A category mistake in observational claims regarding ultrashort-lived unstable particles

The physics literature contains many claims that ultrashort-lived unstable particles, such as a Higgs boson, have been observed. These claims are a matter of applying the [Formula: see text]-convention in particle physics. This paper, however, shows that by applying this [Formula: see text]-convention a category mistake is made, by which a pure reasoning is passed off as an observation. Not only are these two fundamentally different primitive notions at the very basis of science, but the pure reasoning in question is also weaker than an observation: what we have in each case is that the existence of the ultrashort-lived unstable particle is inferred to the best explanation, but that does absolutely not merit the stronger claim that the particle in question has been “observed”. Consequently, the observational claims in question will thus have to be dismissed as overstatements. On a general note, this demonstrates that the empirical support for the Standard Model of particle physics is significantly less than hitherto thought.

QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum

We present a quantum field theoretical derivation of the nondecay probability of an unstable particle with nonzero three-momentum p. To this end, we use the (fully resummed) propagator of the unstable particle, denoted as S, to obtain the energy probability distribution, called dSp(E), as the imaginary part of the propagator. The nondecay probability amplitude of the particle S with momentum p turns out to be, as usual, its Fourier transform: aSp(t)=∫mth2+p2∞dEdSp(E)e-iEt (mth is the lowest energy threshold in the rest frame of S and corresponds to the sum of masses of the decay products). Upon a variable transformation, one can rewrite it as aSp(t)=∫mth∞dmdS0(m)e-imth2+p2t [here, dS0(m)≡dS(m) is the usual spectral function (or mass distribution) in the rest frame]. Hence, the latter expression, previously obtained by different approaches, is here confirmed in an independent and, most importantly, covariant QFT-based approach. Its consequences are not yet fully explored but appear to be quite surprising (such as the fact that the usual time-dilatation formula does not apply); thus its firm understanding and investigation can be a fruitful subject of future research.

Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles

The relativistic quantum decay laws of moving unstable particles are analyzed for a general class of mass distribution densities which behave as power laws near the (nonvanishing) lower bound μ0 of the mass spectrum. The survival probability Pp(t), the instantaneous mass Mp(t), and the instantaneous decay rate Γp(t) of the moving unstable particle are evaluated over short and long times for an arbitrary value p of the (constant) linear momentum. The ultrarelativistic and nonrelativistic limits are studied. Over long times, the survival probability Pp(t) is approximately related to the survival probability at rest P0(t) by a scaling law. The scaling law can be interpreted as the effect of the relativistic time dilation if the asymptotic value Mp∞ of the instantaneous mass is considered as the effective mass of the unstable particle over long times. The effective mass has magnitude μ0 at rest and moves with linear momentum p or, equivalently, with constant velocity 1/1+μ02/p2. The instantaneous decay rate Γp(t) is approximately independent of the linear momentum p, over long times, and, consequently, is approximately invariant by changing reference frame.

Moving Unstable Particles and Special Relativity

In Poincaré-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that, just like time translations, boost transformations have a nontrivial effect on internal variables of interacting systems. In this respect, boosts are different from space translations and rotations, whose actions are always universal, trivial, and interaction-independent. Applying this theory to unstable particles viewed from a moving reference frame, we prove that the decay probability cannot be invariant with respect to boosts. Different moving observers may see different internal compositions of the same unstable particle. Unfortunately, this effect is too small to be noticeable in modern experiments.

Can vanishing mass-on-shell interactions generate a dip at colliders?

We categorize new physics signatures that manifest themselves as a “dip” structure at colliders. One potential way to realize a dip is to require interactions to be zero when all particles are mass on-shell, but not if one or more are mass off-shell. For three particle interactions, we have found three interesting cases: one massive gauge boson with two identical scalars; one massless gauge boson with two different scalars; one massive gauge boson with two identical massless gauge bosons. For each case, we identify the relevant effective operators to explore its dip signature at the LHC. Unfortunately, the unstable particle with a vanishing mass-on-shell interaction has a complex mass which is coincident with the complex pole in its propagator. As a result, a contact-like amplitude without a dip is produced. Some interesting collider signatures for “fermion-phobic” vector bosons are also discussed.

Complex-Mass Definition and the Structure of Unstable Particle’s Propagator

The propagators of unstable particles are considered in framework of the convolution representation. Spectral function is found for a special case when the propagator of scalar unstable particle has Breit-Wigner form. The expressions for the dressed propagators of unstable vector and spinor fields are derived in an analytical way for this case. We obtain the propagators in modified Breit-Wigner forms which correspond to the complex-mass definition.

INADEQUACY OF ZERO-WIDTH APPROXIMATION FOR A LIGHT HIGGS BOSON SIGNAL

The zero-width approximation (ZWA) restricts the intermediate unstable particle state to the mass shell and, when combined with the decorrelation approximation, fully factorizes the production and decay of unstable particles. The ZWA uncertainty is expected to be of [Formula: see text], where M and Γ are the mass and width of the unstable particle. We review the ZWA and demonstrate that errors can be much larger than expected if a significant modification of the Breit–Wigner lineshape occurs. A thorough examination of the recently discovered candidate Standard Model Higgs boson is in progress. For MH≈125 GeV, one has ΓH/MH < 10-4, which suggests an excellent accuracy of the ZWA. We show that this is not always the case. The inclusion of off-shell contributions is essential to obtain an accurate Higgs signal normalization at the 1% precision level. For gg→H→VV, V = W, Z, [Formula: see text] corrections occur due to an enhanced Higgs signal in the region MVV > 2MV, where also sizable Higgs-continuum interference occurs. We discuss how experimental selection cuts can be used to suppress this region in search channels where the Higgs mass cannot be reconstructed. We note that H→VV decay modes in non-gluon-fusion channels are similarly affected.