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SppC Based Energy Frontier Lepton-Proton Colliders: Luminosity and 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 [Q.sup.2] and small x, HERA (the first and still unique lepton-hadron collider) with [square root of 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.sup.-5]) and high [Q.sup.2] ([greater than or equal to] 10Ge[V.sup.2]) simultaneously, where saturation of parton densities should manifest itself, has not been reached yet. Hopefully, LHeC [5] with [square root of s] = 1.3 TeV will give opportunity to touch this region.

Construction of linear [e.sup.+][e.sup.-] colliders (or dedicated linac) and muon colliders (or dedicated muon ring) tangential to the future circular [micro]p 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, [gamma]p, eA, and [gamma]A colliders, see reviews [6, 7] and papers [8-14]).

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 [micro]p colliders have been considered recently (see [18] and references therein).

In this paper we consider SppC based ep and [micro]p 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 Bjorken 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 Based ep and [mu]p Colliders

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

[mathematical expression not reproducible], (1)

where [N.sub.l] and [N.sub.p] are numbers of leptons and protons per bunch, respectively; [mathematical expression not reproducible] are the horizontal and vertical proton (lepton) beam sizes at interaction point (IP); [mathematical expression not reproducible] and SppC bunch frequencies. [f.sub.c] is expressed by [f.sub.c] = [N.sub.b][f.sub.rep], where Nh denotes number of bunches and [f.sub.rep] means revolution frequency for SppC/[mu]C 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 [L.sub.lp] 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

[mathematical expression not reproducible], (2)

where [r.sub.e] = 2.82 x [10.sup.-15] m is classical radius for electron, [[gamma].sup.e] is the Lorentz factor of electron beam, and [mathematical expression not reproducible] are horizontal and vertical proton beam sizes at IP, respectively. [mathematical expression not reproducible] is bunch length of proton beam. Beam- beam parameter for proton beam is given by

[mathematical expression not reproducible], (3)

where [r.sub.p] is classical radius for proton, [r.sub.p] = 1.54 x [10.sup.-18] m, [[beta].sup.*.sub.p] is beta function of proton beam at IP, and [[gamma].sub.p] is the Lorentz factor of proton beam. [mathematical expression not reproducible] are horizontal and vertical sizes oflepton beam at IP, respectively.

Beam-beam parameter for muon beam is given by

[mathematical expression not reproducible], (4)

where [r.sub.[mu]] = 1.37 x [10.sup.-17] m is classical muon radius, [[beta].sup.*.sub.u] is beta function of muon beam at IP, and [[gamma].sub.[mu]] the Lorentz factor of muon beam. [mathematical expression not reproducible] are horizontal and vertical sizes of proton beam at IP, respectively.

2.1. ep Option. Preliminary study of CepC-SppC based e-p collider with [square root of s] = 4.1 TeV and [L.sub.ep] = [10.sup.33] [cm.sup.-2] [s.sup.-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.

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

[mathematical expression not reproducible]. (5)

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

[mathematical expression not reproducible], (6)

where [[epsilon].sub.np] is normalized transverse emittance of proton beam.

Using nominal parameters of ILC, PWFA-LC, and SppC, we obtain values of [L.sub.ep], [D.sub.e], and [[xi].sub.p] parameters for LC[cross product]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.

In order to increase luminosity of ep collisions LHeC-like upgrade of the SppC proton beam parameters has been used. Namely, [beta] 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 [D.sub.e] 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.

In principle "dynamic focusing scheme" [24], which was proposed for THERA, could provide additional factor of 34. Therefore, luminosity values exceeding [10.sup.32] [cm.sup.-2] [s.sup.-1] can be achieved for all options. Concerning ILC[cross product]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 [L.sub.ep] exceeding [10.sup.33] [cm.sup.-2] [s.sup.-1]. Unfortunately, this scheme can not be applied at PWFA-LC[cross product]SppC.

2.2. [mu]p Option. Muon-proton colliders were proposed almost two decades ago: construction of additional proton ring in [square root of s] = 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 [micro]p collider with 50 TeV proton ring in [square root of s] = 100 TeV muon collider tunnel was suggested in [27]. Here, we consider construction of TeV energy muon colliders ([mu]C) [28] tangential to the SppC. Parameters of [mu]C are given in Table 5.

Keeping in mind that both SppC and [mu]C have round beams, luminosity equation (1) turns to

[L.sub.PP] = [f.sub.pp] [N.sup.2.sub.p]/4[pi][[sigma].sup.2.sub.p], [L.sub.[mu][mu]] = [f.sub.[mu][mu]] [N.sup.2.sub.[mu]]/4[pi][[sigma].sup.2.sub.[mu]], (7)

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

[L.sub.[mu]p] = ([N.sub.p]/[N.sub.[mu]])[([[delta].sub.[mu]]/max[[[sigma].sub.p], [[sigma].sub.[mu]]).sup.2][L.sub.[mu][mu]]. (8)

Using nominal parameters of [mu][mu] colliders given in Table 5, parameters of the SppC based [mu]p 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

[[xi].sub.p] = [N.sub.[mu]][r.sub.p][[beta].sup.*.sub.p]/4[pi][[gamma].sub.p][[sigma].sup.2.sub .[mu]] = [N.sub.[mu]][r.sub.p]/4[pi][[epsilon].sub.np], (9)

[[xi].sub.p] = [N.sub.p][r.sub.[mu]][[beta].sup.*.sub.[mu]]/4[pi][[gamma].sub.[mu]][[sigma].sup .2.sub.p] = [N.sub.p][r.sub.[mu]]/4[pi][[epsilon].sub.n[mu]], (10)

respectively.

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

2.3. Ultimate [mu]p 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 [micro]p 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.

CM energy, luminosity, and tune shifts for ultimate [mu]p collider are given in Table 8. It is seen that the [[xi].sub.p] 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.

3. Physics

In order to evaluate physics search potential of the SppC based lp colliders we consider two phenomena; namely, small Bjorken 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 Bjorken x. As mentioned above, investigation of extremely small x region (x < [10.sup.-5]) at sufficiently large [Q.sup.2] (>10 Ge[V.sup.2]), where saturation of parton density should manifest itself, is crucial for understanding of QCD basics. Smallest achievable x at lp colliders is given by [Q.sup.2]/S. For LHeC with [square root of s] = 1.3 TeV minimal achievable value is x = 6 x [10.sup.-6]. In Table 9, we present smallest x values for different SppC based lepton-proton colliders ([E.sub.p] is chosen as 68 TeV). It is seen that proposed machines has great potential for enlightening of QCD basics.

3.2. Color Octet [L.sub.ep]tons. Color octet leptons ([l.sup.8]) are predicted in preonic models with colored preons [31]. There are various phenomenological studies on [l.sub.8] at TeV energy scale colliders [32-39]. Resonant production of color octet electron ([[epsilon].sub.8]) and muon ([[mu].sub.8]) 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 [[epsilon].sub.8] and [[mu].sub.8] in [mathematical expression not reproducible] case (where [LAMBDA] 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 [l.sub.8] is approximately half of CM energies. It is seen that [l.sub.8] 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]).

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

4. Conclusion

It is shown that construction of linear [e.sup.+][e.sup.-]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 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 in eA and [micro]A 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[cross product]SppC based [gamma]p and [gamma]A colliders. Studies on these topics are ongoing.

In conclusion, systematic study of accelerator, detector, and physics search potential issues of the SppC based ep, eA, [gamma]p, [gamma]A, [mu]p, and [mu]A 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.

https://doi.org/10.1155/2017/4021493

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

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

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

(1) TOBB University of Economics and Technology, Ankara, Turkey

(2) Department of Physics, Ankara University, Ankara, Turkey

(3) Departmentof EngineeringPhysics, Ankara University Ankara, Turkey

(4) ANAS 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 Jose Sanz-Cillero

Caption: FIGURE 1: Possible configuration for SppC, linear collider (LC), and muon collider ([micro]C).
TABLE 1: Main parameters of proton beams in SppC.

Beam energy (TeV)                                       35.6    68.0
Circumference (km)                                      54.7    100.0
Peak luminosity ([10.sup.34] [cm.sup.-2] [s.sup.-1])     11      102
Particle per bunch ([10.sup.10])                         20      20
Norm. transverse emittance ([micro]m)                   4.10    3.05
[[beta].sup.*] amplitude function at IP (m)             0.75    0.24
IP beam size ([micro]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, [[xi].sub.pp]                      0.006   0.008

TABLE 2: Main parameters of the ILC (second column) and
PWFA-LC (third column) electron beams.

Beam energy (GeV)                    500          5000
Peak luminosity ([10.sup.34]        4.90          6.27
  [cm.sup.-2] [s.sup.-1])
Particle per bunch ([10.sup.10])    1.74          1.00
Norm. horiz. emittance ([micro]m)   10.0          10.0
Norm. vert. emittance (nm)          30.0          35.0
Horiz. [[beta].sup.*]               11.0          11.0
  amplitude function at IP (mm)
Vert. [[beta].sup.*]                0.23         0.099
  amplitude function at IP (mm)
Horiz. IP beam size (nm)             335          106
Vert. IP beam size (nm)             2770          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 x [10.sup.4]
Bunch length (mm)                   0.225         0.02


TABLE 3: Main parameters of LC[cross product]SppC based ep colliders.

[E.sub.e],    [E.sub.p],    [square root (s)],
TeV               TeV              TeV

0.5              35.6              8.44
0.5               68              11.66
5                35.6             26.68
5                 68              36.88

[E.sub.e],    [L.sub.ep], [cm.sup.-2]     [D.sub.e]   [[xi].sub.p],
TeV                  [s.sup.-1]                        [10.sup.-3]

0.5           3.35 (6.64) x [10.sup.30]     0.537          0.5
0.5           2.69 (5.33) x [10.sup.31]     0.902          0.7
5             0.98 (1.94) x [10.sup.30]     0.054          0.3
5             0.78 (1.56) x [10.sup.31]     0.090          0.4

TABLE 4: Main parameters of LC [cross product] SppC based ep
colliders with upgraded [[beta].sup.*].

[E.sup.e],    [E.sup.p],    [square root (s)],
TeV               TeV               TeV

0.5              35.6              8.44
0.5               68               11.66
5                35.6              26.68
5                 68               36.88

[E.sup.e],    [L.sup.ep], [cm.sup.-2]     [D.sub.e]   [[xi].sub.p]
TeV                  [s.sup.-1]                        [10.sup.-3]

0.5           2.51 (4.41) x [10.sup.31]     4.03           0.5
0.5           6.45 (10.8) x [10.sup.31]     2.16           0.7
5             7.37 (13.3) x [10.sup.30]     0.403          0.3
5             1.89 (3.75) x [10.sup.31]     0.216          0.4

TABLE 5: Main parameters of the muon beams.

Beam energy (GeV)                      750         1500
Circumference (km)                     2.5          4.5
Average luminosity ([10.sup.34]       1.25          4.4
  [cm.sup.-2] [s.sup.-1])
Particle per bunch ([10.sup.12])        2            2
Norm. trans. emitt. (mm-rad)          0.025        0.025
[[beta].sup.*] amplitude            1 (0.5-2)   0.5 (0.3-3)
  function at IP (cm)
IP beam size ([micro]m)                 6            3
Bunches per beam                        1            1
Repetition rate (Hz)                   15           12
Bunch spacing (ns)                    8300         15000
Bunch length (cm)                       1           0.5

TABLE 6: Main parameters of SppC based pp colliders.

[E.sub.[mu]],    [E.sub.p],   [square root (S)],
TeV                 TeV               TeV

0.75                35.6             10.33
0.75                 68              14.28
1.5                 35.6             14.61
1.5                  68              20.2

[E.sub.[mu]],    [L.sub.[mu]P], [cm.sup.-2]     [[xi].sub.[mu]]
TeV                      [s.sup.-1]

0.75                  5.5 x [10.sup.32]        8.7 x [10.sup.-3]
0.75                 12.5 x [10.sup.32]        8.7 x [10.sup.-3]
1.5                   4.9 x [10.sup.32]        8.7 x [10.sup.-3]
1.5                  42.8 x [10.sup.32]        8.7 x [10.sup.-3]

[E.sub.[mu]],      [[xi].sub.p]
TeV

0.75             6.0 x [10.sup.-2]
0.75             8.0 x [10.sup.-2]
1.5              6.0 x [10.sup.-2]
1.5              8.0 x [10.sup.-2]

TABLE 7: Main parameters of the ultimate muon beam.

Beam energy (TeV)                    50
Circumference (km)                  100
Average luminosity ([10.sup.34]     100
  [cm.sup.-2] [s.sup.-1])
Particle per bunch ([10.sup.12])    0.80
Norm. trans. emitt. (mm-mrad)       8.7
[[beta].sup.*] amplitude            2.5
  function at IP (mm)
IP beam size ([micro]m)             0.21
Bunches per beam                     1
Repetition rate (Hz)                7.9
Bunch spacing ([micro]s)            333
Bunch length (mm)                   2.5

TABLE 8: Main parameters of the ultimate
SppC based [micro]p collider.

[E.sub.[mu]],    [E.sub.p],    [square root of (S)],
TeV                  TeV                TeV

50                   68                116.6

[E.sub.[mu]],    [L.sub.[mu]p], [cm.sup.-2]     [[xi].sub.[mu]]
TeV                      [s.sup.-1]

50                    1.2 x [10.sup.33]        2.6 x [10.sup.-2]

[E.sub.[mu]],      [[xi].sub.p]
TeV

50               3.5 x [10.sup.-2]

TABLE 9: Attainable Bjorken x values at [Q.sup.2] = 10
[GeV.sub.2].

[E.sub.l],          0.5                5                1.5
(TeV)

x             7 x [10.sup.-8]   7 x [10.sup.-9]   2 x [10.sup.-8]

[E.sub.l],           50
(TeV)

x             7 x [10.sup.-10]

FIGURE 2: Discovery mass limits for color octet electron
at different pp, [e.sup.+][e.sup.-], and ep colliders.

[e.sub.8] Mass limit (TeV)

Proton colliders            LHC 14        LHC 136
                            TeV, 500      TeV, 10
                            [fb.sup.-1]   [ab.sup.-1]

Electron colliders          ILC 1         PWFA-LC 10
                            TeV, 10       TeV, 500
                            [fb.sup.-1]   [fb.sup.-1]

Electron-proton colliders   LHC x SppC    LHC x SppC
                            11.78 TeV,    36.9 TeV,
                            10            1
                            [fb.sup.-1]   [fb.sup.-1]

Note: Table made from bar graph.

FIGURE 3: Discovery mass limits for color octet muon at different
pp, [p.sup.+][p.sup.-], and [micro]p colliders.

[[mu].sub.8] Mass limit (TeV)

Proton colliders          LHC 14        SppC 136
                          TeV, 500      TeV, 10
                          [fb.sup.-1]   [ab.sup.-1]

Muon colliders            1.5           3.0
                          TeV, 125      TeV, 440
                          [fb.sup.-1]   [fb.sup.-1]

Muon - Proton colliders   20.2          117
                          TeV, 10       TeV, 10
                          [fb.sup.-1]   [fb.sup.-1]

Note: Table made from bar graph.
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Title Annotation:Research Article
Author:Canbay, Ali Can; Kaya, Umit; Ketenoglu, Bora; Oner, Bilgehan Baris; Sultansoy, Saleh
Publication:Advances in High Energy Physics
Date:Jan 1, 2017
Words:4914
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