Advances in High Energy Physics
Volume 2017 (2017), Article ID 4021493, 6 pages
https://doi.org/10.1155/2017/4021493

Research Article

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

Ali Can Canbay,1,2 Umit Kaya,1,2 Bora Ketenoglu,³ Bilgehan Baris Oner,¹ and Saleh Sultansoy1,4

¹TOBB University of Economics and Technology, Ankara, Turkey
²Department of Physics, Ankara University, Ankara, Turkey
³Department of Engineering Physics, Ankara University, Ankara, Turkey
⁴ANAS Institute of Physics, Baku, Azerbaijan

Correspondence should be addressed to Umit Kaya; umit.kaya@cern.ch

Received 14 April 2017; Accepted 15 June 2017; Published 1 August 2017

Academic Editor: Juan José Sanz-Cillero

Copyright © 2017 Ali Can Canbay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³.

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, ultimate collider which assumes construction of additional 50 TeV muon ring in the SppC tunnel is considered. It is shown that luminosity values exceeding 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 region as an example of SM physics and resonant production of color octet leptons as an example of BSM physics.

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 and small , HERA (the first and still unique lepton-hadron collider) with  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 (<10⁻⁵) and high (≥10 GeV²) simultaneously, where saturation of parton densities should manifest itself, has not been reached yet. Hopefully, LHeC [5] with  TeV will give opportunity to touch this region.

Construction of linear 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 , , , and 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 and 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 ( )
11
102

Particle per bunch ()
20
20

Norm. transverse emittance (m)
4.10
3.05

amplitude function at IP (m)
0.75
0.24

IP beam size (m)
9.0
3.04

Bunches per beam
5835
10667

Bunch spacing (ns)
25
25

Bunch length (mm)
75.5
15.8

Beam-beam parameter,
0.006
0.008

In this paper we consider SppC based and 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 colliders have been evaluated in Section 3, where small Björken 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 Based and Colliders

General expression for luminosity of SppC based colliders is given by ( denotes electron or muon)

where and are numbers of leptons and protons per bunch, respectively; () and () are the horizontal and vertical proton (lepton) beam sizes at interaction point (IP); and are LC/μC and SppC bunch frequencies. is expressed by , where denotes number of bunches and means revolution frequency for SppC/μC and pulse frequency for LC. In order to determine collision frequency of collider, minimum value should be chosen among lepton and hadron bunch frequencies. Some of these parameters can be rearranged in order to maximize 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

where  m is classical radius for electron, is the Lorentz factor of electron beam, and and are horizontal and vertical proton beam sizes at IP, respectively. is bunch length of proton beam. Beam-beam parameter for proton beam is given by

where is classical radius for proton,  m, is beta function of proton beam at IP, and is the Lorentz factor of proton beam. and are horizontal and vertical sizes of lepton beam at IP, respectively.

Beam-beam parameter for muon beam is given by

where  m is classical muon radius, is beta function of muon beam at IP, and is the Lorentz factor of muon beam. and are horizontal and vertical sizes of proton beam at IP, respectively.

2.1. Option

Preliminary study of CepC-SppC based collider with  TeV and 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 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)

Peak luminosity ( )

Particle per bunch ()

Norm. horiz. emittance (m)

Norm. vert. emittance (nm)

Horiz. amplitude function at IP (mm)

Vert. amplitude function at IP (mm)

Horiz. IP beam size (nm)

Vert. IP beam size (nm)

Bunches per beam

Repetition rate (Hz)

Beam power at IP (MW)

Bunch spacing (ns)

Bunch length (mm)

It 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

For transversely matched electron and proton beams at IP, equations for electron beam disruption and proton beam tune shift become

where is normalized transverse emittance of proton beam.

Using nominal parameters of ILC, PWFA-LC, and SppC, we obtain values of , , and parameters for LCSppC based 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 colliders.

Table 3: Main parameters of LCSppC based colliders.

, TeV
, TeV
, TeV
,

,

0.5
35.6
8.44
3.35
0.537
0.5

0.5
68
11.66
2.69
0.902
0.7

5
35.6
26.68
0.98
0.054
0.3

5
68
36.88
0.78
0.090
0.4

In order to increase luminosity of collisions LHeC-like upgrade of the SppC proton beam parameters has been used. Namely, 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 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 LCSppC based colliders with upgraded .

, TeV
, TeV
, TeV
,

,

0.5
35.6
8.44
2.51
4.03
0.5

0.5
68
11.66
6.45
2.16
0.7

5
35.6
26.68
7.37
0.403
0.3

5
68
36.88
1.89
0.216
0.4

In principle “dynamic focusing scheme” [24], which was proposed for THERA, could provide additional factor of 3-4. Therefore, luminosity values exceeding can be achieved for all options. Concerning ILCSppC based colliders, a new scheme for energy recovery proposed for higher-energy LHeC (see Section in [5]) may give an opportunity to increase luminosity by an additional order, resulting in exceeding . Unfortunately, this scheme can not be applied at PWFA-LCSppC.

2.2. Option

Muon-proton colliders were proposed almost two decades ago: construction of additional proton ring in = 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 collider with 50 TeV proton ring in = 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)

Circumference (km)

Average luminosity ( )

Particle per bunch ()

Norm. trans. emitt. (mm-rad)

amplitude function at IP (cm)
1 (0.5–2)
0.5 (0.3–3)

IP beam size (m)

Bunches per beam

Repetition rate (Hz)

Bunch spacing (ns)

Bunch length (cm)

Keeping in mind that both SppC and μC have round beams, luminosity equation (1) turns to

for SppC- and μC, respectively. Concerning muon-proton collisions one should use larger transverse beam sizes and smaller collision frequency values. Keeping in mind that is smaller than by more than two orders, the following correlation between and luminosities takes place:

Using nominal parameters of colliders given in Table 5, parameters of the SppC based 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

respectively.

Table 6: Main parameters of SppC based colliders.

, TeV
, TeV
S, TeV
,

0.75
35.6
10.33

0.75
68
14.28

1.5
35.6
14.61

1.5
68
20.2

As one can see from Table 6, where nominal parameters of SppC proton beam are used, is unacceptably high and should be decreased to 0.02 which seems acceptable for colliders [26]. According to (9), can be decreased, for example, by decrement of which leads to corresponding reduction of luminosity (three times and four times for 35.6 TeV and 68 TeV, resp.). Alternatively, crab crossing [29] can be used for decreasing of without change of the luminosity.

2.3. Ultimate 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 of 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)

Circumference (km)

Average luminosity ( )

Particle per bunch ()

Norm. trans. emitt. (mm-mrad)

amplitude function at IP (mm)

IP beam size (m)

Bunches per beam

Repetition rate (Hz)

Bunch spacing (s)

Bunch length (mm)

CM energy, luminosity, and tune shifts for ultimate collider are given in Table 8. It is seen that the 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 based collider.

, TeV
, TeV
S, TeV
,

50
68
116.6

3. Physics

In order to evaluate physics search potential of the SppC based colliders we consider two phenomena; namely, small Björken 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 Björken

As mentioned above, investigation of extremely small region () at sufficiently large (>10 GeV²), where saturation of parton density should manifest itself, is crucial for understanding of QCD basics. Smallest achievable at colliders is given by . For LHeC with  TeV minimal achievable value is . In Table 9, we present smallest values for different SppC based lepton-proton colliders ( is chosen as 68 TeV). It is seen that proposed machines has great potential for enlightening of QCD basics.

Table 9: Attainable Björken values at .

(TeV)
0.5
5
1.5
50

3.2. Color Octet Leptons

Color octet leptons () are predicted in preonic models with colored preons [31]. There are various phenomenological studies on at TeV energy scale colliders [32–39]. Resonant production of color octet electron () and muon () at the FCC based colliders (http://collider-reach.web.cern.ch/collider-reach) have been considered in [40] and [41], respectively. Performing similar analyses for SppC based colliders we obtain mass discovery limits for and in case (where 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 is approximately half of CM energies. It is seen that search potential of SppC based colliders overwhelmingly exceeds that of LHC and lepton colliders. Moreover 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, , and colliders.

Figure 3: Discovery mass limits for color octet muon at different pp, , and colliders.

It should be noted that FCC/SppC based colliders have great potential for search of a lot of BSM phenomena, such as excited leptons (see [45] for ), contact interactions, and R-parity violating SUSY.

4. Conclusion

It is shown that construction of linear colliders (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 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 in and 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 LCSppC based and colliders. Studies on these topics are ongoing.

In conclusion, systematic study of accelerator, detector, and physics search potential issues of the SppC based , , , , , and 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.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This study is supported by TUBITAK under Grant no. 114F337.

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