A recent CERN publication reports the decay of the
H0 (called the Higgs boson)
into four leptons of the electron or the muon
flavor. This process is one kind of result measured by detectors of the
proton-proton LHC collider.
An intermediate state of this process is a virtual production of
ZZ bosons (see
here).
The Z boson is an experimentally well-known particle and
lepton pairs like e+e-,
μ+μ-
are included among its decay modes (see
here).
Therefore, two Z bosons can produce the following lepton combinations:
e+e-e+e-, e+e-μ+μ-, μ+μ-μ+μ-.
Fig. 1 illustrates the second case.
Fig. 1: H0→ZZ→e+e-
μ+
μ-
The black circle denotes a H0 boson and each of the grey
circles denotes a virtual Z boson. The arrows denote leptons
produced in the decay of each of the Z boson.
The H0 and the two Z bosons
of fig. 1 are enclosed
inside a spatial volume whose linear size is about 10-13 cm.
This is the volume of two colliding protons of the LHC facility.
The outgoing leptons are detected by devices that are
located several meters away from the very small spatial volume
of the collision.
The following points explain why the
Standard Model cannot provide a consistent explanation
for this effect.
The four outgoing leptons travel a relatively long distance before
their detection by appropriate devices. Their data indicate
that they have been produced by a proton-proton collision event which has
specific space-time coordinates.
Therefore, a theoretical interpretation of this event must
provide a consistent expression that describes particle
location.
Quantum theories describe particle location by means of a consistent
expression for density. Density is the 0-component of the
4-current jμ.
The Dirac theory of the e,μ leptons provides a consistent
expression for density
ρ = ψ†ψ
(1)
(see [1] p. 9).
Unfortunately, the electroweak Z boson and the Higgs
H0 boson have no consistent expression for density.
One reason for this fault is that
the quantum function of each of these particles takes
a mathematically real form.
An indication of the validity of
this claim relies on the fact that no textbook
on quantum field theory (QFT) shows a consistent expression for
density of the Z or the Higgs
H0 bosons. By contrast, many textbooks on the Dirac
theory of a spin-1/2 particle show the density expression (1)
or an equivalent form of it.
A refutation of the previous claim should simply indicate the
page number, the title and the year of publication of a
textbook that proves the existence of a consistent expression
for density of either the Z or the H0 bosons.
The foregoing general argument holds in quantum mechanics and
in QFT as well. For example, S. Weinberg makes the following statement.
"First, some good news: quantum field theory is based on the same quantum
mechanics that was invented by Schroedinger, Heisenberg, Pauli, Born,
and others in 1925-1926, and has been used ever since in atomic,
molecular, nuclear and condense matter physics"
([2], p. 49).
References:
[1] J. D. Bjorken and S.D. Drell, Relativistic Quantum
Mechanics (McGraw-Hill, New York, 1964).
[2] S. Weinberg, The Quantum Theory of Fields, Vol. I (Cambridge
University Press, Cambridge, 1995). (See the following link
here.)
