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

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

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Status of asymptotic safety in gravity-matter systems Masatoshi Yamada (Ruprecht-Karls-Universitt Heidelberg) KEK Theory workshop 2019 General relativity Einstein theory Well describes observed facts: Mercury perihelion

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Status of asymptotic safety in gravity-matter systems

Masatoshi Yamada

(Ruprecht-Karls-Universität Heidelberg)

KEK Theory workshop 2019

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General relativity

  • Einstein theory
  • Well describes observed facts:
  • Mercury perihelion
  • Gravitational wave
  • etc.
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Towards quantum gravity

  • The quantized Einstein-Hilbert action is not

perturbatively renormalizable.

  • Higher derivative gravity
  • Perturbatively renormalizable
  • Ghost (unitarity) problem
  • G. ’t Hooft and M. Veltman, Annales Poincare Phys.Theor.,A20,69

Stelle, K.S. Phys.Rev. D16 (1977) 953-969

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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.

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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)
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Asymptotic safety

  • Suggested by S. Weinberg
  • Existence of non-trivial UV fixed point
  • Continuum limit k→∞.
  • UV critical surface (UV complete theory) is spanned by

relevant operators.

  • Dimension of UV critical surface = number of free parameters.
  • Generalization of asymptotic free
  • Non-perturbatively renormalizable gravity
  • S. Weinberg, Chap 16 in General Relativity
  • Fig. from A.Eichhorn, Front.Astron.Space Sci. 5 (2019) 47
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Asymptotic freedom

  • Asymptotic freedom
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Asymptotic safety

  • Asymptotic safety
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Functional renormalization group

k∂kΓk = 1 2Str[(Γ(2)

k

+ Rk)−1k∂kRk]

g1 g2 gi

Γk = Z d4x[g1O1 + g2O2 + · · · + giOi + · · · ]

Γk ' Z d4x[g1O1 + g2O2]

S = ΓΛ Γ = Γk=0

exact flow truncated flow

projection

Wetterich equation

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Critical exponent

  • RG eq. around FP g*
  • Solution of RG eq.

negative eigenvalue

k → 0 θi > 0

θi < 0

relevant irrelevant

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Relevant: θ> 0

  • Free parameter
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Irrelevant θ< 0

  • Predictable parameter

Landau pole

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Irrelevant θ< 0

  • Predictable parameter

Landau pole Prediction

UV complete (no Landau pole)

No dangerous divergence =Safe!

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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

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Earlier studies

  • Truncated system for pure gravity
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Earlier studies

  • Truncated system for pure gravity

Einstein-Hilbert truncation

e.g. M. Reuter, F. Saueressig, Phys.Rev. D65 (2002) 065016

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Earlier studies

  • Truncated system for pure gravity

f(R) truncation

e.g. K. Falls, D. Litim, J. Schröder, Phys.Rev. D99 (2019) no.12, 126015 G.Brito, N.Ohta, A. Pereira, A.Tomaz, M.Y., Phys.Rev. D98 (2018) no.2, 026027

R71

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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

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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

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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

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Earlier studies

  • These studies have shown the finite

number of relevant directions.

  • There are 3 relevant directions (?)
  • which means 3 free parameters
  • For details, listen Prof. Ohta’s talk.
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Open questions

  • What is degrees of freedom associated to

the non-trivial (Reuter) fixed point?

  • Unitarity problem (or ghost problem)
  • Robustness of number of relevant operators.
  • Scheme-independent calculations.
  • …
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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

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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)
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The SM and gravity

  • Working assumption:
  • Consider the system where the SM is

coupled to gravity.

  • No new matter.
  • Einstein-Hilbert truncation
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Beta function

  • For a matter coupling α
  • γα is the anomalous dimension induced by

quantum gravity effects.

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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

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RG flow of quartic coupling

QG decoupled

Irrelevant Landau pole Irrelevant Landau pole

The red trajectory is the prediction.

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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.

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Top quark mass vs. Higgs mass

  • For mt=171.3 GeV, mH=126.5 GeV
  • For mt=230 GeV, mH=233 GeV
  • Current experimental results (LHC)
  • mt=170.5±0.7 GeV, mH=125.10±0.14 GeV

arXiv: 1904.05237; PDG

Prediction of Higgs mass = Prediction of top mass

M.Shaposhnikov, C.Wetterich, Phys.Lett. B683 (2010) 196-200

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RG flow of Yukawa

QG decoupled

Irrelevant Landau pole

Irrelevant Asymptotically safe

relevant Asymptotically free

The red trajectory is the prediction.

  • A. Eichhorn, A.Held, Phys.Lett. B777 (2018) 217-221
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RG flow of Yukawa

QG decoupled

⭐

Irrelevant Landau pole

Predicted point Irrelevant Asymptotically safe

relevant Asymptotically free

The red trajectory is the prediction.

The SM

  • A. Eichhorn, A.Held, Phys.Lett. B777 (2018) 217-221
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Prediction of top mass

FP value of Newton constant FP value of Cosmological constant

  • A. Eichhorn, A.Held, Phys.Lett. B777 (2018) 217-221
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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)
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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

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RG flow of scalar mass

“Classical” scale invariance

QG decoupled

Resurgence mechanism

C.Wetterich, M.Y., Phys.Lett. B770 (2017) 268-271 W.Bardeen, FERMILAB-CONF-95-391-T C.Wetterich, M.Y., Phys.Lett. B770 (2017) 268-271

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Higgs portal interaction

  • An additional scalar field
  • We find the Gaussian FP at which the couplings

become irrelevant.

S

A.Eichhorn, Y.Hamada, J.Lumma, M.Y., Phys.Rev. D97 (2018) no.8, 086004

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Possible extension of the SM

  • The boundary condition at the Planck scale
  • To generate finite values in low energy
  • Additional fermion and U(1) gauge field

χ Xμ

at

Kinetic mixing

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RG flow of scalar couplings

The additional fermion is stable. Dark matter candidate

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

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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