Relaxion dynamics after reheating. Toyokazu Sekiguchi (IBS-CTPU)

Transcription

1 Relaxion dynamics after reheating Toyokazu Sekiguchi (IBS-CTPU) 5th UTQuesT workshop YITP, Dec 12, 2016

2 Outline High reheating temperature in relaxion model Dynamics of relaxion with anomalous coupling with U(1) Parameter constraints Summary References: Hyunjing Kim, Kiwoon Choi, TS, arxiv: Hyunjing Kim

3 Cosmological relaxation Graham, Kaplan, Rajendran 2015 Dynamical solution for hierarchy problem V ( )= 2 f e h f e + b (hhi) 4 cos f hhi =0 2 } = f e

4 Cosmological relaxation Graham, Kaplan, Rajendran 2015 Dynamical solution for hierarchy problem V ( )= 2 f e h f e + b (hhi) 4 cos f hhi 6=0 hhi =0 m 2 h( )= (90GeV) 2 2 } = f e = f

5 Dynamics after inflation? Two primary possibilities: Treheat < TEW EW symmetry is never restored Barrier potential persists Selected EW scale is preserved Treheat > TEW : often required by e.g. baryogenesis EW symmetry is restored Barrier potential disappears and relaxion starts rolling again Relaxion may overshoot EW scale

6 Relaxion excursion after reheating } T = T reheat >T EW = f e T = T EW = f To stop relaxion within EW scale, d /dt T =TEW < 2 b is required.

7 Relaxion excursion after reheating Problem: Hubble friction is not effective Slope should be extremely flat f & 2 b M Pl v 2 O(1) On the other hand, for cosmological scanning of EW scale to take place f e f This leads to relaxion scale >> Planck scale

8 Alternative possibility? U(1) gauge field X μ anomalously coupled to relaxion L 1 4 X µ X µ 4F X µ X µ For the time being, we assume X μ is in hidden sector out of thermal equilibrium

9 Gauge field production Field equation of X μ : Ẍ ± k 2 ± k F! X ± =0 One of helicity states can be tachyonic at k< /F Exponential production of gauge fields tachyonic frequency: ' F

10 Relaxion motion Backreaction: frictional force onto relaxion motion +2H a 2 V 0 1 ( )= Fa 2 hx X µ µ i X 2 X + " X ± 2 / exp ± # with F Terminal velocity is achieved when friction saturates ' F H Relaxion velocity is decreasing function of time ξ is constant with logarithmic dependences on e.g. model parameters and/or initial conditions etc.

11 Numerical calculation 10 3 = 25FH T = 10 7 GeV

12 When does relaxion stop? Barrier potential develops at T=T EW If d /dt T =TEW < 2 b Relaxion is trapped immediately at T=Λ EW If d /dt T =TEW > 2 b Relaxion continues rolling but soon is trapped as velocity decreases / T 2 In most of parameter region, former is the actual case

13 Parameter Constraints Conventional relaxion is subject of a variety of constraints Choi & Im (2016); Flacke et al. (2016) Fifth force & Casimir effect CMB, BBN, EBL SN1987A, globular clusters K- & B-meson decay, beam dump (CHARM) LEP, LHC f [GeV] m ϕ =μev mev ev kev MeV BBN Λ tp =145 GeV, Λ cq =10 7 GeV Λ tp =2 TeV, Λ cq =10 8 GeV EBL CMB η B N eff GeV 5th force Λ tp =100 TeV, Λ cq =10 9 GeV SN CHARM LHC K B LEP GCe Λbr >(Λbr) max Λ br [GeV] Flacke et al., arxiv: In our setup, however, relaxion can dominantly decay into X μ Many of cosmological constraints (+beam dump) can be evaded

14 Parameter Constraints Conventional relaxion is subject of a variety of constraints Choi & Im (2016); Flacke et al. (2016) Fifth force & Casimir effect CMB, BBN, EBL SN1987A, globular clusters K- & B-meson decay, beam dump (CHARM) LEP, LHC f [GeV] m ϕ =μev mev ev kev MeV BBN Λ tp =145 GeV, Λ cq =10 7 GeV Λ tp =2 TeV, Λ cq =10 8 GeV EBL CMB η B N eff GeV 5th force Λ tp =100 TeV, Λ cq =10 9 GeV SN CHARM LHC K B LEP GCe Λbr >(Λbr) max Λ br [GeV] Flacke et al., arxiv: In our setup, however, relaxion can dominantly decay into X μ Many of cosmological constraints (+beam dump) can be evaded

15 Additional constraints Gauge field overproduction from relaxion During excursion Produced X μ should not dominate the Universe V = 4 f e ' 4b f. T 4 EW cf. constraint from Δm h 2 turns out to be weaker V. v 2 2 Decay of coherent oscillation in the barrier potential ' 1 a 3 d dt 2 T =T EW Late time decay into X μ with ' m3 64 F 2 X μ should not produce ΔN eff >0.3 Planck 2015

16 Parameter constraints h = Fifth force h = N e h = BXμ~ Gauge field overproduction

17 Parameter constraints h = Fifth force h = Globular Cluster h = 10 5 N e 0.3 Gauge field overproduction SN1987A SN1978A BXμ~

18 Hyper U(1) can be X μ? Precluded by the following requirements Hyper U(1) is in thermal equilibrium with charged particles in SM Due to landau damping, gauge field production is less efficient Smaller 1/F is required Severe constraints from ALP search (Seto-san s talk & Ringwald s talk on Wednesday) 1/F is no more than GeV -1 for m φ of our interest * Provided that we don t exclude the possibility of relation domination

19 Issue of perturbations Gauge field production peaks at particular scales Inhomogeneity in relaxion may develop through backreaction? This is unlikely at least at observably large scales (CMB, LSS) Terminal behaviour is attractor solution. Negative feedback works onto small deviations in velocity from terminal one. Our mechanism is resilient to perturbations.

20 Summary Conventional relaxion mechanism is hardly compatible with reheating temperature higher than the EW scales. This is because if EW symmetry is restored, further excursion of relaxion likely to spoil the selection of EW scales. We proposed a new scenario of relaxion mechanism with anomalous relaxion coupling to a hidden U(1) gauge field. Relaxion motion causes a tachyonic instability in the gauge field. As backreacion, significant frictional force acts on the relaxion motion and suppresses the relaxion excursion. Many of cosmological constraints applicable to the conventional relation model can be circumvented in our setup. Meanwhile, primary constraints arise from the overproduction of hidden gauge fields. Still, there are parameter regions where our scenario is viable.

21 backup slides

22 X μ in thermal equilibrium Thermal correction to dispersion relation (1-loop)! 2 k 2 ± k T (!,k)=m 2 D! k F = T (!,k) apple! k + 1! 1 2 k 2 ln! + k! k (conformal) Debye mass: m 2 D = g2 X a2 T 2 X 6 Tachyonic frequency = k2 m 2 D F F Tachyonic growth is suppressed by (k 2 /T 2) compared to vacuum Given availability of tachyonic modes:! k at X

23 X μ in thermal equilibrium T = 520 TeV term = FH(m D /H) 2/ Terminal behaviour is available but with velocity much larger than vacuum = F H(mD /H) 2/3 F H Larger relaxion excursion & production of Xμ

24 Parameter constraints apple g X T X T Gauge field overproduction Fifth force h = h = N e 0.3 h = BXμ~

25 Parameter constraints apple g X T X T Fifth force Gauge field overproduction N e 0.3 Globular Cluster h = h = SN1987A SN1978A 10 6 h = 10 5 BXμ~

26 Dependence of terminal velocity 10 2 =5.2FH(mD /H) 2/3 at T =1TeV = 25FH at T = 100 TeV