Quintessence Saves Higgs Instability

Chengcheng Han
Based on arXiv:1809.05507, with Shi Pi and Misao Sasaki

Beyond the BSM
The 4th Kavli IPMU -Durham IPPP -KEK -KIAS workshop

Outline❖

The Higgs instability problem❖

Quintessence-Higgs Model❖

Swampland conjecture

Chengcheng Han-Kavli IPMU

Higgs potential and self coupling
In SM, the Higgs potential is:

V = (H† Hd1=d ln µ2(4⇡)2 ✓v 2 )212+ 6yt2

⇠ 0.13
9g222

9g1210◆v ⇠ 174 GeV

9g2427g14
9g22 g1243yt +++1640040D. Buttazzo, et al arXiv:1307.3536

Chengcheng Han-Kavli IPMU

Higgs potential and self coupling
To study the vacuum structure of the Higgs, RG-improved effective potential:

For hvD. Buttazzo, et al arXiv:1307.3536

h4Ve↵ = e↵ (h)4(h) ⌘Z(µ)d ln µ

is the Higgs field anomalous dimension
New stable vacuum is developed at high energy scale!

Chengcheng Han-Kavli IPMU

Higgs stability
Should we worried about this?

D. Buttazzo, et al arXiv:1307.3536

Fortunately for human being: electroweak vacuum is metastable!
(maybe not that fortunate for people who study new physics)
Chengcheng Han-Kavli IPMU

Up to here
No Higgs instability problem

But this is not the end of the story

Chengcheng Han-Kavli IPMUInflation
fluctuations in CMB❖

Explains the origin of the large-scale structure of the cosmos.

❖Horizon problem❖

Flatness problem❖

Magnetic-monopole problem …
Chengcheng Han-Kavli IPMU

Higgs instability during inflation⇤I ⇠ 1010 GeV⇤I

Surviving probability per horizon

J. R. Espinosa, et al arXiv:1505.04825

p2⇡⇤IpP (h < ⇤I , Ntot ) = erf ()Hinf Ntoterf (x) ' 1

1x2
p e⇡x

Total e3Nhor horizons
Surviving probability 1(1P)

e3NhorFor Nhor = 60, Ntot = 1000, we need Hinf < 10 2 ⇤I
So-called Higgs instability problem during inflation
recent review, see arXiv:1809.06923
Chengcheng Han-Kavli IPMU

Some solutions❖

Add new field to change Higgs self coupling.
J. Elias-Miró, J. R. Espinosa, G. F. Giudice, Hyun Min Lee, A. Strumia, arXiv:1203.0237
arXiv:1203.0237❖Add Higgs coupling to inflaton.
O. Lebedev, A. Westphal, arXiv:1210.6987

L❖⇠ 2 h2Higgs self coupling is dynamical: changing with time.
C. Han, Shi Pi and Misao Sasaki, arXiv:1809.05507

Chengcheng Han-Kavli IPMU

Do we have a dynamical field at hand?
Quintessence as an explanation of dark energy
E. J Copeland, A. R Liddle, D. Wands, arXiv:9711068

V( )V ( ) = e ⇠ ⇤0t

Smaller in future, larger in the past!
Fit our requirement perfectly.

Chengcheng Han-Kavli IPMU

Quintessence-Higgs Model
F. Denef, A. Hebecker, T. Wrase, arXiv:1807.06581

Potentially solve the higgs instability problem,• How large enhancement do we need?
• Whether quintessence provide such a factor?
• How to test it?
Chengcheng Han-Kavli IPMU

How large enhancement do we need?
Just effectively change the higgs self coupling0(v) = (v)eC. Han, Shi Pi and Misao Sasaki, arXiv:1809.05507

Chengcheng Han-Kavli IPMU⇠

Whether quintessence provide such a factor?
C. Han, Shi Pi and Misao Sasaki, arXiv:1809.05507

From Planck 2018

Chengcheng Han-Kavli IPMU

How to test it?
Dark energy experiment already exclude⇠ > 0.6

Y. Akrami, R. Kallosh, A. Linde, V. Vardanyan, arxiv:1808.09440

Exclusion limit combing
SNeIa, CMB, BAO, H

0Future reach: Euclid and the SKA(large-scale structure surveys)(within 10 years)

Chengcheng Han-Kavli IPMU

Swampland Conjecture(my own understanding)
All the theories not consistent with quantum gravity is swampland.

Swampland

Swampland
conjecture

G. Obied, H. Ooguri, L. Spodyneiko, C. Vafa, arXiv:1806.08362

Swampland conjecture: a quantum gravity theory should satisfy:|rV |/V > c, c ⇠ O(1)Chengcheng Han-Kavli IPMU

Swampland Conjecture|rV |/V > c, c ⇠ O(1)Chengcheng Han-Kavli IPMU

Swampland Conjecture

Implications I: dark energy
Cosmological constant do not exist!

V =⇤Dark energy should be explained dynamically:
Quintessence:V = ⇤e⇠rV /V = ⇠Chengcheng Han-Kavli IPMU

Swampland Conjecture

Implications II: Higgs
rV = 0
Higgs sector need to be enlarged!
0Not consistent!

Quintessence-Higgs Model|rH V = 0|, |r V | = ⇠VF. Denef, A. Hebecker, T. Wrase, arXiv:1807.06581|rV |/V = ⇠Chengcheng Han-Kavli IPMU

Summary❖

The Higgs instability can be solvedin Quintessence-Higgs Model.

❖It may be tested within 10 years.

❖UV completion?

Chengcheng Han-Kavli IPMU