Status of asymptotic safety in gravity-matter systems Masatoshi - PowerPoint PPT Presentation

Status of asymptotic safety in gravity-matter systems Masatoshi Yamada (Ruprecht-Karls-Universität Heidelberg) KEK Theory workshop 2019

General relativity • Einstein theory • Well describes observed facts: • Mercury perihelion • Gravitational wave • etc.

Towards quantum gravity • The quantized Einstein-Hilbert action is not perturbatively renormalizable. G. ’t Hooft and M. Veltman, Annales Poincare Phys.Theor.,A20,69 • Higher derivative gravity Stelle, K.S. Phys.Rev. D16 (1977) 953-969 • Perturbatively renormalizable • Ghost (unitarity) problem

In this talk • We introduce quantum gravity based on asymptotic safety. • Pure gravity case will be presented by Prof. Ohta. • We focus on AS for gravity-matter systems. • The key word is the anomalous dimension induced by quantum gravity effects.

Contents • What is Asymptotic Safety (AS)? • AS for the standard model and gravity • Prediction for the Higgs mass, ~125 GeV • Prediction for top-quark mass, ~170 GeV • AS for beyond the standard model and gravity • The gauge hierarchy problem • Dark matter physics (Higgs portal type)

Asymptotic safety relevant operators. S. Weinberg, Chap 16 in General Relativity • Suggested by S. Weinberg • Existence of non-trivial UV fixed point • Continuum limit k→∞. • UV critical surface (UV complete theory) is spanned by Fig. from A.Eichhorn, Front.Astron.Space Sci. 5 (2019) 47 • Dimension of UV critical surface = number of free parameters. • Generalization of asymptotic free • Non-perturbatively renormalizable gravity

Asymptotic freedom • Asymptotic freedom

Asymptotic safety • Asymptotic safety

Functional renormalization group exact flow projection truncated flow Wetterich equation Γ = Γ k =0 g i Z d 4 x [ g 1 O 1 + g 2 O 2 + · · · + g i O i + · · · ] Γ k = g 2 S = Γ Λ Z d 4 x [ g 1 O 1 + g 2 O 2 ] Γ k ' g 1 k ∂ k Γ k = 1 2Str[( Γ (2) + R k ) − 1 k ∂ k R k ] k

Critical exponent negative eigenvalue relevant irrelevant • RG eq. around FP g * θ i < 0 • Solution of RG eq. k → 0 θ i > 0

Relevant: θ> 0 • Free parameter

Irrelevant θ< 0 Landau pole • Predictable parameter

Irrelevant θ< 0 Landau pole Prediction UV complete (no Landau pole) No dangerous divergence =Safe! • Predictable parameter

RG flow of g (dimensionless Newton constant) g Irrelevant at Gaussian FP Relevant at non-trivial FP Found.Phys. 48 (2018) no.10, 1407-1429

Earlier studies • Truncated system for pure gravity

Earlier studies • Truncated system for pure gravity Einstein-Hilbert truncation e.g. M. Reuter, F. Saueressig, Phys.Rev. D65 (2002) 065016

Earlier studies • Truncated system for pure gravity e.g. K. Falls, D. Litim, J. Schröder, Phys.Rev. D99 (2019) no.12, 126015 f(R) truncation G.Brito, N.Ohta, A. Pereira, A.Tomaz, M.Y ., Phys.Rev. D98 (2018) no.2, 026027 R 71

Earlier studies • Truncated system for pure gravity Higher derivative truncation I e.g. D. Benedetti et al. Mod.Phys.Lett. A24 (2009) 2233-2241 Y.Hamada, M.Y ., JHEP 1708 (2017) 070

Earlier studies • Truncated system for pure gravity Higher derivative truncation II L.Bosma, B.Knorr, F.Saueressig, Phys.Rev.Lett. 123 (2019) no.10, 101301

Earlier studies • Truncated system for pure gravity Higher derivative truncation III B.Knorr, C.Ripken, F.Saueressig, Class.Quant.Grav. 36 (2019) no.23, 234001

Earlier studies number of relevant directions. • These studies have shown the finite • There are 3 relevant directions (?) • which means 3 free parameters • For details, listen Prof. Ohta’s talk.

Open questions the non-trivial (Reuter) fixed point? • What is degrees of freedom associated to • Unitarity problem (or ghost problem) • Robustness of number of relevant operators. • Scheme-independent calculations. • …

Potential solution to the ghost problem • Action for asymptotically safe gravity What is their pole structure? L.Bosma, B.Knorr, F.Saueressig, Phys.Rev.Lett. 123 (2019) no.10, 101301 B.Knorr, C.Ripken, F.Saueressig, Class.Quant.Grav. 36 (2019) no.23, 234001

Contents • What is Asymptotic Safety (AS)? • AS for the standard model and gravity • Prediction for the Higgs mass, ~125 GeV • Prediction for top-quark mass, ~170 GeV • AS for beyond the standard model and gravity • The gauge hierarchy problem • Dark matter physics (Higgs portal type)

The SM and gravity coupled to gravity. • Working assumption: • Consider the system where the SM is • No new matter. • Einstein-Hilbert truncation

Beta function quantum gravity effects. • For a matter coupling α • γ α is the anomalous dimension induced by

Prediction of Higgs mass • Prediction of quartic coupling constant • RG equation • We find the Gaussian FP, λ * =0. • Critical exponent (anomalous dimension) J.Pawlowski, M.Reichert, C.Wetterich, M.Y .,Phys.Rev. D99 (2019) no.8, 086010

RG flow of quartic coupling QG decoupled Irrelevant Landau pole Irrelevant Landau pole The red trajectory is the prediction.

RG flow of quartic coupling QG decoupled The top-Yukawa induces positive λ. Predicted point Irrelevant Landau pole Irrelevant Landau pole ⭐ The red trajectory is the prediction.

Top quark mass vs. Higgs mass arXiv: 1904.05237; PDG M.Shaposhnikov, C.Wetterich, Phys.Lett. B683 (2010) 196-200 • For m t =171.3 GeV, m H =126.5 GeV • For m t =230 GeV, m H =233 GeV • Current experimental results (LHC) • m t =170.5±0.7 GeV, m H =125.10±0.14 GeV Prediction of Higgs mass = Prediction of top mass

RG flow of Yukawa QG decoupled Irrelevant Landau pole Irrelevant Asymptotically safe relevant Asymptotically free A. Eichhorn, A.Held, Phys.Lett. B777 (2018) 217-221 The red trajectory is the prediction.

RG flow of Yukawa QG decoupled Irrelevant Landau pole Predicted point Irrelevant Asymptotically safe relevant Asymptotically free A. Eichhorn, A.Held, Phys.Lett. B777 (2018) 217-221 The SM ⭐ The red trajectory is the prediction.

Prediction of top mass A. Eichhorn, A.Held, Phys.Lett. B777 (2018) 217-221 FP value of Newton constant FP value of Cosmological constant

Contents • What is Asymptotic Safety (AS)? • AS for the standard model and gravity • Prediction for the Higgs mass, ~125 GeV • Prediction for top-quark mass, ~170 GeV • AS for beyond the standard model and gravity • The gauge hierarchy problem • Dark matter physics (Higgs portal type)

Gravitational corrections to scalar mass parameter • RG equations • Anomalous dimension • Graviton induced anomalous dimension J.Pawlowski, M.Reichert, C.Wetterich, M.Y .,Phys.Rev. D99 (2019) no.8, 086010

0 RG flow of scalar mass QG decoupled C.Wetterich, M.Y., Phys.Lett. B770 (2017) 268-271 Resurgence mechanism “Classical” scale invariance W.Bardeen, FERMILAB-CONF-95-391-T C.Wetterich, M.Y., Phys.Lett. B770 (2017) 268-271

Higgs portal interaction S • An additional scalar field • We find the Gaussian FP at which the couplings become irrelevant. A.Eichhorn, Y.Hamada, J.Lumma, M.Y ., Phys.Rev. D97 (2018) no.8, 086004

Possible extension of the SM • The boundary condition at the Planck scale at • To generate finite values in low energy X μ • Additional fermion and U(1) gauge field χ Kinetic mixing

RG flow of scalar couplings Y.Hamada, K.Tsumura, M.Y .,Working in progress C.f. M.Hashimoto, S.Iso, Y.Orikasa, Phys.Rev. D89 (2014) no.1, 016019 Realize the Coleman-Weinberg mechanism The additional fermion is stable. Dark matter candidate

Summary • Asymptotically safe gravity is a possible quantum gravity. • Irrelevant couplings are predictable. • Higgs mass and top-quark mass • Conditions for extensions of the SM. • What I could not talk • RG flow of U(1) gauge coupling • Mass hierarchy in the quark sector