[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127888-en":3,"doc-seo-127888-105":31,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},127888,2336474459895,"Aria","https://ap-avatar.wpscdn.com/avatar/22000baeef7a5ed0655?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786071322749376916",8,"Research & Report","Flavor dependent Critical endpoint from holographic QCD through machine learning","Quantum chromodynamics phase structure in the T-μ plane and the equation of state for pure gluon, 2-flavor, 2+1-flavor, and 2+1+1-flavor matter are studied within the Einstein-Maxwell-Dilaton framework at finite temperature and chemical potential. Lattice QCD inputs at zero chemical potential for the equation of state and baryon susceptibility are used to determine holographic parameters via machine learning. Results show first-order deconfinement for pure gluon with Tc=0.265 GeV, while multi-flavor cases exhibit crossover at μ=0 and become first-order at high μ. Critical endpoints are located at (μcB,Tc)=(0.46,0.147),(0.74,0.094),(0.87,0.108) GeV for increasing flavor content, with corresponding thermodynamic behavior and visible shifts at finite μ.","arXiv :2405 .06179v1 [hep-ph] 10 May 2024  \nPrepared for submission to JHEP  \nFlavor dependent Critical endpoint from holographic QCD through machine learning  \nXun Chena and Mei Huangb  \na School of Nuclear Science and Technology, University of South China, Hengyang 421001, China b School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China  \nE-mail: [chenxun@usc.edu.cn](chenxun@usc.edu.cn), [huangmei@ucas.ac.cn](huangmei@ucas.ac.cn)  \nAbstract: QCD phase diagram in the T −µ plane and the equation of state for pure gluon, 2-􀀍avor, 2+1-􀀍avor systems, and 2+1+1-􀀍avor systems have been investigated using the Einstein-Maxwell-Dilaton (EMD) framework at 􀀌nite temperature and chemical potential. By inputting lattice QCD data for the equation of state and baryon susceptibility at zero chemical potential into holographic model, all the parameters can be determined with the aid of machine learning algorithms. Our 􀀌ndings indicate that the decon􀀌nement phase transition is of 􀀌rst order for the pure gluon system with critical temperature Tc = 0.265GeV at vanishing chemical potential. The phase transition for the 2-􀀍avor, 2+1-􀀍avor systems, and 2+1+1-􀀍avor systems are crossover at vanishing chemical potential and 􀀌rstorder at high chemical potential, and the critical endpoint(CEP) in the T −µ plane locatesat (µcB=0.46 GeV, Tc =0.147 GeV), (µcB = 0.74 GeV, Tc = 0.094 GeV), and (µcB= 0.87 GeV,Tc = 0.108 GeV), respectively. Additionally, the thermodynamic quantities of the system for di􀀋erent 􀀍avors at 􀀌nite chemical potential are presented in this paper. It is observed that the di􀀋erence between the 2+1 􀀍avor and 2+1+1 􀀍avor systems is invisible at vanishing chemical potential and low temperature. The location of CEP for 2+1+1 􀀍avor system deviates explicitly from that of the 2+1 􀀍avor system with the increase of chemical potential. Both 2+1 􀀍avor and 2+1+1 􀀍avor systems di􀀋er signi􀀌cantly from the 2-􀀍avor system.  \n\n| Contents\u003Cbr>1 Introduction\u003Cbr>2 The review of EMD model\u003Cbr>3 Determining the parameters with machine learning\u003Cbr>4 Thermodynamics at vanishing chemical potential for di􀀋erent 􀀍avors\u003Cbr>5 Thermodynamics for di􀀋erent 􀀍avors at 􀀌nite chemical potential\u003Cbr>5.1 Thermodynamics of 2 􀀍avor system at 􀀌nite chemical potential\u003Cbr>5.2 Thermodynamics of 2+1 􀀍avor system at 􀀌nite chemical potential\u003Cbr>5.3 Thermodynamics of 2+1+1-􀀍avor system at 􀀌nite chemical potential\u003Cbr>6 QCD Phase diagram for di􀀋erent 􀀍avors\u003Cbr>7 Conclusion and outlook | 1\u003Cbr>3\u003Cbr>7\u003Cbr>9\u003Cbr>13\u003Cbr>13\u003Cbr>15\u003Cbr>16\u003Cbr>17\u003Cbr>18 |\n| --- | --- |\n\n1 Introduction  \nThe exploration of the high-energy domain has been propelled forward by the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN), which has been in operation since 2009 [1–3] . It has extended our experimental knowledge of the QCD phase diagram in the direction of high temperature, getting closer to the beginning of the universe. The next frontier on the phase diagram is the high-density regime [4], where 􀀌rst principles calculations are known to encounter the fermion sign problem [5] . Estimations based on the chiral model suggest that the quark-hadron transition turns from a crossover to a 􀀌rst-order phase transition at a 􀀌nite baryon chemical potential, implying the existence of a critical point [6–13] .  \nThe equation of state (EoS) constitutes a cornerstone relation in the realm of thermodynamic quantities. The inception of explorations into the QCD EoS can be traced back to the pioneering MIT bag model [14] . Subsequently, an enriched comprehension of QCD thermodynamics has unfolded through the introduction of various model-based approaches, such as the potential model [15] and the Nambu-Jona-Lasinio (NJL) model [16 , 17] and their extensions. Theoretical endeavors have surged in recent years to probe the QCD phase transition and the associated EoS under conditions of 􀀌nite temperature and chemical potential. Noteworthy among these a","cbCaio7lPsnH8Le9","https://ap.wps.com/l/cbCaio7lPsnH8Le9","pdf",1039504,2,1,26,"English","en",105,"# Introduction\n# The review of EMD model\n# Determining the parameters with machine learning\n# Thermodynamics at vanishing chemical potential for different flavors\n# Thermodynamics for different flavors at finite chemical potential\n## Thermodynamics of 2 flavor system at finite chemical potential\n## Thermodynamics of 2+1 flavor system at finite chemical potential\n## Thermodynamics of 2+1+1 flavor system at finite chemical potential\n# QCD Phase diagram for different flavors\n# Conclusion and outlook","[{\"question\":\"Which framework and inputs are used to determine the holographic model parameters?\",\"answer\":\"The study uses the Einstein-Maxwell-Dilaton (EMD) framework at finite temperature and chemical potential. It inputs lattice QCD data for the equation of state and baryon susceptibility at zero chemical potential, with parameters determined via machine learning algorithms.\"},{\"question\":\"How do the deconfinement transition orders differ between pure gluon and multi-flavor systems?\",\"answer\":\"The pure gluon system shows a first-order deconfinement transition at vanishing chemical potential with Tc=0.265 GeV. For 2-flavor, 2+1-flavor, and 2+1+1-flavor systems, the transition is crossover at μ=0 and becomes first-order at sufficiently high chemical potential.\"},{\"question\":\"What are the predicted locations of the critical endpoint (CEP) in the T-μ plane?\",\"answer\":\"The CEP coordinates in the T-μ plane are given as (μcB=0.46 GeV, Tc=0.147 GeV) for one case, (μcB=0.74 GeV, Tc=0.094 GeV) for another, and (μcB=0.87 GeV, Tc=0.108 GeV) for the 2+1+1-flavor case, respectively.\"}]","Flavor dependent Critical endpoint from holographic QCD through machine learning | PDF",1785942633,66,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":29},"flavor-dependent-critical-endpoint-from-holographic-qcd-through-machine-learning","",{"@graph":37,"@context":86},[38,54,69],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,48,51],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":20},"https://docshare.wps.com/document/","Document",{"item":49,"name":12,"@type":44,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":44,"position":53},"https://docshare.wps.com/document/flavor-dependent-critical-endpoint-from-holographic-qcd-through-machine-learning/127888/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":42,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-27","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"Which framework and inputs are used to determine the holographic model parameters?","Question",{"text":76,"@type":77},"The study uses the Einstein-Maxwell-Dilaton (EMD) framework at finite temperature and chemical potential. It inputs lattice QCD data for the equation of state and baryon susceptibility at zero chemical potential, with parameters determined via machine learning algorithms.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How do the deconfinement transition orders differ between pure gluon and multi-flavor systems?",{"text":81,"@type":77},"The pure gluon system shows a first-order deconfinement transition at vanishing chemical potential with Tc=0.265 GeV. For 2-flavor, 2+1-flavor, and 2+1+1-flavor systems, the transition is crossover at μ=0 and becomes first-order at sufficiently high chemical potential.",{"name":83,"@type":74,"acceptedAnswer":84},"What are the predicted locations of the critical endpoint (CEP) in the T-μ plane?",{"text":85,"@type":77},"The CEP coordinates in the T-μ plane are given as (μcB=0.46 GeV, Tc=0.147 GeV) for one case, (μcB=0.74 GeV, Tc=0.094 GeV) for another, and (μcB=0.87 GeV, Tc=0.108 GeV) for the 2+1+1-flavor case, respectively.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":47,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":47,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":47,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":47,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]