The
muon (or mu lepton or m^{-}) is
the famous "Who ordered that?" particle.It is heavier brother of the electron.It has the same negative charge and spin ½ as the electron but with a
mass about 207 times larger.Like
the electron, it is subject to the weak and electromagnetic forces but not to
the strong force.Unlike
the electron, however, the muon is unstable to decay into lighter particles,
with a mean lifetime of 2.2 microseconds.It
undergoes a parity-violating 3-body decay into lighter particles: an electron, a
mu neutrino, and an electron antineutrino, i.e., m^{-
} → e^{-}
+ n_{m}
+ anti-n_{e}.The m^{+}, the
positive-charge antimatter twin of the m^{-}
similarly decays into a positron and two neutrinos, i.e., m^{+
} → e^{+}
+ anti-n_{m} + n_{e}.

When
cosmic rays, mainly in the form of near-lightspeed protons, collide with atoms
of the upper atmosphere, the collisions make many negative pi mesons, which
decay with a mean lifetime of 26 nanoseconds into a muon and a mu anti-neutrino,
i.e., p^{-} → m^{-}
+ anti-n_{m}.If special relativity were not involved, the resulting muons would decay
near where they were produced and never reach the surface of the Earth.On average, they would travel only about 660 meters before decaying to
electrons and neutrinos in the upper atmosphere.

However,
because of relativistic time dilation,
the internal decay clocks of near-lightspeed muons are slowed.This greatly extends their lifetimes, allowing them to reach the surface
well before they decay.For this
reason, we surface dwellers are bombarded by about one muon per minute for every
square centimeter of surface area.Every
second, roughly one muon passes through your head.Cosmic-ray muons reaching the Earth's surface produced unexpectedly
stiff tracks in a large cloud chamber at Caltech, making possible their
discovery in 1936 by Carl D. Anderson and my late friend and colleague Seth
Neddermeyer.

We
are focusing on muons in this AV column because they play an important role in
two recent experimental results, both of which appear to be in conflict with the
Standard Model (SM) of Particle Physics: (1) the decay of B mesons into muons as
observed at the LHC, and (2) the precise measurement of the muon gyro-magnetic
factor g, as measured at Fermi
Lab.Perhaps it is only a
coincidence that both of these challenges to the SM involve muons, but the
correspondence suggests that some significant property of muons, perhaps buried
in the details of the weak interaction, is missing from the SM.We will discuss these measurements in the order above.

The
bottom (or beauty) quark is the heaviest member of the quark family having an
electrical charge of -1/3,
the other family members being the down and strange quarks.An anti-bottom quark combined with an up quark form the B^{+}
meson, which has a rest mass of 5,279.3 MeV/c^{2} and a mean lifetime of
about 1.6 picoseconds. With the very
small probability of about once in two million decays, the B^{+} meson
decays to a charged K^{+} meson (mass 493.7 MeV/c^{2}) and two
oppositely charged leptons, i.e., either B^{+}→K^{+} + e^{+}
+^{ }e^{-}
or B^{+}→K^{+} + m^{+}
+ m^{-}.According to the SM, in this decay process the available energy (about
4.8 GeV) is so large that the difference between the e-masses and m-masses must have a
negligible effect on the strengths of these two decay branches, and therefore
they should be equal.This SM
prediction can be checked experimentally.

The
Large Hadron Collider (LHC) at CERN has four major detectors, ATLAS, CMS, ALICE,
and LHC-b.The LHC-b detector,
located at beam-intersection Region 8 deep under the town of Ferny-Voltaire,
France
, is devoted exclusively to the physics of the B meson.On March 23, 2021, the LHC-b Collaboration announced that they had found
in these two B^{+} meson decay branches a major discrepancy in the ratio
of muon to electron decay strength.The
ratio, based on multiple years of data collection at LHC-b, was measured to be
R=0.846±0.044 instead of 1.0.In other words, for unknown reasons the B^{+} kaon decay into
muons is observably weaker than the decay into electrons.The SM principle of "lepton universality" dictates that the branches
are equal.

The
reported ratio has a statistical significance of 3.1 standard deviations.In the physics community, a "solid" result requires a statistical
significance of 5 standard deviations, so the result qualifies as an
"observation" rather than as "evidence".Nevertheless, it represents a strong indication that the muon is not
behaving as the SM predicts that it should.

This
brings us to the other anomaly, the muon's g-2
factor.We will begin with the
gyromagnetic factor g.Consider a
spherical particle with mass m and electric charge q.If it spins on some axis with an angular momentum L, its moving charge will
produce a magnetic field with a dipole moment m.Classical electromagnetism
tells us that the ratio L/m = g(q/2m)
will be a constant, independent of spin rate.Moreover, if the mass and charge are both distributed in the same way
within the sphere, the gyromagnetic factor g
will be exactly 1.However, if the
mass of the sphere is distributed uniformly within the volume, while the charge
is localized on the surface, then g = 5/3 ~ 1.67.If
the mass is uniformly distributed while the charge is concentrated in a surface
ring around the equator, then g
= 5/2 = 2.5.In other words,
classical physics says that measuring g
should tell us something about the particle's geometrical relation between
mass and charge.

Naïvely
one would expect the mass and charge of leptons to have about the same
distribution, leading to g = 1. Therefore, it is
somewhat surprising that for both electrons and muons the experimentally
measured value of g
is slightly larger than 2.Does this
mean that these particles have some weird relation between their mass and charge
distributions?No.It means that we cannot use naïve geometrical arguments and classical
electromagnetism to describe particles that are quantum-mechanical in nature.

For
all charged spin ½ particles, the Dirac equation predicts that g=2.This is one of several peculiarities of the half-integer-spin particles
called "fermions": they all have antimatter twins with opposite
mirror-symmetry, they must be rotated by twice
360 degrees to return to their original state, and they have about twice the
value of g that one would expect from classical physics.

But
that is not the whole story.For the
g
of both the electron and the muon, there are many additional higher-order
magnetic contributions that together add up toa bit over a 0.2% increase.Physicists
like to characterize this anomalous extra contribution to the gyromagnetic
factor as a_{i} = (g-2)/2,
where i=e for the electron and i=m for the muon.The measured value of a_{e} for the
electron is a_{e}=0.001 159 652 180 73(28).It agrees with Standard Model predictions (a summation of 12,672 Feynman
diagrams) to more than 10 significant figures, making
it the most accurately verified theoretical prediction in all of physics.

However, it should be noted that the magnetic contribution to a_{e} from processes involving a particle of mass M
scales as (m_{e}/M)^{2}.Therefore, contributions for M
greater than about 100
electron masses
will be very small.For a_{m},
with m_{m}
207 times larger than m_{e},
these contributions will be larger and more significant, providing more
sensitivity to new physics.

The
measurement of the muon g has been done at both Brookhaven National Lab (2004
publication) and at Fermi Lab (2021 publication), both experiments using the
same dedicated magnetic storage ring, which was transported from BNL to Fermi
Lab.In the experiment, an intense
accelerated proton beam collides with a target to produce p^{+} mesons that decay into positive
muons.Muons of a selected momentum
range are injected into the storage ring and "kicked" electrically into
stable orbits.They circle the ring
before undergoing weak-interaction decays into two neutrinos and a positron.The positrons are deflected out of the ring and detected by scintillation
counters arrayed around the ring.

Because
the g of the muon is not
precisely 2, as the muons orbit in the storage ring's magnetic field, their
spin vectors will precess, changing direction at a rate proportional to a_{m}.Because the weak-interaction decay of the muon violates conservation of
parity, the positron tends to be emitted along the changing spin direction, so
the preferred decay direction varies as the muons orbit.This gives the positron rate of detection a sinusoidal variation with
time, which the experimenters call a "wiggle plot".The value of a_{m}
can be extracted from the wiggle frequency of the plot.And it is a maxim in physics that the most accurate results are done with
frequency measurements.

Accurate
extraction of this frequency, which sounds simple, is actually a very
complicated process, because it depends slightly on many characteristics of the
beam of muons, the storage ring, and the detection apparatus, and these must be
corrected.The experimenters, in the
recent announcement, have provided a detailed account of all the many
calibrations and corrections that went into their final result.

And
what they found was that a_{m}=0.001
165 920 40(54).When combined with
the previous 2004 Brookhaven experimental result, the overall result is a_{
m}=0.001 165 920 61(41).The best theoretical predictions from the Standard Model give a_{m
}=0.001 165 918 10(43).Therefore the Standard Model and experiment differ by 4.2 standard
deviations.As I said above, a
"solid" result requires a statistical significance of 5 standard deviations,
so the muon a_{m} discrepancy is also classified as an "observation" rather than "evidence".

Nevertheless,
these two "observations" involving the muon, taken together, suggest that
the Standard Model of Particle Physics is on the verge of being falsified in the
muon weak-interaction sector.There
are already suggestions that what is missing may be an additional "5^{th}
force" that has previously been missed, or that some unknown massive particle
that couples to leptons but not quarks awaits discovery.

But
I am hoping that these experimental results lead to more than just the discovery
of a new particle, or even a new force.The
present Standard Model of Particle Physics is rather a paste-up, with two dozen
adjustable parameters that lack any fundamental basis. Further, as I have said
in previous columns, it has become increasingly apparent that the workhorse
theories of QED and QFT, pillars of the Standard Model, have infinities that
must be subtracted, are incompatible with General Relativity, can give
ridiculously wrong predictions, and are in urgent need of replacement.I hope that these emerging cracks in the Standard Model will lead to its
replacement with a better and more fundamental theory that can explain all of
the experimental results while avoiding the pitfalls of the current approach.

Watch
this AV column for further developments.

John
G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of
quantum mechanics, The
Quantum Handshake - Entanglement, Nonlocality, and Transactions,
(Springer, January-2016) is available online as a hardcover or eBook at:http://www.springer.com/gp/book/9783319246406
or https://www.amazon.com/dp/3319246402.

Alternate
View Columns Online: Electronic reprints of 212 or more "The Alternate
View" columns by John G. Cramer published in Analog
between 1984 and the present are currently available online at: http://www.npl.washington.edu/av
.

References:

B Meson Decay into Muons:

The
LHCB Collaboration, "Measurement of CP -averaged observablesin
the B^{0}→ K^{∗0}μ^{+}μ^{−} decay",
preprint ArXiv 2003.04831.

Measurement of the Muon g-2:

B.
Abi, et al. (Muon g−2 Collaboration), "Measurement of the
Positive Muon Anomalous Magnetic Moment to 0.46 ppm", Phys. Rev. Lett. 126,
141801 (2021), LINK.