Geometric scaling is well confirmed for transverse-momentum distributions observed in proton-proton collisions at Large Hadron Collider (LHC) energies. We introduced multiplicity dependence on a saturation momentum of the geometrical scaling, assuming the scaling holds for semi-inclusive distributions as well as for inclusive distributions. The saturation momentum is usually given by Bjorken's variable, but redefinition of the scaling variable can make the saturation momentum a function of collision energy . We treat the energy as a free parameter (denoted to distinguish it from ) and associate the energy-dependent saturation momentum with particle number density. By using for a scaling variable , we show semi-inclusive distributions can be geometrically scaled, i.e., all semi-inclusive spectra observed at , 2.76, and 7.00 TeV overlap one universal function. The particle density dependencies of mean transverse momentum for LHC energies scales in terms of . Furthermore, our model explains a scaling property of event-by-event fluctuation measure at LHC energies for collisions, where is a two-particle transverse-momentum correlator. Our analysis of the fluctuation makes possible to evaluate a nonperturbative coefficient of the gluon correlation function.
{ "_oai": { "updated": "2021-08-28T22:18:12Z", "id": "oai:repo.scoap3.org:49985", "sets": [ "PRC" ] }, "authors": [ { "raw_name": "Takeshi Osada", "affiliations": [ { "country": "Japan", "value": "Department of Physics, Faculty of Liberal Arts and Sciences, and Tokyo City University, Tamazutsumi 1-28-1, Setagaya-ku, Tokyo 158-8557, Japan" } ], "surname": "Osada", "given_names": "Takeshi", "full_name": "Osada, Takeshi" }, { "raw_name": "Takuya Kumaoka", "affiliations": [ { "country": "Japan", "value": "Department of Physics, Shinshu University, Matsumoto 390-8621, Japan" } ], "surname": "Kumaoka", "given_names": "Takuya", "full_name": "Kumaoka, Takuya" } ], "titles": [ { "source": "APS", "title": "Saturation momentum scale extracted from semi-inclusive transverse spectra in high-energy <math><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions" } ], "dois": [ { "value": "10.1103/PhysRevC.100.034906" } ], "publication_info": [ { "journal_volume": "100", "journal_title": "Physical Review C", "material": "article", "journal_issue": "3", "year": 2019 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2021-08-25T10:38:49.666058", "source": "APS", "method": "APS", "submission_number": "810b323c058f11ecb53772fd3742099d" }, "page_nr": [ 8 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2019" } ], "control_number": "49985", "record_creation_date": "2019-09-26T16:30:04.787865", "_files": [ { "checksum": "md5:e5b87b2cf278c64183a3dfefe2af4abf", "filetype": "pdf", "bucket": "e01f1491-ce93-40f0-afff-1fb88abeb1b2", "version_id": "3ddd252d-8a2b-4e64-9fce-afd0769ac804", "key": "10.1103/PhysRevC.100.034906.pdf", "size": 791154 }, { "checksum": "md5:019eefd5bec627c52cc37e121278ea8b", "filetype": "xml", "bucket": "e01f1491-ce93-40f0-afff-1fb88abeb1b2", "version_id": "25b0b1d3-076a-416c-a184-5d7b06948f0f", "key": "10.1103/PhysRevC.100.034906.xml", "size": 181194 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-ph", "nucl-th" ], "value": "1904.10823" } ], "abstracts": [ { "source": "APS", "value": "Geometric scaling is well confirmed for transverse-momentum distributions observed in proton-proton collisions at Large Hadron Collider (LHC) energies. We introduced multiplicity dependence on a saturation momentum of the geometrical scaling, assuming the scaling holds for semi-inclusive distributions as well as for inclusive distributions. The saturation momentum is usually given by Bjorken's <math><mi>x</mi></math> variable, but redefinition of the scaling variable can make the saturation momentum a function of collision energy <math><mi>W</mi></math>. We treat the energy as a free parameter (denoted <math><msup><mi>W</mi><mo>*</mo></msup></math> to distinguish it from <math><mi>W</mi></math>) and associate the energy-dependent saturation momentum <math><mrow><msub><mi>Q</mi><mi>sat</mi></msub><mrow><mo>(</mo><msup><mi>W</mi><mo>*</mo></msup><mo>)</mo></mrow></mrow></math> with particle number density. By using <math><mrow><msub><mi>Q</mi><mi>sat</mi></msub><mrow><mo>(</mo><msup><mi>W</mi><mo>*</mo></msup><mo>)</mo></mrow></mrow></math> for a scaling variable <math><mi>\u03c4</mi></math>, we show semi-inclusive distributions can be geometrically scaled, i.e., all semi-inclusive spectra observed at <math><mrow><mi>W</mi><mo>=</mo><mn>0.90</mn></mrow></math>, 2.76, and 7.00 TeV overlap one universal function. The particle density dependencies of mean transverse momentum <math><mrow><mo>\u2329</mo><msub><mi>p</mi><mi>T</mi></msub><mo>\u232a</mo></mrow></math> for LHC energies scales in terms of <math><mrow><msub><mi>Q</mi><mi>sat</mi></msub><mrow><mo>(</mo><msup><mi>W</mi><mo>*</mo></msup><mo>)</mo></mrow></mrow></math>. Furthermore, our model explains a scaling property of event-by-event <math><msub><mi>p</mi><mi>T</mi></msub></math> fluctuation measure <math><mrow><msqrt><msub><mi>C</mi><mi>m</mi></msub></msqrt><mo>/</mo><mrow><mo>\u2329</mo><msub><mi>p</mi><mi>T</mi></msub><mo>\u232a</mo></mrow></mrow></math> at LHC energies for <math><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions, where <math><msub><mi>C</mi><mi>m</mi></msub></math> is a two-particle transverse-momentum correlator. Our analysis of the <math><msub><mi>p</mi><mi>T</mi></msub></math> fluctuation makes possible to evaluate a nonperturbative coefficient of the gluon correlation function." } ], "imprints": [ { "date": "2019-09-26", "publisher": "APS" } ] }