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In es iga ing he na u e o he K0(700) s a e wi h π±K0S co ela ions a he LHC
© 2024 The Au ho (s). Published by Else ie B.V. Funded by SCOAP³.
Published e sion
ALICE Collabo a ion
ALICE Collabo a ion. (2024). In es iga ing he na u e o he K0(700) s a e wi h π±K0S
co ela ions a he LHC. Physics Le e s B, 856, A icle 138915.
h ps://doi.o g/10.1016/j.physle b.2024.138915
2024
Phys. Le . B 856 (2024) 138915
A ailable online 30 July 2024
0370-2693/© 2024 The Au ho (s). Published by Else ie B.V. Funded by SCOAP³. This is an open access a icle unde he CC BY license
(h p://c ea i ecommons.o g/licenses/by/4.0/).
Con en s lis s a ailable a ScienceDi ec
Physics Le e s B
jou nal homepage: www.else ie .com/loca e/physle b
Le e
In es iga ing he composi ion o he K∗
0(700) s a e wi h 𝜋±K0
Sco ela ions a
he LHC
.ALICE Collabo a ion⋆
A R T I C L E I N F O A B S T R A C T
Edi o : M. Dose
Da ase link: h ps://
www .hepda a .ne / eco d /ins2739149
The fi s measu emen s o em oscopic co ela ions wi h he pa icle pai combina ions 𝜋±K0
Sin pp collisions a
√𝑠=13TeV a he La ge Had on Collide (LHC) a e epo ed by he ALICE expe imen . Using he em oscopic
app oach, i is shown ha i is possible o s udy he elusi e K∗
0(700) pa icle ha has been conside ed a e aqua k
candida e o o e o y yea s. Sou ce and final-s a e in e ac ion pa ame e s a e ex ac ed by fi ing a model
assuming a Gaussian sou ce o he expe imen ally measu ed wo-pa icle co ela ion unc ions. The final-s a e
in e ac ion in he 𝜋±K0
Ssys em is modeled h ough a esonan sca e ing ampli ude, defined in e ms o a mass
and a coupling pa ame e , The ex ac ed mass and B ei –Wigne wid h, de i ed om he coupling pa ame e , o
he final-s a e in e ac ion a e ound o be consis en wi h p e ious measu emen s o he K∗
0(700). The small alue
and inc ease o he co ela ion s eng h wi h inc easing sou ce size suppo he hypo hesis ha he K∗
0(700) is a
ou -qua k s a e, i.e. a e aqua k s a e o he o m (q1, q2, q3, q3)in which q1, q2and q3indica e he fla o o he
alence qua ks o he 𝜋and K0
S. This la e end is also confi med ia a simple geome ic model ha assumes a
e aqua k s uc u e o he K∗
0(700) esonance.
1. In oduc ion
Fem oscopy wi h iden ical cha ged pions has been a use ul ool o
many yea s o expe imen ally p obe he geome y o he space- ime
s uc u e o he eeze-ou p obabili y dis ibu ion in high-ene gy pp
and hea y-ion collisions [1]. Iden ical-kaon em oscopic measu emen s
ha e also been ca ied ou o complemen he iden ical pion s udies, ex-
amples o which a e measu emen s in Au–Au collisions a cen e -o -mass
ene gy pe nucleon pai
√𝑠NN = 200 GeV a he Rela i is ic Hea y-Ion
Collide by he STAR Collabo a ion [2](K
0
SK0
S) and PHENIX Collabo a-
ion [3](K
±K±), and o pp collisions a
√𝑠=5.02, 7, and 13 TeV and
Pb–Pb collisions a √𝑠NN =2.76 TeV a he CERN LHC by he ALICE
Collabo a ion [4–7](K
0
SK0
Sand K±K±).
In he em oscopic me hod, he momen um co ela ions o pai s o
pa icles when in e ac ions wi h he o he pa icles in he collision sys-
em cease, i.e. du ing “ eeze ou ” [8], can be u ilized o ge insigh in o
he s eng h o he pai in e ac ion, i.e. he final-s a e in e ac ion (FSI),
a low ela i e momen um. The homogenei y egion size, he s eng h,
and e en he na u e o he FSI a eeze ou can be de e mined by fi ing
he expe imen al wo-pa icle co ela ion unc ion o a model based on
he FSI. Resul s on non-iden ical kaon em oscopy wi h K0
SK±pai s we e
published by ALICE in pp collisions a
√𝑠=5.02, 7, and 13 TeV and Pb–
Pb collisions a
√𝑠NN =2.76 TeV [7,9,10]. Al hough he gene al goals
⋆E-mail add ess: alice -publica ions @ce n .ch.
o non-iden ical kaon em oscopy s udies o e lap wi h hose o iden i-
cal kaon em oscopy, e.g. o ex ac in o ma ion abou he space– ime
geome y o he collision egion and de e mine he pai -wise in e ac ion
s eng h, he la e is diffe en in each case. Fo he iden ical kaon cases,
in which pai -wise quan um s a is ical co ela ions a e p esen , he in-
e ac ions a e he ollowing: K±K±– Coulomb in e ac ion, and K0
SK0
S–
s ong FSI h ough he 0(980)/a0(980) esonances. Fo he K0
SK±pai s,
he e a e no quan um s a is ical co ela ions and he only in e ac ion
p esen is he s ong FSI h ough he a0(980) esonance.
K0
SK± em oscopy should hus be sensi i e o he p ope ies o he
a0(980) esonance. I has been sugges ed in many pape s in he li e a u e
ha he a0(980) could be a ou -qua k o e aqua k s a e [11]. I was
fi s p oposed in 1977 ha expe imen ally-obse ed low-lying mesons,
such as he a0(980) and K∗
0(700), a e pa o a SU(3) e aqua k none
using he MIT Bag model [12], which was la e ollowed up wi h la ice
QCD calcula ions [13]. The e ha e been a numbe o QCD s udies o
hese mesons ha can be ca ego ized as QCD-inspi ed models, see o
example Re s. [11,14–16], and la ice QCD calcula ions, see o example
Re s. [17–19].
Indeed, he esul s o he ALICE K0
SK±s udies men ioned abo e sug-
ges ed ha he a0(980) is a e aqua k s a e. This sugges ion is based on
compa ing he ex ac ed pai -wise in e ac ion s eng h o K0
SK±be ween
pp and Pb–Pb collisions as well as wi h he K0
SK0
Ss udies [4,6,7,9,10].
h ps://doi.o g/10.1016/j.physle b.2024.138915
Recei ed 6 Janua y 2024; Recei ed in e ised o m 21 June 2024; Accep ed 25 July 2024
Physics Le e s B 856 (2024) 138915
2
ALICE Collabo a ion
F om a geome ic pic u e, since a e aqua k e sion o he a0(980) con-
ains a s ange – an i-s ange qua k pai , a FSI h ough i should be
supp essed o a small sys em as in pp collisions due o an inc eased
annihila ion p obabili y, whe eas o a la ge Pb–Pb collision his sup-
p ession should no be p esen . Thus, a s ong FSI would be expec ed
om Pb–Pb collisions and weak FSI om pp collisions, and his is wha
was obse ed in expe imen s. I would also be expec ed ha a s ong
pai -wise co ela ion would be seen o K0
SK0
Ss udies since quan um
s a is ics is dominan o e FSI effec s. This excep ion is co obo a ed
by expe imen al findings [4,6,7].
The success o he ALICE K0
SK±s udies on he na u e o he a0(980)
esonance mo i a ed he fi s em oscopic s udy e e o 𝜋±K0
Sco -
ela ions in √𝑠=13 TeV pp collisions. Ano he esonance ha is a
e aqua k candida e is he K∗
0(700) ha decays wi h a b anching a io o
∼ 100% in o 𝜋K pai s [12]. The K∗
0(700) is lis ed in he Re iew o Pa i-
cle Physics [20]as a s ange meson wi h spin 0 and isospin
1
2, he qua k
con en o he K∗
0(700)+s a e being us. I s mass is lis ed as 845 ±17
MeV/𝑐2and i is a e y b oad esonance wi h B ei –Wigne wid h o
468 ±30MeV/𝑐2. The mass o he K∗
0(700) is abo e he 𝜋±K0
S h esh-
old, ha is o abou 637.18 MeV/𝑐2, and i s wid h is seen o encompass
his h eshold and below. The e aqua k e sion o he K∗
0(700)+would
ha e qua k con en usddand would decay by di ec qua k ans e in o
a 𝜋+K0pai [12]. Thus by measu ing 𝜋±K0
Sco ela ions i should be
possible o s udy he qua k na u e o he K∗
0(700) using simila me hods
as men ioned abo e o he a0(980) s udies, i.e. measu ing he s eng h
o he FSI, assuming ha he 𝜋±K0
SFSI goes solely h ough he K∗
0(700).
This scena io will be s udied by ex ac ing he mass and wid h pa am-
e e s o he FSI and compa ing hem wi h p e ious measu emen s o
he K∗
0(700) [21]. In he p esen Le e , a s udy o em oscopic co ela-
ions wi h he non-iden ical pai combina ion 𝜋±K0
Sin pp collisions a
√𝑠=13TeV is p esen ed o he fi s ime o s udy he na u e o he
K∗
0(700) esonance. The choice o using pp collisions o his wo k e-
sponds o he necessi y o s udying he FSI in a small sys em in which
he s eng h o he FSI is expec ed o be mo e sensi i e o he sys em
size and hus o he qua k na u e o he esonance [7]. Due o he sho -
ange na u e o he s ong in e ac ion which migh p oduce he esonan
s a e, measu emen s in pp collisions a e mo e sui ed since in e pa icle
dis ances o a ew m a e ob ained [8]. Mo eo e , i has al eady been
obse ed ha he p esence o esonances in he co ela ion unc ion is
enhanced o measu emen s in small colliding sys ems, since he signal-
o-backg ound o he conside ed s a e scales as 1∕mul iplici y [8].
The esul s p esen ed in his Le e a e ob ained using da a collec ed
by he ALICE Collabo a ion [22,23]du ing he 2015–2018 pp LHC un.
The Le e is o ganized in o se en sec ions: In oduc ion, Da a Analysis,
Co ela ion Func ion, Fi ing, Sys ema ic unce ain ies, Resul s and Dis-
cussion, and Summa y. The Da a Analysis sec ion gi es de ails on how
he da a we e aken and how he 𝜋±and K0
Swe e econs uc ed and
iden ified. The Co ela ion Func ion sec ion desc ibes how he 𝜋±K0
S
pai s we e used o cons uc he co ela ion unc ions o his analy-
sis. The Fi ing sec ion desc ibes he model used o fi he co ela ion
unc ions in o de o ex ac he sou ce pa ame e s and FSI pa ame-
e s. The Sys ema ic unce ain ies sec ion discusses how he sys em-
a ic unce ain ies we e calcula ed. The Resul s and Discussion sec ion
p esen s he esul s o he ex ac ed pa ame e s and discusses hei in-
e p e a ion. The Summa y sec ion summa izes he esul s o he p esen
wo k.
2. Da a analysis
The ALICE de ec o and i s pe o mance a e desc ibed in de ail in
Re s. [22,24]. Collision e en s a e selec ed by using he in o ma ion
om he V0 de ec o s composed o he V0C and V0A scin illa o a -
ays [25,26], loca ed on bo h sides o he in e ac ion poin , co e ing
he pseudo apidi y in e als −3.7 <𝜂<−1.6and 2.8 <𝜂<5.1, espec-
i ely. In he analysis 5 ×10
8minimum bias igge ed pp collisions a
√𝑠=13TeV we e used. Cha ged pa icle mul iplici y classes, gi en in
e ms o mul iplici y pe cen ile in e als o he isible inelas ic pp c oss
sec ion, we e also de e mined om he V0 de ec o s [27].
The Time P ojec ion Chambe (TPC) [28]and he Inne T acking
Sys em (ITS) [22]we e used o cha ged pa icle acking. These de ec-
o s co e he pseudo apidi y ange o |𝜂| <0.9and a e loca ed wi hin
a solenoid magne wi h a field s eng h o magni ude 𝐵=0.5T. The
momen um (𝑝) de e mina ion o cha ged acks was made using only
he TPC space poin s. The ITS p o ided excellen spa ial esolu ion in
de e mining he p ima y collision e ex. This e ex was used o con-
s ain he acks econs uc ed wi h he TPC, equi ing i o be wi hin
±10 o he cen e o he ALICE de ec o . The a e age momen um es-
olu ion ypically ob ained in his analysis o cha ged acks was less
han 10 MeV/𝑐[24]. The selec ions based on he quali y o ack fi -
ing [24,28,29], in addi ion o he s anda d ack quali y c i e ia [24],
we e used o ensu e ha only well- econs uc ed acks we e aken in o
accoun in he analysis. The quali y o he ack was de e mined by he
𝜒2∕𝑁 alue o he Kalman fi o he pa icle ajec o y in he TPC,
whe e N is he numbe o TPC clus e s a ached o he ack [24]. The
ack was ejec ed i he alue was la ge han 4.0.
Analysis specific e en selec ion c i e ia we e also applied. The
e en mus ha e one accep ed possible 𝜋±K0
Spai . To educe he e -
ec s o mini-je s which end o p oduce non-fla s uc u es in he wo-
pa icle co ela ion unc ions used in em oscopy [30], a selec ion on
he e en ans e se sphe ici y, calcula ed om he azimu hal dis i-
bu ion o acks, was applied by equi ing 𝑆T>0.7. 𝑆Tis a scala
quan i y ha akes alues in he ange 0 −1cha ac e izing he e en
shape, i.e. 𝑆T∼0 alues ep esen elonga ed e en s ha a e “je -like”
and esul om a single ha d-sca e ing o pa ons, whe eas 𝑆T∼1 al-
ues ep esen sphe ical “non-je -like” e en s esul ing om many so
pa on sca e ings o se e al ha d pa on sca e ings. See Re . [30] o
mo e de ails. No e ha he 𝑆T>0.7selec ion is es ima ed o ha e <10%
effec on he mul iplici y o acks en e ing he em oscopy analysis
since his selec ion ends o emo e single ha d-sca e ing e en s. Pile-
up e en s we e ejec ed using he iming in o ma ion om he V0 ( o
ou o bunch pile-up) and mul iple econs uc ed e ices om acks (o
ack segmen s in he Silicon Pixel De ec o laye s o he ITS) [29,30].
The possible effec due o emaining pile-up e en s passing he e en
selec ion c i e ia desc ibed abo e was in es iga ed by pe o ming he
analysis using only low in e ac ion- a e da a- aking pe iods. No signi -
ican diffe ence was ound in he esul s o he analysis compa ed wi h
he highe in e ac ion- a e uns used. Bo h se s o uns we e combined
o he p esen analysis.
Cha ged pa icles we e iden ified wi h he cen al ba el de ec o s.
Pa icle Iden ifica ion (PID) o econs uc ed acks was ca ied ou
using bo h he TPC and Time-O -Fligh (TOF) de ec o s. Fo he TPC,
he specific ioniza ion ene gy loss d𝐸∕d𝑥was measu ed, and o he
TOF, he fligh ime o he pa icle in he pseudo apidi y ange |𝜂| <0.9
was measu ed [29,31]. Fo he PID signal, a alue (𝑁𝜎) was assigned
o each ack deno ing he numbe o s anda d de ia ions be ween he
measu ed PID signal and he expec ed alues, assuming a mass hypo h-
esis, di ided by he de ec o esolu ion o bo h de ec o s [6,24,29,31].
A pa ame ized Be he-Bloch o mula [24]was used o he TPC PID o
calcula e he expec ed ene gy loss ⟨d𝐸∕d𝑥⟩in he de ec o o a pa i-
cle wi h a gi en cha ge, mass, and momen um. The pa icle mass was
used o calcula e he expec ed ime-o -fligh as a unc ion o ack leng h
and momen um o he TOF PID. The de ailed desc ip ion o he pa icle
iden ifica ion me hods is gi en in Re . [32].
Fo Mon e Ca lo (MC) calcula ions, pa icles om pp collisions simu-
la ed by he gene al-pu pose gene a o PYTHIA8 [33]wi h he Monash
2013 une [34]we e anspo ed h ough a GEANT3 [35]model o he
ALICE de ec o . The o al numbe o simula ed pp collisions used in his
analysis is 5 ×10
8.
Physics Le e s B 856 (2024) 138915
3
ALICE Collabo a ion
Table 1
𝜋±and K0
Sselec ion c i e ia.
Neu al kaon selec ion Value
Daugh e 𝑝T>0.15 GeV/𝑐
Daugh e |𝜂|<0.8
Daugh e DCA (3D) o p ima y e ex >0.4cm
Daugh e TPC PID [𝑁𝜎]<3
Daugh e TOF PID [𝑁𝜎]( o 𝑝>0.8GeV/𝑐)<3
Kalman fi 𝜒2∕𝑁≤4
|𝜂|<0.8
DCA (3D) be ween daugh e s <0.3cm
DCA (3D) o p ima y e ex <0.3cm
Decay leng h (3D, lab ame) <30 cm
Decay adius (2D, lab ame) >0.2cm
Cosine o poin ing angle >0.99
In a ian mass 0.485 <𝑚<0.510 GeV/𝑐2
P ima y pion selec ion Value
𝑝T0.15 <𝑝
T<1.2GeV/𝑐
|𝜂|<0.8
T ans e se DCA o p ima y e ex <2.4cm
Longi udinal DCA o p ima y e ex <3.0cm
TOF PID [𝑁𝜎] wi h alid TOF signal and 𝑝>0.5GeV/𝑐<2
TPC PID [𝑁𝜎] i no TOF signal o all 𝑝<2
Kalman fi 𝜒2∕𝑁≤4
The me hods used o selec and iden i y indi idual K0
Sand 𝜋±pa i-
cles a e simila o hose used o he ALICE K±K0
Sanalysis in pp collisions
a
√𝑠=13TeV [7].
K0
Sa e econs uc ed om hei decay in o 𝜋+𝜋−, which has a
b anching a io o 69% [20]. The neu al K0
Sdecay e ices and pa ame-
e s a e econs uc ed and calcula ed om pai s o de ec ed 𝜋+𝜋− acks,
and selec ed based on hei in a ian mass and he K0
Sdecay opology.
The selec ion c i e ia o he K0
Sand he daugh e pions a e shown in
Table 1.
The selec ion c i e ia a e based on decay opology, i.e. dis ance-o -
closes -app oach (DCA) be ween cha ged pion daugh e s, DCA o daugh-
e pion o he p ima y e ex, DCA o econs uc ed K0
S o he p ima y
e ex, cosine o poin ing angle, and decay leng h o K0
S, and we e uned
o op imize pu i y and s a is ical significance. I wo econs uc ed K0
S
pa icles sha e a daugh e ack, bo h a e emo ed om he analysis.
The MC samples we e used o s udy any bias ha migh be induced
by his p ocedu e, which esul ed in ejec ing <1% o he K0
Scandi-
da es [6,7]. Recons uc ed K0
Scandida es wi hin in a ian mass ange
0.485 <𝑚(𝜋+𝜋−) <0.510 GeV/𝑐2a e used in his analysis which gi es
98 ±1%pu i y o K0
S. The pu i y he e is defined as signal/(signal + back-
g ound). The signal and backg ound coun s a e calcula ed by fi ing a
ou h-o de polynomial o he side-bands o he signal egion o es i-
ma e he backg ound he e and sub ac ing his om he in a ian mass
his og am. A Gaussian is used o fi he signal peak in he in a ian mass
dis ibu ion (see Fig. 2 o Re . [6]).
P ima y cha ged pions a e selec ed using he PID in o ma ion om
he TPC and TOF de ec o s. The TPC is used o PID in he ull momen-
um ange, excep i a alid TOF signal is a ailable o 𝑝 >0.5GeV/𝑐
hen TOF PID is used. Fo mo e de ails, e e o Re s. [5,6]. Table 1
summa izes he c i e ia used o he cha ged pion selec ion. The a e -
age cha ged pion pu i y is ound using MC simula ions o be 98.1 ±0.1%,
in ag eemen wi h he cha ged pion pu i y epo ed in Re . [6].
Two- ack effec s, such as he me ging o wo eal acks in o one
econs uc ed ack and he spli ing o one eal ack in o wo econ-
s uc ed acks, a e an impo an challenge o em oscopic s udies. A
selec ion on he minimum sepa a ion dis ance be ween he p ima y pion
and a daugh e pion om he decay o he K0
Sin he 𝜋±K0
Spai was made
om he co esponding TPC acks using he same me hod as desc ibed
in Re . [7]. The dis ance be ween he wo acks was calcula ed in diffe -
en posi ions along hei ajec o y in he TPC (a adial dis ances om
85 o 150 cm om he in e ac ion poin ) and a minimum sepa a ion
dis ance o 20 cm was equi ed.
3. Measu emen o co ela ion unc ions
The momen um co ela ions o 𝜋±K0
Spai s using he wo-pa icle
co ela ion unc ion a e s udied in his analysis. The co ela ion unc-
ion is defined as 𝐶(𝑘∗) =𝐴(𝑘∗)∕𝐵(𝑘∗), whe e 𝐴(𝑘∗)is he measu ed
dis ibu ion o pai s om he same e en and 𝐵(𝑘∗)is he e e ence dis-
ibu ion o pai s om mixed e en s. The denomina o 𝐵(𝑘∗)is o med
by mixing pa icles om one e en wi h pa icles om 10 diffe en
e en s ha sa is y he condi ions ha he p ima y e ex posi ions along
he beam di ec ion a e wi hin 2 cm o each o he , and ha e simila mul-
iplici y, i.e. e en s wi hin 2% diffe ence in mul iplici y pe cen ile a e
mixed. O he sizes o he mixed e en s buffe we e also in es iga ed
wi h no significan effec on he esul s o his wo k. All e en s used a e
equi ed o sa is y he 𝑆T>0.7selec ion. The 𝑘∗is he magni ude o he
momen um o each o he pa icles in he pai es ame. In he p esen
case o unequal mass pa icles in he pai , 𝑚1and 𝑚2, 𝑘∗is gi en by
𝑘∗=√
√
√
√𝑎2−𝑚2
1𝑚2
2
2𝑎+𝑚2
1+𝑚2
2
(1)
whe e,
𝑎≡(𝑞2
in +𝑚2
1+𝑚2
2)∕2.(2)
Fo con enience, he squa e o he in a ian momen um diffe ence
𝑞2
in =|𝑝1−𝑝2|2−|𝐸1−𝐸2|2is e alua ed wi h he momen a and ene gies
o he wo pa icles measu ed in he labo a o y ame. In he case whe e
𝑚1=𝑚2, 𝑘∗can be exp essed as 𝑘∗=𝑞in ∕2. A 𝑘∗bin size o 20 MeV/𝑐
was used in he analyses p esen ed in his Le e .
Co ela ion unc ions a e analyzed o h ee cases: 1) 0 − 100% mul-
iplici y class and 𝑘𝑇>0GeV/𝑐, 2) 0 − 100% mul iplici y class and
𝑘𝑇<0.5GeV/𝑐, and 3) 0 −5%mul iplici y class and 𝑘𝑇<0.5GeV/𝑐,
whe e 𝑘T=|𝑝T1 +𝑝T2|∕2, and whe e 𝑝T1 and 𝑝T2 a e he ans e se
momen a o he pa icles in he pai . The h ee cases co espond o
he ollowing a e age 𝑘𝑇and a e age cha ged-pa icle pseudo apidi y
densi y (⟨𝑑𝑁∕𝑑𝜂⟩in he |𝜂| <0.8 ange) alues [27]: 1) ⟨𝑘𝑇⟩=0.655
GeV/𝑐, ⟨𝑑𝑁∕𝑑𝜂⟩=6.89, 2) ⟨𝑘𝑇⟩=0.323 GeV/𝑐, ⟨𝑑𝑁∕𝑑𝜂⟩=6.89, and
3) ⟨𝑘𝑇⟩=0.326 GeV/𝑐, ⟨𝑑𝑁∕𝑑𝜂⟩= 21.2. The pu pose o analyzing hese
Physics Le e s B 856 (2024) 138915
4
ALICE Collabo a ion
Fig. 1. Top ow: 𝜋±K0
Sco ela ion unc ions expe imen ally measu ed (blue do s) compa ed wi h PYTHIA8+GEANT3 simula ions ( ed squa es) ob ained in pp
collisions a
√𝑠=13TeV o 0 − 100% mul iplici y class and 𝑘𝑇>0(le ), 0 − 100% mul iplici y class and 𝑘T<0.5GeV/𝑐(cen e ), and 0–5%mul iplici y class and
𝑘T<0.5GeV/𝑐( igh ). The PYTHIA8+GEANT3 co ela ion unc ion is no malized o he da a a 𝑘∗=0.5GeV/c. Bo om ow: Ra io o Da a o PYTHIA8+GEANT3
simula ions o he h ee s udied cases. S a is ical unce ain ies a e ep esen ed by ba s.
cases is o ob ain diffe en em oscopic sou ce sizes and o s udy he
effec o sou ce size on he FSI. I has been ound om em oscopy mea-
su emen s in pp collisions ha he sou ce size depends on bo h ⟨𝑘𝑇⟩and
⟨𝑑𝑁∕𝑑𝜂⟩[4,36]. In addi ion, case 1) was chosen o maximize he sam-
ple size and o p o ide a selec ion- ee case o compa e wi h he o he
cases ha ing mul iplici y and 𝑘𝑇selec ions.
Mon e Ca lo simula ions we e used o simula e co ela ion unc-
ions which we e compa ed wi h expe imen al da a. Fig. 1shows in he
op ow he co ela ion unc ions expe imen ally measu ed (blue) along
wi h he simula ed ones ( ed). The MC co ela ion unc ions a e no -
malized o he expe imen al ones a 𝑘∗=0.5GeV/𝑐 o he h ee cases
men ioned abo e. The single-e en and mixed-e en dis ibu ions o he
co ela ion unc ions a e summed o e 𝜋+K0
Sand 𝜋−K0
Spai s, since i
is ound ha he e is no significan diffe ence be ween he 𝜋+K0
Sand
𝜋−K0
Sco esponding co ela ion unc ions. The decay o he K∗(892) me-
son is clea ly seen a 𝑘∗∼0.3GeV/𝑐 o all cases. Fo 𝑘∗>0.35 GeV/𝑐
a non-fla baseline is also obse ed in all cases. This non-fla baseline
is associa ed wi h so pa on agmen a ion, o mini-je s, ha a e no
comple ely supp essed by he ans e se sphe ici y selec ion [36–38], as
well as he p esence o momen um conse a ion effec s. Non-fla base-
lines in wo-pa icle co ela ion unc ions ob ained in pp collisions a e
o en obse ed [9,36,37]. In pa icula , measu ed co ela ion unc ions
show a dec easing dependence o he baseline wi h inc easing 𝑘∗ o low
mul iplici y classes, and a e e sal o his dependence o highe mul-
iplici y classes, as seen in Fig. 1. This effec in he da a is seen o be
p esen as well in he PYTHIA8 simula ions. The simula ions well ep o-
duce he K∗(892) peak and he backg ound isible a la ge 𝑘∗, hence in
o de o emo e hese wo con ibu ions, he measu ed co ela ion unc-
ion is subsequen ly di ided by he simula ed one, defined as 𝐶′(𝑘∗),
as shown in he bo om panels o Fig. 1. The s a is ical unce ain y om
he MC co ela ion unc ion is p opaga ed wi h he unce ain y om
he expe imen al one in he a io, which becomes he final co ela ion
unc ion.
Fini e ack momen um esolu ion can smea he ela i e momen-
um co ela ion unc ions used in his analysis. This effec is co ec ed
using MC simula ions as done in p e ious wo ks [22,23]. I is ound
ha he effec o he momen um esolu ion co ec ion is small o he
e y lowes 𝑘∗bin wi h he la ges s a is ical e o ba s and negligible
o he es o he bins, esul ing in a <3% effec on he ex ac ed fi
pa ame e s.
4. Fi ing
The momen um esolu ion co ec ed a io o he expe imen al 𝜋±K0
S
co ela ion unc ion o he MC co ela ion unc ion was fi ed by a model
in o de o ex ac in o ma ion on he size o he sou ce, as well as he
s eng h and na u e o he FSI be ween he pa icles in he pai . The fi
unc ion is gi en by,
𝐶′(𝑘∗)=𝜅[𝐶Lednicky(𝑘∗)+𝜀𝑑𝑁𝐵𝑊
𝑑𝑚
𝑑𝑚
𝑑𝑘∗](3)
whe e,
𝑑𝑁𝐵𝑊
𝑑𝑚 ∝Γ892
(𝑚−𝑚892)2+Γ
2
892∕4 (4)
is he B ei –Wigne esonance dis ibu ion. This las e m fi s ou any
esidual p esence o he K∗(892) peak (see below).
The quan i ies 𝜀and 𝜅, whe e 𝜀is he magni ude o a co ec ion
e m on he MC modeling o he K∗(892) (see below) and 𝜅is an o e all
no maliza ion ac o , a e fi pa ame e s, and Γ892 and 𝑚892 a e he ull-
wid h a hal maximum (FWHM) and mass o he K∗(892), espec i ely,
aken om he Re iew o Pa icle Physics [20]. The fi s e m in Eq. (3)
is a modified e sion o he Lednicky pa ame iza ion [2,39,40] which
assumes ha he pai in e ac ion is due o s ong final-s a e in e ac ion
o a nea - h eshold esonance. The second e m in Eq. (3)is used o
fi ou he small esidual bump in he a io ha esul s om a sligh
o e compensa ion o he MC in modeling he K∗(892) peak in he da a
ha can be seen in Fig. 1, loca ed a 𝑘∗∼0.3GeV/𝑐. Fi ing ou his
esidual bump esul s in an imp o ed 𝜒2∕nd o all o he fi s.
A Gaussian dis ibu ion o he sou ce size in he pai e e ence ame
is assumed in he FSI pa ame e iza ion. Mo e gene al o ms o his dis-
ibu ion could be used, bu using he Gaussian esul s in he analy ic
o m o he Lednicky equa ion. Ano he mo i a ion o s aying wi h he
Gaussian is o acili a e compa isons wi h p e ious published esul s ha
also used he Gaussian dis ibu ion.

Physics Le e s B 856 (2024) 138915
5
ALICE Collabo a ion
Fig. 2. Example fi o Eq. (5) o he co ec ed co ela ion unc ions a e Eq. (3)has been used o emo e he PYTHIA8+GEANT3 o e compensa ion o he K∗(892), o
𝜋±K0
S om
√𝑠=13TeV pp collisions o 0 − 100% mul iplici y class and 𝑘𝑇>0(le ), 0 − 100% mul iplici y class and 𝑘T<0.5GeV/𝑐(cen e ), and 0–5%mul iplici y
class and 𝑘T<0.5GeV/𝑐( igh ). S a is ical unce ain ies a e ep esen ed as ba s.
The quan i y 𝐶Lednicky(𝑘∗)has he o m
𝐶Lednicky(𝑘∗)=1+(𝜆𝛼
2)[||||
𝑓(𝑘∗)
𝑅||||
2
+4𝑓(𝑘∗)
√𝜋𝑅 𝐹1(2𝑘∗𝑅)
−2𝑓(𝑘∗)
𝑅𝐹2(2𝑘∗𝑅)+Δ𝐶](5)
and
𝐹1(𝑧)=
𝑧
∫
0
𝑑𝑥𝑒𝑥2−𝑧2
𝑧;𝐹2(𝑧)= 1−𝑒−𝑧2
𝑧.(6)
𝛼is he symme y pa ame e and is se o 0.5 assuming symme y in
K0and K0p oduc ion since he K0
Sis a linea combina ion o hese; 𝑅
is he adius pa ame e o he sou ce; and 𝜆is he co ela ion s eng h.
The e m 𝑓(𝑘∗)is he s-wa e 𝜋±K0
Ssca e ing ampli ude whose FSI con-
ibu ion is he nea - h eshold esonance. A ela i is ic B ei –Wigne
ampli ude is assumed,
𝑓(𝑘∗)= 𝛾
𝑀2
𝑅−𝑠−𝑖𝛾𝑘∗.(7)
In Eq. (7), 𝑀𝑅is he mass o he esonance, and 𝛾is he coupling o
he esonance o i s decay channel, i.e. 𝜋±K0
S. Also, 𝑠 =(
√𝑚2
K+𝑘∗2 +
√𝑚2
𝜋+𝑘∗2)2is he squa e o he ene gy o he pai in i s es ame. A
B ei –Wigne o m was chosen o 𝑓(𝑘∗)since he fi ed 𝑀𝑅and 𝛾 o
he FSI esonance om he p esen wo k will be compa ed wi h o he
measu emen s ha used he B ei –Wigne o m in o de o iden i y he
esonance [41,42].
The quan i y Δ𝐶is a co ec ion o he de i a ion o Eq. (5), ha as-
sumes sphe ical ou going wa es, o accoun o he ue sca e ed wa es
in he inne egion o he sho - ange po en ial [2,7], and is gi en by,
Δ𝐶=(2 + 𝑚𝜋∕𝑚K+𝑚K∕𝑚𝜋)
2√𝜋𝑅3𝛾|𝑓(𝑘∗)|2.(8)
As a es , a p-wa e e m was added o he s-wa e e m in he sca e -
ing ampli ude in de i ing he Lednicky equa ion o s udy whe he he e
was in e e ence o he K∗(892) wi h he s-wa e FSI. I was ound ha
he p-wa e e m had a negligible effec on he fi s, and was hus igno ed.
The fi ing s a egy was o make a six-pa ame e fi o Eq. (3) o
he co ec ed a io o he expe imen al 𝜋±K0
Sco ela ion unc ion o he
co esponding MC co ela ion unc ion o ex ac 𝑅, 𝜆, 𝑀𝑅, 𝛾, 𝜀, and 𝜅.
The nominal fi ange is 0 <𝑘
∗<0.76 GeV/𝑐in all cases. The nominal
maximum o 0.76 GeV/𝑐o he fi ange was se o gi e he op imal
o e lap be ween he expe imen al and MC co ela ion unc ions in he
baseline egion.
Fig. 2shows he co ela ion unc ions and fi s. The MC o e compen-
sa ion o he K∗(892) has been emo ed om he “Da a/MC” poin s by
sub ac ing ou he second e m in Eq. (3)in o de o show how well
𝐶Lednicky(𝑘∗)fi s he a io, and he a io has been di ided by 𝜅. The
𝜒2∕nd o he fi s shown in Fig. 2a e 1.6, 1.8, and 0.92, wi h p- alues
o 1.7% and 0.36% and 60%, espec i ely.
5. Sys ema ic unce ain ies
Table 2shows he o al sys ema ic unce ain ies on he 𝑅, 𝜆𝑀
𝑅,
and 𝛾pa ame e s ex ac ed om he 𝜋±K0
Sco ela ion unc ion in pp
collisions a
√𝑠=13TeV.
The “fi sys ema ic unce ain y” column epo s he sys ema ic un-
ce ain y due o a ying he 𝑘∗fi ange. Va ying he fi ange by 20%
esul ed in <3% effec on he fi pa ame e s. Fi ing unce ain ies we e
calcula ed including co ela ions among he fi pa ame e s as done us-
ing a MINOS algo i hm in o de o ob ain conse a i e es ima es o he
unce ain ies [43].
The “selec ion sys ema ic unce ain y” column epo s he sys ema ic
unce ain y ela ed o he a ia ion o ack and PID selec ion c i e ia
used in he da a analysis. To de e mine his, he single pa icle selec ion
c i e ia shown in Table 1we e a ied by ±10%, and he alue chosen
o he minimum sepa a ion dis ance o same-sign acks was a ied by
±20%[7]. The sys ema ic unce ain y ela ed o he sphe ici y selec ion
o 𝑆T>0.7is also included in his sou ce o sys ema ic unce ain y,
whe e 𝑆Twas a ied by ±10% om i s nominal selec ion alue. The
unce ain y was es ima ed om he a ia ion o he esul s wi h espec
o hose ob ained wi h he nominal selec ions. The esul ing ela i e
sys ema ic unce ain ies a e o abou 10% o 𝜆, abou 5% o 𝑅, and
abou 2% o he o he pa ame e s.
The “ o al sys ema ic unce ain y” column is ob ained as he sum
in quad a u e o he con ibu ion o he wo sou ces desc ibed abo e.
The “ o al unce ain y” column is he sum in quad a u e o he s a is i-
cal unce ain y and he o al sys ema ic unce ain y. As seen, he o al
sys ema ic unce ain ies end o be g ea e han o compa able o he
s a is ical unce ain ies. Table 3shows an app oxima e b eakdown o
he ela i e sys ema ic unce ain ies (in pe cen age) om he diffe en
a ia ions conside ed. See Table 1in Sec ion 2 o he nominal alues o
he selec ion c i e ia. No e ha “min. sep. a .” e e s o he a ia ion
o he selec ion o minimum sepa a ion be ween K0
Sdaugh e and p i-
ma y pions in he TPC, men ioned ea lie , and “𝑚(𝜋+𝜋−)and p ima y
e ex a ia ions” e e o he combined effec o a ying he in a ian
mass selec ion o K0
Sand a ying he selec ion o he p ima y e ex o
he e en . As seen, in gene al he a ia ions ha e he la ges effec on 𝜆
and he smalles effec on 𝑀𝑅and 𝛾, wi h he 𝑆T a ia ion ha ing he
la ges single- a ia ion effec on all o he pa ame e s.
6. Resul s and discussion
The 𝑅, 𝜆, 𝑀𝑅, and 𝛾pa ame e s ex ac ed om he p esen anal-
ysis o 𝜋±K0
Sco ela ion unc ions in pp collisions a √𝑠=13TeV a e
epo ed in Table 2 o he h ee cases men ioned abo e. The 𝜆pa ame-
Physics Le e s B 856 (2024) 138915
6
ALICE Collabo a ion
Table 2
Fi esul s o R, 𝜆, 𝑀𝑅, and 𝛾showing s a is ical and sys ema ic unce ain ies om he p esen analysis.
Unce ain ies a e symme ic unless specified o he wise. See he ex o he desc ip ion o he a ious
sou ces o unce ain ies.
𝑅,𝜆,𝑀𝑅,o 𝛾fi alue s a is ical
unce ain y
fi sys ema ic
unce ain y
selec ion
sys ema ic
unce ain y
o al
sys ema ic
unce ain y
o al
unce ain y
0 − 100%
mul iplici y class
𝑘𝑇>0
𝑅( m) 0.912 0.037 0.011 0.053 0.054 0.065
𝜆0.0783 +0.0096 0.0032 0.0078 0.0084 +0.0127
-0.0086 -0.0121
𝑀𝑅(GeV/𝑐2) 0.833 0.002 0.006 0.013 0.015 0.015
𝛾(GeV) 0.890 0.015 0.012 0.016 0.020 0.025
0 − 100%
mul iplici y class
𝑘𝑇<0.5GeV/𝑐
𝑅( m) 1.063 0.058 0.015 0.064 0.066 0.088
𝜆0.111 0.017 0.004 0.013 0.014 0.022
𝑀𝑅(GeV/𝑐2) 0.804 0.003 0.005 0.013 0.014 0.014
𝛾(GeV) 0.801 0.023 0.020 0.014 0.024 0.033
0−5%
mul iplici y class
𝑘𝑇<0.5GeV/𝑐
𝑅( m) 1.618 +0.136 0.015 0.089 0.090 +0.163
-0.109 -0.142
𝜆0.274 +0.077 0.001 0.026 0.026 +0.081
-0.053 -0.059
𝑀𝑅(GeV/𝑐2) 0.765 0.004 0.002 0.012 0.013 0.013
𝛾(GeV) 0.714 +0.042 0.005 0.013 0.014 +0.044
-0.037 -0.039
Table 3
B eakdown o he ela i e sys ema ic unce ain ies o R, 𝜆, 𝑀𝑅, and 𝛾 om he a ia ion o ack, PID and mixed-
e en selec ion c i e ia. The %Δ ow is he pe cen age ha he quan i y was changed. See he ex o he desc ip ion
o he a ious unce ain ies.
Quan i y
changed
Fi
ange
Min. sep.
a .
TOF, TPC
𝑁𝜎
DCA a . 𝑚(𝜋+𝜋−)and
p ima y e ex
a .
Mul iplici y
diffe ence o
e en mixing
Decay
leng h
𝑆T a .
%Δ 20 20 10 10 10 10 10 10
%𝑅11221 1 13
%𝜆35333 2 25
%𝑀𝑅1<1<1<1<1<1<12
%𝛾21 <1<1<1<1<12
e s a e co ec ed o pu i y by di iding he ex ac ed 𝜆 alues wi h he
p oduc o he 𝜋±and K0
Spu i ies (see Sec ion 2).
Since he main goal o his measu emen is o s udy he K∗
0(700) es-
onance, one mus fi s es ablish ha he FSI o he 𝜋±K0
Spai occu s
indeed h ough his esonance. This can be done by compa ing he mea-
su ed 𝑀𝑅and 𝛾pa ame e s ex ac ed om his analysis wi h p e iously
measu ed alues o 𝑀𝑅and Γ𝑅 o he K∗
0(700) [41,42], whe e Γ𝑅is he
FWHM o he ela i is ic B ei –Wigne esonance dis ibu ion, whose
ampli ude is exp essed as [44],
𝑓(𝑠)∼ 1
𝑀2
𝑅−𝑠−𝑖𝑀𝑅Γ𝑅
.(9)
Compa ing his denomina o wi h he denomina o o Eq. (7), one
can ob ain an es ima e o Γ𝑅 om he p esen esul s,
Γ𝑅=⟨𝑘∗⟩𝛾
𝑀𝑅
,(10)
whe e ⟨𝑘∗⟩is he a e age o 𝑘∗de e mined by weigh ing 𝑘∗by he ex-
pe imen al 𝑑𝑁∕𝑑𝑘∗dis ibu ion o e he fi ange used in fi ing Eq. (3)
o he co ela ion unc ion. Table 4lis s he alues o Γ𝑅ex ac ed om
he p esen wo k using Eq. (10) o he h ee cases s udied. The unce -
ain ies shown o ⟨𝑘∗⟩a e es ima ed by conside ing diffe en 𝑘∗ anges
Table 4
The ⟨𝑘∗⟩and co esponding Γ𝑅ex ac ed om he h ee cases measu ed
in he p esen wo k using Eq. (10).
Case ⟨𝑘∗⟩(GeV/𝑐)Γ𝑅(GeV/𝑐2)
0 − 100% mul iplici y class, 𝑘𝑇>00.403+0.093
−0.056 0.430+0.088
−0.053
0 − 100% mul iplici y class, 𝑘𝑇<0.5GeV/𝑐0.408+0.060
−0.050 0.406+0.050
−0.042
0 – 5% mul iplici y class, 𝑘𝑇<0.5GeV/𝑐0.418+0.072
−0.053 0.390+0.068
−0.051
o calcula ing he a e age, namely 0 <𝑘
∗<0.6GeV/𝑐and 0 <𝑘
∗<2
GeV/𝑐, and aking he diffe ences om he nominal ⟨𝑘∗⟩ o ob ain con-
se a i e es ima es o he unce ain ies.
Fig. 3compa es he alues o 𝑀𝑅and Γ𝑅ex ac ed in he p esen
wo k wi h measu emen s o hese quan i ies o he K∗
0(700) om he
BES [41]and E791 Collabo a ions [42]. The BES Collabo a ion mea-
su ed he ela i is ic B ei –Wigne pa ame e s o he K∗
0(700) h ough
he decay o he J/𝜓meson, whe eas he E791 Collabo a ion measu ed
hem h ough he decay o he D+meson. The o al unce ain ies de-
fined as he quad a ic sum o he s a is ical and sys ema ic unce ain ies
a e shown on he poin s o all cases. As seen, he alues epo ed in his
wo k ag ee wi hin unce ain ies wi h he K∗
0(700) B ei –Wigne pa am-
Physics Le e s B 856 (2024) 138915
7
ALICE Collabo a ion
Fig. 3. The ex ac ed B ei –Wigne pa ame e s om he 𝜋±K0
S em oscopic co -
ela ion in pp collisions a
√𝑠=13TeV compa ed wi h hose o K∗
0(700) om
he BES [41]and he E791 [42] expe imen s. The ho izon al and e ical ba s
ep esen he o al unce ain ies. The “ALICE a e age” alue is he weigh ed a -
e age o he h ee ALICE poin s.
Fig. 4. The 𝜆pa ame e as a unc ion o sou ce size 𝑅ex ac ed om he 𝜋±K0
S
em oscopy measu emen in pp collisions a
√𝑠=13TeV. Resul s a e compa ed
wi h he p e ious ALICE measu emen s, ob ained om K0
SK0
S[6,7]and 𝜋𝜋 [36]
em oscopy s udies in pp and Pb–Pb collisions and he calcula ions om a oy
geome ic model (see ex ). The model calcula ions o he e aqua k and di-
qua k hypo heses o he K∗
0(700) a e shown as black and ligh g een dashed
lines, espec i ely, he sho dashed lines ep esen ing he Gaussian 𝜌(𝑟)and he
long dashed lines ep esen ing he exponen ial 𝜌(𝑟).
e e s measu ed in he o he wo expe imen s. I is seen ha he p esen
esul s ha e smalle unce ain ies han he p e ious measu emen s. I
is also seen ha al hough he h ee Γ𝑅 alues om he p esen wo k
ag ee wi hin unce ain ies, he diffe ences among he h ee 𝑀𝑅 alues
a e ou side o hei unce ain ies. This could be a consequence o us-
ing he B ei –Wigne unc ion o fi a esonance whe e he condi ion
Γ𝑅≪𝑀
𝑅is no ulfilled, which can lead o kinema ic dependences on
he ex ac ed 𝑀𝑅and Γ𝑅[20,44]. Howe e , hese diffe ences in 𝑀𝑅
a e small compa ed wi h he ex ac ed 𝑀𝑅 alues, and hus i is judged
ha hese esul s s ongly suppo he assump ion ha he esonance e-
sponsible o he FSI o he 𝜋±K0
Spai s s udied in he p esen wo k is
he K∗
0(700) esonance.
The ex ac ed 𝑅and 𝜆pa ame e s shown in Table 2can be used o
ob ain in o ma ion abou he qua k configu a ion o he K∗
0(700). Fig. 4
compa es he alues o 𝑅and 𝜆ex ac ed in he p esen wo k wi h pub-
lished esul s o hese pa ame e s om ALICE measu emen s in pp and
Pb–Pb collisions in which 𝜋𝜋 and K0
SK0
Spai s we e analyzed [4,6,7,36].
The 𝜋±K0
S esul s a e shown wi h sepa a e s a is ical (e o ba s) and
sys ema ic (boxes) unce ain ies, whe eas o he p e ious esul s, he
e o ba s ep esen he combina ion o he s a is ical and sys ema ic
unce ain ies. Fo he 𝜋𝜋 em oscopic measu emen s in pp collisions a
√𝑠=7TeV epo ed in [36]wi h a e age 𝑘T alues o ∼0.15 and ∼0.35
GeV/𝑐, he 𝜆 alues a e gi en as a ying in he ange 0.42 −0.55, so 𝜆
is plo ed as he cen e o his ange wi h unce ain ies ex ending o he
uppe and lowe limi s o he ange.
Fo he 𝑅pa ame e , he alues om he p esen 𝜋±K0
Sanalysis a e
compa able wi h he published 𝜋𝜋 and K0
SK0
Smeasu emen s in pp colli-
sions, i.e. in he ange 1–2 m, as would be expec ed om pp collisions
whe e he sou ce size is ∼1 m. Fo he 𝜆pa ame e , whe eas he esul s
om 𝜋𝜋 and K0
SK0
Sa e compa ible wi h alues o abou 0.5o g ea e , o
he p esen 𝜋±K0
Sanalysis significan ly lowe alues a e ob ained, ang-
ing om abou 0.05 o abou 0.25 depending on 𝑅. The expec a ion is
ha 𝜆would be he same o 𝜋±K0
Sas o he iden ical-meson measu e-
men s. The 𝜆 alue o ∼0.5has been shown o be due o he p esence
o long-li ed esonances whose decay in o he de ec ed mesons impac s
he measu emen o he “di ec ” mesons coming om he sou ce o in-
e es [7,45]. Ano he significan diffe ence be ween he p esen 𝜋±K0
S
esul s and he 𝜋𝜋 and K0
SK0
S esul s is ha 𝜆has a s ong 𝑅dependence
o he o me , whe eas he e is no significan dependence o 𝜆on 𝑅
o he la e , i.e. e en ex ending 𝑅 o he alue om Pb–Pb collisions
shows no significan effec on 𝜆.
As discussed in Re s. [7] and [9], a physics effec ha could cause his
diffe ence in 𝜆 alues o 𝜋±K0
Spai s is ela ed o he possibili y ha he
K∗
0(700) esonance, ha is assumed o be solely esponsible o he FSI
in he 𝜋±K0
Spai , is ac ually a e aqua k s a e o he o m (q1, q2, q3, q3),
in which q1, q2and q3indica e he fla o o he alence qua ks o he
𝜋and K0
S. In pa icula , q1and q2can be a u o s qua k, while q3is
a d qua k. Fo example, he qua k con en o a e aqua k K∗
0(700)+
would be usdd, whe eas he diqua k e sion would be us. The s eng h
o he FSI h ough a e aqua k K∗
0(700)+could be dec eased by he small
sou ce size o he 𝜋±K0
Ssou ce, i.e. a 𝑅 ∼1 m as is measu ed in hese
collisions. This could occu since d−d annihila ion would be enhanced
due o he p oximi y o he 𝜋±and K0
Sa hei c ea ion, which would
open up a non- esonan channel in he sca e ing p ocess ha would be
eflec ed by educing 𝜆. Fo a FSI h ough a diqua k K∗
0(700)+, wi h he
o m us, he small sou ce geome y should no educe i s s eng h. Fo
he K0
SK0
Sand 𝜋𝜋 cases, 𝜆should no be affec ed by he sou ce size since
he pai co ela ion is domina ed by he effec o quan um s a is ics, o
which in he ideal case 𝜆does no depend on 𝑅, and which is ound o
be much s onge han he s ong FSI p esen o hese iden ical pa icle
pai s [2].
In o de o demons a e he 𝑅dependence o 𝜆 o a e aqua k o a
diqua k K∗
0(700) based on he geome ic conside a ions discussed abo e,
a simple oy model is cons uc ed, aking he o m o he 𝜆 ac o o a
e aqua k s a e,
𝜆=𝜆0(1 − 𝑎𝑃 )(11)
and o a diqua k,
𝜆=𝜆0𝑎𝑃 (12)
whe e,
𝑃≡∫𝜌(𝑟)𝜌(|𝑟 −
𝑅|)𝑑𝑉
∫|𝜌(𝑟)|2𝑑𝑉 (13)
can be conside ed he “o e lap p obabili y” be ween he 𝜋and K0
Sin he
pai as hey a e emi ed om he pp collision. The quan i y 𝜌(𝑟)is he
meson olume dis ibu ion, assumed o be he same o he 𝜋and K0
S, 𝜆0
is he maximum alue o 𝜆, and 𝑎is essen ially he “d−d annihila ion
efficiency” ha in p inciple could ake any alue in he ange 0 −1. As-
suming 𝜌(𝑟) ∼𝑒−𝑟2∕(2𝜎2)o ∼𝑒−𝑟∕𝑟0, 𝜆0=0.6, he a e age alue o 𝜋𝜋
and K0
SK0
Smeasu emen s om Re s. [36]and [6,7], and assuming 100%
d−d annihila ion efficiency o any non-ze o o e lap, 𝑎 =1, he ee pa-
ame e s o he model, i.e. 𝜎and 𝑟0, a e adjus ed o gi e a good fi o he
𝜋±K0
Smeasu emen s. The esul s om Eqs. (11) and (12)a e shown in
Fig. 4, along wi h he esul s om 𝜋±K0
Smeasu emen s o his wo k and
Physics Le e s B 856 (2024) 138915
8
ALICE Collabo a ion
published ALICE measu emen s o K0
SK0
S[6,7]and 𝜋𝜋 pai s [36] om
pp and Pb–Pb collisions. The ee model pa ame e s a e se o 𝜎=1.1 m
and 𝑟0=0.85 m o he Gaussian (sho dashed lines) and exponen ial
(long dashed lines) dis ibu ions, espec i ely, which a e conside ed ea-
sonable alues since had onic sizes a e expec ed o be ∼1 m. As seen,
using easonable model pa ame e alues, he e aqua k case, Eq. (11),
desc ibes he 𝑅dependence o 𝜆 om he p esen measu emen s well
o bo h he Gaussian and exponen ial meson shapes as being a geome -
ic effec . The diqua k case is seen o p edic an 𝑅dependence ha is
incompa ible wi h he measu ed one.
The e o e, he p esen esul s o 𝜋±K0
S em oscopy in pp collisions a
√𝑠=13TeV sugges ha he K∗
0(700) is a e aqua k s a e.
7. Summa y
Fem oscopic co ela ions wi h he pa icle pai combina ion 𝜋±K0
S
a e s udied in pp collisions a √𝑠=13TeV o he fi s ime by he
ALICE expe imen a he LHC. Sou ce pa ame e s and final-s a e in e -
ac ion pa ame e s a e ex ac ed by fi ing a model based on a Gaussian
dis ibu ion o he sou ce o he expe imen al wo-pa icle co ela ion
unc ions. The model used assumes ha solely he final-s a e in e ac ion
h ough a esonance de e mines he co ela ions, and is defined in e ms
o a mass and he coupling pa ame e o he decay in o a 𝜋±K0
Spai . The
ex ac ed mass and wid h pa ame e s o he FSI a e consis en wi h p e-
ious measu emen s o he K∗
0(700) esonance, and he smalle alue and
inc easing beha io o he 𝜆pa ame e wi h 𝑅compa ed wi h iden ical
boson measu emen s gi e suppo ha he K∗
0(700) is a ou -qua k s a e,
i.e. a e aqua k s a e [19]. A simple geome ic model ha assumes a
e aqua k FSI desc ibes well he 𝑅dependence o 𝜆ex ac ed om he
measu ed co ela ion unc ions.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing financial
in e es s o pe sonal ela ionships ha could ha e appea ed o influence
he wo k epo ed in his pape .
Da a a ailabili y
This manusc ip has associa ed da a in a HEPDa a eposi o y a :
h ps://www .hepda a .ne / eco d /ins2739149.
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 Collabo a ion g a e ully ac-
knowledges he esou ces and suppo p o ided by all G id cen es and
he Wo ldwide LHC Compu ing G id (WLCG) collabo a ion. The ALICE
Collabo a ion acknowledges he ollowing unding agencies o hei
suppo in building and unning 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, Technolo-
gie und En wicklung, Aus ia; Minis y o Communica ions and High
Technologies, Na ional Nuclea Resea ch Cen e , Aze baijan; Conselho
Nacional de Desen ol imen o Cien ífico e Tecnológico (CNPq), Finan-
ciado 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 Fede al do Rio
G ande do Sul (UFRGS), B azil; Bulga ian Minis y o Educa ion and Sci-
ence, wi hin he Na ional Roadmap o Resea ch In as uc u es 2020-
2027 (objec CERN), Bulga ia; 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 Apli-
caciones Tecnológicas y Desa ollo Nuclea (CEADEN), Cubaene gía,
Cuba; The Minis y o Educa ion, You h and Spo s o he Czech Re-
public, 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), Denma k; Helsinki Ins i u e o Physics (HIP), Fin-
land; Commissa ia à l’Éne gie A omique (CEA) and 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), 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 Re-
sea 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, Hun-
ga y; Depa men o A omic Ene gy, Go e nmen o India (DAE), De-
pa men o Science and Technology, Go e nmen o India (DST), Uni-
e si y G an s Commission, Go e nmen o India (UGC) and Council o
Scien ific and Indus ial Resea ch (CSIR), India; Na ional Resea ch and
Inno a ion Agency - BRIN, Indonesia; Is i u o Nazionale di Fisica Nu-
clea e (INFN), I aly; 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 (CONA-
CYT) y Tecnología, h ough Fondo de Coope ación In e nacional en
Ciencia y Tecnología (FONCICYT) and Di ección Gene al de Asun os del
Pe sonal Académico (DGAPA), Mexico; Nede landse O ganisa ie oo
We enschappelijk Onde zoek (NWO), Ne he lands; The Resea ch Coun-
cil 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 Educa ion and Science,
Na ional Science Cen e and WUT ID-UB, Poland; Ko ea Ins i u e o Sci-
ence and Technology In o ma ion and Na ional Resea ch Founda ion o
Ko ea (NRF), Republic o Ko ea; Minis y o Educa ion and Scien ific Re-
sea ch, Ins i u e o A omic Physics, Minis y o Resea ch and Inno a ion
and Ins i u e o A omic Physics and Uni e si a ea Na ionala de S iin a
si Tehnologie Poli ehnica Bucu es i, Romania; Minis y o Educa ion,
Science, Resea ch and Spo o he Slo ak Republic, Slo akia; Na ional
Resea ch Founda ion o Sou h A ica, Sou h A ica; Swedish Resea ch
Council (VR) and Knu and Alice Wallenbe g Founda ion (KAW), Swe-
den; 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 (NSTDA) and Na ional Science, Resea ch and In-
no a ion Fund (NSRF ia PMU-B B05F650021), Thailand; Tu kish En-
e gy, Nuclea and Mine al Resea ch Agency (TENMAK), 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 Uni ed S a es Depa men o
Ene gy, Office o Nuclea Physics (DOE NP), Uni ed S a es o Ame ica.
In addi ion, indi idual g oups o membe s ha e ecei ed suppo om:
Czech Science Founda ion (g an no. 23-07499S), Czech Republic; Eu o-
pean Resea ch Council, S ong 2020 - Ho izon 2020 (g an nos. 950692,
824093), Eu opean Union; ICSC -Cen o Nazionale di Rice ca in High
Pe o mance Compu ing, Big Da a and Quan um Compu ing, Eu opean
Union - Nex Gene a ionEU; Academy o Finland (Cen e o Excellence
in Qua k Ma e ) (g an nos. 346327, 346328), Finland.
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Physics Le e s B 856 (2024) 138915
15
ALICE Collabo a ion
96 Physik Depa men , Technische Uni e si ä München, Munich, Ge many
97 Poli ecnico di Ba i and Sezione INFN, Ba i, I aly
98 Resea ch Di ision and Ex eMe Ma e Ins i u e EMMI, GSI Helmhol zzen um ü Schwe ionen o schung GmbH, Da ms ad , Ge many
99 Saga Uni e si y, Saga, Japan
100 Saha Ins i u e o Nuclea Physics, Homi Bhabha Na ional Ins i u e, Kolka a, India
101 School o Physics and As onomy, Uni e si y o Bi mingham, Bi mingham, Uni ed Kingdom
102 Sección Física, Depa amen o de Ciencias, Pon ificia Uni e sidad Ca ólica del Pe ú, Lima, Pe u
103 S e an Meye Ins i u ü Suba oma e Physik (SMI), Vienna, Aus ia
104 SUBATECH, IMT A lan ique, Nan es Uni e si é, CNRS-IN2P3, Nan es, F ance
105 Sungkyunkwan Uni e si y, Suwon Ci y, Republic o Ko ea
106 Su ana ee Uni e si y o Technology, Nakhon Ra chasima, Thailand
107 Technical Uni e si y o Košice, Košice, Slo ak Republic
108 The Hen yk Niewodniczanski Ins i u e o Nuclea Physics, Polish Academy o Sciences, C acow, Poland
109 The Uni e si y o Texas a Aus in, Aus in, TX, Uni ed S a es
110 Uni e sidad Au ónoma de Sinaloa, Culiacán, Mexico
111 Uni e sidade de São Paulo (USP), São Paulo, B azil
112 Uni e sidade Es adual de Campinas (UNICAMP), Campinas, B azil
113 Uni e sidade Fede al do ABC, San o And e, B azil
114 Uni e si a ea Na ionala de S iin a si Tehnologie Poli ehnica Bucu es i, Bucha es , Romania
115 Uni e si y o Cape Town, Cape Town, Sou h A ica
116 Uni e si y o De by, De by, Uni ed Kingdom
117 Uni e si y o Hous on, Hous on, TX, Uni ed S a es
118 Uni e si y o Jy äskylä, Jy äskylä, Finland
119 Uni e si y o Kansas, Law ence, KS, Uni ed S a es
120 Uni e si y o Li e pool, Li e pool, Uni ed Kingdom
121 Uni e si y o Science and Technology o China, He ei, China
122 Uni e si y o Sou h-Eas e n No way, Kongsbe g, No way
123 Uni e si y o Tennessee, Knox ille, TN, Uni ed S a es
124 Uni e si y o he Wi wa e s and, Johannesbu g, Sou h A ica
125 Uni e si y o Tokyo, Tokyo, Japan
126 Uni e si y o Tsukuba, Tsukuba, Japan
127 Uni e si ä Müns e , Ins i u ü Ke nphysik, Müns e , Ge many
128 Uni e si é Cle mon Au e gne, CNRS/IN2P3, LPC, Cle mon -Fe and, F ance
129 Uni e si é de Lyon, CNRS/IN2P3, Ins i u de Physique des 2 Infinis de Lyon, Lyon, F ance
130 Uni e si é de S asbou g, CNRS, IPHC UMR 7178, F-67000 S asbou g, F ance
131 Uni e si é Pa is-Saclay, Cen e d’E udes de Saclay (CEA), IRFU, Dépa men de Physique Nucléai e (DPhN), Saclay, F ance
132 Uni e si é Pa is-Saclay, CNRS/IN2P3, IJCLab, O say, F ance
133 Uni e si à degli S udi di Foggia, Foggia, I aly
134 Uni e si à del Piemon e O ien ale, Ve celli, I aly
135 Uni e si à di B escia, B escia, I aly
136 Va iable Ene gy Cyclo on Cen e, Homi Bhabha Na ional Ins i u e, Kolka a, India
137 Wa saw Uni e si y o Technology, Wa saw, Poland
138 Wayne S a e Uni e si y, De oi , MI, Uni ed S a es
139 Yale Uni e si y, New Ha en, CT, Uni ed S a es
140 Yonsei Uni e si y, Seoul, Republic o Ko ea
141 Zen um ü Technologie und T ans e (ZTT), Wo ms, Ge many
142 Affilia ed wi h an ins i u e co e ed by a coope a ion ag eemen wi h CERN
143 Affilia ed wi h an in e na ional labo a o y co e ed by a coope a ion ag eemen wi h CERN
IDeceased.
II Also a : Max-Planck-Ins i u u Physik, Munich, Ge many.
III Also a : I alian Na ional Agency o New Technologies, Ene gy and Sus ainable Economic De elopmen (ENEA), Bologna, I aly.
IV Also a : Dipa imen o DET del Poli ecnico di To ino, Tu in, I aly.
VAlso a : Yildiz Technical Uni e si y, Is anbul, Tü kiye.
VI Also a : Depa men o Applied Physics, Aliga h Muslim Uni e si y, Aliga h, India.
VII Also a : Ins i u e o Theo e ical Physics, Uni e si y o W oclaw, Poland.
VIII Also a : An ins i u ion co e ed by a coope a ion ag eemen wi h CERN.