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Advances in High Energy Physics
Volume 2014 (2014), Article ID 315826, 8 pages
Search for the Anomalous Interactions of Up-Type Heavy Quarks in Collision at the LHC
Department of Physics, Cumhuriyet University, 58140 Sivas, Turkey
Received 22 March 2013; Revised 6 August 2013; Accepted 23 August 2013; Published 20 January 2014
Academic Editor: Amir H. Fatollahi
Copyright © 2014 M. Köksal and S. C. İnan. 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.
We investigate the anomalous interactions of heavy up-type quark in a collision at the LHC. We have obtained 95% confidence level (CL) limit of () anomalous coupling by taking into account three forward detector acceptances: , , and .
The Standard Model (SM) ensures a conspicuously successful description of high energy physics at an energy scale of up to a few hundred GeV. However, the number of fermion families is arbitrary in the Standard Model (SM). The only limitation on number of fermion families comes from asymptotic freedom . We should use at least three fermion families to obtain CP violation  in the SM. CP violation could explain the matter-antimatter asymmetry in the universe. The SM with three families is not enough to show the reel magnitude for matter-antimatter asymmetry of universe. However, this problem can be solved when the number of family reaches four . Also, the existence of three or four families is equally consistent with the updated electroweak precision data [3, 4]. The possible discovery of the fourth SM family may help to respond to some unanswered questions about electroweak symmetry breaking [5–7], fermion’s mass and mixing pattern [8–10], and flavor structure of the SM [11–14].
Higgs boson is a theoretical particle that is suggested by the SM. Many experiments were conducted so far to detect Higgs boson. A boson consistent with this boson was a detected in 2012, but it may take quite time to demonstrate certainly whether this particle is indeed a Higgs boson. If the lately surveyed 125 GeV boson is Higgs boson of the SM [15, 16], the presence of the fourth family would be disfavoured [17–19]. Besides, a theory with extended Higgs sector beyond the SM  can still include a fourth fermion family even though the 125 GeV boson is one of the forecasted extended Higgs bosons. Moreover, the other models estimate the presence of a heavy quark as a partner to the top quark [21, 22].
Current bounds on the masses of the fourth SM fermion families are given as follows: GeV , GeV , GeV, GeV for Dirac (Majorana) neutrinos . When we analyze our results we have taken into account LHC limits in TeV. For this purpose, we have assumed mass to be greater than its current experimental limits. The fourth SM quarks would be produced abundantly in pairs at the LHC via the strong interaction for masses below O(1 TeV) [26–29], with fairly large cross sections. The exact designation of their properties can ensure important advantage in the determination of new physics which is established upon high energy scales. Moreover, we can expect a crucial addition from anomalous interactions for production of fourth family quarks. These interactions have been investigated at lepton colliders [30, 31], colliders , colliders [10, 33–35], and hadron colliders [8, 28, 36–45].
The LHC has high energetic proton-proton collisions with high luminosity. It provides high statistics data. We expect that this collider will answer many open questions in particle physics. Research of exclusive production of proton-proton interactions opens a new field of surveying high energy photon-induced reactions such as photon-photon and photon-proton interactions. ATLAS and CMS Collaborations established a program of forward physics with new detectors located in a region almost 100 m–400 m from the central detectors. These detectors are called very forward detectors. They can detect intact protons which are scattered after the collisions. Very forward detectors can label intact protons with some momentum fraction loss given the formula . Here, is the momentum of intact scattered proton after the collision and is the momentum of incoming proton. ATLAS Forward Physics Collaboration (AFP) proposed an acceptance of for the forward detectors . Two types of measurements will be planned to examine with high precision using the AFP [47–49]: first, exploratory physics (anomalous couplings between and or bosons, exclusive production, etc.) and second, standard QCD physics (double Pomeron exchange, exclusive production in the jet channel, single diffraction, physics, etc.). These studies will develop the HERA and Tevatron measurements to the LHC kinematical region. Also, CMS-TOTEM forward detector scenario has acceptance regions and [50, 51]. The TOTEM experiment at the LHC is concentrated on the studies of the total proton-proton cross-section, the elastic scattering, and all classes of diffractive phenomena. Detectors housed in Roman Pots which can be moved close to the outgoing proton beams allow to trigger on elastic and diffractive protons and to determine their parameters like the momentum loss and the transverse momentum transfer. Moreover, charged particle detectors in the forward domains can detect nearly all inelastic events. Together with the CMS detector, a large solid angle is covered enabling precise studies [52–54]. The forward detectors of ATLAS and CMS were not built in the first phase of the LHC. However, the CMS forward detectors were commissioned in 2009. The first measurement of the forward energy flow has been carried out and forward jets at have been analyzed for the first time at Hadron Colliders . Also, two photon reactions , were examined with the help of forward detectors by the CMS Collaboration in 2012 [56, 57]. On the other hand, AFP Collaboration has not yet installed the forward detectors. The forward detectors are planned to be built 210 m away from the central detectors in 2013. Additionally, 420 m additional detectors will be installed if physics motivates it later . Forward detectors allow to determine high energy photon-photon process. This process occurred by two almost real photons with low virtuality emitted from protons. The proton structure does not spoil in this process due to low virtuality of photons. Therefore, intact scattered protons after the collision can be detected by the aid of the forward detectors. Searching new physics via photon-induced reactions have been studied in earlier works [59–69].
Photon-photon interaction can be explained by equivalent photon approximation [70, 71]. Emitted quasireal photons by protons with low virtuality produce an object via process. The cross section of this process can be found by where is the invariant mass of the two-photon system, is the cross section for subprocess , and is the luminosity spectrum of photon-photon collisions. can be given as follows : with where and are functions of equivalent photon energy spectrum. The photon spectrum with energy and virtuality is given by the following : where The terms in the previous equations are the following: is the energy of the proton beam which is related to the photon energy by , is the proton mass, is function of the magnetic form factor, and is function of the electric form factor and is the proton magnetic moment.
In this study, we have examined the anomalous interaction of up-type quark via the () process by considering three forward detector acceptances; , , and .
2. Anomalous Interaction of Quark
The fourth family quark can interact with the ordinary quarks via SM gauge bosons (, , , ). The lagrangian of this interaction is expressed by where is the electromagnetic coupling constant, is the strong coupling constant, is the weak neutral current coupling constant, and are the vector and axial-vector type couplings of the neutral weak current with quark, are the Gell-Mann matrices, and is the electric charge of quark. The vector fields , , , and represent photon, gluon, -boson, and -boson, respectively. Finally, the are the elements of the extended CKM mixing matrix. In  they found that the maximum value of the fourth generation quark mass is ~300 GeV for a Higgs boson mass of ~125 GeV, which is already in conflict with bounds from direct searches. Therefore, we have considered that is a heavy quark instead of fourth generation quark. The quark is heavier than the top quark. It is accepted as the heaviest particle, and it is couple the flavor changing neutral currents, leading to an enhancement in the resonance processes at the LHC. The interaction Lagrangian for the anomalous interactions between the quark, ordinary quarks , , , and the gauge bosons , , is given as follows: where , , and are the anomalous couplings with photon, boson, and gluon, respectively. is new physics scale and . , , and are the field stress tensor of the photon, boson, and gluons, respectively. Jets that originate from light quarks (, , and ) differ from heavy quarks ( and ) in the final state at the LHC. Therefore, anomalous coupling can be distinguished from coupling via the process , if anomalous couplings are not equal to . It can be understood that the bound on product through the process can be also examined. However, we consider that is equal to in our paper. For the fourth family leptons coupling was calculated in the literature for the photon-photon fusion at the LHC . Also, coupling can be examined through the process . But study of the and couplings is difficult for this process since and quarks cannot be distinguished from each other.
Using interaction Lagrangian in (7) anomalous decay widths of quarks can be obtained as follows: where is the mass of the quark and is the electromagnetic coupling constant.
The subprocess consists of and channel tree-level SM diagrams. Additionally, there are two Feynman diagrams containing quark propagators in and channels. The whole polarization summed amplitude square of this process has been calculated as follows: where , , and are the Mandelstam variables and we omit the mass of ordinary quark . We have supposed TeV to be center of mass energy of the proton-proton system during calculations.
The leading order background process comes from QCD-induced reactions (pomeron exchange). Pomerons emitted from incoming protons can interact with each other, and they can occur at the same final state. However, survival probability for a pomeron exchange is quite smaller than survival probability of induced photons. Therefore, pomeron background is expected to have minor effect on sensitivity bounds [73, 74].
In Figure 1, we have plotted the SM and total cross sections of () process as a function ( cut) transverse momentum of final state quarks for three forward detector acceptances: , , and . Here, and are taken to be GeV, 1 TeV, respectively. From these figures, we see that the SM and total cross sections can be distinguished from each other at large values of the cut. Then, it can be understood that imposing higher values of cut can reduce the SM background. These cuts allow to obtaining better sensitivity bounds.
In this motivation, we show the SM event numbers of for different values of cut and luminosities in Tables 1, 2, and 3 for acceptance regions , , and , respectively. During statistical analysis we use two different techniques. In the first approach we apply cuts on the of the final state quarks to suppress the SM cross section. We make the number of SM event smaller than . Then it is very appropriate to set bounds on the couplings using a Poisson distribution since the number of SM events with these cuts is small enough. From our calculations, cuts are obtained as 380 GeV and 452 GeV for two acceptance regions and in order to be less than the number of SM event, respectively. Since the invariant mass of the final state quarks for is greater than 1400 GeV, the SM cross section is very small. Hence, it does not need a high cut for acceptance region. Moreover, ATLAS and CMS have central detectors with a pseudorapidity for the tracking system at the LHC. Therefore, for all of the calculations in this paper, we also apply cut. The parameter plane is plotted at CL using Poisson analysis for the three different acceptances , and in Figure 2. In Figures 2(a) and 2(b), we use the different values for every acceptance region to obtain less than event number of SM: (a) GeV for ; (b) GeV for as mentioned above. In Figure 2(c), we applied a cut of GeV for for detection of the final state quarks in central detectors.
Second analyze technique, we have used to one-parameter analyze when the SM event number larger than . The function is given as follows: where is the cross section of SM, is the cross section containing new physics effects, and is the statistical error. In Figure 3, the parameter plane is plotted at CL using analysis for the two different acceptances and . For the acceptance region we cannot use analysis due to SM event number being smaller than as seen from Table 3. We have found from Figure 3 that acceptance region provides more restrictive limit than acceptance region because new physics effect comes from high energy region.
Forward detector equipments at the LHC can discern intact scattered protons after the collision. Hence, we can distinguish exclusive photon-photon processes with respect to deep inelastic scattering which damages the proton structure. Since photon-photon interaction has very clean environment, it is important to examine new physics for a given detector acceptance region through photon-induced reactions. Moreover, this interaction can isolate to coupling from the other gauge boson couplings. In these motivations, we have researched the anomalous interaction of quark via process at the LHC to investigate anomalous coupling. Our results show that the sensitivity of the anomalous TeV coupling can be reached at TeV and fb−1 for the GeV, . As a result, the exclusive reaction at the LHC offers us an important opportunity to probe anomalous couplings of quark.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
- M. Kobayashi and T. Maskawa, “CP-violation in the renormalizable theory of weak interaction,” Progress of Theoretical Physics, vol. 49, 62, no. 2, pp. 652–657, 1973.
- W. S. Hou, “Source of CP violation for the baryon asymmetry of the universe,” Chinese Journal of Physics, vol. 47, no. 2, p. 134, 2009.
- G. D. Kribs, T. Plehn, M. Spannowsky, and T. M. P. Tait, “Four generations and higgs physics,” Physical Review D, vol. 76, no. 7, Article ID 075016, 2007.
- R. Fok and G. D. Kribs, “Four generations, the electroweak phase transition, and supersymmetry,” Physical Review D, vol. 78, no. 7, Article ID 075023, 2008.
- B. Holdom, “Heavy quarks and electroweak symmetry breaking,” Physical Review Letters, vol. 57, no. 20, pp. 2496–2499, 1986.
- C. T. Hill, M. A. Luty, and E. A. Paschos, “Electroweak symmetry breaking by fourth-generation condensates and the neutrino spectrum,” Physical Review D, vol. 43, no. 9, pp. 3011–3025, 1991.
- T. Elliot and S. F. King, “Heavy quark condensates from dynamically broken flavour symmetry,” Physics Letters B, vol. 283, no. 3–4, pp. 371–378, 1992.
- B. Holdom, “The discovery of the fourth family at the LHC: what if?” Journal of High Energy Physics, vol. 2006, article 076, 0608, 2006.
- P. Q. Hung and M. Sher, “Experimental constraints on fourth generation quark masses,” Physical Review D, vol. 77, no. 3, Article ID 037302, 2008.
- O. Cakir, A. Senol, and A. T. Tasci, “Single production of fourth-family quarks at the CERN large hadron electron collider,” Europhysics Letters, vol. 88, no. 1, article 11002, 2009.
- H. Fritzsch, “Hierarchical chiral symmetries and the quark mass matrix,” Physics Letters B, vol. 184, no. 4,5, pp. 391–396, 1987.
- A. Datta, “Flavour democracy calls for the fourth generation,” Pramana, vol. 40, no. 6, pp. L503–L509, 1993.
- A. Çelikel, A.K. Çiftçi, and S. Sultansoy, “A search for the fourth SM family,” Physics Letters B, vol. 342, no. 1–4, pp. 257–261, 1995.
- B. Holdom, “The heavy quark search at the LHC,” Journal of High Energy Physics, vol. 2007, article 069, 0708, 2007.
- ATLAS Collaboration, “Search for the Standard Model higgs boson in the decay mode with of ATLAS data TeV,” Physics Letters B, vol. 716, no. 1, pp. 62–81, 2012.
- CMS Collaboration, “Search for high-mass resonances decaying into τ-lepton pairs in pp collisions at TeV,” Physics Letters B, vol. 716, no. 1, article 30, pp. 82–102, 2012.
- O. Eberhardt, G. Herbert, H. Lacker, et al., “Joint analysis of higgs boson decays and electroweak precision observables in the standard model with a sequential fourth generation,” Physical Review D, vol. 86, no. 1, Article ID 013011, 2012.
- O. Eberhardt, G. Herbert, H. Lacker, et al., “Impact of a higgs boson at a mass of 126 geV on the standard model with three and four fermion generations,” Physical Review Letters, vol. 109, no. 24, Article ID 241802, 2012.
- J. Bulava, K. Jansen, and A. Nagy, “Constraining a fourth generation of quarks: non-perturbative higgs boson mass bounds,” Physics Letters B, vol. 723, no. 1–3, pp. 95–99, 2013.
- N. Chen and H.-J. He, “LHC signatures of two-higgs-doublets with fourth family,” Journal of High Energy Physics, vol. 2012, article 062, 2012.
- D. Choudhury, T. Tait, and C. Wagner, “Beautiful mirrors and precision electroweak data,” Physical Review D, vol. 65, no. 5, Article ID 053003, 2002.
- M. Schmaltz, “Physics beyond the standard model (theory): introducing the Little higgs,” Nuclear Physics B—Proceedings Supplements, vol. 117, pp. 40–49, 2003.
- ATLAS Collaboration, “Search for exotic same-sign dilepton signatures ( quark, and four top quarks production) in of pp collisions at teV with the ATLAS detector,” Tech. Rep. ATLAS-Conf-2012-130, 2012.
- CMS Collaboration, “Search for heavy bottom-like quarks in of pp collisions at teV,” Journal of High Energy Physics, vol. 2012, article 123, 2012.
- Particle Data Group, “Review of particle physics,” Journal of Physics G, vol. 37, no. 7A, Article ID 075021, 2010.
- ATLAS Collaboration, “ATLAS detector and physics performance: technical design report, 1,” Tech. Rep. CERNLHCC-99-14/15, section 18.2, 1999.
- S. Sultansoy, “Four remarks on physics at LHC,” Tech. Rep. AU-HEP-97-05, 1997.
- E. Arik, S. Atağ, Z. Z. Aydin, et al., “Search for the fourth family up quarks at CERN LHC,” Physical Review D, vol. 58, no. 11, Article ID 117701, 1998.
- J. A. Aguilar-Saavedra, “Identifying top partners at LHC,” Journal of High Energy Physics, vol. 2009, article 030, 2009.
- A. K. Ciftci, R. Ciftci, and S. Sultansoy, “Fourth standard model family neutrino at future linear colliders,” Physical Review D, vol. 72, no. 5, Article ID 053006, 2005.
- A. Senol, A. T. Tasci, and F. Ustabas, “Anomalous single production of fourth generation quarks at ILC and CLIC,” Nuclear Physics B, vol. 851, no. 2, pp. 289–297, 2011.
- R. Çiftçi, A. K. Çiftçi, and S. Sultansoy, “Possible single resonant production of the fourth-generation charged leptons at γ e colliders,” Europhysics Letters, vol. 90, no. 4, Article ID 41001, 2010.
- A. T. Alan, A. Senol, and O. Çakir, “Anomalous production of fourth-family up-quarks at future lepton hadron colliders,” Europhysics Letters, vol. 66, no. 5, Article ID 657660, pp. 657–660, 2004.
- R. Ciftci and A. K. Ciftci, “A comperative study of the anomalous single production of the fourth generation quarks at ep and gamma-p colliders,” http://arxiv.org/abs/0904.4489.
- O. Çakir and V. Çetlnkaya, “Single production of fourth family quarks at the large hadron electron collider,” Modern Physics Letters A, vol. 25, no. 30, article 2571, 2010.
- V. E. Özcan, S. Sultansoy, and G. Ünel, “Prospects for the discovery of 4th family quarks with the ATLAS detector,” European Physical Journal C, vol. 57, pp. 621–626, 2008.
- O. Çakır, İ. T. Çakır, H. Duran Yıldız, and R. Mehdiyev, “Prospects for the discovery of 4th family quarks with the ATLAS detector,” European Physical Journal C, vol. 56, pp. 537–543, 2008.
- İ. T. Çakır, H. Duran Yıldız, O. Çakır, and G. Ünel, “Anomalous resonant production of the fourth-family up-type quarks at the LHC,” Physical Review D, vol. 80, no. 9, Article ID 095009, 12 pages, 2009.
- V. E. Özcan, S. Sultansoy, and G. Ünel, “A possible discovery channel for new charged leptons at the LHC,” Journal of Physics G, vol. 36, no. 9, Article ID 095002, 2009.
- İ. T. Çakır, H. Duran Yıldız, O. Çakır, and G. Ünel, “Anomalous resonant production of the fourth-family up-type quarks at the LHC,” Physical Review D, vol. 80, no. 9, Article ID 095009, 2009.
- O. Çakır, I. T. Çakır, A. Senol, and A. T. Tasci, “Anomalous single production of fourth family up-type quark associated with neutral gauge bosons at the LHC,” Journal of Physics G, vol. 39, no. 5, Article ID 055005, 2012.
- M. Şahin, S. Sultansoy, and S. Turkoz, “Search for the fourth standard model family,” Physical Review D, vol. 83, no. 5, Article ID 054022, 2011.
- B. Holdom and Q-S. Yan, “Searches for the of a fourth family,” Physical Review D, vol. 83, no. 11, Article ID 114031, 5 pages, 2011.
- B. Holdom, “ at the LHC: the physics of discovery,” Journal of High Energy Physics, vol. 2007, article 063, 0703, 2007.
- M. Geller, S. Bar-Shalom, and G. Eilam, “The need for new search strategies for fourth generation quarks at the LHC,” Physics Letters B, vol. 715, no. 1–3, pp. 121–128, 2013.
- M. G. Albrow, R. B. Appleby, M. Arneodo et al., “The FP420 R&D project: higgs and new physics with forward protons at the LHC,” http://arxiv.org/abs/0806.0302.
- ATLAS Collaboration, “Letter of Intent for the phase-i upgrade of the ATLAS experiment,” Tech. Rep. CERN-LHCC-2011-012. LHCC-I-020, The European Organization for Nuclear Research, Geneva, Switzerland, 2011.
- L. Adamczyk, R. B. Appleby, P. Bank, et al., “AFP: a proposal to install proton detectors at 220 m around ATLAS to complement the ATLAS high luminosity physics program,” Tech. Rep. ATL-COM-LUM-2011-006, CERN, 2011.
- O. Kepka, C. Royon, L. Schoeffel, R. Staszewski, M. Trzebinski, and R. Zlebcik, “Physics cases within the AFP project,” Tech. Rep. ATL-COM-PHYS-2012-775, CERN, 2012.
- O. Kepka and C. Royon, “Anomalous WWγ coupling in photon-induced processes using forward detectors at the CERN LHC,” Physical Review D, vol. 78, no. 7, Article ID 073005, 2008.
- V. Avati and K. Osterberg, “Acceptance calculations methods for low-beta*optics,” Tech. Rep. CERN-TOTEM-NOTE-2005-002, 2006.
- The TOTEM Collaboration, “First measurement of the total proton-proton cross-section at the LHC energy of TeV,” Europhysics Letters, vol. 96, no. 2, article 21002, CERN-PH-EP-2011-158, 2011.
- The TOTEM Collaboration, “Measurement of the forward charged-particle pseudorapidity density in collisions at TeV with the TOTEM experiment,” Europhysics Letters, vol. 98, no. 2, article 31002, CERN-PH-EP-2012-106, 2012.
- The TOTEM Collaboration, “Measurement of proton-proton elastic scattering and total cross-section at TeV,” CERN-PH-EP-2012-239, 2012.
- D. Volyanskyy, “Forward physics with the CMS experiment at the large hadron collider,” http://arxiv.org/abs/1011.5575.
- CMS Collaboration, “Exclusive production in proton-proton collisions at TeV,” Journal of High Energy Physics, vol. 2012, article 052, 1201, 2012.
- CMS Collaboration, “Search for exclusive or semi-exclusive γγ production and observation of exclusive and semi-exclusive e+e− production in pp collisions at TeV,” Journal of High Energy Physics, vol. 2012, article 080, 2012.
- C. Royon, “The ATLAS forward physics project,” http://arxiv.org/abs/1302.0623.
- V. A. Khoze, A. D. Martin, and M. G. Ryskin, “Prospects for new physics observations in diffractive processes at the LHC and Tevatron,” European Physical Journal C, vol. 23, no. 2, pp. 311–327, 2002.
- N. Schul and K. Piotrzkowski, “Detection of two-photon exclusive production of supersymmetric pairs at the LHC,” Nuclear Physics B—Proceedings Supplements, vol. 179–180, no. 2, pp. 289–297, 2008.
- S. M. Lietti, A. A. Natale, C. G. Roldao, and R. Rosenfeld, “Searching for anomalous higgs couplings in peripheral heavy ion collisions at the LHC,” Physics Letters B, vol. 497, no. 3–4, pp. 243–248, 2001.
- E. Chapon, C. Royon, and O. Kepka, “Anomalous quartic , , and trilinear couplings in two-photon processes at high luminosity at the LHC,” Physical Review D, vol. 81, no. 7, Article ID 074003, 2010.
- S. Atag, S. C. İnan, and I. Şahin, “Extra dimensions in photon-induced two lepton final states at the CERN LHC,” Physical Review D, vol. 80, no. 7, Article ID 075009, 2009.
- İ. Şahin and S. C. İnan, “Probe of unparticles at the LHC in exclusive two lepton and two photon production via photon-photon fusion,” Journal of High Energy Physics, vol. 2009, article 069, no. 9, 2009.
- S. Atağ, S. C. İnan, and İ. Şahin, “Extra dimensions in γγγγ process at the CERN-LHC,” Journal of High Energy Physics, vol. 2002, article 42, 2010.
- S. C. İnan, “Exclusive excited leptons search in two lepton final states at the CERN LHC,” Physical Review D, vol. 81, no. 11, Article ID 115002, 2010.
- S. Atag and A. A. Billur, “Possibility of determining τ Lepton electromagnetic moments in process at the CERN-LHC,” Journal of High Energy Physics, vol. 2010, no. 11, article 60, 2010.
- İ. Şahin and M. Köksal, “Search for electromagnetic properties of the neutrinos at the LHC,” Journal of High Energy Physics, vol. 2011, article 100, 2011.
- S. C. İnan, “Direct graviton production via photon-photon fusion at the CERN-LHC,” Chinese Physics Letters, vol. 29, no. 3, Article ID 031301, 2012.
- V. M. Budnev, I. F. Ginzburg, G. V. Meledin, and V. G. Serbo, “The two-photon particle production mechanism. Physical problems. applications. equivalent photon approximation,” Physics Reports, vol. 15, no. 4, pp. 181–282, 1975.
- G. Baur, K. Hencken, D. Trautmann, et al., “Coherent γγ and γA interactions in very peripheral collisions at relativistic ion colliders,” Physics Reports, vol. 364, no. 5, pp. 359–450, 2002.
- S. C. İnan, “Fourth generation leptons search in process at the CERN-LHC,” International Journal of Modern Physics A, vol. 26, no. 21, article 3605, 2011.
- M. G. Albrow, R. B. Appleby, M. Arneodo, et al., “The FP420 R&D project: higgs and new physics with forward protons at the LHC,” Journal of Instrumentation, vol. 4, no. 10, article T10001, 2009.
- İ. Şahin and B. Şahin, “Anomalous quartic couplings in collision at the LHC,” Physical Review D, vol. 86, no. 11, Article ID 115001, 2012.