Probe of electromagnetic moments of the tau lepton in gamma-gamma collisions at the CLIC
aa r X i v : . [ h e p - ph ] F e b Probe of the electromagnetic moments of the tau lepton ingamma-gamma collisions at the CLIC
A. A. Billur ∗ and M. K¨oksal † Department of Physics, Cumhuriyet University, 58140, Sivas, Turkey
Abstract
We have investigated the electromagnetic moments of the tau lepton in e + e − → e + γ ∗ γ ∗ e − → e + τ ¯ τ e − process at the CLIC. We have obtained 95% confidence level bounds on the anomalousmagnetic and electric dipole moments for various values of the integrated luminosity and the centerof mass energy. We have shown that the e + e − → e + γ ∗ γ ∗ e − → e + τ ¯ τ e − process at the CLIC leadsto a remarkable improvement in the existing experimental bounds on the anomalous magnetic andelectric dipole moments. ∗ [email protected] † [email protected] . INTRODUCTION The Land´e g-factor or gyromagnetic factor g is described by the formula between particle’smagnetic moment ~µ and it’s spin ~s : ~µ = g ( µ B / ~ ) ~s where µ B is the Bohr magneton. Inthe Dirac equation, the value of g is 2 for a point-like particle. Deviation from this value a = ( g − is called as the anomalous magnetic moment, and without anomalous and radiativecorrections a = 0. However, the anomalous magnetic moment a e of the electron was firstlyobtained using radiative corrections by Schwinger as a e = α π = 0 . a e was examined by many theoretical and experimental studies. Thesestudies have provided the most precise determination of fine-structure constant α QED , since a e is quite senseless to the strong and weak interactions. On the other hand, the anomalousmagnetic moment a µ of the muon enables testing the Standart Model (SM) and investigatingalternative theories to the SM. The a e and a µ can be obtained with high sensitivity throughspin precession experiment. Otherwise, the spin precession experiment cannot be used tomeasure the anomalous magnetic moment a τ of the tau, because of the relatively shortlifetime 2 . × − s of tau [2]. So the current bounds of the a τ are obtained by collisionexperiments. The theoretical value of the a τ from QED is given as a SMτ = 0 . a τ are provided by the L3: − . < a τ < .
058 ,OPAL: − . < a τ < .
065 and DELPHI: − . < a τ < .
013 collaborations at the LEPat 95% C.L. [5–7].CP violation was firstly observed in a small fractions of K L mesons decaying to two pionsin the SM [8]. This phenomenology in the SM can be easily introduced by the Cabibbo-Kobayashi-Maskawa mechanism in the quark sector [9]. On the other hand, there is no CPviolation in the lepton sector. However, CP violation in the quark sector causes a very smallelectric dipole moment of the leptons. At least to three-loop are required in order to producea nonzero contributing in the SM and it’s crude estimate is obtained as | d τ | ≤ − e cm [10].If at least two of the three neutrinos have different mass values, CP violation in the leptonsector can occur as similar to the CP violation in the quark sector [11]. There are manydifferent models beyond the SM inducing to CP violation in the lepton sector. These modelsare leptoquark [12, 13], SUSY [14], left-right symmetric [15, 16] and more Higgs multiplets[17, 18]. 2he bounds at 95% C. L. on the anomalous electric dipole moment of the tau yield byLEP experiments L3: | d τ | < . × − e cm , OPAL: | d τ | < . × − e cm , and DELPHI: | d τ | < . × − e cm . The most restrictive experimental bounds are obtained by BELLE: − . < Re ( d τ ) < . × (10 − e cm ) and − . < Im ( d τ ) < . × (10 − e cm ). There aremodel dependent and independent studies on the anomalous dipole moments of the taulepton in the literature [19–27].We consider that difference between a SMτ ( d SMτ ) and a expτ ( d expτ ) can be reduced to deter-mine precisely a new term proportional to F ( F ) to the SM τ τ γ vertex. For this reason,the electromagnetic vertex factor of the tau lepton can be parameterizedΓ ν = F ( q ) γ ν + i m τ F ( q ) σ νµ q µ + 12 m τ F ( q ) σ νµ q µ γ (1)where σ νµ = i ( γ ν γ µ − γ µ γ ν ), q is the momentum transfer to the photon and m τ = 1 . F = 1, F = 0 and F = 0. Besides,in the loop effects arising from the SM and the new physics, F and F may be not equal tozero. For example, the anomalous coupling F is given by F (0) = a SMτ + a NPτ (2)where a SMτ is the contribution of the SM and a NPτ is the contribution of the new physics[28–31].Therefore, the q -dependent form factors F ( q ) , F ( q ) and F ( q ) in limit q → F (0) = 1 , F (0) = a τ , F (0) = 2 m τ d τ e . (3)The Compact Linear Collider (CLIC) is a proposed future e + e − collider, designed tofulfill e + e − collisions at energies from 0 . γγ and γe interactions by converting the original e − or e + beam into a photon beam through thelaser backscattering procedure [51–53]. One of the other well-known applications of theCLIC is the γ ∗ γ ∗ process, where the emitted quasireal photon γ ∗ is scattered with small3ngle from the beam pipe of e − or e + [54–58]. Since these photons have a low virtuality( Q max = 2 GeV ), they are almost on mass shell. γ ∗ γ ∗ processes can be described byequivalent photon approximation, i.e. using the Weizsacker-Williams approximation [19, 59–70]. Such processes have experimentally observed at the LEP, Tevatron and LHC [71–77].There are two reasons why we have chosen the CLIC in this work: First, the observation ofthe most stringent experimental bound on the anomalous magnetic dipole moment of the taulepton by using multiperipheral collision at the LEP through the process e + e − → e + τ ¯ τ e − [7]. Secondly, the importace of high center-of-mass energies to examine the electromagneticproperties of tau lepton since anomalous τ τ γ couplings depend on more energy than SM τ τ γ couplings at the tree level. Therefore, we investigate the potential of CLIC via theprocess e + e − → e + τ ¯ τ e − to examine the anomalous magnetic and electric dipole momentsof tau lepton. II. CROSS SECTIONS AND NUMERICAL ANALYSIS
During calculations, the CompHEP-4 . . | η τ | < . p τT >
20 GeV for transverse momentum cut of the final state particles, ∆ R τ ¯ τ > . e + e − → e + γ ∗ γ ∗ e − → e + τ ¯ τ e − asa function of the anomalous couplings F and F in Fig. 1 for three different center-of-massenergies. As can be seen in Fig. 1, while the total cross section is symmetric for anomalouscoupling F , it is nonsymmetric for F .We estimate 95% C. L. bounds on anomalous coupling parameters F and F using χ test. The χ function is described by the following formula χ = (cid:18) σ SM − σ ( F , F ) σ SM δ (cid:19) , (4)where δ = p ( δ st ) + ( δ sys ) ; δ st = √ N SM is the statistical error and δ sys is the systematicerror. The number of expected events is calculated as the signal N = L int × BR × σ where L int is the integrated luminosity. The tau lepton decays roughly 35% of the time leptonicallyand 65% of the time to one or more hadrons. So we consider one of the tau leptons decays4eptonically and the other hadronically for the signal. Thereby, we assume that branchingratio of the tau pairs in the final state to be BR = 0 . e + e − → e + e − τ + τ − , systematic errors are experimentally studied be-tween 4 .
3% and 9% at the LEP [7, 79]. Recently, exclusive lepton production at the LHC hasbeen examined and its systematic uncertainty is 4 .
8% [74]. Also, the process pp → pτ + τ − p with 2% of the total systematic error at the LHC has investigated phenomenologically inRef. [19]. Therefore, the sensitivity limits on the anomalous magnetic and electric dipolemoments of the tau lepton through the process e + e − → e + e − τ + τ − have calculated by con-sidering three systematic errors: 2%, 5% and 10%. On the other hand, there may occur anuncertainty arising from virtuality of γ ∗ used in the Weizsacker-Williams approximation. InFigs. 2-4, we have calculated the integrated cross sections as a function of F and F fordifferent Q max values. We can see from these figures the total cross section changes slightlywith the variation of the Q max value. The sensitivity limits on the anomalous couplings a τ and d τ for different values of photon virtuality, center-of-mass energy and luminosity hasbeen given in Table I. It has shown that the bounds on the anomalous couplings do notvirtually change when Q max increases. Therefore, we can understand that the large valuesof Q max do not bring an important contribution to obtain sensitivity limits on the anomalouscouplings [5, 6, 66].In Tables II-IV, we show 95% C.L. sensitivity bounds of the coupling a τ and d τ for varioussystematic uncertainties, integrated CLIC luminosities and center of mass energies. Whilecalculating the table values, we assumed that at a given time, only one of the anomalouscouplings deviated from the SM. In Fig. 5, we demonstrate the sensitivity contour plot at95% C.L. for the anomalous couplings F and F at the √ s = 0 .
5, 1 . e + e − → e + γ ∗ γ ∗ e − → e + τ ¯ τ e − . III. CONCLUSIONS
The CLIC as a γ ∗ γ ∗ collider using the Weizsacker-Williams virtual photon fields of the e − and e + provides an ideal venue to investigate the electromagnetic moments of the taulepton. For this reason, we have studied the potential of e + e − → e + γ ∗ γ ∗ e − → e + τ ¯ τ e − at the CLIC to examine the anomalous magnetic and electric dipole moments of the tau5epton. The findings of this study show that the CLIC can improve the sensitivity boundson anomalous couplings electromagnetic dipole moments of tau lepton with respect to theLEP bounds. 6
1] J. Schwinger, Phys. Rev. 73 (1948) 416, Phys. Rev. 76 (1949) 790.[2] J. Beringer et al. , (Particle Data Group), Journal of Phy. G 86 (2012) 581651.[3] M. A. Samuel, G. Li and R. Mendel, Phys. Rev. Lett. 67 (1991) 668 ; Erratum ibid. 69 (1992)995.[4] F. Hamzeh and N. F. Nasrallah, Phys. Lett. B 373 211 (1996).[5] L3 Collaboration, M. Acciarri et al., Phys. Lett. B 434 (1998) 169.[6] OPAL Collaboration, K. Ackerstaff et al., Phys. Lett. B 431 (1998) 188.[7] DELPHI Collaboration, J. Abdallah et al., Eur. Phys. J. C 35 (2004) 159.[8] J. H. Christenson, J. W. Cronin, V. L. Fitch and R. Turlay, Phys. Rev.Lett. 13, 138 (1964);C. Jarlskog, Editor, CP Violation, 3 of Advanced Series on Directions in High Energy Physics,World Scientific, Singapore, (1989).[9] M. Kobayashi and T. Maskawa, Prog. Teor. Phys. 49 (1973) 652.[10] F. Hoogeveen, Nucl. Phys. B 341 (1990) 322.[11] S. M. Barr and W. J. Marciano, Electric Dipole Moments, in CP Violation, edited by C.Jarlskog, page 455, World Scientific, Singapore, (1989).[12] J. P. Ma and A. Brandenburg, Z. Phys. C 56 (1992) 97.[13] S. M. Barr, Phys. Rev. D 34 (1986) 1567.[14] J. Ellis, S. Ferrara and D.V. Nanopulos, Phys. Lett. B 114 (1982)231.[15] J. C. Pati and A. Salam, Phys. Rev. D 10 (1974) 275.[16] A. Gutirrez-Rodrguez, M. A. Hernndez-Ruz and L.N. Luis-Noriega, Mod.Phys.Lett. A 19(2004) 2227.[17] S. Weinberg, Phys. Rev. Lett. 37 (1976) 657.[18] S. M. Barr and A. Zee, Phys. Rev. Lett. 65 (1990) 21.[19] S. Atag and A. Billur, JHEP 11 (2010) 060.[20] G. A. Gonzalez-Sprinberg, A. Santamaria, J. Vidal, Nucl.Phys.B 582 (2000) 3.[21] T. Ibrahim and P. Nath, Phys. Rev. D 81 (2010) 033007.[22] A. Gutierrez-Rodriguez, M. A. Hernandez-Ruiz and M. A. Perez, Int. J. Mod. Phys. A 22(2007) 3493.[23] A. Gutierrez-Rodriguez, Mod. Phys. Lett. A 25 (2010) 703. et al. , CLIC e + e − Linear Collider Studies, arXiv:1208.1402.[34] K. Seidel et al. , arXiv:1303.3758.[35] L. Xiao-Zhou et al. , Phys. Rev. D 87 (2013) 056008.[36] P. Lebrun et al. , The CLIC Programme: Towards a Staged e+e- Linear Collider Exploringthe Terascale : CLIC Conceptual Design Report, arXiv:1209.2543.[37] M. Battaglia et al. , JHEP 0507 (2005) 033.[38] A. Senol, Phys. Rev. D 85 (2012) 113015[39] A. Ozansoy and A.A. Billur Phys.Rev. D 86 (2012) 055008.[40] S. O. Kara et al. , JHEP 1108 (2011) 072.[41] O.Cakir and K.O.Ozansoy, Europhys.Lett. 83 (2008) 51001.[42] T. Han, Y.-P. Kuang and B. Zhang, Phys.Rev.D 73 (2006)055010.[43] L. A. Anchordoqui et al.
Phys.Rev.D 83 (2011) 106006.[44] D. Lopez-Val, J. Sola and N. Bernal, Phys.Rev.D 81 (2010) 113005.[45] O. Cakir, I. T. Cakir, A. Senol and A. T. Tasci, Eur. Phys. J. C 70 (2010) 295-303.[46] R. N. Hodgkinson, D. Lopez-Val and J. Sola, Phys. Lett. B 673 (2009) 47-56.[47] E. R. Barreto, Y. A. Coutinho and J. S Borges, Phys. Lett. B 632 (2006)675-679.[48] F. del Aguila and J. A. Aguilar-Saavedra, JHEP 0505 (2005) 026.[49] J.E. Cieza Montalvo, G.H. Ramrez and M.D. Tonasse, Eur. Phys. J. C 72 (2012) 2210.[50] P. Jankowski, M. Krawczyk and A. De Roeck, 2000, DESY 123F, arXiv:hep-ph/0002169.[51] The CLIC Programme: towards a staged e + e − Linear Collider exploring the Terascale, CLIC onceptual Design Report, edited by P. Lebrun, L. Linssen, A. Lucaci-Timoce, D. Schulte, F.Simon, S. Stapnes, N. Toge, H. Weerts, J. Wells, CERN-2012-005.[52] I. F. Ginzburg, G. L. Kotkin, S. L. Panfil, V. G. Serbo and V. I. Telnov, Nucl. Instrum. Meth.A 219 (1984) 5.[53] I. F. Ginzburg, G. L. Kotkin, V. G. Serbo and V. I. Telnov, Nucl. Instrum. Meth. 205 (1983)47.[54] G. Baur et al. , Phys. Rep. 364 (2002) 359.[55] V. Budnev et al. , Phys. Rep. 15C (1975) 181.[56] V. M. Budnev, I. F. Ginzburg, G. V. Meledin and V. G. Serbo, Phys. Rep. 15 (1975) 181.[57] K. Piotrzkowski, Phys. Rev. D 63 (2001) 071502.[58] H. Murayama and M. E. Peskin, Ann. Rev. Nucl. Part. Sci. 46 (1996) 533-608.[59] S. Atag, S. C. ˙Inan and ˙I. S¸ahin, Phys. Rev. D 80 (2009) 075009.[60] ˙I. S¸ahin and S. C. ˙Inan, JHEP 09 (2009) 069.[61] S. C. ˙Inan, Phys. Rev. D 81 (2010) 115002.[62] E. Chapon, C. Royon and O. Kepka, Phys. Rev. D 81 (2010) 074003.[63] ˙I. S¸ahin and M. K¨oksal, JHEP 11 (2011) 100.[64] S. C. ˙Inan and A. Billur, Phys. Rev. D 84 (2011) 095002.[65] R. S. Gupta, Phys. Rev. D 85 (2012) 014006.[66] ˙I. S¸ahin, Phys. Rev. D 85 (2012) 033002.[67] L. N. Epele et al. , Eur. Phys. J. Plus 127 (2012) 60.[68] ˙I. S¸ahin and B. S¸ahin, Phys. Rev. D 86 (2012) 115001.[69] A. A. Billur, Europhys. Lett. 101 (2013) 21001.[70] C. Carimalo, P. Kessler and J. Parisi, Phys.Rev. D 20 (1979) 1057.[71] CDF Collaboration, A. Abulencia et al. , Phys. Rev. Lett. 98 (2007) 112001.[72] CDF Collaboration, T. Aaltonen et al. , Phys. Rev. Lett. 102 (2009) 222002.[73] CDF Collaboration, T. Aaltonen et al. , Phys. Rev. Lett. 102 (2009) 242001.[74] CMS Collaboration, S. Chatrchyan et al. , JHEP 1201 (2012) 052.[75] CMS Collaboration, S. Chatrchyan et al. , JHEP 1211 (2012) 080.[76] D0 Collaboration, V. M. Abazov et al. , Phys.Rev. D 88 (2013) 012005.[77] CMS Collaboration, S. Chatrchyan et al. , JHEP 07 (2013) 116.[78] A. Pukhov et al., Report No. INP MSU 98-41/542; arXiv: hep-ph/9908288; rXiv:hep-ph/0412191.[79] L3 Collaboration, Phys. Lett. B 585 (1998) 53. σ ( pb ) F √ s=0.5 TeV √ s=1.5 TeV √ s=3 TeV 0 5 10 15 20 25 -0.04 -0.02 0 0.02 0.04 σ ( pb ) F √ s=0.5 TeV √ s=1.5 TeV √ s=3 TeV FIG. 1: The integrated total cross-section of the process e + e − → e + γ ∗ γ ∗ e − → e + τ ¯ τ e − as a functionof anomalous couplings F and F for three different center-of-mass energies. σ ( pb ) F Q =2 GeV Q =16 GeV Q =64 GeV σ ( pb ) F Q =2 GeV Q =16 GeV Q =64 GeV FIG. 2: The total cross section as a function of F and F for different values of Q at the centerof mass energy √ s = 0 . e + e − → e + γ ∗ γ ∗ e − → e + τ ¯ τ e − .Fig. σ ( pb ) F Q =2 GeV Q =16 GeV Q =64 GeV σ ( pb ) F Q =2 GeV Q =16 GeV Q =64 GeV FIG. 3: The same as Fig. 2 but for √ s = 1 . σ ( pb ) F Q =2 GeV Q =16 GeV Q =64 GeV σ ( pb ) F Q =2 GeV Q =16 GeV Q =64 GeV FIG. 4: The same as Fig. 2 but for √ s = 3 TeV. s=0.5 TeV √ s=1.5 TeV √ s=3 TeV-0.008 -0.006 -0.004 -0.002 0 0.002F -0.004-0.002 0 0.002 0.004 F FIG. 5: The contour plot for the upper bounds of the anomalous couplings F and F with 95%C.L. at the √ s = 0 .
5, 1 . e + e − → e + γ ∗ γ ∗ e − → e + τ ¯ τ e − . ABLE I: The sensitivity limits on the anomalous couplings a τ and d τ for different values of photonvirtuality, center-of-mass energy and luminosity. Q max ( GeV ) √ s ( T eV ) Luminosity(fb − ) a τ d τ ( e, cm )2 0 . − . , . . × − . − . , . . × − − . , . . × − − . , . . × −
16 0 . − . , . . × −
16 0 . − . , . . × −
16 3 200 ( − . , . . × −
16 3 590 ( − . , . . × −
64 0 . − . , . . × −
64 0 . − . , . . × −
64 3 200 ( − . , . . × −
64 3 590 ( − . , . . × − ABLE II: 95% C.L. sensitivity bounds of the coupling a τ and d τ for various integrated CLICluminosities and systematic uncertainties at the √ s = 0 . − ) δ sys a τ d τ ( e, cm )50 δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × − δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × − δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × −16
10 ( − . , . . × −16 ABLE III: 95% C.L. sensitivity bounds of the coupling a τ and d τ for integrated CLIC luminositiesand various systematic uncertainties at the √ s = 1 . − ) δ sys a τ d τ ( e, cm )100 δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × − δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × − δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × −16
10 ( − . , . . × −16 ABLE IV: 95% C.L. sensitivity bounds of the coupling a τ and d τ for integrated CLIC luminositiesand various systematic uncertainties at the √ s = 3 TeV.Luminosity(fb − ) δ sys a τ d τ ( e, cm )200 δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × − δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × − δ sys = 0 ( − . , . . × − δ sys = 0 .
02 ( − . , . . × − δ sys = 0 .
05 ( − . , . . × − δ sys = 0 .
10 ( − . , . . × −16