Hadronic contribution to $α(M_Z^2)$ and the anomalous magnetic moment of the muon
In this contribution recent developments are discussed which lead to a significant reduction of the error for $α(M_Z^2)$ and $(g-2)_μ$.
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arXiv subjects
M. Steinhauser
Publications and source records attributed to M. Steinhauser.
Automatic Computation of Feynman Diagrams
Quantum corrections significantly influence the quantities observed in modern particle physics. The corresponding theoretical computations are usually quite lengthy which makes their automation mandatory. This review reports on the current status of automatic calculation of Feynman diagrams in particle physics. The most important theoretical techniques are introduced and their usefulness is demonstrated with the help of simple examples. A survey over frequently used programs and packages is provided, discussing their abilities and fields of applications. Subsequently, some powerful packages which have already been applied to important physical problems are described in more detail. The review closes with the discussion of a few typical applications for the automated computation of Feynman diagrams, addressing current physical questions like properties of the $Z$ and Higgs boson, four-loop corrections to renormalization group functions and two-loop electroweak corrections.
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Non-Singlet Corrections of O(α_s^2 G_F M_t^2) to Γ(Z\to b\bar{b})
The partial decay rate of the $Z$ boson into bottom quarks constitutes an important decay channel. This is mainly due to the virtual presence of the top quark in the loop diagrams giving rise to correction factors which are quadratic in the top quark mass. At one- and two-loop order it turned out that the leading term in the heavy-top expansion leads to very good approximations to the exact result. In this work the non-singlet diagrams at O(α_s^2 G_F M_t^2) are considered.
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Completely Automated Calculations of Multi-Loop Diagrams
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This makes it necessary to automate the calculations as much as possible. A program package will be described which generates automatically the Feynman diagrams, manipulates the expressions in the desired way and performs the computation. As a physical application O(αα_s) corrections to the decay rate of the $Z$ boson into bottom quarks are discussed.
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A theory driven analysis of the effective QED coupling at $M_Z$
An evaluation of the effective QED coupling at the scale M_Z is presented. It employs the predictions of perturbative QCD for the cross section of electron positron annihilation into hadrons up to order α_s^2, including the full quark mass dependence, and of order α_s^3 in the high energy region. This allows to predict the input for the dispersion relations over a large part of the integration region. The perturbative piece is combined with data for the lower energies and the heavy quark thresholds. The result for the hadronic contribution to the running of the coupling Δα^{(5)}_{\rm had}(M_Z^2)= (277.5 \pm 1.7)\times 10^{-4} leads to (α(M_Z^2))^{-1}=128.927 \pm 0.023. Compared to previous analyses the uncertainty is thus significantly reduced.
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Effective QCD Interactions of CP-odd Higgs Bosons at Three Loops
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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Leptonic contribution to the effective electromagnetic coupling constant up to three loops
In this note the leptonic contribution to the running of the electromagnetic coupling constant is discussed up to the three-loop level. Special emphasize is put on the evaluation of the double-bubble diagrams.
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Complete Corrections of O(αα_s) to the Decay of the Z Boson into Bottom Quarks
For the vertex corrections to the partial decay rate $Γ(Z \to b\bar{b})$ involving the top quark only the leading terms of order $αα_s$ in the $1/M_t$ expansion are known. In this work we compute the missing next-to-leading corrections. Thus at $O(αα_s)$ the complete corrections to the decay of the Z boson into bottom quarks are at hand.
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Three-loop vacuum integrals in FORM and REDUCE
The implementation of an algorithm for three-loop massive vacuum integrals, based on the explicit solution of the recurrence relations, in REDUCE and FORM is described.
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Singlet Polarization Functions at O(α_s^2)
We consider the three-loop singlet diagrams induced by axial-vector, scalar and pseudo-scalar currents. Expansions for small and large external momentum $q$ are presented. They are used in combination with conformal mapping and Padé approximations in order to arrive at results for the polarization functions valid for all $q^2$. Results are presented for the imaginary parts which are directly related to physical quantities like the production of top quarks or the decay of scalar or pseudo-scalar Higgs bosons.
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Higher Order Corrections to the Hadronic Higgs Decay
A Higgs boson in the intermediate mass range is considered. An effective Lagrangian approach is used in order to evaluate the top-induced QCD corrections of order $α_s^3$ to the decay into light quarks and $O(α_s^4)$ corrections to the gluonic decay mode. The connection to the decoupling relations for $α_s$ and the light quark masses is discussed.
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O(α_s^2) Corrections to Current Correlators
In this contribution three-loop QCD corrections to current correlators are considered. The application of the large momentum procedure, which provides a systematic expansion in $(m^2/q^2)^n$, allows the computation of terms up to $n=6$ for the vector and axial-vector correlator and up to $n=4$ for the scalar and pseudo-scalar correlator. Some physical applications are discussed.
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Massive Quark Production in Electron Positron Annihilation to Order $α_s^2$
Recent analytical and numerical results for the three-loop polarization function allow to present a phenomenological analysis of the cross section for massive quark production in electron positron annihilation to order $α_s^2$. Numerical predictions based on fixed order perturbation theory are presented for charm and bottom production above 5 and 11.5 GeV, respectively. The contribution from these energy regions to $α(M_Z^2)$, the running QED coupling constant at scale M_Z, are given. The dominant terms close to threshold, i.e. in an expansion for small quark velocity $β$, are presented.
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O(α_s^2) Corrections to Top Quark Production at $e^+e^-$ Colliders
In this article we evaluate mass corrections up to $O((m^2/q^2)^6)$ to the three-loop polarization function induced by an axial-vector current. Special emphasis is put on the evaluation of the singlet diagram which is absent in the vector case. As a physical application $O(α_s^2)$ corrections to the production of top quarks at future $e^+e^-$ colliders is considered. It is demonstrated that for center of mass energies $\sqrt{s} >~ 500$ GeV the inclusion of the first seven terms into the cross section leads to a reliable description.
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Decoupling Relations to O(alpha_s^3) and their Connection to Low-Energy Theorems
If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant alpha_s and the quark masses m_q exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, zeta_g and zeta_m, respectively. Adopting the modified MS (MS-bar) scheme, we derive simple formulae which reduce the calculation of zeta_g and zeta_m to the solution of vacuum integrals. This allows us to evaluate zeta_g and zeta_m through three loops. We also establish low-energy theorems, valid to all orders, which relate the effective couplings of the Higgs boson to gluons and light quarks, due to the virtual presence of a heavy quark h, to the logarithmic derivatives w.r.t. m_h of zeta_g and zeta_m, respectively. Fully exploiting present knowledge of the anomalous dimensions of alpha_s and m_q, we thus calculate these effective couplings through four loops. Finally, we perform a similar analysis for the coupling of the Higgs boson to photons.
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Complete QCD Corrections of Order O(α_s^3) to the Hadronic Higgs Decay
We consider the decay of an intermediate mass Higgs boson into hadrons up to order O(α_s^3). The results from the diagrams containing only light degrees of freedom were recently computed in a previous work by K.G. Ch. (Phys. Lett. B 390 (1997) 309). In this letter the remaining contributions involving the top quark are evaluated analytically using an effective field theory approach. Coupled with the previous result the present calculation determines the complete next-next-to-leading order correction to the hadronic decay rate of an intermediate mass Higgs boson.
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Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
We present in analytic form the matching conditions for the strong coupling constant alpha_s^(n_f)(mu) at the flavour thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient beta_3 of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for alpha_s^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavours n_f.
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Heavy Quark Current Correlators to O(α_s^2)
In this paper the three-loop polarization functions Π(q^2) are calculated for the cases of an external vector, axial-vector, scalar or pseudo-scalar current. Results are presented for the imaginary part which directly leads to the cross section $σ(e^+e^- \to Z \to hadrons)$ and to the Higgs decay rates, respectively.
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