research article on current conversion between particle rapidity...
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Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2013 Article ID 710534 4 pageshttpdxdoiorg1011552013710534
Research ArticleOn Current Conversion between Particle Rapidity andPseudorapidity Distributions in High Energy Collisions
Fu-Hu Liu Ya-Hui Chen Ya-Qin Gao and Er-Qin Wang
Institute of Theoretical Physics Shanxi University Taiyuan Shanxi 030006 China
Correspondence should be addressed to Fu-Hu Liu fuhuliu163com
Received 27 June 2013 Accepted 29 September 2013
Academic Editor Sakina Fakhraddin
Copyright copy 2013 Fu-Hu Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
In high energy collisions one usually needs to give a conversion between the particle rapidity and pseudorapidity distributions Cur-rently two equivalent conversion formulas are used in experimental and theoretical analyses An investigation in the present workshows that the two conversions are incomplete Then we give a revision on the current conversion between the particle rapidityand pseudorapidity distributions
1 Introduction
High energy collisions are an important research field in par-ticle and nuclear physics In the collisions a lot of particlesare produced and the rapidity andor pseudorapidity distri-butions can be obtained and studied [1ndash3] Usually one needsto do a conversion between the rapidity and pseudorapiditydistributions in the case of only one of the two distributionsbeing obtainedThere are two equivalent conversion formulasused in the current literature [4ndash11] Naturally one thinks thatthe two conversions are perfect in investigations of the rapid-ity and pseudorapidity distributions
However our incidental find shows that the two conver-sions are incomplete In obtaining the Jacobian in the currentliterature [4ndash11] a nongiven quantity namely transversemomentum is erroneously used as a given onewhich rendersan incomplete conversion In this paper we will give a reanal-ysis on the Jacobian A revised conversion between the rapid-ity and pseudorapidity distributions will be presented
2 General Definition
We consider a system of high energy projectile-target colli-sions The incident projectile direction is defined as 119900119911 axisand the reaction plane is defined as 119909119900119911 plane Let 119864 119901 119901
119871
119901119879 1198980 and 120579 denote respectively the energy momentum
longitudinal momentum transverse momentum rest massand emission angle of a concerned particle According to
general textbooks on particle physics [12 13] the rapidity(which is in fact the longitudinal rapidity) is defined by
119910 equiv
1
2
ln(119864 + 119901119871
119864 minus 119901119871
) (1)
where
119864 = radic1199012+ 1198982
0
119901119871= 119901 cos 120579
(2)
In the case of 119901 ≫ 1198980 we have
119910 asymp
1
2
ln(119901 + 119901119871
119901 minus 119901119871
) =
1
2
ln(1 + cos 1205791 minus cos 120579
) = minus ln tan(1205792
) equiv 120578
(3)
where 120578 is the pseudorapidityBecause the condition of 119901 ≫ 119898
0is not always satisfied
the pseudorapidity distribution (density function) 119891120578(120578) =
(1119873)(119889119873119889120578) and the rapidity distribution (density func-tion) 119891
119910(119910) = (1119873)(119889119873119889119910) are not approximately equal
to each other where 119889119873 denotes the particle number inthe pseudorapidity or rapidity bin and 119873 denotes the totalnumber of considered particles
2 Advances in High Energy Physics
3 Current Conversion
To give a conversion between 119889119873119889120578 and 119889119873119889119910 in thecase of one of them being obtained one has two equivalentmethods which are currently used in the literature [4ndash11]According to [4 5 11] the first conversion relation between119889119873119889120578 and 119889119873119889119910 can be given by
119889119873
119889120578
=
119889119873
119889119910
119889119910
119889120578
=
119901
119864
119889119873
119889119910
(4)
where
119901
119864
=
radic1198642minus 1198982
0
119864
=radic1 minus
1198982
0
1198642
= radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
(5)
Then the first conversion is given by [4ndash6]
119889119873
119889120578
=
119901
119864
119889119873
119889119910
= radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
119889119873
119889119910
(6)
whereradic1199012119879+ 1198982
0equiv 119898119879is the transversemassWe see that the
first conversion is related to 119901119879
The second conversion is given in [5 7ndash11] We have
119889119873
119889120578
=
cosh 120578
radic1 + 1198982
0119901minus2
119879+ sinh2120578
119889119873
119889119910
=
cosh 120578
radic1198982
119879119901minus2
119879+ sinh2120578
119889119873
119889119910
=
cosh 120578
radiccosh2120578 + 11989820119901minus2
119879
119889119873
119889119910
(7)
which is also related to 119901119879 In [11] a similar conversion which
uses 1198982119875minus2 instead of 11989820119901minus2
119879in (7) is given where 119898 =
350MeV 119875 = 013GeV + 032GeV(radic1199041TeV)0115 and radic119904
denotes the center-of-mass energy The conversion used in[11] is a mutation of the second conversion
We now give the eduction of the current conversionAccording to [12]
119910 =
1
2
ln(119864 + 119901119871
119864 minus 119901119871
) =
1
2
ln(radic1199012+ 1198982
0+ 119901119871
radic1199012+ 1198982
0minus 119901119871
)
=
1
2
ln(radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
)
(8)
In the case of 119901119879being a given quantity we have
119889119910
119889120578
=
1
2
sdot
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
sdot
119889
119889120578
(
radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
)
=
1
2
sdot[
[
[
1
radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
sdot
119889
119889120578
(radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578)
minus
1
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
sdot
119889
119889120578
(radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578)]]
]
=
1
2
sdot[
[
[
1
radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
times(
1199012
119879cosh 120578 sinh 120578
radic1199012
119879cosh2120578 + 1198982
0
+ 119901119879cosh 120578)
minus
1
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
times (
1199012
119879cosh 120578 sinh 120578
radic1199012
119879cosh2120578 + 1198982
0
minus 119901119879cosh 120578)]
]
]
=
1
2
sdot
1
1199012
119879+ 1198982
0
sdot[
[
[
(
1199012
119879cosh 120578 sinh 120578
radic1199012
119879cosh2120578 + 1198982
0
+119901119879cosh 120578)
times (radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578)
minus(
1199012
119879cosh 120578 sinh 120578
radic1199012
119879cosh2120578 + 1198982
0
minus 119901119879cosh 120578)
times(radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578)]]
]
Advances in High Energy Physics 3
=
1
2
sdot
1
1199012
119879+ 1198982
0
sdot
2 (1199012
119879+ 1198982
0) 119901119879cosh 120578
radic1199012
119879cosh2120578 + 1198982
0
=
119901119879cosh 120578
radic1199012
119879cosh2120578 + 1198982
0
=
cosh 120578
radiccosh2120578 + 11989820119901minus2
119879
=
119901
119864
= 120573
(9)
where 120573 denotes the velocity of the concerned particle Thenwe obtain the current conversion
However we would like to point out that the previousconversion is incomplete due to the fact that 119901
119879= 119901 cosh 120578
is also a function of 120578 which should be considered in doingthe differential treatment Instead 119901 and 119864 can be regardedas given quantities
4 Revised Conversion
In the differential treatment we think that both the 119901119879=
119901 cosh 120578 and 119901119871= 119901 tanh 120578 are functions of 120578 Contrarily
119901 and 119864 have the fixed values for a given particle Then
119910 =
1
2
ln(119864 + 119901119871
119864 minus 119901119871
) =
1
2
ln(119864 + 119901 tanh 120578119864 minus 119901 tanh 120578
)
=
1
2
ln(1 + 120573 tanh 1205781 minus 120573 tanh 120578
) equiv ℎ (120578)
(10)
119889119910
119889120578
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot
119889
119889120578
(
1 + 120573 tanh 1205781 minus 120573 tanh 120578
)
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot [
1
1 minus 120573 tanh 120578+
1 + 120573 tanh 120578(1 minus 120573 tanh 120578)2
] sdot 120573
119889
119889120578
(tanh 120578)
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot
2120573
(1 minus 120573 tanh 120578)2sdot
1
cosh2120578
=
120573
1 minus 1205732tanh2120578
sdot
1
cosh2120578
=
120573
cosh2120578 minus 1205732sinh2120578=
120573
1 + (1 minus 1205732) sinh2120578
=
1 minus (1 minus 1205732) cosh2119910
120573
(11)
It is different from the first conversion which gives that 119889119910119889120578 = 120573 Correspondingly
120578 =
1
2
ln(119901 + 119901119871
119901 minus 119901119871
) =
1
2
ln(119901 + 119864 tanh119910119901 minus 119864 tanh119910
)
=
1
2
ln(120573 + tanh119910120573 minus tanh119910
) equiv 120593 (119910)
(12)
119889120578
119889119910
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot
119889
119889119910
(
120573 + tanh119910120573 minus tanh119910
)
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot [
1
120573 minus tanh119910+
120573 + tanh119910(120573 minus tanh119910)2
]
sdot
119889
119889119910
(tanh119910)
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot
2120573
(120573 minus tanh119910)2
sdot
1
cos h2119910=
120573
1205732minus tanh2119910
sdot
1
cosh2119910
=
120573
1205732cosh2119910 minus sinh2119910
=
120573
1 minus (1 minus 1205732) cosh2119910
=
1 + (1 minus 1205732) sinh2120578
120573
(13)
The expressions after the last equal marks in (11) and (13) areobtained from the expressions before the last equal marks in(13) and (11) respectively It is obvious that the eduction ofthe revised conversion is simpler than that of the currentconversion
To use (10)ndash(13) we have relations
119891120578(120578)
10038161003816100381610038161198891205781003816100381610038161003816= 119891119910(119910)
10038161003816100381610038161198891199101003816100381610038161003816= 119891119910[ℎ (120578)]
sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 + (1 minus 1205732) sinh2120578
100381610038161003816100381610038161003816100381610038161003816
sdot10038161003816100381610038161198891205781003816100381610038161003816
119891119910(119910)
10038161003816100381610038161198891199101003816100381610038161003816= 119891120578(120578)
10038161003816100381610038161198891205781003816100381610038161003816= 119891120578[120593 (119910)]
sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 minus (1 minus 1205732) cosh2119910
100381610038161003816100381610038161003816100381610038161003816
sdot10038161003816100381610038161198891199101003816100381610038161003816
(14)
Then we have further
119891120578(120578) = 119891
119910[ℎ (120578)] sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 + (1 minus 1205732) sinh2120578
100381610038161003816100381610038161003816100381610038161003816
(15)
119891119910(119910) = 119891
120578[120593 (119910)] sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 minus (1 minus 1205732) cosh2119910
100381610038161003816100381610038161003816100381610038161003816
(16)
Equations (15) and (16) translate the rapidity distribution topseudorapidity one and the pseudorapidity distribution torapidity one respectively
In the previous discussions
120573 = radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
=
cosh 120578
radiccosh2120578 + 11989820119901minus2
119879
(17)
which can be used in the conversion Then the conversion isrelated to 119901
119879and 119898
0 To do a conversion we need to know
119901119879and119898
0for each particle
4 Advances in High Energy Physics
5 Conclusion and Discussion
We have given a revision on the current conversion betweenthe particle rapidity and pseudorapidity distributions It isshown that comparing to the current first conversion therevised one ((15) or (16)) has an additional term (1 minus
1205732)sinh2120578 or minus(1 minus 1205732)cosh2119910 in the denominator In central
rapidity region sinh 120578 asymp 0 and cosh119910 asymp 1 then (15) and(16) change to the current conversion However in forwardrapidity region the difference between the revised conversionand current one is obvious
Our conclusion does not mean that the current con-version between the unit-density functions 1198892119873119889119901
119879119889120578 and
1198892119873119889119901
119879119889119910 that is
1198892119873
119889119901119879119889120578
= radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
1198892119873
119889119901119879119889119910
(18)
is also erroneous or incomplete [12] In fact the conversionbetween the two unit-density functions is correct due to 119901
119879
being a series of fixed values in (18) To use (18) we also needto know 119901
119879and119898
0for each particle
Because the conversion between rapidity and pseudora-pidity distributions is not simpler than a direct calculationbased on the definitions of rapidity and pseudorapidity wewould rather use the direct calculation in modeling analysisIn fact in the epoch of high energy collider the dispersionbetween rapidity and pseudorapidity distributions is small[7] This means that we would also like to not distinguishstrictly rapidity and pseudorapidity distributions in generalmodeling analysis
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China under Grant no 10975095 the ChinaNational Fundamental Fund of Personnel Training underGrant no J1103210 the Open Research Subject of the ChineseAcademy of Sciences Large-Scale Scientific Facility underGrant no 2060205 and the Shanxi Scholarship Council ofChina
References
[1] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoMea-surement of the pseudorapidity and centrality dependence ofthe transverse energy density in Pb-Pb collisions at radic119904NN=276 TeVrdquo Physical Review Letters vol 109 no 15 Article ID152303 16 pages 2012
[2] I Bautista C Pajares J GMilhano and J D deDeus ldquoRapiditydependence of particle densities in pp and AA collisionsrdquo Phys-ical Review C vol 86 no 3 Article ID 034909 5 pages 2012
[3] B Zabinski ldquoMethods of multiplicity reconstruction in heavyion collisions in the ATLAS experimentrdquo Acta Physica PolonicaB vol 42 no 7 pp 1729ndash1736 2011
[4] M Biyajima M Ide T Mizoguchi and N Suzuki ldquoScalingbehavior of (119873ch)
minus1119889119873ch119889120578 at radic119878NN = 130GeV by PHOBOS
collaboration and its analyses in terms of stochasticapproachrdquohttparxivorgabshep-ph0110305
[5] M Biyajima M Ide T Mizoguchi and N Suzuki ldquoScalingbehavior of (119873ch)
minus1119889119873ch119889120578 at radic119878NN = 130GeV by the PHO-
BOS collaboration and its implicationrdquo Progress of TheoreticalPhysics vol 108 no 3 pp 559ndash569 2002
[6] P A Steinberg ldquoGlobal observables at RHICrdquo Nuclear PhysicsA vol 698 no 1ndash4 pp 314cndash322c 2002
[7] G Wolschin ldquoPseudorapidity distributions of produced charg-ed hadrons in pp collisions at RHIC and LHC energiesrdquo Euro-physics Letters vol 95 no 6 Article ID 61001 6 pages 2011
[8] D Kharzeev and E Levin ldquoManifestations of high density QCDin the first RHIC datardquo Physics Letters B vol 523 no 1-2 pp 79ndash87 2001
[9] D M Rohrscheid and G Wolschin ldquoCentrality dependence ofcharged-hadron pseudorapidity distributions in PbPb collisionsat energies available at the CERN large hadron collider in therelativistic diffusion modelrdquo Physical Review C vol 86 no 2Article ID 024902 7 pages 2012
[10] C Merino C Pajares and Y M Shabelski ldquoProduction of sec-ondaries in high-energy d+Au collisionsrdquo European PhysicalJournal C vol 59 no 3 pp 691ndash703 2009
[11] J L Albacete A Dumitru H Fujii and Y Nara ldquoCGC predic-tions for p + Pb collisions at the LHCrdquo Nuclear Physics A vol897 pp 1ndash27 2013
[12] C Y Wong Introduction to High-Energy Heavy-Ion CollisionsWorld Scientific Singapore 1994
[13] N S ZhangParticle Physics Science Press Beijing China 1986
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2 Advances in High Energy Physics
3 Current Conversion
To give a conversion between 119889119873119889120578 and 119889119873119889119910 in thecase of one of them being obtained one has two equivalentmethods which are currently used in the literature [4ndash11]According to [4 5 11] the first conversion relation between119889119873119889120578 and 119889119873119889119910 can be given by
119889119873
119889120578
=
119889119873
119889119910
119889119910
119889120578
=
119901
119864
119889119873
119889119910
(4)
where
119901
119864
=
radic1198642minus 1198982
0
119864
=radic1 minus
1198982
0
1198642
= radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
(5)
Then the first conversion is given by [4ndash6]
119889119873
119889120578
=
119901
119864
119889119873
119889119910
= radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
119889119873
119889119910
(6)
whereradic1199012119879+ 1198982
0equiv 119898119879is the transversemassWe see that the
first conversion is related to 119901119879
The second conversion is given in [5 7ndash11] We have
119889119873
119889120578
=
cosh 120578
radic1 + 1198982
0119901minus2
119879+ sinh2120578
119889119873
119889119910
=
cosh 120578
radic1198982
119879119901minus2
119879+ sinh2120578
119889119873
119889119910
=
cosh 120578
radiccosh2120578 + 11989820119901minus2
119879
119889119873
119889119910
(7)
which is also related to 119901119879 In [11] a similar conversion which
uses 1198982119875minus2 instead of 11989820119901minus2
119879in (7) is given where 119898 =
350MeV 119875 = 013GeV + 032GeV(radic1199041TeV)0115 and radic119904
denotes the center-of-mass energy The conversion used in[11] is a mutation of the second conversion
We now give the eduction of the current conversionAccording to [12]
119910 =
1
2
ln(119864 + 119901119871
119864 minus 119901119871
) =
1
2
ln(radic1199012+ 1198982
0+ 119901119871
radic1199012+ 1198982
0minus 119901119871
)
=
1
2
ln(radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
)
(8)
In the case of 119901119879being a given quantity we have
119889119910
119889120578
=
1
2
sdot
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
sdot
119889
119889120578
(
radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
)
=
1
2
sdot[
[
[
1
radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
sdot
119889
119889120578
(radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578)
minus
1
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
sdot
119889
119889120578
(radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578)]]
]
=
1
2
sdot[
[
[
1
radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578
times(
1199012
119879cosh 120578 sinh 120578
radic1199012
119879cosh2120578 + 1198982
0
+ 119901119879cosh 120578)
minus
1
radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578
times (
1199012
119879cosh 120578 sinh 120578
radic1199012
119879cosh2120578 + 1198982
0
minus 119901119879cosh 120578)]
]
]
=
1
2
sdot
1
1199012
119879+ 1198982
0
sdot[
[
[
(
1199012
119879cosh 120578 sinh 120578
radic1199012
119879cosh2120578 + 1198982
0
+119901119879cosh 120578)
times (radic1199012
119879cosh2120578 + 1198982
0minus 119901119879sinh 120578)
minus(
1199012
119879cosh 120578 sinh 120578
radic1199012
119879cosh2120578 + 1198982
0
minus 119901119879cosh 120578)
times(radic1199012
119879cosh2120578 + 1198982
0+ 119901119879sinh 120578)]]
]
Advances in High Energy Physics 3
=
1
2
sdot
1
1199012
119879+ 1198982
0
sdot
2 (1199012
119879+ 1198982
0) 119901119879cosh 120578
radic1199012
119879cosh2120578 + 1198982
0
=
119901119879cosh 120578
radic1199012
119879cosh2120578 + 1198982
0
=
cosh 120578
radiccosh2120578 + 11989820119901minus2
119879
=
119901
119864
= 120573
(9)
where 120573 denotes the velocity of the concerned particle Thenwe obtain the current conversion
However we would like to point out that the previousconversion is incomplete due to the fact that 119901
119879= 119901 cosh 120578
is also a function of 120578 which should be considered in doingthe differential treatment Instead 119901 and 119864 can be regardedas given quantities
4 Revised Conversion
In the differential treatment we think that both the 119901119879=
119901 cosh 120578 and 119901119871= 119901 tanh 120578 are functions of 120578 Contrarily
119901 and 119864 have the fixed values for a given particle Then
119910 =
1
2
ln(119864 + 119901119871
119864 minus 119901119871
) =
1
2
ln(119864 + 119901 tanh 120578119864 minus 119901 tanh 120578
)
=
1
2
ln(1 + 120573 tanh 1205781 minus 120573 tanh 120578
) equiv ℎ (120578)
(10)
119889119910
119889120578
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot
119889
119889120578
(
1 + 120573 tanh 1205781 minus 120573 tanh 120578
)
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot [
1
1 minus 120573 tanh 120578+
1 + 120573 tanh 120578(1 minus 120573 tanh 120578)2
] sdot 120573
119889
119889120578
(tanh 120578)
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot
2120573
(1 minus 120573 tanh 120578)2sdot
1
cosh2120578
=
120573
1 minus 1205732tanh2120578
sdot
1
cosh2120578
=
120573
cosh2120578 minus 1205732sinh2120578=
120573
1 + (1 minus 1205732) sinh2120578
=
1 minus (1 minus 1205732) cosh2119910
120573
(11)
It is different from the first conversion which gives that 119889119910119889120578 = 120573 Correspondingly
120578 =
1
2
ln(119901 + 119901119871
119901 minus 119901119871
) =
1
2
ln(119901 + 119864 tanh119910119901 minus 119864 tanh119910
)
=
1
2
ln(120573 + tanh119910120573 minus tanh119910
) equiv 120593 (119910)
(12)
119889120578
119889119910
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot
119889
119889119910
(
120573 + tanh119910120573 minus tanh119910
)
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot [
1
120573 minus tanh119910+
120573 + tanh119910(120573 minus tanh119910)2
]
sdot
119889
119889119910
(tanh119910)
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot
2120573
(120573 minus tanh119910)2
sdot
1
cos h2119910=
120573
1205732minus tanh2119910
sdot
1
cosh2119910
=
120573
1205732cosh2119910 minus sinh2119910
=
120573
1 minus (1 minus 1205732) cosh2119910
=
1 + (1 minus 1205732) sinh2120578
120573
(13)
The expressions after the last equal marks in (11) and (13) areobtained from the expressions before the last equal marks in(13) and (11) respectively It is obvious that the eduction ofthe revised conversion is simpler than that of the currentconversion
To use (10)ndash(13) we have relations
119891120578(120578)
10038161003816100381610038161198891205781003816100381610038161003816= 119891119910(119910)
10038161003816100381610038161198891199101003816100381610038161003816= 119891119910[ℎ (120578)]
sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 + (1 minus 1205732) sinh2120578
100381610038161003816100381610038161003816100381610038161003816
sdot10038161003816100381610038161198891205781003816100381610038161003816
119891119910(119910)
10038161003816100381610038161198891199101003816100381610038161003816= 119891120578(120578)
10038161003816100381610038161198891205781003816100381610038161003816= 119891120578[120593 (119910)]
sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 minus (1 minus 1205732) cosh2119910
100381610038161003816100381610038161003816100381610038161003816
sdot10038161003816100381610038161198891199101003816100381610038161003816
(14)
Then we have further
119891120578(120578) = 119891
119910[ℎ (120578)] sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 + (1 minus 1205732) sinh2120578
100381610038161003816100381610038161003816100381610038161003816
(15)
119891119910(119910) = 119891
120578[120593 (119910)] sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 minus (1 minus 1205732) cosh2119910
100381610038161003816100381610038161003816100381610038161003816
(16)
Equations (15) and (16) translate the rapidity distribution topseudorapidity one and the pseudorapidity distribution torapidity one respectively
In the previous discussions
120573 = radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
=
cosh 120578
radiccosh2120578 + 11989820119901minus2
119879
(17)
which can be used in the conversion Then the conversion isrelated to 119901
119879and 119898
0 To do a conversion we need to know
119901119879and119898
0for each particle
4 Advances in High Energy Physics
5 Conclusion and Discussion
We have given a revision on the current conversion betweenthe particle rapidity and pseudorapidity distributions It isshown that comparing to the current first conversion therevised one ((15) or (16)) has an additional term (1 minus
1205732)sinh2120578 or minus(1 minus 1205732)cosh2119910 in the denominator In central
rapidity region sinh 120578 asymp 0 and cosh119910 asymp 1 then (15) and(16) change to the current conversion However in forwardrapidity region the difference between the revised conversionand current one is obvious
Our conclusion does not mean that the current con-version between the unit-density functions 1198892119873119889119901
119879119889120578 and
1198892119873119889119901
119879119889119910 that is
1198892119873
119889119901119879119889120578
= radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
1198892119873
119889119901119879119889119910
(18)
is also erroneous or incomplete [12] In fact the conversionbetween the two unit-density functions is correct due to 119901
119879
being a series of fixed values in (18) To use (18) we also needto know 119901
119879and119898
0for each particle
Because the conversion between rapidity and pseudora-pidity distributions is not simpler than a direct calculationbased on the definitions of rapidity and pseudorapidity wewould rather use the direct calculation in modeling analysisIn fact in the epoch of high energy collider the dispersionbetween rapidity and pseudorapidity distributions is small[7] This means that we would also like to not distinguishstrictly rapidity and pseudorapidity distributions in generalmodeling analysis
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China under Grant no 10975095 the ChinaNational Fundamental Fund of Personnel Training underGrant no J1103210 the Open Research Subject of the ChineseAcademy of Sciences Large-Scale Scientific Facility underGrant no 2060205 and the Shanxi Scholarship Council ofChina
References
[1] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoMea-surement of the pseudorapidity and centrality dependence ofthe transverse energy density in Pb-Pb collisions at radic119904NN=276 TeVrdquo Physical Review Letters vol 109 no 15 Article ID152303 16 pages 2012
[2] I Bautista C Pajares J GMilhano and J D deDeus ldquoRapiditydependence of particle densities in pp and AA collisionsrdquo Phys-ical Review C vol 86 no 3 Article ID 034909 5 pages 2012
[3] B Zabinski ldquoMethods of multiplicity reconstruction in heavyion collisions in the ATLAS experimentrdquo Acta Physica PolonicaB vol 42 no 7 pp 1729ndash1736 2011
[4] M Biyajima M Ide T Mizoguchi and N Suzuki ldquoScalingbehavior of (119873ch)
minus1119889119873ch119889120578 at radic119878NN = 130GeV by PHOBOS
collaboration and its analyses in terms of stochasticapproachrdquohttparxivorgabshep-ph0110305
[5] M Biyajima M Ide T Mizoguchi and N Suzuki ldquoScalingbehavior of (119873ch)
minus1119889119873ch119889120578 at radic119878NN = 130GeV by the PHO-
BOS collaboration and its implicationrdquo Progress of TheoreticalPhysics vol 108 no 3 pp 559ndash569 2002
[6] P A Steinberg ldquoGlobal observables at RHICrdquo Nuclear PhysicsA vol 698 no 1ndash4 pp 314cndash322c 2002
[7] G Wolschin ldquoPseudorapidity distributions of produced charg-ed hadrons in pp collisions at RHIC and LHC energiesrdquo Euro-physics Letters vol 95 no 6 Article ID 61001 6 pages 2011
[8] D Kharzeev and E Levin ldquoManifestations of high density QCDin the first RHIC datardquo Physics Letters B vol 523 no 1-2 pp 79ndash87 2001
[9] D M Rohrscheid and G Wolschin ldquoCentrality dependence ofcharged-hadron pseudorapidity distributions in PbPb collisionsat energies available at the CERN large hadron collider in therelativistic diffusion modelrdquo Physical Review C vol 86 no 2Article ID 024902 7 pages 2012
[10] C Merino C Pajares and Y M Shabelski ldquoProduction of sec-ondaries in high-energy d+Au collisionsrdquo European PhysicalJournal C vol 59 no 3 pp 691ndash703 2009
[11] J L Albacete A Dumitru H Fujii and Y Nara ldquoCGC predic-tions for p + Pb collisions at the LHCrdquo Nuclear Physics A vol897 pp 1ndash27 2013
[12] C Y Wong Introduction to High-Energy Heavy-Ion CollisionsWorld Scientific Singapore 1994
[13] N S ZhangParticle Physics Science Press Beijing China 1986
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Advances in High Energy Physics 3
=
1
2
sdot
1
1199012
119879+ 1198982
0
sdot
2 (1199012
119879+ 1198982
0) 119901119879cosh 120578
radic1199012
119879cosh2120578 + 1198982
0
=
119901119879cosh 120578
radic1199012
119879cosh2120578 + 1198982
0
=
cosh 120578
radiccosh2120578 + 11989820119901minus2
119879
=
119901
119864
= 120573
(9)
where 120573 denotes the velocity of the concerned particle Thenwe obtain the current conversion
However we would like to point out that the previousconversion is incomplete due to the fact that 119901
119879= 119901 cosh 120578
is also a function of 120578 which should be considered in doingthe differential treatment Instead 119901 and 119864 can be regardedas given quantities
4 Revised Conversion
In the differential treatment we think that both the 119901119879=
119901 cosh 120578 and 119901119871= 119901 tanh 120578 are functions of 120578 Contrarily
119901 and 119864 have the fixed values for a given particle Then
119910 =
1
2
ln(119864 + 119901119871
119864 minus 119901119871
) =
1
2
ln(119864 + 119901 tanh 120578119864 minus 119901 tanh 120578
)
=
1
2
ln(1 + 120573 tanh 1205781 minus 120573 tanh 120578
) equiv ℎ (120578)
(10)
119889119910
119889120578
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot
119889
119889120578
(
1 + 120573 tanh 1205781 minus 120573 tanh 120578
)
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot [
1
1 minus 120573 tanh 120578+
1 + 120573 tanh 120578(1 minus 120573 tanh 120578)2
] sdot 120573
119889
119889120578
(tanh 120578)
=
1
2
sdot
1 minus 120573 tanh 1205781 + 120573 tanh 120578
sdot
2120573
(1 minus 120573 tanh 120578)2sdot
1
cosh2120578
=
120573
1 minus 1205732tanh2120578
sdot
1
cosh2120578
=
120573
cosh2120578 minus 1205732sinh2120578=
120573
1 + (1 minus 1205732) sinh2120578
=
1 minus (1 minus 1205732) cosh2119910
120573
(11)
It is different from the first conversion which gives that 119889119910119889120578 = 120573 Correspondingly
120578 =
1
2
ln(119901 + 119901119871
119901 minus 119901119871
) =
1
2
ln(119901 + 119864 tanh119910119901 minus 119864 tanh119910
)
=
1
2
ln(120573 + tanh119910120573 minus tanh119910
) equiv 120593 (119910)
(12)
119889120578
119889119910
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot
119889
119889119910
(
120573 + tanh119910120573 minus tanh119910
)
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot [
1
120573 minus tanh119910+
120573 + tanh119910(120573 minus tanh119910)2
]
sdot
119889
119889119910
(tanh119910)
=
1
2
sdot
120573 minus tanh119910120573 + tanh119910
sdot
2120573
(120573 minus tanh119910)2
sdot
1
cos h2119910=
120573
1205732minus tanh2119910
sdot
1
cosh2119910
=
120573
1205732cosh2119910 minus sinh2119910
=
120573
1 minus (1 minus 1205732) cosh2119910
=
1 + (1 minus 1205732) sinh2120578
120573
(13)
The expressions after the last equal marks in (11) and (13) areobtained from the expressions before the last equal marks in(13) and (11) respectively It is obvious that the eduction ofthe revised conversion is simpler than that of the currentconversion
To use (10)ndash(13) we have relations
119891120578(120578)
10038161003816100381610038161198891205781003816100381610038161003816= 119891119910(119910)
10038161003816100381610038161198891199101003816100381610038161003816= 119891119910[ℎ (120578)]
sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 + (1 minus 1205732) sinh2120578
100381610038161003816100381610038161003816100381610038161003816
sdot10038161003816100381610038161198891205781003816100381610038161003816
119891119910(119910)
10038161003816100381610038161198891199101003816100381610038161003816= 119891120578(120578)
10038161003816100381610038161198891205781003816100381610038161003816= 119891120578[120593 (119910)]
sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 minus (1 minus 1205732) cosh2119910
100381610038161003816100381610038161003816100381610038161003816
sdot10038161003816100381610038161198891199101003816100381610038161003816
(14)
Then we have further
119891120578(120578) = 119891
119910[ℎ (120578)] sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 + (1 minus 1205732) sinh2120578
100381610038161003816100381610038161003816100381610038161003816
(15)
119891119910(119910) = 119891
120578[120593 (119910)] sdot
100381610038161003816100381610038161003816100381610038161003816
120573
1 minus (1 minus 1205732) cosh2119910
100381610038161003816100381610038161003816100381610038161003816
(16)
Equations (15) and (16) translate the rapidity distribution topseudorapidity one and the pseudorapidity distribution torapidity one respectively
In the previous discussions
120573 = radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
=
cosh 120578
radiccosh2120578 + 11989820119901minus2
119879
(17)
which can be used in the conversion Then the conversion isrelated to 119901
119879and 119898
0 To do a conversion we need to know
119901119879and119898
0for each particle
4 Advances in High Energy Physics
5 Conclusion and Discussion
We have given a revision on the current conversion betweenthe particle rapidity and pseudorapidity distributions It isshown that comparing to the current first conversion therevised one ((15) or (16)) has an additional term (1 minus
1205732)sinh2120578 or minus(1 minus 1205732)cosh2119910 in the denominator In central
rapidity region sinh 120578 asymp 0 and cosh119910 asymp 1 then (15) and(16) change to the current conversion However in forwardrapidity region the difference between the revised conversionand current one is obvious
Our conclusion does not mean that the current con-version between the unit-density functions 1198892119873119889119901
119879119889120578 and
1198892119873119889119901
119879119889119910 that is
1198892119873
119889119901119879119889120578
= radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
1198892119873
119889119901119879119889119910
(18)
is also erroneous or incomplete [12] In fact the conversionbetween the two unit-density functions is correct due to 119901
119879
being a series of fixed values in (18) To use (18) we also needto know 119901
119879and119898
0for each particle
Because the conversion between rapidity and pseudora-pidity distributions is not simpler than a direct calculationbased on the definitions of rapidity and pseudorapidity wewould rather use the direct calculation in modeling analysisIn fact in the epoch of high energy collider the dispersionbetween rapidity and pseudorapidity distributions is small[7] This means that we would also like to not distinguishstrictly rapidity and pseudorapidity distributions in generalmodeling analysis
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China under Grant no 10975095 the ChinaNational Fundamental Fund of Personnel Training underGrant no J1103210 the Open Research Subject of the ChineseAcademy of Sciences Large-Scale Scientific Facility underGrant no 2060205 and the Shanxi Scholarship Council ofChina
References
[1] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoMea-surement of the pseudorapidity and centrality dependence ofthe transverse energy density in Pb-Pb collisions at radic119904NN=276 TeVrdquo Physical Review Letters vol 109 no 15 Article ID152303 16 pages 2012
[2] I Bautista C Pajares J GMilhano and J D deDeus ldquoRapiditydependence of particle densities in pp and AA collisionsrdquo Phys-ical Review C vol 86 no 3 Article ID 034909 5 pages 2012
[3] B Zabinski ldquoMethods of multiplicity reconstruction in heavyion collisions in the ATLAS experimentrdquo Acta Physica PolonicaB vol 42 no 7 pp 1729ndash1736 2011
[4] M Biyajima M Ide T Mizoguchi and N Suzuki ldquoScalingbehavior of (119873ch)
minus1119889119873ch119889120578 at radic119878NN = 130GeV by PHOBOS
collaboration and its analyses in terms of stochasticapproachrdquohttparxivorgabshep-ph0110305
[5] M Biyajima M Ide T Mizoguchi and N Suzuki ldquoScalingbehavior of (119873ch)
minus1119889119873ch119889120578 at radic119878NN = 130GeV by the PHO-
BOS collaboration and its implicationrdquo Progress of TheoreticalPhysics vol 108 no 3 pp 559ndash569 2002
[6] P A Steinberg ldquoGlobal observables at RHICrdquo Nuclear PhysicsA vol 698 no 1ndash4 pp 314cndash322c 2002
[7] G Wolschin ldquoPseudorapidity distributions of produced charg-ed hadrons in pp collisions at RHIC and LHC energiesrdquo Euro-physics Letters vol 95 no 6 Article ID 61001 6 pages 2011
[8] D Kharzeev and E Levin ldquoManifestations of high density QCDin the first RHIC datardquo Physics Letters B vol 523 no 1-2 pp 79ndash87 2001
[9] D M Rohrscheid and G Wolschin ldquoCentrality dependence ofcharged-hadron pseudorapidity distributions in PbPb collisionsat energies available at the CERN large hadron collider in therelativistic diffusion modelrdquo Physical Review C vol 86 no 2Article ID 024902 7 pages 2012
[10] C Merino C Pajares and Y M Shabelski ldquoProduction of sec-ondaries in high-energy d+Au collisionsrdquo European PhysicalJournal C vol 59 no 3 pp 691ndash703 2009
[11] J L Albacete A Dumitru H Fujii and Y Nara ldquoCGC predic-tions for p + Pb collisions at the LHCrdquo Nuclear Physics A vol897 pp 1ndash27 2013
[12] C Y Wong Introduction to High-Energy Heavy-Ion CollisionsWorld Scientific Singapore 1994
[13] N S ZhangParticle Physics Science Press Beijing China 1986
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
4 Advances in High Energy Physics
5 Conclusion and Discussion
We have given a revision on the current conversion betweenthe particle rapidity and pseudorapidity distributions It isshown that comparing to the current first conversion therevised one ((15) or (16)) has an additional term (1 minus
1205732)sinh2120578 or minus(1 minus 1205732)cosh2119910 in the denominator In central
rapidity region sinh 120578 asymp 0 and cosh119910 asymp 1 then (15) and(16) change to the current conversion However in forwardrapidity region the difference between the revised conversionand current one is obvious
Our conclusion does not mean that the current con-version between the unit-density functions 1198892119873119889119901
119879119889120578 and
1198892119873119889119901
119879119889119910 that is
1198892119873
119889119901119879119889120578
= radic1 minus(
1198980
radic1199012
119879+ 1198982
0cosh119910
)
2
1198892119873
119889119901119879119889119910
(18)
is also erroneous or incomplete [12] In fact the conversionbetween the two unit-density functions is correct due to 119901
119879
being a series of fixed values in (18) To use (18) we also needto know 119901
119879and119898
0for each particle
Because the conversion between rapidity and pseudora-pidity distributions is not simpler than a direct calculationbased on the definitions of rapidity and pseudorapidity wewould rather use the direct calculation in modeling analysisIn fact in the epoch of high energy collider the dispersionbetween rapidity and pseudorapidity distributions is small[7] This means that we would also like to not distinguishstrictly rapidity and pseudorapidity distributions in generalmodeling analysis
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China under Grant no 10975095 the ChinaNational Fundamental Fund of Personnel Training underGrant no J1103210 the Open Research Subject of the ChineseAcademy of Sciences Large-Scale Scientific Facility underGrant no 2060205 and the Shanxi Scholarship Council ofChina
References
[1] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoMea-surement of the pseudorapidity and centrality dependence ofthe transverse energy density in Pb-Pb collisions at radic119904NN=276 TeVrdquo Physical Review Letters vol 109 no 15 Article ID152303 16 pages 2012
[2] I Bautista C Pajares J GMilhano and J D deDeus ldquoRapiditydependence of particle densities in pp and AA collisionsrdquo Phys-ical Review C vol 86 no 3 Article ID 034909 5 pages 2012
[3] B Zabinski ldquoMethods of multiplicity reconstruction in heavyion collisions in the ATLAS experimentrdquo Acta Physica PolonicaB vol 42 no 7 pp 1729ndash1736 2011
[4] M Biyajima M Ide T Mizoguchi and N Suzuki ldquoScalingbehavior of (119873ch)
minus1119889119873ch119889120578 at radic119878NN = 130GeV by PHOBOS
collaboration and its analyses in terms of stochasticapproachrdquohttparxivorgabshep-ph0110305
[5] M Biyajima M Ide T Mizoguchi and N Suzuki ldquoScalingbehavior of (119873ch)
minus1119889119873ch119889120578 at radic119878NN = 130GeV by the PHO-
BOS collaboration and its implicationrdquo Progress of TheoreticalPhysics vol 108 no 3 pp 559ndash569 2002
[6] P A Steinberg ldquoGlobal observables at RHICrdquo Nuclear PhysicsA vol 698 no 1ndash4 pp 314cndash322c 2002
[7] G Wolschin ldquoPseudorapidity distributions of produced charg-ed hadrons in pp collisions at RHIC and LHC energiesrdquo Euro-physics Letters vol 95 no 6 Article ID 61001 6 pages 2011
[8] D Kharzeev and E Levin ldquoManifestations of high density QCDin the first RHIC datardquo Physics Letters B vol 523 no 1-2 pp 79ndash87 2001
[9] D M Rohrscheid and G Wolschin ldquoCentrality dependence ofcharged-hadron pseudorapidity distributions in PbPb collisionsat energies available at the CERN large hadron collider in therelativistic diffusion modelrdquo Physical Review C vol 86 no 2Article ID 024902 7 pages 2012
[10] C Merino C Pajares and Y M Shabelski ldquoProduction of sec-ondaries in high-energy d+Au collisionsrdquo European PhysicalJournal C vol 59 no 3 pp 691ndash703 2009
[11] J L Albacete A Dumitru H Fujii and Y Nara ldquoCGC predic-tions for p + Pb collisions at the LHCrdquo Nuclear Physics A vol897 pp 1ndash27 2013
[12] C Y Wong Introduction to High-Energy Heavy-Ion CollisionsWorld Scientific Singapore 1994
[13] N S ZhangParticle Physics Science Press Beijing China 1986
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of