Physics Le e s B 749 (2015) 98–103
Con en s lis s a ailable a ScienceDi ec
Physics Le e s B
www.else ie .com/loca e/physle b
Exci ed cha monium supp ession in p o on–nucleus collisions as
a consequence o como e s
E.G. Fe ei o
Depa amen o de Física de Pa ículas, Uni e sidade de San iago de Compos ela, 15782 San iago de Compos ela, Spain
a i c l e i n o a b s a c
A icle his o y:
Recei ed 8 Janua y 2015
Recei ed in e ised o m 1 July 2015
Accep ed 25 July 2015
A ailable online 29 July 2015
Edi o : J.-P. Blaizo
Recen esul s om p o on(deu e on)–nucleus collisions a RHIC and LHC ene gies ha e shown an
unexpec ed supp ession o exci ed qua konium s a es as compa ed o hei g ound s a es. In pa icula ,
s onge supp ession o he ψ(2S) ela i e o he J/ψ has been de ec ed. Simila obse a ions we e
made a lowe ene gies and we e easily explained by nuclea abso p ion. A highe ene gies, a simila
explana ion would iola e he Heisenbe g p inciple, since he calcula ions based on he unce ain y
p inciple lead o a cha monium o ma ion ime expec ed o be la ge han he nuclea adius, which
esul s in iden ical nuclea b eak-up p obabili y o he ψ(2S)and J/ψ. On he con a y, his beha io is
na u ally explained by he in e ac ions o he qua konium s a es wi h a como ing medium. We p esen
ou esul s on J/ψ and ψ(2S)p oduc ion o d+Au collisions a
√s=200 GeV and o p+Pb collisions
a
√s=5.02 TeV.
©2015 The Au ho . Published by Else ie B.V. This is an open access a icle unde he CC BY license
(h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by SCOAP3.
Cha monium mesons ha e cap u ed ou a en ion o decades.
Due o he high scale p o ided by hei la ge masses, hey a e
conside ed o be ou s anding p obes o Quan um Ch omodynam-
ics (QCD). The in e es in his field conce ns he issue o hei
p oduc ion mechanisms in p o on–p o on collisions oge he wi h
hei in e ac ion wi h he nuclea ma e c ea ed in ul a ela i is ic
hea y-ion collisions.
This is so since la ice QCD calcula ions p edic ha , a suffi-
cien ly la ge ene gy densi ies, had onic ma e unde goes a phase
ansi ion o a plasma o deconfined qua ks and gluons, he so-
called qua k–gluon plasma (QGP), whe e he QCD binding po en ial
is sc eened. Gi en he exis ence o se e al qua konium s a es, each
o hem wi h di e en binding ene gies, hey a e expec ed o se-
quen ially mel in o open cha m o bo om mesons abo e ce ain
ene gy densi y h esholds. Thus, he p oduc ion and abso p ion o
qua konium in a nuclea medium p o ide quan i a i e inpu s o
he s udy o QCD a high densi y and empe a u e.
The in e es on qua konium p oduc ion is no es ic ed o he
s udy o deconfinemen . Puzzling ea u es in p o on(deu e on)–nu-
cleus collision da a, whe e he deconfinemen canno be eached,
e eal new aspec s o cha monium physics in nuclea eac ions,
namely he ole o cold nuclea ma e e ec s.
In pa icula , he measu emen o p oduc ion a es o mul i-
ple qua konium s a es, wi h di e en physical sizes and binding
E-mail add ess: elena@ paxp1.usc.es.
ene gies, o e s an excellen ool o p obing he ime scale o he
e olu ion o hea y qua k–an iqua k pai s in o bound colo single
qua konium s a es which ep esen s a challenge wi hin QCD.
As a ma e o ac , ecen unexpec ed esul s on ψ(2S)p o-
duc ion in d+Au and p+Pb collisions om PHENIX [1] and
ALICE [2,3] Collabo a ions ha e shown an impo an supp ession
o i s yield wi h espec o p o on–p o on p oduc ion. Fu he mo e,
his supp ession is s onge han he one p e iously ob ained o
he J/ψ p oduc ion. Fo me measu emen s o J/ψ and ψ(2S)
p oduc ion a es in p o on–nucleus collisions a lowe ene gies
by E866/NuSea [4] and by NA50 [5] Collabo a ions also show a
s onge supp ession o he exci ed s a e nea xF≈0. A hose
lowe ene gies, his dissimila i y has been in e p e ed as he e -
ec o c¯
cb eak-up in in e ac ions wi h he p imo dial nucleons,
he so-called nuclea abso p ion. When he ime spen a e sing
he nucleus by he c¯
cpai becomes longe han he cha monia o -
ma ion ime, he la ge ψ(2S)meson will be u he supp essed
by a s onge nuclea b eak-up e ec .
Howe e , a highe ene gies, he cha monium o ma ion ime is
expec ed o be la ge han he nucleus adius [6]. Following he
unce ain y p inciple, he o ma ion ime is ela ed o he ime
needed – in hei es ame – o dis inguish he ene gy le els
o he 1Sand 2Ss a es, τ =2Mc¯
c
(M2
2S−M2
1S)=2 ×3.3GeV/4GeV
2=
0.35 m o he ψ. Mo eo e , his o ma ion ime has o be con-
side ed in he es ame o he a ge nucleus, i.e. he Au beam a
RHIC and he Pb beam a LHC. In his case, he o ma ion ime is
h p://dx.doi.o g/10.1016/j.physle b.2015.07.066
0370-2693/©2015 The Au ho . Published by Else ie B.V. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by
SCOAP3.
E.G. Fe ei o / Physics Le e s B 749 (2015) 98–103 99
inc eased by he Lo en z boos ac o , =γτ. The boos ac o γ
is ob ained om he apidi y o he pai co ec ed by he nucleus
beam apidi y, γ=cosh(y −yAu
beam)whe e yAu
beam =− ln(√s
mN) =
−5.36 o RHIC, esul ing in a boos ac o bigge han 100 a mid
and o wa d apidi ies [6]. Consequen ly, in he mid and o wa d
apidi y egions a RHIC, is significan ly la ge han he Au a-
dius, =36.7 m o y =0 and la ge o o wa d apidi ies. A
he LHC, o a lead beam o 1.58 TeV in pPb mode,1yPb
beam =−8.11,
which esul s in a boos o mo e han 1000 a LHC mid apidi-
ies [7]. This implies ha he cha monium o ma ion ime will
be la ge han he Pb adius p ac ically in he whole apidi y e-
gion. This means ha he c¯
cis nea ly always in a p e- esonan
s a e when a e sing he nuclea ma e , which esul s in iden i-
cal b eak-up p obabili y o he ψ(2S)and J/ψ, since hese s a es
canno be dis inguished a he ime hey a e se he nucleus.2
O he usual explana ions, as he one based on he shadowing o
he hea y pai s due o he modifica ion o he gluon pa on dis i-
bu ion unc ions in he nucleus, canno be in oked he e, since he
nuclea pa on shadowing e ec s a e indis inguishable be ween
ψ(2S)and J/ψ [6].
He e, we will demons a e ha he final s a e in e ac ions o
he c¯
cpai wi h he dense medium c ea ed in he collision can
cause he puzzling anomalies seen in qua konium p oduc ion, i.e.
he s onge ψ(2S)supp ession ela i e o he J/ψ, wi hin he so-
called como e scena io. In a como e amewo k, he supp ession
a ises om sca e ing o he nascen ψwi h p oduced pa icles –
he como e s – ha happen o a el along wi h he c¯
cpai [8,9].
By como e in e ac ion one means he in e ac ion o he J/ψ and
ψ(2S)pa icle wi h he p oduced medium: he qua konium pa i-
cle is como ing wi h he so pa icles p oduced in he collision,
hei o ma ion imes being bo h boos ed by Lo en z dila ion. This
implies ha he como e s can con inue o in e ac well ou side o
he nuclea olume, playing an impo an ole.
Le us ecall wo common ea u es o he como e app oaches.
Fi s , he como e dissocia ion a ec s s ongly he ψ(2S) ela i e
o he J/ψ, due o he la ge size o he fi s . Second, he como e
supp ession is s onge whe e he como e densi ies a e la ge ,
i.e. i inc eases wi h cen ali y and, o asymme ic collisions as
p o on(deu e on)–nucleus, i will be s onge in he nucleus-going
di ec ion.
In he ollowing, we will show ha aking in o accoun he
abo e ea u es we ob ain a su p isingly good and cohe en quan-
i a i e desc ip ion o he a ailable deu e on–nucleus and p o on–
nucleus da a a RHIC and LHC ene gies. We will apply he well-
es ablished como e in e ac ion model (CIM) [9–14]. In his model,
he a e equa ion ha go e ns he densi y o cha monium a a
gi en ans e se coo dina e s, impac pa ame e band apidi y y,
ρψ(b, s, y), obeys he simple exp ession
τdρψ
dτ(b,s,y)=−σco−ψρco(b,s,y)ρψ(b,s,y), (1)
whe e σco−ψis he c oss sec ion o cha monium dissocia ion due
o in e ac ions wi h he como ing medium o ans e se densi y
ρco(b, s, y).
In o de o ob ain he su i al p obabili y Sco
ψ(b, s, y)o a ψin-
e ac ing wi h como e s, his equa ion is o be in eg a ed be ween
ini ial ime τ0and eeze-ou ime τ . We conside longi udinal
1Due o he LHC design, he colliding beams ha e di e en ene gies pe nucleon,
Ep=4TeV, EPb =1.58 TeV, and canno be uned sepa a ely. As a consequence, he
cen e o mass o he nucleon–nucleon collision is shi ed by y =0.465 wi h e-
spec o he labo a o y ame in he di ec ion o he p o on beam [2].
2Mo eo e , his nuclea abso p ion can be aken as negligible a he LHC ene -
gies.
boos in a iance and neglec ans e se expansion since we ha e
es ima ed ha he ans e se expansion, unlike he longi udinal
one, is a e y smoo h p ocess ha akes place la e .3Thus, assum-
ing a dilu ion in ime o he densi ies due o longi udinal mo ion
which leads o a τ−1dependence on p ope ime, he equa ion can
be sol ed analy ically. The esul depends only on he a io τ /τ0
o final o e ini ial ime. Using he in e se p opo ionali y be ween
p ope ime and densi ies, we pu τ /τ0=ρco(b, s, y)/ρpp(y), i.e.
we assume ha he in e ac ion s ops when he densi ies ha e di-
lu ed, eaching he alue o he p+p densi y a he same ene gy.
Thus, he solu ion o Eq. (1) is gi en by
Sco
ψ(b,s,y)=exp −σco−ψρco(b,s,y)ln ρco(b,s,y)
ρpp(y),(2)
whe e he a gumen o he log is he in e ac ion ime o he ψ
wi h he como e s.
The main ing edien in o de o compu e he su i al p obabil-
i y Sco
ψo he qua konium due o in e ac ions wi h he como ing
medium is he densi y o como e s ρco. This densi y is no a ee
pa ame e , since i has he cons ain ha he o al apidi y dis i-
bu ion dN/dy o he obse ed pa icles mus be ep oduced. We
ake i as p opo ional o he numbe o collisions,
ρco(b,s,y)=n(b,s)Ssh
co(b,s)3
2(dNpp
ch /dy), (3)
whe e n(b, s)co esponds o he numbe o bina y nucleon–
nucleon collisions pe uni ans e se a ea a a gi en impac pa-
ame e , Ssh
co e e s o he shadowing o he pa on dis ibu ion
unc ions in a nucleus ha a ec s he como e mul iplici y, ch
e e s o he cha ged pa icle densi y in p+p and he ac o
3/2 akes in o accoun he neu al como e s. In o de o compu e
he como e densi ies in nuclea collisions we ha e in oduced
he shadowing co ec ions ha a ec he como e mul iplici ies
[15–17]. Wi hin his app oach, a good desc ip ion o he cen ali y
dependence o cha ged mul iplici ies in nuclea collisions is ob-
ained bo h a RHIC [18] and LHC ene gies [15].
Finally, he como e densi y in p+p collisions is gi en by
ρpp(y) =3
2(dNpp
ch /dy)/πR2
p, whe e Rpis he p o on adius. We
apply he expe imen al alues and heo e ical ex apola ions [15]
o he cha ged pa icle mul iplici ies in p o on–p o on colli-
sions. We ge , a mid apidi y, he alues ρpp(0) =2.24 m−2a
√s=200 GeV [13] and ρpp(0) =3.37 m−2a √s=5.02 TeV,
which co espond o he alues o cha ged pa icle mul iplici-
ies dNch
pp/dη=2a √s=200 GeV and dNch
pp/dη=4.5a √s=
5.02 TeV.
Wi h he numbe s quo ed abo e, one ob ains o he como e
mul iplici ies he alues dNco
dAu/dη=15.75 o minimum bias d+
Au collisions a √s=200 GeV a mid apidi y, and dNco
pPb/dη=
26.4a mid apidi y, dNco
pPb/dη=22.5in he p-going di ec ion,
2.03 <y <3.53, and dNco
pPb/dη=31.2in he Pb-going di ec-
ion, −4.46 <y <−2.96, o minimum bias p+Pb collisions a
√s=5.02 TeV. These alues a e consis en wi h he expe imen al
cha ged pa icle mul iplici ies [19,20].
The only adjus able pa ame e o he como e in e ac ion
model is he c oss sec ion o cha monium dissocia ion due o in e -
ac ions wi h he como ing medium, σco−ψ. I was fixed [10] om
fi s o low-ene gy expe imen al da a o be σco−J/ψ =0.65 mb o
he J/ψ and σco−ψ(2S)=6mb o he ψ(2S). The magni ude o
he cha monium abso p ion c oss sec ion in medium is heo e i-
cally no well unde con ol. Di e en heo e ical calcula ions o
3The e ec o a small ans e se expansion can p esumably be aken in o accoun
by a small change o he final s a e in e ac ion c oss sec ions.
100 E.G. Fe ei o / Physics Le e s B 749 (2015) 98–103
Fig. 1. (Colo online.) The J/ψ (blue con inuous line) and ψ(2S)( ed con inuous
line) nuclea modifica ion ac o RdAu as a unc ion o he numbe o collisions Ncoll
compa ed o he PHENIX da a [1]. The supp ession due o he shadowing co ec ions
(discon inuous line) is also shown.
he J/ψ-had on c oss sec ion based on he mul ipole expansion in
QCD [21] di e om hose which include o he non-pe u ba i e
e ec s by o de s o magni ude [22]. Mo eo e , i s ene gy beha io
can be qui e di e en . Mo e ecen heo e ical calcula ions based
on QCD sum ules [23] o on chi al e ec i e heo y using a chi al
qua k model [24] show a mode a e inc ease o he c oss sec ion
wi h he ene gy abo e h eshold. On he o he hand, an in a i-
an dissocia ion c oss sec ion o cha monium on ligh mesons,
assumed o be ene gy independen , is a common ea u e o a ious
como e models [25]. We a e awa e ha i could change when he
ene gy inc eases. We do no expec his e ec o be ex emely im-
po an abo e
√s=20 GeV – well abo e h eshold – and, since we
a e unable o e alua e he magni ude o his e en ual change, we
ha e chosen o keep i fixed o i s low ene gy alue. This alue has
been also success ully applied a highe ene gies o ep oduced he
RHIC [26] and LHC [27] da a on J/ψ om nucleus–nucleus colli-
sions.
No e ha , oge he wi h he como e in e ac ion, ano he im-
po an e ec ha plays a ole in qua konium nuclea p oduc ion
is he ini ial shadowing o he hea y pai s due o he modifica-
ion o he gluon pa on dis ibu ion unc ions in he nucleus. I
can be calcula ed analy ically in he abo e men ioned amewo k
o using any o he a ailable pa ame iza ions o he nuclea pa -
on dis ibu ion unc ions [7,28]. No e also ha his e ec is o
be aken iden ical o he s a es 1S and 2S [6], i.e. o he J/ψ
and he ψ(2S). This nuclea modifica ion o he pa on dis ibu-
ion unc ions will p oduce a common dec ease o he J/ψ and
he ψ(2S)yields in he mid and o wa d apidi y egions bo h a
RHIC and LHC ene gies. I can induce an inc ease o bo h yields in
he backwa d apidi y egion.
I is now s aigh o wa d o calcula e he nuclea modifica ion
ac o , i.e. he a io o he ψyield in p o on(deu e on)–nucleus col-
lisions o he ψyield in p o on–p o on collisions mul iplied by he
a e age numbe o bina y nucleon–nucleon collisions:
Rψ
pA(b)=
dNψ
pA/dy
n(b)dNψ
pp/dy
=d2sσpA(b)n(b,s)Ssh
ψ(b,s)Sco
ψ(b,s)
d2sσpA(b)n(b,s),(4)
whe e Sco
ψ e e s o he su i al p obabili y due o he medium
in e ac ions while Ssh
ψ akes in o accoun he shadowing o he
pa on dis ibu ion unc ions in a nucleus ha a ec s he ψp o-
duc ion. Any nuclea e ec a ec ing qua konium p oduc ion leads
o a de ia ion o RpA om uni y.
Fig. 1 shows he nuclea modifica ion ac o RdAu as a unc ion
o he numbe o collisions Ncoll o he J/ψ and ψ(2S)p oduc-
ion in d+Au collisions a √s=200 GeV compa ed o PHENIX
expe imen al da a [1]. We obse e a s ong supp ession o ψ(2S)
p oduc ion wi h inc easing cen ali y. This supp ession is a ac o
o 2 imes la ge han he obse ed supp ession o J/ψ p oduc-
ion o he mos cen al e en s. The supp ession due o he shad-
owing co ec ions, calcula ed wi hin he EPS09 LO pa ame iza ion
[29] and iden ical o he J/ψ and ψ(2S), has been aken in o ac-
coun . I ep esen s mo e han 50% o he o al J/ψ supp ession,
while he ψ(2S)is mos ly supp essed due o he como e in e ac-
ion.
No e ha , in o de o include he shadowing, he o iginal anal-
ysis EPS09 LO has been used [29]. The cen ali y dependence o
shadowing is no add essed in his model. I can be pa ame e ized
[30,31] assuming ha he inhomogeneous shadowing is p opo -
ional o he local densi y ρAo he hickness unc ion TA,
RA
i(b,x,Q2)=1+[RA
i(x,Q2)−1]NρdzρA(b,z)
dzρA(0,z),(5)
whe e band za e he ans e se and longi udinal loca ion in
posi ion space, ρA(b, z)co esponds o he Woods–Saxon dis ibu-
ion o he nucleon densi y in he nucleus, ela ed o he nuclea
p ofile unc ion TA(b)by dzρA(b, z) =A TA(b), ρ0is he cen-
al densi y, gi en by he no maliza ion d2b
dzρA(b, z) =A
and RA
i(x, Q2)is he shadowing unc ion om EPS09 LO. Nρis
he no maliza ion ac o , and i is chosen so ha
(1/A)
d2b
dzρA(b, z) RA
i(b, x, Q2) =RA
i(x, Q2).4
We p oceed now wi h he analysis o J/ψ and ψ(2S)p oduc-
ion in p+Pb collisions a √s=5.02 TeV, ha o e s an excellen
oppo uni y o e i y he ole o como e s on qua konium supp es-
sion. Acco ding o a ailable expe imen al da a [2,3], he supp es-
sion o he J/ψ shows a s ong di e ence be ween he o wa d
and backwa d apidi y egions, while he ψ(2S)shows as onishing
simila supp ession in bo h apidi y in e als.
No e ha any e ec ela ed o nuclea shadowing would p o-
duce a sligh an ishadowing in he backwa d egion while i would
induce a supp ession in he o wa d egion, hese e ec s being
iden ical o he J/ψ and ψ(2S).
In ac , he expe imen al finding o a di e en supp ession o
he ψ(2S) ela i e o he J/ψ, in pa icula in he backwa d apid-
i y egion, is a clea indica ion o como e in e ac ions. Ac ually,
he densi y o como e s is smalle in he o wa d egion (p-going
di ec ion) han in he backwa d egion (Pb-going di ec ion), he
di e ence inc easing wi h cen ali y, which is easily confi med by
expe imen al da a on cha ged pa icle mul iplici ies [20]. As a con-
sequence, he e ec o como e s – which di e s on he J/ψ and
ψ(2S)case – will be s ong in he backwa d egion, while he
supp ession ound in he o wa d egion will be mainly due o
he ini ial shadowing o he nuclea pa on dis ibu ion unc ions,
iden ical in bo h cases. Thus, one should expec mo e simila J/ψ
and ψ(2S)supp ession in he o wa d han in he backwa d e-
gion.
This is illus a ed in Fig. 2, whe e expe imen al da a [2] on J/ψ
and ψ(2S)p oduc ion in p+Pb collisions a √s=5.02 TeV a e
compa ed o ou esul s. We ha e conside ed a common EPS09
LO shadowing [7,29] o bo h he J/ψ and ψ(2S). The in e ac ion
wi h como e s, mos ly a play in he backwa d egion, is able o
explain he s onge ψ(2S)supp ession.
4This scena io co esponds o wha is e e ed o as “1-pa ame e app oach” in
EPS09s [32], i.e. EPS09 wi h aspa ial (impac pa ame e ) dependence in oduced in
e ms o powe s o he nuclea hickness unc ions TA(s). The 1-pa ame e app oach
(n =1in he powe se ies) ag ees well wi h he ull EPS09s in he LO app oxima-
ion, while i may in oduce di e ences in he slope o he NLO app oxima ion.
E.G. Fe ei o / Physics Le e s B 749 (2015) 98–103 101
Fig. 2. (Colo online.) The J/ψ (blue line) and ψ(2S)( ed line) nuclea modifica ion
ac o RpPb as a unc ion o apidi y compa ed o he ALICE da a [2]. The supp ession
due o he shadowing co ec ions (discon inuous line) is also shown.
Fig. 3. (Colo online.) The J/ψ (uppe figu e) and ψ(2S)(lowe figu e) nuclea
modifica ion ac o RpPb as a unc ion o he numbe o collisions in he backwa d
−4.46 <y <−2.96 (blue con inuous line) and o wa d 2.03 <y <3.53 ( ed con in-
uous line) apidi y in e als. The modifica ion due o he an ishadowing co ec ions
in he backwa d egion (blue discon inuous line) and o he shadowing co ec ions
in he o wa d egion ( ed discon inuous line) is also shown.
Ou esul s o J/ψ and ψ(2S)p oduc ion e sus cen ali y in
p+Pb collisions a √s=5.02 TeV a e shown in Fig. 3. Two apid-
i y in e als a e s udied, he p-going di ec ion, 2.03 <y <3.53 and
he Pb-going di ec ion, −4.46 <y <−2.96. The e ec o he EPS09
LO shadowing is comple ely di e en depending on he apidi y in-
e al conside ed. While i induces an inc ease – an ishadowing –
in he backwa d egion, i p oduces a supp ession – shadowing –
in he o wa d egion. On he o he hand, he in e ac ion wi h co-
mo e s in oduces a supp ession, s onge in backwa d egion due
o he highe como e densi y. Thei e ec will be mo e impo -
an on he ψ(2S) han on he J/ψ p oduc ion, due o he highe
σco−ψo he fi s . In ac , we ob ain a nuclea modifica ion ac o
Fig. 4. (Colo online.) The a io o he ψ(2S)o e J/ψ nuclea modifica ion ac o s
Rψ(2S)
pPb /RJ/ψ
pPb as a unc ion o he numbe o collisions in he backwa d −4.46 <
y <−2.96 (blue con inuous line) and o wa d 2.03 <y <3.53 ( ed con inuous line)
apidi y in e als.
RJ/ψ
pPb compa ible wi h one o he J/ψ in he backwa d egion e-
sul ing o he combined e ec o EPS09 LO nuclea modifica ion
oge he wi h he como e supp ession, while he o al supp es-
sion o he J/ψ in he o wa d egion achie es almos 50%, mainly
due o he shadowing e ec .
Conce ning he ψ(2S)p oduc ion, we ob ain a simila supp es-
sion o he backwa d and o wa d apidi y egions. No e, ne e -
heless, ha he o igin o his dec ease co esponds o di e en
e ec s depending on he egion o conside a ion: in he backwa d
egion, he e is an an ishadowing iden ical o one p e iously ound
o he J/ψ which is hidden by he s ong e ec o como e sup-
p ession in his egion; on he o he side, in he o wa d egion,
bo h he shadowing and a limi ed como e e ec con ibu e o he
supp ession.
The a io o bo h nuclea modifica ion ac o s, i.e. Rψ(2S)
pPb /RJ/ψ
pPb ,
also defined as he double a io [ψ(2S)/ J/ψ]pPb
[ψ(2S)/ J/ψ]pp , is shown in Fig. 4
o he backwa d and o wa d apidi y egions. In his double a io
he co ec ions due o he modifica ion o he nuclea pa on dis-
ibu ion unc ions cancel, and only como e in e ac ion is a play.
We ob ain a double a io lowe han one in bo h apidi y e-
gions, due o he s onge e ec o he como e s on he ψ(2S).
Mo eo e , his dec ease below one is mo e p onounced in he
backwa d apidi y egion due o highe como e densi y which
p oduces s onge dissocia ion on he ψ(2S), due o i s highe in-
e ac ion c oss sec ion.
In he abo e esul s, he eeze-ou ime, τ , is no malized by
means o he pe inen densi y in p+p collisions a he co e-
sponding ene gy. This leads in ou app oach o simila in e ac ion
imes o RHIC d+Au and LHC p+Pb collisions. I ha monizes
wi h he ac ha he d+Au and p+Pb sys ems, acco ding o HBT
measu emen s, a e compa able in size [33,34].
Howe e , as a limi ing case and in o de o ake in o accoun
he possibili y o a longe in e ac ion ime in he p+Pb case, we
ha e also calcula ed he supp ession i he p+Pb eeze-ou den-
si y is dec eased by a ac o o 2, i.e. inc easing he li e ime o a
fi eball by a ac o o 2. We find ha his could induce a s onge
supp ession, in pa icula o he exci ed s a es. This addi ional
supp ession will depend on he cen ali y o he collision and will
be mo e impo an o he ψ(2S) han o he J/ψ. In pa icu-
la , while an addi ional 5% o e he o iginal supp ession alue is
ob ained o he J/ψ, he e ec on he ψ(2S)is o he o de o
30%.
In conclusion, we ha e pe o med a de ailed s udy o J/ψ and
ψ(2S)p oduc ion in d+Au and p+Pb collisions a √s=200 GeV
and √s=5.02 TeV espec i ely. F om ou poin o iew, he
102 E.G. Fe ei o / Physics Le e s B 749 (2015) 98–103
a ailable da a cons i u e expe imen al confi ma ion o he in e ac-
ion o ully o med physical qua konia wi h he p oduced pa icles
– he como e s – ha happen o a el along wi h he c¯
cpai .
A he s udied ene gies and apidi ies, mos o he physical
bound s a es a e o med well ou side he a ge nucleus due o
he Lo en z dila ion o he o ma ion imes – in o he wo ds, he
incoming nucleus is con ac ed by he Lo en z ac o . This implies
ha he nucleons ha e swep o e he nascen cha monium s a e,
esul ing in a nuclea abso p ion ha can con ibu e li le o he
cha monium supp ession, and canno accoun o he di e ence
be ween he J/ψ and he ψ(2S)yields.
On he o he hand, he como e s can con inue o in e ac well
ou side o he nuclea olume, playing an impo an ole. The J/ψ
and ψ(2S)p oduced ou side he nucleus a e su ounded by a
dense sys em o had ons (mainly pions) and con e in o open
cha m due o in e ac ions in he medium. In pa icula , he co-
mo e supp ession can explain he ela i e modifica ion o he
ψ(2S) o he J/ψ, Rψ(2S)
pPb /RJ/ψ
pPb , in p o on(deu e on)–nucleus colli-
sions a RHIC and LHC ene gies. O he cold nuclea ma e e ec s,
as he nuclea modifica ion o he pa on dis ibu ion unc ions,
canno accoun o his di e ence ei he since hey impac simi-
la ly he J/ψ and he ψ(2S).
The como e e ec , ound o be o he o de o 10% in p o on–
nucleus collisions a SPS ene gy, inc eases wi h he o al pa icle
mul iplici y and achie es significan influence in p o on(deu e on)–
nucleus collisions a RHIC and LHC ene gies, in pa icula in he
A-going di ec ion.
Ou ini ial como e densi ies a e p opo ional o he numbe
o c ea ed had ons. In he ans e se space, hese densi ies, o
minimum bias collisions, i.e. a e aged o e b, in he mid apid-
i y egion a e: ρco ≈4 m
−2 o p+Pb collisions a 5.02 TeV, and
ρco ≈2.5 m
−2 o d+Au collisions a 200 GeV. These numbe s
ag ee wi h he mul iplici ies quo ed abo e when hey a e di ided
by he ans e se a ea o e which como e s a e p oduced, which
co esponds o he collision o e lap a ea, app oxima ely equal o
σinel
pp =70 mb o p+Pb collisions a 5.02 TeV, and σ=πR2
d
o d+Au collisions a 200 GeV. In his la e case, due o he
asymme ic na u e o he deu e on in i sel , his o e lap a ea can
ange be ween one o wo imes he p+p alue a 200 GeV
(σinel
pp =40 mb). We ake R2
d=3.22/3 m2[35,36] esul ing in σ=
πR2
d=68 mb a 200 GeV. No e ha ou size pa ame e s a e e y
simila o he expe imen al HBT adii [33–35,37] and o o he he-
o e ical es ima es [36,38,39].
In o de o pu hese quan i ies in o con ex wi h equilib-
ium ma e , i is in e es ing o s udy he 3-dimensional densi ies
o como e s, which co espond simply o ρco(τ) =ρco/τ. Taking
τ0=1 m, equi alen o he o ma ion ime o he so pa icles,
one ob ains 3-dimensional ini ial densi ies o he o de o 4 m
−3
in p+Pb LHC collisions and 2.5 m
−3in d+Au RHIC collisions.
These es ima es can be compa ed wi h he es ima e o he pa -
icle densi y in a qua k–gluon plasma [40], n =g
π2¯
h3T3whe e g
is he numbe o deg ees o eedom (spin +colo +fla o ), 16
o gluons and 24 o ligh u and d qua ks, i.e. g≈40. La ice
QCD p edic s ha he ansi ion o he qua k–gluon plasma occu s
nea Tc≈190–170 MeV [41]. Since ¯
hc =197 MeV m, one ob ains
n ≈3.75–2.60 m−3a Tc. One sees ha he sys em is abo e he
c i ical densi y only in p+Pb LHC collisions i τ<1–1.5 m. In
o he wo ds, he li e ime o an e en ual qua k–gluon plasma would
be app oxima ely 1 m.
We a e awa e o he exis ence o hin s o collec i e e ec s
in p+Pb collisions a 5.02 TeV. In pa icula , CMS [42,43] and
ALICE [44] Collabo a ions epo ed a nea -side idge, i.e. enhanced
emission o pa icles wi h simila azimu hal angles and di e en
pseudo apidi ies de eloping in high-mul iplici y p+p and p+Pb
collisions, ha can be associa ed wi h hyd odynamic flow. When
a fi eball o s ongly in e ac ing ma e is o med, azimu hal co -
ela ions due o collec i e flow appea in he in e ac ion. The in-
e p e a ions a e mos ly based on collec i e ha monic flow [45] o
on he colo -glass condensa e app oach o he ini ial s a e [46,47].
Mo eo e , in [48], final-s a e ho medium e ec s, inspi ed on he
o ma ion o a qua k–gluon plasma, ha e been p oposed o s udy
he qua konium p oduc ion in p+Pb collisions a 5.02 TeV.
He e we p opose ano he mechanism, he final s a e in e ac-
ions wi h como e s. I should be s essed ha he in e ac ion o
como e s a he ea ly ime τ0in ol es la ge densi ies, which ap-
pea high o ee mesons. Had onic ma e in his si ua ion is
ce ainly a away om he ideal pion gas, bu can be app oxi-
ma ed as p e-had ons o d essed mesons [49], i.e. spec al densi-
ies wi h he quan um numbe s o he had onic s a es ha show
up a high ene gy densi y, abo e 1GeV m
−3. As known om la -
ice QCD [50–53], he co ela o s o pions can su i e abo e his
ene gy densi y. Such mesons a e expec ed o ha e a mo e compac
size in space.
We would like o hank Al ons Capella, F ede ic Fleu e , Jean-
Philippe Lansbe g, Michael Lei ch and Ral Rapp o s imula ing
and use ul discussions and F ancois A leo, Robe a A naldi, Zaida
Conesa del Valle, To s em Dahms, An hony F awley, Ramona Vog ,
Pe e Pe eczky and En ico Scompa in o insigh ul commen s.
We hank he Ins i u e o Nuclea Theo y a he Uni e si y o
Washing on (g an INT-14-3) o i s hospi ali y and pa ial suppo
du ing he comple ion o his wo k. We also hank he Ins i u
de Physique Nucléai e de l’Uni e si é Pa is-Sud and Labo a oi e
LeP ince-Ringue de l’Ecole Poly echnique o hospi ali y. This wo k
was suppo ed by he Minis e io de Economía y Compe i i idad o
Spain (g an FPA2011-22776).
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