{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T09:56:43Z","timestamp":1776419803375,"version":"3.51.2"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T00:00:00Z","timestamp":1547596800000},"content-version":"vor","delay-in-days":15,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. High Energ. Phys."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n          <\/jats:title>\n          <jats:p>Recent dark matter (DM) direct searches place very stringent constraints on the possible DM candidates proposed in extensions of the Standard Model. There are however models where these constraints are avoided. One of the simplest and most striking examples comes from a straightforward Higgs-portal pseudo-scalar DM model featured with a softly broken U(1) symmetry. In this model the tree-level DM-nucleon scattering cross section vanishes in the limit of zero momentum transfer. It has also been argued that the leading-order DM-nucleon cross section appears at the one-loop level. In this work we have calculated the exact cross section in the zero momentum transfer at the leading order i.e., at the one-loop level of perturbative expansion. We have concluded that, in agreement with expectations, the amplitude for the scattering process is UV finite and approaches zero in the limit of vanishing DM masses. Moreover, we made clear that the finite DM velocity correction at tree level is subdominant with respect to the one-loop contribution. Based on the analytic formulae, our numerical studies show that, for a typical choice of model parameters, the DM nuclear recoiling cross section is well below <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$ \\mathcal{O} $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>O<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>(10<jats:sup>\u221250<\/jats:sup> cm<jats:sup>2<\/jats:sup>), which indicates that the DM direct detection signal in this model naturally avoids present strong experimental limits on the cross section.<\/jats:p>","DOI":"10.1007\/jhep01(2019)138","type":"journal-article","created":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T22:52:52Z","timestamp":1547765572000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":48,"title":["One-loop contribution to dark-matter-nucleon scattering in the pseudo-scalar dark matter model"],"prefix":"10.1007","volume":"2019","author":[{"given":"Duarte","family":"Azevedo","sequence":"first","affiliation":[]},{"given":"Mateusz","family":"Duch","sequence":"additional","affiliation":[]},{"given":"Bohdan","family":"Grzadkowski","sequence":"additional","affiliation":[]},{"given":"Da","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Michal","family":"Iglicki","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7948-0355","authenticated-orcid":false,"given":"Rui","family":"Santos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,16]]},"reference":[{"key":"9773_CR1","unstructured":"Particle Data Group, Review of particle physics, Phys. 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Astrophys.\n                           48 (2010) 495 [arXiv:1003.0904] [INSPIRE].","journal-title":"Ann. Rev. Astron. Astrophys."},{"key":"9773_CR5","unstructured":"XENON collaboration, Dark matter search results from a one ton-year exposure of XENON1T, Phys. Rev. Lett.\n                           121 (2018) 111302 [arXiv:1805.12562] [INSPIRE]."},{"key":"9773_CR6","doi-asserted-by":"crossref","unstructured":"J. McDonald, Gauge singlet scalars as cold dark matter, Phys. Rev.\n                           D 50 (1994) 3637 [hep-ph\/0702143] [INSPIRE].","DOI":"10.1103\/PhysRevD.50.3637"},{"key":"9773_CR7","volume":"D 79","author":"V Barger","year":"2009","unstructured":"V. Barger et al., Complex singlet extension of the standard model, Phys. Rev.\n                           D 79 (2009) 015018 [arXiv:0811.0393] [INSPIRE].","journal-title":"Phys. Rev."},{"key":"9773_CR8","volume":"D 82","author":"V Barger","year":"2010","unstructured":"V. Barger, M. McCaskey and G. Shaughnessy, Complex scalar dark matter vis-\u00e0-vis CoGeNT, DAMA\/LIBRA and XENON100, Phys. Rev.\n                           D 82 (2010) 035019 [arXiv:1005.3328] [INSPIRE].","journal-title":"Phys. Rev."},{"key":"9773_CR9","volume":"D 86","author":"M Gonderinger","year":"2012","unstructured":"M. Gonderinger, H. Lim and M.J. Ramsey-Musolf, Complex scalar singlet dark matter: vacuum stability and phenomenology, Phys. Rev.\n                           D 86 (2012) 043511 [arXiv:1202.1316] [INSPIRE].","journal-title":"Phys. Rev."},{"key":"9773_CR10","doi-asserted-by":"publisher","first-page":"191801","DOI":"10.1103\/PhysRevLett.119.191801","volume":"119","author":"C Gross","year":"2017","unstructured":"C. Gross, O. Lebedev and T. Toma, Cancellation mechanism for dark-matter-nucleon interaction, Phys. Rev. Lett.\n                           119 (2017) 191801 [arXiv:1708.02253] [INSPIRE].","journal-title":"Phys. Rev. Lett."},{"key":"9773_CR11","volume":"D 98","author":"W Cheng","year":"2018","unstructured":"W. Cheng and L. Bian, From inflation to cosmological electroweak phase transition with a complex scalar singlet, Phys. Rev.\n                           D 98 (2018) 023524 [arXiv:1801.00662] [INSPIRE].","journal-title":"Phys. Rev."},{"key":"9773_CR12","unstructured":"D. Azevedo et al., Testing scalar versus vector dark matter, arXiv:1808.01598 [INSPIRE]."},{"key":"9773_CR13","unstructured":"XENON collaboration, Physics reach of the XENON1T dark matter experiment, JCAP\n                           04 (2016) 027 [arXiv:1512.07501] [INSPIRE]."},{"key":"9773_CR14","unstructured":"B.J. Mount et al., LUX-ZEPLIN (LZ) technical design report, arXiv:1703.09144 [INSPIRE]."},{"key":"9773_CR15","unstructured":"DARWIN collaboration, DARWIN: towards the ultimate dark matter detector, JCAP\n                           11 (2016) 017 [arXiv:1606.07001] [INSPIRE]."},{"key":"9773_CR16","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.dark.2012.10.006","volume":"1","author":"L Baudis","year":"2012","unstructured":"L. Baudis, Direct dark matter detection: the next decade, Phys. Dark Univ.\n                           1 (2012) 94 [arXiv:1211.7222] [INSPIRE].","journal-title":"Phys. Dark Univ."},{"key":"9773_CR17","unstructured":"T. Han, H. Liu, S. Mukhopadhyay and X. Wang, Dark matter blind spots at one-loop, arXiv:1810.04679 [INSPIRE]."},{"key":"9773_CR18","unstructured":"ATLAS, CMS collaboration, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at\n                           $$ \\sqrt{s}=7 $$\n                           and 8 TeV, JHEP\n                           08 (2016) 045 [arXiv:1606.02266] [INSPIRE]."},{"key":"9773_CR19","doi-asserted-by":"crossref","unstructured":"J.M. Cline, K. Kainulainen, P. Scott and C. Weniger, Update on scalar singlet dark matter, Phys. Rev.\n                           D 88 (2013) 055025 [Erratum ibid.\n                           D 92 (2015) 039906] [arXiv:1306.4710] [INSPIRE].","DOI":"10.1103\/PhysRevD.88.055025"},{"key":"9773_CR20","volume":"D 85","author":"JM Alarcon","year":"2012","unstructured":"J.M. Alarcon, J. Martin Camalich and J.A. 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Veltman, One loop corrections for e\n                           +\n                           e\n                           \u2212\n                           annihilation into \u03bc\n                           +\n                           \u03bc\n                           \u2212\n                           in the Weinberg model, Nucl. Phys.\n                           B 160 (1979) 151 [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"9773_CR25","first-page":"307","volume":"41","author":"A Denner","year":"1993","unstructured":"A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys.\n                           41 (1993) 307 [arXiv:0709.1075] [INSPIRE].","journal-title":"Fortsch. Phys."},{"key":"9773_CR26","doi-asserted-by":"crossref","unstructured":"T. Hahn and M. P\u00e9rez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. 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