# SppC Based Energy Frontier Lepton-Proton Colliders: Luminosity and Physics

Authors: Ali Can Canbay; Umit Kaya; Bora Ketenoglu; Bilgehan Baris Oner; Saleh Sultansoy
Journal: Advances in High Energy Physics
 (2017)

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## Abstract

Main parameters of Super proton-proton Collider (SppC) based lepton-proton colliders are estimated. For electron beam parameters, highest energy International Linear Collider (ILC) and Plasma Wake Field Accelerator-Linear Collider (PWFA-LC) options are taken into account. For muon beams, 1.5 TeV and 3 TeV center of mass energy muon collider parameters are used. In addition, ultimateμp collider which assumes construction of additional 50 TeV muon ring in the SppC tunnel is considered. It is shown that luminosity values exceeding 1032cm-2s-1 can be achieved with moderate upgrade of the SppC proton beam parameters. Physics search potential of proposed lepton-proton colliders is illustrated by considering small Björken x region as an example of SM physics and resonant production of color octet leptons as an example of BSM physics.


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## Body

## 1. Introduction

It is known that lepton-hadron scattering had played crucial role in our understanding of deep inside of matter. For example, electron scattering on atomic nuclei reveals structure of nucleons in Hofstadter experiment [1]. Moreover, quark parton model was originated from lepton-hadron collisions at SLAC [2]. Extending the kinematic region by two orders of magnitude both in high Q2 and small x, HERA (the first and still unique lepton-hadron collider) with s=0.32 TeV has shown its superiority compared to the fixed target experiments and provided parton distribution functions (PDF) for LHC and Tevatron experiments (for review of HERA results see [3, 4]). Unfortunately, the region of sufficiently small x (<10−5) and high Q2 (≥10 GeV2) simultaneously, where saturation of parton densities should manifest itself, has not been reached yet. Hopefully, LHeC [5] with s=1.3 TeV will give opportunity to touch this region.Construction of lineare+e-colliders (or dedicated linac) and muon colliders (or dedicated muon ring) tangential to the future circular pp colliders, FCC or SppC, as shown in Figure 1, will give opportunity to use highest energy proton beams in order to obtain highest center of mass energy in lepton-hadron and photon-hadron collisions (for earlier studies on linac-ring type ep, γp, eA, and γA colliders, see reviews [6, 7] and papers [8–14]).Figure 1
Possible configuration for SppC, linear collider (LC), and muon collider (μC).FCC is the future 100 TeV center of mass energy pp collider studied at CERN and supported by European Union within the Horizon 2020 Framework Programme for Research and Innovation [15]. SppC is the Chinese analog of the FCC. Main parameters of the SppC proton beam [16, 17] are presented in Table 1. The FCC based ep and μp colliders have been considered recently (see [18] and references therein).Table 1
Main parameters of proton beams in SppC.
Beam energy (TeV)
35.6
68.0
Circumference (km)
54.7
100.0
Peak luminosity (1034 cm-2s-1)
11
102
Particle per bunch (1010)
20
20
Norm. transverse emittance (μm)
4.10
3.05
β
∗ amplitude function at IP (m)
0.75
0.24
IP beam size (μm)
9.0
3.04
Bunches per beam
5835
10667
Bunch spacing (ns)
25
25
Bunch length (mm)
75.5
15.8
Beam-beam parameter,ξpp
0.006
0.008In this paper we consider SppC basedep and μp colliders. In Section 2, main parameters of proposed colliders, namely, center of mass energy and luminosity, are estimated taking into account beam-beam tune shift and disruption effects. Physics search potential of the SppC based lp colliders have been evaluated in Section 3, where small Björken x region is considered as an example of the SM physics and resonant production of color octet leptons is considered as an example of the BSM physics. Our conclusions and recommendations are presented in Section 4.


## 2. Main Parameters of the SppC Basedep and μp Colliders

General expression for luminosity of SppC basedlp colliders is given by (l denotes electron or muon)(1)Llp=NlNp4πmax⁡σxp,σxlmax⁡σyp,σylmin⁡fcp,fcl,where Nl and Np are numbers of leptons and protons per bunch, respectively; σxp (σxl) and σyp (σyl) are the horizontal and vertical proton (lepton) beam sizes at interaction point (IP); fcl and fcp are LC/μC and SppC bunch frequencies. fc is expressed by fc=Nbfrep, where Nb denotes number of bunches and frep means revolution frequency for SppC/μC and pulse frequency for LC. In order to determine collision frequency of lp collider, minimum value should be chosen among lepton and hadron bunch frequencies. Some of these parameters can be rearranged in order to maximize Llp but one should note that there are main limitations due to beam-beam effects that should be kept in mind. While beam-beam tune shift affects proton and muon beams, disruption has influence on electron beams.Disruption parameter for electron beam is given by(2)Dxe=2Npreσzpγeσxpσxp+σyp,Dye=2Npreσzpγeσypσyp+σxp,where re=2.82×10-15 m is classical radius for electron, γe is the Lorentz factor of electron beam, and σxp and σyp are horizontal and vertical proton beam sizes at IP, respectively. σzp is bunch length of proton beam. Beam-beam parameter for proton beam is given by(3)ξxp=Nlrpβp∗2πγpσxlσxl+σyl,ξyp=Nlrpβp∗2πγpσylσyl+σxl,where rp is classical radius for proton, rp=1.54×10-18 m, βp∗ is beta function of proton beam at IP, and γp is the Lorentz factor of proton beam. σxl and σyl are horizontal and vertical sizes of lepton beam at IP, respectively.Beam-beam parameter for muon beam is given by(4)ξxμ=Nprμβμ∗2πγμσxpσxp+σyp,ξyμ=Nprμβμ∗2πγμσypσyp+σxp,where rμ=1.37×10-17 m is classical muon radius, βμ∗ is beta function of muon beam at IP, and γμ is the Lorentz factor of muon beam. σxp and σyp are horizontal and vertical sizes of proton beam at IP, respectively.


### 2.1.ep Option

Preliminary study of CepC-SppC basede-p collider with s=4.1 TeV and Lep=1033cm-2s-1 has been performed in [19]. In this subsection, we consider ILC (International Linear Collider) [20] and PWFA-LC (Plasma Wake Field Accelerator-Linear Collider) [21] as a source of electron/positron beam for SppC based energy frontier ep colliders. Main parameters of ILC and PWFA-LC electron beams are given Table 2.Table 2
Main parameters of the ILC (second column) and PWFA-LC (third column) electron beams.
Beam energy (GeV)
500
5000
Peak luminosity (1034 cm-2s-1)
4.90
6.27
Particle per bunch (1010)
1.74
1.00
Norm. horiz. emittance (μm)
10.0
10.0
Norm. vert. emittance (nm)
30.0
35.0
Horiz.β∗ amplitude function at IP (mm)
11.0
11.0
Vert.β∗ amplitude function at IP (mm)
0.23
0.099
Horiz. IP beam size (nm)
335
106
Vert. IP beam size (nm)
2.70
59.8
Bunches per beam
2450
1
Repetition rate (Hz)
4.00
5000
Beam power at IP (MW)
27.2
40
Bunch spacing (ns)
366
20
×
1
0
4
Bunch length (mm)
0.225
0.02It is seen that bunch spacings of ILC and PWFA-LC are much greater than SppC bunch spacing. On the other hand, transverse size of proton beam is much greater than transverse sizes of electron beam. Therefore, (1) for luminosity turns into (5)Lep=NeNp4πσp2fce.For transversely matched electron and proton beams at IP, equations for electron beam disruption and proton beam tune shift become(6)De=Npreσzpγeσp2,ξp=Nerpβp∗4πγpσp2=Nerp4πϵnp,where ϵnp is normalized transverse emittance of proton beam.Using nominal parameters of ILC, PWFA-LC, and SppC, we obtain values ofLep, De, and ξp parameters for LC⊗SppC based ep colliders, which are given in Table 3. The values for luminosity given in parentheses represent results of beam-beam simulations by ALOHEP software [22], which is being developed for linac-ring type ep colliders.Table 3
Main parameters of LC⊗SppC based ep colliders.
E
e, TeV
E
p, TeV
s, TeV
L
e
p, cm-2s-1
D
e
ξ
p, 10-3
0.5
35.6
8.44
3.35(6.64)×1030
0.537
0.5
0.5
68
11.66
2.69(5.33)×1031
0.902
0.7
5
35.6
26.68
0.98(1.94)×1030
0.054
0.3
5
68
36.88
0.78(1.56)×1031
0.090
0.4In order to increase luminosity ofep collisions LHeC-like upgrade of the SppC proton beam parameters has been used. Namely, β function of proton beam at IP is arranged to be 7.5/2.4 times lower (0.1 m instead of 0.75/0.24 m) which corresponds to LHeC [5] and THERA [23] designs. This leads to increase of luminosity and De by factor 7.5 and 2.4 for SppC with 35.6 TeV and 68 TeV proton beam, respectively. Results are shown in Table 4.Table 4
Main parameters of LC⊗SppC based ep colliders with upgraded β∗.
E
e, TeV
E
p, TeV
s, TeV
L
e
p, cm-2s-1
D
e
ξ
p, 10-3
0.5
35.6
8.44
2.51(4.41)×1031
4.03
0.5
0.5
68
11.66
6.45(10.8)×1031
2.16
0.7
5
35.6
26.68
7.37(13.3)×1030
0.403
0.3
5
68
36.88
1.89(3.75)×1031
0.216
0.4In principle “dynamic focusing scheme” [24], which was proposed for THERA, could provide additional factor of 3-4. Therefore, luminosity values exceeding 1032cm-2s-1 can be achieved for all options. Concerning ILC⊗SppC based ep colliders, a new scheme for energy recovery proposed for higher-energy LHeC (see Section 7.1.5 in [5]) may give an opportunity to increase luminosity by an additional order, resulting in Lep exceeding 1033cm-2s-1. Unfortunately, this scheme can not be applied at PWFA-LC⊗SppC.


### 2.2.μp Option

Muon-proton colliders were proposed almost two decades ago: construction of additional proton ring ins = 4 TeV muon collider tunnel was suggested in [25], construction of additional 200 GeV energy muon ring in the Tevatron tunnel was considered in [26], and ultimate μp collider with 50 TeV proton ring in s = 100 TeV muon collider tunnel was suggested in [27]. Here, we consider construction of TeV energy muon colliders (μC) [28] tangential to the SppC. Parameters of μC are given in Table 5.Table 5
Main parameters of the muon beams.
Beam energy (GeV)
750
1500
Circumference (km)
2.5
4.5
Average luminosity (1034 cm-2s-1)
1.25
4.4
Particle per bunch (1012)
2
2
Norm. trans. emitt. (mm-rad)
0.025
0.025
β
∗ amplitude function at IP (cm)
1 (0.5–2)
0.5 (0.3–3)
IP beam size (μm)
6
3
Bunches per beam
1
1
Repetition rate (Hz)
15
12
Bunch spacing (ns)
8300
15000
Bunch length (cm)
1
0.5Keeping in mind that both SppC andμC have round beams, luminosity equation (1) turns to(7)Lpp=fppNp24πσp2,Lμμ=fμμNμ24πσμ2,for SppC-pp and μC, respectively. Concerning muon-proton collisions one should use larger transverse beam sizes and smaller collision frequency values. Keeping in mind that fμμ is smaller than fpp by more than two orders, the following correlation between μp and μμ luminosities takes place: (8)Lμp=NpNμσμmax⁡σp,σμ2Lμμ.Using nominal parameters ofμμ colliders given in Table 5, parameters of the SppC based μp colliders are calculated according to (8) and presented in Table 6. Concerning beam tune shifts, for round and matched beams, (3) and (4) turn to(9)ξp=Nμrpβp∗4πγpσμ2=Nμrp4πϵnp,(10)ξμ=Nprμβμ∗4πγμσp2=Nprμ4πϵnμ,respectively.Table 6
Main parameters of SppC basedμp colliders.
E
μ, TeV
E
p, TeV
√S, TeV
L
μ
p, cm-2s-1
ξ
μ
ξ
p
0.75
35.6
10.33
5.5
×
1
0
32
8.7
×
1
0
-
3
6.0
×
1
0
-
2
0.75
68
14.28
12.5
×
1
0
32
8.7
×
1
0
-
3
8.0
×
1
0
-
2
1.5
35.6
14.61
4.9
×
1
0
32
8.7
×
1
0
-
3
6.0
×
1
0
-
2
1.5
68
20.2
42.8
×
1
0
32
8.7
×
1
0
-
3
8.0
×
1
0
-
2As one can see from Table6, where nominal parameters of SppC proton beam are used, ξp is unacceptably high and should be decreased to 0.02 which seems acceptable for μp colliders [26]. According to (9), ξp can be decreased, for example, by decrement of Nμ which leads to corresponding reduction of luminosity (three times and four times for μp 35.6 TeV and 68 TeV, resp.). Alternatively, crab crossing [29] can be used for decreasing of ξp without change of the luminosity.


### 2.3. Ultimateμp Option

This option can be realized if an additional muon ring is constructed in the SppC tunnel. In order to estimate CM energy and luminosity ofμp collisions we use muon beam parameters from [30], where 100 TeV center of mass energy muon collider with 100 km ring circumference has been proposed. These parameters are presented in Table 7.Table 7
Main parameters of the ultimate muon beam.
Beam energy (TeV)
50
Circumference (km)
100
Average luminosity (1034 cm-2s-1)
100
Particle per bunch (1012)
0.80
Norm. trans. emitt. (mm-mrad)
8.7
β
∗ amplitude function at IP (mm)
2.5
IP beam size (μm)
0.21
Bunches per beam
1
Repetition rate (Hz)
7.9
Bunch spacing (μs)
333
Bunch length (mm)
2.5CM energy, luminosity, and tune shifts for ultimateμp collider are given in Table 8. It is seen that the ξp value is approximately two times higher than the limiting value 0.02 [26]. This problem can be solved by reducing muon bunch population, which leads to decrease of luminosity by factor of 1.75. Alternatively, crab crossing can be used without change of the luminosity.Table 8
Main parameters of the ultimate SppC basedμp collider.
E
μ, TeV
E
p, TeV
√S, TeV
L
μ
p, cm-2s-1
ξ
μ
ξ
p
50
68
116.6
1.2
×
1
0
33
2.6
×
1
0
-
2
3.5
×
1
0
-
2


## 2.1.ep Option

Preliminary study of CepC-SppC basede-p collider with s=4.1 TeV and Lep=1033cm-2s-1 has been performed in [19]. In this subsection, we consider ILC (International Linear Collider) [20] and PWFA-LC (Plasma Wake Field Accelerator-Linear Collider) [21] as a source of electron/positron beam for SppC based energy frontier ep colliders. Main parameters of ILC and PWFA-LC electron beams are given Table 2.Table 2
Main parameters of the ILC (second column) and PWFA-LC (third column) electron beams.
Beam energy (GeV)
500
5000
Peak luminosity (1034 cm-2s-1)
4.90
6.27
Particle per bunch (1010)
1.74
1.00
Norm. horiz. emittance (μm)
10.0
10.0
Norm. vert. emittance (nm)
30.0
35.0
Horiz.β∗ amplitude function at IP (mm)
11.0
11.0
Vert.β∗ amplitude function at IP (mm)
0.23
0.099
Horiz. IP beam size (nm)
335
106
Vert. IP beam size (nm)
2.70
59.8
Bunches per beam
2450
1
Repetition rate (Hz)
4.00
5000
Beam power at IP (MW)
27.2
40
Bunch spacing (ns)
366
20
×
1
0
4
Bunch length (mm)
0.225
0.02It is seen that bunch spacings of ILC and PWFA-LC are much greater than SppC bunch spacing. On the other hand, transverse size of proton beam is much greater than transverse sizes of electron beam. Therefore, (1) for luminosity turns into (5)Lep=NeNp4πσp2fce.For transversely matched electron and proton beams at IP, equations for electron beam disruption and proton beam tune shift become(6)De=Npreσzpγeσp2,ξp=Nerpβp∗4πγpσp2=Nerp4πϵnp,where ϵnp is normalized transverse emittance of proton beam.Using nominal parameters of ILC, PWFA-LC, and SppC, we obtain values ofLep, De, and ξp parameters for LC⊗SppC based ep colliders, which are given in Table 3. The values for luminosity given in parentheses represent results of beam-beam simulations by ALOHEP software [22], which is being developed for linac-ring type ep colliders.Table 3
Main parameters of LC⊗SppC based ep colliders.
E
e, TeV
E
p, TeV
s, TeV
L
e
p, cm-2s-1
D
e
ξ
p, 10-3
0.5
35.6
8.44
3.35(6.64)×1030
0.537
0.5
0.5
68
11.66
2.69(5.33)×1031
0.902
0.7
5
35.6
26.68
0.98(1.94)×1030
0.054
0.3
5
68
36.88
0.78(1.56)×1031
0.090
0.4In order to increase luminosity ofep collisions LHeC-like upgrade of the SppC proton beam parameters has been used. Namely, β function of proton beam at IP is arranged to be 7.5/2.4 times lower (0.1 m instead of 0.75/0.24 m) which corresponds to LHeC [5] and THERA [23] designs. This leads to increase of luminosity and De by factor 7.5 and 2.4 for SppC with 35.6 TeV and 68 TeV proton beam, respectively. Results are shown in Table 4.Table 4
Main parameters of LC⊗SppC based ep colliders with upgraded β∗.
E
e, TeV
E
p, TeV
s, TeV
L
e
p, cm-2s-1
D
e
ξ
p, 10-3
0.5
35.6
8.44
2.51(4.41)×1031
4.03
0.5
0.5
68
11.66
6.45(10.8)×1031
2.16
0.7
5
35.6
26.68
7.37(13.3)×1030
0.403
0.3
5
68
36.88
1.89(3.75)×1031
0.216
0.4In principle “dynamic focusing scheme” [24], which was proposed for THERA, could provide additional factor of 3-4. Therefore, luminosity values exceeding 1032cm-2s-1 can be achieved for all options. Concerning ILC⊗SppC based ep colliders, a new scheme for energy recovery proposed for higher-energy LHeC (see Section 7.1.5 in [5]) may give an opportunity to increase luminosity by an additional order, resulting in Lep exceeding 1033cm-2s-1. Unfortunately, this scheme can not be applied at PWFA-LC⊗SppC.


## 2.2.μp Option

Muon-proton colliders were proposed almost two decades ago: construction of additional proton ring ins = 4 TeV muon collider tunnel was suggested in [25], construction of additional 200 GeV energy muon ring in the Tevatron tunnel was considered in [26], and ultimate μp collider with 50 TeV proton ring in s = 100 TeV muon collider tunnel was suggested in [27]. Here, we consider construction of TeV energy muon colliders (μC) [28] tangential to the SppC. Parameters of μC are given in Table 5.Table 5
Main parameters of the muon beams.
Beam energy (GeV)
750
1500
Circumference (km)
2.5
4.5
Average luminosity (1034 cm-2s-1)
1.25
4.4
Particle per bunch (1012)
2
2
Norm. trans. emitt. (mm-rad)
0.025
0.025
β
∗ amplitude function at IP (cm)
1 (0.5–2)
0.5 (0.3–3)
IP beam size (μm)
6
3
Bunches per beam
1
1
Repetition rate (Hz)
15
12
Bunch spacing (ns)
8300
15000
Bunch length (cm)
1
0.5Keeping in mind that both SppC andμC have round beams, luminosity equation (1) turns to(7)Lpp=fppNp24πσp2,Lμμ=fμμNμ24πσμ2,for SppC-pp and μC, respectively. Concerning muon-proton collisions one should use larger transverse beam sizes and smaller collision frequency values. Keeping in mind that fμμ is smaller than fpp by more than two orders, the following correlation between μp and μμ luminosities takes place: (8)Lμp=NpNμσμmax⁡σp,σμ2Lμμ.Using nominal parameters ofμμ colliders given in Table 5, parameters of the SppC based μp colliders are calculated according to (8) and presented in Table 6. Concerning beam tune shifts, for round and matched beams, (3) and (4) turn to(9)ξp=Nμrpβp∗4πγpσμ2=Nμrp4πϵnp,(10)ξμ=Nprμβμ∗4πγμσp2=Nprμ4πϵnμ,respectively.Table 6
Main parameters of SppC basedμp colliders.
E
μ, TeV
E
p, TeV
√S, TeV
L
μ
p, cm-2s-1
ξ
μ
ξ
p
0.75
35.6
10.33
5.5
×
1
0
32
8.7
×
1
0
-
3
6.0
×
1
0
-
2
0.75
68
14.28
12.5
×
1
0
32
8.7
×
1
0
-
3
8.0
×
1
0
-
2
1.5
35.6
14.61
4.9
×
1
0
32
8.7
×
1
0
-
3
6.0
×
1
0
-
2
1.5
68
20.2
42.8
×
1
0
32
8.7
×
1
0
-
3
8.0
×
1
0
-
2As one can see from Table6, where nominal parameters of SppC proton beam are used, ξp is unacceptably high and should be decreased to 0.02 which seems acceptable for μp colliders [26]. According to (9), ξp can be decreased, for example, by decrement of Nμ which leads to corresponding reduction of luminosity (three times and four times for μp 35.6 TeV and 68 TeV, resp.). Alternatively, crab crossing [29] can be used for decreasing of ξp without change of the luminosity.


## 2.3. Ultimateμp Option

This option can be realized if an additional muon ring is constructed in the SppC tunnel. In order to estimate CM energy and luminosity ofμp collisions we use muon beam parameters from [30], where 100 TeV center of mass energy muon collider with 100 km ring circumference has been proposed. These parameters are presented in Table 7.Table 7
Main parameters of the ultimate muon beam.
Beam energy (TeV)
50
Circumference (km)
100
Average luminosity (1034 cm-2s-1)
100
Particle per bunch (1012)
0.80
Norm. trans. emitt. (mm-mrad)
8.7
β
∗ amplitude function at IP (mm)
2.5
IP beam size (μm)
0.21
Bunches per beam
1
Repetition rate (Hz)
7.9
Bunch spacing (μs)
333
Bunch length (mm)
2.5CM energy, luminosity, and tune shifts for ultimateμp collider are given in Table 8. It is seen that the ξp value is approximately two times higher than the limiting value 0.02 [26]. This problem can be solved by reducing muon bunch population, which leads to decrease of luminosity by factor of 1.75. Alternatively, crab crossing can be used without change of the luminosity.Table 8
Main parameters of the ultimate SppC basedμp collider.
E
μ, TeV
E
p, TeV
√S, TeV
L
μ
p, cm-2s-1
ξ
μ
ξ
p
50
68
116.6
1.2
×
1
0
33
2.6
×
1
0
-
2
3.5
×
1
0
-
2


## 3. Physics

In order to evaluate physics search potential of the SppC basedlp colliders we consider two phenomena; namely, small Björken x region is considered as an example of the SM physics and resonant production of color octet electron and muon is considered as an example of the BSM physics.


### 3.1. Small Björkenx

As mentioned above, investigation of extremely smallx region (x<10-5) at sufficiently large Q2 (>10 GeV2), where saturation of parton density should manifest itself, is crucial for understanding of QCD basics. Smallest achievable x at lp colliders is given by Q2/S. For LHeC with s=1.3 TeV minimal achievable value is x=6×10-6. In Table 9, we present smallest x values for different SppC based lepton-proton colliders (Ep is chosen as 68 TeV). It is seen that proposed machines has great potential for enlightening of QCD basics.Table 9
Attainable Björkenx values at Q2=10GeV2.
E
l (TeV)
0.5
5
1.5
50
x
7
×
1
0
-
8
7
×
1
0
-
9
2
×
1
0
-
8
7
×
1
0
-
10


### 3.2. Color Octet Leptons

Color octet leptons (l8) are predicted in preonic models with colored preons [31]. There are various phenomenological studies on l8 at TeV energy scale colliders [32–39]. Resonant production of color octet electron (e8) and muon (μ8) at the FCC based lp colliders (http://collider-reach.web.cern.ch/collider-reach) have been considered in [40] and [41], respectively. Performing similar analyses for SppC based lp colliders we obtain mass discovery limits for e8 and μ8 in Λ=Ml8 case (where Λ is compositeness scale) which are presented in Figures 2 and 3, respectively. Discovery mass limit value for LHC and SppC is obtained by rescaling ATLAS/CMS second-generation LQ results [42, 43] using the method developed by Salam and Weiler [44]. For lepton colliders, it is obvious that discovery mass limit for pair production of l8 is approximately half of CM energies. It is seen that l8 search potential of SppC based lp colliders overwhelmingly exceeds that of LHC and lepton colliders. Moreover lp colliders will give an opportunity to determine compositeness scale (for details see [40, 41]).Figure 2
Discovery mass limits for color octet electron at different pp,e+e-, and ep colliders.Figure 3
Discovery mass limits for color octet muon at different pp,μ+μ-, and μp colliders.It should be noted that FCC/SppC basedlp colliders have great potential for search of a lot of BSM phenomena, such as excited leptons (see [45] for μ∗), contact interactions, and R-parity violating SUSY.


## 3.1. Small Björkenx

As mentioned above, investigation of extremely smallx region (x<10-5) at sufficiently large Q2 (>10 GeV2), where saturation of parton density should manifest itself, is crucial for understanding of QCD basics. Smallest achievable x at lp colliders is given by Q2/S. For LHeC with s=1.3 TeV minimal achievable value is x=6×10-6. In Table 9, we present smallest x values for different SppC based lepton-proton colliders (Ep is chosen as 68 TeV). It is seen that proposed machines has great potential for enlightening of QCD basics.Table 9
Attainable Björkenx values at Q2=10GeV2.
E
l (TeV)
0.5
5
1.5
50
x
7
×
1
0
-
8
7
×
1
0
-
9
2
×
1
0
-
8
7
×
1
0
-
10


## 3.2. Color Octet Leptons

Color octet leptons (l8) are predicted in preonic models with colored preons [31]. There are various phenomenological studies on l8 at TeV energy scale colliders [32–39]. Resonant production of color octet electron (e8) and muon (μ8) at the FCC based lp colliders (http://collider-reach.web.cern.ch/collider-reach) have been considered in [40] and [41], respectively. Performing similar analyses for SppC based lp colliders we obtain mass discovery limits for e8 and μ8 in Λ=Ml8 case (where Λ is compositeness scale) which are presented in Figures 2 and 3, respectively. Discovery mass limit value for LHC and SppC is obtained by rescaling ATLAS/CMS second-generation LQ results [42, 43] using the method developed by Salam and Weiler [44]. For lepton colliders, it is obvious that discovery mass limit for pair production of l8 is approximately half of CM energies. It is seen that l8 search potential of SppC based lp colliders overwhelmingly exceeds that of LHC and lepton colliders. Moreover lp colliders will give an opportunity to determine compositeness scale (for details see [40, 41]).Figure 2
Discovery mass limits for color octet electron at different pp,e+e-, and ep colliders.Figure 3
Discovery mass limits for color octet muon at different pp,μ+μ-, and μp colliders.It should be noted that FCC/SppC basedlp colliders have great potential for search of a lot of BSM phenomena, such as excited leptons (see [45] for μ∗), contact interactions, and R-parity violating SUSY.


## 4. Conclusion

It is shown that construction of lineare+e-colliders (http://collider-reach.web.cern.ch/collider-reach) (or dedicated linac) and muon colliders (or dedicated muon ring) tangential to the SppC will give opportunity to handle lepton-proton collisions with multi-TeV CM energies and sufficiently high luminosities. Concerning SM physics, these machines will certainly shed light on QCD basics. BSM search potential of lp colliders essentially exceeds that of corresponding lepton colliders. Also these types of colliders exceed the search potential of the SppC itself for a lot of BSM phenomena.Acceleration of ion beams at the SppC will give opportunity to provide multi-TeV center of mass energy ineA and μA collisions. In addition, electron beam can be converted to high energy photon beam using Compton backscattering of laser photons which will give opportunity to construct LC⊗SppC based γp and γA colliders. Studies on these topics are ongoing.In conclusion, systematic study of accelerator, detector, and physics search potential issues of the SppC basedep, eA, γp, γA, μp, and μA colliders are essential to foresee the future of particle physics. Certainly, realization of these machines depends on the future results from the LHC as well as FCC and/or SppC.



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*Source: 4021493-2017-08-01.xml*