Strong longitudinal color field effects in pp collisions at energies available at the Large Hadron Collider

0.67 MB·English

by  V. Topor Pop

Strong longitudinal color-field effects in
pp collisions at energies available at the CERN Large Hadron Collider.
V. Topor Pop,1 M. Gyulassy,2 J. Barrette,1 C. Gale,1 and A. Warburton1
1McGill University, Montreal, Canada, H3A 2T8
2Columbia University, New York, N.Y. 10027
(Dated: January 25, 2011)
Westudytheeffectofstronglongitudinalcolorfields(SCF)inp+preactionsuptoLargeHadron
Collider energies in the framework of theHIJING/BB¯ v2.0 model that combines (collinear factor-
ized)pQCDmultipleminijet productionwithsoft longitudinalstringexcitation andhadronization.
The default vacuum string tension, κ0 = 1 GeV/fm, is replaced by an effective energy dependent
string tension, κ(s) = κ0(s/s0)0.06 that increases monotonically with center-of-mass energy. The
1 exponent λ=0.06 is found sufficient to reproduce well the energy dependence of multiparticle ob-
1
servables in RHIC, Tevatron, as well as recent LHC data. This exponent is half of that predicted
0
by the Color Glass Saturation (CGC) model, λCGC =0.115, where gluon fusion multiparticle pro-
2 duction mechanisms are assumed. In HIJING/BB¯ v2.0, the rapid growth of dNch/dη with energy

n is due to the interplay of copious minijet production with increasing of strong color field (SCF)
a contributions. The large (strange)baryon-to-meson ratios measured at Tevatron energies are well
J described. Asignificant enhancement oftheseratios ispredicteduptothehighest LHCenergy (14
6 TeV).Theeffect ofJJ¯loopsandSCFon baryon-anti-baryonasymmetry,anditsrelation tobaryon
2 numbertransport, is also discussed.

] PACSnumbers: 12.38.Mh,24.85.+p,25.40Ve, 25.75.-q
h
p
-
p I. INTRODUCTION projectile and target create confined color flux tubes of
e tension( 1GeV/fm),thatmustneutralizethroughpair
≈
h production or color singlet hadronization approximately
[ With the commissioning of the Large Hadron Collider uniformly in rapidity. In nucleus-nucleus collisions, the

(LHC),itwillsoonbepossibletotestmodelsofmultipar- A1/3 enhancement of the local parton density of high x
2
ticle productionin hadron-hadroncollisionsup to anen-
v partonsallowsforhighercolorCasimirrepresentationsto
ergy of 14 TeV. Charged particle densities, dN /dη, es-
9 ch be excited. Those flux tubes with stronger longitudinal
3 pecially the values at mid-rapidity and their dependence colorfields than in averagepp reactionshave been called
4 on center-of-mass energy √s (c.m.s.) are important for colorropes[46]andnaturallyhavehigherstringtensions
5 understanding the mechanism of hadron production and
[47]. Recently, an extension of Color Glass Condensate
0. the interplayof softandhardscattering contributionsin (CGC) theory has proposed a more detailed dynamical
1 the LHC energy range. The rate of parton-parton and “GLASMA” model [48, 49] of color ropes.
0 multiparton-parton(MPI)scatteringarestronglycorre-
Inthe HIJINGmodel[42]thesoftbeamjetfragmenta-
1 latedtotheobservedparticlemultiplicity(relatedalsoto
tionismodeledbysimplediquark-quarkstringsasinthe
v: initial entropyandinitial energydensitygeneratedinthe LUND model with multiple gluon kinks induced by soft
i collisionprocess). Newdataoninclusivechargedparticle
X gluon radiations. Hard collisions are included with stan-
distributions from the LHC in pp collisions have become
dard perturbative QCD (pQCD) as programmed in the
r available[1–12]. Theseresultscomplementpreviousdata
a PYTHIA generator [50]. However, HIJING differs from
onppandpp¯collisionstakenatlowerenergies√s=0.02
PYTHIA by the incusion of a geometric scaling multi-
- 1.96 TeV [13–23]. Many of these measurements have
plejetproductionmodel. Thusthismodelcontainsboth
been used to constrainphenomenologicalmodels of soft-
longitudinalfieldinducedsoftbeamjetmultiparticlepro-
hadronic interactionsand to predict propertiesat higher
duction and collinear factorized pQCD based hard mul-
energies [24–37]. The recent LHC data may lead to a
tiple jet production for p p =2 GeV/c.
T 0
better theoretical understanding based on a Quantum ≥
A systematic comparison with data on pp and pp¯col-
Chromodynamics (QCD) approach [38–41].
lisions in a wide energy range [42] revealed that minijet
The Heavy Ion Jet Interacting Generator (HIJING) productionandfragmentationasimplementedinthe HI-
[42] and HIJING/BB¯ v1.10 models [43] have been used JINGmodelprovideasimultaneousandconsistentexpla-
extensively to study particle production in pp collisions nation of several effects: the inclusive spectra at moder-
and to determine the physical properties of the ultra- atetransversemomentum(p );theenergydependenceof
T
densematterproducedinrelativisticheavy-ioncollisions. the central rapidity density; the two particle correlation
In the LUND [44] and Dual-Parton (DPM) [45] models function; and the degree of violation of Koba-Nielsen-
multi QCD strings or flux tubes were proposed to de- Olesen (KNO) scaling [51], [52] up to Tevatron energy
scribe soft multiparticle production in longitudinal color (√s = 1.8 TeV). However, the model failed to describe
fields. Color exchange between high x partons in the the dependence of the mean value of transverse momen-
2
tum (< p >) on charged particle multiplicity (N ). mented. In a dual superconductor model of color con-
T ch
Wang argued [52] that by requiring high N within a finement for the three-quark positioning in a Y - geom-
ch
limited pseudorapidity (η) range one necessarily biases etry, the flux tubes converge first toward the center of
the data towards higher p minijets, hence the observed the triangle and there is also another component that
T
increaseof<p >versus(vs.) dN /dη [52]. This effect runs inthe opposite direction(like a Mercedes star) [68].
T ch
has also been associated with the presence of transverse Unlike the conventional diquark-quark implemented in
flow of the hadronic matter [53, 54] and was proposed LUNDandtheHIJINGmodel[42],theHIJING/BB¯ v1.10
as possibly due to quark-gluon plasma (QGP) formation [43] model allows the diquark-quark to split with the
already in pp collisions. three independent flux lines tied together with an ǫ
ijk
Initial states of color gauge fields produced in high- a junction and terminating on three delocalized funda-
energy heavy-ion collisions have also recently been dis- mental Casimir quarks. We introduced [67] a new ver-
cussed in Ref. [55]. Decay of a strong color electric field sion (v2.0) of HIJING/BB¯ that differs from HIJING/BB¯
(SCF) (E > E =1018 V/m) due to the Schwinger v1.10 [43] in its implementation of additional more com-
critical
mechanisms [56] plays an important role at the initial plexfluxtopologiesviajunctionanti-junction(JJ¯)loops.
stageofheavy-ioncollisionsatultra-relativisticenergies. We parametrize the probability that a junction loop oc-
A thermalizationscenario basedon the analogybetween curs in the string. Moreover, we enhance the intrinsic
Schwinger mechanisms and the Hawking-Unruh effect (anti)diquark-quark p kick (by a factor f = 3) of all
T
has been proposed [57]. It was also suggested that the (q-qq)stringsthatcontainoneormultiple JJ¯loops. The
back-reaction and screening effects of quark and anti- reason for this is the mechanism behind the dynamic of
quark pairs on external electric field could even lead to diquark-quark breaking (see Ref. [64] for details).
the phenomenon of plasma oscillations [58–60]. In string fragmentation phenomenology, it has been
Recently, the Schwingermechanismhas been revisited proposed that the observed strong enhancement of
[61]andpairproductionintime-dependentelectricfields strangeparticle productionin nuclearcollisions couldbe
has been studied [62]. It was concluded that particles naturally explained via strong color field (SCF) effects
with large momentum were likely to have been created [47] . For a uniform chromoelectric flux tube with field
earlier, and for very short temporal widths (∆τ 10t , (E),thepairproductionrate[46,47,61]perunitvolume
c
≈
where the Compton time t = 1/m ) and as a conse- for a (light)heavy quark (Q) is given by
c c
quence the Schwinger formula could underestimate the
reachable particle number density. In previous papers, κ2 πm2
Q
Γ= exp , (1)
wehaveshownthatthe dynamicsofstrangenessproduc- 4π3 − κ !
tion in pp and Au + Au collisions at Relativistic Heavy
Ion Collider (RHIC) energies deviates considerably from where Q = qq (diquark), s (strange), c (charm) or b
calculationsbasedonSchwinger-likeestimatesforhomo- (bottom). The current quark masses are m = 0.45
qq
geneous and constant color fields and point to the con- GeV [69], m = 0.12 GeV, m = 1.27 GeV, and m =
s c b
tribution of fluctuations of transient strong color fields 4.16 GeV [70]. The constituent quark masses of light
(SCF) [63–66]. non-strange quarks are M = 0.23 GeV, of the strange
u,d
Inthispaperweextendourstudy ofthe dynamiccon- quarkisM =0.35GeV[71],andofthe diquarkisM =
s qq
sequences of SCF in the framework of the HIJING/BB¯ 0.55 0.05 GeV [69].
±
v2.0 model [64] to particle production in hadron-hadron Note that κ = eE = C (A)/C (F)κ is the
eff 2 2 0
collisionsat LHC energies. We exploredynamicaleffects effective string tens|ion|in low energy pp reactions with
associatedwithlongrangecoherentfields(i.e,stronglon- κ 1 GeV/fm and C (A), Cp(F) are the second order
0 2 2
gitudinal color fields, SCF), including baryon junctions Cas≈imir operators (see Ref. [47]). An enhanced rate for
and loops [63, 67], with emphasis on the new observ- spontaneouspairproductionisnaturallyassociatedwith
ables measured in pp collisions at the LHC by the AL- “strong chromo-electric fields”, such that κ/m2 > 1 at
Q
ICE, ATLAS and CMS collaborations. Our study aims least some of the time. In a strong longitudinal color
to investigate a broad set of observables sensitive to the electric field, the heavier flavor suppression factor γQQ¯
dynamicsofthecollisions,coveringbothlongitudinaland varies with string tension via the well known Schwinger
transverse degree of freedom. In addition, this study is formula [56], since
intended to provide the pp baseline to future extrapo-
nlautciolenuss-tnoucLleHuCs (sAtu+diAes)ocfolplisriootnosn.-nucleus (p + A) and γQQ¯ = ΓΓQqQq¯¯ =exp −π(MQ2κ0−m2q)!<1 (2)
for Q = qq, s, c or b and q = u, d. In our calculations,
II. OUTLINE OF HIJING/BB¯ V2.0 MODEL. we assumethatMeff =0.5 GeV, Meff = 0.28GeV, Meff
qq s c
=1.30GeV.Therefore,the aboveformulaimplies asup-
InHIJING/BB¯ v2.0, inadditionto conventionalquark- pression of heavier quark production according to u : d
diquarklongitudinalelectricfields,novelcolorfluxtopol- : qq : s : c 1 : 1 : 0.02 : 0.3 : 10−11 for the vac-
ogy junction anti-junction (JJ¯) loops are also imple- uum string te≈nsion κ = 1 GeV/fm. For a color rope,
0
3
on the other hand, if the average string tension value κ 6
Effective String Tension p+p
increases,thesuppressionfactorsγQQ¯ increase. Weshow
belowthatthisdynamicalmechanismimprovesconsider- ] 5 k (s) = Q2(s/s )0.06
m 0 0
aabtltyhethTeedvaestcrorinptainond oafttLhHeCsterannerggeiems.eson/hyperon data V/f 4 Q2sat(s) = Q02(s/s0)0.115
e
G
Saturation physics is based on the observation that
[
small-x hadronic and nuclear wave functions, and, thus s) 3
(
the scatteringcrosssectionsaswell,aredescribedbythe 2Qsat
same internal momentum scale known as the saturation ), 2
scale (Qsat). A recent analysis of pp data up to LHC 7 (s
TeVhasshownthat,withthekT factorized(GLR)gluon k 1
fusionapproximation[72],thegrowthofthedN /dηcan
ch
beaccountedforifthesaturationscalegrowswithc.m.s.
0
-1
energy as 10 1 10
s1/2 [TeV]
Q2 (s)=Q2(s/s )λCGC, (3)
sat 0 0
with λ 0.115. The saturation scale is also increas-
CGC
ing with ato≈mic number as A1/6 [57]. It was arguedthat FIG. 1: (Color online) Energy dependence of the effective
theeffectivestringtension(κ)ofcolorropesshouldscale string tension κ(s) in pp collisions (Eq. 4). The values Q2sat
with Q2 [57, 58]. (Eq.3)arefromCGCmodelfitstoLHCdatafromRef.[29].
sat
However, in HIJING the string/rope fragmentation
is the only soft source of multiparticle production and
multiple minijets provide a semi-hard additional source
are taken from Eq. 4 in comparison with the values pre-
that is computable within collinear factorized standard
dicted using Q2 (Eq. 3 from the CGC model fit [29]).
pQCD with initial and final radiation (DGLAP evolu- sat
tion [73]). In order to achieve a quantitative descrip-
0.8
tion, within our HIJING/BB¯ framework we will show g
s Strange/Light Suppression in p+p
that combined effects of hard and soft sources of multi- 0.7
g with k (s) = k (s/s )0.06
particle production can reproduce the available data in s 0 0
the range 0.02 < √s < 20 TeV only with a reduced de- 0.6 g with Q2 (s) = Q2(s/s )0.115
s sat 0 0
pendence of the effective string tension on √s. We find 0.5
that the data can be well reproduced taking
0.4
κ(s)=κ (s/s )0.06 GeV/fm Q Q (s), (4)
0 0 0 sat
≈ 0.3
whereκ =1GeV/fmisthevacuumstringtensionvalue,
0
s = 1 GeV2 is a scale factor, and Q is adjusted to give 0.2
0 0
κ=1.88GeV/fmattheRHICenergy√s=0.2TeV.Our 0.1
phenomenological κ(s) is compared to Q2 (s) in Fig. 1,
sat
where κ = 1.40GeV/fm at √s = 0.017TeV increases to 0 -1
10 1 10
κ = 3.14 GeV/fm at √s = 14 TeV. s1/2 [TeV]
The energy dependence of the string tension leads to
a variation of the diquark/quark suppression factors, as
well as the enhanced intrinsic transverse momentum k .
T FIG. 2: (Color online) Energy dependence of the strange to
Theseinclude i)the ratioofproductionratesofdiquark-
light quark suppression factors, γs = s/u, using κ(s) from
quarkto quarkpairs(diquark-quarksuppressionfactor), Eq. 4 and using Q2sat(s) from Ref. [29] are compared. (Note
γ = P(qqqq)/P(qq¯); ii) the ratio of production rates
qq thatthisSchwingersuppressionfactorisnotusedintheCGC
of strange to non-strange quark pairs (strangeness sup- model).
pression factor), γ = P(ss¯)/P(qq¯); iii) the extra sup-
s
pression associated with a diquark containing a strange
The contributions of multiple jets to the multiplicity
quark compared to the normal suppression of strange
distributions inpp andpp¯collisionshavebeenstudied in
quark (γ ), γ = (P(usus)/P(udud))/(γ ); iv) the sup-
s us s detail in Ref. [74]. Within the HIJING model, one as-
pression of spin 1 diquarks relative to spin 0 ones (apart
sumes that nucleon-nucleoncollisionsat highenergy can
from the factor of 3 enhancement of the former based
be divided into soft andhard processeswith at least one
on counting the number of spin states), γ ; and v)
10 pair of jet production with p > p . A cut-off scale p
′′ T 0 0
the (anti)quark (σq = κ/κ0 · σq) and (anti)diquark in the transverse momentum of the final jet production
(σ′′ = κ/κ f σ ) Gaussian width. As an example has to be introduced below which the interaction is con-
qq 0· · qq p
we plot in Fig. 2 the energy dependence of the suppres- sidered non-perturbative and can be characterized by a
p
sionfactor γ =s/u,when the string tension values κ(s) finite soft parton cross section σ . The inclusive jet
s soft
4
cross section σ at leading order (LO) [75] is fortheSDcomponent,involvingmodeldependentcalcu-
jet
lations.
σ = s/4dp2dy dy 1 dσjet , (5) The results of the model calculations for both NSD
jet Zp20 T 1 22dp2Tdy1dy2 (left panel) and INEL (right panel) are also shown in
Fig. 3. Solid lines depict results including the strong
where, colorfield(SCF)effectswhereastheresultswithoutSCF
effects are shown as dashed lines. Without SCF effects
dσ dσab(sˆ,tˆ,uˆ)
jet =K x f (x ,p2)x f (x ,p2) themodelstronglyoverestimatesthecentralchargedpar-
dp2Tdy1dy2 a,b 1 a 1 T 2 b 2 T dtˆ ticle density. The absolute value and energy increase of
X thecentralrapiditydensityarewellreproducedassuming
(6)
depends on the parton-partoncrosssection σab and par- the energy dependent string tension given in Eq. 4. At
tondistributionfunctions(PDF)f (x,p2). Thesumma- higher LHC energies (2.36 and 7 TeV), a discrepancy of
a T
10-15 % is observed.
tion runs over all parton species; y and y are the ra-
1 2
pidities ofthe scatteredpartons; x andx are the light-
cone momentum fractions carried1by the i2nitial partons. )h=0190 )h=0190
The factor K 2 accounts for the next-to-leading order hd 8 hd 8
(NLO) correct≈ions to the leading order jet cross section. N/ch 7 N/ch 7
d 6 d 6
In the default HIJING model (v.1.383), the Duke-Owens ( (
5 5
parameterization[76] of PDFs in nucleons is used. With 4 4
the Duke-Owens parameterization of PDFs, an energy 3 3
independent cut-off scale p =2 GeV/c and a constant 2 2
0
1 1
soft parton cross section σ = 57 mb are sufficient to
soft 0 0
reproduce the experimental data on total and inelastic 102 103 104 102 103 104
s1/2 [GeV] s1/2 [GeV]
cross sections and the hadron central rapidity density in
p+p(p¯)collisions[51,52]. Ourresultshavebeenobtained
using the same set of parameters for hard scatterings as
in the latest version of HIJING (v1.383). FIG. 3: (Color online) Comparison of HIJING/BB¯ v2.0 pre-
dictionsforcentralchargedparticlepseudorapiditydensityin
pp and pp¯ interactions for non-single-diffractive (NSD) (left
panel) and inelastic (INEL) (right panel) interactions as a
III. CHARGED PARTICLES
function of c.m.s. energy. The solid and dashed lines are
the results with and without SCF, respectively. The data
A. Charged Hadron Pseudorapidity are from Refs. [1–3, 6, 10, 16–19, 21] (left panel) and from
Refs. [3, 19, 21, 23] (right panel). Only statistical error bars
Charged hadron multiplicity measurements are the are shown. Theopen stars at 7 and 14 TeV (ALICEfit), are
firstresultsoftheLHCphysicsprogram. Dataforppcol- obtained by a power law fit to lower energy data from Refs.
[6], [34].
lisions were reported by the ALICE, ATLAS, and CMS
collaborations [1–11]. The new data at mid-rapidity for
non single diffractive interactions (NSD) and inelastic As the colliding energy increases, the rate of multi-
scattering (INEL) are shown in Fig. 3, which includes plepartoninteractions(MPI)alsoincreases,producinga
also similar results at lower energies. The main result is rise in the centralmultiplicity. The increase with energy
anobservedsizeable increaseof the centralpseudorapid- in our phenomenology is due to the interplay of the in-
ity density with c.m.s. energy. creasedmini-jetproductioninhighcollidingenergywith
The main contribution to the multiplicity comes from SCF effects. For an increase of strangeness suppression
soft interactions with only a small component originat- factors due to an increase of string tension with energy
ing from hard scattering of the partonic constituents of (κ = κ(s)), the model predicts a decrease of produced
the proton. In contrastto the higher p regime,well de- pions due to energy conservation. Lower values of κ(s)
T
scribed by pQCD, particle production in soft collisions imply smaller values for strangeness suppression factors,
is generally modeled phenomenologically to describe the therefore a higher multiplicity of mesons (mostly pions).
different pp scattering processes: elastic scattering (el), Changing the effective value κ(s) = 2.89 GeV/fm to
single diffractive (SD), double diffractive dissociation κ(s)=2.0GeV/fmresultsinanincreasedmultiplicityof
(DD), and inelastic non-diffractive scattering (ND). Ex- 11% at 7 TeV where the effect is greatest. In addition,
perimentally, minimum bias events are a close approxi- the multiplicity depends also on the value of the cut-
mationofNSDinteractions,i.e.,σ =σ σ σ , off parameter p . Low values of p imply high rates of
NSD tot el SD 0 0
− −
where σ is the total cross section. The selection of parton-partonscatteringandhencehighlevelsofparticle
tot
NSD events is energy dependent and differs somewhat multiplicity. Evidently for increasing values of p the
0
for different experimental triggers. The event selection opposite is expected. At 7 TeV, where the effect is also
of inelastic processes (INEL) includes SD interactions: thelargest,changingp by 0.5GeVresultsinachange
0
±
σ =σ σ . Thedatathereforemustbecorrected of only 1.8% for the central pseudorapidity density.
INEL tot el
− ∓
5
10
formedinthecentralrapidityregionandcoverawidep
T
hd range(0.15<p <10GeV/c),wherebothhardandsoft
/h9 T
c processesareexpectedtocontribute. ThedataofATLAS
N
d andCMSaremeasuredinlargerpseudorapidityintervals
8
(η <2.5). In contrast, ALICE and CDF measurements
| |
are in a very central region (η < 0.8 and η < 1.0, re-
7 | | | |
spectively). Thecalculationtakesintoaccountthediffer-
ence in acceptance, but as canbe concluded fromFig. 4,
6
this difference in pseudorapidity range has a negligible
5 effect on the measured cross section.
4
4
10
]
2
3 -c) 103
/
V 2
10
2 e
G
10
(
1 [
1
hd -1
0 T10
0 2 4 6 8 10 p -2
pseudorapidity, h /dh10 -3
Nc10
2 -4
d 10
)
T -5
FIG. 4: (Color online) Comparison of HIJING/BB¯ v2.0 pre- p 10
dictions for the pseudorapidity distribution of charged parti- p2 -6
/ 10
cles in p + p (p¯) collisions at various c.m.s. energies. The 1 -7
(
solid histograms are the results with SCF and JJ¯ loops. The 10
-8
data are from Refs. [22] (UA5), [13] (STAR), [17] (CDF), 10
[3, 5] (ALICE), [1, 2] (CMS). Only statistical error bars are -9
10
shown.
-10
10
2 4 6 8 10 12 14
p [GeV/c]
Data on the charged particle pseudorapidity distribu- T
tionarealsoavailableoveralimitedηrange[1,2][3,5,6].
These are presented in Fig. 4 where we also include re-
sults obtained at 0.2 TeV by the UA5 [22] and STAR FIG.5: (Coloronline)Comparison withdataofHIJING/BB¯
[13] collaborations, and with CDF results [17] obtained v2.0predictionsofcharged-hadrontransversemomentumdis-
tributions at LHC energies. The calculated spectra include
at the Tevatron for pp¯collisions at 1.8 TeV. Consistent
the combined effects of SCF and JJ¯ loops. The histograms
with the discussion above, a scenario with SCF effects
anddatahavebeenscaledforclaritybythefactorsindicated.
(solid histograms) reproduces the measured multiplicity
The data are from Refs. [77] (CDF), [4] (ALICE), [7] (AT-
distributions well. At all energies considered,theoretical
LAS), [1, 2] (CMS). Error bars include only the statistical
calculations predict a central dip at mid-rapidity that is uncertainties.
consistent with the observations. At 0.9 and 2.36 TeV,
the shape of the distribution measured by the ALICE
The model calculations including SCF effects describe
collaborationis verywell reproduced,while the CMS re-
the data well at √s = 0.63 TeV, but lead to a harder
sults show a much flatter distributions than calculated
spectrum that observed at higher energy. The model
(also the case at 7 TeV). Data over a larger rapidity
gives a fair description of the spectral shape at low p
range are needed to determine the shape of the falling T
but overestimate the data at high p . The discrepancy
density in the fragmentation region. For completeness, T
is highest (up to a factor of three) at √s = 7 TeV. We
predictions at 10 and 14 TeV, the higher LHC energies,
do not understand the source of this discrepancy and
are also shown.
await higher p data to draw a firm conclusion. How-
T
ever, in our phenomenology this could indicate that jet
quenching, i.e. suppression of high p particles like that
T
B. Transverse momentum spectra observed at RHIC energies in nucleus-nucleus collisions,
couldalsoappearinppcollisionsineventswithlargemul-
The measured transverse momentum distributions for tiplicity. This overestimation of high p yield leads also
T
NSD events over an energy range √s = 0.63 7 TeV to a similar overestimation of the mean transverse mo-
−
areshowninFig.5. Theserecentmeasurementsareper- mentum(<p >)andofthecorrelationofmean<p >
T T
6
as a function of N , which we do not discuss here. [85] and at the Tevatron [86]. In pp collisions, however,
ch
Within our model we generate events with different a coalescence/hadronization scenario is not favored due
numbers of mini-jets up to some maximum values. High to low phase space density in the final state. Our HI-
numbers of mini-jets lead to higher multiplicity events. JING/BB¯ model, with SCF effects included, provides an
For events with ten mini-jets (the maximum assumed in alternative dynamical explanation of the heavy-ion data
our calculation), the central charged particle pseudora- at RHIC energies. We have shown that the model also
pidity density could increase up to 20 and the total predicts an increasing yield of (multi)strange particles,
≈
multiplicitycouldbegreaterthan150atTevatronenergy thereby better describing the experimental data [64].
(1.8TeV).Themeasurementsoftwoparticlecorrelations
overthe entire azimuth could revealthe jet structure re- -2]c) 10
lated to high pT particles [78]. The study of these cor- eV/ 10
relations in events with high multiplicity could help us G
to draw a firm conclusion with regard to a possible jet [dy (101-1 1
quenching phenomenon in pp collisions. dpT10-2
N/10-3 -1
2d -4 10
)T10
p -5
IV. IDENTIFIED PARTICLE SPECTRA AND 10
RATIOS p(1/210-60 2 p4 [GeV/c6] 10-20 2 p4 [GeV/c6]
T T
A. Baryon-to-Meson ratio
FIG. 7: (Color online) Predictions of the HIJING/BB¯ v2.0
The pp single particle inclusive p spectra measure-
T model for baryon and mesons transverse momentum in the
ments are important for understanding collision dynam-
rapidityrange 2<y<2(a)andtheirratio(b)forminimum
ics, since the various particles show different systematic bias pp¯ collisio−ns at √s = 7.0 TeV. The solid and dashed
behavior,asobservedatRHICenergy[78]. Detailedthe- lines have the same meaning as in Fig. 3. The experimental
oretical predictions for single inclusive hadron produc- results(a)arefromRef.[87](CMSCollaboration). Errorbars
tion (including strange hyperons) are discussed in this includeonlythestatistical uncertainties. Theratios (b)have
section. Baryon-to-mesonratios(B/M)areexperimental been calculated byus, dividingthespectrain thepanel (a).
observables that can be used at the LHC for investigat-
ing multi-parton interactions and helping to understand Figure 6 (b) shows a comparison of model predictions
the underlying physics [79–81]. with CDF experimental data [86] of the strange baryon-
to-meson ratio (Λ0 +Λ¯0)/K0 at 1.8 TeV. The particle
S
-2]c) praTtiospiesctfarairlayreweslhlodwenscrinibetdhewpitahnienlo(ua)r.phTehneommeenaosluorgeyd.
eV/ 10 10 The larger string tension parameterization results in a
G
[dy (101-1 1 tporredoicfted 1in0craetasteheofTtehveatrraotnioe(nΛe0rg+y.Λ¯0T)/hKe S0p byspaecftarca-
dpT10-2 show th≈at the increased ratio is due almost eTntirely to
2dN/10--43 10-1 an increase of the Λ cross section that is well described
p)T1100-5 with κ(s) = κ0 (s/s0)0.06 GeV/fm. The model underes-
p1/210-6 10-2 timates the kaon production by 15-25 %.
( 0 2 4 p [6GeV/c8] 0 2 4 p [6GeV/c8] The model predictions at 7 TeV, currently the maxi-
T T
mumenergywheretherearedata[87],areshowninFig.7
(b). The model gives a gooddescription of hyperonpro-
FIG. 6: (Color online) HIJING/BB¯ v2.0 predictions at √s duction (Λ0+Λ¯0), for which an increase by a factor of
ten is still predicted if SCF effects are considered. How-
= 1.8 TeV of baryon and mesons transverse momentum at
ever, our calculations underestimate by approximately a
mid-rapidity ( 1 < y < 1) (a) and their ratios for single
strange particl−es (Λ0+Λ¯0)/KS0 (b) in minimum bias pp¯col- factor of two the yield of KS0 and, as a consequence, re-
lisions. The solid and dashed lines have the same meaning sult in a higher ratio than that observed. This result
as in Fig. 3. Experimental results at √s = 1.8 TeV are from needs further investigation (theoretical and experimen-
Ref. [86] (CDF Collaboration). Error bars include only the tal)on heavyflavourproductionat this energy. We note
statistical uncertainties. The ratios (b) have been calculated thatthemodelsPYTHIA[88,89]andEnergy-conserving
by us, dividingthespectra in the panel(a). Partons Off-shell remnants and Spliting of partons lad-
ders(EPOS)[90,91]cannotreproducetheobservedhigh
UnexpectedlyhighB/MratiosobservedinA+Acolli- B/M ratio (see Fig. 6 and Fig. 7 from Ref. [80]). The
sions have been discussed in terms of recombination and preliminary data reported by the CMS collaboration in-
coalescence mechanisms [82–84]. Such high ratios at in- dicate high hyperon yield. Comparisons with PYTHIA
termediatep werealsoreportedinppcollisionsatRHIC resultsshowthatthismodelsignificantlyunderestimates
T
7
the hyperon yields in pp collisions at 0.9 and 7 TeV [87]. -
The strange particle ratios could also be the manifes- _pp/
tationof new collectivephenomena. In the EPOSmodel o
such an increase is obtained if the production of a mini- ati1
R
plasma is considered in pp collisions [24], [91]. If con-
firmed by future measurements, the study of these ob-
servables could open a perspective on new physics in pp
interactions.
-1
Similar conclusionsareobtainedfromthe study ofthe 10
proton/pion (p/π+, p¯/π−) ratios where data exist at
lower energies [92, 93]. These data, shown in Figure 8,
are limited to low p < 2 GeV/c. Adding SCF effects
T
results ina verysizableincreaseofthe ratioandourcal-
-2
culations provide a good description of the data in the 10 0 0.5 1 1.5 2 2.5 3 3.5 4
p [GeV/c]
measured range. However, as the calculations indicate, T
to draw a finalconclusionmeasurementsat intermediate
and high p are needed.
T
FIG. 9: (Color online) Predictions of the HIJING/BB¯ v2.0
)10 - 10 model of non-strange baryon over meson ratios (p¯/π−) for
-
p+ _p/p minimum bias events at mid-rapidity at LHC energies. The
+ o uppercurvescorrespondtocalculationswhichincludetheef-
_pp)/( 1 Rati 1 fects of SCF and JJ¯ loops. The lower curves corresponds to
p+ calculations without SCF effects. The results are at 0.9 TeV
atio (10-1 10-1 (TdeoVtd(daoshtteedd-hhiissttooggrraammss)),aatnd7TateV14(dTaesVhe(dsholiisdtohgirsatmogsr)a,mats)1.0
R
-2 -2
10 10
0 2 p [4GeV/c]6 0 2 4p [G6eV/c]8 also supported by more sophisticated theoretical calcu-
T T lations, in a scenario in which a time-dependent pulse
for the initial strength of the color field is considered
[95, 96]. The large enhancement of the baryon-to-meson
FIG. 8: (Color online) Comparison of HIJING/BB¯ v2.0 pre- ratios demonstrates that SCF could play an important
dictions with data on thenon-strange baryon overmeson ra-
role in multiparticle production in pp collisions at LHC
tios from minimum bias events in the rapidity range y <2.
| | energies and that high energy density fluctuations can
ThesolidanddashedlineshavethesamemeaningasinFig.3.
reachveryhighdensities,potentiallycomparabletothose
Experimentalresultsfor y <2at√s=0.54TeV(leftpanel)
| | reached in central Au + Au collisions at RHIC energies
and at √s = 1.8 TeV (right panel) are from Ref. [92] (E735
Collaboration). Theresultsatmid-rapidityat√s=0.54TeV [97].
(left panel) are from Ref. [93] (UA2 Collaboration). Error
bars include only thestatistical uncertainties.
B. Baryon-anti-baryon asymmetry
To the extent that the LHC experiments are able to
identifyhadronspecies,suchdatawillprovidevitalinput From the study of the baryon-anti-baryon asymme-
to validate this interpretation. The model predictions at try one can learn about the mechanism of baryon num-
−
LHCenergiesforthep dependenceofthep¯/π ratioare ber transport. Baryon production via the conventional
T
showninFig.9. AnenhancementuptothehighestLHC default quark-diquark mechanisms in the Lund string
energyandaweakenergydependence, witha saturation model are known to be inadequate even in e++e− phe-
that sets in for a c.m.s. energy √s > 2.36 TeV, is pre- nomenology. Thisisoneofthe mainreasonsforourcon-
dicted. Note that preliminary data at 0.9 TeV reported tinued exploration of alternative baryon junction mech-
by the ALICEcollaborationfor p spectraofpions(π+) anisms. The details of the new implementation of JJ¯
T
andprotons(p)[94]covertopT <2.5GeV/c. Themodel loops in HIJING/BB¯ v2.0 are described in Ref. [64] Sec
results,withSCFeffectsincluded(dot-dashedhistogram II A. In HIJING/BB¯ v2.0 the main two mechanisms for
in Fig. 9) are consistent with a p/π+ ratio derived from baryonproductionarequark-diquark(q qq)stringfrag-
the spectra reported by ALICE at 0.9 TeV in Ref. [94]. mentation and junction anti-junction (−JJ¯) loops [68] in
In our approach,the dynamical mechanism that leads which baryons are produced approximately in pairs. In
to such high values of B/M ratios is SCF appear- ajunction loopacolorflux line splits atsome intermedi-
ing at the initial stage of the interaction. The SCF atepointintotwofluxlines atonejunctionandthenthe
mechanismstronglymodifiesthefragmentationprocesses flux lines fuse back at an anti-junction somewhere fur-
(strangeness suppression factors) and thus results in a theralongthe originalfluxline. Thedistanceinrapidity
huge increase of (strange)baryons. This interpretation is between these points is chosen via a Regge distribution
8
[64]. We assume that, out of the non single diffractive p y 2
jfnuruancccltetiiooonnn-nfluJoJco¯lpe=.onTσJ(hNJe¯/Np()σroIiNnbEtaeLbria−licttσyioStDnh)acrtooftshtsheseeincetcviieodnnetn(stσeNbxSacDrity)e,onaa _Ratio p/00..189 dN/d111..27.555
0.7
has a JJ¯ loop in p(A)+A collisions after n simulated 0.6 1
hits
binary collisions is given by 0.5 0.75
0.4
0.5
0.3
0.25
PJJ¯=1−(1−fJJ¯)nhits, (7) 0.2 0 1 2 p 3[GeV4/c] 0 -5 0 rapidi5ty, y
T
whereσJJ¯=17mb,σSD isparametrizedinthemodel,
and the totalinelastic nucleon-nucleoncrosssections are
calculated [42]. These cross sections imply that a junc-
FIG.10: (Color online) HIJING/BB¯ v2.0 predictions pT dis-
tion loop occurs in pp collisions with a rather high prob-
tributions (a) at mid-rapidity for the p¯/p ratio at √s = 0.9
ability (at RHIC energy fJJ¯≈ 0.5 for σINEL = 42 mb). TeV; rapidity distributions are shown in part (b). The re-
TakingaconstantvalueforσJJ¯resultsinadecreasewith sultsarefromthreepossiblescenarios: withoutcontributions
energy of the probability PJJ¯, due to a faster increase from SCF and JJ¯ loops (dotted histograms), including only
with energy of σINEL relative to σSD. The actual proba- theeffectofJJ¯loops(dashedhistograms)andincludingboth
bility is modified also by string fragmentation processes effects (SCF and JJ¯ loops) (solid histograms). The data are
for which we consider a threshold cutoff mass M = 6 fromRef.[99](ALICECollaboration). Onlystatisticalerrors
c
GeV/c2 in order to have enough kinematic phase space are shown.
to produce BB¯ pairs. We have investigated the sensitiv-
ity of the results to the value of parameters σJJ¯and Mc without JJ¯ loops and SCF effects while the dashed line
andfoundno significantvariationonpseudorapiditydis-
includes the effect of JJ¯ loops only. Over the measured
tributions ofchargedparticles for 15 mb<σJJ¯< 25 mb
and for 4 GeV/c2 <M < 6 GeV/c2. rangesthe rapiditydistributionofthe ratiop¯/pdistribu-
c
tion is not sensitive to the various scenarios presented.
Baryonnumber transportis quantified in terms of the
The scenariowith combinedeffects results in a wider ra-
rapidityloss(δy =δy δy ,wherey and
loss beam baryon beam
− pidity distribution at y > 3 (b). The narrow structure
y are the rapidity of incoming beam and outgoing
baryon
observed near y = 0 has no physical significance and we
baryon, respectively) and has been discussed within our
believe that it is likely due to a numerical artifact of our
model phenomenology for A+A collisions in Refs. [63–
65]. It was shownthat HIJING/BB¯ v1.0 overestimatethe current implementation of fragmentation scheme.
Separateprotonandanti-protonrapiditydistributions
stopping power and give a mild energy dependence of
are,however,muchmoresensitivetoSCFeffects,asseen
net-baryons at mid-rapidity. The energy dependence of
inFig.11. The modelpredicts asubstantialincrease(by
net-baryons at mid-rapidity per participant pair within
HIJING/BB¯ v2.0 is proportional to (s/s0)−1/4+∆/2, sim- acofuanctt.orDoufe≈to5t)hefohrigph(p¯c),utwohffemnaSsCsFMar=e t6akGeenVi/nct2otahce-
ilar to the dependence predicted in Ref. [98], with the c
assumption that JJ¯ is the dominant mechanism. This effect of JJ¯ loops is very small over the entire rapidity
region. Analysis of the 7 TeV data leads to similar con-
dependence is obtained assuming the following parame-
ters [65]: s0 = 1 GeV2 (the usual parameter of Regge clusions, but shows less effect at high pT.
theory), α(0) = 1/2 (the reggeon intercept of the tra-
0.2 0.2
jectory), and α (0) = 1+∆ (where ∆ 0.01) for the
P ≈ 0.18 0.18
pomeron intercept.
0.16 0.16
Recently, the ALICE Collaboration reported results 0.14 0.14
[99] on mid-rapidity anti-proton-to-proton ratio in pp 0.12 0.12
collisions at √s = 0.9 and 7 TeV and equivalently the 0.1 0.1
0.08 0.08
proton-anti-proton asymmetry, A = (N N )/(N +
p − p¯ p 0.06 0.06
N ). These data could be used to constrain Regge in-
p¯ 0.04 0.04
spiredmodeldescriptionsofbaryonasymmetry. Theau- 0.02 0.02
thors state that, within statistical errors, the observed 0 0
-5 -2.5 0 2.5 5 -5 -2.5 0 2.5 5
p¯/pratioshowsnodependenceontransversemomentum
or rapidity in the limited measured acceptance ( 0.8 <
−
y < 0.8; 0 < p < 1 GeV/c). In Fig. 10 (a) are com-
T
pared the HIJING/BB¯ v2.0 model predictions with the FIG. 11: (Color online) Predictions of the HIJING/BB¯ v2.0
publisheddataat0.9TeV.Ourmodelpredictsnegligible model for rapidity distributions of protons (a) and anti-
dependence on p for 0 < p < 2 GeV/c, and a slight protons(b) at √s = 0.9 TeV. Thehistograms havethesame
T T
p dependenceathigherp ,wherebotheffects(JJ¯loops meaning as in Fig. 10.
T T
andSCF)couldcontribute. Thefullcalculationisshown
by the solid histogram. The dotted line is the prediction Overthemeasuredrangethefeed-down-correcteddata
9
for the p¯/p ratio rises from 0.957 0.006 at 0.9 TeV to pears at the initial stage of the interaction. The mecha-
±
0.991 0.005at7TeV[99]. Althoughthemeasuredmid- nismsofhadronproductionareverysensitivetotheearly
±
rapidityratioisclosetounitythereisasmallbutsignifi- phaseofthecollisions,whenfluctuationsofthecolorfield
cantexcessofprotonsoveranti-protonscorrespondingto strengtharehighest. StrongColorFieldeffectsaremod-
anasymmetryofA=0.022 0.003andA=0.005 0.003 eled by varying the effective string tension that controls
± ±
at √s = 0.9 and 7 TeV, respectively. Within our model the qq¯andqqqq pair creationrates andstrangenesssup-
using a Regge intercept of α = 1/2 results in a proton- pression factors. SCF, therefore, may modify the frag-
0
anti-protonasymmetryA =0.032(0.002)at0.9TeV mentation processes with a resultant huge increase of
model
(7 TeV). The result overestimates the value of asymme- (strange)baryons.
try at 0.9 TeV. These values show that a fraction of We show that both JJ¯ loops and SCF effects could
the baryon number associated with the beam particles play an important role in baryon (anti-baryon) produc-
is transported over rapidity intervals of less than seven tionatmid-rapidity inppcollisionsatLHC energies. In-
units. However, a better understanding of the baryon troducing a new JJ¯ loop algorithm in the framework of
transport would require measuring the rapidity depen- HIJING/BB¯ v2.0leads toa consistentandsignificantim-
dence of the asymmetry over a larger range. provement in the description of the recent experimen-
In Ref. [64] we discuss the predicted rapidity correla- tal results for proton-anti-proton and for baryon-anti-
tion length for production of baryon-anti-baryon pairs baryon asymmetry in comparison to the older versions
within our model. The predicted rapidity correlation HIJING/B or HIJING/BB¯ v1.0 [43]. We have shown
length(1 α(0))−1 depends uponthe valueoftheRegge that baryon number transport is suppressed for δy > 7,
−
intercept α(0) [43]. A value of α(0) 0.5 leads to rapid- aresultthatisconfirmedbyrecentALICEmeasurements
≃
ity correlationsin the range |yB−yB¯|∼2, while a value [99].
α(0) 1.0[100]is associatedwithinfinite rangerapidity The present study is limited to the effect of initial
≃
correlations. This kind of analysis and future measure- state baryon production via possible junction dynamics
ments at LHC energies will help us to determine bet- in strong fields. It would be very useful to consider a
ter the specific parameters characterizing JJ¯ loops used generalization of back reaction effects [58] to the case
in the calculations of baryon number transport and/or notonlyofpairproductionrelevantformesonsbuttothe
baryon-anti-baryonasymmetrywhilehelpingtoestablish moredifficultthreestringjunctionconfigurationsneeded
the validity of Regge inspired models. to describe baryonproduction.
AgreatersensitivitytoSCFeffectsisexpectedalsofor
open charm and bottom production [66]. In particular,
V. SUMMARY AND CONCLUSIONS
measurements of rapidity and p distributions for parti-
T
clesinvolvingcharmandbottomquark,wouldprovidean
We have studied the influence of strong longitudinal importanttestoftherelevanceofSCFfluctuations,help-
color fields and of possible multi-gluon dynamics (gluon ingustodeterminevaluesofthesuppressionfactorsγQQ¯
junctions) in particle production in pp collisions, with (whereQ=qq,s,c,b),whichhavestrongdependenceon
a focus on RHIC, to Tevatron, and LHC energies. We the main parameters of QCD (the constituent and cur-
haveinvestigatedasetofobservablessensitivetothedy- rentquarkmasses)andonthe systemsize. Eventhough
namics of the collisions, covering both longitudinal and the success of this procedure has been clearly illustrated
transverse degree of freedom. A detailed comparison here,afullerunderstandingofparticleproductionandes-
with newly available experimental data from the LHC peciallyof(multi)strangeparticlesinultra-relativisticpp
has been performed. collisionsatthe LHC remains anexciting openquestion,
We found that the inclusion of the multiple minijet and will continue to challenge many theoretical ideas.
source limits the growth of the string tension κ(s) to
be approximately only linear as a function of saturation
scale Q (Eq. 4), in contrast to recent approaches [29]
sat
where κ(s) scales as Q2 (Eq. 3). The reason for this is VI. ACKNOWLEDGMENTS
sat
that in the CGC model the collinear factorized minijet
mechanism is suppressed by geometric scaling to much
Acknowledgments: We thank S. Das Gupta and S.
higherp . FuturemeasurementsatLHC energies(√s =
T Jeon for useful discussions and continued support. We
7 and 14 TeV), extended to high p , will help to clarify
T thank P. Levai for helpful discussions and suggestions
the validity of this mechanism.
throughout this project. VTP acknowledges computer
WehaveshownthatSCFcouldplayanimportantrole
facilities at Columbia University, New York, where part
in particle production at mid-rapidity in pp collisions.
ofthesecalculationswereperformed. Thisworkwassup-
Our calculations show that high-energy density fluctua-
portedbytheNaturalSciencesandEngineeringResearch
tions in pp collisions at LHC can reach densities compa-
CouncilofCanada. Thisworkwasalsosupportedbythe
rabletothosereachedincentralnuclear(A+A)collisions
Division of Nuclear Science, of the U. S. Department of
at RHIC. A large enhancement of the (strange)baryon-
Energy under Contract No. DE-AC03-76SF00098 and
to-meson ratios that persists up to the highest LHC
DE-FG02-93ER-40764.
energy can be explained as an effect of SCF that ap-
10
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