{"paper":{"title":"A Euclidean bridge to the relativistic constituent quark model","arxiv_id":"1608.07319","primary_cat":"nucl-th","submitted_at":"2016-08-25T21:53:54+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"${\\bf Background}$ Knowledge of nucleon structure is today ever more of a precision science, with heightened theoretical and experimental activity expected in coming years.","hedge":{"p":0.91,"label":"asserted"},"own_p":0.03,"main_claim_p":0.01,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.72,"id":"s1","own":false,"role":"gap","text":"At the same time, a persistent gap lingers between theoretical approaches grounded in Euclidean methods (e.g., lattice QCD, Dyson-Schwinger Equations [DSEs]) as opposed to traditional Minkowski field theories (such as light-front constituent quark models).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.19,"role_probabilities":{"gap":0.72,"method":0.0,"result":0.0,"background":0.28,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.96,"id":"s2","own":false,"role":"contribution","text":"${\\bf Purpose}$ Seeking to bridge these complementary worldviews, we explore the potential of a Euclidean constituent quark model (ECQM).","hedge":{"p":0.55,"label":"hedged_possibility"},"own_p":0.43,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.01,"contribution":0.96,"interpretation":0.0}},{"i":3,"p":0.97,"id":"s3","own":true,"role":"contribution","text":"This formalism enables us to study the gluonic dressing of the quark-level axial-vector vertex, which we undertake as a test of the framework.","hedge":{"p":0.95,"label":"asserted"},"own_p":0.64,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.97,"interpretation":0.0}},{"i":4,"p":1.0,"id":"s4","own":true,"role":"method","text":"${\\bf Method}$ To access its indispensable elements with a minimum of inessential detail, we develop our ECQM using the simplified quark $+$ scalar diquark picture of the nucleon.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.93,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":1.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":1.0,"id":"s5","own":true,"role":"method","text":"We construct a hyperspherical formalism involving polynomial expansions of diquark propagators to marry our ECQM with the results of Bethe-Salpeter Equation (BSE) analyses, and constrain model parameters by fitting electromagnetic form factor data.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.95,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":1.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":6,"p":0.75,"id":"s6","own":true,"role":"contribution","text":"${\\bf Results}$ From this formalism, we define and compute a new quantity --- the Euclidean density function (EDF) --- an object that characterizes the nucleon's various charge distributions as functions of the quark's Euclidean momentum.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.25,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.75,"interpretation":0.0}},{"i":7,"p":1.0,"id":"s7","own":true,"role":"result","text":"Applying this technology and incorporating information from BSE analyses, we find the dressing effect on the proton's axial-singlet charge to be small in magnitude and consistent with zero.","hedge":{"p":0.87,"label":"asserted"},"own_p":0.97,"main_claim_p":0.29,"quantitative":true,"quantitative_p":0.68,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":8,"p":0.46,"id":"s8","own":false,"role":"future_work","text":"${\\bf Conclusions}$ The scalar quark $+$ diquark ECQM is a step toward a realistic quark model in Euclidean space, and urges additional refinements.","hedge":{"p":0.82,"label":"asserted"},"own_p":0.46,"main_claim_p":0.49,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.01,"background":0.0,"limitation":0.4,"future_work":0.46,"contribution":0.02,"interpretation":0.11}},{"i":9,"p":1.0,"id":"s9","own":true,"role":"interpretation","text":"The small size we obtain for the impact of the dressed vertex on the axial-singlet charge suggests that models without this effect are on firm ground to neglect it.","hedge":{"p":0.99,"label":"hedged_possibility"},"own_p":0.86,"main_claim_p":0.28,"quantitative":true,"quantitative_p":0.62,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":1.0}}]},"compiled":{"main_claim":{"p":0.62,"text":"${\\bf Conclusions}$ The scalar quark $+$ diquark ECQM is a step toward a realistic quark model in Euclidean space, and urges additional 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