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Non-global structure of the \(\mathcal{O}\left( {\alpha_s^2} \right) \) dijet soft function. (English) Zbl 1298.81390
J. High Energy Phys. 2011, No. 8, Paper No. 054, 55 p. (2011); erratum ibid. 2017, No. 10, Paper No. 101, 2 p. (2017).
Summary: High energy scattering processes involving jets generically involve matrix elements of light-like Wilson lines, known as soft functions. These describe the structure of soft contributions to observables and encode color and kinematic correlations between jets. We compute the dijet soft function to \(\mathcal{O}\left( {\alpha_s^2} \right) \) as a function of the two jet invariant masses, focusing on terms that have a non-separable dependence on these masses and are not determined by the renormalization group evolution of the soft function. Our results include non-global single and double logarithms, and analytic results for the full set of non-logarithmic contributions as well. Using a recent result for the thrust constant, we present the complete \(\mathcal{O}\left( {\alpha_s^2} \right) \) soft function for dijet production in both position and momentum space.

MSC:
81V05 Strong interaction, including quantum chromodynamics
81U05 \(2\)-body potential quantum scattering theory
81T17 Renormalization group methods applied to problems in quantum field theory
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
Software:
Hypexp
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References:
[1] G.F. Sterman, Partons, factorization and resummation, hep-ph/9606312 [SPIRES].
[2] Catani, S.; Turnock, G.; Webber, BR; Trentadue, L., Thrust distribution in \(e\)\^{}{+}\(e\)\^{}{−} annihilation, Phys. Lett., B 263, 491, (1991)
[3] Catani, S.; Trentadue, L.; Turnock, G.; Webber, BR, Resummation of large logarithms in \(e\)\^{}{+}\(e\)\^{}{−} event shape distributions, Nucl. Phys., B 407, 3, (1993)
[4] Contopanagos, H.; Laenen, E.; Sterman, GF, Sudakov factorization and resummation, Nucl. Phys., B 484, 303, (1997)
[5] Bauer, CW; Fleming, S.; Luke, ME, Summing Sudakov logarithms in \(B\) → \(X\)_{\(s\)}\(γ\) in effective field theory, Phys. Rev., D 63, 014006, (2000)
[6] Bauer, CW; Fleming, S.; Pirjol, D.; Stewart, IW, An effective field theory for collinear and soft gluons: heavy to light decays, Phys. Rev., D 63, 114020, (2001)
[7] Bauer, CW; Stewart, IW, Invariant operators in collinear effective theory, Phys. Lett., B 516, 134, (2001)
[8] Bauer, CW; Pirjol, D.; Stewart, IW, Soft-collinear factorization in effective field theory, Phys. Rev., D 65, 054022, (2002)
[9] Bauer, CW; Fleming, S.; Pirjol, D.; Rothstein, IZ; Stewart, IW, Hard scattering factorization from effective field theory, Phys. Rev., D 66, 014017, (2002)
[10] Farhi, E., A QCD test for jets, Phys. Rev. Lett., 39, 1587, (1977)
[11] Clavelli, L., Jet invariant mass in quantum chromodynamics, Phys. Lett., B 85, 111, (1979)
[12] Berger, CF; Kucs, T.; Sterman, GF, Event shape/energy flow correlations, Phys. Rev., D 68, 014012, (2003)
[13] Fleming, S.; Hoang, AH; Mantry, S.; Stewart, IW, Jets from massive unstable particles: top-mass determination, Phys. Rev., D 77, 074010, (2008)
[14] Schwartz, MD, Resummation and NLO matching of event shapes with effective field theory, Phys. Rev., D 77, 014026, (2008)
[15] Fleming, S.; Hoang, AH; Mantry, S.; Stewart, IW, Top jets in the peak region: factorization analysis with NLL resummation, Phys. Rev., D 77, 114003, (2008)
[16] Becher, T.; Schwartz, MD, A precise determination of \(α\)_{\(s\)} from LEP thrust data using effective field theory, JHEP, 07, 034, (2008)
[17] Hornig, A.; Lee, C.; Ovanesyan, G., Effective predictions of event shapes: factorized, resummed and gapped angularity distributions, JHEP, 05, 122, (2009)
[18] Abbate, R.; Fickinger, M.; Hoang, AH; Mateu, V.; Stewart, IW, Thrust at \(N\)\^{}{3}LL with power corrections and a precision global fit for alphas(mz), Phys. Rev., D 83, 074021, (2011)
[19] Bauer, CW; Fleming, SP; Lee, C.; Sterman, GF, Factorization of \(e\)\^{}{+}\(e\)\^{}{−} event shape distributions with hadronic final states in soft collinear effective theory, Phys. Rev., D 78, 034027, (2008)
[20] Dasgupta, M.; Salam, GP, Resummation of non-global QCD observables, Phys. Lett., B 512, 323, (2001)
[21] Dasgupta, M.; Salam, GP, Resummed event-shape variables in DIS, JHEP, 08, 032, (2002)
[22] A.H. Hoang and S. Kluth, Hemisphere soft function at\( \mathcal{O}\left( {α_s^2} \right) \)for dijet production in e\^{}{+}\(e\)\^{}{−}annihilation, arXiv:0806.3852 [SPIRES].
[23] Chien, Y-T; Schwartz, MD, Resummation of heavy jet mass and comparison to LEP data, JHEP, 08, 058, (2010)
[24] Catani, S.; Seymour, MH, The dipole formalism for the calculation of QCD jet cross sections at next-to-leading order, Phys. Lett., B 378, 287, (1996)
[25] Catani, S.; Seymour, MH, A general algorithm for calculating jet cross sections in NLO QCD, Nucl. Phys., B 485, 291, (1997)
[26] Jain, A.; Scimemi, I.; Stewart, IW, Two-loop jet function and jet mass for top quarks, Phys. Rev., D 77, 094008, (2008)
[27] Stewart, IW; Tackmann, FJ; Waalewijn, WJ, Factorization at the LHC: from PDFs to initial state jets, Phys. Rev., D 81, 094035, (2010)
[28] Stewart, IW; Tackmann, FJ; Waalewijn, WJ, \(N\)-jettiness: an inclusive event shape to veto jets, Phys. Rev. Lett., 105, 092002, (2010)
[29] Dasgupta, M., On deglobalization in QCD, Pramana, 62, 675, (2004)
[30] Ellis, SD; Vermilion, CK; Walsh, JR; Hornig, A.; Lee, C., Jet shapes and jet algorithms in SCET, JHEP, 11, 101, (2010)
[31] Banfi, A.; Dasgupta, M.; Khelifa-Kerfa, K.; Marzani, S., Non-global logarithms and jet algorithms in high-pt jet shapes, JHEP, 08, 064, (2010)
[32] Rubin, M., Non-global logarithms in filtered jet algorithms, JHEP, 05, 005, (2010)
[33] Catani, S.; Trentadue, L., Inhibited radiation dynamics in QCD, Phys. Lett., B 217, 539, (1989)
[34] Catani, S.; Trentadue, L., Resummation of the QCD perturbative series for hard processes, Nucl. Phys., B 327, 323, (1989)
[35] Burby, SJ; Glover, EWN, Resumming the light hemisphere mass and narrow jet broadening distributions in \(e\)\^{}{+}\(e\)\^{}{−} annihilation, JHEP, 04, 029, (2001)
[36] Korchemsky, GP; Marchesini, G., Resummation of large infrared corrections using Wilson loops, Phys. Lett., B 313, 433, (1993)
[37] Balzereit, C.; Mannel, T.; Kilian, W., Evolution of the light-cone distribution function for a heavy quark, Phys. Rev., D 58, 114029, (1998)
[38] Becher, T.; Neubert, M., Threshold resummation in momentum space from effective field theory, Phys. Rev. Lett., 97, 082001, (2006)
[39] Ligeti, Z.; Stewart, IW; Tackmann, FJ, Treating the b quark distribution function with reliable uncertainties, Phys. Rev., D 78, 114014, (2008)
[40] P.F. Monni, G. Luisoni and T. Gehrmann, Resummation of large IR logarithms for the Thrust distribution, talk presented at Loopfest X, Northwestern University, Chicago U.S.A., May 12-14 2011.
[41] Bauer, CW; Lee, C.; Manohar, AV; Wise, MB, Enhanced nonperturbative effects in Z decays to hadrons, Phys. Rev., D 70, 034014, (2004)
[42] Hoang, AH; Stewart, IW, Designing gapped soft functions for jet production, Phys. Lett., B 660, 483, (2008)
[43] Gatheral, JGM, Exponentiation of eikonal cross-sections in nonabelian gauge theories, Phys. Lett., B 133, 90, (1983)
[44] Frenkel, J.; Taylor, JC, Nonabelian eikonal exponentiation, Nucl. Phys., B 246, 231, (1984)
[45] V. Mateu, R. Abbate, A. Hoang, M.D. Schwartz and I.W. Stewart, Status of HJM fits: towards a precise determination of α_{\(s\)}(\(M\)_{\(Z\)}), talk presented at SCET 2011 Workshop, Carnegie Mellon University, Pittsburgh U.S.A., March 6-8 2011.
[46] Sterman, GF, Mass divergences in annihilation processes 2 cancellation of divergences in cut vacuum polarization diagrams, Phys. Rev., D 17, 2789, (1978)
[47] Hornig, A.; Lee, C.; Ovanesyan, G., Infrared safety in factorized hard scattering cross-sections, Phys. Lett., B 677, 272, (2009)
[48] C. Lee, A. Hornig, I.W. Stewart, J.R. Walsh and S. Zuberi, Non-global logs in SCET, talk presented at SCET 2011 Workshop, Carnegie Mellon University, Pittsburgh U.S.A., March 6-8 2011.
[49] Kelley, R.; Schwartz, MD, Threshold hadronic event shapes with effective field theory, Phys. Rev., D 83, 033001, (2011)
[50] R. Abbate, M. Fickinger, A. Hoang, V. Mateu and I.W. Stewart, Global fit of α_{\(s\)}(\(m\)_{\(Z\)}) to Thrust at NNNLL order with power corrections, PoS(RADCOR2009)040 [arXiv:1004.4894] [SPIRES].
[51] M.H. Seymour, private communication.
[52] Lee, KSM; Stewart, IW, Factorization for power corrections to \(B\) → \(X\)_{\(s\)}\(γ\) and \( B → {X_u}l\bar{ν } \), Nucl. Phys., B 721, 325, (2005)
[53] Bauer, CW; Hornig, A.; Tackmann, FJ, Factorization for generic jet production, Phys. Rev., D 79, 114013, (2009)
[54] Ellis, SD; Hornig, A.; Lee, C.; Vermilion, CK; Walsh, JR, Consistent factorization of jet observables in exclusive multijet cross-sections, Phys. Lett., B 689, 82, (2010)
[55] Stewart, IW; Tackmann, FJ; Waalewijn, WJ, The quark beam function at NNLL, JHEP, 09, 005, (2010)
[56] R. Kelley, R.M. Schabinger, M.D. Schwartz and H.X. Zhu, The two-loop hemisphere soft function, arXiv:1105.3676 [SPIRES].
[57] P.F. Monni, T. Gehrmann and G. Luisoni, Two-loop soft corrections and resummation of the Thrust distribution in the dijet region, arXiv:1105.4560 [SPIRES].
[58] Korchemsky, GP; Radyushkin, AV, Renormalization of the Wilson loops beyond the leading order, Nucl. Phys., B 283, 342, (1987)
[59] Korchemskaya, IA; Korchemsky, GP, On lightlike Wilson loops, Phys. Lett., B 287, 169, (1992)
[60] Huber, T.; Maître, D., Hypexp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters, Comput. Phys. Commun., 175, 122, (2006)
[61] Huber, T.; Maître, D., Hypexp 2, expanding hypergeometric functions about half-integer parameters, Comput. Phys. Commun., 178, 755, (2008)
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