Gauge-invariant Set Of Diagrams Research Articles

Probing the Anomalous Wtb couplings in different schemes of tWb associated production modeling

The impact of anomalous Wtb couplings on tWb process of the single top quark production has been tested in different schemes of tWb modeling. The scenario with right-handed vector operator (RV) in Wtb vertex with and without the presence of Standard model (SM) left-handed vector operator in Wtb vertex has been considered. It is shown that for anomalous Wtb couplings searches in tWb process usage of the full gauge invariant set of diagrams, with the same final state for the pair top quark production as well as for the single top quark production, is more justified than the usage of the schemes with deletion of some part of diagrams.

Hyperfine splitting in muonium and positronium

Calculation of hard three-loop corrections of order [Formula: see text] to hyperfine splitting in muonium and positronium is reviewed. All these contributions are generated by the graphs with photon, electron and/or muon loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams.

Hard three-loop corrections to hyperfine splitting

We consider hard three-loop nonlogarithmic corrections of order [Formula: see text] to hyperfine splitting in muonium and positronium. All these contributions are generated by the graphs with photon, electron and/or muon loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams.

Hard nonlogarithmic corrections of ordermα7to hyperfine splitting in positronium

We consider hard three-loop nonlogarithmic corrections of order $m{\ensuremath{\alpha}}^{7}$ to hyperfine splitting in positronium. All these contributions are generated by the graphs with photon and/or electron loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge-invariant sets of diagrams. The total result for all these diagrams is $\mathrm{\ensuremath{\Delta}}E=\ensuremath{-}1.2917(1)m{\ensuremath{\alpha}}^{7}/{\ensuremath{\pi}}^{3}=\ensuremath{-}5.672\text{ }\text{ }\mathrm{kHz}$.

Muon loop light-by-light contribution to hyperfine splitting in muonium.

Three-loop corrections to hyperfine splitting in muonium, generated by the gauge-invariant sets of diagrams with muon and tauon loop light-by-light scattering blocks, are calculated. These results complete calculations of all light-by-light scattering contributions to hyperfine splitting in muonium.

Higgs boson signal at complete tree level in the SM extension by dimension-six operators

Deviations from the standard Higgs sector generated by some new (nonstandard) physics at an energy scale \Lambda could be described by an effective SU(3)_c x SU(2)_L x U(1) invariant non-renormalizable Lagrangian terms of dimension six. The set of dimension-six operators involving the Higgs field is chosen in such a way that the form of gauge bosons kinetic terms remains untouched, preserving all high-precision electroweak constraints. A systematic study of effects in various Higgs boson production channels (\gamma \gamma, ZZ, WW, bb-bar, \tau \tau-bar) caused by effecive operators is carried out beyond the {production x decay} approximation (or infinitely small width approximation). Statistical methods are used to establish consistency of the standard Higgs sector with the available LHC data. A global fit in the two-parametric anomalous coupling space indicating to possible deviations from the standard Higgs-fermion and Higgs-gauge boson couplings is performed, using post-Moriond 2012 data and more precise LC 2013 data. We find that the standard Higgs sector is consistent with the current CMS and ATLAS experimental results both in the infinitely small width approximantion and the calculation with complete gauge invariant sets of diagrams. However, visible difference of the exclusion contours is found for some combinations of production and decay channels, although minor for the global fits for all possible channels. Updates of the signal strength and the signal strength error reported at LC 2013 result in a significant improvements of the allowed regions in the anomalous coupling space, which are recalculated also at complete tree level.

Light-by-light scattering nonlogarithmic corrections to hyperfine splitting in muonium

We consider three-loop corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These diagrams produce both recoil and nonrecoil contributions to hyperfine splitting. Recoil corrections are enhanced by large logarithms of the muon-electron mass ratio. Both nonrecoil and logarithmically enhanced radiative-recoil corrections where calculated some time ago. Here we calculate nonlogarithmic radiative-recoil corrections generated by the insertions of the light-by-light scattering block.

Light-by-light scattering single-logarithmic corrections to hyperfine splitting in muonium

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These corrections are enhanced by the large logarithms of the electron-muon mass ratio. We present the results of an analytic calculation of the single-logarithmic radiative-recoil corrections of order ${\ensuremath{\alpha}}^{2}(Z\ensuremath{\alpha})(m/M){E}_{F}$ to hyperfine splitting in muonium generated by these diagrams.

Three-loop contribution to hyperfine splitting in muonium: Polarization corrections to light-by-light scattering contributions

We calculate corrections of order ${\ensuremath{\alpha}}^{3}(Z\ensuremath{\alpha}){E}_{F}$ to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with polarization insertions in the light-by-light scattering diagrams. This nonrecoil contribution turns out to be $\ensuremath{-}2.63$ Hz. The total contribution of all known corrections of order ${\ensuremath{\alpha}}^{3}(Z\ensuremath{\alpha}){E}_{F}$ is equal to $\ensuremath{-}4.28$ Hz.

Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium: Diagrams with Polarization Loops

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with electron and muon vacuum polarizations. We calculate single-logarithmic and nonlogarithmic contributions of order alpha;{3}(m/M)E_{F} generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining these corrections with the older results, we obtain total contribution to hyperfine splitting generated by all diagrams with electron and muon polarization loops. The calculation of this contribution completes an important stage in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz. The new results improve the theory of hyperfine splitting and affect the value of the electron-muon mass ratio extracted from experimental data on muonium hyperfine splitting.

Three-loop radiative corrections to Lamb shift and hyperfine splitting

We consider three-loop radiative corrections to the Lamb shift and hyperfine splitting. Corrections of order α3(Zα)5m are the largest still unknown contributions to the Lamb shift in hydrogen. We calculate radiative corrections to the Lamb shift and hyperfine splitting generated by the diagrams with insertions of one radiative photon and electron polarization loops in the graphs with two external photons. We also obtain corrections generated by the gauge-invariant sets of diagrams with two reducible radiative photon insertions in the electron line and a polarization operator insertion in one of the radiative photons, and diagrams with two reducible radiative photon insertions in the electron line and a polarization operator insertion in one of the external photons. Corrections to the Lamb shift and hyperfine splitting generated by the diagrams with insertions of the three-loop one-particle reducible diagrams with radiative photons in the electron line are calculated in the Yennie gauge.PACS Nos.: 12.20.Ds, 31.30.Jv, 32.10.Fn, 36.10.Dr

Three-loop radiative-recoil corrections to hyperfine splitting in muonium

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium. These corrections are enhanced by the large logarithm of the electron–muon mass ratio. The leading logarithm-cubed and logarithm-squared contributions were obtained a long time ago. We calculate the single-logarithmic and nonlogarithmic contributions of order α3(m/M)EF generated by gauge invariant sets of diagrams with one- and two-loop polarization insertions in diagrams with two exchanged photons and radiative photons, and by diagrams with one-loop radiative photon insertions both in the electron and muon lines. The results of this paper constitute a next step in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz. They improve the theory of hyperfine splitting, and affect the value of the electron–muon mass ratio extracted from experimental data on the muonium hyperfine splitting.PACS Nos.: 12.20.Ds, 31.30.Jv, 32.10.Fn, 36.10.Dr

Analytic contribution of orderα2(Zα)5m to the Lamb shift

The analytic result for the radiative correction of order ${\mathrm{\ensuremath{\alpha}}}^{2}$(Z\ensuremath{\alpha}${)}^{5}$m to the Lamb shift connected with a polarization insertion in one of the two external Coulomb lines is obtained. This correction arises from a gauge-invariant set of diagrams which contain, besides the polarization insertion in the Coulomb leg, all one-loop radiative photon insertions in the electron line with two external Coulomb lines.

Bern-Kosower rule for scalar QED.

We derive a full Bern-Kosower-type rule for scalar QED starting from quantum field theory: we derive a set of rules for calculating $S$-matrix elements for any processes at any order of the coupling constant. Gauge-invariant set of diagrams in general is first written in the worldline path-integral expression. Then we integrate over $x(\tau)$, and the resulting expression is given in terms of correlation function on the worldline $\left< x(\tau) x(\tau') \right>$. Simple rules to decompose the correlation function into basic elements are obtained. Gauge transformation known as integration by parts technique can be used to reduce the number of independent terms before integration over proper-time variables. The surface terms can be omitted provided the external scalars are on-shell. Also, we clarify correspondence to the conventional Feynman rule, which enabled us to avoid any ambiguity coming from the infinite dimensionality of the path-integral approach.

First corrections of order α2 ( Zα) 5 to hyperfine splitting and Lamb shift induced by two-loop insertions in the electron line

Contributions to the hyperfine splitting and Lamb shift intervals of order α 2( Zα) 5 induced by two-loop insertions in the electron line are considered. It is shown that this gauge invariant set of diagrams contains nineteen topologically different graphs. The contributions both to the hyperfine splitting and the Lamb shift induced by graphs containing the one-loop electron self-energy as a subgraph and also by the graph containing two one-loop vertices are obtained.

New correction to Lamb shift induced by one-loop polarization insertions in the radiative electron factor

A radiative correction of order α 2( Zα) 5 m to the Lamb shift induced by polarization insertions in the radiative electron factor is obtained. This correction arises from a gauge invariant set of diagrams which contain all one-loop polarization insertions in the radiative photon attached by both ends to the electron line with two external Coulomb lines. A new contribution to the Lamb shift in an arbitrary hydrogen-like ion is equal to −0.073( α 2( Zα) 5/( πn 3)) m for any S-level with the principal quantum number n. For hydrogen itself we obtain a correction −0.39 kHz for the 2S state.

An α2( Zα) 5m correction to the Lamb shift from the radiative electron factor and Coulomb line polarization

A radiative correction of order α 2( Zα) 5 m to the Lamb shift connected with a polarization insertion in one of the two external Coulomb lines is obtained. This correction arises from a gauge invariant set of diagrams which contain, besides the polarization insertion in the Coulomb leg, all one-loop radiative photon insertions in the electron line with two external Coulomb lines. A new contribution to the Lamb shift in an arbitrary hydrogen-like ion is equal to 0.611 [ α 2(Zα) 5 πn 3 ]m for any S-level with the principal quantum number n. For hydrogen itself we obtain a correction 3.31 kHz for the 2S state and 26.5 kHz for the 1S state. The contribution for the 2S state is larger than the accuracy of contemporary experiments while the contribution for the 1S state is comparable with the experimental error.

Coulomb line vacuum polarization corrections to Lamb shift of order α2( Zα) 5m

Radiative corrections of order α 2( Zα) 5 m to the lamb shift are considered. It is shown that all contributions of this order are induced by six gauge invariant sets of diagrams with two external Coulomb lines and different radiative insertions. Corrections connected with diagrams containing polarization insertions in external Coulomb lines are calculated and their contribution is equal to 0.056[ α 2(Zα) 5 π ]m for the hydrogen state with principal quantum number of two. This gives 2.42 kHz as a correction.