[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-154169-en":59,"doc-seo-154169-105":80},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"language":72,"language_code":73,"site_id":74,"html_lang":73,"table_of_contents":75,"faqs":76,"seo_title":77,"seo_description":66,"update_tm":78,"read_time":79,"preview_page_count":4},154169,549768702563,"Fahsai","https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","The Cheshire Cat Bag Model - Color Anomaly and η′ Properties","Color can leak from a QCD bag when pseudoscalar isoscalar singlet (η′) coupling is allowed at the bag surface. An additional boundary term is proposed to enforce total confinement of color. New relations are derived connecting the η′ mass and decay constant with QCD gluon condensates, and the results are compared with empirical parameters. The framework is discussed alongside confinement boundary conditions for gluons and quarks and a Cheshire-cat interpretation of bag wall matching.","arXiv :hep-ph/ 92 10220v 1 8 Oct 1992  \nThe Cheshire Cat Bag Model: Color Anomaly and η′  \nProperties ∗  \nA. Wirzba  \nNordita  \nBlegdamsvej 17 DK-2100 Copenhagen  \nDenmark  \nAbstract  \nWe show that color can leak from a QCD bag if we allow for pseudoscalar isoscalar singlet (􀀑′) coupling at the surface. To enforce total con􀀌nement of color an additional boundary term is suggested. New relations between the 􀀑′ mass and decay constant and the QCD gluon condensates are derived and compared with the empirical parameters.  \nNordita-92/68 Nhep-ph/yymmnn  \n􀀃 Talk presented at the International Nuclear Physics Conference, Wiesbaden (Germany), July 26-Aug. 1, 1992  \n1. INTRODUCTION  \nThe bag model was originally introduced in order to have color con􀀌nement by hand [1]: the bag exterior acts as a perfect color dielectric, while the color degrees of freedom are con􀀌ned to the bag interior. The latter has been achieved by forbidding color to 􀀍ow from the bag interior to the exterior. This means that, at the surface of the bag, the gluons are subject to the following con􀀌ning boundary equations  \nnˆ · ~Ea = 0 , nˆ × ~Ba = 0 , (1)  \nwhere nˆ is the outward normal to the bag surface. The color electric 􀀌elds Ea􀀖 have to point along the surface of the bag (a is the color index), while the color magnetic 􀀌elds Ba􀀖 have to be orthogonal to the surface. For the quarks, the con􀀌ning boundary equation states that the 􀀍ux of the isoscalar current through the bag surface is forbidden: n􀀖 γ􀀖 q = 0, where n􀀖 = (0 , nˆ) is the space-like 4-vector generalization of the normal vector at the bag surface. In comparison to this traditional picture of the bag model, the bag from the “Cheshire cat” point of view serves just as a formal separation of space-time in a bag region where the underlying QCD still acts, an exterior region where QCD is “integrated out” (practically meaning “replaced”) by an e􀀋ective action formulated in hadronic degrees of freedom, and a boundary where both regimes are matched so generally that it doesn’t matter where the bag walls are located [2, 3, 4] . In other words, the bag itself has no physical signi􀀌cance, only its formalism is used. Therefore the name “Cheshire cat bag” as inspired by the vanishing of the Cheshire cat in the Lewis Caroll’s tale Alice in Wonderland [5] . Of course it should be clear that in 3+1 dimensions the Cheshire cat bag can only work approximately in practice, since we know from e.g. large Nc arguments that an e􀀋ective action trying to replace QCD must eventually involve in􀀌nitely many local terms. In the Cheshire cat formulation of the bag model it is obvious that the con􀀌ning conditions for gluons and quarks will be not satis􀀌ed in general, since the bag wall can be moved at will.  \n2. TOY MODEL IN 1+1 DIMENSIONS  \nAs mentioned, we can at most expect an approximate formulation of the Cheshire cat bag model in the physical 3+1 space-time, since we have only an approximate bosonization of QCD at our disposal, as inspired by large Nc arguments. In the 1 + 1 dimensional toy world, however, fermion and boson formulations are exactly equivalent. Because of this, we can expect that the 1 + 1 dimensional analogon of the 3 + 1 Cheshire cat bag will work exactly [3, 4] . For that purpose, let us start out with the simplest case: massless fermions in the bag interior, massless bosons in the exterior, and the usual hybrid bag model coupling [6] between the fermions and bosons at the boundary in order to guarantee chiral invariance. The bag lagrangian reads therefore  \nLbag = 􀀒i 12γ􀀖  ψ 􀀓 􀀂 in − 12ei􀀍5 􀀞/f ψ􀀁S + 􀀒 12∂􀀖 φ∂􀀖 φ􀀓 􀀂 out (2) where ψ is the fermion 􀀌eld, φ the (pseudo-)scalar boson 􀀌eld, 􀀂in/out are step-functions with support on the bag interior/exterior and 􀀁 S is the surface delta-function. We know  \nthat massless fermions can be exactly bosonized into massless bosons – both theories are equivalent. Thus we can ask the question what will happen to a e.g. right-moving (right-handed) fermion wave packet ","cbCaifAywAIQ2xlo","https://ap.wps.com/l/cbCaifAywAIQ2xlo","pdf",105685,"English","en",105,"# Introduction\n## Toy Model in 1+1 Dimensions","[{\"question\":\"How does color leakage occur in the Cheshire cat bag model?\",\"answer\":\"Color can leak from a QCD bag when pseudoscalar isoscalar singlet (η′) coupling is permitted at the bag surface.\"},{\"question\":\"Why is an additional boundary term introduced?\",\"answer\":\"An extra boundary term is suggested to enforce total confinement of color despite the surface coupling that enables leakage.\"},{\"question\":\"What new relations are derived in the paper?\",\"answer\":\"The work derives relations linking the η′ mass and decay constant to QCD gluon condensates, then compares them with empirical parameters.\"}]","The Cheshire Cat Bag Model - Color Anomaly and η′ Properties | PDF",1787889190,18,{"code":4,"msg":81,"data":82},"ok",{"site_id":74,"language":73,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":78},"the-cheshire-cat-bag-model-color-anomaly-and-properties","",{"@graph":86,"@context":138},[87,101,121],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,99],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":40,"@type":93,"position":98},"https://docshare.wps.com/document/research-report/",3,{"item":100,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/the-cheshire-cat-bag-model-color-anomaly-and-properties/154169/",{"url":100,"name":65,"@type":102,"image":103,"author":108,"headline":65,"publisher":110,"fileFormat":113,"inLanguage":73,"description":66,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/the-cheshire-cat-bag-model-color-anomaly-and-properties/154169.png","ImageObject",300,407,{"name":63,"@type":109},"Person",{"url":91,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-10-29","2026-08-28",true,{"@type":118,"interactionType":119,"userInteractionCount":52},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"How does color leakage occur in the Cheshire cat bag model?","Question",{"text":128,"@type":129},"Color can leak from a QCD bag when pseudoscalar isoscalar singlet (η′) coupling is permitted at the bag surface.","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"Why is an additional boundary term introduced?",{"text":133,"@type":129},"An extra boundary term is suggested to enforce total confinement of color despite the surface coupling that enables leakage.",{"name":135,"@type":126,"acceptedAnswer":136},"What new relations are derived in the paper?",{"text":137,"@type":129},"The work derives relations linking the η′ mass and decay constant to QCD gluon condensates, then compares them with empirical parameters.","https://schema.org",{"og:url":100,"og:type":140,"og:title":65,"og:site_name":111,"og:description":66},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":61,"site_id":74}]