High-energy factorization, TMD, off-shell amplitudes and nuclear effects
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2022
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Institute of Nuclear Physics Polish Academy of Sciences
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Abstract
W niniejszej rozprawie badamy faktoryzację procesów hadronowych w wysokoener-getycznych zderzeniach hadronów, ze szczególnym uwzględnieniem pędu poprzecznego. Praca jest podzielona na trzy etapy : badanie nTMDs, przedstawienie metody otrzymywania amplitud poza powłaką masy amplitud niezmienniczych ze względu na cechowanie oraz badanie ewolucji dżetów w QGP, zgodnie z równaniami BDIM.
W pierwszej części otrzymano rozkłady nTMD metodą PB. Był to pierwszy zestaw rozkładów partonowych (Pb) TMD uzyskany tą metodą. Ten rozkład partonów został użyty z generatorem MC KaTie w celu opisu danych CMS na produkcję bozonów Z Drell-Yann (gdzie zachodzi faktoryzacja k_T). Działało to zaskakująco dobrze, biorąc pod uwagę, że elementy macierzowe poza powłoką masy były obliczane tylko na poziomie drzewiastym. Była to również okazja do oszacowania efektów jądrowych i różnych wzorów faktoryzacji (faktoryzacja wysokoenergetyczna, hybrydowa, kolinearna).
Technika obliczeń elementów macierzowych poza powłaką masy jest tematem kolejnego rozdziału. Metoda partonów pomocniczych opiera się na wprowadzeniu rozważanego procesu poza powłoką masy w większym procesie na powłoce masy, aby zagwarantować niezmienność cechowania i skorzystać z szerokiwj wiedzy o amplitudach na powłoce masy. Pierwotnie ta metoda została opracowana do obliczeń na poziomie drzewiastym. W przedstawionej pracy jeden z pierwszych kroków w celu uogólnienia metody partonów pomocniczych na poziomie pętli został wykonany przez obliczenie amplitudy jedno pętlowej dla jednego gluonu poza powłoką masy i dowolnej liczby gluonów o dodatniej skrętności. Analizowano również możliwość zastosowania tej metody do otrzymania innych amplitud jednopętlowych.
Ostatni temat dotyczy ewolucji funkcji fragmentacji dżetu (opisujących rozkład energii i pędu poprzecznego jego składowej) w gęstym ośrodku, z wykorzystaniem równania BDIM. Równania te opisują utratę energii dżetu przez oddziaływanie dżetu z plazmą oraz rozszczepienie wywołane przez ośrodek, biorąc pod uwagę tylko gluony oraz zakładając że plazma jest statyczna. W pierwszym kroku opracowaliśmy kilka metod rozwiązywania równania BDIM, zanim rozważyliśmy pęd poprzeczny w funkacjach rozszczepień. Na etapie końcowym uogólniliśmy równanie BDIM, aby uwzględnić wkład kwarków do ewolucji.
Niniejsza praca opiera się na następujących publikacjach :
E. Blanco, A. van Hameren, H. Jung, A. Kusina, and K. Kutak, “Z boson production in proton-lead collisions at the LHC accounting for transverse momenta of initial partons,” Phys. Rev. D, vol. 100, no. 5, p. 054 023, 2019. doi: 10.1103/PhysRevD.100.054023. arXiv: 1905.07331 [hep-ph]
E. Blanco, A. van Hameren, P. Kotko, and K. Kutak, “All-plus helicity off-shell gauge invariant multigluon amplitudes at one loop,” JHEP, vol. 12, p. 158, 2020. doi: 10.1007/JHEP12(2020)158. arXiv: 2008.07916 [hep-ph]
E. Blanco, K. Kutak, W. Placzek, M. Rohrmoser, and R. Straka, “Medium induced QCD cascades: broadening and rescattering during branching,” JHEP, vol. 04, p. 014, 2021. doi: 10.1007/JHEP04(2021)014. arXiv: 2009.03876 [hep-ph]
E. Blanco, K. Kutak, W. Placzek, M. Rohrmoser, and K. Tywoniuk, “System of evolution equations for quark and gluon jet quenching with broadening,” Eur. Phys. J. C, vol. 82, no. 4, p. 355, 2022. doi: 10.1140/epjc/s10052-022-10311-2. arXiv:2109.05918 [hep-ph].
Bardziej ogólne tematy w tej pracy oparte są na następujących podręcznikach :
F. Halzen and A. D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics. 1984, isbn: 978-0-471-88741-6
Y. V. Kovchegov and E. Levin, Quantum chromodynamics at high energy. Cambridge University Press, Aug. 2012, vol. 33, isbn: 978-0-521-11257-4. doi: 10 . 1017/CBO9781139022187
H. Nastase, Classical Field Theory. Cambridge University Press, Mar. 2019, isbn: 978-1-108-47701-7
M. D. Schwartz, Quantum Field Theory and the Standard Model. Cambridge University Press, Mar. 2014, isbn: 978-1-107-03473-0
Ponadto bardzo przydatne okazały się następujące tezy :
M. Bury, “Phenomenology of transverse-momentum dependent factorizations in
hadronic collisions,” Ph.D. dissertation, IFJ-PAN, 2020
F. Van der Veken, “Wilson lines : applications in QCD,” Ph.D. dissertation, Antwerp
U., 2014
A. Lelek, “Determination of TMD parton densities from HERA data and appli-
cation to pp processes,” Ph.D. dissertation, Hamburg U., Hamburg, 2018. doi:
10.3204/PUBDB-2018-02949
V. Vila Perez, “Jet quenching and heavy ion collisions,” Ph.D. dissertation, Santiago
de Compostela U., 2020
M. De Angelis, “QCD Evolution At Amplitude Level,” Ph.D. dissertation, The
University of Manchester, 2021.
In this thesis, we explore the factorization of hadronic processes in heavy-ion collision at high energy with a focus on accounting for transverse momentum. This exploration is separated into three stages : the study of nuclear Transverse Momentum Dependant PDFs (nTMD), the presentation of a method to calculate gauge invariant off-shell amplitudes, and the study of jet evolution in Quark-Gluon Plasma (QGP), following Blaizot-Dominguez-Iancu-Mehtar-Tani (BDIM) equations. In the first part, a set of nTMD has been obtained using the Parton Branching (PB) method (which solves the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation, keeping track of the transverse momentum during the evolution). It was the first lead (Pb) Transverse Momentum Dependant PDF (TMD) set obtained through this method. This set has been tested with the Monte-Carlo (MC) generator KaTie to reproduce CMS data for Drell-Yann Z-boson production (where kT -factorization holds). It worked surprisingly well considering that the (off-shell) matrix elements were only calculated at tree level. This was also the occasion to test, in this context, nuclear effects and different factorization formulas (high energy, hybrid, collinear). The method used to obtain the off-shell matrix elements is the focus of the next part. The auxiliary parton method is based on embedding the considered off-shell process into a larger one, on-shell, to guarantee gauge invariance and to benefit from our knowledge of on-shell amplitudes. Originally, it was developed for tree-level calculation only. In this thesis, one of the first steps to generalize the auxiliary parton method at loop-level has been done through the calculation of the one-loop amplitude for one off-shell-gluon and an arbitrary number of plus helicity gluons. Also, some of the difficulties related to the application of this method to other one-loop amplitudes were studied. The last topic concerns the evolution of jet fragmentation functions (describing the energy and transverse momentum component of its constituents) in a dense medium, through the BDIM equation. These equations describe the jet energy loss through jet broadening and medium-induced splitting, accounting for gluons only and considering the medium static. We first developed several methods to solve the integrated BDIM before accounting for transverse momentum in branching. Finally, we have generalized the BDIM to account for quarks. This thesis is based on the following publications : • E. Blanco, A. van Hameren, H. Jung, A. Kusina, and K. Kutak, “Z boson production in proton-lead collisions at the LHC accounting for transverse momenta of initial partons,” Phys. Rev. D, vol. 100, no. 5, p. 054 023, 2019. doi: 10.1103/PhysRevD.100.054023. arXiv: 1905.07331 [hep-ph] • E. Blanco, A. van Hameren, P. Kotko, and K. Kutak, “All-plus helicity off-shell gauge invariant multigluon amplitudes at one loop,” JHEP, vol. 12, p. 158, 2020. doi: 10.1007/JHEP12(2020)158. arXiv: 2008.07916 [hep-ph] • E. Blanco, K. Kutak, W. Placzek, M. Rohrmoser, and R. Straka, “Medium induced QCD cascades: broadening and rescattering during branching,” JHEP, vol. 04, p. 014, 2021. doi: 10.1007/JHEP04(2021)014. arXiv: 2009.03876 [hep-ph] • E. Blanco, K. Kutak, W. Placzek, M. Rohrmoser, and K. Tywoniuk, “System of evolution equations for quark and gluon jet quenching with broadening,” Eur. Phys. J. C, vol. 82, no. 4, p. 355, 2022. doi: 10.1140/epjc/s10052-022-10311-2. arXiv:2109.05918 [hep-ph]. The more general topics in this thesis are based on the following textbooks : • F. Halzen and A. D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics. 1984, isbn: 978-0-471-88741-6 • Y. V. Kovchegov and E. Levin, Quantum chromodynamics at high energy. Cambridge University Press, Aug. 2012, vol. 33, isbn: 978-0-521-11257-4. doi: 10.1017/CBO9781139022187 • H. Nastase, Classical Field Theory. Cambridge University Press, Mar. 2019, isbn: 978-1-108-47701-7 • M. D. Schwartz, Quantum Field Theory and the Standard Model. Cambridge University Press, Mar. 2014, isbn: 978-1-107-03473-0 Moreover, the following theses were highly useful : • M. Bury, “Phenomenology of transverse-momentum dependent factorizations in hadronic collisions,” Ph.D. dissertation, IFJ-PAN, 2020 • F. Van der Veken, “Wilson lines : applications in QCD,” Ph.D. dissertation, Antwerp U., 2014 • A. Lelek, “Determination of TMD parton densities from HERA data and application to pp processes,” Ph.D. dissertation, Hamburg U., Hamburg, 2018. doi: 10.3204/PUBDB-2018-02949 • V. Vila Perez, “Jet quenching and heavy ion collisions,” Ph.D. dissertation, Santiago de Compostela U., 2020 • M. De Angelis, “QCD Evolution At Amplitude Level,” Ph.D. dissertation, The University of Manchester, 2021.
In this thesis, we explore the factorization of hadronic processes in heavy-ion collision at high energy with a focus on accounting for transverse momentum. This exploration is separated into three stages : the study of nuclear Transverse Momentum Dependant PDFs (nTMD), the presentation of a method to calculate gauge invariant off-shell amplitudes, and the study of jet evolution in Quark-Gluon Plasma (QGP), following Blaizot-Dominguez-Iancu-Mehtar-Tani (BDIM) equations. In the first part, a set of nTMD has been obtained using the Parton Branching (PB) method (which solves the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation, keeping track of the transverse momentum during the evolution). It was the first lead (Pb) Transverse Momentum Dependant PDF (TMD) set obtained through this method. This set has been tested with the Monte-Carlo (MC) generator KaTie to reproduce CMS data for Drell-Yann Z-boson production (where kT -factorization holds). It worked surprisingly well considering that the (off-shell) matrix elements were only calculated at tree level. This was also the occasion to test, in this context, nuclear effects and different factorization formulas (high energy, hybrid, collinear). The method used to obtain the off-shell matrix elements is the focus of the next part. The auxiliary parton method is based on embedding the considered off-shell process into a larger one, on-shell, to guarantee gauge invariance and to benefit from our knowledge of on-shell amplitudes. Originally, it was developed for tree-level calculation only. In this thesis, one of the first steps to generalize the auxiliary parton method at loop-level has been done through the calculation of the one-loop amplitude for one off-shell-gluon and an arbitrary number of plus helicity gluons. Also, some of the difficulties related to the application of this method to other one-loop amplitudes were studied. The last topic concerns the evolution of jet fragmentation functions (describing the energy and transverse momentum component of its constituents) in a dense medium, through the BDIM equation. These equations describe the jet energy loss through jet broadening and medium-induced splitting, accounting for gluons only and considering the medium static. We first developed several methods to solve the integrated BDIM before accounting for transverse momentum in branching. Finally, we have generalized the BDIM to account for quarks. This thesis is based on the following publications : • E. Blanco, A. van Hameren, H. Jung, A. Kusina, and K. Kutak, “Z boson production in proton-lead collisions at the LHC accounting for transverse momenta of initial partons,” Phys. Rev. D, vol. 100, no. 5, p. 054 023, 2019. doi: 10.1103/PhysRevD.100.054023. arXiv: 1905.07331 [hep-ph] • E. Blanco, A. van Hameren, P. Kotko, and K. Kutak, “All-plus helicity off-shell gauge invariant multigluon amplitudes at one loop,” JHEP, vol. 12, p. 158, 2020. doi: 10.1007/JHEP12(2020)158. arXiv: 2008.07916 [hep-ph] • E. Blanco, K. Kutak, W. Placzek, M. Rohrmoser, and R. Straka, “Medium induced QCD cascades: broadening and rescattering during branching,” JHEP, vol. 04, p. 014, 2021. doi: 10.1007/JHEP04(2021)014. arXiv: 2009.03876 [hep-ph] • E. Blanco, K. Kutak, W. Placzek, M. Rohrmoser, and K. Tywoniuk, “System of evolution equations for quark and gluon jet quenching with broadening,” Eur. Phys. J. C, vol. 82, no. 4, p. 355, 2022. doi: 10.1140/epjc/s10052-022-10311-2. arXiv:2109.05918 [hep-ph]. The more general topics in this thesis are based on the following textbooks : • F. Halzen and A. D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics. 1984, isbn: 978-0-471-88741-6 • Y. V. Kovchegov and E. Levin, Quantum chromodynamics at high energy. Cambridge University Press, Aug. 2012, vol. 33, isbn: 978-0-521-11257-4. doi: 10.1017/CBO9781139022187 • H. Nastase, Classical Field Theory. Cambridge University Press, Mar. 2019, isbn: 978-1-108-47701-7 • M. D. Schwartz, Quantum Field Theory and the Standard Model. Cambridge University Press, Mar. 2014, isbn: 978-1-107-03473-0 Moreover, the following theses were highly useful : • M. Bury, “Phenomenology of transverse-momentum dependent factorizations in hadronic collisions,” Ph.D. dissertation, IFJ-PAN, 2020 • F. Van der Veken, “Wilson lines : applications in QCD,” Ph.D. dissertation, Antwerp U., 2014 • A. Lelek, “Determination of TMD parton densities from HERA data and application to pp processes,” Ph.D. dissertation, Hamburg U., Hamburg, 2018. doi: 10.3204/PUBDB-2018-02949 • V. Vila Perez, “Jet quenching and heavy ion collisions,” Ph.D. dissertation, Santiago de Compostela U., 2020 • M. De Angelis, “QCD Evolution At Amplitude Level,” Ph.D. dissertation, The University of Manchester, 2021.
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