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1
A proposed electro-gravitational seesaw
mechanism applicable to all elementary
particles and offering an alternative to SUSY
*
Andrei-Lucian Drăgoi
1
,
2
*
DOI: 10.13140/RG.2.2.17449.11360 [URL-RG]
*
Abstract
This paper proposes an electro-gravitational seesaw
mechanism applicable to all elementary particles, offering an
alternative to supersymmetry (SUSY) which states a profound
bijective connection between bosons and fermions and predicts new
types of elementary particles, including two distinct types of
massless right-handed Majorana neutrinos (moving at the speed of
light in vacuum), suggesting a cosmology based on an inflationary
global fermionic superfluid aether.
***
I. The main section of this paper
I-1. A zero-energy hypothesis (ZEH). This paper proposes a
simple zero-energy hypothesis (ZEH) applied on any elementary
particle-antiparticle virtual pair (VP) (with total rest energy
2
22
VP
E E mc==
and total charge
( )
0qqC+ − =
) popping
out from the quantum vacuum at hypothetical length scales
comparable to the Planck length
Pl
l
( )
35
10 m
−
. More
specifically, ZEH states that the total rest energy of that VP
( )
2
VP
EE=
is nullified by the sum of both the negative
gravitational energy of attraction
g
E
(between that EP and its
anti-EP composing that VP) and the negative
electrostatic/electromagnetic energy of attraction
q
E
inside that
same VP (with ZEH being essentially an energy conservation
principle applied to a hypothetical ex-nihilo creation of VPs) at
non-relativistic speeds (in a plane/Euclidean plane micro-region of
space):
( )
0(J)
gq
VP
E E E+ + =
(1)
*
Remark 1. This ZEH is actually the simplest case possible, as
it considers only two types fields acting simultaneously inside a VP
(in Euclidean spacetime, at non-relativistic speeds), ignoring the
strong and weak interactions that may also manifest inside that VP.
ZEH considers a generic VP composed from any elementary
particle (EP) with non-zero rest mass and its antiparticle, in which
the gravitational and electrostatic inverse-square laws are just
hypothesized to be valid down to
Pl
l
scales (where spacetime is
presumed to be Euclidean, at non-relativistic speeds) so that
2
() /
r
gr
E G m r=−
and
2
() /
r
qr
E k q r=−
, with
r
being the
distance between the two point-like EPs composing that same VP,
[
1
] Emails: dr.dragoi@yahoo.com & Andrei.Dragoi@doc.utm.ro
[
2
] Mailing address: Str. Moldovei nr.1, bl. 47, Sc. B, Ap. 21, parter, Târgoviște,
Dâmbovița (county), România (country); cod postal (zip code): 130077
r
G
being the value of the Newtonian gravitational constant
( )
G
at that
r
-length scale and
r
k
being the value of Coulomb’s
constant
( )
e
k
at that same
r
-length scale. By also defining the
ratios
() /
r
gr Gr
=
and
() /
r
er kr
=
the previous eq.1 is
equivalent to
( ) ( ) 0(J)
VP
g r q r
E E E− + =
which “translates”
to the following simple electro-gravitational quadratic eq. with
unknown
( )
xm=
:
( )
2 2 2
( ) ( )
20
g r e r
x c x q
− + =
(2)
The previous eq.2 is easily solvable and has two possible
solutions which are both positive reals only if
42
( ) ( )g r e r
cq
:
2 4 2
( ) ( )
( , ) ()
g r e r
qr gr
c c q
m
−
=
(3)
*
Remark 2a. One may easily note from these simple
( , )qr
m
conjugated solutions that, if one of them goes up the other one goes
down (and vice versa), which allows the interpretation of ZEH as
an electrogravitational "seesaw" mechanism (as detailed later in
this paper). It is also important to note that
( , )qr
m
depends on the
squared electromagnetic charge
2
q
so that it generates pairs of
identical masses
(q,r) ( q,r)
mm
+ + −
=
and
(q,r) ( q,r)
mm
− − −
=
for a
particle (with charge
q
) and its antiparticle (with charge
q−
) at
the same r-length scale: however, ZEH also allows conjugated
distinct solutions
( q,r) ( q,r)
mm
+ −
so that it suggests other
interesting unexpected potential connections between known and/or
unknown types of EPs (as also detailed later in this paper).
*
Remark 2b. For neutral EPs with
0qC=
, formula (3) allows
both zero rest masses
(0,r) 0m kg
−=
and non-zero rest masses
2
(0, ) ( )
2/
r g r
mc
+=
which is very convenient for any particle
theory in general, because that’s what nature actually shows: some
known neutral EPs have zero rest masses (possessing only
relativistic masses, like the photon and the gluon) and some other
known neutral EPs have non-zero rest masses (like the three types
of known neutrinos, the Z boson and the Higgs boson). Even if
ZEH initially considered only EPs with non-zero rest masses, the
zero solutions
( )
0m kg
−=
(for
0q=
) may actually (and
conveniently!) correspond to known/unknown massless bosons
(having only relativistic mass, thus moving at the speed of light in
vacuum
c
) and to unknown massless neutrinos (having only
relativistic mass, thus also moving with speed
c
). The power of
prediction of formula (3) may thus be extended to all EPs (with
zero and non-zero rest masses).
2
Also note that for
0qC
we have
2 4 2
( ) ( )g r e r
c c q
−
and
( ) ( )
( ,r) ( , ) ( ,r)
0
q q r q
m kg m m
+ −
implicitly, so that
formula (3) does not allow the existence of charged EPs with zero
rest mass (aka elementary Weyl fermions).
*
Remark 2c. Based on its formula (3), ZEH predicts that the
rest masses
( ,r)q
m
of both neutral & charged EPs are actually a
function of
q
, as if both zero and non-zero quantum
q
can
impose fixed/discrete positive mass gaps
( )
m f q=
. In this way,
ZEH may significantly help in the theoretical understanding of the
subtle "positive mass gap" quantum mechanical property, in the
framework of the quantum Yang-Mills theory (the current
foundation the foundation of the theory of EPs). Prediction. From
formula (3), it is obvious that
( , )qr
m
can take discrete values
only if distance
r
(the common denominator of both
()gr
and
()er
ratios) takes discrete values around
Pl
l
scale: based on this
simple observation on formula (3), ZEH predicts that the single
possible explanation of a positive mass gap
( )
0m
would be
that
m
is both a function of a discrete zero/non-zero quantum of
charge
q
and a function of a set of discrete distances
r
(in the
cases of all EPs), a quantized
r
-length scale which is plausibly the
consequence of a quantized structure of space around
Pl
l
scale.
*
Remark 3a. The realness condition
( )
42
( ) ( )g r e r
cq
implies the existence of a minimum allowed (charge-dependent, but
mass-independent!) distance between any two EPs (composing the
same VP)
2
0( , ) /
rr
qr
r q G k c=
, which is actually a self-
referential function. For the special case
r
GG=
and
re
kk=
,
the
0( , )qr
r
function generates a set of “practical” radii (for any
charged EP inside a VP, not to be confused with the real radii of
point-like charged EPs which are zero)
ee
12
33
0(CEP) 0( )
0( ) 0( )
,,
35 17 10
Pl Pl Pl
e
l l l
R r r r
=
for
any known charged EP having one of the three known possible
absolute charges
q
from the set
12
33
* , ,Q e e e=
).
However, for neutral EPs, the
0( , )qr
r
function loses its power of
prediction, because
0(0, ) 0
r
r=
: this fact doesn’t necessarily mean
that VPs composed from neutral EPs don’t also have a minimal
allowed finite and non-infinitesimal size (measured by a theoretical
practical radii) explained the fact that they also have discrete
zero/non-zero rest masses (which can only be functions of discrete
r-length scales is formula 3 is truly valid).
*
I-2. A proposed electro-gravitational seesaw mechanism
(ESM). We propose an electro-gravitational seesaw mechanism
(ESM) based on eq. 2 of ZEH, with ESM being actually a ZEH
extension theoretically applicable to all conceivable (known and
unknown) electromagnetically charged/neutral elementary particles
(EPs). ESM is based on a simple proposed 2x2 mass matrix such
as:
( , )
( , ) ( , ) ( )
0eg qr
qr eg g
q r r
M
AMM
=
(4)
( )
() /
rr
eg r
M q k G=−
is an electro-gravitational mass
component (valued with a complex number) and
( )
2
( ) ( )
2/
gr g r
Mc
=
is a pure gravitational mass component
(valued with a real number) of any EP.
(q,r)
A
was chosen so that
its characteristic/determinantal (quadratic) equation to coincide
with equation (2) of ZEH, so that the conjugated solutions
( , )qr
m
to also represent the eigenvalues of
( , )qr
A
. In 1987, another author
has also launched the hypothesis that all fermions acquire their
(rest) masses via a universal seesaw mechanism providing a
plausible explanation for the mass hierarchy of elementary particles
(and offering an explanation on the super-lightness of neutrinos)
[
1
].
It is also obvious that
( , )qr
m
rest masses can have discrete
zero/non-zero values (as observed for all EPs) only if the
r
-length
scale takes only discrete values (at least at scales comparable to
Pl
l
). Prediction. Based on this simple observation, ESM predicts
that space is probably quantized around
Pl
l
-scale and allows only
discrete finite (and non-infinitesimal) distances between EPs (of the
same VP) at those scales.
We can define a (finite) set of finite (and non-infinitesimal)
r
-
length scales
1
1 2 1
( ) 1
, ( ),... ( ),... ( )
nn
n
q k k
R r r r r r r r −
−
=
for each quantum
qQ
of electromagnetic charge in part
(containing a positive integer finite number
n
of possible distinct
r
-length scales and indexed by a positive integer finite index
k
assigned to each
r
-length scale in part).
For each
k
r
element of the set
()
nq
R
we can also define a
specific distinct set (for any given charge
q
)
g
( ) ( ) ( ) ( , ) ( , )
, , , , ,
k k k k
e
k q k r r q r q r
P r q m m
+−
=
, essentially
defining a pair of distinct rest masses
( , ) ( , )
kk
q r q r
mm
+−
which
can only be assigned to exactly two distinct types of EPs (each with
its antiparticle) sharing the same
k
r
-length scale, the same
absolute charge
q
and the same
g()
k
r
and
()
k
er
ratios.
Let us analyze the simplest case in which, for each
k
r
-length
scale we choose only one allowed electromagnetic charge
( )
k
q
(shared by those two distinct types of EPs with conjugated masses
( , )qr
m
), so that we can easily build a global 6-columns wide
3
matrix
()
nq
E
(for each type of
qQ
in part) containing a
()kq
P
set on each row indexed with the positive integer index
k
.
The
()
nq
E
matrix actually organizes the conjugated mass solutions
( , )qr
m
generated by the characteristic equation of the
( , )qr
A
matrix (which are its eigenvalues), such as:
0 0 0 0
1 1 1 1
g
0( ) ( ) ( , ) ( , )
g
1( ) ( ) ( , ) ( , )
() g( ) ( ) ( , ) ( , )
g( ) ( ) ( , ) ( , )
... ... ... ... ... ...
... ... ... ... ... ...
k k k k
n n n n
e
r r q r q r
e
r r q r q r
nqe
k r r q r q r
ne
r r q r q r
r q m m
r q m m
Er q m m
r q m m
+−
+−
+−
+−
=
(5)
Both
( , )qr
A
and
()
nq
E
matrices can be also applied on zero
charge
( )
0qC=
to produce very interesting results: more
specifically, the ESM-proposed
(0, )r
A
generates pairs of neutral
EPs in which one has zero rest mass
( )
(0, ) 0
r
m kg
−=
and the
other one has positive (and possibly very large) non-zero pure
gravitational rest mass
2
(0, ) ( ) ( )
2/
g
r r g r
m M c
+==
.
Furthermore: (1) those pairs of neutral EPs with larger
()
k
gr
ratios (implying smaller
k
r
-scales, thus smaller k indexes) occupy
the first rows of the
(0)
n
E
matrix and (2) those pairs of neutral
EPs with smaller
()
k
gr
ratios (implying larger
k
r
-scales, with
larger k indexes) occupy the subsequent rows of the same
(0)
n
E
matrix.
()
nq
E
can thus use all charges from the extended set
* {0C}QQ=
.
*
ESM is essentially an extended ZEH which assumes and
assigns mass matrix
( , )qr
A
(together with its conjugated
eigenvalues
( , )qr
m
) not only on virtual particle-antiparticle pairs
(composed from the same type of EP) but also distinct types of EPs
which are coined here as “mass-conjugates” (MCs) (as they are
based on the conjugated eigenvalues
( , )qr
m
), which MCs are
defined by ESM to share not only the same zero/non-zero
electromagnetic charge
( )
q
but also the same
k
r
-length scale and
the same
()
k
gr
&
()
k
er
ratios (all these parameters being the
elements of a generic k-row of the
()
nq
E
matrix).
**
I-3. A SUSY alternative (SUSYA) offered by the here
proposed electro-gravitational seesaw mechanism (ESM). If we
try to apply ESM on specific boson-fermion pairs of mass-
conjugates (MCs), we may get a very “seductive” supersymmetry
theory (SUSY) alternative (abbreviated here as “SUSYA”) in
which the MCs (described by any generic k-row of an
()
nq
E
matrix) are the ESM-proposed alternative to the concept of partner-
superpartner pair used in SUSY.
This SUSYA not only defines various MCs (by using the same
()
nq
E
matrix), but also states that the heavier MC can always
decay into its lighter MC partner and possibly to other EPs (in
respect to the energy and charge conservation principles): however,
the decay of a heavier MC (hMC) into its lighter MC is stated to
not always be the single mode in which that hMC decays, but it is
stated to always respect both energy and charge conservation
principles.
This proposed SUSYA additionally (co-)states/conjectures
that: if a specific bosonic EP is its own antiparticle (like in the case
of the photon, the gluon, the Z boson and the Higgs boson), then its
fermionic MC is also its antiparticle, thus it is actually a Majorana
neutrino.
SUSYA establishes some interesting symmetries (called
"conjugations") between: (1) some known bosonic EPs and
fermionic EPs, but also between (2) some known bosonic EPs and
some theoretically-predicted fermionic EPs (*not yet proven by
experiments until present) and between (3) some known fermionic
EPs and some theoretically-predicted bosonic EPs (*).
Analogously to SUSY but in a slightly distinct manner (as
based on the
()
nq
E
matrix), SUSYA formally defines each pair of
k-MCs (described by a k-row of the
()
nq
E
matrix) as being
actually resulted from a broken-symmetry of a specific and distinct
hypothetical ultra-heavy boson called “k-electrograviton” (k-EG)
(here defined as the quantum of a hypothetical unified electro-
gravitational field acting at that specific
k
r
-scale which is close
the Planck scale), with k-EG having a generic relativistic energy
() /
eg k k
E hc r=
close to the Planck energy
( )
19
10
Pl
E GeV
and much larger than the rest-masses/energies of each MC from
that pair of k-MCs. In this specific interpretation given to the
()
nq
E
matrix, ESM and its special case called SUSYA can both be
regarded as quantum gravity (toy-)theories. Furthermore, the pure
gravitational real mass component
()gr
M
of any EP is stated (and
predicted) by SUSYA to be plausibly determined by the
hypothetical spin-2 graviton (the quantum of the spacetime
“scene”, as predicted by the quantum field theory):
complementarily, the electro-gravitational complex mass
component
()eg r
M
of any EP is stated to be plausibly determined
by these proposed hypothetical ultra-heavy
k-electrogravitons (acting on very small Planck scales) which may
mediate an ultra-strong quantum electro-gravitational field acting
at those Planck scales (a field that unifies both the electroweak and
the gravitational fields, and plausibly the strong nuclear field also)
and very plausibly generating a Planck big G scalar
( )
Pl
GG
much larger than the universal gravitational constant
G
measured
macroscopically, implying that the hypothetical variable
r
G
function actually grows (with the progressive decrease of the r-
scale) up to
( )
Pl
GG
.
4
The existence of
( )
Pl
GG
also indicates that both
gravitational field (GF) and electromagnetic field (EMF) may
reach a reciprocal equilibrium of strengths around Planck-length
scale so that
22
() e
g Pl mq
(with
() /
g Pl Pl
Gr
=
). Other
authors have also emphasized the plausible crucial role of strong
gravity (which reaches equilibrium of strength with electromagnetic
field) in the formation of elementary particles [
2
]: this team of
physicists has obtained some theoretical results similar to this
prediction of SUSYA. **
I-3a. Two predicted right-handed Majorana massless
neutrinos (defined as mass-conjugates of the Higgs boson and Z
boson). SUSYA starts the estimations with the
(0)
n
E
matrix
(containing only pairs of neutral EPs that are reciprocally defined
as mass-conjugates), because neutral EPs are easier to be analyzed
by ESM.
In a first step and defining the unit of measure of
( )
2
2/
gcm
=
as
2 2 1
u m s kg
−−
=
, SUSYA focuses on the
heaviest known neutral EPs (which are the easiest to analyze by
ESM) and directly estimates
g
for the Z boson (Zb) and Higgs
boson (Hb) (with both Zb and Hb having non-zero rest energies)
such as
242
() ()
210
g Zb Zb
cu
m
+
=
and
241
() ()
28 10
g Hb Hb
cu
m
+
=
.
Based on ESM, SUSYA predicts that both Zb and Hb have two
distinct correspondent/conjugated Majorana massless neutrinos
(described by specific rows of the
(0)
n
E
matrix with small index
k), which are stated by SUSYA to be their own antiparticle (thus to
be Majorana neutrinos) because their heavier mass-conjugates Zb
and Hb are also their own antiparticles (and this Majorana property
was stated by SUSYA to be shared between any two mass-
conjugates from the same row of any
()
nq
E
matrix): these two
Majorana massless neutrinos are formally called here the “Z
neutrino” (Zn) (which shares the same
()g Zb
with Zb) and the
“Higgs neutrino” (Hn) (which shares the same
(H )gb
with Hb)
with zero rest masses
22
() ()
Zn g Zb
cc
m
−
−
=
and
22
() ()
Hn g Hb
cc
m
−
−
=
(thus both moving with the speed of light in vacuum and possessing
only relativistic masses instead of rest masses). In some variants of
SUSY, massless Majorana fermions are also considered
hypothetical “natural” superpartners of neutral spin-1 or spin-0
bosonic EPs (like also proposed by this SUSY, as Zn and Hn as
mass-conjugates of the spin-1 Zb and spin-0 Hb respectively).
Because Zb is a spin-1 vector boson (and its own antiparticle),
SUSYA also defines its mass-conjugate Zn as being a Majorana
vector-fermion. Because Hb is a spin-0 (scalar) boson (and its own
antiparticle), SUSYA also defines its mass-conjugate Hn as being a
Majorana scalar-fermion.
Because all the currently known (active) neutrinos were
observed to be left-handed neutrinos, SUSYA “naturally” assumes
Zn and Hn to be actually the “missing” right-handed neutrinos
(RHNs): SUSYA is not the first to predict that RHNs could be
actually massless and thus may compose an ubiquitous fermionic
dark radiation [
3
].
Zn and Hn are both defined by SUSYA to interact mainly
gravitationally and very plausibly to also interact with the Higgs
field and the Z-boson weak nuclear field (as Hb and Zb are also
stated by SUSYA to can produce hard-to-detect Hns and Zns
respectively, by their normal known various types of decay): Zn
and Hn are thus predicted by SUSYA to be plausibly right-handed,
but not sterile.
SUSYA defines both Zn and Hn to be maximally stable and to
can not decay (thus with practically infinite lifetimes): more
exactly, Hn and Zn are both stated to be actually the final ultra-
stable products of various possible decays of heavier EPs (mainly
the decays of their heavier mass-conjugates, the Z and Higgs
bosons).
Being both fermions, these predicted Zn and Hn are also stated
by SUSYA to obey Pauli’s exclusion principle and thus to be
“volume-hungry”: that is why such a hypothetical Zn/Hn-based
dark radiation may actually behave like an almost perfect
(fermionic) ultrarelativistic gas (modeled as a fermionic
condensate composed from Zns and Hns, possibly organized in Zn-
Zn / Hn-Hn / Zn-Hn pairs analogously to Cooper pairs from the
electron condensates) which expands progressively thus possibly
explaining the accelerated cosmic inflation (and potentially
explaining “dark energy” as a fermionic dark energy implicitly):
other authors have also considered Big-Bounce-like fermionic
cosmologies (in which a global fermionic field, a so-called
fermionic aether, can behave as an accelerated-inflation field in the
early universe, giving then place to a matter-dominated period
characterized by cosmic decelerated inflation) [
4
]. Predictions. (1)
SUSYA predicts that the hypothetical Big Bang may have actually
produced huge quantities of Zns and Hns, creating a kind of 3D
fermionic “scene” (and potentially explaining the 3D “empty”
space appearance of our universe). (2) SUSYA also predicts that all
stars may currently produce very large quantities of Zns/ Hns which
may progressively add volume to the present Zn/Hn-based dark
fermionic radiation and to produce an accelerated global expansion
of our universe implicitly. **
I-3b. The proposed mass-conjugation between the three
known types of neutrinos and the photon, the gluon and a
hypothetical graviton. In a second step, SUSYA continues the
focus on other known (lighter) neutral EPs and estimates the lower
bounds of
2
() ()
2
gn n
c
m
+
=
for all known three neutrinos (n), as
deducted from the currently estimated upper bounds of the non-zero
rest energies of all three known types of neutrino: the electron
neutrino (en) with
1
en
E eV
[
5
], the muon neutrino (mn) with
0.17
mn
E MeV
[
6
] and the tau neutrino (tn) with
18.2
tn
E MeV
[
7
], resulting
53
() 10
g en u
,
47
()6 10
g mn u
and
45
() 6 10
g tn u
. SUSYA cannot
directly estimate the values of
g
for the massless photon (ph)
()g ph
and the gluon (gl)
()g gl
, given the division-by-zero
2
2
0
gc
kg
=
. However, SUSYA additionally proposes that,
5
because the photon and the gluon are massless EPs (thus having
low
k
r
-scales corresponding to the inferior rows of the same
(0)
n
E
matrix),
()g ph
and
()g gl
may actually have very large
(real) values, coinciding with
()g en
,
()g mn
and
()g tn
: more
specifically, SUSYA proposes that
( ) ( )g ph g gl
and that there
also exists a massless graviton (gr) defined by
( )
( ) ( ) ( )g gr g ph g gl
so that:
( ) ( )g gr g en
=
,
( ) ( )g ph g mn
=
and
( ) ( )g gl g tn
=
, thus predicting three
additional pairs of mass-conjugates (MCs): (gr, en), (ph, mn) and
(gl-tn); furthermore because gr, ph and gl are their own
antiparticles, SUSYA predicts that en, mn and tn (here defined as
the MCs of gr, ph and gl respectively) are also their own
antiparticles, thus they are predicted to be actually elementary
Majorana neutrinos too (like the previously SUSYA-predicted Zn
and Hn). SUSYA is thus in agreement with the currently most-
favored explanation of the smallness of neutrino mass, the type-1
seesaw mechanism of neutrinos (in which all neutrinos are
“naturally” Majorana fermions). **
I-3c. The proposed mass-conjugation between the electron
and the W boson; two proposed bosonic mass-conjugates for
the muon and the tauon. In a third step, SUSYA additionally
states that the W boson and the electron may also form a boson-
fermion pair of mass-conjugates with a common
( )
( ) ( )g W g e
=
ratio, a common term
42
( ) ( )g W e W
T c e
=−
and rest masses
2
() (W)
eg
cT
m
−
−
=
and
2
() (W)
Wg
cT
m
+
+
=
. The common term
T
of
both rest masses (
()e
m−
and
()W
m+
) disappears when summing
2
( ) ( ) (W)
2/
e W g
m m c
−+
+=
, from which their shared
( )
( ) ( )g W g e
=
ratio can be reversely estimated as
242
(W) 21.25 10
geW
cu
mm
=
+
, which is relatively close to (but
smaller than)
()g Zb
and
(H )gb
.
In the case of the muon (m) and tauon (t) (which are currently
considered two distinct excited states of the electron) SUSYA
predicts that they may also be conjugated with two predicted
hypothetical bosons (which are analogously considered two distinct
excited (ultra-heavy) states of the W boson) called here the “W-
muonic boson” (Wm) (with
(Wm) (W)gg
) and the “W-
tauonic boson” (Wt) (with
(Wt) ( ) (W)g g Wm g
)
respectively. **
I-3d. The proposed mass-conjugation between the three
known generations of quarks and three predicted generations
of fractional-charge bosons (aka “leptoquarks”). SUSYA also
predicts that the six known quarks may have as mass-conjugates a
set of six fractional-charge bosons known as leptoquarks (LQs)
(hypothetical EPs that would carry information between each
generation of quarks and a correspondent generation of leptons,
thus allowing quarks and leptons to interact). LQs were first
predicted by various extensions of the Standard Model, such as
technicolor theories and Grand unified theories based on Pati–
Salam model, SU(5) or E6, etc
LQs were predicted by standard SUSY to be considerably
unstable and heavy EPs (nearly as heavy as an atom of lead) that
may only be produced in LHC at very high energies of collisions:
the quantum numbers (like spin, fractional electromagnetic charge
and weak isospin) vary among theories. However, SUSYA
specifically predicts that LQs (the mass-conjugates of quarks) also
organize in three generations and can only have the same
fractional charge as quarks (an essential ESM-imposed condition
for being “mass-conjugates” of those known quarks):
(1a) A so-called 1st generation LQ named “up-leptoquark”
(uLQ) with rest mass
( )
uq
uLQ Hb
m m m
,
2
(uLQ) (uq) 2
gg
uq uLQ
c
mm
==
+
( )
(Hb)g
and fractional
charge
23e
+
(shared with the up quark), which uLQ may decay (in
respect to charge and energy conservation principles) into: an up
quark (with the same charge
23e
+
) and a Majorana electron
neutrino or may alternatively decay into a down quark (with charge
13e
−
) and a positron (with charge
e+
);
(1b) A so-called 1st generation LQ named “down-leptoquark”
(dLQ) with rest mass
( )
uLQ
dLQ Hb dq
m m m m
,
2
(dLQ) (dq) 2
gg
dq dLQ
c
mm
==
+
( )
(Hb)g
and fractional
charge
13e
−
(shared with the down quark), which dLQ may decay
into a down quark (with the same charge
13e
−
) and an electron
neutrino or may decay into an up quark (with charge
23e
+
) and an
electron (with charge
e−
);
The 2nd and the 3rd generation of LQs are defined similarly to
the 1st one and predicted to contain the pairs: “charm-LQ” (cLQ) &
“strange-LQ” (sLQ) (2nd gen.); “top-LQ” (tLQ) & “bottom-LQ”
(bLQ) (3rd gen.). ***
II. A synthesis of the ESM-based SUSYA,
discussions and conclusions
SUSYA is essentially based on a proposed electro-
gravitational seesaw mechanism (abbreviated as ESM and
previously expressed by the
( )
,A q r
2x2 mass matrix) applicable
to all known/unknown EPs. SUSYA actually replaces the
“superpartner” notion (of SUSY) with the concept of (charge-
based) “mass-conjugate” or simply “conjugate” of a known EP,
which conjugate may be actually an already known EP: in this way
SUSYA more-“economically” predicts only 28 known &
hypothetical EPs (in contrast with standard SUSY which predicts at
least 34 distinct types of EPs, the double of the 17 known types of
EPs).
SUSYA may be regarded as a potential extension of the
Standard model towards the quantum gravity theories and, based on
6
its predicted right-handed Majorana massless “Z-neutrino” and
“Higgs-neutrino”, SUSYA also suggests a cosmology based on an
inflationary global fermionic (superfluid) aether (modelable as a
relativistic perfect gas).
SUSYA considers the simplest case with each
k
r
-length scale
allowing only one type of quantum charge
qQ
, so that all
()
nq
E
matrices (of any
q
) can be concatenated in one unified
13
E
matrix containing all known (plus the SUSYA-predicted) EPs
(plus their antiparticles, where it is the case in the descending order
of their
g()r
ratios, corresponding to the ascending order of their
k
r
-length scale). Each row of this
13
E
matrix describes two
distinct types of elementary mass-conjugates (each with its
antiparticle), thus actually describing four EPs by each matriceal
row: that is a quite compact and elegant arrangement of all known
& many unfound (but plausible) EPs (see next).
Each k-row of
13
E
may actually describe a specific energy
level of a spacetime “atom” and that is why this ESM-based
13
E
may be regarded as a “patch” to quantum gravity and bridge over
the gap between quantum field theory and Einstein’s general
relativity, suggesting a quantized 4D spacetime-“scene”.
For the special case
r
GG
, the length-scales from the set
0 1 13
, ,...r r r
can be inversely deducted/estimated from their
corresponding
( )
g/Gr
=
ratios such as
g( )
/
kk
rG
=
so that:
63
010rm
−
,
58
110rm
−
, …,
52
510rm
−
… . However,
these “unrealistically“ small distances are easily “renormalizable”
up to Planck length scales for the previously predicted
( )
Plr
G G G
scalar generated by k-electrogravitons.
Furthermore, the existence of the
k
r
set (of quantized
distances/practical radii) also implies the existence of a quasi-
quantum time defined by a set of temporal quanta set
( )
/
kk
t r c=
, but also a set of quantum big G
( )
()k g k k
Gr
=
defining the strength of a very strong (electro-)gravitational field
around Planck length scale (according to the 2nd equation of
SUSYA).
53
47
45
42
42
g
0( ) ( ) ( ) ( )
( 10 u)
g
1( ) ( ) ( ) (ph)
( 6 10 )
g
2(tn) ( ) ( ) (gl)
( 6 10 )
g
3(W) ( ) ( ) ( )
( 1.25 10 )
g
4(Zb) (Zb) (Zb) (Zn)
( 10 )
g
5()
(
13
0
0
0
0
0
e
en en en gr
e
mn mn mn
u
etn tn
u
eW W e
u
e
u
Hb
r C m m
r C m m
r C m m
r e m m
r C m m
rC
E
+−
+−
+−
+−
+−
=23
()
13
13
23
41
g()
g(uq)
g()
(Hb) ( ) ( )
8 10 )
g
6(uq) (uq) ( ) (uq)
g
7(dq) (dq) ( ) (dq)
()
g
8(sq) (s ) ( LQ) (s )
g
9(m) ( ) ( ) (m)
()
g
10 (cq) ( ) (cLQ) (
W
W
eHb Hn
u
euLQ
edLQ
eq s q
em Wm
ecq
mm
r e m m
r e m m
r e m m
r e m m
r e m m
+−
+−
+−
+−
+−
+−
13
23
g()
)
g
11 ( ) ( ) ( ) ( )
()
g
12 (bq) (bq) (bLQ) ( )
g
13 (tq) (tq) (tLQ) ( )
m
cq
e
t t Wt t
ebq
etq
r e m m
r e m m
r e m m
+−
+−
+−
The main experimentally testable predictions of SUSYA are
very briefly summarized in the next table:
SUSYA prediction
Ways to test that specific
prediction
1. all currently known neutrinos are
actually Majorana neutrinos with non-
zero rest masses
- the potential observation
in the future of at least one
neutrinoless double beta-
decay (yet unobserved)
2a. two right-handed massless Majorana
neutrinos here called the “Z-neutrino”
(Zn) and the “Higgs neutrino” (Hn)
(because they are predicted by SUSYA to
be the so-called “mass-conjugates” of the
Z boson and the Higgs boson
respectively), coupling with both the Z
and Higgs fields (thus not quite sterile)
2b. Both Zn and Hn are predicted by
SUSYA to not be only the main
constituents of a hypothetical dark hot
radiation, but even the components of a
fermionic superfluid aether which
behaves like an ultrarelativistic
inflationary perfect gas (massively
produced at the Big Bang moment and
then by all stars) explaining both the
global expansion of our universe and
dark energy implicitly
- much harder to detect
than the currently known
neutrinos, but may show
some hints in the Planck
2015 temperature and
polarization data, the
baryon acoustic oscillation
data, the Hubble constant
direct measurement data,
the Planck Sunyaev-
Zeldovich cluster counts
data, the Planck lensing
data, and the cosmic shear
data [Error! Bookmark not
defined.]
3. at least 3 generations of leptoquarks
(LQs) (each generation containing two
LQs, each LQ having the same charge as
its correspondent/mass-conjugated quark)
- potentially provable by
an LHeC in the future
(built by adding an
electron ring to collide
bunches with the existing
7
LHC proton ring)
4. The existence of ultra-massive “k-
electro-gravitons” (kEGs) acting around
Planck length scale (PLS) that quantize
an ultra-strong quantum (unified) electro-
gravitational field (EGF) (acting at that
same PLS) with huge strength
potentially measured by a much larger
universal gravitational constant scalar
( )
16
10
Pl
GG
(at that same PLS)
governing all the other EPs (resulted
from the broken symmetry of those
predicted kEGs), with non-zero rest mass
EPs being also predicted to be actually
quantum/micro black holes extremely
compressed by this ultra-strong quantum
EGF [3]. The existence of
( )
Pl
GG
also indicates that both gravitational and
electromagnetic fields may reach a
reciprocal equilibrium of strengths
around Planck-length scale so that
22
() e
g Pl mq
(with
() /
g Pl Pl
Gr
=
).
- measuring big G at
progressively smaller
scales may offer some
hints on this SUSYA
prediction
***
[
3
] Even if an EP may be “point-like” (or rather modeled as such), the interface
between that EP and its surrounding spacetime is most probably a 2D surface (or a
3D hypersurface) with finite area, which surface is holomorphic with all the other
theoretical surfaces (Riemann surfaces) concentric to that “point-like” EP with
progressively larger distance to that EP so that at least a part of the fields emanated
by that EP decrease their strength with the inverse square of this distance based this
reciprocal holomorphism of all these concentric circular/spherical closed theoretical
(Riemann) surfaces (which cannot be holomorphic to a point/point-like EP, but only
to another surface)
IV. References
1
. Aharon Davidson & Kameshwar C. Wali (August 1987). “Universal seesaw
mechanism?”. Physical Review Letters 59(4):393-395. DOI:
10.1103/PhysRevLett.59.393. URLs: (1)
journals.aps.org/prl/abstract/10.1103/PhysRevLett.59.393 & (2)
www.researchgate.net/publication/13253642 (full text) & (3)
pubmed.ncbi.nlm.nih.gov/10035757 (PubMed)
2
. Alharthy (Ahmed) & Kassandrov (Vladimir V.) (23 October 2020). “On a Crucial
Role of Gravity in the Formation of Elementary Particles”. Universe (by MDPI).
DOI: 10.3390/universe6110193 (open-access article). URLs: www.mdpi.com/2218-
1997/6/11/193 & www.mdpi.com/2218-1997/6/11/193/htm . See also this short
popularization article called „Gravity Might Play a Bigger Role in the Formation of
Elementary Particles Than Scientists Thought” (URL:
https://scitechdaily.com/gravity-might-play-a-bigger-role-in-the-formation-of-
elementary-particles-than-scientists-thought/)
3
. Lu Feng, Jing-Fei Zhang & Xin Zhang (2017). “A search for sterile neutrinos with
the latest cosmological observations” (preprint). URL:
https://arxiv.org/abs/1703.04884
4
. Chimento, L.P.et al. (2010). ”Fermionic cosmologies”. Journal of Physics:
Conference Series 306 (2011) 012052. 5th International Workshop DICE2010 (IOP
Publishing). DOI: 10.1088/1742-6596/306/1/012052. URL:
https://s3.cern.ch/inspire-prod-files-e/ec72e1177e54dc891490ad4afdd1d3e5
5
. Battye, Richard A.; Moss, Adam (2014). "Evidence for Massive Neutrinos from
Cosmic Microwave Background and Lensing Observations". Physical Review
Letters. 112 (5): 051303. arXiv: 1308.5870. Bibcode: 2014PhRvL.112e1303B. DOI:
10.1103/PhysRevLett.112.051303. PMID 24580586. URL:
https://arxiv.org/abs/1308.5870
6
. K. Assamagan, Ch. Brönnimann, M. Daum, H. Forrer, R. Frosch, P. Gheno, R.
Horisberger, M. Janousch, P. -R. Kettle, Th. Spirig, and C. Wigger (1996). “Upper
limit of the muon-neutrino mass and charged-pion mass from momentum analysis of
a surface muon beam”. Phys. Rev. D 53, 6065 – Published 1 June 1996. DOI:
10.1103/PhysRevD.53.6065. URL:
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.53.6065
7
. Barate, R.; Buskulic, D.; Decamp, D. et. al (1998). ”An Upper limit on the tau-
neutrino mass from three-prong and five-prong tau decays”. Europ Phys J C 2
(1998): 395-406. doi:10.1007/s100520050149. URLs: (1)
https://epubs.stfc.ac.uk/work/26893; (2)
www.researchgate.net/publication/30403534