Lepton flavor violating Higgs couplings and single production of the Higgs boson via e γcollision
aa r X i v : . [ h e p - ph ] J un Lepton flavor violating Higgs couplings and single production ofthe Higgs boson via eγ collision Chong-Xing Yue , Cong Pang and Yu-Chen Guo
Department of Physics, Liaoning Normal University, Dalian 116029, P. R. China ∗ Abstract
Taking into account of the constraints on the lepton flavor violation (LFV) couplings of thestandard model (SM) Higgs boson H with leptons from low energy experiments and the recentCMS results, we investigate production of the SM Higgs boson associated with a lepton τ via eγ collision at the ILC and LHeC experiments. The production cross sections are calculated,the LFV signals and the relevant SM backgrounds are examined. The LFV signals of the SMHiggs boson might be observed via eγ collision in future ILC experiments. PACS numbers: 12.15.-y, 14.80.Bn ∗ Electronic address: [email protected] . Introduction During the past decades, neutrino oscillation experiments have provided us with veryconvincing evidence that neutrinos are massive particles mixing with each other [1, 2],which means that lepton flavor is not an exact symmetry and lepton flavor violating(LFV) processes exist in nature. However, in the standard model (SM), these processesare strongly suppressed by GIM mechanism, making them unobservable at current orplanned experiments. Thus, LFV processes provide one of the most interesting probesto physics beyond the SM and the detection of any LFV process would provide a clearevidence of new physics. This fact gives us a strong motivation to search for charged LFV.For example, the LHC has given some of upper limits on the lepton number violation [3]though at this moment more stringent limits are given by Belle Collaboration.At present, it is widely believed that the recently discovered scalar particle at the LHC[4, 5] behaves as the SM Higgs boson related to the mechanism of electroweak symmetrybreaking. The newly values of its mass are M
AT LASH = 125.5 ± CMSH =125.7 ± σ in the2earch for the LFV decay H → µτ [12]: Br ( H → µτ ) = (0 . +0 . − . )% , (1)where the final state is a sum of µ + τ − and µ − τ + . Certainly, this recent hint, whichalthough has received amount of attention in the literature [13, 14], needs to be confirmedor rejected with more data by both ATLAS and CMS experiments at the LHC run II.The proposed international linear collider (ILC) [15], which is an e + e − collider withhigh energy and luminosity, has particularly clean environment and will provide an op-portunity for high precision measuring various observables related the SM Higgs boson,gauge bosons and fermions, and further detecting new physics effects. Such a machine iswell suited to an in-depth analysis of elementary particle interactions within and beyondthe SM. The potential of the ILC can be further enhanced by considering γγ and eγ col-lisions with the photon beam generated by the backward Compton scattering of incidentelectron- and laser-beams [16, 17]. The high energy γγ or eγ collider might provide us agood chance to precision test the SM and further to search new particles.The proposed large hadron electron collider (LHeC) can be realized by colliding theexisting 7 TeV proton beam with E e = 50 ∼
200 GeV electron (positron) beam and itsanticipated integrated luminosity is about at the order of 10 ∼
100 fb − [18]. The LHeCcan provide better condition for studying a lot of phenomena comparing to the ILC dueto the high center-of-mass (c. m.) energy and to the LHC due to more clear environment.Thus, it may play a significant role in the discovery of new physics beyond the SM.The LHeC can also be transformed to eγ collision with the photon beam radiated fromproton and the radiating proton remaining intact; thus providing an extra experimentalhandle(forward proton tagging) to help reduce the background [19]. Despite a loweravailable luminosity, eγ collision occurs under better known initial conditions, with fewerfinal states and thus can be studied as a complementary tool to normal ep collision at theLHeC. In this paper, we investigate single production of the SM Higgs boson H via eγ collision processes eγ → ℓH ( ℓ = µ or τ ) at the ILC and LHeC, which are induced by theLFV couplings Heℓ , and discuss the possibility of detecting its LFV effects.The layout of the present paper is as follows. Taking into account of the constraintsfrom the LFV processes ℓ i → ℓ j γ and ℓ i → ℓ j ℓ k ℓ l on the LFV Higgs couplings Hℓ i ℓ j ,single production of the SM Higgs boson H via eγ collision at the ILC and LHeC are3alculated in sections 2 and 3, respectively. The relevant signals and backgrounds arediscussed in these two sections. Our conclusions are given in section 4.
2. LFV production of the SM Higgs boson H via eγ collision at the ILC In the mass basis, the couplings of the Higgs boson to charged leptons can be generalwritten as L = − Y ij Hℓ iL ℓ jR + h.c., (2)where i, j = e, µ, τ and in the SM Y ij = m τ /υδ ij with υ =246 GeV. The precision measure-ment data and the experimental upper limits on some LFV processes can give constraintson the Yukawa couplings Y ij . The strongest low-energy constraints on the couplings Y µe , Y τµ and Y τe come from the experimental upper limits on the LFV processes µ → eγ , τ → µγ and τ → eγ [20]. References [8, 9] have shown that the constraint on g µe is muchstronger, and require the branching ratio Br ( H → µe ) to be smaller than 2 × − , whichis not likely to be observed at the LHC. While the constraints on the LFV Higgs couplings g τµ and g τe are weaker, allowing for the branching ratio Br ( H → τ µ ) or Br ( H → τ e ) ashigh as ∼ Br ( H → τ τ ) in the SM. We will therefore notconsider single production of the SM Higgs via the LFV process eγ → µH in this paper.So, only the LFV coupling Hτ e is related our calculation. In our numerical estimation,we will assume p | Y τe | + | Y eτ | ≤ Sℓ i ℓ j via eγ collision atthe ILC has been discussed in SUSY and topcolor theories [21]. From above discussions,we can see that the SM Higgs boson H can be produced in association with a lepton τ via eγ collision mediated by the LFV coupling Hτ e , as shown in Fig.1. The differentialcross section for the subprocess eγ → τ H is expressed bydˆ σ (ˆ s, P e )d cos θ = α e q λ ( m τ ˆ s , m H ˆ s )[ Y τe + Y eτ ][ A − ( A + 4 B ) − Bm τ ˆ s ]32ˆ sA − , (3)where α e is the fine-structure constant, ˆ s is c. m. energy of the subprocess eγ → τ H and θ is the scattering angle of the outgoing lepton τ from the beam direction. A ± =1 + B ± λ / ( m τ ˆ s , m H ˆ s ) cos θ with B = m τ − m H ˆ s and λ ( a, b ) = 1 + a + b − a − b − ab .4 τee H (a) γ ττe H (b) FIG. 1: The Feynman diagrams for the subprocess eγ → τ H . After calculating the cross section ˆ σ (ˆ s ) for the subprocess eγ → τ H , the effectivecross section σ ( s ) at the ILC can be evaluated from ˆ σ (ˆ s ) by convoluting with the photonstructure function f γ/e ( x ) as σ ( s ) = Z x max ( m H + m τ ) /s d xf γ/e ( x ) Z (cos θ ) max (cos θ ) min d cos θ dˆ σ (ˆ s, P e )d cos θ . (4)Where x max = ξ/ (1+ ξ ), x = ˆ s/s , in which √ s is the c. m. energy of the ILC experiments.In order to avoid producing e + e − pairs by the interaction of the incident and backscatteredphotons, there should be ξ ≤ .
8. For ξ = 4 .
8, there is x max ≈ .
83. The photondistribution function f γ/e ( x ) can be expressed as [16] f γ/e ( x ) = 1 D ( ξ ) { (1 − x ) + 11 − x − xξ (1 − x ) + 4 x ξ (1 − x ) } (5)with D ( ξ ) = (1 − ξ − ξ ) ln(1 + ξ ) + 12 + 8 ξ − ξ ) . (6)It is known that the forward and backward directions in eγ collision are blind spots fordetection of scattered particles. To make the scattered particles be detected, we imposethe cut 10 ◦ ≤ θ ≤ ◦ .It is obvious that the effective production cross section σ of the subprocess eγ → τ H depends the two free parameters: the c. m. energy √ s and the LFV Higgs coupling Hτ e .Although some new physics models can not explain the maximal value of the
Hτ e couplinggiven by the experimental upper bounds for the LFV process τ → eγ , it is theoreticalpossible. As numerical estimation, we fix p | Y τe | + | Y eτ | = 0.014. Our numerical resultsare showed in Fig.2, in which we plot the effective cross section σ as a function of the c.m. energy √ s for M H = 125 GeV and m τ = 1 .
777 GeV. One can see from Fig.2 that, in5
00 250 300 350 400 450 5002.02.53.03.54.04.5
GeVs ( f b ) FIG. 2: The production cross section σ of the subprocess eγ → τ H at the ILC as afunction of the center-of-mass (c. m.) energy √ s for p | Y τe | + | Y eτ | = 0.014. the case of considering the bound from the process τ → eγ on the LFV Higgs coupling Hτ e , the values of the cross section σ can reach 4 . ∼ . √ s = 200 ∼
500 GeV.For the SM Higgs boson with M H = 125 GeV, the decay process H → bb is a main decaychannel and its branching ratio is about 58% [22]. Then, the signal final state can be seenas τ bb for the LFV Higgs production via eγ collision at the ILC. For √ s = 200 ∼ ∼ τ bb events to be generated in the future ILC experimentwith the integrated luminosity L int = 340 fb − .The main background for the signal state τ bb comes from the process eγ → W Zν → τ bbνν . Certainly, other processes, such as the SM process eγ → W γν → τ bbνν , can alsocontribute to the background, while their contributions are much smaller than those of eγ → W Zν . To more exactly calculate the background, we use MadGraph5 [23] to writedown all the tree Feynman diagrams for eγ → τ bb ( νν ) and to calculate the contributionsto the background cross section. In our numerical estimation, similarly as above, we usethe spectrum of photons obtained by the laser backscattering technique [16, 17], which isembedded in MadGraph. We find that, for √ s = 200 ∼
500 GeV, the background crosssection is in the range of 1.6 × − ∼ × − fb, before any kinematic cuts applied,which is small enough compare to the signal cross section. The backgrounds can stronglybe suppressed by the invariant mass cut for bb . If we further assume that the tau leptondecays into various hadronic and leptonic modes, the signal and the relevant backgrounds6ould become complex. However, the conclusion that the signal cross section is muchlarger than that for the relevant backgrounds is not changed.
200 250 300 350 400 450 5002.02.53.03.54.04.55.05.56.0
GeVs Y ( x10 - ) SS=3 SS=5
200 250 300 350 400 450 5001.01.52.02.53.03.54.0
GeVs Y ( x10 - ) SS=3 SS=5
FIG. 3: Variation of the LFV
Hτ e coupling Y with the c. m. energy √ s for the ILC experimentswith the integrated luminosity L int = 100 fb − (left) and 340 fb − (right). For the statistical significance, we use the definition SS = S/ √ S + B , where Sand B denote the number of signal and background events. It is obvious that SS is afunction of two parameters, namely the c. m. energy √ s and the LFV Hτ e coupling Y = p | Y τe | + | Y eτ | . Performing the scanning over the parameter space we can derivethe experimental evidence region ( SS ≥
3) and experimental discovery region (( SS ≥ Y = p | Y τe | + | Y eτ | is larger than 1 × − , the future ILCexperiment with the integrated luminosity L int = 340 fb − will produce the experimentalevidence for the LFV Higgs coupling Hτ e .Using the CMS results in the search for the LFV decay H → µτ and other existingstringent experimental limits, Ref.[14] has studied the constraint on the coupling LFV Hτ e . The CMS result p | Y τµ | + | Y µτ | < . × − [12] can give the constraint Y = p | Y τe | + | Y eτ | < . × − . So, even if the CMS result is confirmed in near future, thesignals of the LFV subprocess eγ → τ H might be detected in future ILC experiments.
3. LFV production of the SM Higgs boson via eγ collision at the LHeC α s , the LHeC would allow us to predict new particle productioncross sections with sufficient accuracy to distinguish between different explanations of newphysics phenomena. At the LHeC, a quasi-real photon (with low virtuality Q = − q ) canbe emitted from the proton, which is named intact or forward proton and will be detectedby the forward detectors with very large pseudorapidity. The forward proton detectorsare planned to be built at about 220 m from the ATLAS main detector within the AFPproject [24] and the CMS and TOTEM collaborations plan to use their forward protondetectors located at about the same position (CT-PPS project)[25]. Using these detectors,the relevant photon interactions can be detected with an unprecedented precision.The emitted quasi-real photons can be described in the framework of equivalentphoton approximation (EPA) and show a spectrum of virtuality Q and the energy E γ [26] d N γ d E γ d Q = α e π E γ Q [(1 − E γ E )(1 − Q min Q ) F E + E γ E F M ] (7)with Q min = M p E γ E ( E − E γ ) , F E = 4 M p G E + Q G M M p + Q , (8) G E = G M µ p = (1 + Q Q ) − , F M = G M , Q = 0 . GeV . (9)Where M p is the mass of the proton, E is the energy of the incoming proton beam, whichis related to the photon energy by E γ = ξE . The parameter ξ indicates the fractionalproton momentum loss and is also defined as the forward detector acceptance ξ = ∆ E/E ,in which ∆ E is the loss energy of the emitted proton beam. µ p = 7.78 is the magneticmoment of the proton, F E and F M are functions of the electric and magnetic form factorsgiven in the dipole approximation. Then, the Q integrated photon flux can be writtenas f ( E γ ) = Z Q max Q min d N γ d E γ d Q d Q , (10)8here Q max ≈ ∼ . Since the contribution to the above integral formula isvery small for Q max > , in our numerical calculation, we will approximately take Q max = 2 GeV .
80 120 160 2000.120.140.160.180.20 ( f b ) E e (GeV) FIG. 4: At the LHeC, the production cross section σ of the subprocess eγ → τ H as a functionof the electron beam energy E e for Y = p | Y τe | + | Y eτ | = 0.014, and the detectedacceptance region: 0.0015 ≤ ξ ≤ At the LHeC, the effective production cross section σ ( τ H ) for the subprocess eγ → τ H can be written as σ ( τ H ) = Z ξ max Max ( Z,ξ min ) E d ξf ( ξE ) Z (cos θ ) max (cos θ ) min d cos θ dˆ σ (ˆ s )d cos θ , (11)where ˆ s = 4 E e E γ = ξs with E e = 50 ∼
200 GeV and E = 7 TeV, Z = ( m τ + m H ) /s .Similar as above, we also apply the cut 10 ◦ ≤ θ ≤ ◦ . The intact proton radiatingphoton can not be detected from the central detectors. However, the forward detectorscan detect the particles with large pseudorapidity providing some information on the intactproton. Based on the forward proton detectors to be installed by the CMS-TOTEM andthe ATLAS collaborations, we choose the detected acceptance regions as 0.0015 < ξ < . < ξ < .
15 [24, 25, 27].Our numerical results show that the values of the total cross section σ of the LFVsubprocess eγ → τ H at the LHeC for two detected acceptance regions 0.0015 ∼ ∼ σ as a function of the electron beam9 Ee (GeV) L int =100 fb -1 L int =50 fb -1 L int =10 fb -1 SS FIG. 5: Variation of the significance SS = S/ √ S + B with the electron beam energy E e for different values of the integrated luminosity of the LHeC. energy E e for the values of the parameter ξ in the range of 0.0015 ∼ σ is in the range of 0.12 ∼ E = 7 TeV and E e = 50 ∼
200 GeV. Similarly with that at the ILC, the signal final state of the subprocess eγ → τ H at the LHeC is τ bb . For E = 7 TeV and E e = 50 ∼
200 GeV, there onlywill be several τ bb events to be generated at the LHeC experiment with the integratedluminosity L int = 100 fb − . Though the production rate of the signal is much small, wealso use MadGraph to calculate all the signal and background events generated by eγ collision at the LHeC, based on the basic cuts: p lT > GeV, p bT > GeV, / E T > GeV ,where p T denotes the transverse momentum, / E T is the missing transverse momentumfrom the invisible neutrino in the final state. The significance SS = S/ √ S + B are shownin Fig.5 as a function of the electron beam energy E e for different values of the integratedluminosity of the LHeC. One can see from Fig.5 that, even we take the maximal value ofthe LFV coupling Hτ e , Y = 0 . SS is smaller than 2.5 inmost of the parameter space. Thus, it is very challenge to detect the LFV coupling Hτ e via the process eγ → τ H at the LHeC.
4. Conclusions
The transition from the discovery to precision measurement of Higgs boson physics10as begun. There is great potential for the SM Higgs boson as a future harbinger of newphysics. The LFV Higgs couplings appear quite generally in new physics models. Lowenergy constraints are weak for the LFV Higgs couplings involving τ lepton, so that, withthe LHC data continuing to accumulate, the LFV Higgs signals become experimentallyavailable.The existence of the LFV Higgs couplings is an exciting possibility. Observation ofsuch LFV signals in current or future experiments would provide a clear evidence of newphysics beyond the SM. In this work, considering the low energy constraints on the LFVcouplings Hℓ i ℓ j and the CMS results in the search for the LFV decay H → µτ , we studyproduction of the SM Higgs boson via eγ collision mediated by the LFV coupling Hτ e atthe ILC and LHeC experiments. Our numerical results show that the signal final state τ bb is almost background free, which should be detected in future ILC experiments. Theproduction cross section of the subprocess eγ → τ H at the LHeC is much small, which isvery challenge to be detected at the LHeC. Acknowledgments
This work was supported in part by the National Natural Science Foundationof China under Grant No. 11275088, the Natural Science Foundation of the LiaoningScientific Committee (No. 2014020151). [1] K. Olive et al.[Particle Data Group Collaboration], Chin.Phys. C38 (2014) 090001.[2] D. Forero, M. Tortola, J. Valle, Phys. Rev. D 86 (2012) 073012; F. Capozzi et al., Phys.Rev. D 89 (2014) 093018.[3] R. Aaij et al. [LHCb Collaboration], Phys. Lett. B 724 (2013) 36.[4] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 716 (2012) 1.[5] S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B 716 (2012) 30.[6] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 726 (2013) 88.[7] S. Chatrchyan et al. [CMS Collaboration], JHEP 1306 (2013) 081.
8] S. Davidson and P. Verdier, Phys. Rev. D 86 (2012) 111701; A. Celis, V. Cirigliano and E.Passemar, Phys. Rev. D 89 (2014) 013008; S. Bressler, A. Dery and A. Efrati, Phys. Rev.D 90 (2014) 015025.[9] G. Blankenburg, J. Ellis and G. Isidori, Phys. Lett. B 712 (2012) 386; A. Arhrib, Y. Cheng,Otto C. W. Kong, Phys. Rev. D87 (2013) 015025; R. Harnik, J. Kopp and J. Zupan, JHEP1303 (2013) 026; A. Dery, A. Efrati, Y. Hochberg and Y. Nir, JHEP 1305 (2013) 039.[10] P. T. Giang, L. T. Hue, D. T. Huong, and H. N. Long, Nucl. Phys. B864 (2012) 85; M.Arana-Catania, E. Arganda, and M J. Herrero, JHEP 1309 (2013) 160; C. G. Cely, A.Ibarra, E. Molinaro, and S. T. Petcov, Phys. Lett. B 718 (2013) 957; A. Falkowski, D. M.Straub, and A. Vicente, JHEP 1405 (2014) 092.[11] J. Kopp, M. Nardecchia, JHEP 1410 (2014) 156; A. Dery, A. Efrati, Y. Nir, Y. Soreq, V.Susiˇc, Phys. Rev. D90 (2014) 115022; E. Mart´ınez-Pascual, J. J. Toscano, arXiv:1408.3307[hep-ph]; D. A. Sierra, and A. Vicente, Phys. Rev. D90(2014)115004; D. Dasa, A. Kundub,arXiv:1504.01125 [hep-ph].[12] V. Khachatryan et al.[CMS Collaboration], arXiv:1502.07400 [hep-ex].[13] M. D. Campos, A. E. C. Hern´andez, H. P¨as, E. Schumacher, M. A. L´opez-Osorio,arXiv:1408.1652 [hep-ph]; A. Celis, V. Cirigliano, and E. Passemar, arXiv:1409.4439 [hep-ph]; D. A. Sierra and A. Vicente, Phys. Rev. D90 (2014) 115004; C.-J. Lee and J. Tandean,JHEP 1504 (2015) 174; J. Heeck, M. Holthausen, W. Rodejohann, and Y. Shimizu, Nucl.Phys. B896 (2015) 281; A. Crivellin, G. D’Ambrosio, and J. Heeck, Phys. Rev. Lett. 114(2015) 151801; L. de Lima, C. S. Machado, R. D. Matheus, and L. A. F. d. Prado,arXiv:1501.06923 [hep-ph]; Y. Omura, E. Senaha, and K. Tobe, JHEP 1505 (2015) 028;A. Crivellin, G. D’Ambrosio, and J. Heeck, Phys. Rev. D91 (20015) 075006.[14] I. Dorsner et al., arXiv:1502.07784 [hep-ph].[15] T. Behnke et al., arXiv: 1306.6327[physics.acc-ph]; H. Baer et al., arXiv: 1306.6352[hep-ph].[16] I. F. Ginzburg, G. L. Kotkin, V. G. Serbo and V. I. Telnov, Nucl. Instr. and Meth. 205(1983) 47; I. F. Ginzburg, G. L. Kotkin, S. L. Panfil, V. G. Serbo and V. I. Telnov, Nucl.Instr. And Meth. 219 (1984) 5; V. I. Telnov, Nucl. Phys. Proc. Suppl. 82 (2000) 359.[17] D. V. Soa et al., Mod. Phys. Lett. A 27 (2012) 1250126; J. P. Delahaye, Mod. Phys. Lett.A 26 (2011) 2997.
18] J. L. Abelleira Fernandez et al. [LHeC Study Group Collaboration], J. Phys. G 39 (2012)075001; J. L. Abelleira Fernandez et al., arXiv:1211.4831 [hep-ex]; arXiv:1211.5102 [hep-ex];O. Bruening and M. Klein, Mod. Phys. Lett. A 28 (2013) 1330011.[19] M. G. Albrow et al., arXiv:hep-ph/0609209; J. de Favereau de Jeneret et al,arXiv:0908.2020; R. Staszewski (ATLAS Collaboration), Acta Physica Polonica B 42 (2011)1615; C. Royon, arXiv:1302.0623; M. Tasevsky, Int. J. Mod. Phys. A29 (2014) 1446012; AIPConf. Proc. 1654 (2015) 090001.[20] J. Adam et al. [MEG Collaboration], Phys. Rev. Lett. 110 (2013) 201801; B. Aubert et al.[BaBar Collaboration], Phys. Rev. Lett. 104 (2010) 021802.[21] S. Kanemura, K. Tsumura, Phys. Lett. B674 (2009) 295; Chong-Xing Yue, Hui-Di Yang,Hao-Lin Feng, J. Phys. G37 (2010) 015006.[22] S. Dittmaier et al. [LHC Higgs Cross Section Working Group], arXiv:1201.3084[hep-ph].[23] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, JHEP 1106 (2011) 128.[24] ATLAS collaboration, CERN-LHCC-2011-012, Letter of intent, Phase-I upgrade.[25] CMS and TOTEM collaboration, CERN-LHCC-2014-021, CMS-TOTEM Precision ProtonSpectrometer,[26] V. M. Budnev, I. F. Ginzburg, G. V. Meledin and V. G. Serbo, Phys. Rep. 15 (1975) 181;K. Piotrzkowski, Phys. Rev. D 63 (2001) 071502; G. Baur, K. Hencken, D. Trautmann, S.Sadowsky, and Y. Kharlov, Phys. Rep. 364 (2002) 359.[27] V. Avati and K. Osterberg, Report No. CERN-TOTEM-NOTE-2005-002, 2006; C. Royon(RP220 Collaboration), arXiv:0706.1796; O. Kepka and C. Royon, Phys. Rev. D 78 (2008)073005; M. G. Albrow et al. (FP420 R and D Collaboration), JINST 4 (2009) T10001.18] J. L. Abelleira Fernandez et al. [LHeC Study Group Collaboration], J. Phys. G 39 (2012)075001; J. L. Abelleira Fernandez et al., arXiv:1211.4831 [hep-ex]; arXiv:1211.5102 [hep-ex];O. Bruening and M. Klein, Mod. Phys. Lett. A 28 (2013) 1330011.[19] M. G. Albrow et al., arXiv:hep-ph/0609209; J. de Favereau de Jeneret et al,arXiv:0908.2020; R. Staszewski (ATLAS Collaboration), Acta Physica Polonica B 42 (2011)1615; C. Royon, arXiv:1302.0623; M. Tasevsky, Int. J. Mod. Phys. A29 (2014) 1446012; AIPConf. Proc. 1654 (2015) 090001.[20] J. Adam et al. [MEG Collaboration], Phys. Rev. Lett. 110 (2013) 201801; B. Aubert et al.[BaBar Collaboration], Phys. Rev. Lett. 104 (2010) 021802.[21] S. Kanemura, K. Tsumura, Phys. Lett. B674 (2009) 295; Chong-Xing Yue, Hui-Di Yang,Hao-Lin Feng, J. Phys. G37 (2010) 015006.[22] S. Dittmaier et al. [LHC Higgs Cross Section Working Group], arXiv:1201.3084[hep-ph].[23] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, JHEP 1106 (2011) 128.[24] ATLAS collaboration, CERN-LHCC-2011-012, Letter of intent, Phase-I upgrade.[25] CMS and TOTEM collaboration, CERN-LHCC-2014-021, CMS-TOTEM Precision ProtonSpectrometer,[26] V. M. Budnev, I. F. Ginzburg, G. V. Meledin and V. G. Serbo, Phys. Rep. 15 (1975) 181;K. Piotrzkowski, Phys. Rev. D 63 (2001) 071502; G. Baur, K. Hencken, D. Trautmann, S.Sadowsky, and Y. Kharlov, Phys. Rep. 364 (2002) 359.[27] V. Avati and K. Osterberg, Report No. CERN-TOTEM-NOTE-2005-002, 2006; C. Royon(RP220 Collaboration), arXiv:0706.1796; O. Kepka and C. Royon, Phys. Rev. D 78 (2008)073005; M. G. Albrow et al. (FP420 R and D Collaboration), JINST 4 (2009) T10001.