Gauge-Higgs Unification on Flat Space Revised

Transcription

1 Outline Gauge-Higgs Unification on Flat Space Revised Giuliano Panico ISAS-SISSA Trieste, Italy The 14th International Conference on Supersymmetry and the Unification of Fundamental Interactions Irvine, June 2006 Based on Nucl. Phys. B739 (2006) 186 and hep-ph/ with M. Serone and A. Wulzer

2 Outline Outline 1 Introduction GHU on a Flat Space and Its Problems A Possible Way Out 2 Main Features Phenomenological Bounds 3

3 GHU and Its Problems A Possible Way Out Why Extra Dimensions and GHU? SM problems Hierarchy of fermion masses Stabilization of the electroweak scale A possible solution TeV-sized extra dimensions compactified on S 1 /Z 2 Higgs as a wilson line phase (GHU models) Main features Masses generated by non-local effects Higgs mass protected by gauge invariance

4 GHU and Its Problems A Possible Way Out Why Extra Dimensions and GHU? SM problems Hierarchy of fermion masses Stabilization of the electroweak scale A possible solution TeV-sized extra dimensions compactified on S 1 /Z 2 Higgs as a wilson line phase (GHU models) Main features Masses generated by non-local effects Higgs mass protected by gauge invariance

5 GHU and Its Problems A Possible Way Out Problems of GHU Models on a Flat Space Minimal realizations of GHU have common drawbacks. [Scrucca, Serone and Silvestrini (2003)] Yukawa couplings constrained by gauge and Lorentz invariance top mass too small Higgs mass below experimental bounds Too low compactification scale Some attempts to solve these problems: Large localized kinetic terms [Scrucca et al.] Unwanted distorsions of wave functions Fermions in high rank representations [Cacciapaglia et al.] Very low cut-off

6 Getting Larger Yukawa s GHU and Its Problems A Possible Way Out Break the Lorentz symmetry in the bulk: SO(4, 1) SO(3, 1) Fermions: Ψ [ i /D 4 kd 5 γ 5] Ψ Gauge fields: 1 2 Tr F µνf µν ρ 2 Tr F µ5 F µ5 The top mass is increased: m t k t m W The Higgs effective quartic coupling gets larger

7 Getting Larger Yukawa s GHU and Its Problems A Possible Way Out Break the Lorentz symmetry in the bulk: SO(4, 1) SO(3, 1) Fermions: Ψ [ i /D 4 kd 5 γ 5] Ψ Gauge fields: 1 2 Tr F µνf µν ρ 2 Tr F µ5 F µ5 The top mass is increased: m t k t m W The Higgs effective quartic coupling gets larger

8 Getting Larger Yukawa s GHU and Its Problems A Possible Way Out Break the Lorentz symmetry in the bulk: SO(4, 1) SO(3, 1) Fermions: Ψ [ i /D 4 kd 5 γ 5] Ψ Gauge fields: 1 2 Tr F µνf µν ρ 2 Tr F µ5 F µ5 The top mass is increased: m t k t m W The Higgs effective quartic coupling gets larger

9 The Mirror Symmetry GHU and Its Problems A Possible Way Out Addressing the compactification scale problem Doubling part of the bulk fields: φ φ 1, φ 2 and imposing twisted boundary conditions φ 1 (y ± 2πR) = φ 2 (y), φ 1 ( y) = ±φ 2 (y) Requiring interchange symmetry: φ 1 φ 2 Twisted fields give periodic and antiperiodic fields φ ± = φ 1 ± φ 2 2 with charges ±1 under the mirror Z 2 An order of magnitude hierarchy between the EW scale and 1/R is completely natural

10 The Mirror Symmetry GHU and Its Problems A Possible Way Out Addressing the compactification scale problem Doubling part of the bulk fields: φ φ 1, φ 2 and imposing twisted boundary conditions φ 1 (y ± 2πR) = φ 2 (y), φ 1 ( y) = ±φ 2 (y) Requiring interchange symmetry: φ 1 φ 2 Twisted fields give periodic and antiperiodic fields φ ± = φ 1 ± φ 2 2 with charges ±1 under the mirror Z 2 An order of magnitude hierarchy between the EW scale and 1/R is completely natural

11 The Gauge Lagrangian Main Features Phenomenological Bounds Gauge group SU(3) w G 1 G 2 with G i = U(1) i SU(3) i,s Non trivial Z 2 orbifold projection on SU(3) w A M w ( y) = ( ) δ M,y PA M w (y)p P = SU(3) w SU(2) L U(1) w Surviving gauge group at fixed points y=0: SU(2) L U(1) w G + (G + diag. subgr. of G 1 and G 2 ) y=πr: SU(2) L U(1) w G 1 G 2

12 The Fermion Lagrangian (Bulk) Main Features Phenomenological Bounds (Ψ, Ψ) fermion pairs in the bulk: same quantum numbers and opposite parity Mirror symmetry doubling (Ψ 1, Ψ 1 ) charged under G 1 (Ψ 2, Ψ 2 ) charged under G 2 For each quark family (Ψ t 1,2, Ψ t 1,2 ) 3 rep. of SU(3) w (Ψ b 1,2, Ψ b 1,2 ) 6 rep. of SU(3) w both in the fund. rep. of SU(3) 1,2,s and with U(1) 1,2 charge +1/3

13 Main Features Phenomenological Bounds The Fermion Lagrangian (Boundary) Boundary fermions at y = 0 one SU(2) L doublet: Q L = (t L, b L ) t two SU(2) L singlets: t R and b R They have Z 2 mirror charge +1 couple only to Ψ + fields Bulk-boundary couplings Ψ t +, Ψ t + : 3 1/3 2 1/6 1 2/3 Q L t R b R Ψ b +, Ψ b + : 6 1/3 2 1/6 3 2/3 1 1/3

14 The EW Symmetry Breaking Main Features Phenomenological Bounds The 4D gauge group is the surviving group at y = 0: SU(3) QCD SU(2) L U(1) Y U(1) X (U(1) Y is the diagonal subgroup of U(1) w and U(1) + ) The extra U(1) X gauge group is broken by anomaly it is needed to get the correct Weinberg angle The Higgs doublet identified with the A 4,5,6,7 y components of the SU(3) w gauge group

15 The EW Symmetry Breaking Main Features Phenomenological Bounds The 4D gauge group is the surviving group at y = 0: SU(3) QCD SU(2) L U(1) Y U(1) X (U(1) Y is the diagonal subgroup of U(1) w and U(1) + ) The extra U(1) X gauge group is broken by anomaly it is needed to get the correct Weinberg angle The Higgs doublet identified with the A 4,5,6,7 y components of the SU(3) w gauge group

16 The EW Symmetry Breaking Main Features Phenomenological Bounds The 4D gauge group is the surviving group at y = 0: SU(3) QCD SU(2) L U(1) Y U(1) X (U(1) Y is the diagonal subgroup of U(1) w and U(1) + ) The extra U(1) X gauge group is broken by anomaly it is needed to get the correct Weinberg angle The Higgs doublet identified with the A 4,5,6,7 y components of the SU(3) w gauge group

17 The EW Symmetry breaking Main Features Phenomenological Bounds The Higgs potential is generated at one-loop level a non-trivial minimum is induced by bulk fermions Higgs VEV: A w,y = 2α g 5 R t7 spontaneous breaking SU(2) L U(1) Y U(1) em W boson mass: m W = α R cancellation between periodic and antiperiodic α 0.1 1/R 1 TeV completely natural

18 The Universal Parameters Main Features Phenomenological Bounds Flavor-conserving new physics can be parametrized by: [e.g. Han and Skiba(2005); Grojean et al.; Cacciapaglia et al.(2006)] Universal parameters: Ŝ, T, Û, V, X, W and Y distorsion of the Z 0 couplings: C q, δε q, δε b In Our Model: Light quarks are nearly exactly localized coupling to the Z 0 unperturbed C q, δε q negligible b quark partially delocalized Z b L b L vertex modified by Mixing with the A X tower (anomaly) Mixing with fields with different SU(2) L charges δε b is negligible for 1/R 3 TeV

19 Universal parameters Introduction Main Features Phenomenological Bounds Relevant universal parameters in our model (compared to generic flat ED model [Barbieri et al. (2004)]) Ŝ = 2 ( 3 π2 α 2 = 2 ) 3 π2 α 2 W = 1 ( ( T = π 2 α 2 1 ) 3 π2 α 2 = 1 ) 3 π2 α 2 3 tan2 (θ w )π 2 α 2 Y 1 ( 3 π2 α 2 = 1 ) 3 π2 α 2 H H H H Z A X Z The large value of T is explained by the distorsion of the ρ parameter

20 EWPT fit Introduction Main Features Phenomenological Bounds Bounds % CL 600 Compatification scale 1/R 4 5 TeV mh (GeV) % CL 90 % CL / R (TeV ) Allowed Higgs masses up to 600 GeV Predictions (blue dots) The bounds can be satisfied with some tuning (O(few %)) The Higgs mass is in the range GeV

21 Summary Introduction Common problems of GHU models on 5D flat orbifolds can be solved by: breaking the SO(4, 1) Lorentz symmetry in the bulk, introducing a Z 2 mirror symmetry. In this way a realistic model has been constructed which is compatible with the EW experimental measurements. The compactification scale has a bound 1/R 4 5 TeV; the Higgs mass is predicted in the range GeV.

22 Outlook Introduction Some amount of fine-tuning is required to satisfy the EW precision tests. Is it possible to do better? Due to the mirror symmetry, the first Kaluza-Klein modes of the antiperiodic fields are stable. Can they provide a viable dark matter candidate? Find an appropriate way to introduce the flavour structure.

23 Appendices Cut-off One-loop polarization corrections for the gauge fields compared with the tree level couplings (Pauli-Villard regularization) (Λ (µ) s R) α s 1 ( ) 6 2 k t k b (Λ (5) s R) α s 1 ) (12k t + 24k b 6 2 (Λ w (µ) R) α w 6 (Λ (5) w R) α w ( ) 2 k t k b ) (12k t + 60k b 1 Λ (µ) s 6 R, ρ 2 s Λ (5) s 3ρ2 s R, 1 Λ (µ) w 5 R, 1 Λ (5) w 4 R. For k t 2 3 and k b 1 the cut-off is Λ 4 R

24 Appendices Is Our Model Really 5D? The Lorentz symmetry breaking can have a simple origin We introduce an axion-like field Φ invariant under the shift Φ Φ + 2π with periodicity conditions Φ(y + 2πR) = Φ(y) + 2π The background configuration is Φ 0 (y) = y R This generates a spontaneous symmetry breaking of the SO(4, 1)/SO(3, 1) Lorentz symmetry. The Lorentz-violating factors can be reinterpreted as α M Φ N Φ Ψγ M D N Ψ f 2 Φ

25 Appendices Fine-Tuning and Sensitivity Using the logarithmic derivative to quantify the fine-tuning [Barbieri and Giudice (1988)] C Max { log α log i } at 1/R 5 TeV one finds a fine-tuning f = 1/C O(1%) With a more refined procedure [Anderson and Castano (1995)] f = αρ(α) αρ(α) a tuning of O(10%) is found f 100% 50% 30% 10% 5% 3% 1% 0,5% 0,3% ,8 0,4 1/R (TeV)

26 Embedding Leptons Appendices Bulk fields (Ψ l 1,2, Ψ l 1,2 ) 3 rep. of SU(3) w (Ψ ν 1,2, Ψ ν 1,2 ) 6 rep. of SU(3) w Localized fields (y=0) doublet: L L (e L, ν t L ) singlets: e R and ν R Bulk-boundary couplings Ψ l +, Ψ l + : 3 2/3 2 1/2 1 1 L L e R ν R Ψ ν +, Ψ ν + : 6 2/3 2 1/

27 The Effective Potential Appendices Contributions to the effective potential (massless fermions) periodic: V P (α) = 3k P 4 1 8π 6 R 4 n 5 cos(2πnqα) antiperiodic: V A (α) = 3k 4 A 8π 6 R 4 n=1 ( 1) n cos(2πnqα) n=1 n 5 The leading cosine term cancels out between periodic and antiperiodic contributions if they have k P = k A.