Full color two-loop six-gluon all-plus helicity amplitude

Form factors, as quantities involving both local operators and asymptotic particle states, contain information of both the spectrum of operators and the on-shell amplitudes. So far the studies of form factors have been mostly focused on the large Nc planar limit, with a few exceptions of Sudakov form factors. In this paper, we discuss the systematical construction of full color dependent form factors with generic local operators. We study the color decomposition for form factors and discuss the general strategy of using on-shell unitarity cut method. As concrete applications, we compute the full two-loop non-planar minimal form factors for both half-BPS operators and non-BPS operators in the SU(2) sector in $$ \mathcal{N} $$ N = 4 SYM. Another important aspect is to investigate the color-kinematics (CK) duality for form factors of high-length operators. Explicit CK dual representation is found for the two-loop half-BPS minimal form factors with arbitrary number of external legs. The full-color two-loop form factor result provides an independent check of the infrared dipole formula for two-loop n-point amplitudes. By extracting the UV divergences, we also reproduce the known non-planar SU(2) dilatation operator at two loops. As for the finite remainder function, interestingly, the non-planar part is found to contain a new maximally transcendental part beyond the known planar result.

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“…Similar relations have been considered at higher loop level and applied for computing amplitudes, see e.g. [50][51][52][53][54][55][56].…”

Section: Trivalent (Ddm) Color Basismentioning

confidence: 99%

“…Similar strategy was also considered in loop amplitudes computation, see e.g. [50][51][52][53][54][55][56]. For form factors of high dimension operators, an important difference comparing to amplitudes is that one can focus on a small set of density loop correction functions.…”

Section: Jhep04(2021)176mentioning

confidence: 99%

Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

Lin

Yang

2021

J. High Energ. Phys.

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“…The first results for non-planar five-point amplitudes were obtained in N = 4 super-Yang-Mills theory [26,27] and in N = 8 supergravity [28,29], followed by the full-color five-gluon amplitude with all positive helicities [30]. Also the full-color six-gluon all-plus helicity amplitude was obtained in [31]. Important progress has been made in evaluation of five-point amplitudes and integrals with one massive leg [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Pentagon functions for scattering of five massless particles

Chicherin

Sotnikov

2020

J. High Energ. Phys.

103

118

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We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

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“…For this reason a lot of theoretical effort has been invested in their evaluation and in the development of ever-more efficient methods for their calculation. A number of gauge theories are being studied, starting from string and supersymmetric theories [1][2][3][4][5][6][7][8][9][10][11][12][13], to gravity [14][15][16], to Yang-Mills [17,18], to QED [19] and QCD [20][21][22][23][24][25][26][27][28][29][30][31][32] and ultimately to the full Standard Model [33][34][35][36][37][38][39][40][41][42]. Research on generic methods for solving multi-loop integrals is also ongoing [43][44][45][46][47][48]…”

Section: Introductionmentioning

confidence: 99%

Two-loop leading-color helicity amplitudes for three-photon production at the LHC

Chawdhry

Czakon

Mitov

et al. 2021

J. High Energ. Phys.

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We calculate all planar contributions to the two-loop massless helicity amplitudes for the process $$ q\overline{q} $$ q q ¯ → γγγ. The results are presented in fully analytic form in terms of the functional basis proposed recently by Chicherin and Sotnikov. With this publication we provide the two-loop contributions already used by us in the NNLO QCD calculation of the LHC process pp → γγγ [Chawdhry et al. (2019)]. Our results agree with a recent calculation of the same amplitude [Abreu et al. (2020)] which was performed using different techniques. We combine several modern computational techniques, notably, analytic solutions for the IBP identities, finite-field reconstruction techniques as well as the recent approach [Chen (2019)] for efficiently projecting helicity amplitudes. Our framework appears well-suited for the calculation of two-loop multileg amplitudes for which complete sets of master integrals exist.

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Full color two-loop six-gluon all-plus helicity amplitude

Abstract: We present the full color two-loop six-point all-plus Yang-Mills amplitude in compact analytic form. The computation uses four dimensional unitarity and augmented recursion.

Cited by 16 publications

References 33 publications

Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

Pentagon functions for scattering of five massless particles

Two-loop leading-color helicity amplitudes for three-photon production at the LHC

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