Fitting safely some non-standard models

Átírás

1 Fitting safely some non-standard models Janusz Gluza DESY-Zeuthen and University of Silesia Fitting safely some non-standard models 8 December Warsaw p./??

2 Cases Left-right symmetric models Muon decay (low energy) M. Czakon J. Gluza M. Zrałek Nucl. Phys. B (000) qualitative considerations M. Czakon J. Gluza J. Hejczyk Nucl. Phys. B64 57 (00) numerics More general statements (higher energies) M. Czakon J. Gluza F. Jegerlehner M. Zrałek Eur. Phys. J. C3 75 (000). SM with an additional Higgs triplet T. Blank and W. Hollik Nucl. Phys. B 54 (998) 3 SM with additional gauge group [ boson] G. Degrassi and A. Sirlin Phys. Rev. D 40 (989) The Littlest Higgs Model Mu-Chun Chen Sally Dawson hep-ph0303 Fitting safely some non-standard models 8 December Warsaw p./??

3 Cases Left-right symmetric models Muon decay (low energy) M. Czakon J. Gluza M. Zrałek Nucl. Phys. B (000) qualitative considerations M. Czakon J. Gluza J. Hejczyk Nucl. Phys. B64 57 (00) numerics More general statements (higher energies) M. Czakon J. Gluza F. Jegerlehner M. Zrałek Eur. Phys. J. C3 75 (000). SM with an additional Higgs triplet T. Blank and W. Hollik Nucl. Phys. B 54 (998) 3 SM with additional gauge group [ boson] G. Degrassi and A. Sirlin Phys. Rev. D 40 (989) The Littlest Higgs Model Mu-Chun Chen Sally Dawson hep-ph0303 Fitting safely some non-standard models 8 December Warsaw p./??

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5 Basic Issue of the Talk Tree level processes: restoration of the results of the Standard Model for Fitting safely some non-standard models 8 December Warsaw p.4/??

6 Basic Issue of the Talk Tree level processes: restoration of the results of the Standard Model for One-loop (and beyond) processes: is the same true there? Fitting safely some non-standard models 8 December Warsaw p.4/??

7 Basic Issue of the Talk Tree level processes: restoration of the results of the Standard Model for One-loop (and beyond) processes: is the same true there? Muon decay SM: Fitting safely some non-standard models 8 December Warsaw p.4/??

8 Basic Issue of the Talk Tree level processes: restoration of the results of the Standard Model for One-loop (and beyond) processes: is the same true there? Muon decay SM: Muon decay non-standard model: Fitting safely some non-standard models 8 December Warsaw p.4/??

9 Basic Issue of the Talk Such a factorization is generally not true moreover the sentence: Since we assume that the SM provides the dominant contribution any additional non-sm higher order correction is a subleading effect. Therefore only SM radiative corrections are included which is a basic philosophy for many fits (see PDG tables) is also not true. Fitting safely some non-standard models 8 December Warsaw p.5/??

10 ) $% # + 0 Decoupling non-decoupling? e.g.: vs. at the tree level Higgs bosons and heavy neutrinos contribution to the muon decay at -loop level within extended models (' '' "! )65 34 $%! * 0. /. - Fitting safely some non-standard models 8 December Warsaw p.6/??

11 Why beyond SM? SM ordered many things: bosons and local gauge symmetries: Fitting safely some non-standard models 8 December Warsaw p.7/??

12 Why beyond SM? SM ordered many things: bosons and local gauge symmetries: basic elements of the matter: fermion particles included into representations Fitting safely some non-standard models 8 December Warsaw p.7/??

13 Why beyond SM? SM ordered many things: bosons and local gauge symmetries: basic elements of the matter: fermion particles included into representations spontanous symmetry breaking (SSB) in the spinless world: masses of fermions and bosons Fitting safely some non-standard models 8 December Warsaw p.7/??

14 LR model The model has been constructed in Pati Salam Senjanovic Mohapatra gauge group restore lepton-quark symmetry to the weak interactions: Interpretation of the hypercharge as the difference of the baryon and lepton numbers: Fitting safely some non-standard models 8 December Warsaw p.8/??

15 Fitting safely some non-standard models 8 December Warsaw p.9/??

16 Deshpande Gunion Kayser Olness Phys. Rev. D (99) Fitting safely some non-standard models 8 December Warsaw p.0/??

17 Higgs sector The minimal Higgs sector consists of two triplets and one bidoublet with vacuum expectation values allowed for the neutral particles Fitting safely some non-standard models 8 December Warsaw p./??

18 Higgs particles in LR The result is 0 real scalar fields of which 4 are physical (the rest are Goldstone bosons): 4 neutral scalars: (the first can be considered to be the light Higgs of the SM at tree level) neutral pseudo-scalars: charged scalars: doubly-charged scalars:. Fitting safely some non-standard models 8 December Warsaw p./??

19 $ ) $ ) $ $ $ $ $ ) ) $ ) $ )) $ )) $ )) $. Invariant under ) )) $ ) ) $ $ 555 ) Fitting safely some non-standard models 8 December Warsaw p.3/??

20 Neutrinos in LR see-saw mechanism for the generation of light neutrino masses with specific SB sectors. The neutrino mass matrix with. if light neutrino masses of the order of ev. Fitting safely some non-standard models 8 December Warsaw p.4/??

21 Large mixing of heavy neutrinos? Constraints: Fitting safely some non-standard models 8 December Warsaw p.5/??

22 Simple arguments... toy model: J.G. Acta Physica Polonica B33 (00) 735 Let us assume that in the are real numbers) basis the neutrino mass matrix is (elements abc The masses and a mixing angle are given by I. It is just a see-saw mechanism II. (due to symmetry!). Then if which is however not a natural assumption and Fitting safely some non-standard models 8 December Warsaw p.6/??

23 Gauge bosons in LR The SSB leads to the following gauge-boson mass matrices % $ ) The diagonalization: Fitting safely some non-standard models 8 December Warsaw p.7/??

24 Fitting safely some non-standard models 8 December Warsaw p.8/??... neutral sector where:

25 Muon decay in LR: e.g. boxes µ ν j µ ν j µ ν j µ ν j Z W W Z W Z Z W ν i () e ν i () e ν i (3) e ν i (4) e µ ν j µ ν j µ ν j µ ν j C.Sc. Z Z N.Sc. C.Sc. N.Sc. N.Sc. C.Sc. ν i (5) e ν i (6) e ν i (7) e ν i (8) e µ ν j µ ν j µ ν j µ ν j Z C.Sc. N.Sc. Z C.Sc. N.Sc. N.Sc. C.Sc. ν i (9) e ν i (0) e ν i () e ν i () e µ ν j ν i (3) W γ e Fitting safely some non-standard models 8 December Warsaw p.9/??

26 Muon decay in LR model: assumptions Goal: getting contraints on heavy sector (masses of heavy neutrinos masses of gauge boson masses their mixings). Tree level diagrams to the muon decay: exchanged exchanged exchanged charged Higgs particles. We assume: no mixing in the charged gauge sector: mixings among neutrino states are neglected Fitting safely some non-standard models 8 December Warsaw p.0/??

27 . assumptions... Effects of heavy neutrinos remain: (build up gauge-boson self energies); Nice feature: constraints on the heavy (right) sector come directly from -loop level! (Loops Legs NPB) Fitting safely some non-standard models 8 December Warsaw p./??

28 Fitting safely some non-standard models 8 December Warsaw p./?? where:..

29 To have neutrino mixings properly included: then: Fitting safely some non-standard models 8 December Warsaw p.3/??

30 (-6) parameters possible and Standard approach: to make the fitting procedure of the at all at the tree-level we have to naively rely on SM corrections: and GeV. Fitting safely some non-standard models 8 December Warsaw p.4/??

31 r βζ with the very worst bound it gives without heavy neutrino mixing (means ): and Fitting safely some non-standard models 8 December Warsaw p.5/??

32 Gauge Sector Renormalization Fitting safely some non-standard models 8 December Warsaw p.6/??

33 We exploit the one-to-one correspondence of the parameters: Result: Fitting safely some non-standard models 8 December Warsaw p.7/??

34 at tree level s W v R [GeV] In MLRM is expressable by and a heavy scale SM: Fitting safely some non-standard models 8 December Warsaw p.8/??

35 from the SM to the LRM is included in The change of then: - complete vertex box and external line corrections within MLRM. Fitting safely some non-standard models 8 December Warsaw p.9/??

36 Fitting safely some non-standard models 8 December Warsaw p.30/?? Natural scalar potential: 0. (a) (b) 0. (c) (d) r v R [GeV] #

37 All Higgs particle masses equal (apart from ): 0. (a) r 0. (a ) (b) (b ) (c) (c ) v R [GeV] For (and large Remark: fine tuned masses ) can be accomodated Fitting safely some non-standard models 8 December Warsaw p.3/??

38 Variaton of is negligible: 0.04 r m H0 (SM) [GeV] The heavy particle spectrum is chosen to fit approximately to the shaded region namely GeV TeV TeV. Fitting safely some non-standard models 8 December Warsaw p.3/??

39 is effectively light and is not predictable by in LRM: 0.0 r 0.00 m t =5 GeV m t =75 GeV m t =5 GeV m t =75 GeV v R [GeV] Leading terms: Fitting safely some non-standard models 8 December Warsaw p.33/??

40 Heavy neutrinos decouple (c) r (b) (a) v R [GeV] With increasing (a) Non-decoupling: heavy particles decouple and the lines aim at the SM contribution. GeV; (b) GeV; (c) TeV. Fitting safely some non-standard models 8 December Warsaw p.34/??

41 First Conclusions LRM can be fitted to muon decay width however: heavy neutrino masses and Higgs masses must be very tuned to get proper Must have consequences for [some] NPM also for high energy processes: Czakon Gluza Jegerlehner Zrałek EPJ C3 75 (000) see also: Lynn Nardi NPB Fitting safely some non-standard models 8 December Warsaw p.35/??

42 First Conclusions LRM can be fitted to muon decay width however: heavy neutrino masses and Higgs masses must be very tuned to get proper corrections coming from SM particles within LR model do not constitute a structure equivalent to their SM structure e.g. top quark and Higgs; the lightest Must have consequences for [some] NPM also for high energy processes: Czakon Gluza Jegerlehner Zrałek EPJ C3 75 (000) see also: Lynn Nardi NPB Fitting safely some non-standard models 8 December Warsaw p.35/??

43 "".. SM: If several Higgs multiplets couple to gauge bosons then: so! 43 0 )/. +-% )* 798 #+-6 0 )/. +-% ()* ' #$% 53 is predicted by SM (=) but beyound SM is not known in general it is an additional independent parameter which must be fixed to experimental data Fitting safely some non-standard models 8 December Warsaw p.36/??

44 # ' $ in LEP physics (with loop corrections)!"! " $ %!" ( $ ' $ $ % $ ) +!" $ % *$ in the SM (corrected by loop results) depend $ %! " and!" Relations for 0 : 0/. #- 354 on muon decay Fitting safely some non-standard models 8 December Warsaw p.37/??

45 $ ) - % 6 5!" - 6 % $ %! " $ % % 6 / 6 $ $ % % % + % 3 4 % Fitting safely some non-standard models 8 December Warsaw p.38/??

46 ) The chain of relations leading to the succes of the SM in prediction for as in the MLRM: break down 3 4 Can we make reasonable fits of the new parameters without any knowledge of the radiative corrections in the NPM? Solution: parameters depending strongly on $ %! " (no SM corrections) must be free parameters: $ % Fitting safely some non-standard models 8 December Warsaw p.39/??

47 / % % % Physical data ( % ) as a function of free parameters!"!" %! " %.! " and Result: GeV % Fitting safely some non-standard models 8 December Warsaw p.40/??

48 ) % Top quark Constraint on comes from Zbb vertex namely: GeV+ " % Fitting safely some non-standard models 8 December Warsaw p.4/??

49 SM with an additional Higgs triplet In this model we have additional independent parameter VEV which can be translated to consequences: 8. M W [GeV] SM: M H0 = 60 GeV SM: M H0 = 300 GeV SM: M H0 = 000 GeV TM: M H0 = 60 GeV TM: M H0 = 300 GeV TM: M H0 = 000 GeV m t [GeV] The predictions of the standard model and the triplet model coincide for all observables in the experimental range of the top mass not really mean that these models are on the same foot GeV... does Fitting safely some non-standard models 8 December Warsaw p.4/??

50 . 7 /!. * + SM with additional gauge group [ boson] from Abstract:...it is found that the definition of must be carefully chosen to ensure consistency and avoid the emergence of radiative corrections of nonanalytic terms in the neighborhood of i.e. 0/. The formulation developed in this paper prevents the occurrence of such potentially catastrophic terms and leads to a definition of corresponding!" in terms of 3 and expression. which is very close to the they call it constrained model why nature like this? by brutal force Fitting safely some non-standard models 8 December Warsaw p.43/??

51 $ ). ( ) ) ).. ( ). Little (Littlest?) Higgs models Many papers for models which try to solve hierarchy problem in theory for this global symmetry additional fermions triplets of Higgs particles etc depending on man s creativity : )) -loop 354. ( They confirmed in hep-ph soon. dependence for revised version of their paper will appear Fitting safely some non-standard models 8 December Warsaw p.44/??

52 Summary: Even this can be different (depending on the considered version of the model!) and have logarithmic character as in the model with an additional group: Fitting safely some non-standard models 8 December Warsaw p.45/??

53 # Summary: Even this can be different (depending on the considered version of the model!) and have logarithmic character as in the model with an additional group: Similarly the model with triplets and Little(st) Higgs models. Fitting safely some non-standard models 8 December Warsaw p.45/??

54 # Summary: Even this can be different (depending on the considered version of the model!) and have logarithmic character as in the model with an additional group: Similarly the model with triplets and Little(st) Higgs models. Decoupling does not always work in phenomenology and we can not make an easy division between SM and NS effects: carefully with fits neglecting heavy sectors etc.. Fitting safely some non-standard models 8 December Warsaw p.45/??

55 Which models are then fine? Only some class of models have this feature: supersymmetric models Fitting safely some non-standard models 8 December Warsaw p.46/??

56 Which models are then fine? Only some class of models have this feature: supersymmetric models SM with additional scalar singlets and doublets Fitting safely some non-standard models 8 December Warsaw p.46/??

57 Which models are then fine? Only some class of models have this feature: supersymmetric models SM with additional scalar singlets and doublets models with additional fermion families Fitting safely some non-standard models 8 December Warsaw p.46/??

58 Which models are then fine? Only some class of models have this feature: supersymmetric models SM with additional scalar singlets and doublets models with additional fermion families... Fitting safely some non-standard models 8 December Warsaw p.46/??