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 0.1m >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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