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E idence o esca e ing e ec in Pb–Pb collisions a he LHC h ough p oduc ion o
K*(892)0 and ϕ(1020) mesons
© 2020 The Au ho s. Published by Else ie B.V.
Published e sion
ALICE Collabo a ion
ALICE Collabo a ion. (2020). E idence o esca e ing e ec in Pb–Pb collisions a he LHC
h ough p oduc ion o K*(892)0 and ϕ(1020) mesons. Physics Le e s B, 802, A icle 135225.
h ps://doi.o g/10.1016/j.physle b.2020.135225
2020
Physics Le e s B 802 (2020) 135225
Con en s lis s a ailable a ScienceDi ec
Physics Le e s B
www.else ie .com/loca e/physle b
E idence o esca e ing e ec in Pb–Pb collisions a he LHC h ough
p oduc ion o K∗(892)0and φ(1020)mesons
.ALICE Collabo a ion
a i c l e i n o a b s a c
A icle his o y:
Recei ed 21 No embe 2019
Recei ed in e ised o m 10 Janua y 2020
Accep ed 13 Janua y 2020
A ailable online 16 Janua y 2020
Edi o : L. Rolandi
Measu emen s o K∗(892)0and φ(1020) esonance p oduc ion in Pb–Pb and pp collisions a
√sNN =5.02
TeV wi h he ALICE de ec o a he La ge Had on Collide a e epo ed. The esonances a e measu ed
a mid apidi y (|y|<0.5) ia hei had onic decay channels and he ans e se momen um (pT)
dis ibu ions a e ob ained o a ious collision cen ali y classes up o pT=20 GeV/c. The pT-in eg a ed
yield a io K∗(892)0/K in Pb–Pb collisions shows significan supp ession ela i e o pp collisions
and dec eases owa ds mo e cen al collisions. In con as , he φ(1020)/K a io does no show any
supp ession. Fu he mo e, he measu ed K∗(892)0/K a io in cen al Pb–Pb collisions is significan ly
supp essed wi h espec o he expec a ions based on a he mal model calcula ion, while he φ(1020)/K
a io ag ees wi h he model p edic ion. These measu emen s a e an expe imen al demons a ion o
esca e ing o K∗(892)0decay p oduc s in he had onic phase o he collisions. The K∗(892)0/K yield
a ios in Pb–Pb and pp collisions a e used o es ima e he ime du a ion be ween chemical and
kine ic eeze-ou , which is ound o be ∼4–7 m/c o cen al collisions. The pT-di e en ial a ios
o K∗(892)0/K, φ(1020)/K, K∗(892)0/π, φ(1020)/π, p/K∗(892)0and p/φ(1020)a e also p esen ed
o Pb–Pb and pp collisions a √sNN =5.02 TeV. These a ios show ha he esca e ing e ec is
p edominan ly a low-pTphenomenon.
©2020 The Au ho (s). 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.
1. In oduc ion
Se e al measu emen s in high-ene gy hea y-ion collisions a
he La ge Had on Collide (LHC) [1–3] and he Rela i is ic Hea y
Ion Collide (RHIC) [4–9]ha e shown ha a s ongly-coupled
Qua k-Gluon Plasma (QGP) is o med ha subsequen ly had onizes.
Resonances, sho li ed had ons ha decay ia s ong in e ac ions,
play an impo an ole in cha ac e izing he p ope ies o had onic
ma e o med in hea y-ion collisions [10–16]. Se e al esonances
ha e been obse ed in pp and nuclea collisions [10–19]: 2(1270),
ρ(770)0, (1232)++, 0(980), K∗(892)0,±, (1385), (1520)and
φ(1020)wi h li e imes o he o de o 1.1 m/c, 1.3 m/c, 1.6
m/c, 2.6 m/c, 4.16 m/c, 5.5 m/c, 12.6 m/cand 46.3 m/c, e-
spec i ely [20]. The wide ange o hei li e imes allows hem o
be good p obes o he dynamics o he sys em o med in ul a-
ela i is ic hea y-ion collisions [21–27].
In he had onic phase o he e olu ion o he sys em o med
in hea y-ion collisions, he e a e wo impo an empe a u es and
co esponding imescales: he chemical eeze-ou , when he in-
elas ic collisions among he cons i uen s a e expec ed o cease,
and he la e kine ic eeze-ou , when all (elas ic) in e ac ions
E-mail add ess: alice -publica ions @ce n .ch.
s op [28–30]. I esonances decay be o e kine ic eeze-ou , hen
hei decay p oduc s a e subjec o had onic esca e ing ha al e s
hei momen um dis ibu ions. This leads o inabili y o econ-
s uc he pa en esonance using he in a ian mass echnique,
esul ing in a dec ease in he measu ed yield ela i e o he p i-
mo dial esonance yield, i.e. he yield a chemical eeze-ou . The
ac ion o esonances ha canno be eco e ed depends on he
li e ime o he had onic phase (defined as he ime be ween chem-
ical and kine ic eeze-ou ), he had onic in e ac ion c oss sec ion
o esonance decay p oduc s, he pa icle densi y in he medium
and he esonance phase space dis ibu ions. Fo example, a pion
om a K∗(892)0meson decay could sca e wi h ano he pion in
he medium as π−π+→ρ0→π−π+. A he same ime, a e
he chemical eeze-ou , pseudoelas ic in e ac ions could egene -
a e esonances in he medium, leading o an enhancemen o hei
yields. Fo example, in e ac ions like πK→K∗(892)0→πK and
K−K+→φ(1020)→K−K+could happen un il kine ic eeze-ou .
Hence, esonances a e p obes o he esca e ing and egene a ion
p ocesses du ing he e olu ion o he fi eball om chemical o ki-
ne ic eeze-ou . Indeed, anspo -based model calcula ions show
ha bo h esca e ing and egene a ion p ocesses a ec he final
esonance yields [31,32]. The mal s a is ical models, which ha e
success ully explained a hos o pa icle yields in hea y-ion colli-
sions ac oss a wide ange o cen e -o -mass ene gies [33–36], a e
h ps://doi.o g/10.1016/j.physle b.2020.135225
0370-2693/©2020 The Au ho (s). 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.
2ALICE Collabo a ion / Physics Le e s B 802 (2020) 135225
able o explain he measu ed esonance yields only a e including
esca e ing e ec s [37,38].
In his pape , he measu emen o he p oduc ion o K∗(892)0
and φ(1020) ec o mesons a mid apidi y in Pb–Pb and pp col-
lisions a √sNN =5.02 TeV is p esen ed. Al hough bo h ec o
mesons ha e simila masses, hei li e ime di e s by a ac o o
la ge han 10. This aspec is exploi ed o es ablish he dominance
o esca e ing in cen al Pb–Pb collisions a he LHC. The kaon
and pion daugh e s o he sho -li ed K∗(892)0→Kπ esca e
wi h o he had ons in he medium. The magni ude o he e ec is
mainly de e mined by he pion-pion in e ac ion c oss sec ion [39],
which is measu ed o be significan ly la ge ( ac o 5) han he o-
al kaon-pion in e ac ion c oss sec ion [40]. The la e de e mines
he magni ude o he egene a ion e ec [41]. Thus wi h esca e -
ing domina ing o e egene a ion, he obse able K∗(892)0yields
should dec ease compa ed o he p imo dial yields, and he e-
o e, a supp ession o he K∗(892)0/K yield a io is expec ed in
hea y-ion collisions ela i e o pp collisions. Fu he mo e, his a-
io is expec ed o dec ease wi h inc ease in sys em size, which is
de e mined by he collision cen ali y (maximum o cen al colli-
sions). In con as , because o a la ge li e ime compa ed o ha o
he had onic phase, he φ(1020)meson yields a e no expec ed
o be a ec ed by esca e ing [14,32]. The φ(1020)mesons a e
also expec ed no o be a ec ed by he egene a ion due o sig-
nifican ly lowe KK c oss sec ion compa ed o Kπand ππ c oss
sec ions [39,40]. Hence he independence o he φ(1020)/K yield
a io o he sys em size will ac as a baseline o co esponding
K∗(892)0/K measu emen s, he eby suppo ing he p esence o he
esca e ing e ec in hea y-ion collisions. The lowe K∗(892)0/K
yield a io in Pb–Pb collisions compa ed o pp a he same √sNN
can hen be used o es ima e he ime span be ween chemical
and kine ic eeze-ou in hea y-ion collisions. Fu he mo e, due o
he sca e ing o he decay p oduc s, he low-pTK∗(892)0a e less
likely o escape he had onic medium be o e decaying, compa ed
o high-pTK∗(892)0[32]. This could al e he K∗(892)0pTspec a
in Pb–Pb collisions compa ed o pp, while no such e ec is ex-
pec ed o φmesons. The e o e, s udying pT-di e en ial a ios o
K∗(892)0and φ(1020)mesons wi h espec o o he non-s ange
(π) and s ange (K) mesons, and ba yons (p) in Pb–Pb and pp
collisions will help o es ablish he pTdependence o esca e -
ing e ec s and disen angle hem om o he physics p ocesses like
adial flow ha modifies he shapes o he pTdis ibu ions a low
and in e media e ans e se momen a. In addi ion, he measu e-
men s a √sNN =5.02 TeV a e compa ed o esul s om Pb–Pb
collisions a √sNN =2.76 TeV [14,42]. Since p oduc ion o pa i-
cles and an ipa icles is equal a mid apidi y a LHC ene gies, he
a e age o he yields o K∗(892)0and K∗(892)0is p esen ed in his
pape and is deno ed by he symbol K∗0unless specified o he -
wise. The φ(1020)is deno ed by he symbol φ.
The pape is o ganized as ollows: In sec ion 2, he de ec o s
used in he analysis a e b iefly desc ibed. In sec ion 3, he da ase ,
he analysis echniques, he p ocedu e o ex ac ion o he yields
o K∗0and φmesons and he s udy o he sys ema ic unce ain-
ies a e p esen ed. In sec ion 4, he yields ob ained by in a ian
mass econs uc ion o K∗0and φmesons as a unc ion o ans-
e se momen um in Pb–Pb and pp collisions a √sNN =5.02 TeV,
he pT-in eg a ed a ios o K∗0and φ ela i e o cha ged kaons,
and pT-di e en ial a ios ela i e o cha ged π, K and p o ons a e
epo ed. Finally, in sec ion 5 he findings a e summa ized.
2. Expe imen al appa a us
The measu emen s o K∗0and φmeson p oduc ion in pp and
Pb–Pb collisions ha e been pe o med using he da a collec ed by
he ALICE de ec o in he yea 2015. The de ails o he ALICE de-
ec o can be ound in Re s. [43–45]. So we b iefly ocus on he
ollowing main de ec o s used o his analysis. The o wa d V0
de ec o , a scin illa o de ec o wi h a iming esolu ion less han
1 ns, is used o cen ali y selec ion, igge ing and beam-induced
backg ound ejec ion. The V0 consis s o wo sub-de ec o s, V0A
and V0C, placed a asymme ic posi ions, one on each side o he
in e ac ion poin wi h ull azimu hal accep ance and co e he
pseudo apidi y anges 2.8 <η<5.1 and -3.7 <η<-1.7, e-
spec i ely. The cen ali y classes in Pb–Pb collisions a e de e mined
om he sum o he measu ed signal ampli udes in V0A and V0C,
as discussed in Re s. [46,47]. The collision ime in o ma ion is p o-
ided by T0 which consis o wo a ays o Che enko coun e s
T0A and T0C, posi ioned on bo h sides o he in e ac ion poin [48].
The Ze o Deg ee Calo ime e (ZDC) consis s o wo ungs en-qua z
neu on and wo b ass-qua z p o on calo ime e placed a a dis-
ance o 113 m on bo h sides o he in e ac ion poin . I is used o
ejec he backg ound e en s and o measu e he spec a o nucle-
ons.
In he cen al ba el, he Inne T acking Sys em (ITS) and he
Time P ojec ion Chambe (TPC) a e used o cha ged-pa icle ack-
ing and p ima y collision e ex econs uc ion. The ITS consis s o
h ee sub-de ec o s o wo laye s each, co e ing a cen al pseu-
do apidi y ange |η|<0.9: Silicon Pixel De ec o (SPD), Silicon
D i De ec o (SDD) and Silicon S ip De ec o (SSD). The TPC is
he main cha ged pa icle acking de ec o , and has ull azimu hal
co e age in he pseudo apidi y ange |η|<0.9. Along wi h ack
econs uc ion, i also p o ides a measu emen o he momen um
and excellen pa icle iden ifica ion (PID). The TPC p o ides he
measu ed specific ene gy loss (dE/dx) o iden i y he pa icles, es-
pecially in low momen um ange (p<1 GeV/c) whe e he dE/dx
o pa icles a e well sepa a ed. To ex end he pa icle iden ifica ion
o highe pT, he Time o Fligh (TOF) de ec o is used in addi ion
o he TPC in o ma ion. The TOF is based on he Mul igap Resis i e
Pla e Chambe (MRPC) echnology and measu es he a i al imes
o pa icles wi h a esolu ion o he o de o 80 ps. I co e s a
pseudo apidi y ange |η|<0.9 and p o ides excellen PID capabil-
i ies in he in e media e pT ange by exploi ing he ime-o -fligh
in o ma ion.
3. Da a sample and analysis de ails
The pp da a we e collec ed using a minimum bias (MB) igge .
The logic o MB igge equi es a leas one hi in V0A o V0C
and one hi in he cen al ba el de ec o SPD in coincidence wi h
he LHC bunch c ossing [49,50]. In pp collisions, a c i e ion based
on he offline econs uc ion o mul iple p ima y e ices in he
SPD [45]is applied o educe he pileup, which is caused by mul-
iple in e ac ions in he same bunch c ossing. The ejec ed pileup
e en s a e less han 1% o he o al e en s. The Pb–Pb da a we e
also collec ed using a MB igge wi h a logic ha equi es a co-
incidence o signals in V0A and V0C. The MB- igge ed e en s a e
analyzed i hey ha e a econs uc ed collision e ex whose po-
si ion along he beam axis (Vz, zis he longi udinal di ec ion) is
wi hin 10 cm om he nominal in e ac ion poin in bo h pp and
Pb–Pb collisions. Backg ound e en s a e ejec ed using he iming
in o ma ion om he Ze o Deg ee Calo ime e s (ZDCs) and V0 de-
ec o s.
The Pb–Pb analysis is pe o med in 8 cen ali y classes defined
in Re . [46]: 0–10%, 10–20%, 20–30%, 30–40%, 40–50%, 50–60%,
60–70% and 70–80%. The 0–10% class co esponds o he mos
cen al Pb–Pb collisions, wi h small impac pa ame e , while he
70–80% class co esponds o pe iphe al Pb–Pb collisions, wi h la ge
impac pa ame e . The o al numbe o e en s ha a e analyzed
a e passing he e en selec ion c i e ia a e ∼110 million o pp
and ∼30 million o Pb–Pb collisions. Cha ged acks a e selec ed
ALICE Collabo a ion / Physics Le e s B 802 (2020) 135225 3
o analysis based on ack selec ion c i e ia ha ensu e good ack
quali y, as done in p e ious wo k [42]. In pa icula , a ack in he
TPC is eques ed o ha e a minimum o 70 c ossed ows (ho izon-
al segmen s along he ans e se eadou plane o he TPC) ou
o a maximum possible 159 [51]. A pT-dependen selec ion c i-
e ion on he dis ance o closes app oach o he collision e ex
in he ans e se (xy) plane (DCAxy) and along he longi udinal di-
ec ion (DCAz) is used o educe he con amina ion om seconda y
cha ged pa icles coming om weakly decaying had ons. In addi-
ion o hese selec ion c i e ia, acks a e equi ed o ha e pT>
0.15 GeV/cin bo h pp and Pb–Pb collisions. Cha ged pa icles a e
accep ed in he pseudo apidi y ange |η|<0.8, which ensu es a
uni o m accep ance.
The pa icle iden ifica ion exploi s bo h he TPC and he TOF.
Fo K∗0and φ econs uc ion in Pb–Pb collisions, cha ged pa i-
cles a e iden ified as pion o kaon i he mean specific ene gy loss
(dE/dx) measu ed by he TPC alls wi hin wo s anda d de ia-
ions (2σTPC) om he expec ed dE/dx alues o πo K o e he
en i e momen um ange. I he TOF in o ma ion is a ailable o
he ack, in addi ion o he TPC, a TOF-based selec ion c i e ion
3σTOF is applied o e he measu ed momen um ange, whe e σTOF
is he s anda d de ia ion om he expec ed ime-o -fligh o a
gi en species. These equi emen s help in educing he backg ound
unde he signal peak o e a la ge momen um ange and p o ide
a be e sepa a ion be ween signal and backg ound wi h espec
o TPC PID only. Fo K∗0 econs uc ion in pp collisions, he same
PID selec ion c i e ia a e applied o iden i y pion and kaon can-
dida es as a e used in Pb–Pb collisions. Fo he φ econs uc ion
in pp collisions, he kaon candida es a e iden ified using a 6σTPC,
4σTPC and 2σTPC selec ion on he measu ed dE/dxdis ibu ions in
he momen um anges p<0.3 GeV/c, 0.3 <p<0.4 GeV/cand p
>0.4 GeV/c, espec i ely. On op o his, he TOF-based selec ion
c i e ion o 3σTOF is applied o e he en i e measu ed momen um
ange in pp collisions i he TOF in o ma ion is a ailable.
3.1. Yield ex ac ion, co ec ions and no maliza ion
The K∗0and φ esonances a e econs uc ed by calcula ing he
in a ian mass o hei decay p oduc s h ough he had onic decay
channels K∗0(K∗0) →K+π−(K−π+)(B anching Ra io, BR = 66.666
±0.006% [20]) and φ→K+K−(BR = 49.2 ±0.5% [20]), espec-
i ely. Opposi ely cha ged K and π(o K) om he same e en a e
pai ed o econs uc he in a ian mass dis ibu ions o K∗0(φ).
The Kπand KK pai s a e selec ed in he apidi y ange |y|<0.5
in bo h pp and Pb–Pb collisions. The in a ian mass dis ibu ion
exhibi s a signal peak and a la ge combina o ial backg ound e-
sul ing om he unco ela ed Kπ(KK) pai s. The combina o ial
backg ound is es ima ed using a mixed-e en echnique in bo h
collision sys ems. The mixed-e en backg ound is cons uc ed by
combining kaons om one e en wi h he opposi ely cha ged π(K)
om di e en e en s o K∗0(φ). The e en s which a e mixed a e
equi ed o ha e simila cha ac e is ics. In Pb–Pb, wo e en s a e
mixed i hey belong o he same cen ali y class and he di e -
ence be ween he collision e ex posi ion is |Vz|<1 cm. In
pp collisions, wo e en s a e mixed wi h a condi ion o |Vz|<
1 cm and a di e ence in cha ged-pa icle densi y a mid apidi y
(|y| <0.5) o less han 5. To minimize he s a is ical fluc ua-
ions in he backg ound dis ibu ion, each e en is mixed wi h fi e
o he ones. The in a ian mass dis ibu ion om he mixed-e en
is no malized o he same-e en opposi ely-cha ged pai dis ibu-
ion in he mass egion 1.1–1.3 ( esp. 1.04–1.06) GeV/c2 o K∗0
( esp. φ), which is away om he mass peak (6 o K∗0and 7
o φ, is he wid h o he esonance). A e he combina o ial
backg ound sub ac ion, he signal peak is obse ed on op o a
esidual backg ound. The la e is due o he co ela ed Kπo KK
pai s ha o igina e om je s and om he misiden ifica ion o pa -
icles. I is shown in Re . [42] ha he esidual backg ound has a
smoo h dependence on mass and he shape o he backg ound is
well desc ibed by a second o de polynomial [14,42]. The in a i-
an mass dis ibu ions a e mixed-e en backg ound sub ac ion
a e fi ed wi h a B ei -Wigne ( esp. Voig ian) unc ion o he sig-
nal peak o K∗0( esp. φ) plus a second o de polynomial o he
esidual backg ound [42]. The Voig ian unc ion is a con olu ion
o a B ei -Wigne dis ibu ion and a Gaussian, whe e he wid h
σo he Gaussian accoun s o he mass esolu ion. The la e is
pT-dependen and a ies be ween 1 and 2 MeV/c2. The aw yields
a e measu ed as a unc ion o pT o K∗0and φin pp collisions
and in a ious cen ali y classes in Pb–Pb collisions. A de ailed de-
sc ip ion o he yield ex ac ion p ocedu e is gi en in Re . [42].
The measu ed yields a e a ec ed by he de ec o accep ance
and econs uc ion efficiency (A ×ε ec). This is es ima ed by means
o dedica ed Mon e Ca lo simula ions using he PYTHIA (PYTHIA 6
Pe ugia 2011 une and PYTHIA 8 Monash 2013 une) [52,53] and
HIJING [54]e en gene a o s o pp and Pb–Pb collisions, espec-
i ely. The gene a ed pa icles a e hen p opaga ed h ough he
de ec o ma e ial using GEANT3 [55]. The A ×ε ec is calcula ed as
a unc ion o pTand is defined as he a io o he econs uc ed
K∗0(φ) o he gene a ed K∗0(φ), bo h wi hin |y| <0.5. Fo he
econs uc ion o esonances, he same ack and PID selec ion c i-
e ia a e applied o he simula ions as used in he analysis o he
measu ed da a. The A ×ε ec is calcula ed o K∗0(φ) ha decay
h ough he had onic channel K±π∓(K+K−), hence i does no in-
clude he co ec ion o BR. In Pb–Pb collisions, he A ×ε ec has a
weak cen ali y dependence and he aw yields a e co ec ed using
he A ×ε ec o he espec i e cen ali y class.
The p ocedu e o co ec he aw yields is gi en by
1
Ne en
d2N
dydpT=1
Nacc
e en
d2N aw
dydpT
ε ig .ε e .εsig
(A×ε ec).BR .(1)
The aw yields a e no malized o he numbe o accep ed e en s
(Nacc
e en ) and co ec ed o A ×ε ec, igge efficiency (ε ig), e ex
econs uc ion efficiency (ε e ), signal loss (εsig) and he BR o he
decay channel. The yields in pp a e no malized o he numbe o
inelas ic collisions wi h a igge efficiency co ec ion, ε ig = 0.757
±0.019 [56]. The e ex econs uc ion efficiency in pp collisions
is ound o be ε e = 0.958. The signal loss co ec ion ac o εsig
is de e mined based on MC simula ions as a unc ion o pTand
accoun s o he esonance signal los due o igge inefficiencies.
The εsig(pT) co ec ion is only significan o pT<2.5 GeV/cand
has a alue o less han 5% bo h o K∗0and φin pp collisions.
In Pb–Pb collisions, he yields o K∗0and φin a gi en cen ali y
class a e no malized by he numbe o e en s in he espec i e
V0M (sum o V0A and V0C ampli ude) e en cen ali y class. The
co ec ion ac o s ε ig, ε e and εsig(pT) a e compa ible wi h uni y
in he epo ed cen ali y classes in Pb–Pb collisions and hence a e
no used.
3.2. Sys ema ic unce ain ies
The sys ema ic unce ain ies in he measu emen o K∗0and
φyields in pp and Pb–Pb collisions a e summa ized in Table 1.
The sou ces o sys ema ic unce ain ies a e ela ed o he yield ex-
ac ion me hod, PID and ack selec ion c i e ia, global acking
efficiency, he knowledge o he ALICE ma e ial budge and o he
in e ac ion c oss sec ion o had ons in he de ec o ma e ial. The
unce ain ies a e epo ed o h ee ans e se momen um alues,
low, mid and high pT. Fo Pb–Pb collisions all he sys ema ic un-
ce ain ies excep he one ela ed o he yield ex ac ion a e com-
mon in he a ious cen ali y classes and he alues gi en in he
4ALICE Collabo a ion / Physics Le e s B 802 (2020) 135225
Table 1
Sys ema ic unce ain ies in he measu emen o K∗0and φyields in pp and Pb–Pb collisions a √sNN =5.02 TeV. These un-
ce ain ies a e shown o h ee ans e se momen um alues, low, mid and high pT. Fo Pb–Pb collisions all he sys ema ic
unce ain ies excep yield ex ac ion a e common in a ious cen ali y classes and he alues gi en in he able a e a e aged
o e all cen ali y classes.
Sys ema ic a ia ion Pb–Pb pp
K∗0φK∗0φ
pT(GeV/c)pT(GeV/c)pT(GeV/c)pT(GeV/c)
0.6 4.5 18 0.5 4.25 18 0.1 4.25 18 0.5 4.25 18
Yield ex ac ion (%) 7.3 7.5 10.1 4.4 1.9 4.9 11.8 7.9 8.2 2.4 3.5 3.5
T ack selec ion (%) 2.7 1.4 3.0 3.0 1.3 1.0 1.4 1.0 1.9 4.0 2.0 5.5
Pa icle iden ifica ion (%) 5.4 3.0 5.0 1.0 1.5 2.4 2.1 3.2 6.9 0.3 1.7 6.5
Global acking efficiency (%) 4.7 7.4 4.0 4.7 8.2 3.1 2.0 3.1 3.4 2.0 3.2 2.4
Ma e ial budge (%) 1.4 0 0 5.7 0 0 3.4 0 0 5.7 0 0
Had onic In e ac ion (%) 2.4 0 0 1.3 0 0 2.8 0 0 1.3 0 0
To al (%) 10.9 11.0 12.3 9.2 8.6 6.4 13.0 9.1 11.4 7.7 5.4 9.5
Fig. 1. The pTdis ibu ions o (a) K∗0and (b) φmesons in pp collisions and a ious cen ali y classes in Pb–Pb collisions a
√sNN =5.02 TeV. The alues a e plo ed a he
cen e o each bin. The s a is ical and sys ema ic unce ain ies a e shown as ba s and boxes, espec i ely.
able a e a e aged o e all cen ali ies. The yield ex ac ion me hod
includes he unce ain ies due o a ia ions o he fi ing ange,
he choice o combina o ial backg ound es ima ion echnique, no -
maliza ion ange and esidual backg ound shape. The unce ain-
ies due o yield ex ac ion a e es ima ed o be 7.9–11.8% o K∗0
( esp. 2.4–3.5% o he φ) in pp and 7.3–10.1% ( esp. 1.9–4.9%) in
Pb–Pb collisions. The PID sys ema ic unce ain ies a ies be ween
2.1–6.9% (0.3–6.5%) o K∗0(φ) in pp and Pb–Pb collisions. The
con ibu ion o he unce ain y om he global acking efficiency
is calcula ed om he co esponding alues o single cha ged pa -
icles [51] and esul s in a 2.0–8.2% unce ain y by combining he
wo cha ged acks used in he in a ian mass econs uc ion o
K∗0and φ. The con ibu ion om a ia ion o he ack selec-
ion c i e ia is 1.0–5.5%. The sys ema ic unce ain ies due o he
had onic in e ac ion c oss sec ion a e es ima ed o be less han
2.8% and con ibu e only a low pT(<2 GeV/c). The unce ain ies
in he desc ip ion o he ma e ial budge o ALICE de ec o sub-
sys ems in GEANT3 (see Re . [57] o de ails) gi e a con ibu ion
lowe han 5.7% on he yields o K∗0and φin pp and Pb–Pb col-
lisions. The ma e ial budge unce ain y is significan only a pT
<2 GeV/cand negligible a highe pT. The o al pT-dependen
sys ema ic unce ain ies on he K∗0(φ) yields a e es ima ed o be
9.1–13.0% (5.4–9.5%) in pp collisions and 10.9–12.3% (6.4–9.2%)
in Pb–Pb collisions. The common sys ema ic unce ain ies o di -
e en pa icles (global acking efficiency, ma e ial budge and
had onic in e ac ion) a e canceled ou in calcula ing pa icle yield
a ios like K∗0/K and φ/K.
4. Resul s and discussion
4.1. T ans e se momen um spec a in pp and Pb–Pb collisions
The pTdis ibu ions o he K∗0and φmesons o |y| <0.5,
no malized o he numbe o e en s and co ec ed o efficiency,
accep ance and b anching a io o he decay channel, a e shown in
Fig. 1. The esul s o Pb–Pb collisions a e p esen ed o eigh di -
e en cen ali y classes (0–10% up o 70–80% in 10% wide cen al-
i y in e als) oge he wi h he esul s om inelas ic pp collisions
a he same ene gy.
The pT-in eg a ed pa icle yields ha e been ex ac ed using he
p ocedu e desc ibed in Re s. [14,42]. The pTdis ibu ions a e fi ed
wi h a Lé y-Tsallis unc ion [58,59]in pp and a Bol zmann-Gibbs
blas -wa e unc ion [60]in Pb–Pb collisions. The yields ha e been
ex ac ed om he da a in he measu ed pT egion and he fi
unc ions ha e been used o ex apola e in o he unmeasu ed (low
and high pT) egion. The low-pTex apola ion co e s pT<0.4
GeV/c o K∗0(φ) and accoun s o 8.6% (7.2%) and 12.5% (12.7%) o
he o al yield in he 0–10% and 70–80% cen ali y classes in Pb–Pb
collisions, espec i ely. In pp collisions, he K∗0is measu ed in he
ange 0 <pT<20 GeV/c. Fo he φmeson, he low-pTex ap-
ola ion co e s pT<0.4 GeV/c, accoun ing o 15.7% o he o al

ALICE Collabo a ion / Physics Le e s B 802 (2020) 135225 5
Fig. 2. pT-in eg a ed pa icle yield a ios K∗0/K−and φ/K−as a unc ion o
dNch/dη1/3measu ed a mid apidi y in pp, p–Pb and Pb–Pb collisions a √sNN
=5.02 TeV. Fo Pb–Pb collisions a √sNN =2.76 TeV, he φ/K− alues a e aken
om Re . [14]and he K∗0/K− alues a e aken om Re . [42]. The a ios o p–
Pb collisions a e aken om Re . [17]. S a is ical unce ain ies (ba s) a e shown
oge he wi h o al (hollow boxes) and cha ged-pa icle mul iplici y-unco ela ed
(shaded boxes) sys ema ic unce ain ies. The mal model calcula ions wi h chemi-
cal eeze-ou empe a u e Tch =156 MeV o he mos cen al Pb–Pb collisions
[34,64]a e also shown. EPOS3 model p edic ions [32]o K∗0/Kand φ/K a ios in
Pb–Pb collisions a e also shown as iole lines.
yield. The ex apola ed ac ion o he yield is negligible o pT>
20 GeV/c.
4.2. Pa icle a ios
Fig. 2shows he K∗0/K and φ/K a ios as a unc ion o
dNch/dη1/3[46,47,51] o Pb–Pb collisions a √sNN =2.76 [14,
42] and 5.02 TeV, p–Pb collisions a √sNN =5.02 TeV [17] and pp
collisions a √s=5.02 TeV. The kaon yields in Pb–Pb a √sNN
=5.02 TeV a e om Re . [51]. The dNch/dη1/3measu ed a
mid apidi y, is used he e as a p oxy o he sys em size. This is
suppo ed by he obse a ion o he linea inc ease in he HBT
adii wi h dNch/dη1/3[61,62]. The K∗0/K a io dec eases o is-
ing dNch/dη1/3while he φ/K a io is almos independen o
dNch/dη1/3. The a ios exhibi a smoo h end ac oss he di e -
en collision sys ems and collision ene gies s udied. The K∗0/K and
φ/K a ios in Pb–Pb collisions a √sNN =2.76 and 5.02 TeV a e in
ag eemen wi hin unce ain ies.
The esonance yields a e modified du ing he had onic phase by
esca e ing (which would educe he measu ed yields) and egen-
e a ion (which would inc ease he measu ed yields). The obse ed
dependence o he K∗0/K a io on he cha ged-pa icle mul iplici y
is consis en wi h he beha io ha would be expec ed i esca e -
ing is he cause o he supp ession. The ac ha he φ/K a io does
no exhibi supp ession wi h cha ged-pa icle mul iplici y sugges s
ha he φ, which has a li e ime an o de o magni ude la ge
han ha o he K∗0, decays p edominan ly ou side he had onic
medium. Theo e ical es ima es sugges ha abou 55% o he o
K∗0mesons wi h momen um p =1GeV/c, decay wi hin 5 m/c
o p oduc ion (a ypical es ima e o he ime be ween chemical
and kine ic eeze-ou in hea y-ion collisions [22,32,63]), while
only 7% o φmesons wi h p =1GeV/cdecay wi hin ha ime.
This suppo s he hypo hesis ha he expe imen ally obse ed
dec ease o he K∗0/K a io wi h cha ged-pa icle mul iplici y is
caused by esca e ing. A simila supp ession has also been ob-
se ed o ρ0/π[15] and ∗/[13]in cen al Pb–Pb collisions
ela i e o pe iphe al Pb–Pb and pp collisions a √sNN =2.76 TeV.
In addi ion, he K∗0/K a io om he mal model calcula ions wi h-
ou esca e ing e ec s and wi h chemical eeze-ou empe a u e
Fig. 3. Lowe limi on he had onic phase li e ime be ween chemical and kine ic
eeze-ou as a unc ion o dNch/dη1/3in p–Pb [17]and Pb–Pb collisions a
√sNN
=5.02 TeV. The ba s and bands ep esen he s a is ical and sys ema ic unce ain-
ies, espec i ely, p opaga ed o he li e ime om he unce ain ies associa ed wi h
he measu ed K∗0/K a ios in Pb–Pb (p–Pb) and pp collisions a
√sNN =5.02 TeV.
Tch =156 MeV o he mos cen al Pb–Pb collisions [34,64]is
ound o be highe han he co esponding measu emen s, while
he measu ed φ/K a io ag ees wi h he he mal model p edic-
ions. The K∗0/K and φ/K a ios in Pb–Pb collisions a e also com-
pa ed o EPOS3 model calcula ions wi h and wi hou a had onic
cascade phase modeled by U QMD [32]. The EPOS3 model p edic-
ions shown in he figu e a e o Pb–Pb collisions a √sNN =2.76
TeV bu no significan quali a i e di e ences a e expec ed be ween
he wo ene gies. The EPOS3 gene a o wi h U QMD ep oduces
he obse ed end o he K∗0/K and φ/K a ios which u he sup-
po s he expe imen al da a.
The ac ha K∗0/K−dec eases wi h inc easing dNch/dη1/3
implies ha esca e ing o he decay p oduc s o K∗0in he
had onic phase is dominan o e K∗0 egene a ion. This sugges s
ha K∗0↔Kπis no in balance. Hence in Pb–Pb he K∗0/K−
a io can be used o ge an es ima e o he ime be ween chem-
ical and kine ic eeze-ou , τ, as, [K∗0/K−]kine ic =[K∗0/K−]chemical
×e−τ/τK∗0, whe e τK∗0is he K∗0li e ime. He e, τK∗0is aken
as 4.16 m/cigno ing any medium modifica ion o he wid h
o he in a ian mass dis ibu ion o K∗0. Fu he mo e, i is as-
sumed ha [K∗0/K−]chemical is gi en by he alues measu ed in
pp collisions and he Pb–Pb collision da a p o ides an es ima e o
[K∗0/K−]kine ic. This is equi alen o assuming ha all K∗0’s ha
decay be o e kine ic eeze-ou a e los due o esca e ing e ec s
and he e is no egene a ion e ec be ween kine ic and chemi-
cal eeze-ou which is suppo ed by AMPT simula ions [31]. All
he assump ions lis ed abo e lead o an es ima e o τas a lowe
limi o he ime span be ween chemical and kine ic eeze-ou s.
A dec ease in he K∗0/K a io wi h inc easing mul iplici y has p e-
iously also been obse ed in p–Pb collisions a √sNN = 5.02 TeV
[17]. This migh indica e he p esence o esca e ing e ec in high
mul iplici y p–Pb collisions and is sugges i e o a fini e li e ime
o he had onic phase. Fo compa ison we ha e also es ima ed he
had onic phase li e ime in p–Pb da a. Fig. 3shows he esul s o τ
boos ed by a Lo en z ac o (∼1.65 o p–Pb collisions and 1.75 o
Pb–Pb collision) as a unc ion o dNch/dη1/3. Neglec ing highe
o de e ms, he Lo en z ac o is es ima ed as 1+(pT/mc)2.
He e mis he es mass o he esonance and pTis used as
an app oxima ion o p o he measu emen s a mid apidi y. The
ime in e al be ween chemical and kine ic eeze-ou inc eases
wi h he sys em size as expec ed. Fo cen al Pb–Pb collisions a
√sNN =5.02 TeV, he lowe limi o ime be ween chemical and
6ALICE Collabo a ion / Physics Le e s B 802 (2020) 135225
Fig. 4. Pa icle yield a ios (K∗0+K∗0)/(K++K−) in panel (a) and (2φ)/(K++K−) in panel (b), bo h as a unc ion o pT o cen ali y classes 0–10% and 70–80% in Pb–Pb
collisions a
√sNN =5.02 TeV. Fo compa ison, he co esponding a ios a e also shown o inelas ic pp collisions a
√s=5.02 TeV. The s a is ical unce ain ies a e shown
as ba s and sys ema ic unce ain ies a e shown as boxes. In he ex (K∗0+K∗0), (K++K−) a e deno ed by K∗0and K, espec i ely.
Fig. 5. Pa icle yield a ios (K∗0+K∗0)/(π++π−) in panel (a) and (2φ)/(π++π−) in panel (b), bo h as a unc ion o pT o cen ali y classes 0–10% and 70–80% in Pb–Pb
collisions a
√sNN =5.02 TeV. Fo compa ison, he co esponding a ios a e also shown o inelas ic pp collisions a
√s=5.02 TeV. The s a is ical unce ain ies a e shown
as ba s and sys ema ic unce ain ies a e shown as boxes. In he ex (K∗0+K∗0), (π++π−) a e deno ed by K∗0and π, espec i ely.
kine ic eeze-ou is abou 4–7 m/c. This is o he same o de
o magni ude as he K∗0li e ime, bu abou an o de o magni-
ude sho e han he φli e ime. A smoo h inc ease o τwi h
sys em size om p–Pb o Pb–Pb collisions is obse ed. The EPOS3
gene a o wi h U QMD ep oduces he inc easing end o τwi h
mul iplici y quali a i ely [32]. I a cons an chemical eeze-ou
empe a u e is assumed, hen he inc ease o τwi h mul iplici y
in Pb–Pb collisions co esponds o a dec ease o he kine ic eeze-
ou empe a u e. This is in quali a i e ag eemen wi h esul s om
blas -wa e fi s o iden ified pa icle pTdis ibu ions [51], which
a e in e p e ed as dec ease in he kine ic eeze-ou empe a u e
om pe iphe al o cen al collisions.
Fu he , o quan i y he pT-dependence o he esca e ing e -
ec obse ed in Pb–Pb collisions, a se o pT-di e en ial yield
a ios was s udied: K∗0/K, φ/K, K∗0/π, φ/π, p/K∗0and p/φ as
shown in Figs. 4, 5and 6. The choice o he a ios is mo i a ed by
he ollowing easons: (a) he a io o esonance yields ela i e o
he ones o kaons and pions can shed ligh on he shapes o he pT
dis ibu ions o mesons wi h di e en mass and qua k con en , and
(b) he a ios o he p o on yield wi h espec o he yields o he
esonances allow compa isons among had ons o simila mass, bu
di e en ba yon numbe and qua k con en o be made. Fo case
(a), a ios in 0–10%, 70–80% Pb–Pb collisions and pp collisions a
√sNN =5.02 TeV a e compa ed. Fo case (b), a ios in 0–10% Pb–
Pb collisions and pp collisions a √sNN =5.02 TeV a e compa ed
wi h 0–5% in Pb–Pb collisions a √sNN =2.76 TeV. The a ios o
70–80% in Pb–Pb collisions a e close o he co esponding esul s
in pp collisions. No iceably, he e a e dis inc di e ences be ween
cen al and pe iphe al (pp) collisions in he a ios o pTbelow ∼
2 GeV/cand in e media e pT(be ween 2 and 6 GeV/c) bu he
a ios a e consis en a highe pT[42].
A low pT, he K∗0/K and K∗0/π o cen al collisions a e lowe
han in pe iphe al (pp) collisions, while he co esponding yield
a ios o φmeson a e compa able wi hin he unce ain ies. This
obse a ion is consis en wi h he supp ession o K∗0yields due
o esca e ing in he had onic phase. I demons a es ha esca -
e ing a ec s low momen um pa icles. A in e media e pT, bo h
a ios show an enhancemen o cen al Pb–Pb collisions ela i e
o pe iphe al and pp collisions, which is mo e p ominen o φ/K,
φ/πand K∗0/π. This is consis en wi h he p esence o a la ge
ALICE Collabo a ion / Physics Le e s B 802 (2020) 135225 7
Fig. 6. Pa icle yield a ios (p +p)/(K∗0+K∗0) in panel (a) and (p +¯
p)/(2φ) in panel (b), bo h as a unc ion o pT o 0–10% cen al Pb–Pb collisions and inelas ic pp
collisions a √sNN =5.02 TeV. Fo compa ison, simila a ios a e also shown o 0–5% cen al Pb–Pb collisions a √sNN =2.76 TeV [42]. The s a is ical unce ain ies a e
shown as ba s and sys ema ic unce ain ies a e shown as boxes. In he ex (K∗0+K∗0) and (p +p) a e deno ed by K∗0and p, espec i ely.
adial flow in cen al collisions ela i e o pe iphe al and pp colli-
sions [51]. Gi en ha he masses o K∗0and φmesons a e la ge
han hose o he cha ged kaon and pion, he esonances expe i-
ence a la ge adial flow e ec . In cen al Pb–Pb collisions, o pT
below 5 GeV/c, he p/φ a io is obse ed o be independen o
pTand he p/K∗0 a io exhibi s a weak pT-dependence wi hin he
unce ain ies, in con as o he dec ease o bo h a ios wi h pT
obse ed in pp collisions. In u n, his sugges s ha he shapes o
he pTdis ibu ions a e simila o K∗0, φand pin his pT ange.
Al hough he qua k con en s a e di e en , he masses o hese
had ons a e simila , indica ing ha his is he ele an quan i y
in de e mining spec a shapes. This is consis en wi h expec a ions
om hyd odynamic-based models [65,66]. Wi hin he unce ain-
ies, he p/K∗0and p/φ a ios o cen al Pb–Pb collisions a √sNN
= 5.02 TeV and 2.76 TeV [42]a e cons an a in e media e pT. This
is consis en wi h he obse a ion o simila o de adial flow a
bo h ene gies, ob ained om he analysis o pTspec a o pions,
kaons and p o ons [51]. Fo pT>6 GeV/c, he K∗0/K, φ/K, K∗0/π,
φ/π, p/K∗0and p/φ yield a ios in cen al collisions a e simila o
pe iphe al and pp collisions, indica ing ha agmen a ion is he
dominan had on p oduc ion mechanism in his pT egion. This is
consis en wi h p e ious measu emen s a √sNN = 2.76 TeV [42].
5. Summa y
The ans e se momen um dis ibu ions o K∗0and φmesons
ha e been measu ed a mid apidi y (|y| <0.5) o a ious collision
cen ali ies in Pb–Pb and inelas ic pp collisions a √sNN =5.02
TeV using he ALICE de ec o . The K∗0yields ela i e o cha ged
kaons in Pb–Pb collisions show a supp ession wi h espec o pp
collisions, which inc eases wi h he sys em size, quan ified us-
ing dNch/dη1/3measu ed a mid apidi y. In con as , no such
supp ession is obse ed o he φmesons. The lack o supp es-
sion o he φmeson can be a ibu ed o he ac ha mos o
hem decay ou side he fi eball because o i s longe li e ime (τφ=
46.3 ±0.4 m/c). Because o a sho e li e ime (τK∗0= 4.16 ±
0.05 m/c), a significan numbe o p oduced K∗0decays in he
had onic medium. The decay p oduc (s) unde go in e ac ions wi h
o he had ons in he medium esul ing in a significan change in
hei momen um, and no longe con ibu ing o he K∗0signal
econs uc ed in he expe imen . Al hough bo h esca e ing and
egene a ion a e possible, he esul s p esen ed he e ep esen an
expe imen al demons a ion o he p edominance o esca e ing
e ec s in he had onic phase o he sys em p oduced in hea y-
ion collisions. The e ec o esca e ing inc eases wi h he sys em
size. Fu he mo e, he K∗0/Kyield a ios in cen al Pb–Pb collisions
a e significan ly lowe compa ed o he alues om he mal model
calcula ions wi hou esca e ing e ec s, while he measu ed φ/K
yield a io ag ees wi h he model calcula ion. This u he co ob-
o a es he hypo hesis ha esca e ing a ec s he measu ed K∗0
yields in Pb–Pb collisions. A lowe limi o he li e ime o he
had onic phase is de e mined by using he K∗0/K a ios in Pb–Pb
and pp collisions a √sNN =5.02 TeV. The li e ime, as expec ed,
inc eases wi h sys em size. Fo cen al Pb–Pb collisions, i is abou
4–7 m/c.
The pT-di e en ial yield a ios o K∗0/πand K∗0/K a e s udied
in cen al Pb–Pb, pe iphe al Pb–Pb and pp collisions o unde s and
he pT-dependence o he esca e ing e ec . I is obse ed ha
esca e ing dominan ly a ec s he had ons a pT<2 GeV/c. A
in e media e pT(2–6 GeV/c), he φ/K, φ/π, K∗0/π, p/K∗0and
p/φ yield a ios a e enhanced in cen al Pb–Pb collisions ela i e o
pe iphe al Pb–Pb and pp collisions. In addi ion, he spec al shapes
o K∗0, φand p, which ha e compa able masses, a e simila wi hin
he unce ain ies o pTbelow 5 GeV/cin Pb–Pb collisions. These
measu emen s demons a e he e ec o highe adial flow in cen-
al Pb–Pb collisions ela i e o pe iphe al Pb–Pb and pp collisions.
A compa ison o he p/K∗0and p/φ a ios o cen al Pb–Pb col-
lisions a √sNN =5.02 and 2.76 TeV shows he cons ancy o he
a ios wi h pT. This is consis en wi h he obse a ion o compa-
able adial flow a √sNN =5.02 TeV and 2.76 TeV. Fo highe
pT, abo e 6 GeV/c, all he a ios ag ee wi hin he unce ain ies
o cen al and pe iphe al Pb–Pb, and pp collisions, indica ing ha
pa icle p oduc ion ia agmen a ion a high ans e se momen a
is no significan ly modified in he p esence o a medium.
Acknowledgemen s
The ALICE Collabo a ion would like o hank all i s enginee s
and echnicians o hei in aluable con ibu ions o he cons uc-
ion o he expe imen and he CERN accele a o eams o he
ou s anding pe o mance o he LHC complex. The ALICE Collab-
o a ion g a e ully acknowledges he esou ces and suppo p o-
ided by all G id cen e s and he Wo ldwide LHC Compu ing G id
(WLCG) collabo a ion. The ALICE Collabo a ion acknowledges he
8ALICE Collabo a ion / Physics Le e s B 802 (2020) 135225
ollowing unding agencies o hei suppo in building and un-
ning he ALICE de ec o : A. I. Alikhanyan Na ional Science Labo a-
o y (Ye e an Physics Ins i u e) Founda ion (ANSL), S a e Commi -
ee o Science and Wo ld Fede a ion o Scien is s (WFS), A menia;
Aus ian Academy o Sciences, Aus ian Science Fund (FWF): [M
2467-N36] and Na ionals i ung ü Fo schung, Technologie und
En wicklung, Aus ia; Minis y o Communica ions and High Tech-
nologies, Na ional Nuclea Resea ch Cen e , Aze baijan; Conselho
Nacional de Desen ol imen o Cien ífico e Tecnológico (CNPq), Fi-
nanciado a de Es udos e P oje os (Finep), Fundação de Ampa o à
Pesquisa do Es ado de São Paulo (FAPESP) and Uni e sidade Fed-
e al do Rio G ande do Sul (UFRGS), B azil; Minis y o Educa ion o
China (MOEC), Minis y o Science & Technology o China (MSTC)
and Na ional Na u al Science Founda ion o China (NSFC), China;
Minis y o Science and Educa ion and C oa ian Science Founda-
ion, C oa ia; Cen o de Aplicaciones Tecnológicas y Desa ollo Nu-
clea (CEADEN), Cubaene gía, Cuba; Minis y o Educa ion, You h
and Spo s o he Czech Republic, Czech Republic; The Danish
Council o Independen Resea ch | Na u al Sciences, he Villum
Fonden and Danish Na ional Resea ch Founda ion (DNRF), Den-
ma k; Helsinki Ins i u e o Physics (HIP), Finland; Commissa ia à
l’Éne gie A omique (CEA), Ins i u Na ional de Physique Nucléai e
e de Physique des Pa icules (IN2P3) and Cen e Na ional de la
Reche che Scien ifique (CNRS) and Région des Pays de la Loi e,
F ance; Bundesminis e ium ü Bildung und Fo schung (BMBF)
and GSI Helmhol zzen um ü Schwe ionen o schung GmbH, Ge -
many; Gene al Sec e a ia o Resea ch and Technology, Minis y o
Educa ion, Resea ch and Religions, G eece; Na ional Resea ch De-
elopmen and Inno a ion Office, Hunga y; Depa men o A omic
Ene gy, Go e nmen o India (DAE), Depa men o Science and
Technology, Go e nmen o India (DST), Uni e si y G an s Com-
mission, Go e nmen o India (UGC) and Council o Scien ific and
Indus ial Resea ch (CSIR), India; Indonesian Ins i u e o Science,
Indonesia; Cen o Fe mi -Museo S o ico della Fisica e Cen o S udi
e Rice che En ico Fe mi and Is i u o Nazionale di Fisica Nucle-
a e (INFN), I aly; Ins i u e o Inno a i e Science and Technology,
Nagasaki Ins i u e o Applied Science (IIST), Japanese Minis y o
Educa ion, Cul u e, Spo s, Science and Technology (MEXT) and
Japan Socie y o he P omo ion o Science (JSPS) KAKENHI, Japan;
Consejo Nacional de Ciencia (CONACYT) y Tecnología, h ough
Fondo de Coope ación In e nacional en Ciencia y Tecnología (FON-
CICYT) and Di ección Gene al de Asun os del Pe sonal Academico
(DGAPA), Mexico; Nede landse O ganisa ie oo We enschappelijk
Onde zoek (NWO), Ne he lands; The Resea ch Council o No way,
No way; Commission on Science and Technology o Sus ainable
De elopmen in he Sou h (COMSATS), Pakis an; Pon ificia Uni-
e sidad Ca ólica del Pe ú, Pe u; Minis y o Science and Highe
Educa ion and Na ional Science Cen e, Poland; Ko ea Ins i u e o
Science and Technology In o ma ion and Na ional Resea ch Foun-
da ion o Ko ea (NRF), Republic o Ko ea; Minis y o Educa ion
and Scien ific Resea ch, Ins i u e o A omic Physics and Minis y o
Resea ch and Inno a ion and Ins i u e o A omic Physics, Romania;
Join Ins i u e o Nuclea Resea ch (JINR), Minis y o Educa ion
and Science o he Russian Fede a ion, Na ional Resea ch Cen e
Ku cha o Ins i u e, Russian Science Founda ion and Russian Foun-
da ion o Basic Resea ch, Russia; Minis y o Educa ion, Science,
Resea ch and Spo o he Slo ak Republic, Slo akia; Na ional Re-
sea ch Founda ion o Sou h A ica, Sou h A ica; Swedish Resea ch
Council (VR) and Knu & Alice Wallenbe g Founda ion (KAW),
Sweden; Eu opean O ganiza ion o Nuclea Resea ch, Swi ze land;
Su ana ee Uni e si y o Technology (SUT), Na ional Science and
Technology De elopmen Agency (NSDTA) and Office o he Highe
Educa ion Commission unde NRU p ojec o Thailand, Thailand;
Tu kish A omic Ene gy Agency (TAEK), Tu key; Na ional Academy
o Sciences o Uk aine, Uk aine; Science and Technology Facili ies
Council (STFC), Uni ed Kingdom; Na ional Science Founda ion o
he Uni ed S a es o Ame ica (NSF) and (DOE NP), Uni ed S a es o
Ame ica.
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