Pion masses in two-flavor QCD with η condensation
We investigate some aspects of two-flavor QCD with mu≠md at low energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at mu=0 for the fixed md≠0, the neutral pion mass becomes zero at two critical values of mu, between which the neutral p...
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Veröffentlicht in: | Physical Review Letters 2014-04, Vol.112 (14), p.141603-141603, Article 141603 |
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description | We investigate some aspects of two-flavor QCD with mu≠md at low energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at mu=0 for the fixed md≠0, the neutral pion mass becomes zero at two critical values of mu, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the chiral perturbation theory diverges at these two critical points. We briefly discuss a possibility that mu=0 can be defined by the vanishing the "topological susceptibility. We finally analyze the case of mu=md=m with θ=π, which is equivalent to mu=-md=-m with θ=0 by the chiral rotation. In this case, the η condensation occurs at small m, violating the CP symmetry spontaneously. Deep in the η condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at small m that mπ2=O(m2), which, however, is shown to be consistent with the chiral Ward-Takahashi identities. |
doi_str_mv | 10.1103/PhysRevLett.112.141603 |
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While nothing special happens at mu=0 for the fixed md≠0, the neutral pion mass becomes zero at two critical values of mu, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the chiral perturbation theory diverges at these two critical points. We briefly discuss a possibility that mu=0 can be defined by the vanishing the "topological susceptibility. We finally analyze the case of mu=md=m with θ=π, which is equivalent to mu=-md=-m with θ=0 by the chiral rotation. In this case, the η condensation occurs at small m, violating the CP symmetry spontaneously. Deep in the η condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at small m that mπ2=O(m2), which, however, is shown to be consistent with the chiral Ward-Takahashi identities.</description><identifier>ISSN: 0031-9007</identifier><identifier>EISSN: 1079-7114</identifier><identifier>DOI: 10.1103/PhysRevLett.112.141603</identifier><identifier>PMID: 24765943</identifier><language>eng</language><publisher>United States</publisher><subject>CP ; FLAVOR ; HET ; lattice ; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS ; pion ; PIONS ; QCD ; QUANTUM CHROMODYNAMICS</subject><ispartof>Physical Review Letters, 2014-04, Vol.112 (14), p.141603-141603, Article 141603</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c338t-6f3a9a789d429ebe9b8cedc17d8f6243bfd50c3c338712c9ae35b8bf338f80fe3</citedby><cites>FETCH-LOGICAL-c338t-6f3a9a789d429ebe9b8cedc17d8f6243bfd50c3c338712c9ae35b8bf338f80fe3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,885,2876,2877,27924,27925</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/24765943$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/1165925$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Aoki, Sinya</creatorcontrib><creatorcontrib>Creutz, Michael</creatorcontrib><creatorcontrib>Brookhaven National Laboratory (BNL)</creatorcontrib><title>Pion masses in two-flavor QCD with η condensation</title><title>Physical Review Letters</title><addtitle>Phys Rev Lett</addtitle><description>We investigate some aspects of two-flavor QCD with mu≠md at low energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at mu=0 for the fixed md≠0, the neutral pion mass becomes zero at two critical values of mu, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the chiral perturbation theory diverges at these two critical points. We briefly discuss a possibility that mu=0 can be defined by the vanishing the "topological susceptibility. We finally analyze the case of mu=md=m with θ=π, which is equivalent to mu=-md=-m with θ=0 by the chiral rotation. In this case, the η condensation occurs at small m, violating the CP symmetry spontaneously. Deep in the η condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at small m that mπ2=O(m2), which, however, is shown to be consistent with the chiral Ward-Takahashi identities.</description><subject>CP</subject><subject>FLAVOR</subject><subject>HET</subject><subject>lattice</subject><subject>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</subject><subject>pion</subject><subject>PIONS</subject><subject>QCD</subject><subject>QUANTUM CHROMODYNAMICS</subject><issn>0031-9007</issn><issn>1079-7114</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNpNkMtOwzAQRS0EoqXwC1XEik2Kx87LS1SeUiUKgrXlOGM1KI1L7Lbql_EXfBOuUhCr0VydO49LyBjoBIDy6_li515xM0Pvg8AmkEBG-REZAs1FnAMkx2RIKYdYUJoPyJlzH5RSYFlxSgYsybNUJHxI2Ly2bbRUzqGL6jbyWxubRm1sF71Mb6Nt7RfR91ekbVth65QP9Dk5MapxeHGoI_J-f_c2fYxnzw9P05tZrDkvfJwZroTKC1ElTGCJoiw0VhryqjAZS3hpqpRqvodzYFoo5GlZlCb0pqAG-Yhc9nOt87V0uvaoF-GQFrWXAOEBlgboqodWnf1co_NyWTuNTaNatGsnIQVRJCzjLKBZj-rOOtehkauuXqpuJ4HKfajyX6hBYLIPNRjHhx3rconVn-03Rf4Du9t1YA</recordid><startdate>20140411</startdate><enddate>20140411</enddate><creator>Aoki, Sinya</creator><creator>Creutz, Michael</creator><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>OTOTI</scope></search><sort><creationdate>20140411</creationdate><title>Pion masses in two-flavor QCD with η condensation</title><author>Aoki, Sinya ; Creutz, Michael</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c338t-6f3a9a789d429ebe9b8cedc17d8f6243bfd50c3c338712c9ae35b8bf338f80fe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>CP</topic><topic>FLAVOR</topic><topic>HET</topic><topic>lattice</topic><topic>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</topic><topic>pion</topic><topic>PIONS</topic><topic>QCD</topic><topic>QUANTUM CHROMODYNAMICS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Aoki, Sinya</creatorcontrib><creatorcontrib>Creutz, Michael</creatorcontrib><creatorcontrib>Brookhaven National Laboratory (BNL)</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>OSTI.GOV</collection><jtitle>Physical Review Letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Aoki, Sinya</au><au>Creutz, Michael</au><aucorp>Brookhaven National Laboratory (BNL)</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Pion masses in two-flavor QCD with η condensation</atitle><jtitle>Physical Review Letters</jtitle><addtitle>Phys Rev Lett</addtitle><date>2014-04-11</date><risdate>2014</risdate><volume>112</volume><issue>14</issue><spage>141603</spage><epage>141603</epage><pages>141603-141603</pages><artnum>141603</artnum><issn>0031-9007</issn><eissn>1079-7114</eissn><abstract>We investigate some aspects of two-flavor QCD with mu≠md at low energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at mu=0 for the fixed md≠0, the neutral pion mass becomes zero at two critical values of mu, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the chiral perturbation theory diverges at these two critical points. We briefly discuss a possibility that mu=0 can be defined by the vanishing the "topological susceptibility. We finally analyze the case of mu=md=m with θ=π, which is equivalent to mu=-md=-m with θ=0 by the chiral rotation. In this case, the η condensation occurs at small m, violating the CP symmetry spontaneously. Deep in the η condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at small m that mπ2=O(m2), which, however, is shown to be consistent with the chiral Ward-Takahashi identities.</abstract><cop>United States</cop><pmid>24765943</pmid><doi>10.1103/PhysRevLett.112.141603</doi><tpages>1</tpages></addata></record> |
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subjects | CP FLAVOR HET lattice PHYSICS OF ELEMENTARY PARTICLES AND FIELDS pion PIONS QCD QUANTUM CHROMODYNAMICS |
title | Pion masses in two-flavor QCD with η condensation |
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