1) The document discusses revisiting the effects of decoupling in the running cosmological constant. It focuses on the renormalization group running of the cosmological constant within quantum field theory. 2) A case study examines the running of the cosmological constant using a real scalar field model. Calculations are performed in both the MS-bar and MOM renormalization schemes. 3) The standard model is also examined as a case study. The running of the induced and vacuum cosmological constants is calculated. 4) Applications include exploring connections between fine-tuning of the Higgs mass and cosmological constant in massless theories, and generalizing to theories in constant curvature space.

1. BSW, Nis, June12, 2018
Revisiting the decoupling effects in
the running Cosmological Constant
Oleg Antipin (IRB, Zagreb)
Based on: arxiv 1703.10967
in collaboration with Blazenka Melic

2. Outline
• RG running of the Cosmological Constant
• Case study: Standard Model
• Applications
• Conclusions

3. Vacuum energy density Induced vacuum energy density
Experimentally measured value at
Cosmological constant

4. Vacuum energy density Induced vacuum energy density
Cosmological constant
This represents “mathematical” scaling introduced during renormalization
which sometimes can be used to trace the scaling dependence with a physical quantities
The physical running (if there is at all) is not with µ but with some physical external momentum q
or some dynamical property of the background metric, e.g. Hubble scale
The physical scaling of the CC is unknown and we concentrate on its µ-dependence

5. But fine-tuning
However
CC experimentally measured value at
need to RG run to this low scale taking into
account decoupling of the heavy particles
Cosmological constant problem

6. Decoupling effects
On dimensional grounds and for
Decoupling does not hold in the
mass-independent schemes like MS-bar
to analyze decoupling we need to work
in a mass-dependent schemes
Appelquist-Carazzone theorem

7. Cosmological Perspective
⇢⇤(H) = ⇢0
⇤ + const ⇥ M2
P (H2
H2
0 ) + O(H4
)
Sola,Shapiro,….
Running vacuum models (subclass of dynamical vacuum models)
Instead, our goal is to learn how CC problem can
provide constraints on the particle physics models…
µ = H
The physical running of the CC (not derived from the first principles)
and test it using current data…

8. Case study: Real scalar field
One-loop effective potential:
So far we had only classical parameters... now quantum
Toy model :

9. Case study: Real scalar field
Various pieces satisfy RG equations:
- scheme

10. Vacuum and induced CC running
Valid only in the UV regime !

11. Case study: Real scalar field in
Need a mass-dependent scheme, but first :

12. Case study: Real scalar field in MOM

13. Vacuum and induced CC running in MOM
Valid in the UV and IR regime !

14. Case study: Standard Model in

15. Valid in the UV regime only !
Case study: Standard Model in

16. Valid in the UV and IR regimes !
Case study: Standard Model in MOM

17. Applications : SM
Responsible for CC tuningGoldstone terms canceled in the sum !

18. Applications: Massless theories
generalized
Veltman condition
In massless models fine-tuning of Higgs mass and CC are linked

19. Massless theories : SM + real scalar
One-loop induced (Coleman-Weinberg) Higgs mass:
Example of how running of the CC
may be connected to BSM physics
prediction!

20. Applications: SM in constant curvature space

21. Conclusions
• We considered the RG running of the Cosmological Constant
• We showed that only RG running of the total (induced +
vacuum) CC exhibits behaviour consistent with the decoupling
theorem
• We provided a simple extension of the SM with addition of one
massless real scalar where condition of absence of leading RG
effect allowed us to predict the radiative Higgs mass correctly
• We also provided generalization to the constant curvature
space

22. 018.irb.hr
http://hvar2018.irb.hr
The workshop aims at discussing the subject of asymptotic safety
from both perturbative and non-perturbative perspectives, including
modern developments in gravity and ordinary gauge theories.