Effective four-fermion operators in top physics: a roadmap

We write down a minimal basis for dimension-six gauge-invariant four-fermion operators, with some operator replacements with respect to previous ones which make it simpler for calculations. Using this basis we classify all four-fermion operator contributions involving one or two top quarks. Taking into account the different fermion chiralities, possible colour contractions and independent flavour combinations, a total number of 572 gauge-invariant operators are involved. We apply this to calculate all three-body top decay widths t -> d_k u_i dbar_j, t -> d_k e_i+ nu_j, t -> u_k u_i ubar_j, t -> u_k e_j+ e_i-, t -> u_k nu_j nu_i (with i,j,k generation indices) mediated by dimension-six four-fermion operators, including the interference with the Standard Model amplitudes when present. All single top production cross sections in pp, p pbar and e+ e- collisions are calculated as well, namely u_i d_k -> d_j t, dbar_j d_k -> ubar_i t, u_i dbar_j -> dbar_k t, u_i u_k -> u_j t, u_i ubar_j -> ubar_k t, e+ e- -> ubar_k t and the charge conjugate processes. We also compute all top pair production cross sections, ubar_i u_j -> t tbar, dbar_i d_j -> t tbar, u_i u_j -> t t and e+ e- -> t tbar. Our results are completely general, without assuming any particular relation among effective operator coefficients.Comment: LaTeX 43 pages, 1 PS figure. Cross sections for uu,cc -> tt correcte

Model-independent measurement of the top quark polarisation

We introduce a new asymmetry in the decay t -> W b -> l nu b, which is shown to be directly proportional to the polarisation of the top quark along a chosen axis, times a sum of W helicity fractions. The latter have already been precisely measured at the Tevatron and the Large Hadron Collider. Therefore, this new asymmetry can be used to obtain a model-independent measurement of the polarisation of top quarks produced in any process at hadron or lepton colliders.Comment: LaTeX 12 pages. Discussion expanded with a new plot, references added. Final version to appear in PL

A minimal set of top anomalous couplings

We simplify the general form of the fermion-fermion-gauge boson interactions generated by dimension-six gauge-invariant effective operators by using the equations of motion to remove redundant operators. It is found that the most general vertex for off-shell fermions fi, fj and an off-shell boson V=W,Z,gamma,g only involves gamma^mu and sigma^{mu nu} q_nu terms, with q=p_i-p_j. Examples are given for the Wtb, Ztt, gamma tt and gtt interactions, whose general expression is greatly simplified with respect to previous results in the literature. The same arguments apply to top flavour-changing neutral interactions with the Z boson, the photon or the gluon, which can also be parameterised in full generality with only gamma^mu and sigma^{mu nu} q_nu couplings. Explicit expressions are given for these vertices in terms of dimension-six gauge-invariant operators. We also discuss how effective operator coefficients might be determined from eventual measurements of anomalous couplings.Comment: LaTeX 29 pages, 3 PS figures. Minor comments added, final version to appear in NP

A minimal set of top-Higgs anomalous couplings

We use the equations of motion to simplify the general form of fermion-fermion-Higgs interactions generated by dimension-six gauge-invariant effective operators. After removing redundant operators it is found that the most general H f_i f_j vertex for off-shell fermions f_i, f_j and an off-shell Higgs boson only involves scalar and pseudo-scalar terms, without derivatives. Examples are presented for the Htt and Htq interactions, where q=u,c, giving the explicit expressions of the vertices in terms of gauge-invariant operators. The new operator equalities obtained here also reduce the number of operators relevant for the Ztq vertices, although the general form of these interactions is not simplified with respect to previous results.Comment: LaTeX 16 pages, 2 PS figures. Typos corrected. Final version which appeared on the journa

Effective Field Theory for Nonstandard Top Quark Couplings

We present an effective-field-theory calculation of the effect of a dimension-six operator involving the top quark on precision electroweak data via a top-quark loop. We demonstrate the renormalizability, in the modern sense, of the effective field theory. We use the oblique parameter U to bound the coefficient of the operator, and compare with the bound derived from top-quark decay.Comment: 10 pages, 3 figure

W polarisation beyond helicity fractions in top quark decays

We calculate the density matrix for the decay of a polarised top quark into a polarised W boson and a massive b quark, for the most general Wtb vertex arising from dimension-six gauge-invariant effective operators. We show that, in addition to the well-known W helicity fractions, for polarised top decays it is worth to define and study the transverse and normal W polarisation fractions, that is, the W polarisation along two directions orthogonal to its momentum. In particular, a rather simple forward-backward asymmetry in the normal direction is found to be very sensitive to complex phases in one of the Wtb anomalous couplings. This asymmetry, which indicates a normal W polarisation, can be generated for example by a P-odd, T-odd transition electric dipole moment. We also investigate the angular distribution of decay products in the top quark rest frame, calculating the spin analysing powers for a general Wtb vertex. Finally we show that, using a combined fit to top decay observables and the tW cross section, at LHC it will be possible to obtain model-independent measurements of all the (complex) Wtb couplings as well as the single top polarisation. Implications for spin correlations in top pair production are also discussed.Comment: LaTeX 36 pages, 51 EPS figures. Typos corrected. To appear in NP

Profile of multiboson signals

We investigate the visibility of signals characterised by wide bumps over a smoothly falling background that cannot be accurately predicted by Monte Carlo calculations. Examples of such are the wide bumps that triboson and quadriboson resonance cascade decays would yield in diboson resonance searches in fully hadronic final states. We find that the sensitivity to triboson bumps is rather small: signals of a moderate size could be present in current data and yet remain unnoticed. For quadriboson cascade decays the signals can hardly be distinguished from the background in the current searches.Comment: LaTeX 17 pages. v2: fixed typos and comments added; journal versio

Ultraboosted ZtZt and γt\gamma t production at the HL-LHC and FCC-hh

Searches for anomalous $Zt$ and $\gamma t$ production provide an excellent probe of flavour-changing top interactions when the energies considered are very large. In this note we estimate the sensitivity to these interactions at the high luminosity phase of the LHC and a future 100 TeV $pp$ collider (FCC-hh). For the LHC, the expected limits on $t \to uZ / u\gamma$ branching ratios from $Zt$ and $\gamma t$ production will reach the $10^{-5}$ level, one order of magnitude better than the existing projections for $t \to uZ$ from $t \bar t$ production. For the FCC-hh, the limits on $t \to uZ / u\gamma$ could reach an impressive sensitivity at the $10^{-6}$ level, with limits on $t \to cZ / c\gamma$ at the $10^{-5}$ level.Comment: LaTeX 11 pages. Plots fixed, journal versio