p3 for Au+Au and Pb+Pb
increase with beam energy, as well as the lack of sensi- collisions; (b) [(dNch/dη||η|=0.5)/Npp]1/3 vs. √sNN for NSD
tivity to systemtype (Cu+Cu, Cu+Au, Au+Au, U+U), p+pand A+A(B)collisions as indicated.
for a fixed value of √sNN. These results suggest that, in
addition to the expected increase with √sNN, the mean
transverse momentum p or transverse mass m of
T T
h i h i
theemittedparticles,shouldincreaseaslog(dN /dη)at collisions across the full range of beam energies. Eq. 5
ch
a given value of √sNN. They also suggest that the pseu- provides a basis for robust predictions of the value of
dorapiditydensityfactorizesintocontributionswhichde- dNch/dη |η|=0.5 as a function of Nqpp and√s acrosssys-
|
pend on √sNN and Nn1p/p3 respectively. Indeed, the data tems and collision energies. For example, it predicts an
sets shown for each √sNN in Fig. 4(b), can be scaled to ∼20% increase in the dNch/dη||η|=0.5 values for Pb+Pb
a single curve with scaling factors that are proportional collisions (across centralities) at 5.02TeV, compared to
to log(√sNN). the same measurement at 2.76TeV. This increase re-
Figure 4(c) contrasts with Figs. 4(a) and 4(b). It flects the respective contributions linked to the increase
shows that, when N is used instead of N , the in the value of √s and the small growth in the magni-
qpp npp
size dependence of [(dNch/dη |η|=0.5)/Nnpp]1/3, appar- tudes of Nqpp.
|
ent in Fig. 4(b), is suppressed (but not its √sNN In summary, we have performed a systematic study
dependence). We attribute the flat dependence of
of the scaling properties of dN /dη measurements for
[(dN /dη )/N ]1/3 on size (N1/3 or N1/3), to ch
ch ||η|=0.5 qpp npp qpp p+p, p+A and A+A(B) collisions, and Nch measure-
the linear dependence of Nqp/Nnpp on initial size as il- ments for e−+e+, e±+p, and p(p¯)+p chollisiions, to in-
lustrated in Fig. 5(a) for Pb+Pb and Au+Au collisions.
vestigate the mechanism for particle production in these
Note that for central and mid-central p+Pb collisions,
collisions. The wealth of the measurements, spanning
Nqp/Nnpp decreases with Nn1p/p3; this results in a reduc- several orders of magnitude in √s, indicate characteris-
tionofthe energydepositedinthesecollisions,aswellas tic scaling patterns for both dN /dη and N , sugges-
ch ch
h i
large multiplicity fluctuations. tive of a common underlying entropy production mech-
The √sNN dependence of [(dNch/dη||η|=0.5)/Nqpp]1/3 anism for these systems. The scaling patterns for hNchi
for A+A(B) and NSD p+p collisions are compared in validate the essential role of the leading particle effect
Fig. 5(b). The comparison indicates strikingly similar in p(p¯)+p and e±+p collisions and the importance of
trends for NSD p+p, and A+A(B) collisions, as would quark participants in A+A(B) collisions. The patterns
be expected for a common underlying particle produc- forthescaledvaluesofdN /dηand N indicatestrik-
ch ch
tionmechanisminthesecollisions. Notethatfor√sNN . inglysimilartrendsforNSDp+pandhA+Ai (B)collisions,
2TeV,highertemperatures[andlargerhpTi]areimplied and show that the pseudorapidity density and the hNchi
forthesmallerp+pcollisionsystems. Figs.4(c)and5(b) fore−+e+,e±+p,p+p,andA+A(B)collisions,factor-
also indicate that the centrality and √s dependent val- ize into contributions which depend on log(√s) and N
pp
uesofdNch/dη |η|=0.5,obtainedfordifferentcollisionsys- respectively. Thequantificationofthesescalingpatterns,
|
tems,scaleasNqpp andlog(√sNN). AfittotheA+A(B) give expressionswhich serve to systematize the dNch/dη
data in Fig. 5(b), gives the expression and N measurements for e−+e+, e±+p, p(p¯)+p,
ch
h i
3 p+AandA+A(B)collisions,andtopredicttheirmagni-
dNch/dη||η|=0.5 =Nqpp(cid:2)bAA+mAAlog(√s)(cid:3) , (5) tudes as a function ofN and√s. These scaling results
pp
b =0.530 0.008, m =0.258 0.004,
AA ± AA ± have important utility in the study of a broad array of
which systematizes the collision energy and centrality observables which are currently being pursued at both
dependencies of the pseudorapidity density in A+A(B) RHIC and the LHC.
5
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