Journal of High Energy Physics, Gravitation and Cosmology, 2019, 5, 425-437
http://www.scirp.org/journal/jhepgc
ISSN Online: 2380-4335
ISSN Print: 2380-4327
DOI:
10.4236/jhepgc.2019.52024 Mar. 13, 2019 425 Journal of High Energy Physics, Gravitation and Cosmology
An e
+
e
/γγ/ep Accelerator Complex at a Future
Circular Collider
Radoje Belusevic
High Energy Accelerator Research Organization (KEK), Tsukuba, Japan
Abstract
This is the second paper by the author describing versatile accelerator com-
plexes that could be built at a Future Circular Collider (FCC) in
order to
produce
ee
+−
,
γγ
and
ep
collisions. The facility described here features
an ILC-based
ee
+−
collider placed tangentially to the FCC tunnel. If the col-
lider is positioned asymmetrically with respect to the FCC tunnel, electron
(or positron) bunches could be accelerated by both linacs before they are
brought into collision with the 50-
TeV beams from the FCC proton storage
ring (FCC-pp). The two linacs may also form a part of the injector chain for
FCC-pp. The facility could be converted into a
γγ
collider or a source of
multi-MW beams for fixed-target experiments.
Keywords
Accelerator, Future Circular Collider (FCC), Experiments
1. Introduction
The maximum luminosity at a circular
ee
+−
collider, such as the proposed
FCC-ee facility [1], is severely constrained by beamstrahlung effects at high
energies; also, it is very difficult to achieve a high degree of beam polarization [2].
At the
ee
+−
facilities described in this paper and [3], luminosity grows almost
linearly with the beam energy [4] and the initial electron beam polarization can
reach about 80% [5]. The availability of polarized beams is essential for some
important precision measurements in
ee
+−
and
γγ
collisions [6].
The rich set of final states in
ee
+−
and
γγ
collisions would play an essential
role in measuring the mass, spin, parity, two-photon width and trilinear
self-coupling of the
Standard Model
(SM) Higgs boson, as well as its couplings to
fermions and gauge bosons. Some of those measurements require centre-of-mass
How to cite this paper:
Belusevic, R.
(201
9) An
e
+
e
/
γγ
/
ep
Accelerator Com
plex
at a Future Circular Collider
.
Journal of
High Energy Physics
,
G
ravitation and
Cosmology
,
5
, 425-437.
https://doi.org/10.4236/jhepgc.2019.52024
Received:
January 27, 2018
Accepted:
March 10, 2019
Published:
March 13, 2019
Copyright © 201
9 by author(s) and
Scientific
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access
R. Belusevic
DOI:
10.4236/jhepgc.2019.52024 426 Journal of High Energy Physics, Gravitation and Cosmology
(c.m.) energies
ee
s
considerably exceeding those attainable at circular
ee
+−
colliders. For instance, one has to measure separately the HWW, HHH and Htt
couplings at
500GeV
ee
s
in order to determine the corresponding SM
loop contributions to the effective HZZ coupling [7]. This would not be possible
to accomplish using the proposed FCC-ee facility.
The Htt coupling cannot be
directly measured
in
ee
+−
interactions below
500GeV
ee
s
, since the cross-section for the relevant process is negligible
(see
Figure 1). The HHH coupling can be
directly measured
at energies above
the kinematic threshold for
ZHHee
+−
, or by using the WW-fusion channel
at
1TeV
ee
s
.
Indirect
and
model dependent
measurements of the HHH
coupling are possible at lower energies by exploiting the loop corrections to sin-
gle Higgs channels. However, the sensitivity of such measurements is very low,
as can be inferred from Figure 4 in [8].
Figure 1. Centre-of-mass energy dependence of various cross-sections for single and
double SM Higgs-boson production in
ee
+−
annihilations [12].
Since the Higgs-boson mass affects the values of electroweak observables
through radiative corrections, high-precision electroweak measurements provide
a natural complement to direct studies of the Higgs sector. All the measurements
made at LEP and SLC could be repeated at the facility described in this note, but
at much higher luminosities and using 80% polarized electron beams [9]. The
importance of beam polarization for some high-precision measurements was al-
ready stressed.
If electron or positron bunches are brought into collision with the 50-TeV
proton beams from the FCC-pp storage ring, one would obtain an important
source of deep-inelastic
ep
interactions.
1
Such interactions would yield valuable
1
The proposed FCC-eh electron-proton collider [10] would provide a higher luminosity than the fa-
cilities described in this paper and [3]
, but would have a considerably lower electron beam energy
(around 60 GeV).
R. Belusevic
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10.4236/jhepgc.2019.52024 427 Journal of High Energy Physics, Gravitation and Cosmology
information on the quark-gluon content of the proton, which is crucial for pre-
cision measurements at the FCC-pp. The physics potential of a TeV-scale
ep
col-
lider is comprehensively discussed in [11].
A two-linac collider or an SLC-type facility [3] could be constructed in several
stages, each with distinct physics objectives that require particular centre-of-mass
energies (see
Figure 1):
Z,WW;H90 to180GeV
HZ250 GeV
;HH350 GeV
HHZ,500GH,eVH
ee
ee
ee
ee
ees
ees
eetts
eetts
γγ
γγ
νν
+−
+−
+−
+−
•→→
•→
•→→
•→
For some processes within and beyond the SM, the required c.m. energy is
considerably lower in
γγ
collisions than in
ee
+−
or proton-proton interac-
tions. For example, the heavy neutral MSSM Higgs bosons can be created in
ee
+−
annihilations only by associated production (
00
eeHA
+−
), whereas in
γγ
collisions they are produced as single resonances (
00
,HA
γγ
) with
masses up to 80% of the initial
ee
−−
collider energy [3].
2. An ILC-Based e
+
e
/γγ/ep Facility at FCC
The ILC-based facility at a Future Circular Collider (FCC) shown in Figure 2
features a superconducting two-linac
ee
+−
collider placed tangentially to the
FCC tunnel. Using an optical free-electron laser, the linacs could be converted
into a high-luminosity
γγ
collider.
As mentioned in the Introduction, the maximum luminosity at a circular
ee
+−
collider is severely constrained by beamstrahlung effects at high energies;
Figure 2. An ILC-based facility at FCC (BC stands for
bunch compression
). Electron (or
positron) bunches are accelerated by both linacs before their collision with the 50-TeV
proton beam from the FCC-pp storage ring. The two superconducting L-band linacs may
form the low-energy part of the FCC-pp injector chain. A much cheaper alternative to
this facility is described in [3].
R. Belusevic
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10.4236/jhepgc.2019.52024 428 Journal of High Energy Physics, Gravitation and Cosmology
also, it is very difficult to achieve a high degree of beam polarization. At the
ee
+−
facilities described in this paper and [3], luminosity grows almost linearly
with the beam energy and the electron beam polarization can reach 80%.
The baseline parameters for the proposed ILC collider, shown in
Table 1, re-
flect the need to balance the constraints imposed by the various accelerator
sub-systems, as explained in [13]. The rf power is provided by 10 MW mul-
ti-beam klystrons, each driven by a 120 kV pulse modulator. The estimated AC
power is 122 MW at
25GV0e
ee
s=
and 163 MW at
50GV0e
ee
s=
. The
1.3-GHz superconducting niobium rf cavities have average accelerating gra-
dients of 31.5 MeV/m.
Table 1. Baseline ILC parameters [13].
Centre-of-mass energy
ee
s
GeV 250 500
Pulse repetition rate
rep
f
Hz 5 5
Bunch population
e
N
×10
10
2 2
Number of bunches
,be
N
1312 1312
Bunch interval
,be
t
ns 554 554
RMS bunch length
,ze
σ
mm 0.3 0.3
Norm. horizontal emittance at IP
n
x
ε
μm 10 10
Norm. vertical emittance at IP
n
y
ε
nm 35 35
Horizontal beta function at IP
*
x
β
mm 13 11
Vertical beta function at IP
*
y
β
mm 0.41 0.48
RMS horizontal beam size at IP
*
x
σ
nm 729 474
RMS vertical beam size at IP
*
y
σ
nm 7.7 5.9
Vertical disruption parameter
e
D
24.5 24.6
Luminosity
ee
3421
10cms
−−
×⋅
0.75 1.8
In order to maximize luminosity at low centre-of-mass energies, the beam
power could be increased by increasing the pulse repetition rate
rep
f
while re-
ducing the accelerating gradient of the main linacs. At
25
GV0
e
ee
s
=
, the
power consumption of the main 250-GeV linacs is reduced by over a factor of
two when they are running at half their nominal gradient. Under these condi-
tions, one can run the accelerator at the maximum repetition rate of 10 Hz (de-
termined by the cryogenic system and the beam damping time
damp
80t
ms),
thus doubling its luminosity.
The two superconducting L-band linacs in
Figure 2 may also form a part of
the FCC-pp injector chain. Since the collider is positioned asymmetrically with
respect to the FCC tunnel, electron (or positron) bunches could be accelerated
by both linacs before they are brought into collision with the 50-TeV beams
from the FCC-pp proton storage ring. The entire accelerator complex would
serve as a source of
ee
+−
,
γγ
,
pp
and
ep
interactions.
R. Belusevic
DOI:
10.4236/jhepgc.2019.52024 429 Journal of High Energy Physics, Gravitation and Cosmology
3. Main Parameters of a Linac-Ring ep Collider at FCC
The idea to combine a 140-GeV electron linac and a 20-TeV proton storage ring
in order to produce
ep
interactions at very high c.m. energies was put forward in
1979 as a possible option at the SSC proton collider [14]. In 1987 it was proposed
to place a 2-TeV linear
ee
+−
collider (VLEPP) tangentially to a 6-TeV pro-
ton-proton collider (UNK) at IHEP in Protvino [15], with the aim of obtaining
both
ep
and
p
γ
collisions. Similar proposals for lepton-hadron and pho-
ton-hadron colliders at HERA, LHC and FCC have since been made (see [16]
and references therein).
The facility shown in
Figure 2 is an ILC-based version of the original
VLEPPUNK design. Since the collider is positioned asymmetrically with re-
spect to the FCC tunnel, electron (or positron) bunches could be accelerated by
both linacs (which contain
standing wave cavities
) before they are brought into
collision with the 50-TeV beams from the FCC-pp proton storage ring.
An ILC-type linac is a suitable source of electron beams for an electron-proton
collider, because: 1) the spacing between electron bunches can be made to match
that between the proton bunches in the FCC-pp storage ring, and 2) the length
of an electron bunch traincorresponds roughly to the FCC ring circumference.
This is not the case, for instance, with an X-band linac, where the electron bunch
spacing (~1 ns) is much shorter than that between proton bunches at the
FCC-pp (see
Table 2).
Table 2. Baseline FCC-pp parameters [19] [20]. Numbers inside round brackets represent
parameters for 5 ns bunch spacing.
Beam energy
E
p
TeV 50
Initial bunch population
p
N
×10
10
10 (2)
Number of bunches
,bp
N
10,600 (53,000)
Bunch interval
,bp
t
ns 25 (5)
RMS bunch length
,
zp
σ
mm 80
Norm. transverse emittance
n
p
ε
μm 2.2 (0.44)
Beta function at IP
*
p
β
m 0.3
Beam size at IP
p
σ
μm 6.8 (3)
Beam-beam tune shift/IP
p
Q
0.005
Luminosity/IP
ep
3221
10cms
−−
×⋅
2.3
In
head-on collisions
of ultra-relativistic electrons and protons, the cen-
tre-of-mass energy is
2EE
epep
s=
. The total electron beam current
E
eee
I=
is limited by the maximum allowed beam power
e
for a given
electron beam energy
E
e
. Assuming that round electron and proton beams of
equal transverse sizes are colliding head-on at the interaction point (IP),
2
the
2
The two beams are chosen to have roughly equal transverse sizes in order to reduce adverse effects a
much smaller electron beam could have on the proton beam lifetime. Electron bunches are di
s-
carded after each collision.
R. Belusevic
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10.4236/jhepgc.2019.52024 430 Journal of High Energy Physics, Gravitation and Cosmology
luminosity of the collider is given by [17] [18]
2*
4π
e
4
π
epp p
e
epc
n
ppp
NNN
I
f
γ
σεβ
=≡

(1)
In these expressions,
e
N
and
p
N
are the electron and proton bunch popu-
lations, respectively;
c
f
is the bunch collision frequency;
is a correction
factor discussed below; and
*
n
pppp
σεβ γ
=
is the proton beam size at IP, ex-
pressed in terms of the normalized proton beam emitance,
n
p
ε
, the proton beta
function at IP,
*
p
β
, and the Lorentz factor of the proton beam,
p
γ
. Note that
the luminosity is proportional to the electron beam power
eEE
eecee e
NfI==
(
e
is the electron charge), the proton beam energy (
p
γ
), and the proton beam
brightness
n
pp
N
ε
.
In Equation (1),
is a product of three correction factors with values typi-
cally close to unity:
hourglasspinchfilling
HHH≡⋅⋅
(2)
The factor
filling
H
takes into account the filling patterns of the electron and
proton beams. If the number of proton bunches
,
10600
bp
N=
and the bunch
interval
,
25
bp
t∆=
ns (see Table 2), the lengthof the proton beam is
5
2.6510×
ns. This corresponds to 80 km, which means that only 80% of the FCC circum-
ference is filled with proton bunches (
filling
0.8
H=
). In this particular case 20%
of the electron bunches would not collide with the proton beam.
The factor
hourglass
H
accounts for a loss of luminosity when the bunch length
is comparable to or larger than
*
β
. The beta function
(
)
*2*
ss
βββ
=+
grows parabolically as a function of distance
s
from the interaction point, which
causes the beam size to increase:
()()
*
sss
σβεεβ
=⋅≈
(3)
As the beam size increases, the contribution to the luminosity from regions with
large
σ
decreases (
hourglass effect
). For zero crossing angle and
,,zpze
σσ
,
()
()
2
hourglass
π
eerfc
x
Hxxx=
(4)
with
()
()
2
*
2
,
2
2
,erfced
π
1
ep
t
e
x
zp
ep
xxt
εε
β
σ
εε
≡=
+
(5)
where
e
ε
and
p
ε
denote
geometric emittances
[11] [21] (the normalized
emittance
n
εγε
=
is invariant under acceleration); erfc(z) is the complemen-
tary error function(defined as the area under the tailsof a Gaussian distribu-
tion).
The enhancement factor
pinch
H
in Equation (2) is due to the attractive
beam-beam force
. Since the electron bunch charge is relatively small and the
proton energy is high, the beam-beam force acting on electrons has a much
greater strength than that acting on protons. Consequently, the electron bunch is
R. Belusevic
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10.4236/jhepgc.2019.52024 431 Journal of High Energy Physics, Gravitation and Cosmology
focused by the protons during a collision. This leads to a reduction in the trans-
verse electron beam size (pinch effect) and hence to an increase in the lumi-
nosity. The effect can be simulated using the program
Guinea-Pig
(see [10] and
references therein, as well as
Table 3).
Table 3. Parameters of the proposed linac-ring
ep
collider.
Electron beam parameters
Beam energy
E
e
GeV 500
Initial bunch population
e
N
×10
10
2
Number of bunches
,
be
N
3200
Bunch interval
,be
t
ns 211.376
RF frequency
RF
f
MHz 1301
Pulse repetition rate
rep
f
Hz 5
Duty cycle
d
% 0.34
Beam power
e
MW 25.5
Proton beam parameters
Beam energy
E
p
TeV 50
Initial bunch population
p
N
×10
10
10
Number of bunches
,bp
N
5300
RMS bunch length
,zp
σ
mm 80
Bunch interval
,
bp
t
ns 49.7355
RF frequency
RF
f
MHz 401.968
Collider parameters
Beta function at IP
*
p
β
m 0.1
Norm. transverse emittance
n
p
ε
μm 1
Beam-beam tune shift
p
Q
0.0024
Electron beam disruption
e
D
11.3
Hourglass factor
hourglass
H
0.81
Pinch factor
pinch
H
1.3
Proton filling
filling
H
0.79
Luminosity
ep
3221
10cms
−−
×⋅
1.08
One can ignore the longitudinal structure of electron bunches because they
are much shorter than proton bunches. In this case the
transverse disruption
of
the electron beam during a collision is described by the parameter [22] [23]
,
2
pzp
e
e
ep
N
r
D
σ
γσ
=
(6)
where
e
γ
is the Lorentz factor of the electron beam,
15
2.8210
e
r
≈×
m is the
classical radius of the electron, and
,zp
σ
is the proton bunch length. For
*
10
p
β
=
R. Belusevic
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10.4236/jhepgc.2019.52024 432 Journal of High Energy Physics, Gravitation and Cosmology
cm, the disruption parameter can be as large as
20
e
D
in an
ep
linac-ring
collider (see
Figure 3).
Figure 3. Electron beam disruption parameter
e
D
as a function of
*
p
β
[18]. The plot
was made for an
ep
collider based on LHC and an ILC-type electron linac. LHC
*
denotes
an upgraded proton beam scenario (see
Table 1 in [18]).
As already mentioned, the luminosity of an
ep
collider is proportional to the
proton
beam brightenss
N
pp
N
ε
(see Equation (1)). Together with a given
bunch length and energy spread, the beam brightness is a measure of the
phase-space density. In the low-energy part of a proton injector, the quantity
n
pp
N
ε
is limited by space-charge forces that induce a
transverse tune shift
3
()
2
2
1
p
sc
n
p
pp
N
Q
vc
ε
γ
∆∝
(7)
Here
p
v
is the proton velocity and
c
is the speed of light in vacuo [24] [25].
In order to reduce the effect of space-charge forces at low energies and deliver
proton bunches a few mm long, the facility in
Figure 2 features a single 3-GeV
proton injector linac similar to that currently being built at the
European Spalla-
tion Source
(ESS) [26].
At high energies, the beam brightness in a storage ring slowly diminishes due
to Coulomb scattering of protons within a bunch (
intra-beam scattering
) [27].
In the presence of
dispersion
(see footnote 4), the intra-beam scattering also
leads to an increase in emittance. This sets the ultimate limit on the phase-space
density in a proton storage ring. The growth of a beam of charged particles due
to intra-beam scattering is characterized by the horizontal
growth rate
[28].
3
The tuneor
Q
value is defined as the number of betatron oscillations per revolution in a circular
accelerator. The charge and current of a high-inensity beam in an accelerator create self-
fields and
image fields that alter the beam dynamics and influence the single-particle motion as well as coh
e-
rent oscillations of the beam as a whole. The effect of space-charge forces is to change
Q
by an
amount
sc
Q
(“tune shift”) [24].
R. Belusevic
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10.4236/jhepgc.2019.52024 433 Journal of High Energy Physics, Gravitation and Cosmology
1
p
x
nnn
xyl
N
τ
εεε
(8)
where
,
n
xy
ε
are the normalized beam emittances,
,/
n
lzppp
εβγσσ
and
/pp
σ
is the r.m.s. relative momentum
pp
. Note that the growth rate depends li-
nearly on the normalized phase-space density. In the FCC-pp storage ring syn-
chrotron radiation damping is expected to be much stronger than the in-
tra-beam scattering, making the latter effect less of an issue [19].
The space-charge forces that limit the beam brightness are determined by the
longitudinal charge density and thus by the proton bunch length
,zp
σ
. To attain
maximum brightness,
,zp
σ
should be as large as possible. On the other hand,
there is a loss of luminosity when the bunch length is comparable to or larger
than
*
β
(this
hourglass effect
was described earlier). Furthermore, the trans-
verse disruption of the electron beam during an
ep
collision is proportional to
,zp
σ
, as shown in Equation (6). While optimizing the bunch length within these
constraints, the beam stability must be preserved (see below).
A particle in one colliding beam experiences a force due to the electromagnet-
ic interactions with all the particles in the opposing beam. This force depends
upon the displacement of the particle from the equilibrium orbit of the opposing
bunch. For small particle displacements, the beam-beam interaction is nearly li-
near, and its strength is characterized by a parameter known as the
beam-beam
tune shift
[29]:
*
2
4π
4
π
pppe
e
p
n
epp
rrN
N
Q
β
σγε
∆≡≈
(9)
where
18
1.5310
p
r
≈×
m is the classical radius of the proton and
pe
σσ
was
used. Since electron bunches are discarded after each collision, only the tune
shift of the proton beam,
p
Q
, is considered here. The tune shift is approx-
imately given by
10
3
6
10
1.210
10m
e
p
n
p
N
Q
ε


∆≈×⋅


(10)
The parameter
p
Q
must be limited to about
3
410
×
in order to stem the
emittance growth due to random fluctuations of the electron bunch parameters
[30]. This imposes an upper limit of
10
310
e
N
×
if one assumes
6
10
n
p
ε
m
(see also Table 4 in [31]).
A small error
k
in the quadrupole gradient leads to a tune shift
k
Q
. To a
beam particle with momentum
0
ppp=+∆
it appears that all the quadrupoles
in the ring have a quadrupole error proportional to
0
pp
[32]. The dimen-
sionless quantity
ξ
defined by
(
)
0k
Qpp
ξ
∆≡∆
is called the
chromaticity
of
the beam optics. This quantity increases with the strength of the beam focusing.
The main contribution to the chromaticity comes from the final focus quadru-
poles, where the
β
-function is large [33]:
*
*
2
q
qqq
y
k
ξβ
β
+
≈≈

(11)
R. Belusevic
DOI:
10.4236/jhepgc.2019.52024 434 Journal of High Energy Physics, Gravitation and Cosmology
Here
q
β
,
q
k
and
q
denote the beta function, field gradient and length of
the final quadrupole, respectively;
*
is the focal length and
*
y
β
the value of
the vertical
β
-function at the interaction point. Thus, the chromaticity increases
as
*
y
β
decreases.
Since
ξ
grows linearly with the distance between the final-focus quadrupole
and the interaction point, it is desirable to make this distance as small as possible.
For the interaction region at an electron-proton collider, a novel design tech-
nique called the
achromatic telescopic squeezing
(ATS) has been proposed in
order to find the optimal solution that would produce the highest luminosity
while controlling the chromaticity, minimizing the synchrotron radiation
power and maintaining the dynamic aperture required for [beam] stability
[34] [35] (
dynamic aperture
is the stability region of phase space in a circular
accelerator).
The issue of beam stability was addressed earlier concerning the optimization
of the proton bunch length. The proton bunches inside an ILC-type linac are
much shorter than those inside the FCC storage ring (the 3-GeV injector linac
mentioned earlier would deliver bunches a few millimetres long). Thus,
,zp
σ
has to be increased in order to attain the baseline FCC-pp value (see
Table 2). In
principle, the easiest way to increase the bunch length in a circular accelerator is
to switch all RF systems off and let the bunches decaydue to
dispersion.
4
A
faster and more subtle methodwhich could be implemented using a 3-TeV
proton booster placed inside the FCC tunnelis described in [36].
The expressions for beam-beam tune shift, electron beam disruption and
beam growth rate given above do not accurately describe the
time-dependent
beam dynamics
during collisions. To study the time-dependent effects caused by
varying beam sizes, collision point simulations for linac-ring
ep
colliders have
been performed using the ALOHEP software [37]. This numerical program op-
timizes a set of electron and proton beam parameters in order to maximize lu-
minosity [38].
The luminosity
ep
is independent of the electron bunch charge and the col-
lision frequency as long as their product, expressed in terms of the beam power
e
, is constant. One can therefore rewrite Equation (1) as follows [17] [39]
6
3021
11*
10m10cm250GeV
4.810cms
106622.6 MWE
10
pp
e
ep
n
e
pp
N
γ
εβ
−−
=×⋅⋅⋅

(12)
The electron beam current
,
e15
eebe
INf==
mA, where
,be
f
is the inverse
of the bunch interval (see
Table 3). The electron beam power
E25.5
eee
Id==
MW, where
d
is the linac duty cycle. The proton beam current
320
p
I=
mA,
and the total energy stored per proton beam is 4.2 GJ. To calculate
hourglass
H
, we
set
**
ep
ββ
[35]. The value of
pinch
H
was taken from [10].
4
A particle with a momentum difference
pp
has a transverse position
()()
xsDspp+∆
, where
()
xs
is the position a particle of nominal momentum would have and
()
Ds
is the
dispersion
function
.
R. Belusevic
DOI:
10.4236/jhepgc.2019.52024 435 Journal of High Energy Physics, Gravitation and Cosmology
Acknowledgements
I would like to thank K. Yokoya for his valuable comments and suggestions.
Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this pa-
per.
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