Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://lav01.sinp.msu.ru/~igor/seminar/HIN11-005_report_VLK.doc Äàòà èçìåíåíèÿ: Tue Feb 19 15:37:34 2013 Äàòà èíäåêñèðîâàíèÿ: Thu Feb 27 21:07:28 2014 Êîäèðîâêà: koi8-r

Èçìåðåíèå ïîòîêîâûõ ãàðìîíèê â PbPb ñòîëêíîâåíèÿõ ïðè 2.76 ÒýÂ

Â.Ë. Êîðîòêèõ

HIN-11-005 paper - CMS experiment


Ìîòèâàöèÿ
RHIC è LHC ýêñïåðèìåíòû èññëåäóþò áîëåå òîíêèå õàðàêòåðèñòèêè, ÷åì
ýëëèïòè÷åñêèé ïîòîê v2

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Èçó÷åíèå àíèçîòðîïèè ÷àñòèö, âîçíèêàþùåé èç-çà âçðûâà íà÷àëüíîé
ãîðÿ÷åé ñðåäû ÊÃÏ ïîçâîëÿåò òññäåäîâàòü å¸ òàêèå ñâîéñòâà, êàê:
1. Óðàâíåíèå ãèäðîäèíàìè÷åñêîãî ñîñòîÿíèÿ,
2. Îòíîøåíèå ñäâèãîâîé ïîïåðå÷íîé âÿçêîñòè ê ýíòðîïèè,
3. Ñêîðîñòü çâóêà â ñðåäå.
4. Íà÷àëüíûå óñëîâèÿ ñòîëêíîâåíèÿ òèïà ãëàóáåðîâñêîé êàðòèíû
âçàèìîäåéñòâèÿ èíäèâèäóàëüíûõ íóêëîíîâ èëè ýôôåêòîâ ãëþîííîãî
íàñûùåíèÿ â ìîäåëè â ìîäåëè CGS

Ýêñïåðèìåíòàëüíûå óñëîâèÿ ÑMS

2010 run of PbPb ñòîëêíîâåíèé íà ÁÀÊ â ýêñïåðèìåíòå CMS ïðè (sNN =
2:76 TeV

After all selections, 22.6 million events remained in the final
sample, corresponding to an integrated luminosity of approximately 3 µb-
1 .

Àçèìóòàëüíàÿ çàâèñèìîñòü çàðÿæåííûõ ÷àñòèö ïðè (0:3< pT < 8:0
GeV/c), centrality (0-70%), and pseudorapidity (|(|< 2.4).

In the forward region, two steel/quartz-_ber _Cerenkov Hadron
Forward (HF) calorimeters cover a pseudorapidity range of 2.9 < |(|<5.2,





Àíàëèç

4 ìåòîäà :
ìåòîä ïëîñêîñòè ðåàêöèè, ìåòîä êóìóëÿíòîâ, ìåòîä Ëè-ßíã íóëåé (LYZ)
è ìåòîä 2-õ ÷àñòè÷íûõ êîððåëÿöèé ñ òðèããåðíîé ÷àñòèöåé

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n=k*m - íîìåð ãàðìîíèêè,
m=1 îòáèðàåò âñå öåëûå ãàðìîíèêè n=1,2,. ïî îòíîøåíèþ ê (1,EP
m=2 îòáèðàåò ÷¸òíûå ãàðìîíèêè n=2,4,. ïî îòíîøåíèþ ê (2,EP
äëÿ m>2 ó÷èòûâàëèñü òîëüêî ãàðìîíèêè ñ k=1, n=m=3,4,. ïî îòíîøåíèþ
ê (m,EP()

 ìåòîäå ïëîñêîñòè ðåàêöèè óãëû âû÷èñëÿëèñü ñ èñïîëüçîâàíèåì
ïîïåðå÷íîé ýíåðãèè, â àçèìóòàëüíî ñèììåòðè÷íûõ ïåðåäíèõ àäðîííûõ
êàëîðèìåòðîâ (HF)

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Äëÿ êàæäîé ãàðìîíèêè m îïðåäåëÿëèñü 2 ïëîñêîñòè ñîáûòèÿ

(m(HF-)(-5 < |(|<-3) and (m(HF+)(3 < |(|<5)),

ïàðàìåòðû ïîòîêà âû÷èñëÿëèñü êàê

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ãäå äâîéíûå óãëîâûå ñêîáêè îçíà÷àþò: ïåðâûå - óñðåäíåíèå ïî
÷àñòèöàì ñ çàäàííûì (m è âòîðûå - ïî âñåì ñîáûòèÿì. Èñïîëüçîâàëàñü
ìèíèìàëüíàÿ ùåëü ïî ïñåâäîáûñòðîòå ìåæäó âñåìè ÷àñòèöàìè ïðè îïðåäåëåíèè
ïëîñêîñòè ðåàêöèè è âñåìè ÷àñòèöàìè äëÿ âû÷èñëåíèÿ ïàðàìåòðà ïîòîêà
ãàðìîíèêè m.

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Íà ðèñ.1 ïîêàçàíû àçèìóòàëüíûå ðàñïðåäåëåíèÿ ÷àñòèö äëÿ n=2,3,4,5
ïî îòíîøåíèþ ê óãëó ïëîñêîñòè ñîáûòèÿ â èíòåðâàëàõ |(((mEP|˜((m
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Èç ðèñóíêîâ âèäíî, ÷òî ãàðìîíèêà n=2 ñèëüíî, à îñòàëüíûå n=3,4,5
ñëàáî çàâèñÿò îò öåíòðàëüíîñòè

Êîíå÷íûå çíà÷åíèÿ ïàðàìåòðîâ ïîòîêà îïðåäåëÿëèñü ñ ó÷¸òîì ôàêòîðà
ïîïðàâêè íà ðàçðåøåíèå óãëà ïëîñêîñòè ñîáûòèÿ Rma {(m} ïî 3-ì îáëàñòÿì
ôàçîâîãî ïðîñòðàíñòâà (a)HF+, (b)HF- è îáëàñòè (c) CMS òðåêåðà
|(|<0.75
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Ìåòîä êóìóëÿíòîâ è LYZ ìåòîä íå çàâèñÿò îò èçìåðåíèÿ îðèåíòàöèè
ïëîñêîñòè ñîáûòèÿ íà îñíîâå ìíîãî ÷àñòè÷íûõ êîððåëÿöèé.
Ñíà÷àëà âû÷èñëÿëîñü îïîðíîå çíà÷åíèå ïàðàìåòðà ïîòîêà â øèðîêîì
ôàçîâîì îêíå (pT, () ÷åðåç ãåíåðèðóþùóþ ôóíêöèþÂ. Çàòåì
äèôôåðåíöèàëüíûé ïîòîê â óçêîì îêíå èçìåðÿëñÿ ïî îòíîøåíèþ ê îïîðíîìó
ïàðàìåòðó. ×òîáû èçáåæàòü àâòîêîððåëÿöèé, ÷àñòèöû äëÿ äèôôåðåíöèàëüíîãî
ïîòîêà èñêëþ÷àëèñü ïðè âû÷èñëåíèè îïîðíîãî ïàðàìåòðà.
 ìåòîäå LYZ èñïîëüçóåòñÿ ðàçëîæåíèå ïî êóìóëÿíòàì â âûñøåì
ïîðÿäêå, ÷òî ïîçâîëÿåò åñòåñòâåííûì îáðàçîì èññëåäîâàòü èñòèííîå
êîëëåêòèâíîå äâèæåíèå ðàñøèðÿþùåéñÿ ñðåäû. Ïî ïîëîæåíèþ íóëÿ
ãåíåðèðóþùåé ôóíêöèè îïðåäåëÿåòñÿ ïàðàìåòð èíòåãðàëüíîãî ïîòîêà äëÿ
÷àñòèö ñ (0:3< pT < 12:0 GeV/c) è (|(|< 2.4)., çàòåì äèôôåðåíöèàëüíûé
ïàðàìåòð ïîòîêà.
 îáîèõ ìåòîäàõ ïàðàìåòð
(((vm(M
îïðåäåëÿåò «íàä¸æíîñòü» ìåòîäà.
Ïðè ( < 0.8( < 0 îøèáêè ìåòîäà ñòàíîâÿòñÿ áîëüøå ñòàòèñòè÷åñêèõ.
Ýòîò ïàðàìåòð ìàë äëÿ î÷åíü öåíòðàëüíûõ ñòîëêíîâåíèé èç-çà ìàëîñòè vm
è ìàë äëÿ ïåðèôåðè÷åñêèõ ñòîëêíîâåíèé èç=çà ìàëîñòè ìíîæåñòâåííîñòè M.
Ïðèìåð ïðèâåä¸í â òàáëèöå.
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Ìåòîä 2-õ ÷àñòè÷íûõ êîððåëÿöèé ñ òðèããåðíîé ÷àñòèöåé èñïîëüçóåò
ôàêòîðèçàöèþ êîýôôèöèåíòîâ Ôóðüå ðàçëîæåíèÿ â îáëàñòè ìàëûõ ïîïåðå÷íûõ
èìïóëüñîâ íà ïðîèçâåäåíèå îäíî÷àñòè÷íûõ êîýôôèöèåíòîâ, èçìåðåííûõ
ìåòîäîì ïëîñêîñòè ðåàêöèè.

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Òåñò ïðîâåðÿëñÿ êàê â CMS, òàê è â ALICE, è áûëî ïîêàçàíî, ÷òî
ôàêòîðèçàöèÿ õîðîøî âûïîëíÿåòñÿ.
[44] S. Chatrchyan et al. (CMS), Eur.Phys.J. C72, 2012 (2012),
arXiv:1201.3158 [nucl-ex].
Äâóõ- ÷àñòè÷íûé ìåòîä (2Part - ïðèâåä¸í íà ðèñóíêàõ) àíàëîãè÷åí
âòîðîìó êóìóëÿíòó, ò.ê. åñëè äâå ÷àñòèöû êîððåëèðóþò ñ ïëîñêîñòüþ
ðåàêöèè, òî îíè êîððåëèðóþò è ìåæäó ñîáîé.

 ðàçäåëå C ïðèâåäåíû ðåçóëüòàòû äåòàëüíîãî èññëåäîâàíèÿ
ñèñòåìàòè÷åñêèõ îøèáîê, êîòîðûå íå ïðåâûøàþò íåñêîëüêèõ ïðîöåíòîâ äëÿ
ãàðìîíèê n=2,3,4 è íå áîëåå 11% äëÿ ãàðìîíèêè n=5. Ñòàòèñòè÷åñêèå
îøèáêè â áîëüøèíñòâå ñëó÷àåâ ìåíüøå èçîáðàæåíèÿ òî÷åê íà ðèñóíêàõ è
ìåíüøå ñèñòåìàòè÷åñêèõ.



Ýêñöåíòðèñèòåò â Ãëàóáåðîâñêîé ìîäåëè

Äëÿ èññëåäîâàíèÿ ïðîïîðöèîíàëüíîñòè ïàðàìåòðîâ ïîòîêà ïàðàìåòðó
ïðîñòðàíñòâåííîé àíèçîòðîïèè íóêëîíîâ (èäåÿ èäåàëüíîãî
ãèäðîäèíàìè÷åñêîãî ðàñøèðåíèÿ ñãóñòêà ÊÃÏ) â ðàìêàõ ìîäåëè Ãëàóáåðà
âû÷èñëåíû çíà÷åíèÿ ýêñöåíòðèñèòåòîâ ðàçëè÷íûõ ãàðìîíèê.
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Ïàðàìåòðû ðàñ÷¸òà âçÿòû ñîîòâåòñòâóþùèìè ÿäðó Pb è ñå÷åíèþ ðð
âçàèìîäåéñòâèÿ ïðè 2.76 ÃýÂ.
R = 6:62 fm, a = 0:546 fm, _(inel = 64 _ 5 mb.
Ýêñöåíòðèñèòåò âû÷èñëÿëñÿ ñëåäóþùèì îáðàçîì

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è ïðèâåä¸í â òàáëèöå
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Ðåçóëüòàòû

TABLE IX. Summary of experimental conditions for the data shown in
this report. The Figures column indicates the _figures in this report
where the data are shown. The pT range for previously published data
corresponds to that shown in the original report.
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Ðåçóëüòàòû ïî ýëëèïòè÷åñêîìó ïîòîêó v2 îïóáëèêîâàíû â ðàáîòå
[16] S. Chatrchyan et al. (CMS), Physical Review C 87, 014902 (2013)
arXiv:1204.1409 [nucl-ex].
ñ ïîäðîáíûì îïèñàíèåì ìåòîäîâ àíàëèçà.
Íèæå ïðèâåäåíû ñêîïèðîâàííûå ðèñóíêè èõ ïðåäâàðòèåëüíîãî òåêñòà
ðàáîòû CMS ïî ãàðìîíèêàì HIN-11-005.

v2
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Ðåçóëüòàò EPgap (on fig. as vm{(m} áëèçîê ê äâóõ- ÷àñòè÷íîìó
v2{2Part} çà èñêëþ÷åíèåì 70-80 %. Êóìóëÿíò 4-õ ÷àñòè÷íûé v2{4} è
v2{LYZ} áëèçêè ìåæäó ñîáîé. è ìåíüøå ïðåäûäóùèõ èç-çà âû÷åòà âêëàäîâ îò
ôëóêòóàöèè ýêñöåíòðèñèòåòà è íåïîòîêîâûõ ýôôåêòîâ. Îñîáåííî ýòî ñèëüíî
çàìåòíî äëÿ âûñîêèõ ãàðìîíèê.
















FIG. 4. (Color online) Azimuthal asymmetry v3 coefficient for indicated
methods.
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v3{4} è v3{2Part} ïî÷òè íå çàâèñÿò îò öåíòðàëüíîñòè, ÷òî ìîæåò áûòü
èíòåðïðåòèðîâàíî êàê íåçàâèñèìîñòü ôëóêòóàöèé ýêñöåíòðèñèòåòà îò
öåíòðàëüíîñòè, åñëè íå÷¸òíàÿ ãàðìîíèêà â îñíîâíîì ïðîïîðöèîíàëüíà
(scaling) ïðîñòðàíñòâåííîìó ýêñöåíòðèñèòåòó.





















FIG. 5. (Color online) Azimuthal asymmetry v4 coefficient for
indicated methods.

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v4{(4}, è v4{2Part} ñëàáî çàâèñÿò îò öåíòðàëüíîñòè.
v4{(2}, v4{5} and v4{LYZ} ñèëüíî çàâèñÿò îò öåíòðàëüíîñòè


















FIG. 6. (Color online) Azimuthal asymmetry v5 coefficient for
indicated methods.

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Ãàðìîíèêà ñ n=5 äëÿ v5{(5}, è v5{2Part} òàêæå ñëàáî çàâèñèò îò
öåíòðàëüíîñòè

Comparison with other results.

"The odd harmonics are expected to arise entirely from fluctuations
in the initial energy density, while higher order even harmonics will
reflect both fluctuations and the influence of the initial state
geometry. Recent theory calculations are exploring these effects on an
event-by-event basis."












FIG. 9. (Color online) Comparison of the v3 results of the ALICE, ATLAS and
CMS collaborations. References given in Table IX.
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Figure 9 compares results of the three experiments for the pT-
dependent v3 coefficient. The ATLAS results for v3{(3}, are consistently
lower than the CMS results for all but the most peripheral centrality
bin. Good agreement is seen between the two-particle correlation results
of the CMS and ALICE collaborations. This suggests that the
pseudorapidity gap of |((| > 0:8 employed by ALICE is already sufficient
to remove most of the di-jet contribution to these correlations.














The comparison of v4 (see Fig. 10) and v5 (see Fig. 11) values
found by the three experiments lead to similarly consistent results.

FIG. 10. (Color online) Comparison of the v4 results of the ALICE, ATLAS
and CMS collaborations.
FIG. 11. (Color online) Comparison of the v5 results of the ALICE, ATLAS
and CMS collaborations.
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Figure 13 shows the vn{(n}, values as a function of the harmonic
order n for five different pT ranges and for four different centrality
ranges. For all but the most central events, the vn values are found to
decrease with increasing harmonic number.
Considerable attention has been paid to the v4/v22 ratio [18, 20,
33, 42, 57-59] in characterizing the azimuthal anisotropy. It is now
recognized that the value of this ratio of 0.5, obtained through ideal
hydrodynamics [58], is strongly affected by flow fluctuations and non-
flow correlations and that comparisons of theory to the experimental
results needs to account for how the results of the different analysis
methods relate to the event-by-event vn asymmetry [33].
The CMS results are consistently higher than PHENIX.

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Conclusions
The data presented in this paper help to further establish the
pattern of azimuthal particle emission at LHC energies. The results are
directly applicable to the study of the initial spatial asymmetry, time
development, and shear viscosity of the medium form in ultra-
relativistic heavy-ion collisions. Although a number of theory
investigations have significantly increased our understanding of the
initial conditions and hydrodynamics that lead to the experimentally
observed asymmetry patterns, the method dependent deference found for
the flow harmonics emphasize the need for calculations that account for
these differences.





Other results
Èíòåãðàëüíûå vn îò öåíòðàëüíîñòè.
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vn îò ïñåâäîáûñòðîòû
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Îòíîøåíèå vn ê RMS öåíòðàëüíîñòè
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