Dileptonic Bottomonium Decays: Higgs-Boson Signal

Transcription

1 : Higgs-Boson Signal Saime Kerman Dokuz Eylul University, Izmir, TURKEY IOPAS HEP Theory Group Seminar 14 December 2016, Academia Sinica Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

2 Outline Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

3 Heavy Quark Bound States Quarkonium is the name given to a sub-atomic system composed of heavy quark Q and anti-quark Q bound by the strong interaction. Charmonium c c quark pair (J/ψ: Exp. in 1974 with narrow state decaying to e + e and µ + µ by BNL and SLAC groups) [1], [2]. Bottomonium b b quark pair (Υ: Exp. in 1977 in decays to µ + µ by group at FermiLab) [3]. Many other quarkonium states with different quantum numbers were discovered later. Quarkonium states are typicaly categorised according their S, L and J quantum numbers. Q Q: The spectroscopic notation: n 2S+1 L J, J PC. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

4 Q Q quark-model assignments for the observed heavy mesons: Table 1: Quarkonium Spectroscopy [4]. Mesons in bold face are included in the Meson Summary Table. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

5 Mass spectrum for mesons: Figure 1: Mass spectrum [4]. Particles whose masses are used to fix lattice parameters are shown with crosses; the authors distinguish between "predictions" and "postdictions" of their calculation. Lines represent experiment. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

6 We, in particular, focus on the pseudoscalar η b (an S-wave J PC = 0 + state) and the scalar χ b0 (a P-wave J PC = 0 ++ state) bound states because much less is known about the spin singlet (S=0) S-wave states. Also dileptonic decay of χ b0 bound state is available to search Higgs boson signal. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

7 Although, a new particle has been discovered at the CMS and ATLAS experiments [5] which is consisted with the Higgs boson predicted by SM, we do not have enough knowledge what Higgs sector is. In terms of its content and goal, the present work falls in the interface between flavor physics and Higgs physics. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

8 Approaches for Heavy Bound States Theoretical information about quarkonium systems can be understood from the study of decay and collision processes. Two approaches: I. Phenomenological approach: Simple non-relativistic potential models. II. QCD approach: Direct calculation using QCD (with lattice QCD). Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

9 Motivation In this work we aim at answering the following question: By measuring the decay rates of certain (b b) states, preferably but not necessarily into l + l, can we establish the existence and nature of Higgs bosons? Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

10 In what follows, in regard to the question raised above, we study the pseudoscalar η b and the scalar χ b0 decays into l + l in the framework of the Standard Model. Through these studies one may also test the effects of Z Boson and Higgs boson on the aforementioned bottomonium decays into lepton pairs. Additionally, the possibility for an estimate on the dileptonic branchings of the bottomonia, provides motivation on the study of these rare decays of bottomonium systems. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

11 Formalism In our analysis SM higgs sector is taken into account and different potential-models (The decay widths of bottomonium states depend crucially on bottomonium wave function. The wave functions can be derived from bound state potentials of quarkonium states) are considered in order to find the decay widths of bottomonium states. The Coulomb,Cornell [6], Richardson [7] and Wisconsin [8] potential model choices are considered. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

12 The wave functions can be derived from the quark-antiquark potential. So the results are sensitive to the choice of interquark potential model [9] Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

13 R S (0) 2 = m Q dv dr (1) R P (0) 2 = m Q 9 1 r 2 dv dr + 4 (E V ) r 3 (2) where E = M QQ 2m Q, and R S (0) and R P (0) are the radial wave function of S state and the derivative of the radial wave function for the P state at r = 0 Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

14 The potential models are: I. Coulomb Potential (at short distances, less than 1 fm) V (r) = 4 3 α s (m 2 Q ) r (3) with a runnig strong coupling α s, evaluated at a scale m Q, given by α s = 12π (33 2N f )ln(m 2 Q /Λ2 ) (4) N f = 6 and Λ = 0.12 GeV. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

15 II. Cornell Potential (at distance beyond around 1 fm) V (r) = k r + ar (5) with the constants k and a fixed by bb data. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

16 III. Richardson Potential (short-long distance) V (Q) = π N f Q 2 ln(1 + Q 2 /Λ 2 ) (6) Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

17 IV. Wisconsin Potential (at distance beyond around 1 fm) V (r) = V S (r) + V I (r) + ar (7) where V S (r) = 4α s (r)/3r and the intermediate potential V I (r) = r(c 1 + c 2 r)e r/r 0 and this potential should be zero at small and large radii. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

18 Figure 2 shows the S-wave radial wave function squared divided by M 2 η Q [9]. Figure 2: The S-wave radial function squared diveded by Mη 2 Q as a function of the mass of the heavy quark m Q Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

19 Figure 3 shows the square of the derivative of the wave function for the lowest P state [9]. Figure 3: The derivative of P-wave function squared diveded by M 4 χ Q as a function of the mass of the heavy quark m Q Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

20 Figure 4 shows generic diagram for two body decay of the pseudoscalar η b quarkonium state. Figure 4: Feynman diagram for the decay: η b l + l Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

21 Feynman diagram of the scalar χ b0 quarkonium state is shown in Figure 5. Figure 5: Feynman diagram for the decay: χ b0 l + l Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

22 The interaction of Higgs boson with b quark and charged leptons is given by L higgs = h SM f f f h (8) where f = b, l, and hf SM = (g 2 m f )/(2M W ) is the Yukawa coupling of fermion f in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

23 Having specified the framework in both Higgs and meson sides, we now turn to an explicit computation of the decay rates of bottomonia. In this respect, the decay rates of η b and χ b0 into lepton pairs are then given by Γ ( η b l + l ) = 3 8π 2 R S (0) 2 M 2 η b β l 4r l ( g 2 Z 1 r Z ) 2 (9) Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

24 Γ ( χ b0 l + l ) = 27 8π 2 R P (0) 2 M 4 χ b0 β 3 l ( g b h g l h 1 r h ) 2 (10) where R S (0) (R P (0)) is the S-wave (derivative of P-wave) quarkonium wavefunction at the origin and gh f = hsm f is the Yukawa coupling of fermion f in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

25 g Z = e/ (4 sin θ W cos θ W ) (11) r i = m 2 i /M2 X (12) (i = l, h, Z ) and β l = ( 1 4m 2 l /M2 X ) 1/2 (13) where X = η b for η b l + l and X = χ b0 for χ b0 l + l. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

26 Numerical Analysis In this section a numerical study of the decay rates is performed in view of disentangling Z and H effects from the rest. In doing this, different potential model wave functions are examined to probe the arbitrariness in the potential dependency. Moreover, the SM predictions for the branching ratios are compared with those of the MSSM for the mentioned bottomonium systems ( m H = GeV ). Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

27 Decay Rates: Decay Potential SM ( GeV) η b e + e Cornell Richardson Wisconsin Coulomb Table 2: The η b e + e decay width for different potential models in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

28 Decay Potential SM ( GeV) η b µ + µ Cornell Richardson Wisconsin Coulomb Table 3: The η b µ + µ decay width for different potential models in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

29 Decay Potential SM ( GeV) η b τ + τ Cornell Richardson Wisconsin Coulomb Table 4: The η b τ + τ decay width for different potential models in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

30 Decay Potential SM ( GeV) η b l + l Cornell Richardson Wisconsin Coulomb Table 5: Total decay widths of the η b l + l for different potential models in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

31 Decay Potential SM ( GeV) χ b0 e + e Cornell Richardson Wisconsin Coulomb Table 6: The χ b0 e + e decay width for different potential models in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

32 Decay Potential SM ( GeV) χ b0 µ + µ Cornell Richardson Wisconsin Coulomb Table 7: The χ b0 µ + µ decay width for different potential models in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

33 Decay Potential SM ( GeV) χ b0 τ + τ Cornell Richardson Wisconsin Coulomb Table 8: The χ b0 τ + τ decay width for different potential models in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

34 Decay Potential SM ( GeV) χ b0 l + l Cornell Richardson Wisconsin Coulomb Table 9: Total decay width of the χ b0 l + l for different potential models in the SM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

35 Branching Ratios: The branching ratios of the η b and χ b0 decays into l + l pairs for both SM and MSSM processes using two parameter spaces: SPSI and SPSII [10]. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

36 SUSY Parameter Space I (SPSI): m h = 98 ± 5 GeV, m H = 115 ± 5 GeV, m A = 89 ± 5 GeV, tan β = 10 ± 2.5 (14) which is inspired from the reanalysis of the LEP results mentioned in [10]. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

37 SUSY Parameter Space II (SPSII): m h = 115 ± 5 GeV, m H = 425 ± 5 GeV, m A = ± 5 GeV, tan β = 10 ± 2.5 (15) which is inspired from the SPS1a parameter space of the MSSM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

38 Decay Rates for MSSM: Γ ( η b l + l ) = 3 R S (0) 2 8π 2 Mη 2 b { ( g b A ga l 1 r A β l ) 2 + 4r l ( g 2 Z 1 r Z ) r l g 2 Z gb A gl A (1 r A )(1 r Z ) } (16) Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

39 Γ ( χ b0 l + l ) = 27 8π 2 R P (0) 2 M 4 χ b0 β 3 l ( g b h g l h 1 r h + gb H gl H 1 r H ) 2 (17) Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

40 Yukawa couplings are given by gh f = hf SM [sin (β α) tanβcos (β α)] gh f = hsm f [cos (β α) + tanβsin (β α)] ga f = hsm f tanβ (18) tanβ = Hu 0 / H 0 d α = 1 2 arcsin [ ( ) ( ) ] ma 2 + m2 Z / mh 2 m2 h sin2β (19) Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

41 Our findings are presented in Tables below for η b and χ b0 decays, respectively. As input parameters we used Γ ηb = 10 MeV taken from [11] and Γ χb0 = 320 kev from [12]. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

42 Decay Pot. SM MSSM(SPSI) MSSM(SPSII) BR(η b ) Cor Ric Wis Cou Table 10: The branching ratios of the η b decay for different potential models in the SM and in the MSSM. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

43 Decay Pot. SM MSSM(SPSI, SPSII) BR(χ b0 ) Cou ( , ) oth ( , ) Table 11: The branching ratios of the χ b0 decay as in Table for η b decay. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

44 Summary As can be read from Tab. 10 our predictions for the branching ratios of η b l + l decay in MSSM is 1 (SPSII) and 1.2 (SPSI) times larger than the SM values. Also from Tab. 11, MSSM predictions for the χ b0 l + l branching ratio can be as large as 49 (SPSII) or even 8400 (SPSI) times larger than that of the SM predictions. Both of the decays are rare decays and it is possible to enhance the predictions theoreticaly in MSSM or in extended gauge sectors, U(1) model, containing Z gauge boson. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

45 Experimentally, since the predictions of the branching ratios are at the order of 10 7 for the η and for the χ decays, in the MSSM, η b turns out to be a better candidate for the observation of the Higgs bosons over these rare decays. The results found here, can be tested at the LHCb experiments so such a test can provide a confirmation of our strategy for Higgs sectors. Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

46 THANK YOU Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

47 J.E. Augustin et al., SLAC-SP-017 Collaboration. Phys. Rev. Lett 33, (1974). J.J. Aubert et al., E598 Collaboration. J. Phys. Rev. Lett 33, (1974). S.W.Herb et al. Phys. Rev. Lett 39, (1977). C. Patrignani et al. [Particle Data Group Collaboration], Chin. Phys. C, 40, (2016). S. Eidelman et al. [Particle Data Group Collaboration], Phys. Lett. B 592, 1 (2004). E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T. M. Yan, Phys. Rev. D 17, 3090 (1979); 21, 203 (1980). J.L. Richardson, Phys. Lett. B 82, 272 (1979); W. Buchmüller and S.-H. Tye, Phys. Rev. D 24, 132 (1981). Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal

48 Kaoru Hagiwara, Steve Jacobs, M. G. Olsson, and K. J. Miller, Phys. Lett. B 130, 209 (1983); a recent analysis by K. Hagiwara, A. D. Martin and A. W. Peacock, Mod. Phys. C 33, 135 (1986); Relativistic effects are discussed in Steve Jacobs, M. G. Olsson and Casimir Suchyta III, Phys. Rev. D 33, 3338 (1986); 34, 3536 (1986). V. D. Barger, E. W. N. Glover, K. Hikasa, W. Y. Keung, M. G. Olsson, C. J. Suchyta and X. R. Tata, Phys. Rev. D 35, 3366 (1987) [Erratum-ibid. D 38, 1632 (1988)]. D. A. Demir, L. Solmaz and S. Solmaz, Phys. Rev. D 73 (2006). B. Aubert [The BABAR Collaboration], arxiv: [hep-ex]. M. A. Sanchis-Lozano, arxiv:hep-ph/ Saime Kerman Dokuz Eylul University, Izmir, TURKEY : Higgs-Boson Signal