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Effective QCD Interactions of CP-odd Higgs Bosons at Three Loops
High Energy Physics - Phenomenology · Submitted 3 Jul 1998
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23.
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In the virtual presence of a heavy quark t, the interactions of a CP-odd scalar boson A, with mass M_A << 2M_t, with gluons and light quarks can be described by an effective Lagrangian. We analytically derive the coefficient functions of the respective physical operators to three loops in quantum chromodynamics (QCD), adopting the modified minimal-subtraction (MS-bar) scheme of dimensional regularization. Special attention is paid to the proper treatment of the gamma_5 matrix and the Levi-Civita epsilon tensor in D dimensions. In the case of the effective ggA coupling, we find agreement with an all-order prediction based on a low-energy theorem in connection with the Adler-Bardeen non-renormalization theorem. This effective Lagrangian allows us to analytically evaluate the next-to-leading QCD correction to the A -> gg partial decay width by considering massless diagrams. For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23. We compare this result with predictions based on various scale-optimization methods.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the virtual presence of a heavy quark t, the interactions of a CP-odd scalar boson A, with mass M_A << 2M_t, with gluons and light quarks can be described by an effective Lagrangian. | background 1.00 | 0.11 | 0.05 | asserted 0.81 |
| s1 | We analytically derive the coefficient functions of the respective physical operators to three loops in quantum chromodynamics (QCD), adopting the modified minimal-subtraction (MS-bar) scheme of dimensional regularization. | contribution 0.55 | 0.97 | 0.28 | asserted 1.00 |
| s2 | Special attention is paid to the proper treatment of the gamma_5 matrix and the Levi-Civita epsilon tensor in D dimensions. | method 0.97 | 0.77 | 0.03 | asserted 0.68 |
| s3 | In the case of the effective ggA coupling, we find agreement with an all-order prediction based on a low-energy theorem in connection with the Adler-Bardeen non-renormalization theorem. | result 0.93 | 0.91 | 0.21 | asserted 1.00 |
| s4 | This effective Lagrangian allows us to analytically evaluate the next-to-leading QCD correction to the A -> gg partial decay width by considering massless diagrams. | method 0.65 | 0.90 | 0.14 | asserted 0.93 |
| s5 | For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23. | result 1.00 | 0.94 | 0.30 | asserted 1.00 |
| s6 | We compare this result with predictions based on various scale-optimization methods. | contribution 0.47 | 0.90 | 0.05 | asserted 0.75 |
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Original abstract
In the virtual presence of a heavy quark t, the interactions of a CP-odd scalar boson A, with mass M_A << 2M_t, with gluons and light quarks can be described by an effective Lagrangian. We analytically derive the coefficient functions of the respective physical operators to three loops in quantum chromodynamics (QCD), adopting the modified minimal-subtraction (MS-bar) scheme of dimensional regularization. Special attention is paid to the proper treatment of the gamma_5 matrix and the Levi-Civita epsilon tensor in D dimensions. In the case of the effective ggA coupling, we find agreement with an all-order prediction based on a low-energy theorem in connection with the Adler-Bardeen non-renormalization theorem. This effective Lagrangian allows us to analytically evaluate the next-to-leading QCD correction to the A -> gg partial decay width by considering massless diagrams. For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23. We compare this result with predictions based on various scale-optimization methods.
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References
How the literature uses it
38 arXiv papers cite this in 58 sentences
Papers citing it · 41 sentences without a confident label
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In this basis the RGEs read: [equation] where [equation] Note that the $c_A$ ($A = G,W,B$) Wilson coefficients in eq:Xdef do not run, since in the normalization of eq:LaGKRH12 the scale dependence of the operator $a F^AF̃^A$ is accounted for by the running of the gauge couplings [ref] .
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Now the (Lorentz) scalar amplitude $A^ab_gg→A$ can be obtained from $A_gg→A,αβ^μνρσ,ab$ via the projector $P^αβ_μνρσ$ [ref] :[Note that the formulae presented in Ref. [ref] apply to the coefficient function of the effective theory whereas here we invesigate the virtual corrections in the full theory.] [equation] In the actual calculations we use Eq. ([ref]) in the initial diagram, then drop $ϵ_μνρσ$ and obtain $A_gg→A,αβ^μνρσ,ab$.
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In this section we obtain the explicit form of the three-loop correlators of $tr F^2$ and of $tr FF̃$ starting from their imaginary parts that have been computed in [ref] [ref] in the $MS$ scheme.
Ultraviolet asymptotics of glueball propagators · Perturbative check of the universal behavior of correlators · 0.95
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The $𝒪(τ_t^0)$ term is also known at $𝒪(α_s^2)$, where it is still as large as 23% [ref] .
Two-Loop Electroweak Corrections to the A^0 gamma gamma and A^0 g g Couplings of the CP-Odd Higgs Boson · Discussion · 0.80
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Muscinelli we have checked [ref] the aforementioned asymptotic estimates for the scalar, pseudoscalar and $ASD$ Euclidean glueball propagator (they correspond to the case $γ_0=2β_0)$ by means of a very remarkable three-loop perturbative computation by Chetyrkin et al. [ref] , that sums up about $800$ Feynman diagrams [The earlier two-loop computation was performed in [ref] .], by comparing the perturbative computation re-expressed in terms of the two-loop running coupling with the actual asymptotic estimates, finding perfect agreement [ref] .
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[ref] where it was extracted from explicit calculations of different quantities determined in the same renormalization scheme as used here.
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We would also like to point that the relative sign of the CP-even and CP-odd couplings in Eq. ([ref]) is consistent with Refs. [ref] , while the sign was reversed between Refs. [ref] .
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Pulling out one factor of $α_i$ in the definitions of the ALP couplings to gauge fields in ([ref]) ensures that the Wilson coefficients $c_VV$ are scale independent (at least up to two-loop order in gauge couplings), i.e. [equation] For the QCD coefficient $c_GG$ this follows from the explicit calculations performed in [ref] , and an analogous statement holds for $c_WW$ and $c_BB$.
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On the other hand, for the pseudo-scalar case, only next-to-next-to-leading order(NNLO) QCD results [ref] in the effective theory [ref] are known.
Rapidity distribution of pseudo-scalar Higgs boson to $\rm{\textbf{NNLO}_A+\overline{\textbf {NNLL}}}$ · Introduction · 0.83
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[ref] (see also ref.
NLO QCD corrections to pseudoscalar Higgs production in the MSSM · Introduction · 0.81
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On the other hand for the CP-odd pseudo scalar, only NNLO QCD results [ref] in the effective theory [ref] are known.
Pseudo-scalar Form Factors at Three Loops in QCD · Introduction · 0.80
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