删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

Effects of centrality fluctuation and deuteron formation on the proton number cumulant in Au+Au coll

本站小编 Free考研考试/2022-01-01

闂傚倸鍊搁崐宄懊归崶顒夋晪鐟滃繘鍩€椤掍胶鈻撻柡鍛█閵嗕礁鈻庨幘鍐插敤濡炪倖鎸鹃崑鐔兼偘閵夆晜鈷戦柛锔诲幖閸斿銇勯妸銉﹀櫧濠㈣娲樼换婵嗩潩椤撶姴骞嶉梻浣告啞閹稿棝宕ㄩ鐙€鍋ч梻鍌欑劍婵炲﹪寮ㄩ柆宥呭瀭闁割偅娲栨闂佸憡娲﹂崹鎵不濞戙垺鐓曢柟鎹愬皺閸斿秹鏌涚€f柨鍠氬〒濠氭煏閸繄绠抽柛鎺撳閳ь剚顔栭崰鏍ㄦ櫠鎼淬劌绠查柕蹇曞Л閺€浠嬫倵閿濆簼绨介柛鏃撶畱椤啴濡堕崱妤冪懆闁诲孩鍑归崜娑氬垝婵犳艾唯闁挎棁妗ㄧ花濠氭⒑閸濆嫬鏆婇柛瀣崌閺屾稒鎯旈垾铏瘣闂佷紮绲块崗妯讳繆閻戣棄唯闁靛繆鍓濋弶鍛婁繆閻愵亜鈧牕顫忔繝姘仱闁哄倸绨遍弸鏃€淇婇娑氭菇濞存粍绮撻弻銊╁棘閸喒鎸冮梺闈涙椤ㄥ﹤顫忔繝姘<婵﹩鍏橀崑鎾绘倻閼恒儱鈧潡鏌ㄩ弮鍫熸殰闁稿鎸剧划顓炩槈濡娅ч梺娲诲幗閻熲晠寮婚悢鍏煎€绘慨妤€妫欓悾鐑芥⒑缁嬪灝顒㈡い銊ユ婵$敻宕熼姘棟闂佸壊鐓堥崰鎺楀箰閸愵喗鈷戦柛娑樷看濞堟洜鈧厜鍋撻柟闂寸缁犳牗淇婇妶鍌氫壕闂佸疇妫勯ˇ顖炲煝鎼达絺鍋撻敐搴″缂佹劖顨婂缁樻媴閸濄儻绱炵紓渚囧櫘閸ㄦ媽鐏嬮梺鍛婂姦閸犳牠鎷戦悢鍝ョ闁瑰瓨鐟ラ悘鈺呭船椤栫偞鈷戦梻鍫熺〒缁犳岸鏌涢幘瀵哥疄闁诡喚鏁婚弫鍐焵椤掑嫬鐓橀柟杈鹃檮閸婄兘鏌熺紒妯虹瑲闁稿⿴鍨堕幃妤呭礂婢跺﹣澹曢梻浣哥秺濡法绮堟笟鈧幏鎴︽偄閸忚偐鍘梺鍓插亝缁诲秴危閸濄儳纾奸柣娆愮懃濞诧箓鎮¢弴鐔翠簻妞ゆ挾鍠庨悘銉╂煛鐎n剙鏋戠紒缁樼洴瀹曠厧鈹戦崼婵堝幗婵犳鍠栭敃銊モ枍閿濆洦顫曢柟鐑樺殾閻斿吋鍋傞幖瀛樕戠€氭盯姊婚崒娆掑厡閺嬵亞绱掗妸锔姐仢鐎规洘鍔曡灃闁告劑鍔岄悘濠傗攽閻愬弶顥為柛鏃€娲滃▎銏ゆ倷閻戞ḿ鍘甸梻渚囧弿缁犳垶鏅堕悧鍫涗簻闁哄啠鍋撻悽顖椻偓鎰佹綎婵炲樊浜濋崵鍐煃閸︻厼浜鹃悗姘洴濮婃椽宕ㄦ繝鍐ㄩ瀺闂佺儵鏅╅崹鍫曟偘椤旂晫绡€闁稿本顨嗛弬鈧梺璇插嚱缂嶅棝宕戦崱娑樺偍濞寸姴顑嗛埛鎴犵磽娴e厜妫ㄦい蹇撳閸ゆ洟鏌ら幖浣规锭缂佸墎鍋ら弻娑㈠即閵娿儱绠伴梺绋款儐閹搁箖骞夐幘顔肩妞ゆ帒鍋嗗Σ浼存⒒娴g懓顕滄繛鎻掔箻瀹曡绂掔€n亝鐎梺瑙勫婢ф宕愭搴f/闁绘鐓鍛洸濡わ絽鍟悡銉︾節闂堟稒顥㈡い搴㈩殔闇夋繝濠傚暙閳锋梻绱掓潏銊ユ诞妤犵偛顦遍埀顒婄秵閸撴稖鈪甸梻鍌欑閹碱偊鎯夋總绋跨獥闁归偊鍏楃紓姘剁叓閸ャ劍鐓熼柛瀣嚇閺屾盯骞囬妸锔界彟闂侀€炲苯澧紒澶嬫尦閳ユ棃宕橀鍢壯囨煕閳╁厾顏堝汲濡ゅ懏鈷戠痪顓炴噺閻濐亪鏌熼悷鐗堝濞e洤锕獮姗€顢欓懖鈺婂敽闂備浇顫夐幆宀勫储娴犲纾介柣銏犳啞閳锋垿鏌熼鍡楀椤╀即姊虹粙娆惧剰婵☆偅绻冩穱濠勨偓娑欋缚缁♀偓闂佺ǹ鏈〃鍡涘棘閳ь剟姊绘担铏瑰笡闁挎洍鏅犲畷鎴﹀礋椤掑偆娲告俊銈忕到閸燁垶鍩涢幋锔界厱婵炴垶锕崝鐔兼煃閽樺妯€闁哄矉绲鹃獮濠囨煕閺冣偓閸ㄧ敻顢氶敐澶婅摕闁靛鍠楅弲銏ゆ⒑閸涘﹥澶勯柛鎾寸懇閸┾偓妞ゆ巻鍋撻柣鏍с偢瀵鏁愭径濠勭杸濡炪倖鎸鹃崑鐔虹矈閻戣姤鈷戦柟鎯板Г閺佽鲸鎱ㄦ繝鍜佹綈缂佸矁椴哥换婵嬪礋椤忓懎濯伴梻浣呵归張顒勬嚌妤e喛缍栭柛銉墯閳锋垿鏌涘┑鍡楊伀闁绘帟娉曠槐鎺旂磼濡偐鐣甸梺浼欑秮閺€杈╃紦娴犲绀堥柛娆忣槹濞呭洭姊绘笟鈧ḿ褏鎹㈤幒鎾村弿閻庨潧鎽滄稉宥夋煙濞堝灝鏋ょ痪鍙ョ矙閺屾稓浠﹂崜褎鍣梺鍛婃煥缁夌敻濡甸崟顖毼╅柕澶涚畱濞堟鏌﹀Ο鑽ょ疄婵﹤顭峰畷濂告偄閹巻鍋撻幒妤佺厸闁糕槅鍙冨顕€鏌熸笟鍨妞ゎ偅绮撳畷鍗炍旈埀顒佸鎼达絿纾藉ù锝囨嚀閺佸墽绱掗煫顓犵煓婵犫偓娓氣偓濮婃椽骞愭惔锝囩暤闁诲孩鍑归崹鍫曘€佸Δ鍛亜閻犱礁鐏濈紞濠囧箖閳╁啯鍎熼柕蹇曞У閻忓孩绻濆▓鍨灈闁挎洏鍎遍—鍐寠婢跺本娈鹃梺闈涒康婵″洨寮ч埀顒勬⒑缁嬫寧婀扮紒顔奸叄楠炲﹪宕卞Ο鑲╃槇缂佸墽澧楄摫妞ゎ偄锕弻娑氣偓锝庝簼閸d粙鏌熼獮鍨伈鐎规洖銈告俊鐤槻缂佷緤绠撳娲捶椤撶儐鏆┑鐘灪閿曘垽寮荤€n喖鐐婃い鎺嶈兌閸樻悂姊洪幖鐐插姉闁哄懏鐩鎼佸箣閻愮數顔曢梺鍛婁緱閸犳碍鏅堕鍌滅<缂備焦岣块埊鏇熺箾閻撳海绠荤€规洘绮忛ˇ瀵告偖閿濆棛绡€闁汇垽娼ф禒婊堟煙闁垮鐏╃紒杈╁仦閹峰懘宕妷锔筋啎闂備胶鍋ㄩ崕鏌ュ几婵傜ǹ閱囨い蹇撶墛閻撴洘銇勯幇鈺佲偓鏇㈠几鎼淬劍鐓冪憸婊堝礈濞戙垹鏋佸┑鐘宠壘閽冪喖鏌ㄥ┑鍡╂Ц妞ゎ偄鎳橀弻锝呂熼崫鍕€庣紓渚囧枤閺佽顫忓ú顏勭闁绘劖绁撮崑鎾诲箛閺夎法锛涢梺鐟板⒔缁垶鍩涢幒鎳ㄥ綊鏁愰崼顐g秷闂佺ǹ顑囨繛鈧柡灞剧洴瀵剛鎹勯妸鎰╁€濋弻鐔肩嵁閸喚浼堥悗瑙勬礈閸犳牠銆佸鈧幃娆撴嚑椤戝灝鏋堥梻鍌欐祰瀹曞灚鎱ㄩ弶鎳ㄦ椽濡堕崪浣告濡炪倖甯掔€氼剛鐚惧澶嬬厱閻忕偟铏庡▓鏂棵瑰⿰鍫㈢暫闁哄被鍔岄埞鎴﹀幢濞戞墎鍋撳Δ鈧…鑳槺闁告濞婂濠氬Ω閵夈垺顫嶉梺鎯ф禋閸嬪嫰顢旈敓锟�
547闂傚倸鍊搁崐鎼佸磹閹间礁纾瑰瀣捣閻棗霉閿濆浜ら柤鏉挎健濮婃椽顢楅埀顒傜矓閺屻儱鐒垫い鎺嗗亾闁稿﹤婀辩划瀣箳閺傚搫浜鹃柨婵嗙凹缁ㄤ粙鏌ㄥ☉娆戞创婵﹥妞介幃鐑藉级鎼存挻瀵栫紓鍌欑贰閸n噣宕归崼鏇炴槬婵炴垯鍨圭粻铏繆閵堝嫯鍏岄柛姗€浜跺娲传閸曨剙顦╁銈冨妼濡鍩㈠澶婂窛閻庢稒岣块崢浠嬫椤愩垺绁紒鎻掋偢閺屽洭顢涢悙瀵稿幐閻庡厜鍋撻悗锝庡墮閸╁矂鏌х紒妯煎⒌闁哄苯绉烽¨渚€鏌涢幘璺烘灈鐎殿喚绮换婵嬪炊閵婏附鐝冲┑鐘灱濞夋盯鏁冮敃鍌涘仾闁搞儺鍓氶埛鎴︽偡濞嗗繐顏╃紒鈧崘鈹夸簻闁哄洤妫楅幊鎰版儗閸℃稒鐓曢柟鑸妽閺夊搫霉濠婂嫮鐭掗柣鎿冨亰瀹曞爼濡搁敃鈧棄宥咁渻閵堝啫鍔滅紒顔芥崌瀵鏁愭径濠勵啋闁诲酣娼ч幉锟犲礆濞戞ǚ鏀芥い鏃傘€嬮弨缁樹繆閻愯埖顥夐柣锝呭槻铻栭柛娑卞幘椤ρ囨⒑閸忚偐銈撮柡鍛洴瀹曠敻骞掑Δ浣叉嫽婵炶揪绲介幉锟犲箟閹间焦鐓曢柨婵嗗暙閸旓妇鈧娲橀崹鍨暦閻旂⒈鏁嶆繛鎴灻奸幃锝夋⒒娴h櫣甯涢柛銊ュ悑閹便劑濡舵径濠勬煣闂佸綊妫块悞锕傛偂閵夆晜鐓熼柡鍥╁仜閳ь剙婀遍埀顒佺啲閹凤拷1130缂傚倸鍊搁崐鎼佸磹閹间礁纾归柟闂寸绾剧懓顪冪€n亝鎹i柣顓炴閵嗘帒顫濋敐鍛闂佽姤蓱缁诲啴濡甸崟顖氬唨闁靛ě鍛帓闂備焦妞块崢浠嬪箲閸ヮ剙钃熼柨婵嗩槸椤懘鏌曡箛濠冩珕婵絽鐭傚铏圭矙濞嗘儳鍓遍梺鍦嚀濞层倝鎮鹃悿顖樹汗闁圭儤绻冮弲婵嬫⒑閹稿海绠撴繛璇х畵椤㈡ɑ绻濆顓涙嫽婵炴挻鍩冮崑鎾绘煃瑜滈崜娑㈠磻濞戙垺鍤愭い鏍ㄧ⊕濞呯娀鏌涘▎蹇fФ濞存粍绮嶉妵鍕箛閳轰胶鍔村┑鈥冲级濡炰粙寮诲☉銏″亹閻犲泧鍐х矗婵$偑鍊栭幐鎼佸触鐎n亶鍤楅柛鏇ㄥ墰缁♀偓闂佸憡鍔﹂崢楣冨矗閹达附鈷掗柛灞剧懅缁愭棃鏌嶈閸撴盯宕戝☉銏″殣妞ゆ牗绋掑▍鐘绘煙缂併垹鏋熼柣鎾寸洴閹﹢鎮欓惂鏄忣潐閺呭爼鎳犻钘変壕闁割煈鍋呯欢鏌ユ倵濮樼厧娅嶉柛鈹惧亾濡炪倖甯掗敃锔剧矓闂堟耽鐟扳堪閸曨厾鐓夐梺鎸庣箘閸嬬偤骞嗛弮鍫濈參闁逞屽墴瀵劍绂掔€n偆鍘介梺褰掑亰閸ㄤ即鎯冮崫鍕电唵鐟滃酣鎯勯鐐茶摕婵炴垯鍨规儫闂侀潧锛忛崒婵囶€楅梻鍌欐缁鳖喚寰婇崸妤€绀傛慨妞诲亾鐎殿噮鍋婇獮妯肩磼濡桨姹楅梻浣藉亹閳峰牓宕滈敃鈧嵄濞寸厧鐡ㄩ悡鐔兼煟閺傛寧鎲搁柣顓烇功缁辨帞绱掑Ο铏诡儌闂佸憡甯楃敮鎺楀煝鎼淬劌绠荤€规洖娲ら埀顒傚仱濮婃椽宕橀崣澶嬪創闂佸摜鍠嶉崡鎶藉极瀹ュ應鍫柛鏇ㄥ幘閻﹀牓姊洪棃娑㈢崪缂佹彃澧藉☉鍨偅閸愨晝鍙嗛梺鍝勬祩娴滎亜顬婇鈧弻锟犲川椤愩垹濮﹀┑顔硷功缁垶骞忛崨鏉戝窛濠电姴鍊瑰▓姗€姊洪悡搴d粚闁搞儯鍔庨崢杈ㄧ節閻㈤潧孝闁哥喓澧楅弲鑸垫綇閳哄啰锛濋梺绋挎湰缁嬫帒鐣峰畝鍕厵缂佸灏呴弨鑽ょ磼閺冨倸鏋涢柛鈺嬬節瀹曟帒鈽夋潏顭戞闂佽姘﹂~澶娒洪敂鐣岊洸婵犻潧顑呯粻顖炴煕濞戝崬鐏¢柛鐘叉閺屾盯寮撮妸銉ョ閻炴碍鐟╁濠氬磼濮橆兘鍋撴搴g焼濞达綁娼婚懓鍧楁⒑椤掆偓缁夋挳宕掗妸褎鍠愰柡鍐ㄧ墕缁犳牗绻涘顔荤盎閹喖姊虹€圭姵銆冮柤鍐茬埣椤㈡瑩宕堕浣叉嫼闂佸憡鎸昏ぐ鍐╃濠靛洨绠鹃柛娆忣槺婢х敻鏌熼鎯т槐鐎规洖缍婇、鏇㈡偐鏉堚晝娉块梻鍌欒兌閹虫捇顢氶銏犵;婵炴垯鍩勯弫瀣節婵犲倹鍣界痪鍓у帶闇夐柨婵嗘噺閹牊銇勯敐鍛仮闁哄本娲熷畷鎯邦槻妞ゅ浚鍘介妵鍕閳╁啰顦版繝娈垮枓閸嬫捇姊虹€圭姵銆冪紒鈧担鍦彾濠㈣埖鍔栭埛鎺懨归敐鍥ㄥ殌妞ゆ洘绮庣槐鎺斺偓锝庡亜濞搭喚鈧娲樼换鍌炲煝鎼淬劌绠婚悹楦挎閵堬箓姊虹拠鎻掑毐缂傚秴妫濆畷鎶筋敋閳ь剙顕i銏╁悑闁糕剝鐟ч惁鍫熺節閻㈤潧孝闁稿﹨顫夐崚濠囧礂闂傚绠氶梺鍝勮閸庢煡寮潏鈺冪<缂備焦岣跨粻鐐烘煙椤旇崵鐭欐俊顐㈠暙閳藉螖娴gǹ顎忛梻鍌氬€烽悞锕傚箖閸洖绀夌€光偓閳ь剛妲愰悙瀵哥瘈闁稿被鍊曞▓銊ヮ渻閵堝棗濮傞柛濠冾殜閹苯鈻庨幇顏嗙畾濡炪倖鍔戦崐鏍汲閳哄懏鐓曢幖瀛樼☉閳ь剚顨婇獮鎴﹀閻橆偅鏂€闁诲函缍嗘禍鐐哄磹閻愮儤鈷戦梻鍫熻儐瑜版帒纾块柡灞诲労閺佸洦绻涘顔荤凹闁抽攱鍨块弻娑樷攽閸℃浼屽┑鈥冲级閹倿寮婚敐鍛傛梹鎷呴搹鍦帨闁诲氦顫夊ú姗€宕归崸妤冨祦闁圭儤鍤﹂弮鍫濈劦妞ゆ帒瀚憴锔炬喐閻楀牆绗氶柣鎾寸洴閺屾盯骞囬埡浣割瀷婵犫拃鍕创闁哄矉缍侀獮妯虹暦閸モ晩鍟嬮梻浣告惈閺堫剟鎯勯鐐叉槬闁告洦鍨扮粈鍐煃閸濆嫬鏋ゆ俊鑼厴濮婄粯鎷呴崨闈涙贡閹广垽骞囬悧鍫濆壎闂佸吋绁撮弲婊堬綖閺囥垺鐓欓柣鎴烇供濞堛垽鏌℃担闈╄含闁哄本绋栫粻娑㈠箼閸愨敩锔界箾鐎涙ḿ鐭掔紒鐘崇墵楠炲啫煤椤忓嫮顔婇悗骞垮劚濡盯濡堕弶娆炬富闁靛牆楠告禍婊勩亜閿旂偓鏆柣娑卞櫍瀹曞崬鈽夊Ο娲绘闂佸湱鍘ч悺銊╁箰婵犳熬缍栫€广儱顦伴埛鎴︽煕閿旇骞栭柛鏂款儔閺屾盯濡搁妸锔惧涧缂備焦姊婚崰鏍ь嚕閹绢喗鍋勯柧蹇氼嚃閸熷酣姊洪崫鍕垫Ц闁绘妫欓弲鑸电鐎n亞鐣烘繝闈涘€搁幉锟犳偂濞戙垺鐓曟繝濞惧亾缂佲偓娴e湱顩叉繝濠傜墕绾偓闂備緡鍓欑粔鐢告偂閺囩喆浜滈柟閭﹀枛瀛濋梺鍛婃⒐缁捇寮婚敐澶婄閻庢稒岣块ˇ浼存⒑閸濆嫮鐏遍柛鐘崇墵楠炲啫饪伴崗鍓у枔閹风娀寮婚妷褉鍋撳ú顏呪拻濞达絽鎳欒ぐ鎺濇晞闁搞儯鍔庣粻楣冩煃瑜滈崜鐔煎蓟閿涘嫪娌柣锝呯潡閵夛负浜滅憸宀€娆㈠璺鸿摕婵炴垶绮庨悿鈧梺鍝勫暙閸婂爼鍩€椤掍礁绗氱紒缁樼洴瀹曢亶骞囬鍌欐偅婵$偑鍊ら崑鍛崲閸曨垰绠查柛鏇ㄥ€嬪ú顏嶆晜闁告粌鍟伴懜鐟扳攽閻樿尙妫勯柡澶婄氨閸嬫捁顦寸€垫澘锕ョ粋鎺斺偓锝庝簽閺屽牆顪冮妶鍡欏⒈闁稿绋撶划濠氭偐閾忣偄寮垮┑鈽嗗灥椤曆囥€傞幎鑺ョ厱閻庯綆鍋呭畷宀勬煟濞戝崬娅嶇€规洖缍婇、娆撴偂鎼搭喗缍撻梻鍌氬€风粈渚€骞楀⿰鍫濈獥闁规儳顕粻楣冩煃瑜滈崜娑㈠焵椤掑喚娼愭繛鍙夛耿瀹曞綊宕稿Δ鍐ㄧウ濠碘槅鍨伴惃鐑藉磻閹炬枼妲堟繛鍜佸弾娴滎亪銆侀幘璇茬缂備焦菤閹疯櫣绱撻崒娆戝妽闁挎岸鏌h箛銉х暤闁哄被鍔岄~婵嬫嚋閻㈤潧甯楅柣鐔哥矋缁挸鐣峰⿰鍐f闁靛繒濮烽敍娑㈡⒑缂佹ɑ鈷掗柛妯犲洦鍊块柛顭戝亖娴滄粓鏌熼悜妯虹仴闁哄鍊栫换娑㈠礂閻撳骸顫掗梺鍝勭灱閸犳牠銆佸▎鎾村殐闁宠桨鑳堕崢浠嬫煟鎼淬値娼愭繛鍙壝叅闁绘梻顑曢埀顑跨閳藉濮€閳ユ枼鍋撻悜鑺ョ厾缁炬澘宕晶顔尖攽椤曞棝妾ǎ鍥э躬閹瑩顢旈崟銊ヤ壕闁哄稁鍘奸崹鍌氣攽閸屾簱鍦閸喒鏀介柣妯虹枃婢规ḿ绱掗埀顒勫磼閻愭潙鈧爼鏌i幇顓熺凡閻庢艾楠搁湁婵犲﹤瀚惌鎺楁煛瀹€鈧崰鏍嵁閸℃凹妲鹃梺鍦櫕婵炩偓闁哄本绋掔换婵嬪礃閵娿儺娼氶梻浣告惈閻ジ宕伴弽顓溾偓浣糕枎閹炬潙娈愰梺瀹犳〃閼冲爼宕㈡禒瀣厽閹兼番鍊ゅḿ鎰箾閼碱剙鏋戠紒鍌氱Ч瀹曞ジ寮撮悩鑼偊闂備焦鎮堕崕娲礈濞嗘劕鍔旈梻鍌欑窔濞佳囁囬銏犵9闁哄洠鎳炴径濠庢僵妞ゆ垼濮ら弬鈧梻浣虹帛閸旀﹢宕洪弽顑句汗鐟滃繒妲愰幒妤佸殤妞ゆ巻鍋撳ù婊冨⒔缁辨帡宕掑姣櫻囨煙瀹曞洤浠卞┑锛勬焿椤т焦绻涢弶鎴濐伃婵﹥妞介獮鎰償閵忣澁绱╅梻浣呵归鍡涘箲閸ヮ灛娑欐媴閻熸壆绐為梺褰掑亰閸橀箖宕㈤柆宥嗩棅妞ゆ劑鍨烘径鍕箾閸欏澧遍柡渚囧櫍瀹曞ジ寮撮悢鍝勫箥闂備胶枪缁绘劙宕ョ€n喖纾归柟鎵閻撴盯鎮橀悙鍨珪閸熺ǹ顪冮妵鍗炲€荤粣鏃堟煛鐏炲墽顬肩紒鐘崇洴瀵噣宕掑Δ渚囨綌闂傚倸鍊稿ú銈壦囬悽绋胯摕婵炴垯鍨瑰敮濡炪倖姊婚崢褔锝為埡鍐<闁绘劦鍓欓崝銈夋煏閸喐鍊愮€殿喖顭峰鎾偄閾忓湱妲囬梻濠庡亜濞诧箑煤濠婂牆姹查柣妯烘▕濞撳鏌曢崼婵囶棡缂佲偓婢跺⿴娓婚悗娑櫳戦崐鎰殽閻愯尙澧﹀┑鈩冩倐婵¢攱鎯旈敐鍛亖缂備緡鍠楅悷鈺佺暦瑜版帩鏁婄痪鎷岄哺缂嶅秹姊婚崒姘偓鐑芥嚄閼哥數浠氭俊鐐€栭崹闈浳涘┑瀣祦闁归偊鍘剧弧鈧┑顔斤供閸撴盯顢欓崱娑欌拺闁告稑锕g欢閬嶆煕閵娾晙鎲剧€规洑鍗冲畷鍗炩槈濞嗘垵骞堥梻浣告惈濞层垽宕濈仦鐐珷濞寸厧鐡ㄩ悡娑㈡煕閳╁厾顏堝传閻戞ɑ鍙忓┑鐘插鐢盯鏌熷畡鐗堝殗鐎规洦鍋婂畷鐔碱敃閿涘嫬绗¢梻浣筋嚙鐎涒晠顢欓弽顓炵獥婵°倕鎳庣壕鍨攽閸屾簱瑙勵攰闂備礁婀辨晶妤€顭垮Ο鑲╃焼闁告劏鏂傛禍婊堢叓閸ャ劍灏版い銉уТ椤法鎹勯崫鍕典痪婵烇絽娲ら敃顏呬繆閹壆鐤€闁哄洨鍋涢悡鍌炴⒒娴e憡鎲搁柛锝冨劦瀹曞湱鎹勯搹瑙勬闂佺鎻梽鍕磻閹邦喚纾藉ù锝堢柈缂傛岸鏌涘鈧禍璺侯潖濞差亜妫橀柕澶涢檮閻濇棃姊洪崫銉ユ珡闁稿鎳橀獮鍫ュΩ閳轰胶鍔﹀銈嗗笒鐎氼參鍩涢幋鐘电<閻庯綆鍋掗崕銉╂煕鎼淬垹濮嶉柡宀€鍠撶划娆忊枎閸撗冩倯婵°倗濮烽崑娑氭崲濡櫣鏆﹂柕濞р偓閸嬫挸鈽夊▍顓т簼缁傛帡骞嗚濞撳鏌曢崼婵囶棤濠⒀屽墴閺屻倝鎮烽弶搴撴寖缂備緡鍠栭…鐑界嵁鐎n喗鏅滈悷娆欑稻鐎氳棄鈹戦悙鑸靛涧缂佽弓绮欓獮澶愭晸閻樿尙鐣鹃梺鍓插亖閸庢煡鎮¢弴鐐╂斀闁绘ɑ褰冮鎰版煕閿旇骞栫€殿喗鐓″缁樼瑹閳ь剙岣胯閹广垽宕奸妷銉э紮闂佸搫娲㈤崹娲磹閸ф鐓曟い顓熷灥娴滄牕霉濠婂嫮鐭掗柡宀€鍠撻埀顒傛暩鏋ù鐘崇矋閵囧嫰寮撮悢铏圭厒缂備浇椴哥敮妤呭箯閸涱垱鍠嗛柛鏇ㄥ幖閸ゆ帗淇婇悙顏勨偓銈夊矗閳ь剚绻涙径瀣妤犵偛顦甸獮姗€顢欓懖鈺婃Ч婵$偑鍊栧濠氬磻閹惧墎妫柣鎰靛墮閳绘洟鏌熼绛嬫當闁崇粯鎹囧畷褰掝敊閻e奔澹曢梻鍌欐祰濡椼劎绮堟笟鈧垾锕傛倻閽樺)銉ッ归敐鍥┿€婃俊鎻掔墛娣囧﹪顢涘☉姘辩厒闂佸摜濮撮柊锝夊箖妤e啫鐒洪柛鎰硶閻绻涙潏鍓у埌濠㈢懓锕よ灋婵犲﹤瀚弧鈧梺姹囧灲濞佳勭閳哄懏鐓欐繛鑼额唺缁ㄧ晫绱掓潏鈺佷槐闁糕斁鍋撳銈嗗笂闂勫秵绂嶅⿰鍕╀簻闁规壋鏅涢悞鐑樹繆椤栨浜鹃梻鍌欐祰椤曟牠宕抽婊勫床婵犻潧顑呴弰銉╂煃瑜滈崜姘跺Φ閸曨垰绠抽柟瀛樼箥娴犻箖姊洪幎鑺ユ暠閻㈩垽绻濆璇测槈濮橆偅鍕冮梺纭咁潐閸旀洟藟濠靛鈷戦梺顐ゅ仜閼活垶宕㈤崫銉х<妞ゆ梻鏅幊鍥煏閸℃洜顦﹂柍璇查叄楠炲洭顢欓崜褎顫岄梻鍌欑閹测€趁洪敃鍌氱闁挎洍鍋撳畝锝呮健閹垽宕楃亸鏍ㄥ闂備礁鎲¢幐鏄忋亹閸愨晝顩叉繝闈涙川缁犻箖鏌涘▎蹇fШ濠⒀嗕含缁辨帡顢欓崹顔兼優缂備浇椴哥敮鎺曠亽闂傚倵鍋撻柟閭﹀枤濞夊潡姊婚崒娆戭槮婵犫偓闁秴纾婚柟鍓х箑缂傛碍绻涢崱妯诲濠㈣泛饪村ḿ鈺呮煠閸濄儲鏆╅柛姗€浜堕弻锝嗘償椤栨粎校闂佺ǹ顑呴幊鎰閸涘﹤顕遍悗娑欋缚閸樼敻鎮楅悷鏉款伀濠⒀勵殜瀹曠敻宕堕埞鎯т壕閻熸瑥瀚粈鍫ユ煕韫囨棑鑰块柕鍡曠铻i悶娑掑墲閺佺娀姊虹拠鈥崇€婚柛灞惧嚬濡粍绻濋悽闈浶ラ柡浣告啞閹便劑寮堕幊銊︽そ閺佸啴宕掑鎲嬬串闂備礁澹婇悡鍫ュ磻閸℃瑧涓嶅Δ锝呭暞閻撴瑩鎮楀☉娆嬬細缂佺姵锕㈤弻锛勨偓锝庝簻閺嗙喓绱掓潏銊ユ诞闁糕斁鍋撳銈嗗笒閸婄敻宕戦幘缁樻櫜閹肩补鍓濋悘宥夋⒑缂佹ɑ灏柛鐔跺嵆楠炲绮欐惔鎾崇墯闂佸壊鍋呯换鍕囪閳规垿鎮欓弶鎴犱桓濠殿喗菧閸旀垿骞嗗畝鍕耿婵$偞娲栫紞濠囧极閹版澘閱囬柣鏃傝ˉ閸嬫捇宕橀鐣屽幗闂佸湱鍎ら崺濠囩叕椤掑嫭鐓涚€光偓閳ь剟宕版惔銊ョ厺闁规崘顕ч崹鍌涖亜閺冨倹娅曞ù婊勫姍濮婄粯鎷呴崨闈涚秺椤㈡牠宕卞☉妯碱唶闂佸綊妫跨粈渚€鎮¢垾鎰佺唵閻犲搫鎼ˇ顒勬煕鐎n偅宕岀€规洜鍏橀、姗€鎮欓幇鈺佸姕闁靛洤瀚伴弫鍌炲垂椤旇偐銈繝娈垮枛閿曘儱顪冩禒瀣摕闁告稑鐡ㄩ崐鐑芥煠閼圭増纭炬い蹇e弮濮婃椽宕ㄦ繛鎺濅邯楠炲鏁嶉崟顒€搴婂┑鐐村灟閸ㄥ湱鐥閺岀喓鈧數枪娴犳粓鏌$€n剙孝妞ゎ亜鍟存俊鍫曞礃閵娧傜棯闂備焦瀵уú蹇涘垂瑜版帗鍋╅柣鎴犵摂閺佸啴鏌ㄩ弴妤€浜鹃柛鐑嗗灦閹嘲饪伴崘顏嗕紘缂備緡鍣崢钘夘嚗閸曨剛绠鹃柣鎰靛墯閺夋悂姊洪崷顓炲妺濠电偛锕ら悾鐑藉箛閺夎法顔掔紓鍌欑劍閿氶柍褜鍓欏ḿ锟犲蓟閵娾晛绫嶉柍褜鍓欓悾宄拔熺紒妯哄伎闂佹儳娴氶崑鍛村矗韫囨柧绻嗘い鏍ㄦ皑娴犮垽鏌i幘鏉戝闁哄矉缍侀獮妯虹暦閸モ晩鍟嬮梻浣告惈閺堫剟鎯勯鐐叉槬闁告洦鍨扮粈鍐煃閸濆嫬鏋ゆ俊鑼跺煐娣囧﹪鎮欓鍕ㄥ亾瑜忛幏瀣晲閸℃洜绠氶梺鎼炲労閸撴瑩鎮為崹顐犱簻闁瑰搫妫楁禍鎯р攽閻橆偄浜鹃柡澶婄墑閸斿孩绂掑顓濈箚闁绘劦浜滈埀顑惧€濆畷銏$附缁嬪灝绨ラ梺鍝勮閸庢煡宕戦埡鍛厽闁硅揪绲借闂佸搫鎳忛悡锟犲蓟濞戙垹唯妞ゆ牜鍋為宥夋⒑閸涘﹥绀€闁哥喐娼欓~蹇涙惞閸︻厾鐓撻梺鍦圭€涒晠骞忛崡鐑嗘富闁靛牆鍟俊濂告煙閸愯尙绠崇紒顔碱儏椤撳吋寰勬繝鍕毎婵$偑鍊ら崗姗€鍩€椤掆偓绾绢厾绮斿ú顏呯厸濞达絿鎳撴慨宥団偓瑙勬磸閸旀垿銆佸▎鎾崇闁稿繗鍋愰弳顓㈡⒒閸屾艾鈧绮堟笟鈧獮澶愬灳鐡掍焦妞介幃銏ゆ惞闁稓鐟濋梻浣告惈缁嬩線宕㈡總鍛婂珔闁绘柨鍚嬮悡銉︾節闂堟稒锛嶆俊鎻掔秺閺屾稒绻濋崟顐㈠箣闂佸搫鏈粙鎴﹀煝鎼淬倗鐤€闁挎繂妫岄弸鏃€绻濈喊妯活潑闁稿鎳樺畷褰掑垂椤曞懏缍庡┑鐐叉▕娴滄繈鎮炴繝姘厽闁归偊鍨伴拕濂告倵濮橆偄宓嗛柡灞剧☉铻g紓浣姑埀顒佸姍閺屸€崇暆鐎n剛袦濡ょ姷鍋炵敮锟犲箖濞嗘挻鍋ㄩ柛顭戝亝椤旀捇姊虹拠鎻掝劉妞ゆ梹鐗犲畷鎶筋敋閳ь剙鐣峰⿰鍫熷亜濡炲瀛╁▓楣冩⒑閸︻厼鍔嬮柛鈺佺墕宀e潡鍩¢崨顔惧弳濠电娀娼уΛ娆撍夐悩缁樼厱婵炲棗绻愰弳鐐电磼缂佹ḿ绠撻柍缁樻崌瀹曞綊顢欓悾灞煎闂傚倷鑳堕、濠傗枍閺囥垹绠伴柛婵勫劚瀵煡姊绘担铏瑰笡閺嬵亝銇勯弴鍡楁噹椤ユ艾鈹戦悩宕囶暡闁绘挻鐟╅弻鐔碱敍閸℃鍣洪柟鎻掑悑缁绘繂鈻撻崹顔句画闂佺懓鎲℃繛濠傤嚕鐠囨祴妲堟俊顖炴敱椤秴鈹戦绛嬫當闁绘锕顐c偅閸愨斁鎷洪梻鍌氱墐閺呮繄绮欐繝姘厵妞ゆ梻鍘ч埀顒€鐏濋锝嗙節濮橆厽娅滈梺绯曞墲閿氶柛鏂挎嚇濮婃椽妫冨☉姘鳖唺婵犳鍠楅幐鍐差嚕缁嬪簱鏋庨柟鎯ь嚟閸樹粙姊虹紒妯忣亪宕幐搴㈠弿濠㈣埖鍔栭悡鏇㈡煟濡櫣锛嶅褏鏁搁埀顒冾潐濞叉ê顪冩禒瀣槬闁逞屽墯閵囧嫰骞掑澶嬵€栨繛瀛樼矋缁捇寮婚悢琛″亾閻㈢櫥瑙勭濠婂嫨浜滈柡鍥╁枔閻鏌曢崶褍顏柡浣稿暣瀹曟帡濡堕崱鈺傤棝缂傚倸鍊峰ù鍥ㄣ仈閹间礁绠伴柟闂寸贰閺佸洤鈹戦崒婧撶懓顪冮挊澹濆綊鏁愰崵鍊燁潐缁旂喐鎯旈妸锔规嫽婵炶揪绲肩拃锕傚绩閻楀牏绠鹃柛娑卞枟缁€瀣煙椤斻劌娲﹂崑鎰版偣閸ヮ亜鐨洪柣銈呮喘濮婅櫣绱掑Ο鏇熷灥椤啴宕稿Δ鈧弸渚€鏌涢埄鍐姇闁绘挻娲熼弻鐔兼焽閿曗偓閺嬫稑霉濠婂牏鐣洪柡宀嬬畵楠炲鈹戦幇顓夈劎绱撴担浠嬪摵闁圭懓娲ら悾鐑藉箳閹存梹鐎婚梺鐟扮摠缁诲倿鈥栨径鎰拻濞达絽鎲¢崯鐐烘煕閺冣偓濞茬喖鍨鹃敃鍌涘€婚柣锝呰嫰缁侊箓妫呴銏″缂佸甯″鏌ュ箹娴e湱鍙嗛梺缁樻礀閸婂湱鈧熬鎷�28缂傚倸鍊搁崐鎼佸磹閹间礁纾归柟闂寸绾剧懓顪冪€n亜顒㈡い鎰矙閺屻劑鎮㈤崫鍕戙垻鐥幑鎰靛殭妞ゎ厼娼¢幊婊堟濞戞鏇㈡⒑鏉炴壆顦︽い鎴濇喘楠炲骞栨担鍝ョ潉闂佸壊鍋呯粙鍫ュ磻閹惧瓨濯撮柤鍙夌箖濡啫鐣烽妸鈺婃晩闂傚倸顕惄搴ㄦ⒒閸屾瑧鍔嶉柛搴$-閹广垽骞囬濠呪偓鍧楁⒑椤掆偓缁夌敻宕戦崒鐐村€甸柨婵嗛閺嬬喖鏌嶉柨瀣伌闁诡喖鍢查埢搴ょ疀閹垮啩鐥梻浣呵圭€涒晠銆冩繝鍥ц摕婵炴垯鍨规儫闂侀潧锛忓鍥╊槸婵犵數濮伴崹濂革綖婢跺⊕娲偄閻撳孩鐎梺鐟板⒔缁垶寮查幖浣圭叆闁绘洖鍊圭€氾拷
Arghya Chatterjee
, Yu Zhang
, Hui Liu
, Ruiqin Wang
, Shu He
, Xiaofeng Luo ,
,
Corresponding author: Xiaofeng Luo, xfluo@ccnu.edu.cn
Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
Received Date:2021-02-08
Available Online:2021-06-15
Abstract:We studied the effects of centrality fluctuation and deuteron formation on the cumulant ($C_n$) and correlation functions ($\kappa_n$) of protons up to the sixth order in the most central ($b$< 3 fm) Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $= 3 GeV in a microscopic transport model (JAM). The results are presented as a function of rapidity acceptance within the transverse momentum 0.4 < pT < 2 GeV/c. We compared the results obtained by the centrality bin width correction (CBWC) using charged reference particle multiplicities with the CBWC using impact parameter bins. It was found that, at low energies, the centrality resolution for determining the collision centrality using charged particle multiplicities is not sufficient to reduce the initial volume fluctuation effect for higher-order cumulant analysis. New methods need to be developed to classify events with high centrality resolution for heavy-ion collisions at low energies. Finally, we observed that the formation of deuterons suppresses the higher-order cumulants and correlation functions of protons and found it to be similar to the efficiency effect. This work can serve as a noncritical baseline for the QCD critical point search in the high baryon density region.

HTML

--> --> -->
I.INTRODUCTION
One of the primary objectives of relativistic heavy-ion collision experiments is to unravel the Quantum Chromodynamics (QCD) phase structure. At low $ \mu_{B} $, the lattice QCD calculations predict a smooth crossover from hadronic to quark-gluon degrees of freedom [1]. QCD-based models suggest that the transition from Quark-Gluon Plasma (QGP) to hadronic matter is of the first order at large baryon chemical potentials [2-4]. The endpoint of the first-order phase transition line towards low $ \mu_{B} $ is the so-called QCD Critical Point (CP). Although numerous studies have been conducted both theoretically [5-14] and experimentally [15-20], the location of the CP remains unsettled. The experimental validation of the CP would be a breakthrough for the exploration of the QCD phase structure. For this reason, the Beam Energy Scan program at RHIC has been operating since 2010 to map out the phase diagram as a function of baryon chemical potential ($ \mu_{B} $) and temperature ($ T $) [21].
For heavy-ion collisions, one of the foremost methods for the critical point search is measurement of the higher-order cumulants of conserved quantities, such as the net-baryon, net-charge, and net-strangeness numbers. Theoretically, it is expected that the higher-order cumulants of conserved charges will be sensitive to the correlation length ($ \xi $) of the system, which will diverge near the critical point [22-26]. As a result, non-monotonic variation of higher-order cumulant ratios from their baseline values is expected in existence of the critical point. Furthermore, theoretical calculation suggests that the ratio of the sixth and second order cumulants ($ C_6/C_2 $) is sensitive to the phase transition and that it will become negative when the chemical freeze-out is close to the chiral phase transition boundary [27, 28]. Thus, the sixth order fluctuation could serve as a sensitive probe of the signature of the QCD phase transition [29]. Experimentally, due to the detection inefficiency of neutral particles and multi-strange baryons, the net-proton and net-kaon are used as experimental proxies of the net-baryon and net-strangeness, respectively. In the last few years, the measurement of second, third, and fourth order cumulants of net-charge [17, 30], net-proton [15, 16, 20, 31, 32], and net-kaon [18] multiplicity distributions have been conducted by the STAR and PHENIX experiments in the first phase of the beam energy scan (BES-I, 2010-2017) program at the Relativistic Heavy Ion Collider (RHIC). The measurement of the second order mixed cumulant has also been reported [33]. Recently, the HADES experiment published the proton number fluctuations in fixed target Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 2.4 GeV [34]. Within current statistical uncertainties, the cumulants of the net-charge and net-kaon distributions are found to have either modest or monotonic dependence on the beam energy, whereas the fourth order cumulant ratio ($ C_4/C_2 $) of the net-proton distributions exhibits non-monotonic behaviors as a function of $ \sqrt {{s_{{{NN}}}}}\; $, with a 3.1 $ \sigma $ significance [20]. To confirm these non-monotonic behaviors, it is important to perform high precision fluctuation measurements at higher $\mu_B$ regions. To fulfill this goal, RHIC started the second phase of the beam energy scan program (BES-II) in 2018, focusing on collision energies below 27 GeV. From 2018 to 2020, the STAR experiment collected data on high statistics Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 9.2, 11.5, 14.6, 19.6, and 27 GeV (collider mode) and $ \sqrt {{s_{{{NN}}}}}\; $ = 3.0 – 7.7 GeV (fixed target mode). Conversely, to understand the various background contributions from different physics processes, model (without CP) studies are important in that they can provide baselines for the experimental search of the QCD critical point. These background contributions may arise from the limited detector acceptance/efficiency, initial volume fluctuation, autocorrelation and centrality resolution, centrality width, baryon number conservation, and resonance decay. Some of these effects have been studied previously [35-44] but remain to be understood properly before solid physics conclusions can be attained.
In this paper, we studied the effects of centrality fluctuation and deuteron formation on the proton cumulant and correlation functions up to the sixth order in the most central Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV using the JAM model. The paper is organized as follows. In Sec. II, we briefly discuss the JAM model used for this analysis. In Sec. III, we introduce the observables used for the present study. In Sec. IV, we present the cumulants up to the sixth order of the proton multiplicity distribution at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV with the JAM model and discuss the effect of centrality fluctuation and deuteron formation. The article is summarised in Sec. V.
II.THE JAM MODEL
JAM (Jet AA Microscopic Transport Model) is a non-equilibrium microscopic transport model contracted on resonance and string degrees of freedom [45, 46]. In the JAM model, hadrons and their excited states have explicit space and time propagation by the cascade method. Inelastic hadron-hadron collisions with resonance are applied at low energy, whereas the string picture and hard parton-parton scattering are modeled at intermediate and high-energy, respectively. The nuclear mean-field is applied based on the simplified version of the relativistic quantum molecular dynamics (RQMD) approach [47]. Previously, the JAM model has been used to compute several cumulants and to study different effects on particle number fluctuations in heavy-ion collision phenomenology [42, 48]. Greater detail about the JAM model can be found in Refs. [46, 48, 49]. In this study, we analyzed around 25 million central events for the Au+Au system at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV generated using the JAM model with a nuclear mean field. Using the simulated events, we calculated up to sixth order cumulants and correlation functions of event-by-event proton multiplicity distributions. The light nuclei are not generated directly in the JAM model; rather, they are produced with an afterburner code along the coalescence of nucleons with the phase space obtained from the JAM model [50]. The coalescence process is then treated stochastically. The phase space density of the nucleon is obtained when the simulation process is stopped at a certain time (50 fm/c in our simulation). The coalescence conditions are constrained by the relative distance ($ \Delta R $) and relative momentum ($ \Delta P $) in the two body center of mass frame. When the relative distance and momentum of any two nucleons are less than the given parameters ($ R_{0},P_{0} $), the light nuclei are considered to be formed [50-53]. Based on the charge rms radius of the wave function for deuterons, we fixed the coalescence parameters of the deuteron at $ R_0 = 4 $ fm and $ P_0 = 0.3 $ GeV/c.
III.OBSERVABLES AND METHODS
Higher-order multiplicity fluctuations can be characterized by different order cumulants ($ C_{n} $). The $ n^{\rm th} $ order cumulant is expressed via a generating function [54] as
$ C_{n} = \frac{\partial^{n}}{\partial \alpha^{n}} K(\alpha)|_{\alpha = 0}, $
(1)
where $ K(\alpha) $ is the cumulant generating function, which is logarithm of the moment generating function ($ K(\alpha) = $$ \ln(M(\alpha)) $). From event-by-event multiplicity distributions, the various order cumulants can be expressed in terms of the central moment as follows:
$ C_{1} = \langle N \rangle, $
(2)
$ C_{2} = \langle (\delta N)^{2} \rangle, $
(3)
$ C_{3} = \langle (\delta N)^{3} \rangle, $
(4)
$ C_{4} = \langle (\delta N)^{4} \rangle - 3\langle (\delta N)^{2} \rangle^{2}, $
(5)
$ C_{5} = \langle (\delta N)^{5} \rangle - 10\langle (\delta N)^{2} \rangle \langle (\delta N)^{3} \rangle, $
(6)
$\begin{aligned}[b]C_{6} = & \langle (\delta N)^{6} \rangle - 15\langle (\delta N)^{4} \rangle \langle (\delta N)^{2} \rangle - 10\langle (\delta N)^{3} \rangle^{2}\\& + 30\langle (\delta N)^{2} \rangle^{3}, \end{aligned}$
(7)
where $ N $ is the event-by-event particle number and $ \delta N = N - \langle N \rangle $ represents the deviation of $ N $ from its mean. $ \left\langle \ldots \right\rangle $ represents an average over the event sample. The $ n $-th order cumulant $ C_{n} $ is connected to the thermodynamic number susceptibilities of a system at thermal and chemical equilibrium:
$ C_{n} = VT^{3} \chi_{n}, $
(8)
where $ V $ is the system volume, which is difficult to measure in heavy-ion collisions. To cancel out the volume dependence, different order cumulant ratios are measured as experimental observables, which are related to the ratios of thermodynamic susceptibilities [24, 55]:
$ \begin{aligned}[b] \frac{C_{2}}{C_{1}} =& \frac{\chi_{2}}{\chi_{1}} = \frac{\sigma^{2}}{M},\;\;\;\; \frac{C_{3}}{C_{2}} = \frac{\chi_{3}}{\chi_{2}} = S\sigma, \\ \; \frac{C_{4}}{C_{2}} =& \frac{\chi_{4}}{\chi_{2}} = \kappa\sigma^{2},\; \;\;\;\frac{C_{5}}{C_{1}} = \frac{\chi_{5}}{\chi_{1}},\;\;\;\; \frac{C_{6}}{C_{2}} = \frac{\chi_{6}}{\chi_{2}}, \end{aligned} $
(9)
where $ M $, $ \sigma $, $ S $ , and $ \kappa $ are the mean, sigma, skewness, and kurtosis of the multiplicity distribution, respectively. Moreover, the multi-particle correlation function $ \kappa_{n} $ (or factorial cumulant) can also be expressed in terms of single particle cumulants [56, 57]:
$ \kappa_{1} = C_{1}, $
(10)
$ \kappa_{2} = -C_{1} + C_{2}, $
(11)
$ \kappa_{3} = 2C_{1} - 3C_{2} + C_{3}, $
(12)
$ \kappa_{4} = -6C_{1} + 11C_{2} - 6C_{3} + C_{4}, $
(13)
$ \kappa_{5} = 24C_{1} - 50C_{2} + 35C_{3} - 10C_{4} + C_{5}, $
(14)
$\begin{aligned}[b]\kappa_{6} = & -120C_{1} + 274C_{2} - 225C_{3} + 85C_{4}\\&- 15C_{5} + C_{6}. \end{aligned}$
(15)
For the Poisson distribution, the higher-order correlation functions $ \kappa_{n} (n > 2) $ are equal to zero. Thus, $ \kappa_{n} $ can also be used to quantify deviations from the Poisson distribution.
In this study, we analyzed approximately 25 million central events (b < 3 fm) for an Au+Au system generated using the JAM model. We studied the effect of centrality fluctuation and deuteron formation up to the sixth order cumulant of the proton multiplicity distribution in different acceptance windows.
In heavy-ion collision experiments, the collision centralities are usually defined by using charged particle multiplicities ($ N_{\rm ch} $) around mid-rapidity in which the smallest centrality bin is a single multiplicity value. To avoid autocorrelation effects, protons are excluded from $ N_{\rm ch} $ within $ |\eta| < 1 $ for centrality selection. This centrality definition is called Refmult3 [16]. For better statistical accuracy, the cumulant values are reported in wider centrality bins. Therefore, the centrality bin width correction (CBWC) is necessary to suppress volume fluctuations in a wide centrality bin [35]. Conventionally, the CBWC is performed by calculating cumulants in each Refmult3 bin [39]. However, for such a low energy due to the greatly reduced final state particle multiplicity, even a single multiplicity bin may correspond to a wider initial volume fluctuation. We discuss this effect below by comparing the results of the Refmult3-CBWC with the impact parameter (b) CBWC. In CBWC techniques, as shown in Eq. (16), the nth order cumulants ($ C_n $) are first calculated in each bin $ i $ and then are weighted by the number of events in each bin ($ n_{i} $),
$ C_n^{i} = \frac{\sum\nolimits_{i}n_{i}C_n^{i}}{\sum\nolimits_{i}n_{i}}, $
(16)
where $ C_n^{i} $ is the nth order cumulant in the i-th bin (either in the b = 0.1 fm bin or in each Refmult3 bin) and ($ \sum\nolimits_{i}n_{i} $) represents the total number of events. The uncertainties reported in the results are statistical due to the finite size of the event sample, and they are obtained using a standard error propagation method called the Delta theorem [58-60]. Generally, the uncertainty on cumulant measurement is inversely proportional to the number of events and proportional to the certain power of the width of the proton multiplicity distributions.
IV.RESULTS
We start by discussing the proton $ {\rm d}N/{\rm d}y $ distribution. Figure 1 shows the $ {\rm d}N/{\rm d}y $ distribution of protons and deuterons in the most central Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $= 3 GeV in the JAM model. The central Au+Au collisions are chosen with an impact parameter of less than 3 fm. The deuteron formation probability is proportional to the initial proton yield in that event according to coalescence after the kinetic freeze-out [61-63]; i.e.,
Figure1. (color online) Rapidity (${\rm d}N/{\rm d}y$) distributions for protons with and without deuteron formation in the most central (b < 3 fm) Au+Au systems at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV in the JAM model.

$ \lambda_{d} = Bn_{p_{i}}^{2}, $
(17)
where we assume that the neutron yield is proportional to the proton yield in each event. However, the additional checks have been performed assuming that the neutron and protons are uncorrelated [63]. $ B $ and $ n_{p_{i}} $ represent the coalescence parameter and initial proton number, respectively. The above assumption is valid where the volume fluctuation is minimal [64]. The initial proton number (p without d-formation) can thus be approximated by adding the observed proton and deuteron numbers as shown in Fig. 1 and also discussed in an earlier work [64],
$ \frac{{\rm d}N_{p_{i}}}{{\rm d}y} = n_{p_{i}} = n_{p} + n_{d}. $
(18)
Figure 2 shows the event-by-event proton number distribution in the most central Au+Au collision at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV with and without deuteron formation in the JAM model. The distributions are obtained by counting protons within $ 0.4<p_{T}<2.0 $ GeV/c, and the distributions presented in Fig. 2 are not corrected by centrality bin width as described in previous section.
Figure2. (color online) Normalized event-by-event proton multiplicity distributions in the most central (b < 3 fm) Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV with and without deuteron formation in the JAM model.

We first discuss the validity of centrality bin width correction using Refmult3 at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. As we discussed in the previous section, at very low energies, even a single multiplicity bin corresponds to a wide initial volume fluctuation, as demonstrated in Fig. 3. Figure 3(a) shows the two-dimensional correlation plot between Refmult3 and the impact parameter at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. We can observe that at 3 GeV, no strong negative correlation is found between charged particles at the mid-rapidity region (Refmult3) and the impact parameter in contrast to observations for higher energies [39]. This indicates that at low energies the charged particles in the mid-rapidity region are insensitive to the initial collision geometry and have poor centrality resolution. Figure 3(b) shows the b-distributions for two different fixed Refmult3 values, 67 (the peak value of the Refmult3 distribution with maximum weight) and 60. We can clearly see that even a fixed Refmult3 corresponds to all the impact parameter values from 0-3 fm with a weight that is similar to that of the unbiased b-distribution.
Figure3. (color online) (a) Correlation between Refmult3 (charged particles excluding protons within $|\eta|$< 1) and the impact parameter in top central (b< 3 fm) Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. (b) Impact parameter distributions for fixed Refmult3 values.

Figures 4 and 5 show the rapidity acceptance dependence for the cumulants and cumulant ratios of the proton multiplicity distributions for two different centrality definitions in Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV from the JAM model simulation. The results are also compared with the cumulants calculated without the CBWC. We observed that both the cumulants and cumulant ratios obtained from the Refmult3-CBWC have a large deviation from the impact parameter CBWC at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. We used 0.1 fm bins for the impact parameter based CBWC. As for the rapidity acceptance dependence, we also studied the CBWC effect with different tranverse momentum acceptance for the cumulants and cumulant ratios in Figs. 6 and 7, respectively. For this study, we fixed the rapidity acceptance to $ |y|<0.5 $ and the lower limit of transverse momentum to $ {p_{{T}_{\rm min}}} $ = 0.4 GeV/c. We varied the upper limit of transverse momentum ($ {p_{{T}_{\rm max}}} $) acceptance up to 2.4 GeV/c. We observed that the cumulants are saturated after $ {p_{{T}_{max}}}\sim $ 1.5-1.6 GeV/c due to the saturation of the proton yield. Based on this comparison, we can conclude that unlike at higher collision energies, the CBWC using charged-particle multiplicity bins cannot effectively suppress initial volume fluctuations in Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV [39]. New methods for classifying events at low energy heavy-ion collisions are therefore needed to determine the collision centralities. Recently, in Refs. [65, 66], machine learning has been proposed to determine the collision centrality with high resolution in heavy-ion collisions. This might be able to address the centrality fluctuation effect on cumulant analysis at low energies. In the subsequent sections, we use the b-CBWC to understand the effect of deuteron formation on the proton number cumulant and correlation functions.
Figure4. (color online) Rapidity acceptance dependence cumulants of proton multiplicity distributions in top central ($ b $ < 3 fm) Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. The centrality bin width correction is performed with (a) each Refmult3-bin (black squares) and (b) a 0.1 fm impact parameter bin (red circles). The results are also compared with the cumulants calculated without the CBWC (green triangles).

Figure5. (color online) Rapidity acceptance dependence cumulant ratios of proton multiplicity distributions in top central Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. The centrality bin width correction is performed with (a) each Refmult3-bin (black squares) and (b) a 0.1 fm impact parameter bin (red circles). The results are also compared with the cumulants calculated without the CBWC (green triangles).

Figure6. (color online) Transverse momentum acceptance dependence cumulants of proton multiplicity distributions in top central ($ b $ < 3 fm) Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. The centrality bin width correction is performed with (a) each Refmult3-bin (black squares) and (b) a 0.1 fm impact parameter bin (red circles). The results are also compared with the cumulants calculated without the CBWC (green triangles).

Figure7. (color online) Transverse momentum acceptance dependence cumulant ratios of proton multiplicity distributions in top central Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. The centrality bin width correction is performed with (a) each Refmult3-bin (black squares) and (b) a 0.1 fm impact parameter bin (red circles). The results are also compared with the cumulants calculated without the CBWC (green triangles).

Theoretically, it was predicted that the rapidity window dependence of proton cumulants is an important observable when searching for the QCD critical point and for understanding the non-equilibrium effects of dynamical expansion on fluctuations in heavy-ion collisions [57]. It is expected that the proton cumulant and correlation functions will exhibit power law dependence with the rapidity acceptance and number of protons since $ C_{n},\kappa_{n} \propto (\Delta y)^{n} \propto (N_{p})^{n} $ due to the long range correlation close to the critical point. This relationship holds when the rapidity acceptance is less than the typical correlation length near the critical point ($ \Delta y < \xi $) [42, 57]. On the other hand, if the rapidity acceptance is large enough relative to the correlation length ($ \Delta y \gg \xi $), the proton cumulant and multi-particle correlation function will be dominated by statistical fluctuations since $ C_{n},\kappa_{n} \propto \Delta y \propto N_{p} $. However, if the rapidity acceptance is further enlarged, the baryon number conservation effect will dominate the statistical fluctuations.
Figure 8 shows the variation of the cumulants $ C_{n} $ with the rapidity acceptance ($ -y_{\rm max} < y < y_{\rm max}, \; \Delta y $ = 2 $ y_{\rm max} $) of proton multiplicity distributions in the most central Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. The measurements were conducted within the transverse momentum range of 0.4 to 2.0 GeV/c. All cumulants are saturated around $ \Delta y \sim 2.2 $, which is the acceptance up to beam rapidity ($ y_{\rm beam} = 1.039 $ at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV) [39]. $ C_{1} $ and $ C_{2} $ increase linearly as a function of rapidity acceptance up to $ 2y_{\rm beam} $ due to an increase in the proton number with acceptance. We observed an approximately 7% reduction in the mean value of the number of protons in the case including deuteron formation. $ C_{3} $ increases in low rapidity acceptance, exhibits a peak around $ \Delta y \sim $ 0.7-0.8, and then decreases. The fourth order proton cumulant ($ C_4 $) values are negative above $ \Delta y \sim $ 0.6, whereas the fifth and sixth order proton cumulants ($ C_5 $ and $ C_6 $) are consistent with zero with large statistical uncertainties. To better understand the effect of deuteron formation, we randomly reduced the total proton number by 7% in each event using binomial sampling. Although the values are not identical, we found that the effect of randomly dropping 7% of protons was very similar to the case including deuteron formation.
Figure8. (color online) Rapidity acceptance dependence cumulants ($ C_{1} \sim C_{6} $) of proton multiplicity distributions in top central ($ b < 3 $ fm) Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. The results were obtained with/without deuteron formation in the JAM model. The blue cross markers indicate the random reduction of 7% of the protons in each event.

Figure 9 shows the rapidity acceptance dependence of the correlation function $ \kappa_{n} $ of protons in the most central Au+Au collisions at $ \sqrt {s_{NN}}\; $ = 3 GeV within the $ p_{T} $ range 0.4 to 2.0 GeV/c. Different orders of correlation function values are saturated at approximately $ \Delta y \sim $ 2.2 around mid-rapidity. $ \kappa_{1} $ increases as a function of the rapidity window. The two particle correlation function ($ \kappa_{2} $) of protons is found to be negative, and it decreases monotonically up to $ \Delta y \sim 2.2 $. The three particle correlation function ($ \kappa_{3} $) of protons increases with $ \Delta y \sim $ acceptance. The fourth, fifth, and sixth order correlation functions of protons ($ \kappa_{4} $, $ \kappa_{5} $, and $ \kappa_{6} $, respectively) are found to be close to zero up to $ \Delta y \sim 1 $; they start to deviate from zero when further enlarging the rapidity acceptance. Interestingly, the odd order correlation functions are found to be positive while the even order correlation functions show negative values up to the sixth order at large rapidity acceptance at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. The strong rapidity acceptance dependence is mainly attributed to the effects of baryon number conservation [67-70]. In addition, we observed that when we randomly drop 7% of the protons in each event, the cumulants are close to the deuteron formation case.
Figure9. (color online) Rapidity acceptance dependence of the correlation functions ($ \kappa_{1} \sim \kappa_{6} $) of the proton multiplicity distribution in top central ($ b < 3 $ fm) Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV with/without deuteron formation. The blue crosses represent the random dropping of 7% of the protons in each event.

Figure 10 shows the rapidity acceptance dependence of cumulant ratios $ C_{2}/C_{1} $, $ C_{3}/C_{2} $, $ C_{4}/C_{2} $, $ C_{5}/C_{1} $ and $ C_{6}/C_{2} $ of the proton multiplicity distributions in Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. At small rapidity acceptance values, the cumulant ratios follow statistical (Poisson) baseline fluctuations, and the values are close to unity ($ C_{m}/C_{n} \sim 1 $). $ C_{2}/C_{1} $ and $ C_{3}/C_{2} $ decrease smoothly with $ \Delta y $ and saturate around $ \Delta y \sim 2 $. The values of $ C_{4}/C_{2} $ and $ C_{5}/C_{1} $ are positive for small rapidity acceptance, change sign around $ \Delta y \sim 0.6 $, and then further decrease up to $ \Delta y \sim 1 $. $ C_{6}/C_{2} $ is close to 1 within statistical uncertainty at smaller rapidity acceptance and exhibits negative values at larger acceptance values. We observed good agreement between the cumulant ratios for deuteron formation and the case in which random protons were dropped.
Figure10. (color online) Rapidity acceptance dependence cumulant ratios ($ C_{2}/C_{1} $, $ C_{3}/C_{2} $, $ C_{4}/C_{2} $, $ C_{5}/C_{1} $, and $ C_{6}/C_{2} $) of the proton multiplicity distributions in the most central ($ b < 3 $ fm) Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. The results were obtained with/without deuteron formation in the JAM model. The blue crosses indicate the random dropping of 7% of the protons in each event.

V.SUMMARY
In this work, we studied the effects of centrality fluctuation and deuteron formation on the cumulant and correlation functions of protons up to the sixth order in the most central Au+Au collisions at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV using the JAM model. We presented the results as a function of the rapidity acceptance within the transverse momentum range of $ 0.4<p_{T}<2 $ GeV/c. The proton cumulants $ C_{1} $ and $ C_{2} $ increase linearly as a function of the rapidity acceptance up to $ \Delta y \sim 2y_{\rm beam} $. This also leads to the suppression of $ C_3 $ and $ C_{4} $ in the larger rapidity acceptance window ($ \Delta y > 0.6 $). The cumulants are saturated after $ {p_{T}}_{\rm max}\sim $ 1.5-1.6 GeV/c due to the saturation of the proton yield in a fixed rapidity acceptance. Further, we found the odd order correlation functions to be positive, whereas the even order correlation functions were found to be negative up to the sixth order for larger rapidity acceptance at $ \sqrt {{s_{{{NN}}}}}\; $ = 3 GeV. This is mainly due to the effects of baryon number conservation in heavy-ion collisions. The results obtained by the centrality bin width correction (CBWC) using charged reference particle multiplicities were compared with the CBWC using finer impact parameter bins. We observed that the centrality resolution for determining the collision centrality using charged particle multiplicities cannot effectively reduce the centrality fluctuations in heavy-ion collisions at low energies. This presents a challenge when conducting cumulant measurements in low energy heavy-ion collisions. New methods, such as machine learning techniques, need to be developed and applied to determine the collision centrality with high resolution. This will be crucial for precisely measuring the higher-order cumulants in heavy-ion collisions at low energies. We also discussed the effect of deuteron formation on the cumulant and correlation functions of protons and found that it is similar to the binomial efficiency effect due to the loss of protons via deuteron formation. This work can serve as a non-critical baseline for the future QCD critical point search in heavy-ion collisions at high baryon density regions.
ACKNOWLEDGEMENT
X. Luo is grateful for the stimulating discussion with Dr. Jiangyong Jia and Dr. Nu Xu.
相关话题/Effects centrality fluctuation