Global approach to top-quark flavor-changing interactions

We adopt a fully gauge-invariant effective-field-theory approach for parametrizing top-quark flavor-changing-neutral-current interactions. It allows for a global interpretation of experimental constraints (or measurements) and the systematic treatment of higher-order quantum corrections. We discuss some recent results obtained at next-to-leading-order accuracy in QCD and perform, at that order, a first global analysis of a subset of the available experimental limits in terms of effective operator coefficients. We encourage experimental collaborations to adopt this approach and extend the analysis by using all information they have prime access to.

Figure 1

The full standard-model gauge symmetry gives rise to four-point interactions, not included in the Lagrangian of Eq. (3), that contribute at the same order as three-point ones in some FCNC processes: e.g. (a) in $ug\to th$ production (or radiative $t\to hug$ decay), or (b) in $e^{+}{e}^{-}\to t\overline{u}$ (and $t\to u{e}^{+}{e}^{-}$).

Figure 2

Representative $ug\to tZ$ diagrams involving $O_{uG}$ (black dot) and $O_{uW}$ (gray square) operators, at leading-order (first two) and next-to-leading order (last two diagrams). The UV divergence of the fourth diagram involving $O_{uG}$ is regularized by a counterterm of $O_{uW}$ form.

Figure 3

Representative diagrams for $t\to u\gamma$, $qZ$, $qh$ at leading and next-to-leading orders. The gray square represents a contribution from the $O_{uW}$ weak-dipole operator, while the black dot represents a contribution from the $O_{uG}$ color-dipole operator.

Figure 4

The tree-level exchange of a heavy flavor-changing $Z^{\prime }$ would generate four-fermion effective operators. Such operators have been overlooked in many experimental searches.

Figure 5

Invariant mass distribution of lepton pair in $t\to j{\ell }^{+}{\ell }^{-}$. Contributions from two-quark $O_{\phi q}^{-}$ and $O_{uW}$ as well as two-quark–two-lepton $O_{lequ}^3$ operators are compared.

Figure 6

Tree-level diagrams for $pp\to t\gamma$ and $pp\to tZ$.

Figure 7

Tree-level diagrams for $pp\to th$.

Figure 8

Cross section [fb] for $e^{+}{e}^{-}\to tj+\overline{t}j$ for three illustrative choices of parameters at NLO accuracy in QCD (lines); 95% C.L. limits (arrows) set by a combination ALEPH, DELPHI, L3 and OPAL results [15]. The uncertainty bands (${}_{-1.8\%}^{+2.2\%}$ at $\sqrt{s}=207\mathrm{GeV}$) are obtained by running ${\alpha }_s$ from $m_t/2$ to $2m_t$ as the anomalous dimensions of vector operators vanish.

Figure 9

NLO lepton invariant mass distribution in $pp\to t\ell \ell$, from the two-quark operator $O_{\phi u}$ only (red), from the two-quark–two-lepton operators $O_{eu}$ (blue) and from their interference (green).

Figure 10

Complementarity of the $t\to j{\ell }^{+}{\ell }^{-}$ and $pp\to t\gamma ,\overline{t}\gamma$ limits in the $C_{uB}-C_{uW}$ plane. The $C_{uG}$ coefficients are constrained to satisfy the bounds set by the $pp\to t,\overline{t}$ searches. The dark gray and red allowed regions apply for $a=1$ while the blue intersection shows the constraint for $a=2$. The same limits apply to either the real or the imaginary parts of the operator coefficients.

Figure 11

Complementarity of the $e^{+}{e}^{-}\to tj+\overline{t}j$ and $t\to j{e}^{+}{e}^{-}$ limits for constraining two- and four-fermion operators. The operator coefficients not shown in this plane are constrained to satisfy the bound of Fig. 12. The dark gray and red allowed regions apply for $a=1$ while the light gray and blue ones for $a=2$. The same limits apply to either the real or the imaginary parts of the operator coefficients.

Figure 12

The 95% C.L. limits on the moduli of operator coefficients for $\mathrm{\Lambda }=1\mathrm{TeV}$, as deriving from current bounds on $t\to j{\ell }^{+}{\ell }^{-}$, $t\to j\gamma \gamma$, $pp\to t+\overline{t}$, $pp\to t\gamma +\overline{t}\gamma$ and $e^{+}{e}^{-}\to tj+\overline{t}j$. Two-quark–two-lepton operators containing an electron pair are shown; for the one containing a muon pair we refer to the figures in Secs. 5b and 5c. The red allowed regions apply for $a=1$ and the blue ones for $a=2$. A white mark indicates the bound that would have been obtained by fixing all coefficients to zero but the one constrained, instead of performing a global analysis.