status of asymptotic safety in gravity-matter systems
TRANSCRIPT
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.
• 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
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• 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
Functional renormalization group
k@k�k =1
2Str[(�(2)
k +Rk)�1k@kRk]
g1
g2
gi
�k =
Zd4x[g1O1 + g2O2 + · · ·+ giOi + · · · ]
�k '
Zd4x[g1O1 + g2O2]
S = �⇤
� = �k=0
exact flow
truncated flow
projection
Wetterich equation
Critical exponent
• RG eq. around FP g*
• Solution of RG eq. negative eigenvalue k ! 0
✓i > 0
✓i < 0
relevant
irrelevant
Irrelevant θ< 0• Predictable parameter
Landau pole
PredictionUV complete
(no Landau pole)
No dangerous divergence =Safe!
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
Einstein-Hilbert truncation e.g. M. Reuter, F. Saueressig, Phys.Rev. D65 (2002) 065016
Earlier studies• Truncated system for pure gravity
f(R) truncation e.g. K. Falls, D. Litim, J. Schröder, Phys.Rev. D99 (2019) no.12, 126015G.Brito, N.Ohta, A. Pereira, A.Tomaz, M.Y., Phys.Rev. D98 (2018) no.2, 026027
R71
Earlier studies• Truncated system for pure gravity
Higher derivative truncation Ie.g. D. Benedetti et al. Mod.Phys.Lett. A24 (2009) 2233-2241Y.Hamada, M.Y., JHEP 1708 (2017) 070
Earlier studies• Truncated system for pure gravity
Higher derivative truncation IIL.Bosma, B.Knorr, F.Saueressig, Phys.Rev.Lett. 123 (2019) no.10, 101301
Earlier studies• Truncated system for pure gravity
Higher derivative truncation IIIB.Knorr, C.Ripken, F.Saueressig, Class.Quant.Grav. 36 (2019) no.23, 234001
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.
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.
• …
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, 101301B.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• Working assumption:
• Consider the system where the SM is coupled to gravity.
• No new matter.
• Einstein-Hilbert truncation
Beta function• For a matter coupling α
• γα is the anomalous dimension induced by quantum gravity effects.
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 decoupledIrrelevant
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
• 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 GeVarXiv: 1904.05237; PDG
Prediction of Higgs mass = Prediction of top mass
M.Shaposhnikov, C.Wetterich, Phys.Lett. B683 (2010) 196-200
RG flow of YukawaQG 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
RG flow of YukawaQG 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
Prediction of top mass
FP value of Newton constant
FP value of Cosmological constant
A. Eichhorn, A.Held, Phys.Lett. B777 (2018) 217-221
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 dimensionJ.Pawlowski, M.Reichert, C.Wetterich, M.Y.,Phys.Rev. D99 (2019) no.8, 086010
0
RG flow of scalar mass
“Classical” scale invarianceQG decoupled
Resurgence mechanismC.Wetterich, M.Y., Phys.Lett. B770 (2017) 268-271
W.Bardeen, FERMILAB-CONF-95-391-TC.Wetterich, M.Y., Phys.Lett. B770 (2017) 268-271
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
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
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