Higgs Mass Bounds in the Light of Neutrino Oscillation

Transcription

1 Higgs Mass Bounds in the Light of Neutrino Oscillation Qaisar Shafi in collaboration with Ilia Gogoladze and Nobuchika Okada Bartol Research Institute Department of Physics and Astronomy University of Delaware Newark, DE 19716, USA

2 OUTLINE Introduction Higgs Boson and SeeSaw Mechanism(s) Gauge-Higgs Unification Conclusion

3 WHERE is the SM Higgs Boson? From arguments based on vacuum stability and perturbativity, and with no new physics between M Z and M Planck, one finds 130 GeV m h 170 GeV N. Cabibbo, L. Maiani, G. Parisi and R. Petronzio, Nucl. Phys. B 158, 295 (1979); P. Q. Hung, Phys. Rev. Lett. 42, 873 (1979); M. A. B. Beg, C. Panagiotakopoulos and A. Sirlin, Phys. Rev. Lett. 52, 883 (1984); K. S. Babu and E. Ma, Phys. Rev. Lett. 55, 3005 (1985); M. Lindner, Z. Phys. C 31, 295 (1986); M. Sher, Phys. Rept. 179, 273 (1989); G. Altarelli and G. Isidori, Phys. Lett. B 337, 141 (1994); J. A. Casas, J. R. Espinosa and M. Quiros, Phys. Lett. B 342, 171 (1995) [arxiv:hep-ph/ ]; J. A. Casas, J. R. Espinosa and M. Quiros, Phys. Lett. B 382, 374 (1996) [arxiv:hep-ph/ ]; J. R. Espinosa and M. Quiros, Phys. Lett. B 353, 257 (1995) [arxiv:hep-ph/ ].

4 6 5 4 Theory uncertainty α had = α (5) ± ± incl. low Q 2 data χ Excluded m H [GeV]

5 SM Higgs boson mass bounds (M.E.MachacekandM.T.Vaughn) From the Higgs potential in the SM, Higgs quartic coupling determines Once Higgs mass is measured, its high energy behavior can be understood via RGE running of top Yukawa is important

6 The Standard Model Higgs mh GeV Log 10 Μ GeV

7 Physics beyond the SM required by: Neutrino ( Oscillations ) m 2 SM dim ev 2 m 2 ATM, m2 SOL mνi 1 ev δt T (Inflation) 10 5 Non-baryonic DM (Ω CDM 0.25) Baryon Asymmetry ( n B /s 10 10), with Ω B 0.05 Dark Energy

8 Type I Seesaw SM singlet fermion origin Type II Seesaw SM SU(2) triplet scalar origin Type III Seesaw SM SU(2) triplet fermion origin

9 In all seesaw scenarios, new particles couple to Higgs doublet contribute to Higgs quartic RGE for Running mass: We choose SM running Contributions by : type I : type II : type III

10 Type I seesaw Modification of RGEs in the presence of 3 singlet fermions with For simplicity, we assume 3 degenerate N: Light neutrino mass matrix: SM RGEs Casas, Clemente, Ibarra & Quiros, PRD 62, (2000); ( Okada, Gogoladze, QS ) (arxiv: [hep-ph]) * We employ 2-loop SM RGEs + 1-loop new RGEs

11 Fixing the cutoff scale, we investigate Higgs mass bounds Vacuum stability bound: the lowest Higgs boson mass which satisfies for any scale between Perturbativity bound: the highest Higgs boson mass which satisfies for any scale between

12 Type I Seesaw and Higgs Mass Bounds mh GeV Log 10 M R GeV Higgs boson mass bound as a function of M R in the case with hierarchical mass spectrum. The lower and upper lines correspond to the stability and perturbativity bounds, respectively. The Higgs boson mass range is closed for M R = GeV, where m h = 175 GeV. Casas et. al. (hep-ph/ ); Gogoladze et.al. (arxiv: [hep-ph]).

13 Type I Seesaw and Higgs Mass Bounds mh GeV Log 10 M R GeV Higgs boson mass bound as a function of M R in the case with inverted-hierarchical mass spectrum. The lower and upper lines correspond to the stability and perturbativity bounds, respectively. The Higgs boson mass range is closed for M R = GeV, where m h = 173 GeV.

14 Type I Seesaw and Higgs Mass Bounds mh GeV Y Ν Higgs boson mass bound as a function of Y ν. The lower and upper lines correspond to the stability and perturbativity bounds, respectively. The limit Y ν = 0 reproduces the SM result. The Higgs boson mass range is closed for Y ν 1.6.

15 Type II seesaw Gogoladze, Okada & Shafi, arxive: [hep-ph] We introduce a triplet scalar field Scalar potential Many new couplings:

16 Neutrino Yukawa coupling: Tadpole term for the triplet scalar Neutrino mass: After integrating out the heavy triplet, we have SM Higgs quartic is defined as

17 Now we solve RGEs in the presence of Type II seesaw Many free parameters: SM RGEs with the matching condition: * We employ 2-loop SM RGEs + 1-loop new RGEs

18 M. A. Schmidt RGE of is decoupled from other RGEs, but plays an important role through the matching condition

19 Analysis is quite involved.. We focus on most important parameters: appear in Higgs quartic RGE shifts Higgs quartic by the matching condition We analyze RGEs for various at the cutoff with others fixed Fixing the cutoff scale, we investigate Higgs mass bounds Vacuum stability bound: the lowest Higgs boson mass which satisfies for any scale between Perturbativity bound: the highest Higgs boson mass which satisfies for any scale between

20 Sample: Input: top quark pole mass = GeV Running Higgs mass Stability bound Pertubativity bound

21 Higgs mass bounds versus for various Perturbativity bound Stability bound Window is closed parameter constraint

22 Sample: Input: top quark pole mass = GeV Running Higgs mass Stability bound Perturbativity bound

23 Sample: Input: top quark pole mass = GeV Running Higgs mass Stability bound Perturbativity bound

24 Higgs mass bounds versus for various Perturbativity bound Stability bound Window is closed

25 Type III Seesaw and Higgs Mass Introduce 3 generations of fermions ψ i (i = 1, 2, 3), which transform as (3, 0) under the electroweak gauge group SU(2) L U(1) Y : ψ i = ( a σa 2 ψa i = 1 ψ 0 ) i 2ψ + i 2 2ψ i ψi 0. With canonically normalized kinetic terms for the triplet fermions, we introduce the Yukawa coupling L Y = y ij l i ψ j Φ, where Φ is the Higgs doublet.

26 Type III Seesaw and Higgs Mass 180 Gogoladze, Okada, Q.S arxiv: [hep-ph] m h GeV Y Ν Perturbativity (solid) and vacuum stability (dashed) bounds on the Higgs boson pole mass (m h ) versus Y ν with the seesaw scale M = GeV. The upper and lower dotted lines respectively show the perturbativity bound (m h 171 GeV) and the vacuum stability bound (m h 131 GeV) in the SM case.

27 Type III Seesaw and Higgs Mass m h GeV log 10 M GeV Perturbativity and vacuum stability bounds versus M, with a hierarchical mass spectrum (outer region in red), and an inverted-hierarchical mass spectrum (inner region in blue).

28 Low Energy Supersymmetry Resolution of the gauge hierarchy problem; Unification of the SM gauge couplings at M GUT GeV; Cold dark matter candidate (LSP); Predicts new particles accessible at the LHC; Other good reasons: Radiative electroweak breaking; String theory requires susy. Leading candidate is the MSSM (Minimal Supersymmetric Standard Model).

29 m h ( GeV ) The MSSM Higgs Boson M S = 1 TeV, M t = GeV X t = 6 X t = tan

30 Gauge-Higgs Unification Bulk Standard Model 5-dim. theory compactified on orbifold SM y All SM fields reside in the bulk Higgs boson associated with 5 th component of gauge fields in higher dimension

31 [2] V. Barger, J. Jiang, P. Langacker and T. Li, Phys. Lett. B 624, 233 (2005); Nucl. Phys. B 726, 149 (2005); Model with non-canonical normalization for U(1) Y have also been discussed by I. Gogoladze, T. Li, V. N. Senoguz and Q. Shafi, Phys. Rev. D 74, (2006); I. Gogoladze, C. A. Lee, T. Li and Q. Shafi, arxiv: [hep-ph]; A. Kehagias and N.D. Tracas, arxiv:hep-ph/ ; A. Aranda, J. L. Diaz-Cruz and A. Rosado, Int. J. Mod. Phys. A 22, 1417 (2007). [3] I. Gogoladze, T. Li and Q. Shafi, Phys. Rev. D 73, (2006) [4] N. S. Manton, Nucl. Phys. B 158, 141 (1979); D. B. Fairlie, J. Phys. G 5, L55 (1979); Phys. Lett. B 82, 97 (1979). [5] Y. Hosotani, Phys. Lett. B 126, 309 (1983); Phys. Lett. B 129, 193 (1983); Phys. Rev. D 29, 731 (1984); Annals Phys. 190, 233 (1989). [6] N. V. Krasnikov, Phys. Lett. B 273, (1991), 246; H. Hatanaka, T. Inami and C. S. Lim, Mod. Phys. Lett. A 13, (1998), 2601; G. R. Dvali, S. Randjbar-Daemi and R. Tabbash, Phys. Rev. D 65, (2002), ; N. Arkani-Hamed, A. G. Cohen and H. Georgi, Phys. Lett. B 513, (2001), 232; I. Antoniadis, K. Benakli and M. Quiros, New J. Phys. 3, (2001), 20. [7] M. Kubo, C. S. Lim and H. Yamashita, Mod. Phys. Lett. A 17 (2002), 2249; C. A. Scrucca, M. Serone and L. Silvestrini, Nucl. Phys. B 669 (2003), 128; C. A. Scrucca, M. Serone, L. Silvestrini and A. Wulzer, JHEP 0402, 049 (2004); G. Panico and M. Serone, JHEP 0505, 024 (2005) N. Haba, Y. Hosotani, Y. Kawamura and T. Yamashita, Phys. Rev. D 70 (2004), ; N. Haba and T. Yamashita, JHEP 0404 (2004) 016; Y. Hosotani, S. Noda and K. Takenaga, Phys. Rev. D 69 (2004), ; Phys. Lett. B 607 (2005), 276; K. W. Choi, N. Y. Haba, K. S. Jeong, K. I. Okumura, Y. Shimizu and M. Yamaguchi, JHEP 0402, 037 (2004); A. Demaria and K. L. McDonald, Phys. Rev. D 75, (2007). [8] N. Haba, S. Matsumoto, N. Okada and T. Yamashita, JHEP 0602, 073 (2006). [9] M. Sakamoto and K. Takenaga, Phys. Rev. D 75, (2007). [10] N. Maru and T. Yamashita, Nucl. Phys. B 754, 127 (2006). [11] For example, see G. Cacciapaglia, C. Csaki and S. C. Park, JHEP 0603, 099 (2006), and references therein. 7

32 SU(3) gauge = adj doublet doublet singlet Impose non-trivial boundary conditions (parity assignment) are Z2 even fields, others odd fields Zero modes for odd fields are project out, So SU(3) is broken to SU(2) X U(1) by this parity assignment

33 5 th component of 5dim gauge field scalar in 4D theories gauge-higgs unification Kinetic term for Higgs is included as 5dim SU(3) gauge interaction 5 dimensional gauge symmetry No mass and quartic tree Phenomenologically interesting observation ``Gauge-Higgs Condition realization of gauge-higgs unification at UV at Haba, Matsumoto, N.O.&Yamashita, JHEP 0602, 073 (2006)

34 Application of the guage-higgs condition UV completion of the SM by (5D) gauge-higgs unification Higgs boson mass prediction as a function of the compactification scale by imposing the condition Gogoladze, N.O. & Shafi Phys. Lett. B, 257 (2007) LEP2 Bound 114GeV

35 GaugeandtopYukawaUnification y t 0.6 g Log 10 (µ/gev)

36 GaugeandtopYukawaUnification M t = M t = M t = Λ m h

37 6D Gauge-Higgs Unification Gogoladze, Okada, Q.S mh GeV Log 10 GeV Higgs boson mass prediction versus the compactification scale for a given cos(2β). The upper three lines (in blue, black and red) correspond, from bottom to top, to input top quark pole masses, M t =169.1, and GeV, for tan β = 0/ or equivalently cos 2 (2β) = 1. The lower three lines (in blue, black and red) correspond, from bottom to top, to input top quark pole masses, M t =169.1, and GeV, for tan β = 1 or equivalently cos 2 (2β) = 0. The lower lines show the same results as in 5D GHU models. V = 1 2 g2 cos 2 (2β) H 4.

38 6D Gauge-Higgs Unification mh GeV Log 10 GeV PlotofHiggsbosonmassversuscompactificationscale,Log 10 (Λ/GeV),determinedasthe unification scale of the running top Yukawa and the SU(2) gauge couplings. Three solid lines (inred,blackandblue)fromtoptobottomcorrespondtotoppolemasses M t =172.7,170.9 and GeV, respectively.

39 Summary Standard Model + Seesaw mechanism is a well motivated framework: Neutrino Oscillations Grand Unification (especially type I and II) Leptogenesis Discovery of the Higgs boson with mass 130 GeV would favor type I seesaw;

40 Summary However, a somewhat lighter Higgs boson, say with mass of order GeV, would favor: Type II and III seesaw (in principle accessible at LHC); Supersymmetry; Metastable Higgs vacuum.