linear Colliders Sayipjamal Dulat, Kaoru Hagiwara and Yu Matsumoto Xinjiang University, China and KEK, Tsukuba, Japan

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1 Measuring Triple Gauge Boson Couplings at e + e linear Colliders Sayipjamal Dulat, Kaoru Hagiwara and Yu Matsumoto Xinjiang University, China and KEK, Tsukuba, Japan Measuring Triple Gauge Boson Couplings at e + e linear Colliders

2 1 Outline Why do we measure triple gauge boson couplings Effective lagrangian, dimension 6 operators, and T GC Optimal observable method W W γ couplings via e + e ν e ν e γ W W Z couplings via e + e ν e ν e Z Conclusion

3 Why do we measure Triple Gauge-boson Couplings - Test the non-abelian nature of the electroweak sector of the SM - Probe for new physics effects via the TGC anomaly at ILC 2 How? Use an Effective Lagrangian of the SM particles L eff = L SM + i f (6) i O (6) i Λ 2. Λ may characterize the new physics scale, and f i coeffients. are the dimensionless

4 There are 8 gauge invariant bosonic dim. 6 operators with the Higgs boson: 3 O W W ZZ Zγ γγ HH W W V HW W HZZ HZγ Hγγ O W W Φ ŴµνŴ µν Φ O BB Φ ˆBµν ˆB µν Φ O BW Φ ˆBµνŴ µν Φ O W (DµΦ) Ŵ µν (DνΦ) O B (DµΦ) ˆBµν (D νφ) O φ,1 [(DµΦ) Φ][Φ (D µ Φ)] O φ,4 (Φ Φ)[(DµΦ) (D µ Φ)] O 1 φ,2 2 µ(φ Φ) µ (Φ Φ) denotes the nonstandard interactions denotes the no observable effects after renormalization.

5 WWγ and WWZ couplings: 4 L WWV eff = L WWV SM + 1 ( Λ 2 f BW Φ ˆBµνŴ µν Φ + f WW Φ ŴµνŴ µν Φ + f W (DµΦ) Ŵ µν (DνΦ) + f B (DµΦ) ˆBµν ) (D νφ) = ig WWV (g V 1 (W + µν W µ W µν W +µ )V ν + κ V W + µ W ν V µν). g WWγ = e and g WWZ = e cot θ W. g γ 1 = 1, κ γ = 1 + (f B + f W ) m2 W 2Λ 2, κ Z = 1 + m 2 ( Z 2Λ 2 cos 2 θ W f W sin 2 ) θ W f B, g Z 1 = 1 + f W m 2 Z 2Λ 2 We examine how accurately one can measure c 1 κγ = κγ 1, c 2 κ Z = κ Z 1, c 3 g Z 1 = g1 Z 1 at ILC.

6 Optimal observable method 5 dσ dω = Σ SM(Ω) + i c i F i (Ω), (c 1 = κ γ 1, c 2 = κ Z 1, c 3 = g Z 1 1) Number of events in the k th bin of the phase space point Ω k with the bin size Ω: N th k (c 1, c 2,..., c n ) = L Σ SM (Ω k ) Ω + L i c i F i (Ω k ) Ω = N exp k ± Constraints on (c 1, c 2,..., c n ) from the data: N exp k χ 2 (c 1, c 2,..., cn) = k = k ( N th k N exp k N exp k ) 2 = ( L ΣSM (Ω k ) + L i c i F i (Ω k k N exp k ( L i c i F i (Ω k ) Ω ) 2 c i (V 1 ) ij c j L Σ SM (Ω k ) Ω i,j ) Ω Nexp k ) 2

7 6 χ 2 (c 1, c 2,..., c n ) i,j c i (V 1 ) ij c j (V 1 ) ij = L Fi (Ω)F j (Ω) dω Σ SM (Ω) i, j = 1, 2,..., n V ij is called covariance matrix. The diagonal elements V ii is called variance of c i. And square root of the variance gives the error of the measurement c i = V ii, ρ ij = n i,j V ij Vii V jj where ρ ij is the correlation between the error on c i and that on c j.

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9 WWγ couplings via e e + ν e ν e γ diferential cross section dσ dp T dη = Σ SM(P T, η) + c 1 F 1 (P T, η), c 1 = κ γ 1 8 Inverse of the variance of c 1 is (V 1 ) 11 = L k F 2 1 (P T, η) k Σ SM (P T, η) k P T η, c 1 = V 11,

10 Background processes P T and η distr. of the photon with cos θ e ± > 0.995, cos θ γ < 0.995, s = 250GeV for 9

11 P T and rapidity distributions of the photon for e + e ν e ν e γ 10

12 11 At s = 250GeV we obtain Σ SM (P T, η)dp T dη fb, V 1 = L F 1 2 (P T, η) Σ SM (P T, η) dp Tdη L 50fb We find for various s and L: c 1 = V 0.14/ L(fb 1 ) (κγ 1) s(gev ) L(fb 1 ) colliders LEP ILC ILC ILC2 Discussion: We observe that as the cross section increases for higher and higher s, the error in measuring these coupling parameters becomes smaller and smaller.

13 WWZ couplings via e + e ν e ν e Z 12 There are two terms in the WWZ couplings : κ Z 1 = c 2, g Z 1 1 = c 3 (V 1 ) ij = L Fi (Ω)F j (Ω) dω i, j = 2, 3 Σ SM (Ω) c i = V ii, i = 2, 3, ρ 23 = V 23 V22 V 33

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15 P T and rapidity distributions of Z boson for e + e ν e ν e Z 14

16 15

17 We find for various s and L: 16 (κ Z 1) (g1 Z 1) ρ(κ Z 1, g1 Z 1) s(gev ) L(fb 1 ) Discussion: We observe that as the cross section increases for higher and higher s, the error in measuring these couplings becomes smaller and smaller.

18 Conclusion We obtain the parameters of the TGC s for various s and L by studying the processes e + e ν e ν e γ, and e + e ν e ν e Z 17 (κ γ 1) (κ Z 1) (g Z 1 1) ρ(κ Z 1, g Z 1 1) s(gev ) L(fb 1 ) These TGC parameters are sensitive to new physics that contribute to the dim-6 operators, O W and O B. - (κ γ 1) < κ Z 1 for s 500GeV - (κ γ 1) > κ Z 1 for s 1T ev because of σ(e + e ν e ν e Z) > σ(e + e ν e ν e γ) at higher energies.

19 18 Electromagnetic gauge invariance requires that g γ 1 = 1, while the κ γ, κ Z and g Z 1 to the coefficients of the dimension six operators as are related κ γ 1 = (f B +f W ) m2 W 2Λ 2, κ Z 1 = m2 Z 2Λ 2 ( cos 2 θ W f W sin 2 θ W f B ), g Z 1 1 = f W m 2 Z 2Λ 2 We find the constraints on f W and f B f W f B ) ρ(κ Z 1, g1 Z 1) s(gev ) L(fb 1 )

20 19 Thank You!