Beyond Standard Model and Asymptotically Safe Gravity · Conformal Standard Model and Softly Broken...
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Beyond Standard Model and Asymptotically
Safe Gravity
Jan H. Kwapisz
3 July 2019 Warsaw
Beyond General Relativity, Beyond Cosmological Standard Model
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Table of Contents
1. Standard Model of Particle
Physics
2. Asymptotic safety
3. Beyond Standard Model
4. Summary
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Standard Model of Particle Physics
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Standard Model of particle Physics
Figure 1: Standard Model Interactions
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Standard Model of particle Physics
• No experiments particle physics contradicting the Standard
Model predictions
• Experimental problems: dark matter, baryon asymmetry, lack
of right handed neutrinos
• Theoretical problems: strong CP problem, U(1) Landau pole,
hierarchy problem
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Beyond the Standard Model
• Grand Unification Theories
• Supersymmetry: Minimal Supersymmetric Standard Model,
Supergravity, Superstrings
• No new physics scale between EW and Planck scale: minimal
extensions of SM
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Asymptotic safety
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What is asymptotic safety?
Renormalisation group equations (running of the couplings):
k∂gi (k)
∂k= βi ({gi (k)}) . (1)
Asymptotic safety:
• Generalisation of asymptotic freedom. A UV fixed interacting
point.
• Hypothesis: Gravity is asymptotically safe
S. Weinberg (1979) , see Tim Morris talk
• Phenomenological consequence: prediction of irrelevant
couplings, allowed range for relevant couplings
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Matter beta functions with gravitational corrections
The matter beta functions are supplemented by the gravitational
corrections:
β(gj) = βSM(gj) + βgrav (gj , k), (2)
where due to universal nature of gravitational interactions:
βgrav (gj , k) =ajk
2
M2P + ξk2
gj . (3)
The ξ ≈ 0.024 for Standard Model and depends on cosmological
constant and MP fixed points. Depending on a sign of aj , there is
a repelling/attracting fixed point at 0.
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ξ dependence on fields
Constant ξ is field dependent
ξ =1
16πG ∗N,
with
G ∗N ≈ −12π
NS + 2ND − 3NV − 46≥ 0,
where NS ,ND ,NV are number of fermions, scalars and vector
particles. So most of the GUTs and MSSM were excluded. The
minimal extensions seems to be compatible with AS. Also the
predicted Higgs mass can differ depending on the model.
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Standard Model with gravitational corrections
• With the assumption of asymptotic safety of gravity the Higgs
mass (self coupling) was calculated as mH = 126± few GeV
two years before the detection.
M. Shaposhnikov and C. Wetterich (2010) arXiv:0912.0208.
• The top mass was also predicted, “yielding a Higgs mass of
Mh = 132 GeV in our simple truncation. Higher-order
interactions might reconcile global stability of the potential
with a Higgs mass agreeing with the experimental result.”
A. Eichhorn, A. Held (2010) arxiv:1707.01107
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Beyond Standard Model
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Higgs Portal Models
• Sterile complex (real) scalar φ coupled to Higgs doublet:
Lscalar = (DµH)†(DµH) + (∂µφ?∂µφ)− V (H, φ). (4)
V (H, φ) = −m21H†H −m2
2φ?φ+ λ1(H†H)2
+λ2(φ?φ)2 + 2λ3(H†H)φ?φ. (5)
• The scalar particles combined from two states:
m21 = λ1v
2H + λ3v
2φ, m2
2 = λ3v2H + λ2v
2φ, (6)
and the lighter one identified with Higgs particle.
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Model 1: Additional sterile quarks (KSVZ axion)
We add one scalar and electro-weak sterile heavy quarks:
LY = Yqijφ
Nq∑i=1
Q̄ iLQ
jR , (7)
with the UA symmetry and discrete symmetry Q iL → −Q i
L,
Q iR → Q i
R , φ→ −φ, due to SU(3) instanton effects the “phase”
of φ becomes massive: axion particle. We take Yqij = δijYq.
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Model 2: Conformal Standard Model
Include right handed neutrinos coupled to φ with the coupling yM :
L 3 1
2YMji φN
jαN iα, (8)
where YMij = yMδij . To resolve the baryogengesis problem, via
resonant leptogenesis, the right handed neutrinos have to be
unstable:
MN = yMvφ/√
2 > m2. (9)
Furthermore the CSM can resolve the SM problems like: hierarchy
problem, inflation and has dark matter candidate: minoron with
mass: v2/MP .
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Conditions for low energy coupling values and ai values
Impose two conditions:
• absence of Landau poles
• λ1(µ) > 0, λ2(µ) > 0, λ3(µ) > −√λ2(µ)λ1(µ).
And take:
agi = −1, ayt = −0.5, aλ1 = +3 = aλ2 = +3, aλ3 = +3. (10)
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The running of couplings
Consider the following couplings: g1, g2, g3, yt , yM = yq, λ1, λ2, λ3.
The matter beta functions are β̂ = 16π2β:
β̂g1 = 416 g3
1 ,
β̂g2 = −196 g3
2 ,
β̂g3 = (−11 + 4 + 23Nqθ(Mq − µ))g3
3 ,
β̂yt = yt(
92y
2t − 8g2
3 − 94g
22 − 17
12g21
),
β̂yM = 52y
3M ,
β̂λ1 = 24λ21 + 4λ2
3 − 3λ1
(3g2
2 + g21 − 4y2
t
)+ 9
8g42 + 3
4g22 g
21 + 3
8g41 − 6y4
t ,
β̂λ2 =(20λ2
2 + 8λ23 + 6λ2y
2M − 3y4
M
),
β̂λ3 = 12λ3 [24λ1 + 16λ2 + 16λ3
−(9g2
2 + 3g21
)+ 6y2
M + 12y2t
],
(11)
Nq number of sterile quarks and Mq is its mass.14
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Gauge and Yukawa couplings running
The low-energy values at µ0 = 173.34 are: g1(µ0) = 0.35940,
g2(µ0) = 0.64754, g3(µ0) = 1.1888 and yt(µ0) = 0.95113.
Figure 2: The running of g1, g2, g3, yt
With this Yukawa for pure Standard Model: MH = 136 GeV.
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Model I: aλ3 = +3
One gets λ3 = 0, but still the Higgs mass is affected due to change
in g3 running.
Can the model be
extended to Planck scale? Nq Mq Mh
yes 1 200 GeV 133 GeV
no 2 200 GeV -
yes 2 1000 GeV 133.7 GeV
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Model II:aλ2 = +3, aλ3 = −3
Then we calculate λ1(λ3, yM), λ2(λ3, yM). Take the tree level
relations for m1,m2 (the one loop pole matching gives corrections
of order 1 GeV):
m21 = λ1v
2H + λ3v
2φ, (12)
m22 = λ2v
2φ + λ3v
2H , (13)
with m1 = 126GeV, vH = 246 GeV. Then:
300GeV > m2 > 270GeV, (14)
and
yM > 0.8, 350GeV > MN > 300GeV. (15)
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Comparison with experimental data
• The excess of events with four charged leptons at E ∼ 325
GeV seen by the CDF and CMS Collaborations can be
identified with a detection of a new ‘sterile’ scalar particle
proposed by the Conformal Standard Model
K. Meissner H. Nicolai 2013 arXiv:1208.5653
• The hypothetical heavy boson mass is measured to be around
272 GeV (in the 270− 320 GeV range)
arXiv:1506.00612
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Summary
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Thank you for your attention
Talk based on article: arxiv.org/abs/1810.08461
For details check also backup slidesTo contact me use my mail:
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Backup slides
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Non-standard possibilities for couplings
Non standard possibilities are:
• Asymptotic safety, limµ→∞ g 6= 0,∀iβi (g∗) = 0. Theory has a
UV fixed point. Example: Weinberg hypothesis: Gravity.
• Oscillating g . Theory has a limit cycle. Quantum mechanics:
−g/r2 potential [12].
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Softly Broken Conformal Symmetry
We consider an effective theory valid below Λ. We split the bare
parameters mass and self-coupling into renormalised parameters
and counter-terms:
m2B(Λ) = m2
R − fquad(Λ, µ, λR)Λ2 + m2Rg
(λR , log
(Λ
µ
)), (16)
where g(λR , log
(Λµ
))is some function. Assume that the
quadratic divergences depends only on bare couplings:
fquad(Λ, µ, λR) = fquad(λB(Λ)). (17)
So if fquad(λB) = 0 at certain scale, then the hierarchy problem is
solved.
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Conformal Standard Model and Softly Broken Conformal Sym-
metry
For CSM the f̂ quadi = 16π2f quadi are:
f̂ quad1 (λ, g , y) = 6λ1 + 2λ3 +9
4g2
2 +3
4g2
1 − 6y2t , (18)
f̂ quad2 (λ, g , y) = 4λ2 + 4λ3 − 3y2M . (19)
For the Conformal Standard Model Λ . MP is sufficient, while the
Standard Model requires Λ� MP .
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Inflation in Conformal Standard Model
Lagrangian in the Jordan frame [6]:
L = DµH†DµH+∂µφ∂
µφ∗−(M2
P + ξ1H†H + ξ2|φ|2
)2
R−VJ(H, φ),
(20)
with ξi > 0. We get the standard result that:
ns ' 1− 2
N' 0.97, (21)
and:
r ' 12/N2 ' 0.0033, (22)
however it requires that ξ1, ξ2 ∼ O(104).
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Can we have λ3 6= 0? Take aλ3 < 0
(a) λ1 dependence on λ3, yM
(b) λ2 dependence on λ3, yM 24
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Coefficients aλ2 = aλ3 = −3, set of allowed couplings λ2, λ3, yM
Figure 3: Maximal (left) and minimal (right) yM(λ3, λ2),aλ2 = −3, aλ3 = −3
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Coefficient: aλ2 = aλ3 = −3, allowed λ1
Figure 4: Plot of λ1(λ2, λ3, yM)
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Coefficient: aλ3 = +3, aλ2 = +3
Still: λ3 = 0. So SM and φ decouple, but:
Figure 5: λ2 dependence on yM
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Coefficients aλ2 = aλ3 = −3
It constrains the second scalar mass as:
272 GeV < m2 < 328 GeV and yM > 0.71. (23)
The neutrinos masses:
MN = 342+41−41 GeV (24)
and they satisfy instability condition.
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Conditions on m2
One can parametrise the discrepancies from SM as:
tanβ =λ0 − λ1
λ3
vHvφ. (25)
Conditions:
• | tanβ| < 0.35.
• un-stability condition for the second particle: m2 > 2m1.
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Conditions on m2(2)
1. We checked that the analysed parameters satisfy the Softly
Broken Conformal Symmetry requirements at MP with
couplings going to zero (but nowhere else).
2. We analyzed the running of the β functions for m2 and m1,
where we took ami = −1. It gives no new bounds on m2 and
lambda-couplings.
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Higgs portal case: yM = 0.0
For yM = 0.0:
m2 = 160+103−100 GeV, (26)
so classically it is stable.
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Bibliography
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Bibliography i
S. Weinberg General Relativity: An Einstein centenary
survey, Hawking, S.W., Israel, W (eds.). (1979) Cambridge
University Press, pages 790-831.
M. Shaposhnikov and C. Wetterich Phys. Lett. B
683, 196 (2010) doi:10.1016/j.physletb.2009.12.022
[arXiv:0912.0208 [hep-th]].
A. Eichhorn, arXiv:1810.07615 [hep-th].
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Bibliography ii
P. H. Chankowski, A. Lewandowski, K. A. Meissner,
and H. Nicolai, Mod. Phys. Lett. A30 (2015) 1550006.
A. Lewandowski, K. A. Meissner and H. Nicolai,
Phys. Rev. D 97, no. 3, 035024 (2018)
doi:10.1103/PhysRevD.97.035024 [arXiv:1710.06149 [hep-ph]].
J.H. Kwapisz and K.A. Meissner, year 2017, arXiv
1712.03778,Acta Physica Polonica B, Vol. 49, No. 2
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Bibliography iii
K. A. Meissner and H. Nicolai, Phys. Lett. B 718, 943
(2013) doi:10.1016/j.physletb.2012.11.012.
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