The zero-bin and mode factorization in quantum field theory

By A. Manohar, Iain W. Stewart. 2006

282 citations recorded by the source corpus.

We study a Lagrangian formalism that avoids double counting in effective field theories where distinct fields are used to describe different infrared momentum regions for the same particle. The formalism leads to extra subtractions in certain diagrams and to a new way of thinking about factorization of modes in quantum field theory. In nonrelativistic field theories, the subtractions remove unphysical pinch singularities in box-type diagrams, and give a derivation of the known pullup mechanism between soft and ultrasoft fields which is required by the renormalization group evolution. In a field theory for energetic particles, the soft-collinear effective theory (SCET), the subtractions allow the theory to be defined with different infrared and ultraviolet regulators, remove double counting between soft, ultrasoft, and collinear modes, and give results which reproduce the infrared divergences of the full theory. Our analysis shows that convolution divergences in factorization formulas occur due to an overlap of momentum regions. We propose a method that avoids this double counting, which helps to resolve a long-standing puzzle with singularities in collinear factorization in QCD. The analysis gives evidence for a factorization in rapidity space in exclusive decays.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2fcf4697c8ce6ebe951cb6cdac5d59321beee912

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In Nuclear and High Energy Physics

1. A. Larkoski
2. I. Moult
3. D. Neill
4. W. Waalewijn
5. Iain W. Stewart
6. F. Tackmann
7. Rafael A. Porto
8. A. Broggio

Citations in the corpus

• Analytic boosted boson discrimination (2015, methodology): “It proceeds by implementing a zero bin subtraction [119] in factorization theorem space (the meaning of this will become clear shortly) to remove double counting in the overlapping region between the effective theories.”
• Jet shapes and jet algorithms in SCET (2010, methodology): “The labeled fields qn,p, An,p now have spacetime fluctuations in x which are conjugate to “residual” momenta k of the order Eλ2, describing remaining fluctuations within each labeled momentum partition [23, 65].”
• Model independent evolution of transverse momentum dependent distribution functions (TMDs) at NNLL (2012, unknown): “, a matrix element which has no overlap with the soft region [21], and it is given by the bilocal correlator Φ (0) n,αβ = 〈P ~ S| [ ξ̄nαW T n ] (0, y, ~y⊥) [ W n ξnβ ] (0) |P ~ S〉 .”
• Higgs production with a central jet veto at NNLL+NNLO (2010, background): “The SCET gluon field B n⊥ describes n-collinear gluons and includes zero-bin subtractions [95].”
• Foundation and generalization of the expansion by regions (2011, unknown): “[11, 12]).”
• An effective field theory for forward scattering and factorization violation (2016, methodology): “[57, 58], and discuss the structure of zero-bin subtractions [59] in the presence of Glauber modes.”
• The quark beam function at NNLL (2010, methodology): “Our results show that beam functions must be defined with zero-bin subtractions [16], but that in the OPE the subtractions are frozen out into the Wilson coefficients Iij.”
• Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis) (2009, methodology): “In practice when calculating matrix elements, this is implemented using zero-bin subtractions [140] or alternatively by dividing out matrix elements of Wilson lines [120, 134].”
• Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order (2016, methodology): “According to Soft Collinear Effective Theory (SCET) terminology the “zero-bin” represents the soft overlap contribution, that should be removed from the collinear matrix element in order to avoid double counting of soft singularities [27].”
• The Effective Field Theorist's Approach to Gravitational Dynamics (2016, methodology): “Within an EFT formalism the overlapping is avoided by implementing the ‘zero-bin subtraction’ [237].”
• Introduction to Soft-Collinear Effective Theory (2014, methodology): “Finally, [175] analyzed B → χcJK as an example where the factorization breaking effects can be computed perturbatively using non-relativistic QCD and generate a large rescattering phase, casting doubt on the statement in [17, 176] that non-factorizable phases are absent in annihilation contributions”
• Factorization at the LHC: From parton distribution functions to initial state jets (2010, methodology): “In practice when calculating matrix elements, this is implemented using zero-bin subtractions [140] or alternatively by dividing out matrix elements of Wilson lines [120, 134].”
• A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory (2012, methodology): “The mass-shell hyperbolae showing the distinction between the different sectors [5].”
• N-jettiness subtractions for NNLO QCD calculations (2015, background): “In principle, such overlaps can exist and must be removed, which in SCET corresponds to removing so-called zero-bin contributions [88].”