Periodic Reporting for period 1 - RadCor4HEF (Radiative Corrections for Heavy Quark(-onium) Production in High-Energy Factorisation)
Período documentado: 2022-12-01 hasta 2024-11-30
With the Large Hadron Collider (LHC) and the prospects for the Future Hadron-Hadron Circular Collider (FCC-hh), hadronic collisions at high energy will remain for the coming decades our main tools to look for new physical phenomena. In such collisions, the processes involving strong interactions, i.e. Quantum Chromodynamics (QCD), constitute
the main part of the Standard Model (SM) background. With increasing collision energy, the commonly used framework for theoretical predictions in QCD -- the Collinear Factorisation (CF) in the fixed order in strong coupling constant (alpha_s), becomes insufficient. This happens because of the appearance of large higher-order in alpha_s corrections to the hard-scattering coefficient function of CF, enhanced by logarithms of partonic collision energy or rapidity between two particles or jets, produced in the collision. In this project we have used the formalism of High-Energy Factorisation (HEF) to resum such large logarithmic corrections within CF for processes of inclusive and exclusive heavy quarkonium production. We match the HEF-resummed predictions with fixed-order computations in CF to provide uniformly-accurate theoretical predictions across wide range of energies. We also compute one-loop and real-emission Next-to-Leading Order (NLO) corrections to one of the process-dependent part of the HEF-formula -- the impact-factor, with the goal of extending our predictions beyond the Doubly-Logarithmic Approximation (DLA) which had been used so far to provide CF+HEF matched predictions.
the main part of the Standard Model (SM) background. With increasing collision energy, the commonly used framework for theoretical predictions in QCD -- the Collinear Factorisation (CF) in the fixed order in strong coupling constant (alpha_s), becomes insufficient. This happens because of the appearance of large higher-order in alpha_s corrections to the hard-scattering coefficient function of CF, enhanced by logarithms of partonic collision energy or rapidity between two particles or jets, produced in the collision. In this project we have used the formalism of High-Energy Factorisation (HEF) to resum such large logarithmic corrections within CF for processes of inclusive and exclusive heavy quarkonium production. We match the HEF-resummed predictions with fixed-order computations in CF to provide uniformly-accurate theoretical predictions across wide range of energies. We also compute one-loop and real-emission Next-to-Leading Order (NLO) corrections to one of the process-dependent part of the HEF-formula -- the impact-factor, with the goal of extending our predictions beyond the Doubly-Logarithmic Approximation (DLA) which had been used so far to provide CF+HEF matched predictions.
1) We have performed the resummation of higher-order corrections enhanced by logarithms of partonic center-of-mass energy for the process of inclusive photoproduction of J/psi and Upsilon mesons in DLA HEF and matched the resummed results to the NLO CF computation. This allowed us to solve the problem of high-energy instability of the NLO CF computation and to describe experimental data on total cross section of inclusive photoproduction of J/psi over the whole available range of photon-proton collision energies from tens to hundreds of GeV and to provide reliable predictions for the inclusive photoproduction cross seciton at TeV energies, which can be measured in ultra-peripheral ion-proton collisions at the LHC [ArXiv:hep-ph/2409.01756]. These results are published in [Eur.Phys.J.C 84 (2024) 4, 351; ArXiv:hep-ph/2306.02425].
2) We have performed the HEF resummation of higher-order corrections enhanced by logarithms of partonic center-of-mass energy for the process of exclusive photoproduction of J/psi and Upsilon mesons in DLA HEF and matched the resummed results to NLO CF result, which in this case is sensitive to gluon and quark Generalised Parton Distributions (GPDs). This resummation and matching have solved the long-standing problem of perturbative instability of the NLO CF computation at high photon-proton collision energy and we obtain the physically reasonable scaling of the cross section with energy. The results of the computation agree with data form HERA within large scale-uncertainty band, which means that our computation should be supplemented with Next-to-DLA and relativistic corrections to improve agreement with data. These results are published in [Phys.Lett.B 859 (2024) 139117; ArXiv:hep-ph/2409.05738].
3) We have computed the one-loop corrections to impact-factors of inclusive photoproduction of the so-called 1S0^8-state and inclusive forward-in-rapidity hadroproduction of 1S0^8, 1S0^1 and 3S1^8 states of the heavy quark+anti-quark (Q+anti-Q) pair. These impact-factors are needed for the computation of cross sections of inclusive production of charmonia and bottomonia at forward rapidities in the Non-Relativistic QCD factorisation (NRQCD-factorisation) formalism and with the inclusion of the next-to-DLA (NDLA) HEF resummation of partonic energy logarithms. This computation involved the automation of generation of Feynman diagrams within the gauge-invariant EFT for Multi-Regge processes in QCD [Nucl.Phys.B 452 (1995), p. 369], automation of their tensor-reduction down to scalar integrals and computation of one-loop scalar integrals with massive internal lines and rapidity divergences. The convenient procedure for separation of rapidity divergence from the mass-dependence was found. Obtained analytic results for one-loop impact-factors allow one to reproduce the high-energy limit of the exact one-loop QCD amplitude. This had been checked numerically, since exact one-loop QCD amplitudes of quarkonium production processes are too complicated to deal with them in the fully analytic form. The expected level of agreement between one-loop EFT results and the full QCD result in the high-energy limit was found, which is a very strong cross-check of obtained results. These results are published in a preprint [ArXiv:hep-ph/2408.06234] which is already accepted for publication in JHEP.
4) We have computed the real-emission NLO corrections (in quark and gluon channels) to the impact-factor of the forward-in-rapidity hadroproduction of the 1S0^1-state of the Q+anti-Q pair, which is the leading contribution to the production of eta_c and eta_b mesons. We have combined this real-emission correction with one-loop virtual correction to this impact-factor, obtained at the previous step, and with the appropriate counter-terms, renormalising the ultraviolet divergences, collinear PDF of the incoming on-shell gluon and converting the obtained result to the rapidity-factorisation scheme required for the HEF resummation of higher-order QCD corrections enhanced by partonic energy logarithms. We observe, that all divergences cancel in the final result. The obtained finite NLO correction to the impact-factor in the gluon channel is published in the conference proceedings [ArXiv:hep-ph/2408.09440] and the paper with detailed description of the computation is in preparation.
5) We have studied the problem of apparent violation of the standard eikonal approximation which is typically used to study the high-energy limit of QCD amplitudes. The violation happens in presence of insertions of non-renormalisable operators in the amplitude. As an example, we have discussed one-loop amplitudes with the insertion of the operator tr[G_{mu nu} G^{mu nu}], which is also known as an effective coupling between SM Higgs boson and gluons, which arises in the infinite top-quark-mass limit. We find that while terms inconsistent with eikonal approximation appear in separate Feynman diagrams, they cancel in the full amplitude, so that the final result for the Regge limit is consistent with gluon Reggeisation and is correctly predicted by the gauge-invariant EFT for high-energy prcesses in QCD. This results are published in [JHEP 04 (2024) 078; ArXiv:hep-ph/2401.17843].
2) We have performed the HEF resummation of higher-order corrections enhanced by logarithms of partonic center-of-mass energy for the process of exclusive photoproduction of J/psi and Upsilon mesons in DLA HEF and matched the resummed results to NLO CF result, which in this case is sensitive to gluon and quark Generalised Parton Distributions (GPDs). This resummation and matching have solved the long-standing problem of perturbative instability of the NLO CF computation at high photon-proton collision energy and we obtain the physically reasonable scaling of the cross section with energy. The results of the computation agree with data form HERA within large scale-uncertainty band, which means that our computation should be supplemented with Next-to-DLA and relativistic corrections to improve agreement with data. These results are published in [Phys.Lett.B 859 (2024) 139117; ArXiv:hep-ph/2409.05738].
3) We have computed the one-loop corrections to impact-factors of inclusive photoproduction of the so-called 1S0^8-state and inclusive forward-in-rapidity hadroproduction of 1S0^8, 1S0^1 and 3S1^8 states of the heavy quark+anti-quark (Q+anti-Q) pair. These impact-factors are needed for the computation of cross sections of inclusive production of charmonia and bottomonia at forward rapidities in the Non-Relativistic QCD factorisation (NRQCD-factorisation) formalism and with the inclusion of the next-to-DLA (NDLA) HEF resummation of partonic energy logarithms. This computation involved the automation of generation of Feynman diagrams within the gauge-invariant EFT for Multi-Regge processes in QCD [Nucl.Phys.B 452 (1995), p. 369], automation of their tensor-reduction down to scalar integrals and computation of one-loop scalar integrals with massive internal lines and rapidity divergences. The convenient procedure for separation of rapidity divergence from the mass-dependence was found. Obtained analytic results for one-loop impact-factors allow one to reproduce the high-energy limit of the exact one-loop QCD amplitude. This had been checked numerically, since exact one-loop QCD amplitudes of quarkonium production processes are too complicated to deal with them in the fully analytic form. The expected level of agreement between one-loop EFT results and the full QCD result in the high-energy limit was found, which is a very strong cross-check of obtained results. These results are published in a preprint [ArXiv:hep-ph/2408.06234] which is already accepted for publication in JHEP.
4) We have computed the real-emission NLO corrections (in quark and gluon channels) to the impact-factor of the forward-in-rapidity hadroproduction of the 1S0^1-state of the Q+anti-Q pair, which is the leading contribution to the production of eta_c and eta_b mesons. We have combined this real-emission correction with one-loop virtual correction to this impact-factor, obtained at the previous step, and with the appropriate counter-terms, renormalising the ultraviolet divergences, collinear PDF of the incoming on-shell gluon and converting the obtained result to the rapidity-factorisation scheme required for the HEF resummation of higher-order QCD corrections enhanced by partonic energy logarithms. We observe, that all divergences cancel in the final result. The obtained finite NLO correction to the impact-factor in the gluon channel is published in the conference proceedings [ArXiv:hep-ph/2408.09440] and the paper with detailed description of the computation is in preparation.
5) We have studied the problem of apparent violation of the standard eikonal approximation which is typically used to study the high-energy limit of QCD amplitudes. The violation happens in presence of insertions of non-renormalisable operators in the amplitude. As an example, we have discussed one-loop amplitudes with the insertion of the operator tr[G_{mu nu} G^{mu nu}], which is also known as an effective coupling between SM Higgs boson and gluons, which arises in the infinite top-quark-mass limit. We find that while terms inconsistent with eikonal approximation appear in separate Feynman diagrams, they cancel in the full amplitude, so that the final result for the Regge limit is consistent with gluon Reggeisation and is correctly predicted by the gauge-invariant EFT for high-energy prcesses in QCD. This results are published in [JHEP 04 (2024) 078; ArXiv:hep-ph/2401.17843].
1) The application of DLA HEF resummation to the inclusive photoproduciton of J/psi and Upsilon mesons is completely new, as well as the matching procedure between NLO CF and DLA HEF parts of the computation with the use of smooth weight functions.
2) While the possibility to apply the HEF resummation to the exclusive J/psi photoproduction had been discussed before, the matching procedure between NLO CF and DLA HEF computations is completely new.
3) All results for one-loop impact-factors for heavy quarkonium production are completely new. The obtained scalar integrals, used in this computation, are also new.
4) The NLO correction to the eta_c-production impact factor is a completely new result of complexity, which is unprecedented in the field of low-x Physics.
5) The phenomenon of violation of eikonal approximation in separate diagrams with insertions of non-renormalisable operators had been discovered by us for the first time, and have not been noticed before in the literature. Is the cancellation of factorisation-violating terms just a fortunate coincidence in the example we have studied or a general phenomenon, remains to be seen.
2) While the possibility to apply the HEF resummation to the exclusive J/psi photoproduction had been discussed before, the matching procedure between NLO CF and DLA HEF computations is completely new.
3) All results for one-loop impact-factors for heavy quarkonium production are completely new. The obtained scalar integrals, used in this computation, are also new.
4) The NLO correction to the eta_c-production impact factor is a completely new result of complexity, which is unprecedented in the field of low-x Physics.
5) The phenomenon of violation of eikonal approximation in separate diagrams with insertions of non-renormalisable operators had been discovered by us for the first time, and have not been noticed before in the literature. Is the cancellation of factorisation-violating terms just a fortunate coincidence in the example we have studied or a general phenomenon, remains to be seen.