Pati-Salam unification from noncommutative geometry and the TeV-scale WR boson

Transcription

1 Pati-Salam unification from noncommutative geometry and the TeV-scale WR boson Ufuk Aydemir Department of Physics and Astronomy, Uppsala University Collaborators: Djordje Minic, Tatsu Takeuchi, Chen Sun (Virginia Tech) Pati-Salam unification from noncommutative geometry and the TeV-scale WR boson UA, Djordje Minic, Tatsu Takeuchi, Chen Sun, accepted for International Journal of Modern Physics A [arxiv: ] The Higgs Mass, Superconnections and the TeV-scale Left-Right Symmetric Model UA, Djordje edd Minic, Tatsu Takeuchi, Chen Sun, Phys.Rev. D91 (2015) , [arxiv: ] The Higgs mass and the emergence of new Physics UA, Djordje Minic, Tatsu Takeuchi, Physics Letters B 724 (2013) 301, [arxiv: ] 1

2 The Discovery of the Higgs and BSM The last building block of the SM, the Higgs, detected at 126 GeV. - a great success for the high energy physics community. The SM works great in its realm but no answer for questions beyond it. - many issues remains unresolved; need for new physics. No signs of new physics at LHC yet; SUSY, technicolor, extra dims. - A big disappointment for BSM theories. Maybe the picture is completely different than what we expect - maybe time for a paradigm change? Why is the SM so robust? Could it be a sign for a deeper reason than what we see? Like a geometry? Is it possible to get more out of the SM beyond the EFT approach? - A possible UV/IR mixing (due to a geometry)?

3 Lie Supergroup (Graded Lie group), SU(N/M) Z 2 grading H (N) NxN Bosonic (N+M) H (M) MxM θ NxM matrices Fermionic (Grassmanian numbers) Here, unlike in SU(N), the supertrace is invariant not the trace. Therefore, the supertrace is the vanishing quantity. Traceless part of H (N) and H (M) generates SU(N) and SU(M) Nonvanishing trace part defines U(1) SU(N/M) SU(N)xSU(M)xU(1)

4 SU(2/1), superconnections and supercurvatures We write the anti-commutative superconnection in the form M is 2x2 and N is 1x1 supermatrices-- SU(2/1) g-even (valued ever one-form). 3x3 φ and φ are 1x2 and 2x1 supermatrices- SU(2/1) g-odd (valued over zero-form). Supercurvature: Ne eman-sternberg rule for supermatrices.

5 SU(2/1) embedding Compare it to the exp. value sin 2 θ W = Interpreting the sin 2 θ W =0.25 is the value at Λ s, Λ s 4 TeV!

6 Superconnection approach to the SM Ne eman and Sternberg (1990) (uses Quillen s superconnections) Embed SU(2)L x U(1)Y gauge and Higgs fields into a single SU(2/1) superconnection. The formalism gives the EW part of the SM with some extra constraints: - Modulo the Higgs mass. It should either be added ad-hoc which breaks the SU(2/1) structure explicitly or Coleman-Weinberg type of introducing. - But the kinetic and the potential terms for the Higgs sector come out automatically. Gauge-Higgs unification. More aesthetic. Gives Higgs field a geometric meaning. SU(2/1) is not a symmetry of the theory. Gauging it would also be problematic. - Rather, it can be interpreted as an emergent geometric structure. The formalism selects 4 TeV as the energy scale of its emergence. LHC Wrong Higgs mass. Can be corrected by SU(2/2) extension superconnection formalism for the left-right symmetric model. The energy scale here is also 4 TeV! A possible UV/IR connection which manifests itself as the non-decoupling in the Higgs sector of the left-right symmetric model. 6

7 Superconnections? Non-commutative geometry Generalized exterior derivative in superconnection Matrix derivative Chang-Yeong Lee (1997), Non commutative geometry Coquereaux and collaborators. Superconnections make more sense if the underlying theory is NCG. Extra discrete dimension Higgs bridges the gap! The formalism is more meaningful if the underlying theory is Connes non-commutative geometry. Discrete extra dimension consisting of two points. The even part of superconnection (gauge fields) connects the fermions with same chirality in each brane, while its odd part (Higgs field) bridges the gab between two branes and hence connects the fermions with different chirality. fl L Jodd= Higgs Jeven Jeven R fr Requires another new scale Λ! Offers a new approach for Hierarchy problem. Modification of RG running due to UV\IR mixing, -not only ingrate from UV down but IR up to get the self dual fixed point. SM with LRSM could provide such a fixed point. Similar examples in non-commutative field theory. Brane 1 Brane 2

8 Non-commutative geometry of Connes Reformulate the notions of geometry in operator algebraic terms Spectral Triple: {A, H, D} Connes-Lott (1990) Basic objects: a (possibly NC) algebra A a Hilbert space H a self-adjoint operator D on M generalization of manifold metric structure f A, dˆf = [D, ˆf ], d 2 = 0 ˆf : representation of f (C 1 (M),L 2 (M,S), r) Riemannian geometry as a special case: M: Compact spin-4 manifold S: vector bundle of spinors on M L 2 (M,S): Hilbert space of square integrable section of S The action functional gives the pure YM theory in the ordinary Riemannian geometry M F Appropriately generalized Riemannian space: W = W + H SYM= SYM+ SH Regular gauge + Higgs fields Regular YM kinetic terms + Higgs fields generalized Dirac operator A is commutative Similar to superconnection case - The basic fields are spinor fields - The bosonic fields come from diff. forms on H - Input: Enter the fermion representations and the symm. breaking algebra A generalized metric

9 The Spectral Standard Model of NCG M F two point space with NCG Spacetime is extended to a product of a continuous four dimensional manifold by a finite discrete space with non-commutative geometry. Two points: Fermions on sheets at each point. Chirality introduced. Gauge transformations: unitary inner automorphisms of the algebra. S= Cut-off function Spectrum of the Dirac operator SM + GR+CC+ Weyl terms Gravity and the symmetries of the SM emerge. SO(10) boundary conditions from the action RG running from GUT scale. Higgs mass of 170 GeV same as in superconnection approach! Same cure here as well: Taking into account extra dofs (singlet and neutrino) to accommodate the right Higgs mass. Claimed that SU(2)L x SU(2)R x U(1)B-L emerges from SSM! Another sign for a possible SU(2/2) connection.

10 The Spectral Pati-Salam A = C 1 (M) (H R H L M 4 (C)) inner automorphisms 3 versions of Pati-Salam Left-right symmetric one

11 Recent LHC signals ATLAS and CMS recently reported an excess in various search channels in the invariant mass region of TeV. The largest deviation from the background occurs in heavy bosons hadronically decaying to the W Z channel at around 2 TeV with a local significance of 3.4σ and a global of 2.5σ. Potential signals in the HW and dijet final states. It was recently discussed in Brehmer et.al. (arxiv: [hep-ph]) that these signals can be explained by a heavy gauge boson W R of the TeV-scale leftright model, with a single coupling g R =0.4. We analyze the compatibility of the unified left-right symmetric Pati-Salam models motivated by non-commutative geometry and the TeV scale right-handed W boson suggested by recent LHC data. 11

12 Emerges the most general chain for G2213 at MR SU(2) R! U(1) R not relevant { Smaller chains Ordering of scales Boundary/matching conditions 12

13 Talking to the low energy world ai s depend on the particle content in the relevant interval MR=5 TeV and gr(mr)=0.4?? 13

14 ESH Depends on the particle content in each interval. Need to know the scalar content how to determine? In the literature Extended Survival Hypothesis (ESH) used: Minimal fine tuning ESH states that at every step of the symmetry breaking chain, the only scalars which survive below the corresponding symmetry breaking scale are the ones which acquire vacuum expectation values (VEV s) at the subsequent levels of the symmetry breaking. Left-Right Symmetric Pati-Salam: 14

15 Model C Way off.. 15

16 Relax the ESH Light color scalars 16

17 17

18 Outlook: The superconnection approach to the SM based on the supergroup SU(2/1) and its extension to the LRM from the SU(2/2) fits in surprisingly well. This (geometrical approach) may offer a road towards reading the possible implications/signals of Plank scale physics at the low energies via decoupling (possibly in the Higgs sector); there may be more to the EFT approach. We discussed the possibility that non-commutative geometry is the underlying theory of the emergent low energy SU(2/1) SU(2/2) superconnection structure. NCG geometrizes the SM and places it on a similar footing to gravity. Requirement of an extra scale associated with the discrete extra dimension of NCG, with the possibility of UV/IR mixing, can bring in a new insight to hierarchy problem. The framework is restrictive and therefore testable. Pati-Salam type models of NCG will be challenged if the recent LHC signals turn out to be statistically significant. On the other hand, the current treatments available may not capture the true nature and predictions of NCG formalism. 18

19 Thank you.. 19

20 Extra slides 20

21 Schucker, hep-th/ A real spectral triple is given by 5 items: 21

22 Schucker, hep-th/ where the Weyl tensor: 22