Physics Department, Ankara University, Tandoğan, Ankara, TURKEY. Physics Department, Ankara University,

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1 BALKAN PHYSICS LETTERS c Bogazici University Press 19 May 2009 BPL, 17, pp , (2009) SEARCH FOR SCALAR AND VECTOR DIQUARKS AT THE LHC M. ŞAHİN Physics Department, Ankara University, Tandoğan, Ankara, TURKEY. O. ÇAKIR Physics Department, Ankara University, Tandoğan, Ankara, TURKEY. Abstract. - We study the production of scalar and vector diquarks at the LHC. We have calculated the production rates, decay widths and signatures of diquarks using the effective Lagrangian formalism. The corresponding dijet backgrounds are examined in the interested invariant mass distributions. The attainable mass limits and couplings are obtained for uu, ud and dd type scalar and vector diquarks. It is shown that the LHC with the center-of-mass energy s = 14 TeV will be able to discover scalar and vector diquarks with masses up to m DQ = 9 TeV for quark-diquark-quark coupling α DQ = INTRODUCTION According to the composite models [1] of quarks and leptons, a rich spectrum of new particles with the unusual quantum numbers are expected. The diquarks are those of particles which occur beyond the standard model (SM), such as the superstringinspired E 6 models [2] and composite models [3]. Diquarks have scalar and vector form and carry baryon number B = 2/3, and no lepton number. The Collider Detector at Fermilab (CDF) set limits on the masses of E 6 scalar diquarks decaying to dijets with the exclusion of mass range 290 < m DQ < 630 GeV [4], which are expected to be approximately valid for other scalar diquarks. There are also indirect bounds imposed on couplings from electroweak precision data [5] from LEP e + e collider where these bounds allow diquark-quark couplings up to a value α DQ = 0.1. In this work, we study the scalar and vector diquarks. We analyze the signal and background to obtain the observability of diquarks at the LHC.

2 133 Table 1: Quantum numbers of the first generation, color 3 diquarks described by the effective lagrangian (1). SU(3) C SU(2) W U(1) Y Q Couplings Scalar Diquarks DQ /3 1/3 u L d L (g 1L ), u R d R (g 1R ) DQ /3 2/3 d R d R ( g 1R ) DQ /3 4/3 u R u R ( g 1R ) 4/3 u L u L ( 2g 3L ) DQ /3 1/3 u L d L ( g 3L ) 2/3 d L d L ( 2g 3L ) Vector Diquarks ( ) ( ) 1/3 dr u L (g 2 ) DQ 2µ 3 2-1/3 DQ 2µ 3 2 5/3 ( 2/3 4/3 1/3 ) ( d R d L ( g 2 ) ur u L ( g 2 ) u R d L ( g 2 ) ) 2. INTERACTION LAGRANGIAN In this work, we used a model independent, baryon number conserving, most general SU(3) C SU(2) W U(1) Y invariant effective lagrangian for scalar and vector diquarks having the form [6, 7] L B =2/3 = (g 1L q c Liτ 2 q L + g 1R ū c Rd R )DQ c 1 + g 1R dc R d R DQ c 1 + g 1Rū c Ru R DQ c 1 + g 3L q c Riτ 2 τq L DQ c 3 +g 2 q c Lγ µ d R DQ c 2µ + g 2 q c Lγ µ u R DQ c 2µ + H.c. (1) In Eq. (1), q L = (u L,d L ) denotes the left-handed quark spinor and q c = Cq T ( q c = q T C 1 ) is the charge conjugated quark field. For the sake of simplicity, color and generation indices are ommitted in (1). Scalar diquarks DQ 1, DQ 1, DQ 1 are SU(2) W singlets and DQ 3 is a SU(2) W triplet. Vector diquarks DQ 2 and DQ 2 are SU(2) W doublets. At this stage, we assume that each SM generation has its own diquarks and relevant couplings in order to avoid flavour changing neutral currents. A general classification of the first generation, color anti-triplet (3 ) diquarks is shown in table 1 [8]. We consider the color 3 scalar DQ 1 or DQ 0 3 diquarks coupled to ud pairs, DQ 1 or DQ 3 diquarks coupled to dd pair and DQ 1 or DQ + 3 diquarks coupled to uu pair. The vector diquarks DQ 1 2 and DQ 2 2 of type ud, DQ 2 2 of type dd and DQ 1 2 of type uu are considered. Schematic presentation of resonant production of diquarks is shown in Fig. 1.

3 134 BALKAN PHYSICS LETTERS Table 2: Decay width values for scalar and vector diquarks m DQ (GeV ) Γ S DQ (GeV ) (GeV ) Γ V DQ The decay widths Γ DQ for scalar and vector diquarks (with α DQ = 0.1) are calculated for the mass values m DQ = 500,1000,3000,5000,7000,9000 GeV in table SIGNAL AND BACKGROUND In the figure 2, the process for diquark resonant production is shown. The signal for diquark resonant production would clearly manifest itself in two jets cross sections. The total cross section for the resonance production of diquarks at pp collider is given by [8] σ = 1 M 2 DQ /s dx x f q/p(x,q 2 p)f q /p(m 2 DQ/xs,Q 2 p)ˆσ(ŝ) (2) In the equation (2), f q/p (x,q 2 p) and f q /p(m 2 DQ /xs,q2 p) are the quark distribution functions from the proton and we have used CTEQ5L [9] parametrization with Q 2 p = ŝ. The cross section is plotted against the diquark mass in figure (2) for the initial LHC energy ( s = 10TeV) and coupling α DQ = From these figures we find that diquarks with charge Q = 4/3 have the largest cross sections when compared to the other types. The reach for the diquark mass is approximately 4 TeV. If we take α DQ = 0.1 and the LHC nominal energy of ( s = 14TeV) diquark production cross sections becomes approximately 10 times larger and the potential for the discovery of vector diquarks increases to m DQ 10 TeV [8]. The scalar and vector diquarks will decay via DQ q i q j. Therefore, the relevant signal will be a pair of hard jets in the final state. At the LHC energy, major QCD background processes contributing to two-jets (2j) final states are shown in figure 3. The jet p T distribution for the processes pp DQ q i q j X is given in Fig. 4. It is clear that higher p T cuts reduce the background cross sections significantly. Figure 3 shows the dijet invariant mass distribution for the process pp 2j + X including the signal and the QCD backgrounds at the LHC. For comparison signal peaks for scalar and vector diquark masses m DQ = 2,4,6,8 TeV and α DQ = 0.1 are shown on the smooth background distribution. The cross section data for these figures have been generated by CalcHEP program [10] at parton level with various p T cuts on the jets. In order to obtain the observability of diquarks at LHC we have calculated signal (S) and background (B) event estimations for an integrated luminosity of 10 4 pb 1 for one year of operation. The signal generated by a diquark of mass m DQ and decay

4 135 rate Γ DQ is calculated integrating the differential cross section in the two-jet invariant mass interval m DQ Γ DQ < m jj < m DQ + Γ DQ which gives approximately 95% of the events around the resonance. For a realistic analysis of the background events we take into account the finite energy resolution of the ATLAS hadronic calorimeter [11] as δe/e = 0.5/ E for jets with y < 3. The corresponding two-jet invariant mass resolution is given approximately by δm jj = 0.5 m jj m jj. The background is calculated by integrating the cross sections in the range m DQ m < m jj < m DQ + m with m = max(γ DQ,δm jj ). The significance of signal over background is defined as S/ B. In Fig. 5 we present S/ B as a function of the diquark mass for the scalar and vector diquarks with charges Q = 4/3 and 2/3. If we take at least 25 signal events and S/ B 5 as discovery criteria, scalar (vector) diquarks with charge Q = 2/3 can be observed up to 6.4(7.8) TeV. For the diquarks with charge Q = 4/3 it is possible to cover mass ranges up to 8.9(10) TeV at the LHC with L int = 10 4 pb 1. For this luminosity, 10 6 scalar diquark events/year and 10 7 vector diquark events/year are expected for m DQ = 1 TeV. Our results show that even for much lower coupling constants as 10 3, diquarks can be seen at the LHC. 4. CONCLUSION The resonant production of scalar and vector diquarks at LHC have large cross section. With reasonable cuts, it may be possible to cover mass ranges up to 10 TeV for coupling α DQ = 0.1. For smaller couplings as α DQ = 10 3, it is still possible to probe diquarks up to the mass of 4 TeV at an integrated luminosity L = fb 1. REFERENCES [1] H. Terazawa, Subquark model of leptons and quarks, Phys. Rev. D22, 184, [2] J. L. Hewett and T. G. Rizzo, Phys. Rep., 183, 193, [3] B. Schrempp, Talk at the 23rd International Conference on High Energy Physics, MPI-PAE/PTh, 72-86, 1986.;for a review, see W. Buchmuller, Acta Phys. Austriaca,27, 517,1985 [4] CDF Collaboration,Search for new particles decaying to dijets in p p collisions at S = 1.96 TeV.,CDF note 9246,2008. [5] G. Bhattacharyya, D. Choudury and K. Sridhar,Phys. Lett., B355,193, [6] S. Atag, O. Cakir, and S. Sultansoy,Phys. Rev., D59, , [7] E. Arik, S. A. Cetin, O. Cakir and S. Sultansoy, J. High Energy Phys, 09, 024, [8] O. Cakir, and M. Sahin, Phys. Rev., D72, , [9] H. L. Lai et al. (CTEQ Collaboration), Eur. Phys. J., C 12, 375, 2000.

5 136 BALKAN PHYSICS LETTERS [10] A.Pukhov et al.,calchep-a package for calculation of Feynman diagrams and integration over ulti-particle phase space.,preprint arxiv INP MSU,hepph/ ;A. Pukhov., e-print Archive,hep-ph/ ,2004. [11] ATLAS Collaboration, Report No. ATLAS TDR 14, CERN/LHCC 99-14, 1999; Report No. ATLAS TDR 15, CERN/LHCC 99-15, Figure 1: Hadronic process for diquarks Q =4/3 Q =1/3 Q =2/3 σ S (pb) s=10 TeV α DQ = m DQ (TeV) Figure 2: Total cross sections in pp collisions for scalar diquarks for different charges, with coupling strength α DQ = 0.01, depending on their masses. dσ/dm DQ (pb) QCD Background Scalar DQ Vector DQ s=14 TeV α DQ =0.1 P T >250 GeV m DQ (GeV) Figure 3: Dijet invariant mass distributions for pp 2jX. Resonance peaks are shown for scalar and vector diquark masses 2, 4, 6, and 8 TeV for comparison with smooth QCD dijet backgrounds.

6 137 dσ/dp T (pb) QCD Background Scalar DQ Vector DQ s=14 TeV α DQ =0.1 P T >250 GeV P T (GeV) Figure 4: Jet p T distributions for pp 2jX. Resonance peaks are shown for scalar and vector diquark masses 2, 4, and 6 TeV for comparison with smooth QCD dijet backgrounds. Vector DQ, Q =4/ Scalar DQ, Q =4/3 Vector DQ, Q =2/3 Scalar DQ, Q =2/3 5σ 10 3 S/ B s=14 TeV σ m DQ (TeV) Figure 5: The signal significances S/ B for diquarks as a function of diquark mass m DQ at the LHC with s = 14TeV.