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The Z γH decay in the Littlest Higgs Model H → J. I. Aranda(a), I. Cortés-Maldonado(b,c), F. Ram´ırez-Zavaleta(a), E. S. Tututi(a) (a)Facultad de Ciencias F´ısico Matema´ticas, Universidad Michoacana de San Nicolás de Hidalgo, Avenida Francisco J. Mu´jica S/N, 58060, Morelia, Michoacań, México. (b)Departamento de F´ısica, CINVESTAV IPN, Apartado Postal 14-740, 07000, México D. F., México. (c)Cátedras Consejo Nacional de Ciencia y Tecnolog´ıa, México. We present the calculation of the ZH γH decay in the context of the Littlest Higgs model at → one-loop level. Our calculations include the contributions of fermions, scalars and gauge bosons in accordancewiththemostrecentexperimentalconstraintsontheparametersspaceofthemodel. We find branching ratios of the order of 10−5 for the energy scale f =2,3,4 TeV on the 0.1<c<0.9 region. Inordertoprovideacomplementarystudywecalculatedtheproductioncrosssectionofthe 5 ZH bosoninppcollisionsatLargeHadronColliderwithacenterofmassenergyof14TeV.Byusing 1 theintegratedluminosity projectedfortheLargeHadronCollider inthelast stageofoperation, we 0 estimated the number of events for this process. Moreover, we analyze the SM background for the 2 p HSMiggbsa-pckhgortoounnads.sociated production and found that thepp→ZHX →γH production is above the e S 7 I. INTRODUCTION 2 Alternative formulations for the study of electroweak symmetry breaking that have the property of canceling ] h quadratic divergences are the so called little Higgs models (LHM) [1, 2]. These models are based on dimensional p deconstruction [3, 4], where the quadratic divergence induced at the one-loop level by the Standard Model gauge - bosons are canceled via the quadratic divergence introduced by heavy gauge bosons at the same perturbative level. p Also, it is proposed the existence of heavy-mass fermions interacting with the Higgs Field in such a way that the e h one-loop quadratic divergence induced in the Yukawa sector of the Standard Model (SM) due to top quark coupling [ withtheHiggsbosoniscanceled[2,5]. Furthermore,theHiggsfieldsacquiremassbecomingpseudo-Goldstonebosons via an approximate global symmetry breaking, where a massless Higgs appears. Quadratically divergent corrections 2 to the Higgs mass arise at loop level, therefore, this naturally ensure a light Higgs. v 8 As far as the littlest Higgs (LTHM) is concerned, a remarkable feature is that there is no new degrees of freedom 8 beyond the SM below TeV scale. Moreover, above few TeV’s the LTHM needs a very small new degrees of freedom 9 to stabilize the Higgs boson mass. At the TeV energy scale, the arising new particles are a set of four gauge bosons 4 with the same quantum numbers as the electroweak SM gauge bosons, namely, A , Z , and W±, an exotic quark 0 H H H with the same charge as the top quark, and a scalar triplet [2]. The construction details of the model can be found . 1 in Refs. [1, 2, 5]. In general, these extensions of the SM predict new particles emerging at the TeV scale and the 0 new physics that could appear at these energies that soon will be tested at the Large Hadron Collider (LHC) [6]. In 5 particular,little Higgsmodels predictthe existence ofa new neutralmassivegaugeboson,knownasZ ,whichcould 1 H offer another theoretical framework to justify the experimental scrutiny about the possible existence of heavy-mass : v (at the TeV scale) particles like the Z gauge boson of the SM. On the other hand, there are several models that i predict the existence of a neutral massive gauge boson, identified as Z′ gauge boson, such as the 331 model [7] or X grand unified models [8]. These type of particles are under exhaustive search at the LHC [9, 10], where the ATLAS r a andCMScollaborationshaveimposedexperimentalboundsoverthemassofanewparticlerelatedtoZ′ gaugeboson, their results indicate that the mass of the Z′ gauge bosonmust be greaterthan 2.49 TeV and 2.59 TeV, respectively. In this work we are interested in the physics of the Z gauge boson, specifically, the main concern of this paper is H to study the Z Hγ decay in the context of the linearized theory of the littlest Higgs model [5]. The relevance of H → this process brings the possibility of testing the LTHM, since the parameters space has been severely constrained by theHiggsdiscoverychannelsandelectroweakprecisionobservables[11]. AnotherremarkablefeatureoftheZ Hγ H → decayconsistsinthefacttheSMbackgroundisnaturallysuppressed,namely,thepp Hγ reaction,sinceitishighly → suppressed for its electroweak origin [12, 13]. Thus, the Higgs-photon associated production opens a new window to test the gauge sector of the SM and Higgs physics [14–17]. To support our analysis, it is calculated the Higgs-photon associated production at LHC coming from SM background, by using current kinematical cuts employed by ATLAS Collaboration [16, 17]. Previous studies on the Z′ Hγ decay have been performed in the context of left-right → symmetric models [14], where the associated branching ratio is estimated, however, the used parameters such as the mZ′ mass are below the present bounds established by the experimental measurements [9, 10]. The paper is organized as follows. In Section II, we briefly describe the theoretical framework of the LTHM. In Sec. III, we outline the analytical results for the Z Hγ decay in the LTHM. In Sec. IV, it is presented the H → numerical analysis. Finally, the conclusions appear in Sec. V. 2 II. MODEL FRAMEWORK ThelittlestHiggsmodelisbasedonanonlinearsigmamodelwithSU(5)globalsymmetryandthegaugedsubgroup [SU(2) U(1) ] [SU(2) U(1) ] [2, 5]. The global symmetry of the SU(5) group is spontaneously broken down 1 1 2 2 ⊗ ⊗ ⊗ SU(5) SO(5) at the energy scale f, where f is constrained to be of the order of 2–4 TeV [11]. Simultaneously, → the [SU(2) U(1) ] [SU(2) U(1) ] group is also broken to its subgroup SU (2) U (1), which results to be 1 1 2 2 L Y ⊗ ⊗ ⊗ ⊗ the SMelectroweakgaugegroup. The globalsymmetrybreakingpatternleaves14Goldstonebosonswhichtransform under the SU (2) U (1) group as a real singlet 1 , a realtriplet 3 , a complex doublet 2 , and a complex triplet 3 [2, 5]. ThLe sp⊗ontaYneous global symmetry break0ing of the SU(50) group is generated by±t12he vacuum expectation ±1 value (VEV) of the Σ field, denoted as Σ [5], at the scale f, which is parametrized by 0 Σ=eiΠ/fΣ eiΠT/f, (1) 0 with 0 0 1 2×2 2×1 2×2 Σ = 0 1 0 (2) 0 1×2 1×2 1 0 0  2×2 2×1 2×2   and Π being the Goldstone boson matrix given by 0 h†/√2 φ† 2×2 Π= h/√2 0 h∗/√2 . (3)   φ hT/√2 0 2×2   Here, h is a doublet and φ is a triplet under the SU (2) U (1) SM gauge group[5]. By the spontaneous symmetry L Y ⊗ breaking (SSB), both the real singlet and the real triplet are absorbed by the longitudinal components of the gauge bosons at the energy scale f. At this scale, the complex doublet and the complex triplet remain massless. The complex triplet acquires a mass of the order of f by means of the Coleman-Weinberg type potential when the global symmetry of the group SO(5) breaks down. The complex doublet is identified as the SM Higgs field. The effective Lagrangianinvariant under the [SU(2) U(1) ] [SU(2) U(1) ] group is [5] 1 1 2 2 ⊗ ⊗ ⊗ = + + + V , (4) LTHM G F Σ Y CW L L L L L − where represents the gauge bosons kinetic contributions, the fermion kinetic contributions, the non-linear G F Σ L L L sigma model contributions of the LTHM, the Yukawa couplings of fermions and pseudo-Goldstone bosons, and Y L the last term symbolizes the Coleman-Weinberg potential. The standard form of the Lagrangianof the non-linear sigma model is f2 = tr Σ2, (5) Σ µ L 8 |D | where the covariant derivative is written as 2 3 Σ=∂ Σ i g Wa QaΣ+ΣQaT +g′B Y Σ+ΣYT . (6) Dµ µ − " j µj j j j µj j j # j=1 a=1 X X (cid:0) (cid:1) (cid:0) (cid:1) Here,Wa aretheSU(2)gaugefields,B aretheU(1)gaugefields,Qa aretheSU(2)gaugegroupgenerators,Y are µj µj j j the U(1)gaugegroupgenerators,g arethe couplingconstantsofthe SU(2)group,andg′ arethe couplingconstants j j of the U(1) group [5]. After SSB around Σ , it is generated the mass eigenstates of order f for the gauge bosons [5] 0 W′ = cW +sW , (7) µ − µ1 µ2 B′ = c′ +s′ , (8) µ − Bµ1 Bµ2 W = sW +cW , (9) µ µ1 µ2 B = s′ +c′ , (10) µ µ1 µ2 B B 3 where W Wa Qa and B Y for j =1,2; c= g / g2+g2, c′ = g′/ g′2+g′2, s= g / g2+g2, and µj ≡ µj j Bµj ≡ µj j 1 1 2 1 1 2 2 1 2 a=1 s′ = g′/ g′2+Pg′2. Notice that Σ field has been expanded aropund Σ holding dopminant terms in p[5]. At this 2 1 2 0 LΣ stage of SSB the B and W fields remain massless. µ µ p 3 The SSB at the Fermi scale provides mass to the SM gauge bosons (B and W) and induces mixing between heavy and light gauge bosons. The arising masses at the leading order (neglecting terms of order v2 , with v being the O f2 vacuum expectation value at the Fermi scale) are [11] (cid:16) (cid:17) gf m = , (11) ZH 2sc g′f m = , (12) AH 2√5s′c′ gf m = . (13) WH 2sc As it is known c = m /m and takes the value equals to one at the leading order, we may assume that the c WH ZH parameterrangesfrom0.1to0.9[5],inordertohavevaluesforthemassesoftheweakgaugebosonsnotverydifferent, as it occurs in the electroweak sector of the SM. TheLTHMincorporatenewheavyfermionswhichcoupletoHiggsfieldinasuchwaythatthequadraticdivergence of the top quark is canceled [2, 5]. In particular, this model introduces a new set of heavy fermions arranged as a vector-like pair (t˜,t˜′c) with quantum numbers (3,1) and (3¯,1) , respectively. The new Yukawa interactions are Yi −Yi proposed to be 1 = λ fǫ ǫ χ Σ Σ u′c+λ ft˜t˜′c+H.c., (14) LY 2 1 ijk xy i jx ky 3 2 where χ = (b ,t ,t˜); ǫ and ǫ are antisymmetric tensors for i,j,k = 1,2,3 and x,y = 4,5 [2]. Here, λ and λ i 3 3 ijk xy 1 2 are free parameters, where the λ parameter can be fixed such that, for given (f,λ ), the top quark mass adjust to 2 1 its experimental value [11]. Expanding the Σ field and retaining terms up to (v2/f2) after diagonalizing the mass matrix, it can be obtained O the mass states t , tc, T , and Tc, which correspondto SM top quark and the heavy top quark, respectively [5, 11]. L R L R The explicit remaining terms of the Lagrangian as well as the complete set of new Feynman rules can be LTHM L found in Ref. [5]. III. DECAY ZH γH → We now turnour attention to obtainthe analyticalexpressionfor the amplitude anddecaywidth ofthe Z γH H → process. The amplitude was calculated in the unitary gauge. In Fig. 1 we show the contributions at one-loop level to the Z γH coming from fermions, gauge boson and scalars. In the fermion loops we include SM and LTHM H → fermion contributions. The analysis is based on three sets of Feynman diagrams: the set (a) contains the triangle loop contributions mediated by fermions; the set (b) includes triangle and bubble loop contributions mediated by SM charged gauge bosons and new heavy charged gauge bosons, where also it is include the mixing effects between these two types of charged gauge bosons; for the set (c), we take into account the bubble loop contributions induced by scalars and scalars plus gauge bosons, together with triangle loop contributions mediated by gauge bosons and scalars. The respective decay amplitude is given by (Z γH)= µνǫ (q)ǫ (k ), (15) M H → MT µ ν 1 where µν = µν + µν + µν. Here, µν represents the contribution of the set (a), µν contains the MT Mf MG MS Mf MG contribution of the set (b), and µν includes the contribution of the set (c). Moreover, ǫ (q) and ǫ (k ) are the MS µ ν 1 polarization vectors associated to Z boson and photon, respectively. After tedious algebraic manipulations we can H write down a generic expression for the total decay amplitude as follows µν = gµν + kˆµqˆν + εµναβk q , (16) MT AT BT 1 CT 1α β where kˆ = k /m and qˆ = q/m . The , and coefficients are in terms of Passarino-Veltman scalar 1 1 ZH ZH AT BT CT 3 2 3 2 functions. In specific, = + + , = + + and = . Here, f runs AT Af AGi ASi BT Bf BGi BSi CT Cf f i=1 i=1 f i=1 i=1 f over all chargedfermions, GPrepresenPts chargedPgauge bosonsP(W, WP), and SPsymbolizes chargPedscalars (φ+, φ−, i H i φ++, and φ−−). We found that the total contribution arising from tadpole and self-energies diagrams vanishes. 4 γ(k1) ZH(q) f f f H(k2) (a) W,WH ZH(q) V W,WHγ(k1) ZH(q) V γ(k1) ZH(q) V s γ(k1) ZH(q) V s γ(k1) W,WH s H(k2) H(k2) H(k2) H(k2) ZH(q) W,WH γ(k1) ZH(q) W,WH γ(k1) ZH(q)W+,WH+ H(k2) ZH(q) φ+ H(k2) W,WH W,WHH(k2) WH,W W,WHH(k2) φ+ φ+γ(k1) W+,WH+ W+,WH+ ZH(q) WW,W,WHH,W,WHH(k2) ZH(q) φ+ H(k2) γ(k1) γ(k1) W+,WH+ γ(k1) (b) (c) FIG. 1: Feynman diagrams contributing to the ZH γH decay at one-loop level. Here, f = u,d,c,s,t,b,e,µ,τ,T, V = Z,ZH,AH and s=φ+,φ++. → The explicit form for the , , , , , and coefficients are presented below Af AGi ASi Bf BGi BSi C = g2 m2ZH √yf(hL+hR)(2(B B ) f a b A 8m y 1 − W H − +(y 1)(C (4y y +1)+2)), (17) H a f H − − 2 = , (18) f f B (y 1)A H − where B B (m2 ,m2,m2), B B (m2 ,m2,m2) and C m2 C (m2 ,m2 ,m2,m2,m2) are the known a ≡ 0 H f f b ≡ 0 ZH f f a ≡ ZH 0 H ZH f f f Passarino-Veltman scalar functions [18]. Also, we used y = m2/m2 and y = m2 /m2 . Notice that for this f f ZH H H ZH particular process h = 0 and h = gcT3/s, where, as usual T3 represents the third component of isospin being R L T3 =1( 1) for fermions up (down) type [5]. The and coefficients contain the contributions of W and W − AGi BGi H bosons as follows 1 = C (B B )(y (1 2y )+2(1 6y )y ) AG1 G14(y 1)y2 G1a − G1b H − W − W W H − W(cid:16) 2C y y2 (1 6y )+3y 4y2 +4y 1 12y2 6y +2 − G1a W H − W H W W − − W − W + y2 (1 2y(cid:0) )+y 12y2 +4(cid:0)y 1 +2y (6(cid:1)y 1) , (cid:1) (19) H − W H − W W − W W − 2 (cid:0) (cid:1) (cid:17) = , (20) BG1 (y 1)AG1 H − where B B (m2 ,m2 ,m2 ), B B (m2 ,m2 ,m2 ), and C m2 C (m2 ,m2 ,m2 ,m2 ,m2 ). G1a ≡ 0 H W W G1b ≡ 0 ZH W W G1a ≡ ZH 0 H ZH W W W Moreover, y = m2 /m2 and C = 1 cg4s c2 s2 s v3 . The and coefficients can be obtained W W ZH G1 −2f2 − W AG2 BG2 from and by replacing: m m (cid:16)and(cid:16)C C(cid:17) , wh(cid:17)ere C = 1 g4s v c2 s2 . The and AG1 BG1 W → WH G1 → G2 G2 −2cs W − AG3 (cid:16) (cid:16) (cid:17)(cid:17) 5 coefficients are given by BG3 1 = C (B B ) y (y +10y 1) AG3 G32(y 1)y y G3a − G3b − WH H W − H − W WH(cid:16) h (y 1)(y +y ) y2 C (y 1)y y (1 y 5y ) − W − H W − WH − G3a H − W H − W − WH i h + y2 +10y y +y +y2 +5y 2 C (y 1)y W W WH W WH WH − − G3b H − WH i y (1 5y y )+y2 +5y (2y +1)+y2 +y 2 × H − W − WH W W WH WH WH − h i (y 1) y (y +10y 1)+(y 1)(y +y )+y2 (21) − H − WH H W − W − H W WH 2 (cid:0) (cid:1)(cid:17) = , (22) BG3 (y 1)AG3 H − where B B (m2 ,m2 ,m2 ), B B (m2 ,m2 ,m2 ), C m2 C (m2 ,m2 ,m2 ,m2 ,m2 ), and G3a ≡ 0 H W WH G3b ≡ 0 ZH W WH G3a ≡ ZH 0 H ZH W WH W C m2 C (m2 ,m2 ,m2 ,m2 ,m2 ). Inaddition,y =m2 /m2 andC =g4s v(c2 s2)/4cs. Notice G3b ≡ ZH 0 H ZH WH W WH WH WH ZH G3 W − that Eqs. (21) and (22) reflect the mixing between W and W gauge bosons. The and coefficients are H AS1 BS1 1 = C (B B )(y +y y ) AS1 S1(y 1)y S1a − S1b H W − φ H W − (cid:16) + C (y 1)y (y +y y ) C (y 1)y (y y +y 2) S1a H − φ H W − φ − S1b H − W H W φ− + (y 1)(y +y y ) , (23) H H W φ − − 2 (cid:17) = , (24) BS1 (y 1)AS1 H − where B B (m2 ,m2 ,m2), B B (m2 ,m2 ,m2), C m2 C (m2 ,m2 ,m2 ,m2,m2 ), and S1a ≡ 0 H W φ S1b ≡ 0 ZH W φ S1a ≡ ZH 0 H ZH W φ W C m2 C (m2 ,m2 ,m2,m2 ,m2). Here, y =m2/m2 and C =eg3 c2 s2 v′2/(2csv). The and S1b ≡ ZH 0 H ZH φ W φ φ φ ZH S1 − AS2 BS2 coefficients can be get by replacing: m m and C C , where C = eg3(c2 s2) c4+s4 v′2/(4c3s3v). W → WH S1 → S2 S2(cid:0) (cid:1) − The form factor is given by f C (cid:0) (cid:1) ig2 2(h h )y L R f = − (2(B B )+C (y 1)). (25) f a b a H C 8m y 1 − − W H − Therefore, the expression for the decay amplitude of the Z γH can be written as H → 2 (Z γH)= gµν + kˆµqˆν + εµναβk q ǫ (q)ǫ (k ). (26) M H → AT y 1 1 CT 1α β µ ν 1 H h (cid:16) − (cid:17) i Finally, the decay width for the process reads as (1 y )[4 2 + 2m4 (y 1)2] Γ(Z γH)= − H AT CT ZH H − . (27) H → 96πm ZH Itshouldberecalledthatallthe and termsinΓ(Z γH)arefreeofultravioletdivergencesandtheLorentz i f H structure in Eq. (26) satisfies the WAard ideCntity k µν =0→. 1νMT IV. NUMERICAL RESULTS A. Production of extra neutral ZH boson In this part of our work, we present the production cross section of the extra neutral Z gauge boson at LHC H in the context of the LTHM, where it is assumed a search for a mass resonance in the dilepton channel e+e− [19]. Here, we used version 2.1.1 of the WHIZARD event generator, which is a program designed for the calculation of multi-particle scattering cross sections and simulated event samples [20] to perform our calculations. As a test of the WHIZARD package, we carried out the calculation of σ(pp Z X) cross section as a function of m for c =π/4 → H ZH andour resultscoincidedwith previousones reportedinRef. [5]; to do that weemployedCTEQ5partondistribution 6 function [21]. We simulate pp collisions with a center of mass energy of 14 TeV. In Fig. 2, it can be appreciated σ(pp Z X) as a function of the Z boson mass throughout the interval 1.6 TeV< m < 13.13 TeV, where we → H H ZH have employed three different values for f, namely, 2,3,4 TeV. It should be noted that the mass range for Z comes H from the discrete choice of the energy scale f and allowed values for the c parameter, which will be justified below. m [TeV] m [TeV] ZH ZH 6.563.332.281.781.501.351.301.351.66 9.844.993.422.672.262.031.952.032.49 102 101 101 100 X) [pb] 100 X) [pb] 10-1 Excluded region H H10-2 → Z 10-1 Excluded region → Z pp pp 10-3 σ( 10-2 σ( 10-4 10-3 10-5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 c c (a) (b) m [TeV] ZH 13.136.664.563.563.012.722.612.723.32 101 100 10-1 b] p X) [ 10-2 H Z → 10-3 p p σ( 10-4 Permitted region 10-5 10-6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 c (c) FIG. 2: Production cross section of the ZH boson at LHC. (a) For f =2 TeV. (b) For f =3 TeV.(c) For f =4 TeV. B. Branching ratio for the ZH γH decay → Let us analyze the branching ratio behavior of the Z γH decay. Recall that the m is a function of two H → ZH model-dependent parameters c and f, where c and f are the mixing angle of the SU(2) U(1) extended gauge 2 2 × group and the energy scale at which the SU(5) gauge group breaks into SO(5) group, respectively. It is known that experimental data constrain the symmetry breaking scale to be in the interval 2 TeV < f < 4 TeV, for c′ = 1/√2 and c between [0.1,0.995][11]. To make predictions, we will take three distinct values for f, namely, f =2,3,4 TeV and will carry out an exhaustive study at the c parameter region given above. This analysis will provide us crucial information to test the experimental possibility for Z γH decay in the LTHM context. Moreover, it should H → be recalled that the recent results reported by ATLAS and CMS collaborations, established lower mass limits for a new neutral massive gauge boson, identified as Z′. ATLAS collaboration reports that a sequential Z′ gauge boson is excluded at 95% C.L. for masses below 2.39 TeV in the electron channel, 2.19 TeV in the muon channel, and 2.49 TeV in the two channels combined [9]; Z′ bosons coming from E -motivated models are excluded at 95% C.L. for 6 masses below 2.09-2.24 TeV [9]. In accordance with CMS results, in the context of the sequential Z model and the superstring-inspiredmodel,thelowermasslimitsat95%C.L.fortheZ′ gaugebosoncorrespondto2.59TeVand2.26 TeV, respectively [10]. Motivated by the above results, we will take a lower mass limit for the Z gauge boson to be H 7 2.6 TeV in order to explore the physical possibilities for the Z γH decay. In a previous work it has been studied H → the dominant decays of the Z boson [22] in the context of the LTHM. We employ this information to compute the H total decay width of the Z boson for different values of the energy scale f proposed above. H From Fig. 3(a), for f = 2 TeV, it can be observed that the permitted region corresponds to 0.1 < c < 0.26 for a Z mass interval6.56 TeV>m >2.6 TeV, where the branching ratiorangesfrom 1.02 10−6 to 7.77 10−6; the mHaximum value of the branchingZHratio is 7.77 10−6 for c=0.26 and m =2.68 TeV. In×Fig. 3(b), for×f =3 TeV, × ZH we can observe a permitted region for the c parameter ranging between 0.1 < c < 0.41, due to Z mass interval H 9.84 TeV > m > 2.6 TeV, being the associated branching ratio around 3.67 10−7–2.4 10−6; in this case, the maximum valuZeHof the branching ratio is 4.12 10−6 for c=0.29and m =3.×53 TeV. Fina×lly in Fig.3(c), we show × ZH the branching ratio as a function of c and m for f = 4 TeV. This figure tell us that the whole interval for the c ZH parameter 0.1< c < 0.9 is permitted, accordingly with the interval 2.6 TeV < m < 13.13 TeV, where the related ZH branching ratio is as high as 2.47 10−6 for c =0.31 and m =4.43 TeV. Even when predicted branching ratio is small (of the order of 10−5), the L×HC luminosity at final stagZeHof operation (14 TeV at the center of mass energy) is expectedtobearound3000fb−1 [23]whichcouldcounteractthissituation. Infact,toexplorethepredictabilityofthe LTHM,letusconsiderdifferentvaluesoftheZ massforwhichitisproducedfewevents. Forf =2TeVandaround H c=0.19 or equivalently m =3.5 TeV, we estimate 2 events. For f =3 TeV and c=0.28 or m =3.64 TeV, we ZH ZH foundaround1event. Forf =4 TeVandc=0.4orm =3.56TeV,wecalculatedlessthan1event. Moreover,the ZH maximum number of events estimated for f =2,3,4 TeV are 16 (c=0.26,m =2.6 TeV), 4 (c=0.41,m =2.62 ZH ZH TeV) and 0.76 (c=0.45,m =3.25 TeV), respectively. ZH m [TeV] m [TeV] ZH ZH 6.563.332.281.781.501.351.301.351.66 9.844.993.422.672.262.031.952.032.49 10-2 10-2 f = 2 TeV f = 3 TeV 10-3 10-3 10-4 Excluded region 10-4 Excluded region 10-5 10-5 R 10-6 R 10-6 B B 10-7 10-7 10-8 10-8 10-9 10-9 10-10 10-10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 c c (a) (b) m [TeV] ZH 13.136.664.563.563.012.722.612.723.32 10-2 f = 4 TeV 10-3 10-4 Permitted region 10-5 R 10-6 B 10-7 10-8 10-9 10-10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 c (c) FIG. 3: Branching ratio for the ZH γH decay as a function of c parameter and mZ . (a) For f = 2 TeV. (b) For f = 3 → H TeV. (c) For f =4 TeV. 8 C. Background estimation for the γH production in LHC At the LHC, the Higgs boson production in association with a photon may be produced from quark-antiquark annihilation. In gluon-gluon annihilation, the Higgs-photon associated production is forbidden by Furry’s theorem becauseofpropertiesofcolorsingletstateofgluons[12]. DifferentresultswerereportedwheretheHγ finalstatesare producedinpp collisionsviad¯+d Hγ subprocessor viaweak-bosonfusionande+e− colliders[13,24,25]. For the processd¯+d Hγ the crosssecti→onwas obtainedat√s=8TeV using values oftransversemomentum, p , ranging T → from30GeVto300GeV.Forouranalysiswetakeppcollisionswith acenter-of-massenergyof14TeVandintroduce kinematical cuts based on experimental values employed by ATLAS Collaboration for the transverse momentum 30 GeV < p < 150 GeV and transverse energy E from 300 GeV to 1000 GeV for the photon and pseudorapity T T region η <1.37[16,17]. Takinginaccountthis,wesimulatedthepp Hγ processcorrespondingtoSMbackground | | → byusingWhizardEventGeneratorpackage[20]alongwithpartondistributionfunctions(PDFs)CTEQ5,CTEQ6[26] and MSTW2008NLO [27]. We note that the PDFs used produce similar results for the production cross section in question. In addition, we would like to mention that with the used cuts, the SM background results (see Fig. 4) are suppressed in comparison with the corresponding LTHM results. Concretely, at center of mass energy of 14 TeV we found a SM background cross section of 1.077 10−7 pb (for CTEQ5), while in the less optimistic scenario, our calculated cross section via LTHM is 2.19 10−7 ×pb (for f = 4 TeV and m = 3.56 TeV). For f = 2 (f = 3) TeV × ZH andm =3.5(m =3.32)TeVrespectively,weobtainaLTHMproductioncrosssectionσ(pp γH)ofthe order of 10−6ZHpb. ZH → 1.0x10-5 f = 2 TeV f = 3 TeV f = 4 TeV b] p γ ) [ 1.0x10-6 H → p p σ( 1.0x10-7 11 11.5 12 12.5 13 13.5 14 14.5 √s [TeV] FIG.4: SM-backgroundcrosssectionfortheHiggs-photonassociatedproductionatLHCasafunctionofcenterofmassenergy. The various dots represent σ(pp ZHX γH) at √s=14 TeV for mZ =2.6 TeV. → → H To distinguish the LTHM signal from SM background we compute the Higgs gamma Drell-Yan production (background) at 95% of confidence level, where systematic uncertainties has been neglected (see Fig. 4). From this figure, we observe that all the points corresponding to pp Z X γH process at 14 TeV are above the confidence level H → → band of SM background. These LTHM results could be attractive for the search of new physics, however, they must be taken carefully since we have not considered their respective error bars. Moreover, it may be recalled that the purpose of this work relies on the LTHM predictability for the physical parameter space [11] by using the Z γH H → decay, to this end we present at the most a thorough estimation. Finally, it is essential to point out that it has been shown the important influence of K factors on QCD NLO correctionstoDrell-YanproductioninbothTevatronandLHC[28],whereitisfoundthatcorrectionstotheone-loop level under certain scenarios are important. In this sense, one of the goals of this work has been calculating the Z production cross section at the LHC via Z Drell-Yan production, which has been made possible through the H H implementation of PDFs such as MSTW2008NLO [27] in The Whizard event generator. These PDFs already take into accountcorrectionsfor NLO Drell-Yanproductionat the LHC [21, 26, 27]. Indeed, as alreadymentionedbefore, while for the Z production and the SM background analysis it has been used the CTEQ5 PDF, we stress that the H numerical simulationalso was performed using MSTW2008NLO and CTEQ6 and no significant changesbetween the threePDFs areappreciated,asthe resultsprovidedbythese PDFshardlyvaryeveninthe mostsignificantdigit. For consistency, we use CTEQ5 in accordance with previous experimental analyses that consider this PDF for studies of Z′ Drell-Yan production [29]. 9 V. CONCLUSIONS The LTHMresidesona nonlinearsigmamodelwitha SU(5)globalsymmetryandthe gaugedsubgroup[SU(2) 1 ⊗ U(1) ] [SU(2) U(1) ],whereitispredictedtheexistenceofheavygaugebosons,particularly,anewneutralmassive 1 2 2 bosonk⊗nownasZ⊗ . ThisgaugebosonisanotherZ′typegaugebosonwhichatpresentisunderexperimentalscrutiny H atthe LHC.Althoughthe parametersspaceofthe LTHMhasbeenseverelyconstrained,yetthere isroomleftto test the predictability of the model. In specific, the Z γH decay was used to explore the current parameters space H → of the LTHM, where we have analyzed physical regions according with experimental bounds and results; specifically we have taken the following parameters: f = 2,3,4 TeV for 0.1 < c < 0.9. It is found that for f = 2 TeV there is a permitted region 0.1 < c < 0.26 corresponding to 6.56 TeV > m > 2.6 TeV. In particular, for a m = 3.5 TeV ZH ZH it is calculated around 2 events for the Z γH decay at LHC operating at 14 TeV. Similarly, for f = 3 TeV the H → permitted region is 0.1 < c < 0.41 or a Z mass interval 9.84 TeV > m > 2.6 TeV. In this case, for m = 3.64 H ZH ZH TeV it is estimated 1 event for the process in question. Finally, for the same process and taking f =4 TeV we have found the permitted region in the interval of masses 2.6 TeV < m < 13.13 TeV. Here, it is computed less than 1 ZH event for m =3.56 TeV. Although we have chosen specific values of m to get few events, our numerical results ZH ZH tellusthatthereareseveralintervalsinwhichthenumberofeventsarelargerthanthepreviousones. Forinstance,for f =2andc=0.26wecouldobtaintensofeventsfortheZ γH decay. Toexplorefutureexperimentalpossibilities H → of the decay in question, we have performed a careful estimation of the SM background for the pp Hγ reaction, → by using the CTEQ5, CTEQ6, and MSTW2008NLO PDFs included in the WHIZARD event generator. Taking into account current experimental kinematical cuts, the SM-background cross section results below the computed LTHM cross section for the pp Z X Hγ. H → → Acknowledgments This work has been partially supported by CONACYT and CIC-UMSNH. I. Cortés-Maldonado thanks to J. J. Toscano for fruitful discussions. [1] N.Arkani-Hamed,A.G.Cohen,andH.Georgi,Phys.Lett.B513,232(2001);N.Arkani-Hamed,A.G.Cohen,T.Gregoire, and J. G. Wacker, JHEP 08, 020 (2002); N. Arkani-Hamed, A. G. Cohen, E. Katz, A. E. Nelson, T. Gregoire, and J. G. Wacker,JHEP 08, 021 (2002); I.Low, W. Skiba,and D.Smith, Phys.Rev.D66, 072001 (2002). [2] N.Arkani-Hamed,A.G. Cohen, E. Katz, and A. E. Nelson, JHEP 07, 034 (2002). [3] N.Arkani-Hamed,A.G. Cohen, and H. Georgi, Phys. 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