Abstract
We calculate the small-b (or large-qT) matching of transverse momentum de- pendent (TMD) distribution for linearly polarized gluons to the integrated gluon distributions at the next-to-next-to-leading order (NNLO). This is the last missing part for the complete NNLO prediction of the Higgs spectrum within TMD factorization. We discuss the numerical impact of the correction so derived to the qT -differential cross-section for Higgs boson production and to the positivity bound for linearly polarized gluon transverse momentum distribution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.R. Ellis, M.K. Gaillard and D.V. Nanopoulos, A Phenomenological Profile of the Higgs Boson, Nucl. Phys. B 106 (1976) 292 [INSPIRE].
M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas, Higgs boson production at the LHC, Nucl. Phys. B 453 (1995) 17 [hep-ph/9504378] [INSPIRE].
A. Djouadi, The Anatomy of electro-weak symmetry breaking. I: The Higgs boson in the standard model, Phys. Rept. 457 (2008) 1 [hep-ph/0503172] [INSPIRE].
S. Catani, E. D’Emilio and L. Trentadue, The Gluon Form-factor to Higher Orders: Gluon Gluon Annihilation at Small Q− transverse, Phys. Lett. B 211 (1988) 335 [INSPIRE].
J. Collins, Foundations of perturbative QCD, Cambridge University Press (2013) [INSPIRE].
M.G. Echevarria, A. Idilbi and I. Scimemi, Factorization Theorem For Drell-Yan At Low qT And Transverse Momentum Distributions On-The-Light-Cone, JHEP 07 (2012) 002 [arXiv:1111.4996] [INSPIRE].
M.G. Echevarria, A. Idilbi and I. Scimemi, Unified treatment of the QCD evolution of all (un-)polarized transverse momentum dependent functions: Collins function as a study case, Phys. Rev. D 90 (2014) 014003 [arXiv:1402.0869] [INSPIRE].
A. Vladimirov, Structure of rapidity divergences in multi-parton scattering soft factors, JHEP 04 (2018) 045 [arXiv:1707.07606] [INSPIRE].
M.G. Echevarria, T. Kasemets, P.J. Mulders and C. Pisano, QCD evolution of (un) polarized gluon TMDPDFs and the Higgs qT -distribution, JHEP 07 (2015) 158 [Erratum ibid. 05 (2017) 073] [arXiv:1502.05354] [INSPIRE].
S. Catani and M. Grazzini, QCD transverse-momentum resummation in gluon fusion processes, Nucl. Phys. B 845 (2011) 297 [arXiv:1011.3918] [INSPIRE].
D. Boer, W.J. den Dunnen, C. Pisano, M. Schlegel and W. Vogelsang, Linearly Polarized Gluons and the Higgs Transverse Momentum Distribution, Phys. Rev. Lett. 108 (2012) [arXiv:1109.1444] [INSPIRE].
T. Becher, M. Neubert and D. Wilhelm, Higgs-Boson Production at Small Transverse Momentum, JHEP 05 (2013) 110 [arXiv:1212.2621] [INSPIRE].
P.J. Mulders and J. Rodrigues, Transverse momentum dependence in gluon distribution and fragmentation functions, Phys. Rev. D 63 (2001) 094021 [hep-ph/0009343] [INSPIRE].
T. Becher and M. Neubert, Drell-Yan Production at Small qT, Transverse Parton Distributions and the Collinear Anomaly, Eur. Phys. J. C 71 (2011) 1665 [arXiv:1007.4005] [INSPIRE].
T. Gehrmann, T. Luebbert and L.L. Yang, Calculation of the transverse parton distribution functions at next-to-next-to-leading order, JHEP 06 (2014) 155 [arXiv:1403.6451] [INSPIRE].
M.G. Echevarria, I. Scimemi and A. Vladimirov, Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order, JHEP 09 (2016) 004 [arXiv:1604.07869] [INSPIRE].
D. Gutiérrez-Reyes, I. Scimemi and A.A. Vladimirov, Twist-2 matching of transverse momentum dependent distributions, Phys. Lett. B 769 (2017) 84 [arXiv:1702.06558] [INSPIRE].
M.-X. Luo, X. Wang, X. Xu, L.L. Yang, T.-Z. Yang and H.X. Zhu, Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case, JHEP 10 (2019) 083 [arXiv:1908.03831] [INSPIRE].
I. Scimemi and A. Vladimirov, Systematic analysis of double-scale evolution, JHEP 08 (2018) 003 [arXiv:1803.11089] [INSPIRE].
J. Cruz-Martinez, T. Gehrmann, E.W.N. Glover and A. Huss, Second-order QCD effects in Higgs boson production through vector boson fusion, Phys. Lett. B 781 (2018) 672 [arXiv:1802.02445] [INSPIRE].
I. Scimemi and A. Vladimirov, Analysis of vector boson production within TMD factorization, Eur. Phys. J. C 78 (2018) 89 [arXiv:1706.01473] [INSPIRE].
V. Bertone, I. Scimemi and A. Vladimirov, Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production, JHEP 06 (2019) 028 [arXiv:1902.08474] [INSPIRE].
X. Chen et al., Precise QCD Description of the Higgs Boson Transverse Momentum Spectrum, Phys. Lett. B 788 (2019) 425 [arXiv:1805.00736] [INSPIRE].
M.G. Echevarria, I. Scimemi and A. Vladimirov, Transverse momentum dependent fragmentation function at next-to-next-to-leading order, Phys. Rev. D 93 (2016) 011502 [Erratum ibid. D 94 (2016) 099904] [arXiv:1509.06392] [INSPIRE].
M.G. Echevarria, I. Scimemi and A. Vladimirov, Universal transverse momentum dependent soft function at NNLO, Phys. Rev. D 93 (2016) 054004 [arXiv:1511.05590] [INSPIRE].
D. Gutierrez-Reyes, I. Scimemi and A. Vladimirov, Transverse momentum dependent transversely polarized distributions at next-to-next-to-leading-order, JHEP 07 (2018) 172 [arXiv:1805.07243] [INSPIRE].
G. Bozzi, S. Catani, D. de Florian and M. Grazzini, Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC, Nucl. Phys. B 737 (2006) 73 [hep-ph/0508068] [INSPIRE].
S. Mantry and F. Petriello, Factorization and Resummation of Higgs Boson Differential Distributions in Soft-Collinear Effective Theory, Phys. Rev. D 81 (2010) 093007 [arXiv:0911.4135] [INSPIRE].
D. de Florian, G. Ferrera, M. Grazzini and D. Tommasini, Transverse-momentum resummation: Higgs boson production at the Tevatron and the LHC, JHEP 11 (2011) 064 [arXiv:1109.2109] [INSPIRE].
W. Bizoń et al., Fiducial distributions in Higgs and Drell-Yan production at N3 LL+NNLO, JHEP 12 (2018) 132 [arXiv:1805.05916] [INSPIRE].
D. Boer, S.J. Brodsky, P.J. Mulders and C. Pisano, Direct Probes of Linearly Polarized Gluons inside Unpolarized Hadrons, Phys. Rev. Lett. 106 (2011) 132001 [arXiv:1011.4225] [INSPIRE].
A. Metz and J. Zhou, Distribution of linearly polarized gluons inside a large nucleus, Phys. Rev. D 84 (2011) 051503 [arXiv:1105.1991] [INSPIRE].
F. Dominguez, J.-W. Qiu, B.-W. Xiao and F. Yuan, On the linearly polarized gluon distributions in the color dipole model, Phys. Rev. D 85 (2012) 045003 [arXiv:1109.6293] [INSPIRE].
C. Pisano, D. Boer, S.J. Brodsky, M.G.A. Buffing and P.J. Mulders, Linear polarization of gluons and photons in unpolarized collider experiments, JHEP 10 (2013) 024 [arXiv:1307.3417] [INSPIRE].
A. Dumitru, T. Lappi and V. Skokov, Distribution of Linearly Polarized Gluons and Elliptic Azimuthal Anisotropy in Deep Inelastic Scattering Dijet Production at High Energy, Phys. Rev. Lett. 115 (2015) 252301 [arXiv:1508.04438] [INSPIRE].
A. Mukherjee and S. Rajesh, Linearly polarized gluons in charmonium and bottomonium production in color octet model, Phys. Rev. D 95 (2017) 034039 [arXiv:1611.05974] [INSPIRE].
D. Boer, P.J. Mulders, J. Zhou and Y.-j. Zhou, Suppression of maximal linear gluon polarization in angular asymmetries, JHEP 10 (2017) 196 [arXiv:1702.08195] [INSPIRE].
A.V. Efremov, N.Y. Ivanov and O.V. Teryaev, How to measure the linear polarization of gluons in unpolarized proton using the heavy-quark pair leptoproduction, Phys. Lett. B 777 (2018) 435 [arXiv:1711.05221] [INSPIRE].
A.V. Efremov, N.Y. Ivanov and O.V. Teryaev, The ratio R = dσL /dσT in heavy-quark pair leptoproduction as a probe of linearly polarized gluons in unpolarized proton, Phys. Lett. B 780 (2018) 303 [arXiv:1801.03398] [INSPIRE].
R. Kishore and A. Mukherjee, Accessing linearly polarized gluon distribution in J/𝜓 production at the electron-ion collider, Phys. Rev. D 99 (2019) 054012 [arXiv:1811.07495] [INSPIRE].
M.G. Echevarria, Proper TMD factorization for quarkonia production: pp → ηc,b as a study case, JHEP 10 (2019) 144 [arXiv:1907.06494] [INSPIRE].
C. Marquet, C. Roiesnel and P. Taels, Linearly polarized small-x gluons in forward heavy-quark pair production, Phys. Rev. D 97 (2018) 014004 [arXiv:1710.05698] [INSPIRE].
L.D. McLerran and R. Venugopalan, Gluon distribution functions for very large nuclei at small transverse momentum, Phys. Rev. D 49 (1994) 3352 [hep-ph/9311205] [INSPIRE].
artemide web-page, https://teorica.fis.ucm.es/artemide/.
artemide repository, https://github.com/vladimirovalexey/artemide-public.
I. Scimemi, A. Tarasov and A. Vladimirov, Collinear matching for Sivers function at next-to-leading order, JHEP 05 (2019) 125 [arXiv:1901.04519] [INSPIRE].
T. Gehrmann, T. Lubbert and L.L. Yang, Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case, Phys. Rev. Lett. 109 (2012) 242003 [arXiv:1209.0682] [INSPIRE].
M.G. Echevarría, A. Idilbi and I. Scimemi, Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions, Phys. Lett. B 726 (2013) 795 [arXiv:1211.1947] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, The Quark form-factor at higher orders, JHEP 08 (2005) 049 [hep-ph/0507039] [INSPIRE].
T. Gehrmann, E.W.N. Glover, T. Huber, N. Ikizlerli and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, JHEP 06 (2010) 094 [arXiv:1004.3653] [INSPIRE].
A.A. Vladimirov, Correspondence between Soft and Rapidity Anomalous Dimensions, Phys. Rev. Lett. 118 (2017) 062001 [arXiv:1610.05791] [INSPIRE].
Y. Li and H.X. Zhu, Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation, Phys. Rev. Lett. 118 (2017) 022004 [arXiv:1604.01404] [INSPIRE].
J.C. Collins and D.E. Soper, Back-To-Back Jets: Fourier Transform from B to K-Transverse, Nucl. Phys. B 197 (1982) 446 [INSPIRE].
I. Scimemi and A. Vladimirov, Power corrections and renormalons in Transverse Momentum Distributions, JHEP 03 (2017) 002 [arXiv:1609.06047] [INSPIRE].
M.-X. Luo, T.-Z. Yang, H.X. Zhu and Y.J. Zhu, Transverse Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case, arXiv:1909.13820 [INSPIRE].
Y. Li, D. Neill and H.X. Zhu, An Exponential Regulator for Rapidity Divergences, arXiv:1604.00392 [INSPIRE].
M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Low-Energy Theorems for Higgs Boson Couplings to Photons, Sov. J. Nucl. Phys. 30 (1979) 711 [INSPIRE].
M. Krämer, E. Laenen and M. Spira, Soft gluon radiation in Higgs boson production at the LHC, Nucl. Phys. B 511 (1998) 523 [hep-ph/9611272] [INSPIRE].
K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Hadronic Higgs decay to order \( {\alpha}_s^4 \), Phys. Rev. Lett. 79 (1997) 353 [hep-ph/9705240] [INSPIRE].
H.M. Georgi, S.L. Glashow, M.E. Machacek and D.V. Nanopoulos, Higgs Bosons from Two Gluon Annihilation in Proton Proton Collisions, Phys. Rev. Lett. 40 (1978) 692 [INSPIRE].
V. Ahrens, T. Becher, M. Neubert and L.L. Yang, Renormalization-Group Improved Prediction for Higgs Production at Hadron Colliders, Eur. Phys. J. B 62 (2009) 333 [arXiv:0809.4283] [INSPIRE].
V. Ravindran, J. Smith and W.L. van Neerven, NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions, Nucl. Phys. B 665 (2003) 325 [hep-ph/0302135] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nucl. Phys. B 724 (2005) 197 [hep-ph/0501130] [INSPIRE].
V. Ahrens, T. Becher, M. Neubert and L.L. Yang, Origin of the Large Perturbative Corrections to Higgs Production at Hadron Colliders, Phys. Rev. D 79 (2009) 033013 [arXiv:0808.3008] [INSPIRE].
NNPDF collaboration, Parton distributions from high-precision collider data, Eur. Phys. J. C 77 (2017) 663 [arXiv:1706.00428] [INSPIRE].
A. Vladimirov, Pion-induced Drell-Yan processes within TMD factorization, JHEP 10 (2019) 090 [arXiv:1907.10356] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, A Brief Introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].
CMS collaboration, Measurement of differential cross sections for Higgs boson production in the diphoton decay channel in pp collisions at \( \sqrt{s} \) = 8 TeV, Eur. Phys. J. C 76 (2016) 13 [arXiv:1508.07819] [INSPIRE].
V.A. Smirnov, Evaluating Feynman integrals, Springer Tracts Mod. Phys. 211 (2004) 1.
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1907.03780
Electronic supplementary material
ESM 1
(TGZ 35 kb)
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Gutierrez-Reyes, D., Leal-Gomez, S., Scimemi, I. et al. Linearly polarized gluons at next-to-next-to leading order and the Higgs transverse momentum distribution. J. High Energ. Phys. 2019, 121 (2019). https://doi.org/10.1007/JHEP11(2019)121
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)121