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Flat potential and
Higgs inflation濱田雄太(京都大学)
共同研究者川合光(京都)
尾田欣也(大阪)Seong Chan Park(Sungkyunkwan)
2014/05/27 富山大学arXiv:1210.2538(PRD), 1308.6651(PTEP), 1403.6141(PRL), 1404.6141
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Discovery of Higgs boson
mh~126GeV Consistent with SM Higgs
[Strumia et. al. ‘13]
2
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Planck
[Planck ‘13]
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BICEP2:B-mode detection
If this is true, inflation scale is determined!!
[BICEP2 ‘14]B-mode polarization of CMB
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CAUTION•Foreground emissions are larger than expected by BICEP?
•We need to wait for other results such as Planck.
Adam Falkowski’s blog
[Seminar at Princeton by Raphael Flauger, 1405.5857 by Mortonson and Seljak]
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Today’s topic• We consider scenario where SM is valid toward very high scale Λ such as string scale~1017-18GeV.
• pursue possibility that Higgs is inflaton.
• We show SM potential is flat around 1017GeV.• propose Higgs inflation scenario where λ~βλ~0 plays crucial role.
• discuss implications of our scenario on Higgs portal DM.
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Plan
1. Review of inflation2. Flat potential and Higgs inflation3. Z2 scalar DM mass prediction
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Plan
1. Review of inflation2. Flat potential and Higgs inflation3. Z2 scalar DM mass prediction
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Inflation• Inflation solves several problems.
• Flatness problem• Horizon problem
• Inflation can generate density perturbation.• Generate by quantum fluctuation of inflaton• Predictive and good agreement with observation
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Slow roll inflation•Flat potential realize exponential expansion.
•Flatness of potential is characterized by slow roll parameters.
•Expansion is given by e-foldings.
[Picture from web]
for successful inflation
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Scalar and tensor perturbationscalar perturbation tensor perturbation
Knowing As(Planck) and r(BICEP2) Inflation scale!!
spectral index
tensor to scalar ratio
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Observations
[BICEP ’14]
[Planck ’13]
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Plan
1. Review of inflation2. Flat potential and Higgs inflation3. Z2 scalar DM mass prediction
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RGE•We evaluate running λ using two loop RGE.
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λ~βλ~0 at high scale• If Mt=171GeV,λ=0at 1017~18GeV.
•βλ also becomes zeroat 1017~18GeV.
large mt
small mt
[YH,Kawai,Oda ‘12]
[Bezrukov .et.al.’12,Degrassi.et.al. ’12,
……… ]
[Alekhin et.al.’12]
Band : 2σ
[Tevatron]
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•By tuning Mt,SM potential isflat because λ~βλ~0.
• Inflation possible?
Higgs potential at high scale
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No! Too large As•We can realize saddle point by tuning Mt.•For sufficiently expansion N*~60,φ* needs to be close to saddle point(ε<<<1)
•As a result, too largedensity perturbation.(As>>1 in this case)
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Strategy
•So, here, we assumefor field value φ>Λ, potential is flat.
• New physics would make potential flat.
•Though it is ad-hoc assumption,we obtain useful constraint on mt and Λ.
•Later, we show explicit example of potential.
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Strategy
•So, here, we assumefor field value φ>Λ, potential is flat.
• New physics would make potential flat.
•Though it is ad-hoc assumption,we obtain useful constraint on mt and Λ.
•Later, we show explicit example of potential.
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Strategy
•So, here, we assumefor field value φ>Λ, potential is flat.
• New physics would make potential flat.
•Though it is ad-hoc assumption,we obtain useful constraint on mt and Λ.
•Later, we show explicit example of potential.
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Constraint on Mt and Λ•Scalar perturbation and observation of tensor mode give upper bound on potential.
•Potential should be monotonically increasing function to avoid graceful exit problem.(Comment:Numerically, this condition is almost equivalent to stability requirement.)
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Constraint on Mt and Λ•Scalar perturbation and observation of tensor mode give upper bound on potential.
•Potential should be monotonically increasing function to avoid graceful exit problem.(Comment:Numerically, this condition is almost equivalent to stability requirement.)
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Constraint on Mt and Λ•Scalar perturbation and observation of tensor mode give upper bound on potential.
•Potential should be monotonically increasing function to avoid graceful exit problem.(Comment:Numerically, this condition is almost equivalent to stability requirement.)
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Constraint on Mt and ΛEnlarged view
[YH,Kawai,Oda ‘13]
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Constraint on Mt and Λ•Λ<5×1017GeV•String scale appears.•Situation in whichΛ~1017GeV and inflation above Λis OK.
Enlarged view
[YH,Kawai,Oda ‘13]
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Concrete example:ξ|H|2R• Jordan frame
•Conformal transformation
•Potential becomes flat at high φ
[Bezrukov, Shaposhnikov ‘08]
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RG improvement• Where is renormalization scale μ?• Usually, μ~(effective mass of top/gauge boson).
• Prescription1(effective mass in Einstein frame)
• μ becomes constant at high field value.• Prescription2(effective mass in Jordan frame)
• We don’t know which prescription is correct.• Let’s see Higgs inflation in both descriptions.
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Higgs inflation• If λ is not small at high scale (~O(0.1)),small r is predicted.
•But, taking into account λ~0 at high scale,prediction drastically changes.
• In particular, r~O(0.1) is possible.
[Bezrukov, Shaposhnikov ‘08]
[YH,Kawai,Oda,Park ’14,Bezrukov, Shaposhnikov ‘14]
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Prescription1:saddle point•By tuning top mass, we can make saddle point.
• e-folding is earned in passing the saddle point.• Observational density perturbation corresponds to φ* above saddle point.
φ/GeV
ξ=0
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Prescription1:saddle point
Saddle pointφ*
ξ~10φ*~0.9Mplns~0.96r~0.1
φ[Mpl]
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Prescriotion2:chaotic•Around minimum
•Using canonical field in Einstein frame
•Potential becomes
•Putting into SM value, if ξ~100,quadratic chaotic inflation and ns~0.96,r~0.15
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Plan
1. Review of inflation2. Flat potential and Higgs inflation3. Z2 scalar DM mass prediction
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Z2 scalar dark matter•Add gauge singlet real scalar DM S.
• Z2 charge: SM particle is even. S is odd.
•S modifies βλ. At one-loop level,
•λ is larger than λSM at high scale.Positive contribution
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Modification•DM also modifies scalewhere βλ=0.
•DM helps stability ofHiggs potential.
•Central value Mt=173GeV is OKfor κ0~0.25
κ0=κ(mweak)
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Constraint on mDM•mDM and Mt arecorrelated.
•mDM<1000GeV• If we further imposesaddle point at 1017GeV,DM mass is 400~470GeV.
[YH,Kawai,Oda ‘14]
ρ0=ρ(mweak)
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Test
[Cline et. al. ‘13]
Prediction can be tested by XENON.
Log10(mDM/GeV)
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Summary•We consider scenario where SM is valid up to string scale~1017GeV.
• find SM potential is flat around 1017GeV.•propose Higgs inflation scenario where λ~βλ~0 plays crucial role.
• In this scenario, Z2 scalar DM mass is constrained depending on Mt:mDM<1000GeV or 400GeV<mDM<470GeV.