µ = (15.4 ± 0.2) 10 10

Transcription

1 L µ L

2 a Exp µ [1 1 ] a µ = a Exp µ a SM µ [1 1 ] 26.1 ± 8. (3.3 ) 31.6 ± 7.9 (4. ) ± ± 8.2 (4.1 ) 28.3 ± 8.7 (3.3 ) 29. ± 9. (3.2 ) 28.7 ± 8. (3.6 ) a EW µ = (15.4 ±.2) 1 1

3 µ µ L µ L µ

4 µ µ L µ L µ

5 L µ L

6 1..8 a µ +3s +2s +1s s g z ".6.4-1s -2s.2-3s m Z "@GeVD g Z O(1) and m Z O(1) GeV

7 g Z O(1) and m Z O(1) GeV

8 Z, h, R e,µ,, A e,µ, FB, A e,µ,, R b,c, A b,c FB, A b,c, M W, W, a µ, (5) had (M 2 Z), s (M Z ), m t, m h g Z 1 g z " ( h, R µ ) m Z "@GeVD Figure 4: The total 2 in the (m Z,g Z ) plane. 2 /(d.o.f) = 35/(22) (SM) g Z <.4 m Z < 1 GeV

9 (Z ) 1 fb

10 p s =7 8 TeV Z! 4e, 4µ, 2e2µ 8 GeV <m 4l < 1 GeV Events/3. [GeV] ATLAS data Standard Model =6 GeV and g =.3 =8 GeV and g = ATLA Stand mo = 15 mo = [GeV] m Z = 6 GeV m 12 m 12 l + l Figure 6: The m 12 and m 34 distributions for the SM (dashed) and for th m Z = 6 GeV (blue) and 8 GeV (red). All channels (4e, 2e2µ and 4µ) (b)

11 (m Z m Z )

12 m 4l >m Z + 1 GeV m 4l m h > 1 GeV m 34 m Z > 5 GeV h Z Z Z Z

13 7 + 8 TeV ( fb 1 ) Events /3. [GeV] Standard Model =8 GeV and g =.3 Events /3. [GeV] Standard Model =9 GeV and g =.3 Events /3. [GeV] Standard Model =1 GeV and g = m 12 [GeV] [GeV] m [GeV] m 12 [GeV] m 12 [GeV] m 12 [GeV] 14 TeV (3 fb 1 ) m 12 Events /3. [GeV] Standard Model =8 GeV and g =.3 Events /3. [GeV] Standard Model =9 GeV and g =.3 Events /3. [GeV] Standard Model =1 GeV and g = [GeV] m 12 [GeV] m [GeV] m 12 [GeV] m [GeV] m 12 [GeV] m 12

14 p s = 14 TeV (p T, > 2 GeV) (p T,µ > 1 GeV) m > 12 GeV

15 Events /3. [GeV] Standard Model =8 GeV and g =.3 Events /3. [GeV] Standard Model =9 GeV and g =.3 Events /3. [GeV] Standard Model =1 GeV and g = m µµ [GeV] [GeV] m µµ [GeV] m µ + µ [GeV] m µ + µ [GeV] m µ + µ [GeV] m µµ (a) (b) (c) Figure 9: The (m µµ )distributionsinthe2µ2 channel at p s =14TeVfortheSM(dashed line) and for the Z model with m Z =8, 9, and 1 GeV (solid lines, from left to right). The integrated luminosity of 3 fb 1 is assumed. > 5 fb 1 > 29 fb 1 > 73 fb 1 m Z < 1 GeV

16 L µ L

17

18 g z " m Z "@GeVD Figure 3: The vertex correction at the Z-pole (q 2 = m 2 Z )isshownasafunctionofm Z and g Z. g f L =(T 3 f Q f s 2 W )(1 + ), g f R = Q fs 2 W (1 + ).

19 data SM fit pull Z model pull Z model pull Z(GeV) (23) h (nb) (37) R e 2.84(5) R µ 2.785(33) R 2.764(45) A,e FB.145(25) A,µ FB.169(13) A, FB.188(17) pol.: A.1439(43) A e.1498(49) b, c quarks: R b.21629(66) R c.1721(3) A,b FB.992(16) A,c FB.77(35) A b.923(2) A c.67(27) SLD: A e.1516(21) A µ.142(15) A.136(15) W boson: M W (GeV) 8.385(15) W (GeV) 2.85(42) muon g-2: a µ (1 9 ) 2.61(.8) Inputs (5) had (M Z 2 ).2763(14) s (M Z ).1184(7) m t (GeV) 173.1(.9) m h (GeV) (.4) m Z (GeV) g Z /(d.o.f) 35.1/(22) 29.2/(22) 31./(22) Table 3: The EW precision data and theoretical predictions of EW precision observables. The experimental data are taken from Ref. [33] except that M W, W, m t and m h are from Ref. [3], and a µ and (5) had are from Ref. [6]. The best fit values of the SM and sample points for Z model, m Z =(6, 8) GeV and g Z =.3 areshown.

20 R R process cross section [fb] SM Z model (m Z = 8 GeV) LEP ( p s = 2 GeV) e + e! 4µ Tevatron ( p s =1.96 TeV) p p! 4µ LHC ( p s = 8 TeV) pp! 4µ pp! 2µ LHC ( p s = 14 TeV) pp! 4µ pp! 2µ Table 5: Cross sections in typical processes where the Z boson contributes, where p T,l > 5 GeV and m l l + > 5GeV(l = µ and ) arerequired.thenumbersforthez model are for m Z =8GeVandg Z =.3.

21 e + e e + e (4e), µ + µ µ + µ (4µ) ande + e µ + µ (2e2µ) at the Z resonance. We summarize the set of selection cuts they have used as follows: 1. four isolated leptons, which have two opposite sign and same-flavor di-lepton pairs, where p T,µ > 4GeVand µ < 2.7 (p T,e > 7GeVand e < 2.47). 2. the leading three leptons must have p T,` > 2, 15, and 8 GeV, and if the third (p T - ordered) lepton is an electron it must have p T,e3 > 1 GeV. 3. the four leptons are required to be separated as R`` > the invariant masses of the same-flavor and opposite-sign leptons are required to have m l + l > 5 GeV. 5. m 12 > 2 GeV and m 34 > 5 GeV, where m 12 is the invariant mass of the same flavor and opposite sign di-lepton pair which is the closest to the Z boson mass among the possible combinations, while the other one is called m the invariant mass of the four leptons is in the m Z window, 8 GeV <m 4l < 1 GeV.

22 Events/3. [GeV] ATLAS data Standard Model =6 GeV and g =.3 =8 GeV and g =.3 Events/3. [GeV] ATLAS data Standard Model =6 GeV and g = =8 GeV and g = m 12 [GeV] [GeV] m 34 (a) (b) Figure 6: The m 12 and m 34 distributions for the SM (dashed) and for the Z models with m Z = 6 GeV (blue) and 8 GeV (red). All channels (4e, 2e2µ and 4µ) aresummedup. Combined results for the integrated luminosities of 4.6 fb 1 at p p s =7TeVand2.7fb 1 at s =8TeVareshown.

23 N SM N Z,6 Z,6 N Z,8 Z,8 (51, 57) GeV (57, 63) GeV m 12 (63, 69) GeV (69, 75) GeV (75, 81) GeV (3,18) GeV m 34 (18,33) GeV (33,48) GeV Table p 6: Event numbers in several m 12 and m 34 ranges. The luminosities of 4.6 fb 1 at s =7TeVand2.7fb 1 at p s = 8 TeV are combined and event numbers in all channels (4e, 2e2µ and 4µ) aresummedup,asstudiedinref.[38]. N SM and N Z,6 (N Z,8) are numbers of events in the SM and the Z model with m Z = 6 GeV (8 GeV), respectively. We also show the significance Z =(N Z N SM)/ p N SM. SM Z model (m Z = 6 GeV) Z model (m Z = 8 GeV) 2 /(d.o.f) in m /(19) 47.1/(19) 34.1/(19) 2 /(d.o.f) in m /(14) 26.6/(14) 6.5/(14) Table 7: 2 in the m 12 and m 34 distributions in the SM and the Z models with m Z =6 and 8 GeV.

24 4µ channel N SM N Z,6 Z,6 (51, 57) GeV m 12 (57, 63) GeV (63, 69) GeV Table 8: Numbers of events in several m 12 ranges in 4µ channel for the SM (N SM )andz model with m Z =6GeV(N Z ). We also show Z =(N Z N SM )/ p N SM.

25 4.2.2 pp! µ + µ + In our Z model, the Z boson couples to the 2nd and 3rd generation leptons. In order to test the feature, we need to see the pattern of the couplings of the Z boson. One of these interesting processes is 2µ2 channel. To study this channel, we adopt hadronic tagging algorithm of Delphes which roughly reproduce ATLAS and CMS data for Z! + channel [36]. For this channel we require the following cuts: 1. two jets exist satisfying p T, > 2 GeV and < 2.3, only hadronically decaying s. 2. two oppositely charged muons exist satisfying p T,µ > 1 GeV and µ < 2.7, the two muons are well separated as R> requiring the invariant mass cut for the two s, m > 12 GeV, where we adopt the collinear approximation for the momentum reconstruction, that is, the neutrino momentum from decay is assumed to be parallel to the jet direction.

26 m Z =8GeV N SM N Z N Z /N SM R dtl for discovery (fb 1 ) (71, 77) GeV m µµ (77, 83) GeV > 5 (83, 89) GeV m Z =9GeV N SM N Z N Z /N SM R dtl for discovery(fb 1 ) (81, 87) GeV m µµ (87, 93) GeV > 29 (93, 99) GeV m Z =1GeV N SM N Z N Z /N SM R dtl for discovery(fb 1 ) (91, 97) GeV m µµ (97, 13) GeV > 73 (13, 19) GeV Table 13: Number of events in several m µµ ranges in 2µ2 channel at p s =14TeVwith R dtl =3fb 1 in the SM and the Z model with m Z = 8, 9, and 1 GeV. m Z < 1 GeV