Top quark effects in composite vector pair production at the LHC

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1 Top quark effects in composite vector pair production at the LHC Antonio Enrique Cárcamo Hernández. Universidad Tecnica Federico Santa Maria. SILAFAE 01, 10th-14th of December of 01. Based on: A. E. Cárcamo Hernández, Eur. Phys. J. C 7:154 (01). A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 1 / 9

2 1 Introduction. Chiral Lagrangian with massive spin one fields, scalar singlet and SM fermions. 3 Gluon fusion production amplitudes 4 Vector pair production total cross sections via gluon fusion 5 Same-sign di-lepton and tri-lepton events. 6 Conclusions A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 / 9

3 Introduction. A 15 GeV Higgs boson has been found at the LHC. It remains to determine whether Electroweak Symmetry Breaking (EWSB) is weakly or strongly coupled. Weakly coupled, as the Standard Model (SM), HDM, Multi Higgs Models, Little Higgs, Gauge Higgs Unification models, SU (3) C SU (3) L U (1) Y models (3-3-1 models), GUT and their supersymmetric extensions. Strongly coupled, as Technicolor, Composite Higgs, Strongly Interacting Light Higgs (SILH), Composite Higgs with composite Vectors, Randall-Sundrum (RS) models, 10 3 SM copies, Full Hierarchy Quiver Theories (FHQT). The hierarchy problem provides a plausible motivation for considering strongly coupled theories of EWSB. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 3 / 9

4 Chiral Lagrangian with massive spin one fields, scalar singlet and SM fermions. L = v D µ U (D µ U) 1 ˆV µν ˆV µν + M V g V ˆV µν (uw µν u + u B µν u + i + g V 8 + v 4 Wµν g W µν 1 Bµν g B µν V µ ig V µ V ˆV µν [u µ, u ν ] ) 1 8 ( ) V µ V ν uw µν u + u B µν u + ig K 4 [uµ, u ν ][u µ, u ν ] + 1 µh µ h + m h D µ U (D µ U) ( a h v + b h v ( i,j ū (i) L ) ( d (i) L U 1 + c h v v [Vµ, V ν ][u µ, u ν ] h ) + dv 8g V ) ( λ u ij u(j) R λ d ij d (j) ˆV µν [V µ, V ν ] h V µ V µ R A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 4 / 9 ) + h.c.

5 ( ) π U (x) = e i ˆπ(x)/v, ˆπ (x) = τ a π a 0 π + = π π 0, u U D µ U = µ U ib µ U + iuw µ, W µ = g τa Wµ a, B µ = g τ3 Bµ 0, V µ = 1 τ a Vµ a, ˆV µν = µ V ν ν V µ, u µ = u µ = iu D µ Uu, [ µ V = µ V + [Γ µ, V ], Γ µ = 1 u ( ) ( ) ] µ ib µ u + u µ iw µ u Here the following assumptions have been made: 1 Before weak gauging, the Lagrangian responsible for EWSB has a SU() L SU() R global symmetry The strong dynamics produces a composite triplet of heavy vectors and a composite scalar singlet under SU() L+R. 3 Only one vector triplet V a µ of the SU () L+R group has a mass below the cut-off Λ 3 TeV. The new V states couple to fermions only via SM gauge interactions. 4 The light scalar singlet of mass m h = 15 GeV interacts with the Standard Model gauge bosons and fermions only via weak gauging and (proto)-yukawa couplings, respectively. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 5 / 9

6 A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 6 / 9

7 The various amplitudes have the following asymptotic behaviour (Barbieri-Carcamo-Corcella-Trincherini-Torre 010, Carcamo-Torre 010): A (W L W L W L W L ) s v, A (W LW L V L V L ) s v M V The choice: a = A (W L W L hh) s v, A (W LW L V L h) s v A (W L W L f f ) m f (1 ac) s v. 1 3G V v, G V g V M V, G V v/ 3. guarantees a good asymptotic behavior of elastic W L W L scattering, while g V g K = 1 ensures that A ( π a π b VL cv L d ) grows at most like s/v. The gauge model scenario is defined by (Carcamo-Torre 010): a = 1, b = 1 4, d = 1, g K = 1 g V, g V = v M V c = 1 a. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 7 / 9

8 Gluon fusion production amplitudes Figure: Leading order diagram, containing a hvv coupling vertex, of the vector pair production through the gluon fusion process. Crossing the gluon legs yields a second diagram. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 8 / 9

9 A ( gg V + V ) = α ( S π cd 8g V (s M h ) ) ε µ (p, χ) ε ν ( k, χ ) ( ) s δ ab [g µν (p k) p ν k µ ] I g ρσ ( ε ρ (l, ξ) ε σ q, ξ ), ( ) s 1 1 x I mt = dx dy 1 4xy s xy, mt m t A ( gg V + V ) = 1 4 A ( gg V 0 V 0) a,b,χ,χ,ξ,ξ a,b,χ,χ,ξ,ξ = c d α S s 16π gv 4 (s M h ( ) ) s ( s I mt 4M 4 V s M V ) + 3. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 9 / 9

10 Vector pair production total cross sections via gluon fusion σ pp gg V + V (V 0 V 0 ) (S) = 1 M V S dx 1 M V S dyf p/g ( x, µ ) f p/g ( y, µ ) σ gg V + V (V 0 V 0 ) (s), where s = xys and the choice µ = M V is made. σ gg V + V (s) = 1 4 σ gg V 0 V 0 (s) = πs tmax A ( gg V + V ) d t, t min a,b,χ,χ,ξ,ξ ( ) t min = s 4 + s 4 M V, ( ) (1) t max = s 4 s 4 M V. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 10 / 9

11 0.8 σ (pp gg V + V ) for σ (pp gg V + V GV = 5v/4 ) for σ (pp gg V + V GV = v/ and d = 1 6 and d = 1 ) for GV = v/ and d = σ(fb) MV (GeV) Figure 1: Total cross sections for the V + V production via the gluon fusion mechanism at the LHC for S = 14 TeV and d = 1 as functions of the heavy vector mass for different values of the parameter. MV GV 3.5 σ ( pp σ ( gg V 0 V 0) pp σ ( gg V 0 V 0) for GV = 5v/4 pp gg V 0 V 0) for GV = v/ and d = 1 6 and d = 1 for GV = v/ and d = 1 σ(fb) MV (GeV) Figure : Total cross sections for the V 0 V 0 production via the gluon fusion mechanism at the LHC for S = 14 TeV and d = 1 as functions of the heavy vector mass for different values of the parameter. MV GV A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 11 / 9

12 Same-sign di-lepton and tri-lepton events. Since the heavy vector have dominant decay mode into pair of SM Gauge bosons (with branching ratio very close to one), the vector pair production by gluon fusion will lead to 4 SM gauge bosons in the final state. Decay Mode di-leptons (%) tri-leptons (%) V 0 V 0 W + W W + W Table: Dominant decay mode and cumulative branching ratios for the V 0 V 0 charge configuration. G V a di-leptons tri-leptons 5v/4 1/4 4 9 v/ 1/ 9 3 v/ 6 1/ 11 4 Table: Total number of same-sign di-lepton and tri-lepton events (e or µ from W decays) for the vector pair production via gluon fusion at the LHC for S = 14 TeV and Ldt = 100 fb 1 at M V = 500 GeV, M h = 15 GeV and m t = GeV for different values of the parameter G V and for d = 1. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 1 / 9

13 Signal Number of Events pp V 0 V 0 W + W W + W l4j E T 4 Backgrounds t tw WWW j l4j E T HH WWWW l4j E T WWW j l4j E T 53 HW j WWW j l4j E T 100 HWZ WWW j l4j E T 1.5 HWW WWW j l4j E T 6 WWWW l4j E T 3 Table: Number of same-sign di-lepton events and estimation of the corresponding backgrounds at the LHC for S = 14 TeV and Ldt = 100 fb 1. The signal corresponds to the case M V = 500 GeV, M h = 15 GeV, m t = GeV, a = 1/4, d = 1 and G V = 5v/4. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 13 / 9

14 Signal Number of Events pp V 0 V 0 W + W W + W 3lj E T 9 Backgrounds t tw WWW j 3lj E T 10 3 HH WWWW 3lj E T 10 3 WZZ 3lj E T 10 WWW j 3lj E T 80 HW j WWW j 3lj E T 30 HWW WWW j l4j E T 4 WWZZ 3lj E T WWWW 3lj E T HWZ WWW j 3lj E T 0.5 Table: Number of tri-lepton events and estimation of the corresponding backgrounds at the LHC for S = 14 TeV and Ldt = 100 fb 1. The signal corresponds to the case M V = 500 GeV, M h = 15 GeV, m t = GeV, a = 1/4, d = 1 and G V = 5v/4. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 14 / 9

15 Conclusions New particles need are needed to stabilize the weak scale. Strongly coupled EWSB can be described by an Effective Lagrangian with massive spin-1 fields + 1 singlet scalar. The total cross sections for the production of the V + V and V 0 V 0 final states at the LHC by the gluon fusion mechanism are of the order of few fb. For Ldt = 100 fb 1, the N multileptonevents 10. Signals are very suppressed by a factor 10 with respect to the t tw and HH backgrounds. The LHC will shed light in the dynamics responsible for EWSB and the stabilization of EW scale. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 15 / 9

16 Acknowledgements Thank you very much to all of you for the attention. Special thanks for the organizers of SILAFAE 01 for the opportunity. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 16 / 9

17 References A. E. Cárcamo Hernández, [arxiv: [hep-ph]], Eur. Phys. J. C 7 (01) 7:154. A. E. Cárcamo Hernández and R. Torre, [arxiv: [hep-ph]], Nucl. Phys. B 841 (010) , [dx.doi.org/ /j.nuclphysb ]. R. Barbieri, A. E. Cárcamo Hernández, G. Corcella, R. Torre and E. Trincherini, JHEP 0310 (010)068 [arxiv: [hep-ph]]. O. Cata, G. Isidori and J. F. Kamenik, Nucl. Phys. B 8 (009) 30 [arxiv: [hep-ph]]. G. F. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, JHEP 0706 (007) 045 [arxiv:hep-ph/ ]. R. Contino, C. Grojean, M. Moretti, F. Piccinini and R. Rattazzi, JHEP 1005:089 (010) [arxiv: [hep-ph]] A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 17 / 9

18 Extra Slides A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 18 / 9

19 A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 19 / 9

20 A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 0 / 9

21 A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 1 / 9

22 G V a d V + V (fb) V 0 V 0 (fb) 5v/4 1/ v/4 1/ v/4 1/ v/ 1/ v/ 1/ v/ 1/ v/ 6 1/ v/ 6 1/ v/ 6 1/ Table: Total cross sections for the production of the V + V and V 0 V 0 final states by gluon fusion at the LHC for S = 14 TeV as functions of the different parameters for M V = 500 GeV. Here α S = 0.1, M h = 15 GeV and m t = GeV while the factorization scale is taken to be equal to M V. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 / 9

23 G V a d V + V (fb) V 0 V 0 (fb) 5v/4 1/ v/4 1/ v/4 1/ v/ 1/ v/ 1/ v/ 1/ v/ 6 1/ v/ 6 1/ v/ 6 1/ Table: Total cross sections for the production of the V + V and V 0 V 0 final states by gluon fusion at the LHC for S = 14 TeV as functions of the different parameters for M V = 1 TeV. Here α S = 0.1, M h = 15 GeV and m t = GeV while the factorization scale is taken to be equal to M V. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 3 / 9

24 Composite versus gauge models Considering the following SU() L SU() C SU() R Lagrangian [3]: L gauge V = L gauge χ 1 vµν gc v µν 1 Wµν g W µν 1 Bµν g B µν, () where v µ = g C v µτ a a (3) is the SU() C -gauge vector and the symmetry breaking Lagrangian is described by L gauge χ = v D µ Σ RC (D µ Σ RC ) + v Denoting collectively the three gauge vectors by D µ Σ CL (D µ Σ CL ). (4) v I µ = (W µ, v µ, B µ ), I = (L, C, R), (5) one has for the two bi-fundamental scalars Σ IJ D µ Σ IJ = µ Σ IJ iv I µσ IJ + iσ IJ v J µ. (6) A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 4 / 9

25 Σ IJ = σ I σ J, where σ I are the elements of SU() I /H. As the result of a gauge transformation v I µ σ I v I µσ I + iσ I µσ I Ω I µ, Σ IJ σ I Σ IJσ J = 1, (7) and after the gauge fixing σ R = σ + L where u and σ C = 1, one has uµ L gauge χ = v (v µ iγ µ ) + v 4, (8) u µ = Ω R µ Ω L µ, Γ µ = 1 i (ΩR µ + Ω L µ), v µ = V µ + iγ µ (9) by use of the identity: v µν = ˆV µν i[v µ, V ν ] + i 4 [u µ, u ν ] + 1 (uw µνu + u B µν u). (10) With the replacement V µ g C V µ, gauge V coincides with L V for g V = 1 = 1, g C g K g 3 = 1 4, g 6 = 1, f V = g V M V = g C v (11) with G V = g V M V, µ V = µ V + [Γ µ, V ], [ ( ) ( ) ] A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 5 / 9

26 A well behaved theory at all energies Let us consider the following SU() L SU() C U(1) Y invariant non-linear sigma model Lagrangian: L gauge V = L gauge χ 1 vµν gc v µν 1 Wµν g W µν 1 Bµν g B µν, (1) where v µ = g C v µτ a a (13) is the SU() C -gauge vector and the symmetry breaking Lagrangian is described by L gauge χ = v ( Σ RC = 1 + h + H Σ CL = ( 1 + h H v D µ Σ YC (D µ Σ YC ) + v D µ Σ CL (D µ Σ CL ) (14) ) [ ] i U YC, U RC = exp (π + σ), (15) v v ) [ ] i U CL, U CL = exp (π σ), (16) v A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 6 / 9

27 V (Σ YC, Σ CL ) is the scalar potential, which has the form V (Σ YC, Σ CL ) = µ v λv 4 4 Σ YC Σ YC + µ v where π = π a τ a and σ = σ a τ a, with: Σ CL Σ CL λv 4 4 ( Σ CL Σ CL ) κv 4 Σ YC Σ CL Σ CLΣ YC ( ) Σ YC Σ YC. (17) m h = 4v (λ + κ), m H = 4v (λ κ). (18) The covariant derivatives appearing in (14) are given by D µ U YC = µ U YC ib µ U YC + iu YC v µ, D µ U CL = µ U CL iv µ U CL + iu CL W µ. (19) The U fields can be written as U YC = σ Y σ C and U CL = σ C σ L where the σ L,C,Y are elements of SU () L,C,R /H respectively. These σ I with I = L, C, Y transform under the full SU () L SU () C U (1) Y as σ I g I σ I h. A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 7 / 9

28 By applying the gauge transformation v I µ σ I v I µσ I + iσ I µσ I = Ω I µ, U IJ σ I U IJσ J = 1, and after the gauge fixing σ Y = σ L = u = U = e i ˆπ v and σ C = 1, which implies that U YC = U CL (i.e. ˆσ = 0), so we have: ( L gauge χ = v 1 + h + H 4v + h ) ( (vµ ) iγ µ + 1 uµ u µ ) v 4 where 1 (vh + hh) u µ ( v µ iγ µ ), (0) u µ = Ω Y µ Ω L µ = iu D µ Uu, Γ µ = 1 ( ) Ω Y µ + Ω L µ = 1 [ u ( ) ( ) ] µ ib µ u + u µ iw µ u.(1) i Now by setting v µ = V µ + iγ µ, () A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 8 / 9

29 by using the identity v µν = V µν i [ ] i [ ] 1 V µ, V ν + uµ, u ν + 4 f µν +, (3) where f + µν = uw µν u + u B µν u, by redefining V µ g C V µ, and taking the mass of the L-R-parity odd H given in (18) infinitely large, L gauge coincides with L eff up to operators irrelevant for the processes under consideration, only for the values of the parameters: g V = 1 g C = 1 g K = v M V, f V = g V, a = 1, b = 1 4, d = 1, G V = v, M V = g C v = 1 g K v = v g V (4) A.E. Cárcamo Hernández (UTFSM) Top quark effects in composite vector pair production at the LHC 1/1 9 / 9

Teoria e fenomenologia dei modelli di Higgs composto. Roberto Contino - CERN

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