RECORD
Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
High Energy Physics - Phenomenology · Submitted 16 Jul 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms $\Li{a}{-t/s}$, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms $\Li{a}{-t/s}$, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. | contribution 0.99 | 0.95 | 0.43 | asserted 1.00 |
| s1 | Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. | method 0.84 | 0.94 | 0.23 | asserted 1.00 |
| s2 | The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. | method 0.37 | 0.76 | 0.08 | asserted 1.00 |
| s3 | By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms $\Li{a}{-t/s}$, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration. | result 0.82 | 0.93 | 0.66 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms $\Li{a}{-t/s}$, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.
Human review
References
How the literature uses it
13 arXiv papers cite this in 14 sentences
Papers citing it · 7 sentences without a confident label
Uses its method or tool 3 papers
-
Amongst the resulting terms are integrals in $(D+2n)$ dimensions (where $n ∈ℤ$) and with raised powers of propagators. * Higher-dimensional scalar integrals are shifted back to $D$ dimensions using dimensional recurrence relations [ref] . * Using the Mathematica package LiteRed [ref] , the resulting $D$-dimensional scalar integrals are reduced to a basis of masters using integration-by-parts relations (IBPs) [ref] . * Known expressions for the four-point two-loop master integrals [ref] are inserted.
Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes · Integration & transcendental weight · 1.00
-
Moreover, we can use dimensional shift identities [ref] to relate the coefficients of the Laurent expansion of these master integrals in $d=4-2$ to the corresponding ones in $d=2-2$ dimensions.
An analytic solution for the equal-mass banana graph · Notations and conventions · 0.99
-
[ref] and expressed in terms of well-known master integrals [ref] .
Pseudo-Evanescent Feynman Integrals from Local Subtraction · Counterterm Decomposition of Pseudo-Evanescent Integrals · 1.00
Uses its data or values 1 paper
-
These massless double-box (both planar and non-planar) integrals have been previously computed in [ref] to weight 4 and we take the results for the coefficients $c_n,0,0,0$ from there.
Two-Loop QCD-EW Master Integrals for Z Plus Jet Production at Large Transverse Momentum · Massless solutions · 1.00
Cites it as background 3 papers
-
It is well known [ref] that there are $2$ top-level master integrals, which may be chosen as the scalar integral $I_dbox^s$ and the tensor integral $I_dbox^t$, [equation]
Differential equations on unitarity cut surfaces · Double box and comparison with FIRE5 · 0.92
-
Let us consider the massless double-box [ref] in Fig. [ref].
Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers · Massless Double-Box · 0.90
-
That family of Feynman integrals (first computed in [ref] ) was used as the example in ref.
On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals · The double box · 0.89
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.