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Phys. J. C"],"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The estimation of the K\u00e4ll\u00e9n\u2013Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an appropriate inversion method. As proof of concept the SU(2) glueball spectrum for the quantum numbers <jats:inline-formula><jats:alternatives><jats:tex-math>$$J^{PC} = 0^{++}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>J<\/mml:mi>\n                      <mml:mrow>\n                        <mml:mi>PC<\/mml:mi>\n                      <\/mml:mrow>\n                    <\/mml:msup>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:msup>\n                      <mml:mn>0<\/mml:mn>\n                      <mml:mrow>\n                        <mml:mo>+<\/mml:mo>\n                        <mml:mo>+<\/mml:mo>\n                      <\/mml:mrow>\n                    <\/mml:msup>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is investigated for various values of the lattice spacing. The spectral density and the glueball spectrum are estimated using the published data of Yamanaka et al. (Phys Rev D 102(5):054507, <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"doi\" xlink:href=\"https:\/\/doi.org\/10.1103\/PhysRevD.102.054507\">10.1103\/PhysRevD.102.054507<\/jats:ext-link>, <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"http:\/\/arxiv.org\/abs\/1910.07756\">arXiv:1910.07756<\/jats:ext-link> [hep-lat], 2020). Our estimates for the ground state mass are in good agreement with the traditional approach published therein, which is based on the large time exponential behaviour of the correlation functions. Furthermore, the spectral density also contains hints of excites states in the spectrum.<\/jats:p>","DOI":"10.1140\/epjc\/s10052-022-10213-3","type":"journal-article","created":{"date-parts":[[2022,3,23]],"date-time":"2022-03-23T12:06:31Z","timestamp":1648037191000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["K\u00e4ll\u00e9n\u2013Lehmann spectral representation of the scalar SU(2) glueball"],"prefix":"10.1140","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1326-6011","authenticated-orcid":false,"given":"David","family":"Dudal","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8266-3796","authenticated-orcid":false,"given":"Orlando","family":"Oliveira","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8646-7693","authenticated-orcid":false,"given":"Martin","family":"Roelfs","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,23]]},"reference":[{"issue":"5","key":"10213_CR1","doi-asserted-by":"publisher","first-page":"054507","DOI":"10.1103\/PhysRevD.102.054507","volume":"102","author":"N Yamanaka","year":"2020","unstructured":"N. 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