Abstract
We show that soft gluons exchanged between the two colliding protons in multiparton scattering processes can be decoupled, such that their effects are described by the vacuum expectation values of Wilson lines. Our argument relies on nonabelian Ward identities and generalises the proof of factorisation for single Drell-Yan production given by Collins, Soper and Sterman.
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References
P. Bartalini and J.R. Gaunt, Multiple parton interactions at the LHC, Adv. Ser. Direct. High Energy Phys. 29 (2018) 1.
J.C. Collins, D.E. Soper and G.F. Sterman, Factorization for short distance hadron-hadron scattering, Nucl. Phys. B 261 (1985) 104 [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Soft gluons and factorization, Nucl. Phys. B 308 (1988) 833 [INSPIRE].
G.T. Bodwin, Factorization of the Drell-Yan cross-section in perturbation theory, Phys. Rev. D 31 (1985) 2616 [Erratum ibid. D 34 (1986) 3932] [INSPIRE].
J. Collins, Foundations of perturbative QCD, Cambridge University Press, Cambridge U.K. (2013).
M. Diehl, D. Ostermeier and A. Schafer, Elements of a theory for multiparton interactions in QCD, JHEP 03 (2012) 089 [Erratum ibid. 03 (2016) 001] [arXiv:1111.0910] [INSPIRE].
M. Diehl et al., Cancellation of Glauber gluon exchange in the double Drell-Yan process, JHEP 01 (2016) 076 [arXiv:1510.08696] [INSPIRE].
M. Diehl, J.R. Gaunt and K. Schönwald, Double hard scattering without double counting, JHEP 06 (2017) 083 [arXiv:1702.06486] [INSPIRE].
A. Vladimirov, Structure of rapidity divergences in multi-parton scattering soft factors, JHEP 04 (2018) 045 [arXiv:1707.07606] [INSPIRE].
M.G.A. Buffing, M. Diehl and T. Kasemets, Transverse momentum in double parton scattering: factorisation, evolution and matching, JHEP 01 (2018) 044 [arXiv:1708.03528] [INSPIRE].
C.W. Bauer et al., Hard scattering factorization from effective field theory, Phys. Rev. D 66 (2002) 014017 [hep-ph/0202088] [INSPIRE].
A.V. Manohar and W.J. Waalewijn, A QCD analysis of double parton scattering: color correlations, interference effects and evolution, Phys. Rev. D 85 (2012) 114009 [arXiv:1202.3794] [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].
S.B. Libby and G.F. Sterman, Mass divergences in two particle inelastic scattering, Phys. Rev. D 18 (1978) 4737 [INSPIRE].
S.B. Libby and G.F. Sterman, Cancellation of infrared divergences in massive quark potential scattering, Phys. Rev. D 19 (1979) 2468 [INSPIRE].
T. Becher and M. Neubert, Drell-Yan production at small q T , transverse parton distributions and the collinear anomaly, Eur. Phys. J. C 71 (2011) 1665 [arXiv:1007.4005] [INSPIRE].
J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, A formalism for the systematic treatment of rapidity logarithms in quantum field theory, JHEP 05 (2012) 084 [arXiv:1202.0814] [INSPIRE].
D. Boer et al., Colour unwound — Disentangling colours for azimuthal asymmetries in Drell-Yan scattering, SciPost Phys. 3 (2017) 040 [arXiv:1709.04935] [INSPIRE].
G. Grammer, Jr. and D.R. Yennie, Improved treatment for the infrared divergence problem in quantum electrodynamics, Phys. Rev. D 8 (1973) 4332 [INSPIRE].
J.-y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, The rapidity renormalization group, Phys. Rev. Lett. 108 (2012) 151601 [arXiv:1104.0881] [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].
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].
A. Vladimirov, Soft factors for double parton scattering at NNLO, JHEP 12 (2016) 038 [arXiv:1608.04920] [INSPIRE].
M. Mekhfi and X. Artru, Sudakov suppression of color correlations in multiparton scattering, Phys. Rev. D 37 (1988) 2618 [INSPIRE].
G. ’t Hooft, Renormalization of Massless Yang-Mills Fields, Nucl. Phys. B 33 (1971) 173 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Combinatorics of gauge fields, Nucl. Phys. B 50 (1972) 318 [INSPIRE].
T.C. Rogers and P.J. Mulders, No generalized TMD-factorization in hadro-production of high transverse momentum hadrons, Phys. Rev. D 81 (2010) 094006 [arXiv:1001.2977] [INSPIRE].
M. Diehl and J.R. Gaunt, Double parton scattering theory overview, Adv. Ser. Direct. High Energy Phys. 29 (2018) 7 [arXiv:1710.04408] [INSPIRE].
G.F. Sterman, An introduction to quantum field theory, Cambridge University Press, Cambridge U.K. (1993).
C. Itzykson and J.B. Zuber, Quantum field theory, International Series In Pure and Applied Physics, McGraw-Hill, New York, U.S.A. (1980).
M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, U.S.A. (1995).
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: a graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
D. Binosi, J. Collins, C. Kaufhold and L. Theussl, JaxoDraw: a graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Commun. 180 (2009) 1709 [arXiv:0811.4113] [INSPIRE].
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Diehl, M., Nagar, R. Factorisation of soft gluons in multiparton scattering. J. High Energ. Phys. 2019, 124 (2019). https://doi.org/10.1007/JHEP04(2019)124
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DOI: https://doi.org/10.1007/JHEP04(2019)124