Energy dependence and fluctuations of anisotropic flow in Pb-Pb collisions at √sNN = 5.02 and 2.76 TeV

This is a sel -a chi ed e sion o an o iginal a icle. This e sion may di e om he o iginal in pagina ion and ypog aphic de ails. Au ho (s): Ti le: Yea : Ve sion: Copy igh : Righ s: Righ s u l: Please ci e he o iginal e sion: CC BY 4.0 h ps://c ea i ecommons.o g/licenses/by/4.0/ Ene gy dependence and luc ua ions o aniso opic low in Pb-Pb collisions a √sNN = 5.02 and 2.76 TeV © The Au ho s 2018. CERN, o he bene i o he ALICE Collabo a ion. A icle unded by SCOAP3. Published e sion ALICE Collabo a ion ALICE Collabo a ion. (2018). Ene gy dependence and luc ua ions o aniso opic low in Pb-Pb collisions a √sNN = 5.02 and 2.76 TeV. Jou nal o High Ene gy Physics, 2018(7), A icle 103. h ps://doi.o g/10.1007/jhep07(2018)103 2018 JHEP07(2018)103 Published o SISSA by Sp inge Recei ed:May 24, 2018 Accep ed:July 1, 2018 Published:July 16, 2018 Ene gy dependence and luc ua ions o aniso opic low in Pb–Pb collisions a √sNN = 5.02 and 2.76 TeV The ALICE collabo a ion E-mail: [email p o ec ed] Abs ac : Measu emen s o aniso opic low coe icien s wi h wo- and mul i-pa icle cu- mulan s o inclusi e cha ged pa icles in Pb–Pb collisions a √sNN = 5.02 and 2.76 TeV a e epo ed in he pseudo apidi y ange |η|<0.8 and ans e se momen um 0.2< pT< 50 GeV/c. The ull da a sample collec ed by he ALICE de ec o in 2015 (2010), co e- sponding o an in eg a ed luminosi y o 12.7 (2.0) µb−1in he cen ali y ange 0–80%, is analysed. Flow coe icien s up o he six h low ha monic ( 6) a e epo ed and a de- ailed compa ison among esul s a he wo ene gies is ca ied ou . The pTdependence o aniso opic low coe icien s and i s e olu ion wi h espec o cen ali y and ha monic numbe na e in es iga ed. An app oxima e powe -law scaling o he o m n(pT)∼pn/3 T is obse ed o all low ha monics a low pT(0.2< pT<3 GeV/c). A he same ime, he a ios n/ n/m ma e obse ed o be essen ially independen o pT o mos cen ali ies up o abou pT= 10 GeV/c. Analysing he di e ences among highe -o de cumulan s o ellip ic low ( 2), which ha e di e en sensi i i ies o low luc ua ions, a measu emen o he s an- da dised skewness o he e en -by-e en 2dis ibu ion P( 2) is epo ed and cons ain s on i s highe momen s a e p o ided. The Ellip ic Powe dis ibu ion is used o pa ame ise P( 2), ex ac ing i s pa ame e s om i s o cumulan s. The measu emen s a e compa ed o di e en model p edic ions in o de o disc imina e among ini ial-s a e models and o cons ain he empe a u e dependence o he shea iscosi y o en opy-densi y a io. Keywo ds: Hea y Ion Expe imen s A Xi eP in : 1804.02944 Open Access, Copy igh CERN, o he bene i o he ALICE Collabo a ion. A icle unded by SCOAP3. h ps://doi.o g/10.1007/JHEP07(2018)103 JHEP07(2018)103 Con en s 1 In oduc ion 1 2 Da a sample and analysis me hods 3 3 Collision ene gy, ans e se momen um and cen ali y dependence 6 4 Ellip ic low luc ua ions 14 5 Conclusions 21 A Addi ional igu es 24 The ALICE collabo a ion 32 1 In oduc ion The p ima y goal o ul a- ela i is ic hea y-ion collisions is o s udy he p ope ies o QCD ma e a ex emely high empe a u es and/o densi ies and o unde s and he mic oscopic dynamics om which hese p ope ies a ise, especially in he non-pe u ba i e egime. The s udy o aniso opies in he azimu hal dis ibu ion o p oduced pa icles, commonly called aniso opic low, has con ibu ed signi ican ly o he cha ac e iza ion o he sys em c ea ed in hea y-ion collisions [1–5]. Acco ding o he cu en pa adigm o bulk pa icle p oduc ion, aniso opic low is de e mined by he esponse o he sys em o i s ini ial spa ial aniso opies. Ini ial-s a e spa ial aniso opies come in u n om bo h he geome y o he collision and luc ua ions in he wa e unc ion o he inciden nuclei [3–8]. The signi ican magni ude o aniso opic low is in e p e ed as e idence o he o ma ion o a s ongly- coupled sys em, which can e ec i ely be desc ibed as a luid wi h e y low shea iscosi y o en opy-densi y a io (η/s) [9]. Aniso opic low is quan i ied by he coe icien s no a Fou ie se ies decomposi ion o he dis ibu ion in azimu hal angle ϕo inal-s a e pa icles [10] dN dϕ∝1+2 +∞ X n=1 ncos [n(ϕ−Ψn)],(1.1) whe e Ψnco esponds o he symme y plane angle o o de n. The dominan low coe i- cien in non-cen al hea y-ion collisions is he second low ha monic ( 2), called ellip ic low, which is mos ly a esul o he a e age ellipsoidal shape o he o e lapping a ea be ween he colliding nuclei, whe eas highe ha monics o igina e om ini ial-s a e luc ua ions. Fo ans e se momen a pT.3 GeV/c, aniso opic low is hough o be quan i a i ely de e - mined by he whole e olu ion o he sys em, including he phase o had onic esca e ings – 1 – JHEP07(2018)103 ha akes place a e chemical eeze-ou [11]. Flow coe icien s ha e been shown o be sensi i e no only o ini ial-s a e aniso opies, bu also o he anspo pa ame e s (such as shea and bulk iscosi y [12,13]) and he equa ion o s a e o he sys em, and hey ha e he e o e been used o cons ain hese p ope ies [14,15]. Howe e , gi en he di e en he e ogeneous phases ha he sys em is belie ed o unde go, i has no been possible so a o simul aneously cons ain he la ge numbe o model pa ame e s, al hough a emp s ha e been made [16,17]. In his ega d, he ene gy dependence o aniso opic low has been shown o p o ide addi ional disc imina ing powe o e ini ial-s a e models and empe a u e dependence o anspo pa ame e s [18,19]. In ac , some heo e ical unce ain ies in he de e mina ion o aniso opic low coe icien s a e expec ed o pa ially cancel in he a ios o ncoe i- cien s measu ed a di e en collision ene gies, such as hose on he choice o ini ial-s a e model o on he absolu e alue o η/s. These a ios would hen e ec i ely cons ain he a ia ions wi h collision ene gy and, he e o e, sys em empe a u e o he pa ame e s o which aniso opic low is mos sensi i e. I is known ha he magni ude o aniso opic low, being app oxima ely p opo ional o he ini ial-s a e spa ial aniso opy [20], luc ua es om collision o collision e en o ixed cen ali y [6,21–24], and ha i s p obabili y dis ibu ion unc ion (p.d. .) P( n) is o a i s app oxima ion Bessel-Gaussian [1,25], i.e. he p oduc o a modi ied Bessel unc ion and a Gaussian unc ion. I has been poin ed ou ha small de ia ions om a Bessel-Gaussian shape a e o be expec ed independen ly om he de ails o ini ial-s a e luc ua ions [26–28]. E idence o such small de ia ions has been p e iously epo ed [29]. These de ia ions a e due o i s o de o he low p.d. . ha ing a ini e skewness. I s quan i a i e de e mina ion would he e o e imp o e he cha ac e iza ion o hese de ia ions. Fo dimensional easons, i is con enien o use a s anda dised skewness (γ1), de ined as [30] γ1=h( n{RP}−h n{RP}i)3i h( n{RP}−h n{RP}i)2i3/2,(1.2) whe e n{RP} e e s o he aniso opic low wi h espec o he eac ion plane ΨRP, i.e. he plane spanned by he impac pa ame e and he beam axis, and he b acke s h···i indica e an a e age o e all e en s. I is wo hwhile o no e ha he symme y planes Ψndo no gene ally coincide wi h ΨRP because o ini ial-s a e luc ua ions. A obus expe imen al me hod o quan i y low luc ua ions is o measu e nwi h mul i-pa icle cumulan s, which ha e di e en sensi i i ies o he momen s o he unde ly- ing low p.d. . P( n) n{2}=2 ph 2 ni,(1.3) n{4}=4 p2h 2 ni2−h 4 ni,(1.4) n{6}=6 ph 6 ni−9h 2 nih 4 ni+ 12h 2 ni3,(1.5) n{8}=8 ph 8 ni−16h 2 nih 6 ni−18h 4 ni2+ 144h 2 ni2h 4 ni−144h 2 ni4.(1.6) The numbe in cu ly b acke s indica es he o de o he cumulan . – 2 – JHEP07(2018)103 Fo ellip ic low, a la ge di e ence be ween 2{2}and 2{4}and app oxima ely equal alues o he highe o de cumulan s ( 2{4}, 2{6}, 2{8}) ha e been p e iously ob- se ed [29,31], which is indeed consis en wi h an app oxima ely Bessel-Gaussian low p.d. .. Howe e , a ine-spli ing o a ew pe cen among he highe o de cumulan s ( 2{4}, 2{6}, 2{8}) has also been epo ed [29], which is hough o be de e mined by he esidual de ia ions om Bessel-Gaussian shape, in pa icula a non-ze o skewness. A nega i e alue o γ1, which co esponds o P( 2) being le skewed, is expec ed [27] om he necessa y condi ion on he ini ial-s a e eccen ici y ε2<1, which ac s as a igh cu o on P( 2). The Ellip ic Powe dis ibu ion, p oposed in [26,27], was mo i a ed mainly by his obse a ion and i was shown o p o ide a good desc ip ion o P( 2) in a wide cen ali y ange [32]. Mo eo e , γ1has been p edic ed o inc ease in absolu e alue om cen al o pe iphe al collisions [30], being oughly p opo ional o h 2{RP}i and being in e sely p opo ional o he squa e oo o he sys em size [28]. γ1can be es ima ed om he ine-spli ing among wo- and mul i-pa icle cumulan s [30] γexp 1=−6√2 2{4}2 2{4}− 2{6} ( 2{2}2− 2{4}2)3/2.(1.7) I is deno ed as γexp 1 o emphasize ha i does no exac ly ma ch he de ini ion o γ1gi en in eq. (1.2), al hough he wo ha e been es ima ed o coincide wi hin a ew pe cen s [30]. The de i a ion o eq. (1.7) elies on a Taylo expansion o he gene a ing unc ion in powe s o he momen s, unca ed a he o de o he skewness. I is expe imen ally possible o es he alidi y o his app oxima ion h ough he uni e sal equali y ha i implies [30,33] 2{6}− 2{8}=1 11( 2{4}− 2{6}).(1.8) The p ecision up o which his equali y holds depends on he esidual con ibu ion o highe cen al momen s o he low p.d. ., e.g. he ku osis, o he mul i-pa icle cumulan s. A high pT(pT&10 GeV/c) he dominan mechanism ha de e mines azimu hal aniso opies o he p oduced inal-s a e pa icles is hough o be pa h-leng h dependen ene gy-loss o highly ene ge ic pa ons [34–36]. Al hough se e al expe imen al obse a- ions, such as je azimu hal aniso opies [37,38], a e consis en wi h his hypo hesis, he de ails o he p ocess a e la gely uncons ained and measu emen s o aniso opic low o high-pTpa icles can help in his ega d. Al hough he mechanism ha de e mines i is undamen ally di e en , he o igin o aniso opic low a high pTis common o he one a low pT: ini ial-s a e geome y and i s e en -by-e en luc ua ions. Measu emen s epo ed in [39] seem o con i m his in e p e a ion. Recen CMS esul s on non-Gaussian ellip ic low luc ua ions [40] appea ed du ing he w i ing o his a icle. Nume ical da a a e no ye a ailable, bu he obse a ions seem o be essen ially compa ible wi h ou measu emen s and hei conclusions ag ee wi h hose o his a icle. 2 Da a sample and analysis me hods The sample o Pb–Pb collisions used o his measu emen was eco ded wi h he ALICE de ec o [41,42] in No embe and Decembe 2015 (2010), du ing he Run 2 (Run 1) o he – 3 – JHEP07(2018)103 LHC, a a cen e o mass ene gy pe nucleon o √sNN = 5.02 (2.76) TeV. The de ec o s used in he p esen analysis a e he Inne T acking Sys em (ITS) and Time P ojec ion Chambe (TPC), o p ima y e ex de e mina ion and cha ged pa icle acking, and he V0 de ec o , o symme y plane de e mina ion, cen ali y es ima ion [43] and igge . The igge condi ions a e desc ibed in [41]. Abou 78.4×106(12.6×106) minimum-bias e en s in he cen ali y ange 0–80%, co esponding o an in eg a ed luminosi y o 12.7 µb−1(2.0 µb−1), wi h a econs uc ed p ima y e ex posi ion along he beam di ec ion (z x) wi hin ±10 cm om he nominal in e ac ion poin , passed o line selec ion c i e ia [41] o he da a sample a √sNN = 5.02 (2.76) TeV. Cen ali y is de e mined om he measu ed ampli ude in he V0, which is p opo ional o he numbe o cha ged acks in he co esponding accep ance (2.8< η < 5.1 o V0A and −3.6< η < −1.7 o V0C). Cha ged acks wi h ans e se momen um 0.2< pT<50 GeV/cand pseudo apidi y |η|<0.8 a e used in he p esen analysis. These acks a e econs uc ed using combined in o ma ion om he ITS and TPC. A minimum numbe o TPC space poin s o 70 (ou o 159) is equi ed o all acks, oge he wi h a χ2pe TPC space poin (χ2 TPC) in he ange 0.1< χ2 TPC <4. A minimum numbe o 2 ITS hi s, o which a leas one in he wo inne mos laye s, is equi ed, oge he wi h a χ2pe ITS hi pe deg ee o eedom (χ2 ITS) smalle han 36. Only acks wi h a dis ance o closes app oach (DCA) o he p ima y e ex posi ion less han 3.2 cm in he beam di ec ion and 2.4 cm ans e se o i a e used. These ack selec ion c i e ia ensu e an op imum ejec ion o seconda y pa icles and a pT esolu ion be e han 5% in he pT ange used in he p esen analysis [41]. Aniso opic low coe icien s a e measu ed wi h he Q-cumulan me hod [44], using he implemen a ion p oposed in [45]. T ack weigh s (w) a e used in he cons uc ion o he Q- ec o s, in o de o co ec o non-uni o m econs uc ion e iciency and accep ance Qn,m = M X j=1 wj(pT, η, ϕ, z x)meinϕj,(2.1) whe e Mis he cha ged ack mul iplici y, n he ha monic and man in ege exponen o he weigh s. A e applying ack weigh s, he e ec s due o non-uni o mi ies in azimu hal accep ance, which would in oduce a bias in he measu ed low coe icien s, a e obse ed o be negligible. This is e alua ed by measu ing he e en -a e aged alues o he eal and imagina y pa o Qn, which a e consis en wi h ze o. Mul i-pa icle cumulan s a e measu ed on an e en -by-e en basis and hen, in o de o minimise s a is ical luc ua ions, a e aged o e all e en s using he co ec ed cha ged ack mul iplici y as a weigh , ollowing he p ocedu e p oposed in [44]. All obse ables a e compu ed in small cen ali y bins (1%) and hen in eg a ed, when limi ed size o he da a sample makes i necessa y, in wide cen ali y in e als using he cha ged pa icle yield in each 1% cen ali y bin as weigh . This a oids ha he e en weigh ing p ocedu e, based on mul iplici y, would in oduce a bias in he a e age cen ali y wi hin a la ge cen ali y bin, since mul iplici y a ies wi h cen ali y. Fo pT-in eg a ed esul s, he m-pa icle cumulan s a e calcula ed using all acks wi hin gi en pT ange, while o pT-di e en ial esul s one pa icle a a gi en pTis co ela ed wi h m−1 pa icles in he ull pT ange (0.2< pT<50 GeV/c). In e ms o e e ence – 4 – JHEP07(2018)103 (cn{m}) and di e en ial (dn{m}) cumulan s, as de ined in [44], he low coe icien s a e measu ed as n{2}=2 pcn{2},(2.2) n{4}=4 p−cn{4},(2.3) n{6}=6 1 4cn{6},(2.4) n{8}=8 −1 33cn{8},(2.5) n{2}(pT) = dn{2}(pT)/2 pcn{2},(2.6) n{4}(pT) = −dn{4}(pT)/4 p−cn{4}3.(2.7) Fo wo-pa icle co ela ions, a sepa a ion in pseudo apidi y be ween he co ela ed pa icles (∆η) is applied in o de o supp ess sho - ange azimu hal co ela ions which a e no associa ed o he symme y planes, usually called ‘non- low’. These co ela ions a ise om je s, mini-je s and esonance decays. Fo low coe icien s o highe o de ( n{m > 2}), non- low con ibu ion has been p e iously ound o be negligible in Pb–Pb collisions [24,31]. Resul s co esponding o |∆η|>1 (deno ed wi h n{2,|∆η|>1}) a e ob ained wi h he wo-pa icle cumulan co ela ing acks om opposi e sides o he TPC accep ance, −0.8< η < −0.5 and 0.5< η < 0.8. Resul s co esponding o |∆η|>2 (and epo ed as n{2,|∆η|>2}) a e ob ained wi h he scala p oduc me hod [46], co ela ing all acks a mid- apidi y (|η|<0.8) wi h he n- h ha monic Q- ec o QV0A ncalcula ed om he azimu hal dis ibu ion o he ene gy deposi ion measu ed in he V0A de ec o [2,47] n{2,|∆η|>2}=hun,0QV0A* ni hQV0A nQ∗ n,1ihQV0A nQV0C* ni hQn,1QV0C* ni ,(2.8) whe e un,0=einϕ is he uni low ec o om cha ged pa icle acks a mid- apidi y and Qn,1is compu ed om he same ype o acks acco ding o eq. (2.1). Bo h me hods ha e hei own limi a ions and hus a e complemen a y o each o he : n{2,|∆η|>2} can be eliably employed only up o he ou h ha monic, because o he ini e azimu hal segmen a ion o he V0 de ec o s (8 sec o s in 2π), while n{2,|∆η|>1}su e s om bigge s a is ical unce ain ies, due o he limi ed accep ance om which acks a e selec ed, and bigge non- low con ibu ion o pT>10 GeV/c. The sys ema ic unce ain ies a e e alua ed by a ying he ack and e en selec ion c i e ia and compa ing he a ia ion in he low coe icien s ela i e o he de aul esul s. The absolu e alue o he a ia ion i sel is assigned as a sys ema ic unce ain y i i is con- side ed signi ican acco ding o he Ba low c i e ion [48]. Di e en ack quali y a iables a e a ied: numbe o TPC space poin s, χ2 TPC and χ2 ITS, ac ion o sha ed TPC space poin s and numbe o ITS hi s. Fo each o hese, he de aul alues a e a ied in o de o inc ease he ac ion o excluded acks as much as 5 imes. No signi ican di e ences a e obse ed in he epo ed measu emen s be ween posi i ely and nega i ely cha ged pa i- cles. Conce ning he e en selec ion c i e ia, he ollowing a e in es iga ed: pola i y o he – 5 – JHEP07(2018)103 Cen ali y (%) 0 10 20 30 40 50 60 70 80 n 0.05 0.1 0.15 2.76 5.02 TeV |>1}η∆{2,| 2 {4} 2 |>1}η∆{2,| 3 |>1}η∆{2,| 4 |>1}η∆{2,| 5 |>1}η∆{2,| 6 ALICE Pb-Pb c < 3 GeV/ T p0.2 < | < 0.8η| Figu e 1. Aniso opic low coe icien s no inclusi e cha ged pa icles as a unc ion o cen ali y, o he wo-pa icle (deno ed wi h |∆η|>1) and ou -pa icle cumulan me hods. Measu emen s o Pb–Pb collisions a √sNN = 5.02 (2.76) TeV a e shown by solid (open) ma ke s. magne ic ield, econs uc ed p ima y e ex posi ion along he beam di ec ion (selec ing only e en s wi h z x wi hin ±8 cm om he nominal in e ac ion poin ), pile-up ejec ion (imposing s onge o weake cons ain s on he consis ency o di e en e en mul iplici y es ima o s) and a ia ions in he ins an aneous luminosi y deli e ed o he ALICE de ec o by he LHC. The unce ain y on cen ali y de e mina ion is e alua ed using an al e na i e es ima o based on he numbe o hi s in he second ITS laye (|η|<1.4), which is di ec ly p opo ional o he numbe o cha ged pa icles in he co esponding accep ance. Among he a o men ioned sou ces, o all obse ables in his a icle, ack quali y and cen ali y de e mina ion a e he dominan sou ces. The o al sys ema ic unce ain ies a e e alua ed summing in quad a u e he sys ema ic unce ain ies coming om each o he sou ces, i.e. conside ing he di e en sou ces o be unco ela ed. 3 Collision ene gy, ans e se momen um and cen ali y dependence Figu e 2shows he a io o n{2,|∆η|>1}(n= 2,3,4) and 2{4}be ween √sNN = 5.02 and 2.76 TeV, i.e. he ela i e a ia ion o hese low coe icien s be ween hose wo ene gies. Since he sys ema ic unce ain ies o he measu emen s a di e en ene gies a e pa ially – 6 – JHEP07(2018)103 η/s = 0.2η/s(T) pa am1 1 2{2,|∆η|>1}0.712 0.645 0.477 2{4}0.467 0.357 0.028 3{2,|∆η|>1}0.053 0.003 0.001 4{2,|∆η|>1}0.484 0.468 0.022 Table 1.p- alues o he compa ison among a ios o n{2,|∆η|>1}(n= 2,3,4) and 2{4} be ween √sNN = 5.02 and 2.76 TeV and model calcula ions using di e en pa ame isa ions o η/s(T) [18], shown in igu e 2, and uni y, in he cen ali y ange 5-50%. co ela ed, he esul ing sys ema ic unce ain y on he a io is educed. All ha monics a e obse ed o inc ease wi h ene gy, be ween abou 2 and 10%. A hin o a cen ali y depen- dence is obse ed only o 2, wi h he inc ease g owing sligh ly om mid-cen al owa ds mo e pe iphe al collisions. No signi ican di e ence is obse ed in he inc ease o 2mea- su ed wi h wo- o ou -pa icle co ela ions. Since he di e ence be ween 2{2,|∆η|>1} and 2{4}is di ec ly ela ed o low luc ua ions, his obse a ion sugges s ha he luc ua- ions o ellip ic low do no a y signi ican ly be ween he wo ene gies, wi hin expe imen al unce ain ies. The a ios a e compa ed o hyd odynamical calcula ions wi h EKRT ini ial condi ions [51] and di e en pa ame isa ions o he empe a u e dependence o η/s [18]. The p- alues o he compa ison be ween da a and models a e also shown in Tab. 1. Among he wo pa ame isa ions ha p o ide he bes desc ip ion o RHIC and LHC da a [52], bo h a e consis en wi h he measu emen s, excep o 3{2,|∆η|>1}, albei he one wi h cons an η/s = 0.2 ag ees sligh ly be e . These compa isons ake in o accoun he co ela- ion be ween sys ema ic unce ain ies o da a poin s in di e en cen ali y in e als. This obse a ion migh indica e li le o no empe a u e dependence o η/s wi hin he empe - a u e ange a which aniso opic low de elops a he wo cen e o mass ene gies. As a e e ence, he p- alues o he compa ison be ween da a and uni y in he same cen ali y ange (5–50%) a e also epo ed in able 1. Looking a he pTdependence in mo e de ail, he low ha monics a e ound o ollow an app oxima e powe -law scaling up o a ound he maximum, wi h exponen s being p o- po ional o he ha monic numbe n, n(pT)∼pn/3 T, as shown by he dashed i ed lines in igu e 3. In ideal hyd odynamics, he pTdependence o aniso opic low o massi e pa i- cles should ollow a powe -law unc ion n(pT)∼pn Tin he egion o pT/M up o o de one, whe e Mis he pa icle’s mass, and a highe momen a i has been p edic ed o be linea in pT o all n, n(pT)∼pT[53,54]. This pTdependence is no ably di e en om he one obse ed in he da a. A e y low pT his is p esumably because he ele an momen- um egion o inclusi e pa icles, mos ly pions, is below he ange o ou measu emen s, and a highe pTideal hyd o is no expec ed o hold because o momen um dependen iscous co ec ions a eeze ou [55] and/o non-linea mode mixing o n⩾4 [20,56]. The powe -law dependence o n= 2 was no iced be o e and i was a ibu ed o a no el ene gy loss mechanism [57], which howe e canno explain he scaling obse ed o n > 2. The eme gence o his simple powe -law dependence emains unexpec ed and su p ising. – 7 – JHEP07(2018)103 n/m m / n 0.4 1 2 3 10 20 30 0-5%0-5%0-5% n/m m / n 0.4 1 2 3 4 10 20-30%20-30%20-30% )c (GeV/ T p 1 10 n/m m / n 0.4 1 2 3 4 10 50-60%50-60%50-60% 0.4 1 2 3 10 20 30 5-10%5-10%5-10% 0.4 1 2 3 4 10 30-40%30-40%30-40% )c (GeV/ T p 1 10 0.4 1 2 3 4 10 60-70%60-70%60-70% 0.4 1 2 3 10 20 30 10-20%10-20%10-20% 0.4 1 2 3 4 10 40-50%40-50%40-50% ALICE Pb-Pb 5.02 TeV |>2}η∆{2,| n |<0.8, η| 3/2 2 / 3 4/2 2 / 4 4/3 3 / 4 iEBE-VISHNU AMPT-IC + Figu e 8. Ra ios n(pT)/ m(pT)n/m, n = 3,4, m = 2,3 o inclusi e cha ged pa icles o Pb–Pb collisions a √sNN = 5.02, in di e en cen ali y classes, measu ed wi h he scala p oduc me hod wi h espec o he V0A Q- ec o . Dashed lines ep esen a e ages in 0.2< pT<3 GeV/c. The a ios a e also shown o one hyd odynamic model [62] in he ou mos cen al cen ali y in e als; i is quali a i ely simila in he o he cen ali y in e als and o he o he models. 4 Ellip ic low luc ua ions Figu e 9shows he in eg a ed 2in he pT ange 0.2< pT<3 GeV/cas a unc ion o cen ali y, measu ed wi h wo-, ou -, six- and eigh -pa icle cumulan s a √sNN = 5.02 and 2.76 TeV. The co esponding cumulan s (c2{2,4,6,8}) a e epo ed in igu e 10. The cen ali y dependence is simila o all mul i-pa icle cumulan s and simila o wha is shown in igu e 1. The di e ences be ween 2{2}(shown in igu e 9) and 2{2,|∆η|>1} (shown in igu e 1), which ange om abou 4% in mid-cen al collisions o abou 20% in pe iphe al ones, a e mos ly a ibu ed o non- low con ibu ions, which a e supp essed in he case o esul s wi h a pseudo apidi y gap. The possible di e ences a ising om he deco ela ion o e en planes a di e en pseudo apidi ies a e expec ed o be less han 1%, as p e iously a gued. A ine-spli ing o less han 1% is obse ed among 2{4}, 2{6}and 2{8}, as i can be seen om hei a ios, shown in igu e 11 o bo h collision ene gies. The a ios 2{6}/ 2{4} and 2{8}/ 2{4}a √sNN = 5.02 TeV show a signi ican cen ali y dependence: he de ia- ions o he a ios om uni y is abou 0.2% in cen al and inc eases up o abou 1% o mid- cen al collisions. A u he inc ease seems o be obse ed o mo e pe iphe al collisions, up o abou 2% o cen ali ies abo e 50%. The sys ema ic unce ain ies on hese a ios a e g ea ely educed wi h espec o hose on 2{m}(m= 2,4,6,8), since he dominan – 14 – JHEP07(2018)103 Cen ali y (%) 0 10 20 30 40 50 60 70 {m} 2 0 0.05 0.1 ALICE Pb-Pb c < 3 GeV/ T p0.2 < | < 0.8η| 2.76 5.02 TeV {2} 2 {4} 2 {6} 2 {8} 2 Figu e 9. Ellip ic low coe icien 2o inclusi e cha ged pa icles as a unc ion o cen ali y, measu ed wi h he wo- and mul i-pa icle cumulan me hods. Measu emen s o Pb–Pb collisions a √sNN = 5.02 (2.76) TeV a e shown by solid (open) ma ke s. sou ces o sys ema ic unce ain y ( ack quali y a iables and cen ali y de e mina ion) among he wo- and mul i-pa icle cumulan s a e highly co ela ed. This ine-spli ing is consis en wi h non-Bessel-Gaussian beha iou o e en -by-e en low luc ua ions, as p e- iously explained. These a ios a e ound o be independen o he choice o pT ange wi hin 0.2< pT<3 GeV/c, indica ing ha he cha ac e iza ion o low luc ua ions a low pT does no depend on pT, e en o such ine-spli ing. Resul s a √sNN = 2.76 TeV a e ound o be compa ible, indica ing ha hese a ios do no change signi ican ly ac oss collision ene gies. Compa ed o calcula ions [30] employing MC-Glaube ini ial condi ions [80] and iscous hyd odynamics ( -USPhyd o) o Pb–Pb collisions a √sNN = 2.76 TeV, he a ios 2{6}/ 2{4}and 2{8}/ 2{4}a e ound o be compa ible. A good ag eemen is ound be ween he esul s a √sNN = 2.76 TeV and co esponding ATLAS esul s on ellip ic low p.d. . ob ained ia he un olding echnique [29], as shown in igu e 12. Figu e 13 shows he a io be ween 2{8}and 2{6}a √sNN = 5.02 TeV. A hin o a u he ine-spli ing be ween hese wo, o he o de o 0.05%, is obse ed. The esul s sugges li le o no cen ali y dependence wi hin cen ali y 10–50%. This di e ence is also consis en wi h non-Bessel-Gaussian ellip ic low luc ua ions, and can be a ibu ed o di e en con ibu ions o he skewness o hese highe -o de cumulan s [30]. Co esponding esul s a √sNN = 2.76 TeV, he e and in he ollowing, a e no shown because o he la ge s a is ical unce ain ies. Figu e 14 shows 2{6} − 2{8}and ( 2{4} − 2{6})/11 a – 15 – JHEP07(2018)103 Cen ali y (%) 0 10 20 30 40 50 60 70 {2} 2 c 5 10 3− 10× ALICE Pb-Pb c < 3 GeV/ T p0.2 < | < 0.8η| 2.76 5.02 TeV {m} 2 c Cen ali y (%) 0 10 20 30 40 50 60 70 {4} 2 c 40− 20− 0 6− 10× Cen ali y (%) 0 10 20 30 40 50 60 70 {6} 2 c 0 0.5 1 1.5 6− 10× Cen ali y (%) 0 10 20 30 40 50 60 70 {8} 2 c 0.1− 0.05− 0 6− 10× Figu e 10. Cumulan s c2o ellip ic low o inclusi e cha ged pa icles as a unc ion o cen ali y, o he wo-pa icle and mul i-pa icle cumulan me hods. Measu emen s o Pb–Pb collisions a √sNN = 5.02 (2.76) TeV a e shown by solid (open) ma ke s. √sNN = 5.02 TeV: hese wo a e obse ed o be in ag eemen , which demons a es he alidi y o eq. (1.8). This obse a ion se s an uppe limi o 4 ×10−4a 95% con idence le el o possible con ibu ions o mul i-pa icle cumulan s om highe momen s o he low p.d. . (ku osis and beyond) in he cen ali y ange 10–50%. This es ima e is ob ained assuming gaussian sys ema ic unce ain ies and summing hem in quad a u e wi h he s a is ical ones. Figu e 15 shows he measu emen o he s anda dised skewness (γexp 1) a √sNN = 5.02 TeV as a unc ion o cen ali y. To supp ess non- low con ibu ions, he alues o 2{2,|∆η|>1} om igu e 1a e used o 2{2}in eq. (1.7). A nega i e alue o he skewness, wi h a s ong cen ali y dependence, is obse ed: γexp 1dec eases om ze o in cen al o abou −0.4 in pe iphe al collisions. Compa ed o model calcula ions [30] o Pb–Pb collisions a √sNN = 2.76 TeV, he esul s a e ound o be compa ible o he – 16 – JHEP07(2018)103 Cen ali y (%) 0 10 20 30 40 50 60 70 {m} 2 /{n} 2 0.96 0.98 1 1.02 2.76 5.02 TeV {4} 2 /{6} 2 {4} 2 /{8} 2 ALICE Pb-Pb c < 3 GeV/ T p0.2 < | < 0.8η| Figu e 11. Ra ios o ellip ic low coe icien s 2o inclusi e cha ged pa icles be ween measu e- men s wi h di e en mul i-pa icle cumulan me hods, as a unc ion o cen ali y. Measu emen s a √sNN = 5.02 (2.76) TeV a e shown by solid (open) ma ke s. Cen ali y (%) 0 10 20 30 40 50 60 70 {m} 2 /{n} 2 0.96 0.98 1 1.02 Pb-Pb 2.76 TeV {4} 2 /{6} 2 ALICE {4} 2 /{8} 2 ALICE {4} 2 /{6} 2 ATLAS EbyE {4} 2 /{8} 2 ATLAS EbyE Glaube + -USPhyd o c < 3 GeV/ T p0.2 < | < 0.8η| Figu e 12. Ra ios o ellip ic low coe icien s 2o inclusi e cha ged pa icles be ween measu emen s wi h di e en mul i-pa icle cumulan me hods, as a unc ion o cen ali y, a √sNN = 2.76 TeV. Hyd odynamic calcula ions [30] and ATLAS measu emen s [29] a e shown o compa ison. – 17 – JHEP07(2018)103 Cen ali y (%) 5 10 15 20 25 30 35 40 45 50 {6} 2 /{8} 2 0.998 1 1.002 ALICE Pb-Pb 5.02 TeV c < 3 GeV/ T p0.2 < | < 0.8η| Figu e 13. Ra io o ellip ic low coe icien s 2{8}/ 2{6}o inclusi e cha ged pa icles as a unc ion o cen ali y. Cen ali y (%) 0 10 20 30 40 50 60 70 {m} 2 -{n} 2 0.2− 0 0.2 0.4 3− 10× {8} 2 -{6} 2 )/11{6} 2 -{4} 2 ( ALICE Pb-Pb 5.02 TeV c < 3 GeV/ T p0.2 < | < 0.8η| Figu e 14. Di e ences o ellip ic low coe icien s 2o inclusi e cha ged pa icles be ween mea- su emen s wi h di e en mul i-pa icle cumulan me hods, as a unc ion o cen ali y. – 18 – JHEP07(2018)103 Cen ali y (%) 0 10 20 30 40 50 60 70 exp 1 γ 0.6− 0.4− 0.2− 0 0.2 ALICE 5.02 TeV Glaube + -USPhyd o 2.76 TeV Pb-Pb c < 3 GeV/ T p0.2 < | < 0.8η| Figu e 15. Skewness o ellip ic low γexp 1o inclusi e cha ged pa icles as a unc ion o cen ali y, o Pb–Pb collisions a √sNN = 5.02 TeV. Hyd odynamic calcula ions [30] o Pb–Pb collisions a √sNN = 2.76 TeV a e shown o compa ison. en i e cen ali y ange. This obse a ion is consis en wi h he ellip ic low p.d. . being p og essi ely mo e le -skewed going om cen al o pe iphe al collisions. We a ibu e his ea u e o he combina ion o an inc ease in hε2iand he geome ical cons ain ε2<1, as p e iously a gued. In o de o epo he ull p.d. . o ellip ic low P( 2), which can be compa ed o p e- ious expe imen al esul s and heo e ical p edic ions, i is pa ame ised wi h he Ellip ic Powe dis ibu ion [26,27] P( 2) = dε2 d 2 P(ε2) = 1 k2 P 2 k2=2α 2 πk2 2 (1 −ε2 0)α+1/2Zπ 0 (1 − 2 2/k2 2)α−1 (1 − 2ε0cos ϕ/k2)2α+1 dϕ, (4.1) and i s h ee ee pa ame e s (α,ε0and k2) a e ex ac ed om i s o he ellip ic low cumulan s c2{2,|∆η|>1}and c2{m}(m= 4,6,8) a √sNN = 5.02 TeV. The pa ame e αquan i ies he magni ude o ellip ic low luc ua ions, ε0 he mean eccen ici y in he eac ion plane and k2is he p opo ionali y coe icien be ween ini ial-s a e eccen ici y and 2coe icien : 2=k2ε2. The ela ion be ween cumulan s and Ellip ic Powe pa ame e s is gi en by [27] c2{2}=k2 2(1 − 1),(4.2) c2{4}=−k4 21−2 1+ 2 2 1− 2,(4.3) c2{6}=k6 24 + 18 2 1−12 3 1+ 12 1(3 2−1) −6 2− 3,(4.4) c2{8}=−k8 2(33 −288 3 1+ 144 4 1−66 2+ 18 2 2−24 2 1(−11 + 6 2) −12 3+ 4 1(−33 + 42 2+ 4 3)− 4) (4.5) – 19 – JHEP07(2018)103 Cen ali y (%) 0 10 20 30 40 50 60 2 k 0.1 0.2 0.3 0.4 ALICE Pb-Pb 5.02 TeV c < 3 GeV/ T p0.2 < | < 0.8η| Cen ali y (%) 0 10 20 30 40 50 60 α 0 100 200 300 Cen ali y (%) 0 10 20 30 40 50 60 0 ε 0 0.1 0.2 0.3 Figu e 16. Ellip ic powe pa ame e s k2,αand ε0as a unc ion o cen ali y, o Pb–Pb collisions a √sNN = 5.02 TeV, ex ac ed om measu emen s o 2o inclusi e cha ged pa icles wi h wo- pa icle and mul i-pa icle cumulan me hods. whe e k≡ h(1 −ε2 n)ki=α α+k(1 −ε2 0)k2F1k+1 2, k;α+k+ 1, ε2 0(4.6) and 2F1is he hype geome ic unc ion. The esul s a e shown in igu e 16. The sys ema ic unce ain ies a e assigned a ying he i anges and ini ial alues o he pa ame e s and shi ing he da a poin s acco ding o he co esponding sys ema ic unce ain ies. An addi- ional sou ce o unce ain y, which is in es iga ed, is a possible cubic esponse coe icien k0 2, de ined as 2=k2ε2+k0 2ε3 2. This coe icien is in oduced o quan i y he possible inc ease o low luc ua ions ha he hyd odynamic expansion o he medium in oduces wi h espec o geome ical luc ua ions in he ini ial s a e and was a gued o be non-ze o in mid-cen al and pe iphe al collisions due o gene al p ope ies o he hyd odynamic phase [81]. In pa icula , k0 2is expec ed o be ≤0.15 in he cen ali y ange 0–60% [81]. The esidual di e ences in α,ε0and k2when including k0 2as an addi ional ee pa ame e a e conside ed in he sys ema ic unce ain ies. The s a is ical unce ain ies a e e alua ed using he subsampling me hod: he analysed da ase is di ided in o 10 sub-samples and 2{m}is measu ed in each o hem. The Ellip ic Powe pa ame e s a e hen ex ac ed in each subsample and hei dispe sion is used o es ima e he s a is ical unce ain ies. The esul ing p.d. ., cons uc ed using he Ellip ic Powe dis ibu ion (eq. (4.1)) wi h he pa ame e s shown in igu e 16 and scaled by i s mean (h 2i), is epo ed in igu e 17, o cen ali ies 5–10%, 25–30% and 45–50%. The sys ema ic unce ain ies ake in o accoun he co ela ion o he unce ain ies o he Ellip ic Powe pa ame e s. O he cen ali y anges ha a e no shown he e a e epo ed in he appendix A. Scaling by h 2iallows a compa ison o ou da a wi h esul s by he ATLAS collabo a ion [70] ob ained in di e en pT anges. The obse ed ag eemen is also consis en , as p e iously no ed, wi h ellip ic low luc ua ions a low pTno depending on pTand no changing signi ican ly be ween collision ene gies, excep o he i ial inc ease in pT-in eg a ed 2due o he change in hpTi. Compa ison wi h iEBE-VISHNU model calcula ions wi h AMPT and TRENTo ini ial condi ions [62] indica es ha TRENTo ini ial condi ions a e be e a desc ibing he expe imen al da a. The da a a e ound o be in ag eemen also wi h p edic ions om – 20 – JHEP07(2018)103 0 0.5 1 1.5 2 2.5 〉 2 〈)* 2 P( 3− 10 1 0 0.5 1 1.5 2 2.5 〉 2 〈)* 2 P( 3− 10 1 |<0.8ηPb-Pb 5.02 TeV, | <3 GeV/c T ALICE: 0.2<p 〉 2 〈/ 2 0 0.5 1 1.5 2 2.5 〉 2 〈)* 2 P( 3− 10 1 Pb-Pb 5.02 TeV IP-Glasma + MUSIC AMPT-IC + iEBE-VISHNU TRENTo-IC + iEBE-VISHNU 0 0.5 1 1.5 2 2.5 1 5-10% 0 0.5 1 1.5 2 2.5 1 25-30% 〉 2 〈/ 2 0 0.5 1 1.5 2 2.5 1 |<2.5ηPb-Pb 2.76 TeV, | <1 GeV/c T ATLAS: 0.5<p >0.5 GeV/c T ATLAS: p 45-50% Figu e 17. Ellip ic low p.d. . P( 2) escaled by he mean 2(h 2i) o inclusi e cha ged pa icles o Pb–Pb collisions a √sNN = 5.02 TeV, in di e en cen ali y classes. Se e al hyd odynamic calcula ions [61,62] and p e ious measu emen s om ATLAS [70] a lowe ene gies a e shown o compa ison. he IP-Glasma+MUSIC model [61] (wi h ini ial condi ions e y simila o he TRENTo ones), al hough he unce ain ies on he heo e ical p edic ions do no allow o d aw i m conclusions. 5 Conclusions Aniso opic low coe icien s a e measu ed up o he six h ha monic o inclusi e cha ged pa icles a mid- apidi y (|η|<0.8), in a wide cen ali y (0–80%) and pT(0.2< pT< 50 GeV/c) anges, o Pb–Pb collisions a √sNN = 5.02 and 2.76 TeV. Compa ing he e- sul s a √sNN = 5.02 and 2.76 TeV he ene gy dependence o aniso opic low a he LHC is – 21 – JHEP07(2018)103 in es iga ed. Compa ison wi h di e en model calcula ions demons a es ha hese mea- su emen s ha e he po en ial o cons ain ini ial-s a e luc ua ions, anspo pa ame e s o he medium and pa h-leng h dependence o ene gy loss o high-pTpa ons. The e olu ion o n(pT) wi h espec o cen ali y and ha monic numbe nis also in es iga ed. Flow coe icien o all ha monics a e obse ed o ollow an app oxima e powe -law scaling o he o m n(pT)∼pn/3 Tin he pT ange 0.2< pT<3 GeV/c. The a ios n/ n/m mn= 3,4 and m= 2,3 a e also obse ed o be independen o pTwi hin he same pT ange and show de ia ions o abou 10% o 3 < pT<10 GeV/c. The luc ua ions o ellip ic low a e in es iga ed h ough he ine-spli ing o he highe - o de mul i-pa icle cumulan s ( 2{4}, 2{6}, 2{8}), om which he s anda dised skewness (γexp 1) o he low p.d. . is ex ac ed. Resul s a e ound o be compa ible bo h wi h p edic- ions om hyd odynamical models and wi h p e ious ATLAS esul s a lowe ene gies. I is concluded ha he cha ac e iza ion o ellip ic low luc ua ions a low pTdoes no de- pend on he pT ange and on he collision ene gy, excep o he inc ease in pT-in eg a ed 2due o he change in hpTi. Di ec cons ain s on he con ibu ion o highe momen s o he mul i-pa icle cumulan s a e also epo ed. Finally, he ull ellip ic low p.d. ., pa ame ised wi h he Ellip ic Powe dis ibu ion, is epo ed in he cen ali y anges 0– 60%. These esul s a e also ound o be in ag eemen wi h p e ious expe imen al esul s. O e all, calcula ions including ini ial condi ions ma ching he IP-Glasma desc ip ion a e obse ed o be e ep oduce he ellip ic low p.d. . while ailing o desc ibe he pTde- pendence o aniso opic low coe icien s, whe eas he opposi e si ua ion is obse ed o calcula ions ha employ AMPT ini ial condi ions. Acknowledgmen 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 es and he Wo ldwide LHC Compu ing G id (WLCG) collabo a ion. The ALICE Collab- o a ion acknowledges he ollowing unding agencies o hei suppo in building and unning he ALICE de ec o : A. I. 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Mao7, M. Ma chisone132 ,128 ,73 , J. Ma eˇs67 , – 33 – JHEP07(2018)103 G.V. Ma gaglio i27 , A. Ma go i53 , J. Ma gu i63 , A. Ma ´ın103 , C. Ma ke 116 , M. Ma qua d69 , N.A. Ma in103 , P. Ma inengo36 , M.I. Ma ´ınez2, G. Ma ´ınez Ga c´ıa111 , M. Ma inez Ped ei a36 , S. Masciocchi103 , M. Mase a28 , A. Masoni54 , L. Massac ie 61 , E. Masson111 , A. Mas ose io52 , A.M. Ma his102 ,114 , P.F.T. Ma uoka118 , A. Ma yja115 ,127 , C. Maye 115 , M. Mazzilli35 , M.A. Mazzoni57 , F. Meddi25 , Y. Melikyan91 , A. Menchaca-Rocha72 , E. Meninno32 , J. Me cado P´e ez101 , M. Me es15 , C.S. Meza108 , S. Mhlanga122 , Y. Miake130 , L. Michele i28 , M.M. Mieskolainen44 , D.L. Mihaylo 102 , K. Mikhaylo 64 ,75 , A. Mischke63 , A.N. Mish a70 , D. Mi´skowiec103 , J. Mi a138 , C.M. Mi u68 , N. Mohammadi36 ,63 , A.P. Mohan y63 , B. Mohan y85 , M. Mohisin Khan18 ,iii, D.A. Mo ei a De Godoy141 , L.A.P. Mo eno2, S. Mo e o31 , A. Mo eale111 , A. Mo sch36 , V. Mucci o a51 , E. Mudnic126 , D. M¨uhlheim141 , S. 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Alikhanyan Na ional Science Labo a o y (Ye e an Physics Ins i u e) Founda ion, Ye e an, A menia 2Benem´e i a Uni e sidad Au ´onoma de Puebla, Puebla, Mexico 3Bogolyubo Ins i u e o Theo e ical Physics, Na ional Academy o Sciences o Uk aine, Kie , Uk aine 4Bose Ins i u e, Depa men o Physics and Cen e o As opa icle Physics and Space Science (CAPSS), Kolka a, India 5Budke Ins i u e o Nuclea Physics, No osibi sk, Russia – 35 – JHEP07(2018)103 6Cali o nia Poly echnic S a e Uni e si y, San Luis Obispo, Cali o nia, Uni ed S a es 7Cen al China No mal Uni e si y, Wuhan, China 8Cen e de Calcul de l’IN2P3, Villeu banne, Lyon, F ance 9Cen o de Aplicaciones Tecnol´ogicas y Desa ollo Nuclea (CEADEN), Ha ana, Cuba 10 Cen o de In es igaci´on y de Es udios A anzados (CINVESTAV), Mexico Ci y and M´e ida, Mexico 11 Cen o Fe mi - Museo S o ico della Fisica e Cen o S udi e Rice che “En ico Fe mi’, Rome, I aly 12 Chicago S a e Uni e si y, Chicago, Illinois, Uni ed S a es 13 China Ins i u e o A omic Ene gy, Beijing, China 14 Chonbuk Na ional Uni e si y, Jeonju, Republic o Ko ea 15 Comenius Uni e si y B a isla a, Facul y o Ma hema ics, Physics and In o ma ics, B a isla a, Slo akia 16 COMSATS Ins i u e o In o ma ion Technology (CIIT), Islamabad, Pakis an 17 C eigh on Uni e si y, Omaha, Neb aska, Uni ed S a es 18 Depa men o Physics, Aliga h Muslim Uni e si y, Aliga h, India 19 Depa men o Physics, Ohio S a e Uni e si y, Columbus, Ohio, Uni ed S a es 20 Depa men o Physics, Pusan Na ional Uni e si y, Pusan, Republic o Ko ea 21 Depa men o Physics, Sejong Uni e si y, Seoul, Republic o Ko ea 22 Depa men o Physics, Uni e si y o Cali o nia, Be keley, Cali o nia, Uni ed S a es 23 Depa men o Physics, Uni e si y o Oslo, Oslo, No way 24 Depa men o Physics and Technology, Uni e si y o Be gen, Be gen, No way 25 Dipa imen o di Fisica dell’Uni e si `a ‘La Sapienza’ and Sezione INFN, Rome, I aly 26 Dipa imen o di Fisica dell’Uni e si `a and Sezione INFN, Caglia i, I aly 27 Dipa imen o di Fisica dell’Uni e si `a and Sezione INFN, T ies e, I aly 28 Dipa imen o di Fisica dell’Uni e si `a and Sezione INFN, Tu in, I aly 29 Dipa imen o di Fisica e As onomia dell’Uni e si `a and Sezione INFN, Bologna, I aly 30 Dipa imen o di Fisica e As onomia dell’Uni e si `a and Sezione INFN, Ca ania, I aly 31 Dipa imen o di Fisica e As onomia dell’Uni e si `a and Sezione INFN, Pado a, I aly 32 Dipa imen o di Fisica ‘E.R. Caianiello’ dell’Uni e si `a and G uppo Collega o INFN, Sale no, I aly 33 Dipa imen o DISAT del Poli ecnico and Sezione INFN, Tu in, I aly 34 Dipa imen o di Scienze e Inno azione Tecnologica dell’Uni e si `a del Piemon e O ien ale and INFN Sezione di To ino, Alessand ia, I aly 35 Dipa imen o In e a eneo di Fisica ‘M. Me lin’ and Sezione INFN, Ba i, I aly 36 Eu opean O ganiza ion o Nuclea Resea ch (CERN), Gene a, Swi ze land 37 Facul y o Enginee ing and Science, Wes e n No way Uni e si y o Applied Sciences, Be gen, No way 38 Facul y o Nuclea Sciences and Physical Enginee ing, Czech Technical Uni e si y in P ague, P ague, Czech Republic 39 Facul y o Science, P.J. ˇ Sa ´a ik Uni e si y, Koˇsice, Slo akia 40 F ank u Ins i u e o Ad anced S udies, Johann Wol gang Goe he-Uni e si ¨a F ank u , F ank u , Ge many 41 Gangneung-Wonju Na ional Uni e si y, Gangneung, Republic o Ko ea 42 Gauha i Uni e si y, Depa men o Physics, Guwaha i, India 43 Helmhol z-Ins i u ¨u S ahlen- und Ke nphysik, Rheinische F ied ich-Wilhelms-Uni e si ¨a Bonn, Bonn, Ge many 44 Helsinki Ins i u e o Physics (HIP), Helsinki, Finland 45 Hi oshima Uni e si y, Hi oshima, Japan 46 Hochschule Wo ms, Zen um ¨u Technologie ans e und Telekommunika ion (ZTT), Wo ms, Ge many 47 Ho ia Hulubei Na ional Ins i u e o Physics and Nuclea Enginee ing, Bucha es , Romania 48 Indian Ins i u e o Technology Bombay (IIT), Mumbai, India 49 Indian Ins i u e o Technology Indo e, Indo e, India 50 Indonesian Ins i u e o Sciences, Jaka a, Indonesia – 36 – JHEP07(2018)103 51 INFN, Labo a o i Nazionali di F asca i, F asca i, I aly 52 INFN, Sezione di Ba i, Ba i, I aly 53 INFN, Sezione di Bologna, Bologna, I aly 54 INFN, Sezione di Caglia i, Caglia i, I aly 55 INFN, Sezione di Ca ania, Ca ania, I aly 56 INFN, Sezione di Pado a, Pado a, I aly 57 INFN, Sezione di Roma, Rome, I aly 58 INFN, Sezione di To ino, Tu in, I aly 59 INFN, Sezione di T ies e, T ies e, I aly 60 Inha Uni e si y, Incheon, Republic o Ko ea 61 Ins i u de Physique Nucl´eai e d’O say (IPNO), Ins i u Na ional de Physique Nucl´eai e e de Physique des Pa icules (IN2P3/CNRS), Uni e si ´e de Pa is-Sud, Uni e si ´e Pa is-Saclay, O say, F ance 62 Ins i u e o Nuclea Resea ch, Academy o Sciences, Moscow, Russia 63 Ins i u e o Suba omic Physics, U ech Uni e si y/Nikhe , U ech , Ne he lands 64 Ins i u e o Theo e ical and Expe imen al Physics, Moscow, Russia 65 Ins i u e o Expe imen al Physics, Slo ak Academy o Sciences, Koˇsice, Slo akia 66 Ins i u e o Physics, Bhubaneswa , India 67 Ins i u e o Physics o he Czech Academy o Sciences, P ague, Czech Republic 68 Ins i u e o Space Science (ISS), Bucha es , Romania 69 Ins i u ¨u Ke nphysik, Johann Wol gang Goe he-Uni e si ¨a F ank u , F ank u , Ge many 70 Ins i u o de Ciencias Nuclea es, Uni e sidad Nacional Au ´onoma de M´exico, Mexico Ci y, Mexico 71 Ins i u o de F´ısica, Uni e sidade Fede al do Rio G ande do Sul (UFRGS), Po o Aleg e, B azil 72 Ins i u o de F´ısica, Uni e sidad Nacional Au ´onoma de M´exico, Mexico Ci y, Mexico 73 iThemba LABS, Na ional Resea ch Founda ion, Some se Wes , Sou h A ica 74 Johann-Wol gang-Goe he Uni e si ¨a F ank u Ins i u ¨u In o ma ik, Fachbe eich In o ma ik und Ma hema ik, F ank u , Ge many 75 Join Ins i u e o Nuclea Resea ch (JINR), Dubna, Russia 76 Ko ea Ins i u e o Science and Technology In o ma ion, Daejeon, Republic o Ko ea 77 KTO Ka a ay Uni e si y, Konya, Tu key 78 Labo a oi e de Physique Suba omique e de Cosmologie, Uni e si ´e G enoble-Alpes, CNRS-IN2P3, G enoble, F ance 79 Law ence Be keley Na ional Labo a o y, Be keley, Cali o nia, Uni ed S a es 80 Lund Uni e si y Depa men o Physics, Di ision o Pa icle Physics, Lund, Sweden 81 Nagasaki Ins i u e o Applied Science, Nagasaki, Japan 82 Na a Women’s Uni e si y (NWU), Na a, Japan 83 Na ional and Kapodis ian Uni e si y o A hens, School o Science, Depa men o Physics , A hens, G eece 84 Na ional Cen e o Nuclea Resea ch, Wa saw, Poland 85 Na ional Ins i u e o Science Educa ion and Resea ch, HBNI, Ja ni, India 86 Na ional Nuclea Resea ch Cen e , Baku, Aze baijan 87 Na ional Resea ch Cen e Ku cha o Ins i u e, Moscow, Russia 88 Niels Boh Ins i u e, Uni e si y o Copenhagen, Copenhagen, Denma k 89 Nikhe , Na ional ins i u e o suba omic physics, Ams e dam, Ne he lands 90 NRC ‘Ku cha o Ins i u e’ IHEP, P o ino, Russia 91 NRNU Moscow Enginee ing Physics Ins i u e, Moscow, Russia 92 Nuclea Physics G oup, STFC Da esbu y Labo a o y, Da esbu y, Uni ed Kingdom 93 Nuclea Physics Ins i u e o he Czech Academy o Sciences, ˇ Reˇz u P ahy, Czech Republic 94 Oak Ridge Na ional Labo a o y, Oak Ridge, Tennessee, Uni ed S a es 95 Pe e sbu g Nuclea Physics Ins i u e, Ga china, Russia 96 Physics depa men , Facul y o science, Uni e si y o Zag eb, Zag eb, C oa ia 97 Physics Depa men , Panjab Uni e si y, Chandiga h, India – 37 – JHEP07(2018)103 98 Physics Depa men , Uni e si y o Jammu, Jammu, India 99 Physics Depa men , Uni e si y o Rajas han, Jaipu , India 100 Physikalisches Ins i u , Ebe ha d-Ka ls-Uni e si ¨a T¨ubingen, T¨ubingen, Ge many 101 Physikalisches Ins i u , Rup ech -Ka ls-Uni e si ¨a Heidelbe g, Heidelbe g, Ge many 102 Physik Depa men , Technische Uni e si ¨a M¨unchen, Munich, Ge many 103 Resea ch Di ision and Ex eMe Ma e Ins i u e EMMI, GSI Helmhol zzen um ¨u Schwe ionen o schung GmbH, Da ms ad , Ge many 104 Rudje Boˇsko i´c Ins i u e, Zag eb, C oa ia 105 Russian Fede al Nuclea Cen e (VNIIEF), Sa o , Russia 106 Saha Ins i u e o Nuclea Physics, Kolka a, India 107 School o Physics and As onomy, Uni e si y o Bi mingham, Bi mingham, Uni ed Kingdom 108 Secci´on F´ısica, Depa amen o de Ciencias, Pon i icia Uni e sidad Ca ´olica del Pe ´u, Lima, Pe u 109 Shanghai Ins i u e o Applied Physics, Shanghai, China 110 S e an Meye Ins i u ¨u Suba oma e Physik (SMI), Vienna, Aus ia 111 SUBATECH, IMT A lan ique, Uni e si ´e de Nan es, CNRS-IN2P3, Nan es, F ance 112 Su ana ee Uni e si y o Technology, Nakhon Ra chasima, Thailand 113 Technical Uni e si y o Koˇsice, Koˇsice, Slo akia 114 Technische Uni e si ¨a M¨unchen, Excellence Clus e ‘Uni e se’, Munich, Ge many 115 The Hen yk Niewodniczanski Ins i u e o Nuclea Physics, Polish Academy o Sciences, C acow, Poland 116 The Uni e si y o Texas a Aus in, Aus in, Texas, Uni ed S a es 117 Uni e sidad Au ´onoma de Sinaloa, Culiac´an, Mexico 118 Uni e sidade de S˜ao Paulo (USP), S˜ao Paulo, B azil 119 Uni e sidade Es adual de Campinas (UNICAMP), Campinas, B azil 120 Uni e sidade Fede al do ABC, San o And e, B azil 121 Uni e si y College o Sou heas No way, Tonsbe g, No way 122 Uni e si y o Cape Town, Cape Town, Sou h A ica 123 Uni e si y o Hous on, Hous on, Texas, Uni ed S a es 124 Uni e si y o Jy ¨askyl¨a, Jy ¨askyl¨a, Finland 125 Uni e si y o Li e pool, Depa men o Physics Oli e Lodge Labo a o y , Li e pool, Uni ed Kingdom 126 Uni e si y o Spli , Facul y o Elec ical Enginee ing, Mechanical Enginee ing and Na al A chi ec u e, Spli , C oa ia 127 Uni e si y o Tennessee, Knox ille, Tennessee, Uni ed S a es 128 Uni e si y o he Wi wa e s and, Johannesbu g, Sou h A ica 129 Uni e si y o Tokyo, Tokyo, Japan 130 Uni e si y o Tsukuba, Tsukuba, Japan 131 Uni e si ´e Cle mon Au e gne, CNRS/IN2P3, LPC, Cle mon -Fe and, F ance 132 Uni e si ´e de Lyon, Uni e si ´e Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeu banne, Lyon, F ance 133 Uni e si ´e de S asbou g, CNRS, IPHC UMR 7178, F-67000 S asbou g, F ance, S asbou g, F ance 134 Uni e si ´e Pa is-Saclay Cen e d’ ´ E udes de Saclay (CEA), IRFU, Depa men de Physique Nucl´eai e (DPhN), Saclay, F ance 135 Uni e si `a degli S udi di Pa ia, Pa ia, I aly 136 Uni e si `a di B escia, B escia, I aly 137 V. Fock Ins i u e o Physics, S . Pe e sbu g S a e Uni e si y, S . Pe e sbu g, Russia 138 Va iable Ene gy Cyclo on Cen e, Kolka a, India 139 Wa saw Uni e si y o Technology, Wa saw, Poland 140 Wayne S a e Uni e si y, De oi , Michigan, Uni ed S a es 141 Wes ¨alische Wilhelms-Uni e si ¨a M¨uns e , Ins i u ¨u Ke nphysik, M¨uns e , Ge many 142 Wigne Resea ch Cen e o Physics, Hunga ian Academy o Sciences, Budapes , Hunga y 143 Yale Uni e si y, New Ha en, Connec icu , Uni ed S a es 144 Yonsei Uni e si y, Seoul, Republic o Ko ea – 38 –