Two-loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

Jin, Qing jun; Ren, Ke; Yang, Gang

doi:10.1007/jhep04(2021)180

Cited by 15 publications

(24 citation statements)

References 88 publications

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“…In particular, scattering of Higgs and gluons can be understood as form factors of operators appearing in the Higgs effective theory, where Higgs-gluons interaction vertices are obtained by integrating out the heavy top quark loop [45][46][47][48]. Many evidences from form factor results at two loops [23,24,[27][28][29][49][50][51][52][53][54][55][56][57][58] support the intriguing maximal transcendentality principle (MTP) [59,60] which conjectures that N = 4 SYM captures the maximally transcendental part of QCD. The new results obtained in this paper are also expected to provide the maximally transcendental pieces of three-loop QCD results.…”

Section: Introductionmentioning

confidence: 99%

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

Lin

Yang

Zhang

2022

J. High Energ. Phys.

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We present the detailed computation of full-color three-loop three-point form factors of both the stress-tensor supermultiplet and a length-three BPS operator in 𝒩 = 4 SYM. The integrands are constructed based on the color-kinematics (CK) duality and generalized unitarity method. An interesting observation is that the CK-dual integrands contain a large number of free parameters. We discuss the origin of these free parameters in detail and check that they cancel in the simplified integrands. We further perform the numerical evaluation of the integrals at a special kinematics point using public packages FIESTA and pySecDec based on the sector-decomposition approach. We find that the numerical computation can be significantly simplified by expressing the integrals in terms of uniformly transcendental basis, although the final three-loop computations still require large computational resources. Having the full-color numerical results, we verify that the non-planar infrared divergences reproduce the non-dipole structures, which firstly appear at three loops. As for the finite remainder functions, we check that the numerical planar remainder for the stress-tensor supermultiplet is consistent with the known result of the bootstrap computation. We also obtain for the first time the numerical results of the three-loop non-planar remainder for the stress-tensor supermultiplet as well as the three-loop remainder for the length-three operator.

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Section: Introductionmentioning

confidence: 99%

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

Lin

Yang

Zhang

2022

J. High Energ. Phys.

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“…This generalizes the scope of the MTP from anomalous dimensions to kinematics-dependent functions. More correspondence was also observed to Higgs-plus-three-parton amplitudes with high dimensional operators [7][8][9][10][11][12][13][14] and with external quark states [12,15]. There is also other evidence of the correspondence for Wilson lines [16,17].…”

Section: Introductionmentioning

confidence: 76%

Deciphering the Maximal Transcendentality Principle via Bootstrap

Guo¹,

Jin²,

Wang³

et al. 2022

Preprint

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We prove the principle of maximal transcendentality for a class of form factors, including the general two-loop minimal form factors, the two-loop three-point form factor of tr(F 2 ), and the two-loop four-point form factor of tr(F 3 ). Our proof is based on a recently developed bootstrap method using the representation of master integral expansions, together with some unitarity cuts that are universal in general gauge theories. The maximally transcendental parts of the two-loop four-gluon form factor of tr(F 3 ) are obtained for the first time in both planar N = 4 SYM and pure YM theories. This form factor can be understood as the Higgs-plus-four-gluon amplitudes involving a dimension-seven operator in the Higgs effective theory. In this case, we find that the maximally transcendental part of the N = 4 SYM result is different from that of pure YM, and the discrepancy is due to the gluino-loop contributions in N = 4 SYM. In contrast, the scalar-loop contributions have no maximally transcendental parts. Thus, the maximal transcendentality principle still holds for the form factor results in N = 4 SYM and QCD, after a proper identification of the fundamental quarks and adjoint gluinos as n f → 4N c . This seems to be the first example of the maximally transcendental principle that involves fermion-loop contributions. As another intriguing observation, we find that the four-point form factor of the half-BPS tr(φ 3 ) operator is precisely a building block in the form factor of tr(F 3 ). C Two-loop symbol letters and collinear limit 54 C.1 Symbol letters 54 C.2 Collinear limit of the letters 56 D Constraints from higher order of ǫ-expansion 57 E Building-blocks for 2-loop four-point form factor of tr(F 3 ) 59 F Remainders and numerical results for the four-point form factor 62 G One-loop four-gluon amplitude: a counter-example of MTP 63 23 12 23 23 23 12 , 1 − 1 w = 2 312 23 12 23 2 3 .(2.16)These variables are enough to provide the symbol letters for the remainder functions of threepoint form factors of tr(F 2 ) [5,47]. In this case, the collinear limit is relatively trivial, for example, in the limit of p 1 p 3 , one has s 13 → 0, q 2 → s 12 + s 23 and u → u, v → 1 − u, w → 0 .

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“…It would be thus very interesting to consider more general observables based on this method. One application is that it can be used to explain the observed universal maximally transcendental parts for form factors [26,46,47,56,[70][71][72][73][74][75][76][77][78][79]. For example, applying our strategy for the two-loop minimal form factors, it turns out that IR constraint alone is enough to fix the maximally transcendental part; since the maximally transcendental part of IR divergence is universal (i.e.…”

Section: Discussionmentioning

confidence: 99%

Bootstrapping a Two-Loop Four-Point Form Factor

Guo,

Wang,

Yang

2021

Preprint

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We compute the two-loop four-point form factor of a length-3 half-BPS operator in planar N = 4 SYM, which belongs to the class of two-loop five-point scattering observables with one off-shell colorsinglet leg. A new bootstrapping strategy is developed to obtain this result by starting with an ansatz expanded in terms of master integrals and then solving the master coefficients via various physical constraints. We find that consistency conditions of infrared divergences and collinear limits, together with the cancellation of spurious poles, can fix a significant part of the ansatz. The remaining degrees of freedom can be fixed by one simple type of two-double unitarity cut. Full analytic results in terms of both symbol and Goncharov polylogarithms are provided.

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Two-loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

Cited by 15 publications

References 88 publications

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

Deciphering the Maximal Transcendentality Principle via Bootstrap

Bootstrapping a Two-Loop Four-Point Form Factor

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