Singularities in the physical region

Coleman, Sidney; Norton, Richard

doi:10.1007/bf02750472

Cited by 347 publications

(364 citation statements)

References 5 publications

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“…For Glauber exchange between n-collinear,n-collinear, and soft particles we have the cases {a, b} = {2, 2} (n-n Glauber), {a, b} = {2, 1} (s-n Glauber), and {a, b} = {1, 2} (s-n Glauber). momentum regions can be identified either physically, or with analyses that determine the infrared structure of amplitudes [74], use the Coleman-Norton theorem [75], or exploiting the method of regions [76]. (For a detailed analysis of the method of regions that includes the Glauber region see [33].)…”

Section: Jhep08(2016)025mentioning

confidence: 99%

An effective field theory for forward scattering and factorization violation

Rothstein

Stewart

2016

J. High Energ. Phys.

135

291

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Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where |t| s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCET II and SCET I . The one-loop amplitude's rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. We also discuss criteria for factorization violation.

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Section: Jhep08(2016)025mentioning

confidence: 99%

An effective field theory for forward scattering and factorization violation

Rothstein

Stewart

2016

J. High Energ. Phys.

135

291

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“…A study quite similar to the real mass case then follows 12 and the same 10 For general parametric integrals the Landau conditions provide only necessary conditions to face singularities, either of pinched or end-point type. However for Feynman integrals, Coleman and Norton [21] proved these conditions to be sufficient. 11 Let us note by passing that, unlike with standard diagonalization, the phases of the vectors u (i) involved in the Takagi factorization shall be adjusted modulo π in order to fulfill the condition (u…”

Section: Extension To the Complex Mass Casementioning

confidence: 99%

“…(4.1) are separately functions of t in the directional limit s − → 0, s 2 → 0 with s 2 /s 2 − = t fixed, the limit of their sum is actually independent of t. For this purpose we compute the t-derivative of this sum in this limit and prove it to vanish identically in t. We provide an explicit proof for I 4 3 ; the I 6 3 case, albeit more cumbersome, can be handled in a completely similar way. 21 If S has rank ≤ N − 2, such eigenvectors v (1) and v (2) can always be found even if S is complex. In the latter case, consider linearly independent eigenvectors u1 and u2 of S S † associated with the eigenvalue zero: their respective complex conjugates v (1) = u * 1 and v (2) = u * 2 are linearly independent eigenvectors of S associated with the eigenvalue zero.…”

Section: Is Actually Isotropicmentioning

confidence: 99%

Stable one-dimensional integral representations of one-loop N-point functions in the general massive case. I — Three point functions

Guillet

Pilon

Rodgers

et al. 2013

J. High Energ. Phys.

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In this article we provide representations for the one-loop three point functions in 4 and 6 dimensions in the general case with complex masses. The latter are part of the GOLEM library used for the computation of one-loop multileg amplitudes. These representations are one-dimensional integrals designed to be free of instabilites induced by inverse powers of Gram determinants, therefore suitable for stable numerical implementations.

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“…In general, this classification is much easier when we use the Coleman -Norton theorem [ 11]. As a consequence of it, in a 2 → 2 process, two unstable particles in the initial state are needed.…”

Section: Feynman Diagrams Aroud Atmentioning

confidence: 99%