Abstract
The Soft Collinear Effective Theory (SCET) is a powerful framework for studying factorization of amplitudes and cross sections in QCD. While factorization at leading power has been well studied, much less is known at subleading powers in the λ ≪ 1 expansion. In SCET subleading soft and collinear corrections to a hard scattering process are described by power suppressed operators, which must be fixed case by case, and by well established power suppressed Lagrangians, which correct the leading power dynamics of soft and collinear radiation. Here we present a complete basis of power suppressed operators for gg → H, classifying all operators which contribute to the cross section at \( \mathcal{O}\left({\lambda}^2\right) \), and showing how helicity selection rules significantly simplify the construction of the operator basis. We perform matching calculations to determine the tree level Wilson coefficients of our operators. These results are useful for studies of power corrections in both resummed and fixed order perturbation theory, and for understanding the factorization properties of gauge theory amplitudes and cross sections at subleading power. As one example, our basis of operators can be used to analytically compute power corrections for N -jettiness subtractions for gg induced color singlet production at the LHC.
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References
C.W. Bauer, S. Fleming and M.E. Luke, Summing Sudakov logarithms in B → X s γ in effective field theory, Phys. Rev. D 63 (2000) 014006 [hep-ph/0005275] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An Effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
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].
A.J. Larkoski, D. Neill and I.W. Stewart, Soft Theorems from Effective Field Theory, JHEP 06 (2015) 077 [arXiv:1412.3108] [INSPIRE].
K.S.M. Lee and I.W. Stewart, Factorization for power corrections to B → X s γ and \( B\to {X}_u\ell {\overline{\nu}}_{\ell } \), Nucl. Phys. B 721 (2005) 325 [hep-ph/0409045][INSPIRE].
M. Beneke, F. Campanario, T. Mannel and B.D. Pecjak, Power corrections to \( \overline{B}\to {X}_u\ell \overline{\nu} \) decay spectra in the ‘shape-function’ region, JHEP 06 (2005) 071 [hep-ph/0411395] [INSPIRE].
R.J. Hill, T. Becher, S.J. Lee and M. Neubert, Sudakov resummation for subleading SCET currents and heavy-to-light form-factors, JHEP 07 (2004) 081 [hep-ph/0404217] [INSPIRE].
S.W. Bosch, M. Neubert and G. Paz, Subleading shape functions in inclusive B decays, JHEP 11 (2004) 073 [hep-ph/0409115] [INSPIRE].
M. Beneke, Y. Kiyo and D.s. Yang, Loop corrections to subleading heavy quark currents in SCET, Nucl. Phys. B 692 (2004) 232 [hep-ph/0402241] [INSPIRE].
G. Paz, Subleading Jet Functions in Inclusive B Decays, JHEP 06 (2009) 083 [arXiv:0903.3377] [INSPIRE].
M. Benzke, S.J. Lee, M. Neubert and G. Paz, Factorization at Subleading Power and Irreducible Uncertainties in \( \overline{B}\to {X}_s\gamma \) Decay, JHEP 08 (2010) 099 [arXiv:1003.5012] [INSPIRE].
S.M. Freedman, Subleading Corrections To Thrust Using Effective Field Theory, arXiv:1303.1558 [INSPIRE].
S.M. Freedman and R. Goerke, Renormalization of Subleading Dijet Operators in Soft-Collinear Effective Theory, Phys. Rev. D 90 (2014) 114010 [arXiv:1408.6240] [INSPIRE].
I. Moult, L. Rothen, I.W. Stewart, F.J. Tackmann and H.X. Zhu, Subleading Power Corrections for N-Jettiness Subtractions, Phys. Rev. D 95 (2017) 074023 [arXiv:1612.00450] [INSPIRE].
I. Feige, D.W. Kolodrubetz, I. Moult and I.W. Stewart, A Complete Basis of Helicity Operators for Subleading Factorization, arXiv:1703.03411 [INSPIRE].
I. Moult, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Employing Helicity Amplitudes for Resummation, Phys. Rev. D 93 (2016) 094003 [arXiv:1508.02397] [INSPIRE].
D.W. Kolodrubetz, I. Moult and I.W. Stewart, Building Blocks for Subleading Helicity Operators, JHEP 05 (2016) 139 [arXiv:1601.02607] [INSPIRE].
K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Decoupling relations to O(α 3 S ) and their connection to low-energy theorems, Nucl. Phys. B 510 (1998) 61 [hep-ph/9708255] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, N-Jettiness: An Inclusive Event Shape to Veto Jets, Phys. Rev. Lett. 105 (2010) 092002 [arXiv:1004.2489] [INSPIRE].
J.R. Gaunt, Glauber Gluons and Multiple Parton Interactions, JHEP 07 (2014) 110 [arXiv:1405.2080] [INSPIRE].
I.Z. Rothstein and I.W. Stewart, An Effective Field Theory for Forward Scattering and Factorization Violation, JHEP 08 (2016) 025 [arXiv:1601.04695] [INSPIRE].
M. Zeng, Drell-Yan process with jet vetoes: breaking of generalized factorization, JHEP 10 (2015) 189 [arXiv:1507.01652] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Factorization at the LHC: From PDFs to Initial State Jets, Phys. Rev. D 81 (2010) 094035 [arXiv:0910.0467] [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].
J. Chay and C. Kim, Collinear effective theory at subleading order and its application to heavy-light currents, Phys. Rev. D 65 (2002) 114016 [hep-ph/0201197] [INSPIRE].
M. Beneke and T. Feldmann, Multipole expanded soft collinear effective theory with nonAbelian gauge symmetry, Phys. Lett. B 553 (2003) 267 [hep-ph/0211358] [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].
D. Pirjol and I.W. Stewart, A complete basis for power suppressed collinear ultrasoft operators, Phys. Rev. D 67 (2003) 094005 [Erratum ibid. D 69 (2004) 019903] [hep-ph/0211251] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, On power suppressed operators and gauge invariance in SCET, Phys. Rev. D 68 (2003) 034021 [hep-ph/0303156] [INSPIRE].
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett. 98 (2007) 222002 [hep-ph/0703012] [INSPIRE].
R. Boughezal, C. Focke, W. Giele, X. Liu and F. Petriello, Higgs boson production in association with a jet at NNLO using jettiness subtraction, Phys. Lett. B 748 (2015) 5 [arXiv:1505.03893] [INSPIRE].
J. Gaunt, M. Stahlhofen, F.J. Tackmann and J.R. Walsh, N-jettiness Subtractions for NNLO QCD Calculations, JHEP 09 (2015) 058 [arXiv:1505.04794] [INSPIRE].
S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 103 (2009) 082001 [arXiv:0903.2120] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Associated WH production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 107 (2011) 152003 [arXiv:1107.1164] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett. 108 (2012) 072001 [Erratum ibid. 117 (2016) 089901] [arXiv:1110.2375] [INSPIRE].
M. Grazzini, S. Kallweit, D. Rathlev and A. Torre, Zγ production at hadron colliders in NNLO QCD, Phys. Lett. B 731 (2014) 204 [arXiv:1309.7000] [INSPIRE].
F. Cascioli et al., ZZ production at hadron colliders in NNLO QCD, Phys. Lett. B 735 (2014) 311 [arXiv:1405.2219] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Associated ZH production at hadron colliders: the fully differential NNLO QCD calculation, Phys. Lett. B 740 (2015) 51 [arXiv:1407.4747] [INSPIRE].
T. Gehrmann et al., W + W − Production at Hadron Colliders in Next to Next to Leading Order QCD, Phys. Rev. Lett. 113 (2014) 212001 [arXiv:1408.5243] [INSPIRE].
M. Grazzini, S. Kallweit and D. Rathlev, W γ and Zγ production at the LHC in NNLO QCD, JHEP 07 (2015) 085 [arXiv:1504.01330] [INSPIRE].
M. Grazzini, S. Kallweit and D. Rathlev, ZZ production at the LHC: fiducial cross sections and distributions in NNLO QCD, Phys. Lett. B 750 (2015) 407 [arXiv:1507.06257] [INSPIRE].
J.M. Campbell, R.K. Ellis, Y. Li and C. Williams, Predictions for diphoton production at the LHC through NNLO in QCD, JHEP 07 (2016) 148 [arXiv:1603.02663] [INSPIRE].
R. Boughezal et al., Color singlet production at NNLO in MCFM, Eur. Phys. J. C 77 (2017) 7 [arXiv:1605.08011] [INSPIRE].
R. Boughezal, C. Focke, X. Liu and F. Petriello, W -boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett. 115 (2015) 062002 [arXiv:1504.02131] [INSPIRE].
R. Boughezal, X. Liu and F. Petriello, Phenomenology of the Z-boson plus jet process at NNLO, Phys. Rev. D 94 (2016) 074015 [arXiv:1602.08140] [INSPIRE].
R. Boughezal, X. Liu and F. Petriello, W-boson plus jet differential distributions at NNLO in QCD, Phys. Rev. D 94 (2016) 113009 [arXiv:1602.06965] [INSPIRE].
J.M. Campbell, R.K. Ellis and C. Williams, Direct Photon Production at Next-to-Next-to-Leading Order, Phys. Rev. Lett. 118 (2017) 222001 [arXiv:1612.04333] [INSPIRE].
R. Boughezal, X. Liu and F. Petriello, Power Corrections in the N-jettiness Subtraction Scheme, JHEP 03 (2017) 160 [arXiv:1612.02911] [INSPIRE].
I.W. Stewart and C.W. Bauer, Lectures on the soft-collinear effective theory, http://ocw.mit.edu/courses/physics/8-851-effective-field-theory-spring-2013/lecture- notes/MIT8_851S13_scetnotes.pdf.
T. Becher, A. Broggio and A. Ferroglia, Introduction to Soft-Collinear Effective Theory, Lect. Notes Phys. 896 (2015) pp.1-206 [arXiv:1410.1892] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Factorization and endpoint singularities in heavy to light decays, Phys. Rev. D 67 (2003) 071502 [hep-ph/0211069] [INSPIRE].
C. Marcantonini and I.W. Stewart, Reparameterization Invariant Collinear Operators, Phys. Rev. D 79 (2009) 065028 [arXiv:0809.1093] [INSPIRE].
L.J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359 [INSPIRE].
J. Chay, C. Kim, Y.G. Kim and J.-P. Lee, Soft Wilson lines in soft-collinear effective theory, Phys. Rev. D 71 (2005) 056001 [hep-ph/0412110] [INSPIRE].
C.M. Arnesen, J. Kundu and I.W. Stewart, Constraint equations for heavy-to-light currents in SCET, Phys. Rev. D 72 (2005) 114002 [hep-ph/0508214] [INSPIRE].
S. Mantry, D. Pirjol and I.W. Stewart, Strong phases and factorization for color suppressed decays, Phys. Rev. D 68 (2003) 114009 [hep-ph/0306254] [INSPIRE].
M. Beneke and T. Feldmann, Factorization of heavy to light form-factors in soft collinear effective theory, Nucl. Phys. B 685 (2004) 249 [hep-ph/0311335] [INSPIRE].
A.J. Buras and P.H. Weisz, QCD Nonleading Corrections to Weak Decays in Dimensional Regularization and ’t Hooft-Veltman Schemes, Nucl. Phys. B 333 (1990) 66 [INSPIRE].
M.J. Dugan and B. Grinstein, On the vanishing of evanescent operators, Phys. Lett. B 256 (1991) 239 [INSPIRE].
S. Herrlich and U. Nierste, Evanescent operators, scheme dependences and double insertions, Nucl. Phys. B 455 (1995) 39 [hep-ph/9412375] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, The Quark Beam Function at NNLL, JHEP 09 (2010) 005 [arXiv:1002.2213] [INSPIRE].
F.E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev. 110 (1958) 974 [INSPIRE].
T.H. Burnett and N.M. Kroll, Extension of the low soft photon theorem, Phys. Rev. Lett. 20 (1968) 86 [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks, FeynRules 2.0 — A complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
S. Stieberger and T.R. Taylor, Subleading terms in the collinear limit of Yang-Mills amplitudes, Phys. Lett. B 750 (2015) 587 [arXiv:1508.01116] [INSPIRE].
D. Nandan, J. Plefka and W. Wormsbecher, Collinear limits beyond the leading order from the scattering equations, JHEP 02 (2017) 038 [arXiv:1608.04730] [INSPIRE].
Yu.L. Dokshitzer, G. Marchesini and G.P. Salam, Revisiting parton evolution and the large-x limit, Phys. Lett. B 634 (2006) 504 [hep-ph/0511302] [INSPIRE].
G. Grunberg, Threshold resummation to any order in (1 − x), arXiv:0710.5693 [INSPIRE].
E. Laenen, G. Stavenga and C.D. White, Path integral approach to eikonal and next-to-eikonal exponentiation, JHEP 03 (2009) 054 [arXiv:0811.2067] [INSPIRE].
E. Laenen, L. Magnea and G. Stavenga, On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections, Phys. Lett. B 669 (2008) 173 [arXiv:0807.4412] [INSPIRE].
G. Grunberg and V. Ravindran, On threshold resummation beyond leading 1-x order, JHEP 10 (2009) 055 [arXiv:0902.2702] [INSPIRE].
E. Laenen, L. Magnea, G. Stavenga and C.D. White, Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach, JHEP 01 (2011) 141 [arXiv:1010.1860] [INSPIRE].
A.A. Almasy, G. Soar and A. Vogt, Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering, JHEP 03 (2011) 030 [arXiv:1012.3352] [INSPIRE].
D. Bonocore, E. Laenen, L. Magnea, L. Vernazza and C.D. White, The method of regions and next-to-soft corrections in Drell-Yan production, Phys. Lett. B 742 (2015) 375 [arXiv:1410.6406] [INSPIRE].
C.D. White, Diagrammatic insights into next-to-soft corrections, Phys. Lett. B 737 (2014) 216 [arXiv:1406.7184] [INSPIRE].
D. de Florian, J. Mazzitelli, S. Moch and A. Vogt, Approximate N 3 LO Higgs-boson production cross section using physical-kernel constraints, JHEP 10 (2014) 176 [arXiv:1408.6277] [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].
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Moult, I., Stewart, I.W. & Vita, G. A subleading operator basis and matching for gg → H . J. High Energ. Phys. 2017, 67 (2017). https://doi.org/10.1007/JHEP07(2017)067
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DOI: https://doi.org/10.1007/JHEP07(2017)067