New Physics at 1 TeV?

Transcription

1 Pis ma v ZhETF, vol. 103, iss. 9, pp c 016 May 10 New Physics at 1 TeV?. I. Godunov + 1), A. N. Rozanov, M. I. Vysotsky + 1), E. V. Zhemchugov + 1) + Institute for Theoretical and Experimental Physics, Moscow, Russia Novosibirsk tate University, Novosibirsk, Russia The Center for Particle Physics of Marseilles, CPPM-INP3-CNR-AMU, F-1388, Marseille, France Moscow Institute of Physics and Technology, Dolgoprudny, Russia Moscow Engineering Physics Institute, Moscow, Russia ubmitted 4 April 016 If decays of a heavy particle are responsible for the diphoton excess with invariant mass 750 GeV observed at the 13 TeV LHC run, it can be easily accomodated in the tandard Model. Two scenarios are considered: production in gluon fusion through a loop of heavy isosinglet quark(s) and production in photon fusion through a loop of heavy isosinglet leptons. In the second case many heavy leptons are needed or/and they should have large electric charges in order to reproduce experimental data on σ pp X Br( γγ). DOI: /037074X Introduction. ATLA and CM collaborations recently announced a small enhancement over smooth background of two photon events with invariant mass 750 GeV [1, ]. Though statistical significance of this enhancement is not large (within 3 standard deviations), it induced a whole bunch of theoretical papers devoted to its interpretation. The reason for this explosive activity is clear: maybe the tandard Model of Particle Physics is changed at one TeV scale, and we are witnessing the first sign of this change. Let us suppose that the observed enhancement is due to the γγ decay of a new particle. Then it should be a boson with spin different from one; the simplest possibility is a scalar particle with m = 750 GeV. ince it decays to two photons, it should be an U(3) c singlet, and in pp-collisions at the LHC it can be produced in gluon-gluon fusion through the loop of colored particles and in photon-photon fusion through the loop of charged particles. Let us suppose that particles propagating in the loops are heavy, and decays to them are kinematically forbidden. ) Production cross section is evidently larger in the case of gluon fusion, however γγ branching ratio is suppressed in this case since gg decay dominates. We suppose that the particles propagating in the loop are Dirac fermions, so they have tree level masses, and that they are U() L singlets. Nonzero hyper- 1) sgodunov@itep.ru; vysotsky@itep.ru; zhemchugov@itep.ru ) In the opposite case Br( γγ) reduces significantly which makes γγ decays unobservable at the LHC. Письма в ЖЭТФ том 103 вып charges provide couplings of these particles with photon and Z-boson. These particles can be quark(s) (color triplets) T i or lepton(s) (color singlets) L i. They couple with by Yukawa interactions with coupling constants λ i T and λi L correspondingly. In ect. we will consider production and decay in the model with extra heavy quark(s), in which gluon fusion dominates production; in ect. 3 we will consider the model with extra heavy lepton(s), where production occur in photon fusion, and γγ decay dominates.. Quarkophilic. In the case of one heavy quark T the following terms should be added to the tandard Model lagrangian: L = 1 ( µ) 1 m + Tγ µ ( µ i g sa i µλ i ig Y ) T B µ T+m T TT+λT TT, (1) where A i µ and B µ are gluon and U(1) gauge fields respectively, and λ i are Gell-Mann matrices. coupling with gluons is generated by the T-quark loop: M gg = α s λ T F(β)G (1) 6π m T µν G() µν, () where β = (m T /m ), F(β) = 3 [ ] β 1 (β 1)arctan 1, (3) β 1 and F(β) 1 for m T m.

2 636. I. Godunov, A. N. Rozanov, M. I. Vysotsky, E. V. Zhemchugov Inclusive cross section of production in pp collision at the LHC through gluon fusion is given by: ( ) σ pp X = α s λt F(β) m 576π m T dl gg dŝ ŝ=m, (4) where the so-called gluon-gluon luminosity is given by the integral over gluon distributions: dl gg dŝ = 1 s ln τ 0 g( τ0 e y,q )g( τ 0 e y,q )dy, (5) ln τ 0 τ 0 = ŝ/s, s = (13 TeV), and we use Q = m. In Fig. 1 the corresponding Feynman diagram is shown. In- four orders of magnitude smaller than the 45 GeV width which (maybe) follows from the preliminary ATLA data. Thus we conclude that for the models we consider, width should be much smaller than 45 GeV. Let us note that CM data prefer narrow ; see also [6]. T-quark loop contributes to γγ decay as well (see Fig. ). The corresponding matrix element equals M γγ = α 3π λ T m T F(β)F (1) µν F() µν 3 cq T, (8) where the factor 3 c corresponds to the three colors, and Q T is the T-quark electric charge. For γγ width we get: ( α ) (3c Γ γγ = Q 3π T) m3 λ T 16πm F(β) kev, T (9) and ( ) α (3 c Q T Br( γγ) ) α s , (10) where we substituted Q T = /3 and α = 1/15. 3) Finally, from (10) and (6) we obtain: σ pp X Br( γγ) 0.8 fb. (11) Fig. 1. Feynman diagram of production tegrating gluon distributions from [3] for ŝ = 750 GeV, s = 13 TeV, we get dlgg /dŝ 4.0 nb, m dl gg/dŝ (1/0.69 nb) 4.0 nb 5.8. At s = 8 TeV for ŝ = = 750 GeV the luminosity dl gg /dŝ, and therefore cross section (4), is 4.6 times smaller. In order to take into account gluon loop corrections, (4) should be multiplied by the so-called K-factor which is close to for s = 13 TeV, according to [4] (see also Fig. in [5]). Fig.. Feynman diagram of γγ decay In this way for m T = m and λ T = 1, substituting α s (m ) = 0.090, we obtain: σ pp X 41 fb, (6) which should be multiplied by Br( γγ) in order to be compared with experimental observations [1, ]. Total width of is dominated by the gg decay, and from () we get: Γ gg = ( αs ) m 3 8 λ T 6π 16πm F(β) 3.1 MeV, (7) T Experimental data provides a value approximately 36 times larger: [σ pp X Br( γγ)] exp 10 fb, (1) since with 3 fb 1 luminosity collected by each collaboration at 13 TeV and effectivity of γγ registration ε 0.5 [1] they see about 15 events each. In order to reproduce experimental result (1) we should suppose that six T-quarks exist. In this case Γ gg = MeV 110 MeV, Br( γγ) remains the same, while the cross section of production (6) should be multiplied by the same factor 36, and (1) is reproduced. 4) However, unappealing multiplication of the number of T-quarks can be avoided. For m T = 400 GeV we have F(β) = 1.36 andσ pp X Br( γγ) is5.7 times larger than what is given in (11). Thus for λ T =.5 we reproduce the experimental number. 5) In Fig. 3 isolines of the product σ pp X Br( γγ) are shown on (λ T,m T ) plot. 3) Fine structure constant should be substituted by its running value at q = m, α(m ) = 1/15. 4) If at one TeV scale we have a mirror image of the tandard Model with three vector-like generations of quarks and leptons, then experimental result (1) will be reproduced. 5) As far as λ T /4π is a parameter of perturbation theory, this value of λ T is close to the maximum allowed value in order for the perturbation theory to make sense. Письма в ЖЭТФ том 103 вып

3 New Physics at 1 TeV? 637 well below experimental upper bound which, according to Fig. 11 from [8], equals 4 fb/(br(z l)) = 400 fb at σ (see also [9]). Gluon-gluon luminosity is 4.6 times smaller at 8 TeV, so we get (taking into account energy dependence of the K-factor as well) [σ pp X Br( ZZ)] 8 TeV < 9.0 fb, (17) Fig. 3. Contour plot of σ pp X Br( γγ) In the following we consider the model with one additional quark T and m T = 400 GeV, λ T =.5. (13) can mix with the tandard Model Higgs boson due to renormalizable interaction term µφ Φ, where Φ is the Higgs isodoublet. uch an extension of the tandard Model was studied in our recent paper [7]. Doublet admixture in the 750 GeV boson wave function results in tree level decays WW, ZZ, t t and hh, where h is the 15 GeV Higgs boson. According to Eqs. (16) (0) from [7], the sum of these widths equals approximately sin α m 3 /8πv Φ sin α 300 GeV, where α is the mixing angle, and v Φ = 46 GeV is the Higgs boson vacuum expectation value. Ratio of partial widths at small α is Γ WW : Γ ZZ : Γ hh : 1 : 1. (14) As a result, width grows and Br( γγ) diminishes correspondingly. Thus, experimental result (1) will not be reproduced. To reduce this effect we should make the mixing angle α small enough. For example, for sinα < 1/150 we obtain at most 1 MeV (or 11%) increase of the width of, which is acceptable. According to Eq. (7) from [7], sinα µ v Φ m, (15) and it is less than 1/150 for µ below 15 GeV. Let us check if ZZ decays do not exceed experimental bounds on their relative probability obtained at 13 and 8 TeV at the LHC. ince Br( ZZ) is below.3 10, we obtain [σ pp X Br( ZZ)] 13 TeV < 33 fb, (16) which should be compared with 60 fb experimental upper bound (Fig. 1 from [10]). More stringent upper bound comes from the search of hh decays [11] and equals 40 fb, while in our case the cross section does not exceed 10 fb. ince as it has just been written above, at s = = 8 TeV the gluon-gluon luminosity is 4.6 times smaller that at s = 13 TeV, the CM bound from Run 1 [1] [σ pp X Br( γγ)] 8 TeV < 1.5 fb (18) is (almost) not violated in the model considered. It is natural to suppose that T-quark mixes with u-, c-, and t-quark which makes it unstable. To avoid LHC Run 1 bounds on m T following from the search of the decays T Wb, T Zt, and T Ht [13 15] which exclude T-quark with mass below 700 GeV, we suppose that T t mixture is small, and T-quark mixing with u- and c-quarks dominates. In this case bounds [13 15] are avoided [16]. Concerning decays, let us note that the dominant gg decay is hidden by the two jets background produced by strong interactions. At 8 TeV LHC energy the following upper bound was obtained [17]: [σ pp X Br( gg)] exp 8 TeV < 30 pb. (19) In our model Br( gg) 1. From Eq. (4), using gluon-gluon luminosity at s = 8 TeV, parameters from Eq. (13), and K-factor.5 [4, 5], we get [σ pp X ] theor 0.39 pb, Br( gg) 1, (0) two orders of magnitude smaller than the upper bound (19). Three modes of decays to neutral vector bosons do exist and have the following hierarchy: Γ γγ : Γ Zγ : Γ ZZ = 1 : (s W /c W ) : (s W /c W ) 4, (1) where s W (c W ) is the sine (cosine) of electroweak mixing angle. 6) Thus if γγ decays will be observed in future Run data, γz and ZZ decays should be also looked for. 6) In (1) we suppose that mixing of with Higgs doublet is negligible; in the opposite case Γ ZZ can exceed Γ γγ. Письма в ЖЭТФ том 103 вып

4 638. I. Godunov, A. N. Rozanov, M. I. Vysotsky, E. V. Zhemchugov If the existence of will be confirmed with larger statistics at the LHC, then it can be studied at e + e - colliders as well. For the cross section of two-photon production in the reaction e + e e + e, according to [18, Eq. (48.47)], [19], we have: [ where f ( m s f(z) = σ ee ee (s) = 8α Γ γγ )( ( m ln T s m e m m 3 ) 1 ) 1 ( ) ] s 3 ln3, () m ( 1+ 1 ) z ln 1 z 1 (1 z)(3+z), (3) and Γ γγ is given in Eq. (9). For e + e collider CLIC with s = (3 TeV), substituting in Eqs. (9), () λ T =.5, m T = 400 GeV, α(m ) = 1/15, and F(β) = 1.36 we obtain: σee ee CLIC 0.46 fb. (4) With projected CLIC luminosity L = /(cm sec) [18, p. 393], during one accelerator year (t = = 10 7 sec) about 300 resonances should be produced. 3. Leptophilic. production in γγ fusion will be analyzed in this section (see also [0 ]). Let us suppose that heavy leptons L i which couple to have electric charges Q L, and there are N such degenerate leptons. The lagrangian is similar to that of the heavy quarks case (1): L = 1 ( µ) 1 m + + L i γ µ ( µ ig Y L B µ)l i +m L Li L i +λ L Li L i, (5) where we assume equal lepton masses and couplings. For γγ width we obtain: ( α ) ( ) (NQ Γ γγ = 3π L ) m3 λ L 16πm F(β) ml, β =. L m (6) Production of at the LHC occurs through fusion of two virtual photons emitted by quarks which reside in the colliding protons. Let us estimate the production cross section. For the partonic cross section we get: f( m ŝ σ (γγ) q 1q q 1q ) ( ln( 8α (ŝ) = e 1e Γ γγ m Lŝ Λ QCD m m 3 ) ) 1 1 ( ) ŝ 3 ln3, (7) m where e 1 and e are charges of the colliding quarks, ŝ = x 1 x s τs is the invariant mass of the colliding quarks, and f(z) is given by (3). We should multiply (7) by quark distribution functions and integrate over x 1 and x : = q 1,q 1 (γγ) σ m /s σ (γγ) pp X (s) = q (τs)dτ s dl q 1q 1q q 1q (Q,τ), (8) dŝ where the sum should be performed over valence uu,ud, du, and dd quark collisions, and sea quarks should be taken into account as well. 7) Quark luminosity equals: dl q1q (Q,τ) = 1 dŝ s ln τ ln τ q 1 (x 1,Q )q (x,q )dy, (9) x 1 = τe y, x = τe y. We take Q = m and use quark distributions from [3]. Quark and gluon luminosity functions for s = 13 TeV and s = 8 TeV are shown in Fig. 4. Cross sections in the case of one heavy lepton with charge Q L = 1, Yukawa coupling constant λ L = and mass m L = 400 GeV are shown in Table 1. For Λ QCD = 300 MeV and s = 13 TeV we get σ (γγ) pp X 11 ab, 8) while the experimental result (1) is three orders of magnitude larger. We come to the conclusion that NQ L 30 is needed: we need either 30 leptons with unit charges, or one lepton with charge 6, or several multicharged leptons. 9) It is natural to suppose that leptons with charge one mix with the tandard Model leptons and become unstable. earch for such particles was performed at the LHC, and the lower bound m L > 170 GeV was obtained [4]. ee also [5], where bounds on masses and mixings of L are discussed. For masses above 00 GeV the existence of L is still relatively unconstrained. Cross section for quasielastic production can be estimated with the help of the following equation: [ f ( m s σ pp pp = 8α Γ γγ )( ( s ln m m 3 ) 1 ) 1 ( ) ] s 3 ln3. (30) m 7) uu contribution constitutes 50% of the cross section at s = = 13 TeV with another 4% coming from ud and ūu. 8) According to Eq. (1) from the recent paper [3], this cross section equals 5 ab. 9) If σ (γγ) pp X = 5 ab, then 30 should be replaced with 0. Письма в ЖЭТФ том 103 вып

5 New Physics at 1 TeV? 639 with h(15) is obtained. If heavy leptons L are introduced instead of T, then can be produced at LHC in photon fusion. However, in order to reproduce experimental data many leptons L i are needed and/or they should be multicharged. If the existence of will be confirmed by future data then production of heavy vectorlike quarks and/or leptons at the LHC should be looked for. The search for Zγ,ZZ,WW and hh would be also of great importance..g., M.V. and E.Zh. are partially supported under the grants RFBR # and , and by the Russian Federation Government under the grant Nh G. and E.Zh. are also supported by MK and RFBR # In addition,.g. is supported by RFBR under grant , by Dynasty Foundation and by the Russian Federation Government under Grant # 11.G Fig. 4. (Color online) Luminosities (5), (9) for gluongluon, uu, ud, dd and uū collisions at Q = (750 GeV). (a) s = 13 TeV. (b) s = 8 TeV For s = 13 TeV, λ L = and m L = 400 GeV it equals 4.1 ab. 10) Table 1. Cross sections (in ab) for double photon production in the leptophilic model for different values of Λ QCD and proton collision energies s, TeV ΛQCD, GeV Conclusions. We analyze the possibility that the enhancement at 750 GeV diphoton invariant mass observed by ATLA and CM is due to decays of a new scalar. We found that production of in gluon fusion in a minimal model with one additional heavy Dirac quark T can have value of σ pp X Br( γγ) compatible with data. An upper bound on the mixing of 10) According to Eq. (4) from [3], quasielastic cross section is two times smaller. 1. The ATLA collaboration, ATLA-CONF (015).. The CM collaboration, CM-PA-EXO (015). 3. L. A. Harland-Lang, A. D. Martin, P. Motylinkski, and R.. Thorne, Eur. Phys. J. C 75, 04 (015); arxiv: J. Baglio and A. Djouadi, JHEP 1103, 055 (011); arxiv: R.V. Harlander and W. Kilgol, Phys. Rev. Lett. 88, (00). 6. M.R. Buckley, arxiv: I. Godunov, A. N. Rozanov, M. I. Vysotsky, and E. V. Zhemchugov, Eur. Phys. J. C 76, 1 (016); arxiv: The ATLA collaboration, ATLA-CONF R. Franceschini, G.F. Giudice, J. F. Kamenik, M. Mc- Cullough, A. Pomarol, R. Rattazzi, M. Redi, F. Riva, A. trumia, and R. Torre, arxiv: The ATLA collaboration, Eur. Phys. J. C 76(1), 45 (016); arxiv: The ATLA collaboration, Phys. Rev. D 9, (015); arxiv: The CM collaboration, Phys. Lett. B 750, 494 (015); arxiv: The ATLA collaboration, JHEP 1510, 150 (015); arxiv: The ATLA collaboration, JHEP 1508, 105 (015); arxiv: The CM collaboration, Phys. Rev. D 93, (016); arxiv: M. Buchkremer, Proc. of 49th Rencontres de Moriond on Electroweak Interactions and Unified Theories (014), p.519; arxiv: The ATLA collaboration, Phys. Rev. D 91, (015); arxiv: Письма в ЖЭТФ том 103 вып

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