SLAC-PUB Work supported by the Department of Energy contract DE-AC02-76SF00515.

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1 SLAC-PUB Strong Symmetry Breaking Signals in e + e ;! W + W ; at p s = 800 GeV Timothy L. Barklo Stanford Linear Accelerator Center, P.O. Box 4349 Stanford, California Abstract. The sensitivity ofe + e ; linear colliders to strong W + W ; scattering eects in e + e ;! W + W ; is examined. Past studies have concentrated on e + e ; linear colliders ith center-of-mass energies of more than 1 TeV and integrated luminosities of less than 200 fb ;1. Here e revie the strong symmetry breaking signals that can be observed ith center-of-mass energies of 05 ; 08 TeV and luminosities of 300 ; 500 fb ;1. INTRODUCTION Until a Higgs boson resonance is observed it is important to continue to ask hoa collider ith TeV scale parton{parton interactions ill study electroeak symmetry breaking in the absence of such a resonance. If there is no Higgs boson resonance then W + W ; scattering becomes strong above 1TeV in the W + W ; center-of-mass system. At an e + e ; linear collider one ould directly study W + W ; scattering in reactions such as e + e ;! W + W ; [1{3] and e + e ;! tt [4,5]. One can also observe strong symmetry breaking eects in the reaction e + e ;! W + W ;. Previous studies of this reaction have focused on e + e ; colliders ith center-of-mass energies greater than1tev and integrated luminosities of no more than 200 fb ;1 [6,7]. In this paper e examine ho ell one can study strong symmetry breaking in e + e ;! W + W ; if the center-of-mass energy is loered to 05 ; 08 TeV and the integrated luminosity is raised to 300 ; 500 fb ;1. The reaction e + e ;! W + W ; is aected in to ays by strong symmetry breaking. First, anomalous triple gauge boson couplings (TGC's) are induced by the strongly coupled physics responsible for electroeak symmetry breaking. Second, the amplitude for longitudinal W boson pair production, e + e ;! W L W L, is modied by strongly interacting W bosons, just as the amplitude for e + e ;! + ; is modied relative to pointlike charged scalar production by the QCD strong interactions of the pions [8]. Work supported by the Department of Energy contract DE-AC02-76SF Presented at the 5th International Linear Collider Workshop (LCWS 2000), Oct 24-28, 2000, Batavia, IL

2 TRIPLE GAUGE COUPLINGS The interactions of the Standard Model gauge boson elds are described by an eective chiral Lagrangian if the electroeak symmetry breaking sector is strongly interacting L SB = L (2) + L (4) + here L (2) = 1 4 v2 TrD y D L (4) = L h 1 Tr D y D 16 2 i 2 L Tr D 2 y D Tr D y D ;ig L 9L 16 2 Tr W D D y +gg 0 L Tr B y W ; ig 0 L 9R 16 Tr B D 2 y D Here W i and B are the gauge elds and is composed of the Goldstone boson elds i = exp i i i v The terms ith coecients L 9L, L 9R induce anomalous triple gauge boson couplings e2 =1+ (L 32 2 s 2 9L + L 9R ) e2 Z =1+ (L 32 2 s 2 9L ; s2 L c 2 9R ) g Z 1 =1+ e2 L 9L 32 2 s 2 c 2 Assuming QCD values for L 9L and L 9R, is shifted by ;3 10 ;3. This shift is almost an order of magnitude larger than the 410 ;4 measurement precision expected for at an e + e ; collider at p s = 500 GeV ith 300 fb ;1 [9]. MEASURING THE AMPLITUDE e + e ;! W L W L The amplitude for e + e ;! W L W L ill develop a complex form factor F T if the longitudinal W bosons are strongly interacting. We use the folloing expression for this form factor F T =exp[ 1 Z 1 0 ds 0 (s 0 1 M ; )f s 0 ; s ; i ; 1 s 0 g]

3 here (s) = 1 s 96 v " tanh( s ; M 2 M ; )+1 # Here M ; are the mass and idth respectively of a vector resonance in W L W L scattering. The term (s) = 1 s 96 v 2 is the Lo Energy Theorem (LET) amplitude for W L W L scattering at energies belo a resonance. The folloing unitarization scheme is used for the LET amplitude (s) = 8 >< > 1 96 s v 2 if s<s 0 1 s 0 96 v 2 if s s 0 here s 0 = (28 TeV) 2. This scheme produces values for F T hich are similar to those obtained ith the K-matrix unitarization scheme in the LET limit of M!1. The real and imaginary parts of F T are determined experimentally ith a maximum likelihood t. The inputs to this t are the W ; production angle and the four W + W ; decay angles. This type of analysis is commonly used at LEP2 to measure TGC's. We assume 80/0% e ; =e + beam polarization here the e ; beam is all left-handed. We analyze the eqq and qq channels assuming a solid angle coverage of j cos j < 09. To improve our sensitivity e assume that charm jets can be tagged ith 100% purity and 65% eciency. Such a purity/eciency combination is not out of the question given that b jet contamination is not a factor in the eqq and qq channels. Charm tagging provides an improvement in the LET signal hich isequivalent to a 50% increase in luminosity. We use statistical errors only. In practice, one ill also have to consider various sources of systematic errors. Hoever, these are fairly small in the eqq and qq channels, and in any event they ill be oset by an increase in statistical precision hen other W + W ; decay channels, such as qq and qqqq, are included. The expected 95% condence level limits for F T for p s = 800 GeV and a luminosity of 500 fb ;1 are sho in Figure 1. The folloing sets of vector resonance masses and idths ere used to calculate the predictions for F T shon in Figure 1 (M ; ) = ( ) ( ) ( ) TeV Table 1 summarizes the signal signifcance for various vector resonances and for the LET limit. The signicances from e + e ; linear colliders of dierent energies and luminositities are displayed along ith the signicances expected from the LHC [10].

4 LET M ρ = 2.5 TeV 1.6 TeV Im(FT) % C.L Re(FT) FIGURE 1. 95% C.L. contour for F T for p s = 800 GeV and 500 fb ;1. TABLE 1. Signal signicance for various vector resonance masses. p Final s L M = M = M = LET State TeV fb ;1 1.2 TeV 1.6 TeV 2.5 TeV LC W + W ; LC W + W ; LC W + W ; LHC qqw + Z { { LHC qqw + W { 5 From Table 1 e see that e + e ; linear colliders provide a signicant enhancement over LHC in the study of vector resonance production in W L W L scattering. Even at p s = 500 GeV an e + e ; linear collider outperforms LHC in the study of 1.2, 1.6, and 2.5 TeV vector resonances. The LET signal signicance at the LHC and at the 0.8 and 1.5 TeV linear colliders are roughly the same. Hoever, it is interesting that the LET signicance at the 0.8 TeV linear collider is slightly better than the signicance at the 1.5 TeV linear collider.

5 CONCLUSION The reaction e + e ;! W + W ; ill supply important information about a strong symmetry breaking sector hich ill complement the information obtained from other reactions at an e + e ; linear collider and from the LHC. High precision measurements of triple gauge boson couplings ill probe parameters of the eective chiral Lagrangian. The measurement of the form factor for e + e ;! W L W L ill signicantly enhance our knoledege of the I = J = 1 channel in W L W L scattering. Finally, inaninteresting tradeo of energy and luminosity, e observe that a linear collider ith 500 fb ;1 at p s =800GeV gives a larger LET signal than one ith 200 fb ;1 at p s = 1500 GeV. REFERENCES 1. V. Barger, K. Cheung, T. Han and R. J. Phillips, Phys. Rev. D 52, 3815 (1995) [hep-ph/ ]. 2. E. Boos, H. J. He, W. Kilian, A. Pukhov, C. P. Yuan and P. M.Zeras, Phys. Rev. D 57, 1553(1998) [hep-ph/ ]. 3. E. Boos, H. J. He, W. Kilian, A. Pukhov, C. P. Yuan and P. M.Zeras, Phys. Rev. D 61, (2000) [hep-ph/ ]. 4. E. Ruiz Morales and M. E. Peskin, in Physics and Experiments ith Future e + e ; Linear Colliders, E. Fernandez and A. Pacheco, eds. (UAB Publications, Barcelona, 2000) [hep-ph/ ]. 5. T. Han, Y. J. Kim, A. Likhoded and G. Valencia, Nucl. Phys. B593, 415 (2001) [hep-ph/ ]. 6. T. L. Barklo, in Workshop on Physics and Experiments ith Linear Colliders, A. Miyamoto, Y. Fujii, T. Matsui, and S. Iata, eds. (World Scientic, 1996). 7. T. L. Barklo, etal., inne Directions in High Energy Physics Snomass 96, D.G. Cassel, L.T. Gennari, and R.H. Siemann, eds. (SLAC, 1997). hep-ph/ M. Peskin, in Physics in Collisions IV, A. Seiden, ed. (Editions Frontieres, Gif-Sur- Yvette, France, 1984). 9. C. Burgard, in Physics and Experiments ith Future e + e ; Linear Colliders, E. Fernandez and A. Pacheco, eds. (UAB Publications, Barcelona, 2000). 10. ATLAS Detector and Physics Performance Technical Design Report, LHCC 99-14/15 (1999).