We observe that the partition function of the set of all free massless higher spins s=0,1,2,3,... in flat space is equal to one: the ghost determinants cancel against the physical ones or, equivalently, the (regularized) total number of degrees of fr
eedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z=1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z=1 is also true in the conformal higher spin theory (with higher-derivative d^{2s} kinetic terms) expanded near flat or conformally flat S^4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat 4d space. This non-unitary theory has a Weyl-invariant action in curved background and corresponds to partially massless field in AdS_5. We discuss in detail the special case of s=2 (or conformal graviton), compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions.
We have computed the complete one-loop electroweak effects in the MSSM for single top (and single antitop) production in the $t$-channel at hadron colliders, generalizing a previous analysis performed for the dominant $dt$ final state and fully inclu
ding QED effects. The results are quite similar for all processes. The overall Standard Model one-loop effect is small, of the few percent size. This is due to a compensation of weak and QED contributions that are of opposite sign. The genuine SUSY contribution is generally quite modest in the mSUGRA scenario. The experimental observables would therefore only practically depend, in this framework, on the CKM $Wtb$ coupling.
We write explicit and self-contained asymptotic expressions for the tensorial B, C and D Passarino-Veltman functions. These include quadratic and linear logarithmic terms, as well as subleading constant terms. Only mass-suppressed O(m^2/s) contributi
ons are neglected. We discuss the usefulness of such expressions, particularly for studying one-loop effects in 2-to-2 body processes at high energy.
We compute, in the MSSM framework, the sum of the one-loop electroweak and of the total QED radiation effects for the process $pp to t W+X$, initiated by the parton process $bgto tW$. Combining these terms with the existing NLO calculations of SM and
SUSY QCD corrections, we analyze the overall one-loop supersymmetric effects on the partial rates of the process, obtained by integrating the differential cross section up to a final variable invariant mass. We conclude that, for some choices of the SUSY parameters and for relatively small final invariant masses, they could reach the relative ten percent level, possibly relevant for a dedicated experimental effort at LHC.
