Abstract
Factorization theorems in soft-collinear effective theory at subleading order in power counting involve “radiative jet functions”, defined in terms of matrix elements of hard-collinear fields with a soft momentum emitted from inside the jet. Of particular importance are the radiative quark jet functions with an external photon or gluon, which arise e.g. in the factorization theorems for the Higgs-boson amplitudes h → γγ, h → gg and gg → h induced by light-quark loops. While the photon case has been studied extensively in previous work, we present here a detailed study of the radiative jet function with an external gluon. We calculate this jet function at one- and two-loop order, derive its one-loop anomalous dimension and study its renormalization-group evolution.
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References
C.W. Bauer, S. Fleming, D. Pirjol, I.Z. Rothstein and I.W. Stewart, Hard scattering factorization from effective field theory, Phys. Rev. D 66 (2002) 014017 [hep-ph/0202088] [INSPIRE].
M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [INSPIRE].
I. Moult, I.W. Stewart and G. Vita, Subleading power factorization with radiative functions, JHEP 11 (2019) 153 [arXiv:1905.07411] [INSPIRE].
M. Beneke, M. Garny, R. Szafron and J. Wang, Violation of the Kluberg-Stern-Zuber theorem in SCET, JHEP 09 (2019) 101 [arXiv:1907.05463] [INSPIRE].
I. Moult, I.W. Stewart, G. Vita and H.X. Zhu, The soft quark Sudakov, JHEP 05 (2020) 089 [arXiv:1910.14038] [INSPIRE].
M. Beneke, A. Broggio, S. Jaskiewicz and L. Vernazza, Threshold factorization of the Drell-Yan process at next-to-leading power, JHEP 07 (2020) 078 [arXiv:1912.01585] [INSPIRE].
I. Moult, G. Vita and K. Yan, Subleading power resummation of rapidity logarithms: the energy-energy correlator in N = 4 SYM, JHEP 07 (2020) 005 [arXiv:1912.02188] [INSPIRE].
Z.L. Liu and M. Neubert, Factorization at subleading power and endpoint-divergent convolutions in h → γγ decay, JHEP 04 (2020) 033 [arXiv:1912.08818] [INSPIRE].
M. Beneke, M. Garny, S. Jaskiewicz, R. Szafron, L. Vernazza and J. Wang, Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization, JHEP 10 (2020) 196 [arXiv:2008.04943] [INSPIRE].
Z.L. Liu, B. Mecaj, M. Neubert and X. Wang, Factorization at subleading power, Sudakov resummation, and endpoint divergences in soft-collinear effective theory, Phys. Rev. D 104 (2021) 014004 [arXiv:2009.04456] [INSPIRE].
Z.L. Liu, B. Mecaj, M. Neubert and X. Wang, Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution, JHEP 01 (2021) 077 [arXiv:2009.06779] [INSPIRE].
Z.L. Liu and M. Neubert, Two-loop radiative jet function for exclusive B-meson and Higgs decays, JHEP 06 (2020) 060 [arXiv:2003.03393] [INSPIRE].
E. Lunghi, D. Pirjol and D. Wyler, Factorization in leptonic radiative B → γeν decays, Nucl. Phys. B 649 (2003) 349 [hep-ph/0210091] [INSPIRE].
S.W. Bosch, R.J. Hill, B.O. Lange and M. Neubert, Factorization and Sudakov resummation in leptonic radiative B decay, Phys. Rev. D 67 (2003) 094014 [hep-ph/0301123] [INSPIRE].
V. Del Duca, High-energy Bremsstrahlung theorems for soft photons, Nucl. Phys. B 345 (1990) 369 [INSPIRE].
D. Bonocore, E. Laenen, L. Magnea, S. Melville, L. Vernazza and C.D. White, A factorization approach to next-to-leading-power threshold logarithms, JHEP 06 (2015) 008 [arXiv:1503.05156] [INSPIRE].
D. Bonocore, E. Laenen, L. Magnea, L. Vernazza and C.D. White, Non-Abelian factorisation for next-to-leading-power threshold logarithms, JHEP 12 (2016) 121 [arXiv:1610.06842] [INSPIRE].
Z. Liu, M. Neubert, M. Schnubel and X. Wang, Renormalization of the radiative gluon jet function, in preparation.
R.J. Hill and M. Neubert, Spectator interactions in soft collinear effective theory, Nucl. Phys. B 657 (2003) 229 [hep-ph/0211018] [INSPIRE].
A.V. Manohar, T. Mehen, D. Pirjol and I.W. Stewart, Reparameterization invariance for collinear operators, Phys. Lett. B 539 (2002) 59 [hep-ph/0204229] [INSPIRE].
G. ’t Hooft, The background field method in gauge field theories, in Procs. 12th annual winter school of theoretical physics, Karpacz, Poland (1975) [INSPIRE].
D.G. Boulware, Gauge dependence of the effective action, Phys. Rev. D 23 (1981) 389 [INSPIRE].
L.F. Abbott, The background field method beyond one loop, Nucl. Phys. B 185 (1981) 189 [INSPIRE].
L.F. Abbott, Introduction to the background field method, Acta Phys. Polon. B 13 (1982) 33 [INSPIRE].
K.A. Meissner, The background field method in the axial gauge, Acta Phys. Polon. B 17 (1986) 409 [INSPIRE].
T. Becher and G. Bell, The gluon jet function at two-loop order, Phys. Lett. B 695 (2011) 252 [arXiv:1008.1936] [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
A.V. Smirnov and F.S. Chuharev, FIRE6: Feynman Integral REduction with modular arithmetic, Comput. Phys. Commun. 247 (2020) 106877 [arXiv:1901.07808] [INSPIRE].
J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral reduction with Kira 2.0 and finite field methods, Comput. Phys. Commun. 266 (2021) 108024 [arXiv:2008.06494] [INSPIRE].
S.W. Bosch, B.O. Lange, M. Neubert and G. Paz, Factorization and shape function effects in inclusive B meson decays, Nucl. Phys. B 699 (2004) 335 [hep-ph/0402094] [INSPIRE].
A.G. Grozin and M. Neubert, Asymptotics of heavy meson form-factors, Phys. Rev. D 55 (1997) 272 [hep-ph/9607366] [INSPIRE].
B.O. Lange and M. Neubert, Renormalization group evolution of the B meson light cone distribution amplitude, Phys. Rev. Lett. 91 (2003) 102001 [hep-ph/0303082] [INSPIRE].
Z.L. Liu, B. Mecaj, M. Neubert, X. Wang and S. Fleming, Renormalization and scale evolution of the soft-quark soft function, JHEP 07 (2020) 104 [arXiv:2005.03013] [INSPIRE].
G.T. Bodwin, J.-H. Ee, J. Lee and X.-P. Wang, Analyticity, renormalization, and evolution of the soft-quark function, Phys. Rev. D 104 (2021) 016010 [arXiv:2101.04872] [INSPIRE].
G.T. Bodwin, J.-H. Ee, J. Lee and X.-P. Wang, Renormalization of the radiative jet function, Phys. Rev. D 104 (2021) 116025 [arXiv:2107.07941] [INSPIRE].
T. Becher and M. Neubert, On the structure of infrared singularities of gauge-theory amplitudes, JHEP 06 (2009) 081 [Erratum ibid. 11 (2013) 024] [arXiv:0903.1126] [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson loops beyond the leading order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].
I.A. Korchemskaya and G.P. Korchemsky, On lightlike Wilson loops, Phys. Lett. B 287 (1992) 169 [INSPIRE].
A.M. Galda and M. Neubert, Evolution of the B-meson light-cone distribution amplitude in Laplace space, Phys. Rev. D 102 (2020) 071501 [arXiv:2006.05428] [INSPIRE].
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Liu, Z.L., Neubert, M., Schnubel, M. et al. Radiative quark jet function with an external gluon. J. High Energ. Phys. 2022, 75 (2022). https://doi.org/10.1007/JHEP02(2022)075
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DOI: https://doi.org/10.1007/JHEP02(2022)075