Relaxion with Particle Production

Transcription

1 Relaxion with Particle Production Gustavo Marques-Tavares Stanford University with A. Hook:

2 Why is the Higgs mass small? m 2 h?

3 Symmetry +? µ 2

4 Symmetry Where are you? +? µ 2

5 Why is the Higgs mass small? m 2 h! m 2 h( )

6 Landscape m 2 h v 2

7 Landscape Why do we live in such a special point? m 2 h v 2

8 "Relaxion" P. W. Graham, D. E. Kaplan, and S. Rajendran, Phys. Rev. Lett. 115, (2015),

9 Relaxion P. W. Graham, D. E. Kaplan, and S. Rajendran, Phys. Rev. Lett. 115, (2015), L ( ) h 2 V ( ) 3 QCDhhi cos( /f)

10 Relaxion L ( ) h 2 V ( ) 3 QCDhhi cos( /f) V ( ) / V ( ) V 0 ( )=0?

11 Relaxion L ( ) h 2 V ( ) 3 QCDhhi cos( /f) V ( ) / V ( ) hhi 2 f 3 QCD

12 Relaxion V ( ) Stopping mechanism cos() potential Dissipation Hubble friction

13 Relaxion: Slow roll regime V 00 H 2 +3H = V 0 V 0 3H 2 H

14 Relaxion: requires many e-foldings V ( ) Slow Roll /H 1e-fold /H 2

15 Relaxion: requires many e-foldings V ( ) Slow Roll /H 1e-fold /H 2 / N e = H 2 / 2

16 Relaxion: requires many e-foldings V ( ) N e = H 2 / 2 To actually stop: 2 ( /H) 2. 4 b N e & 4 / 4 b

17 Relaxion Stopping mechanism: barrier depends on Higgs vev Tension with strong CP problem Non-trivial to have barrier height larger than v Dissipation mechanism: Hubble Super Planckian field excursions Requires many e-foldings Scanning must happen during inflation

18 Particle production: kill 2 birds with 1 stone Stopping mechanism Friction

19 Outline Basic mechanism Implementing particle production relaxion in the SM Relaxing with particle production: During inflation After inflation

20 Basic Mechanism Toy Model: Abelian Higgs + relaxion (static universe) L ( ) h 2 +( +...) µ 4 s cos f 0 + F F 4f

21 Basic Mechanism Toy Model: Abelian Higgs + relaxion (static universe) L ( ) h 2 +( +...) µ 4 s cos f 0 + F F 4f m 2 h = ( ) < 0 m A g

22 Basic Mechanism Toy Model: Abelian Higgs + relaxion (static universe) L ( ) h 2 +( +...) µ 4 s cos f 0 + F F 4f EOM for gauge fields Ä ± + k 2 + m 2 A k f! A ± =0

23 Basic Mechanism k! 2 = k 2 + m 2 A f Tachyonic modes for: f & m A A(t) e f t

24 Basic Mechanism L ( ) h 2 +( +...) µ 4 s cos f 0 + 4f F F >µ 2 s V(ϕ) m A hhi ϕ f <

25 Basic Mechanism L ( ) h 2 +( +...) µ 4 s cos f 0 + 4f F F Scans until hhi V(ϕ) When & hhi O(100 GeV) f ϕ

26 Finite Temperature Relaxion kinetic energy transferred to gauge fields q T Gauge symmetry restoration m A 0 Plasma effects (screening) m D T

27 Finite Temperature! 2 k 2 ± k f = t(!,k)=m 2 DF (!/k) We are interested in the regime! = i, k m D

28 Finite Temperature! 2 k 2 ± k f = t(!,k)=m 2 DF (!/k) We are interested in the regime! = i, k m D 2 k 2 ± k f m2 D 4k f ( /f) 2 m 2 D

29 Quick Summary L ( ) h 2 +( +...) µ 4 s cos f 0 + 4f F F Tachyonic mode for A: /f selects v creates friction Temperature dilutes tachyon time-scale: ( /f) 3 T 2

30 Can it work in the real world?

31 Particle Production relaxion in SM L ( ) h 2 +( +...) µ 4 s cos f 0 + 4f Y B B W W W

32 Particle Production relaxion in SM L ( ) h 2 +( +...) µ 4 s cos f 0 + 4f Y B B W W W Relaxion does not couple to the photon!

33 Relaxion setup L ( ) h 2 +( +...) µ 4 s cos f 0 + 4f Y B B W W W Sub planckian: > /M P Many minima: µ 4 s > f 0 Fine scanning: f 0 <v 2

34 Relaxion setup µ 2 s < const. V(ϕ) Self-tune to Weak Scale /f v = 246 GeV ϕ Need to ensure energy loss is efficient

35 Energy Loss Not overshooting v m 2 H = t 1 ḟ /f T! 2 m H v t

36 Energy Loss Not overshooting v m 2 H = m H v t T 2 f 3 v 2 <v < v5 µ 4 s T 8

37 Possible realization

38 Initial Conditions Take this inflationary initial conditions H> 2 M P >µ 2 s V(ϕ) ϕ

39 Initial Conditions Take this inflationary initial conditions H> 2 M P >µ 2 s V(ϕ) ϕ H & µ2 s H + (t)

40 Relaxing during inflation q r 2 H 2 T H N e

41 Relaxing during inflation q r 2 H 2 T H N e M P < < v5 µ 4 s T 8 6 <v 5 M P N e

42 Relaxing during inflation q r 2 H 2 T H N e M P < < v5 µ 4 s T 8 6 <v 5 M P N e N e GeV H N e f f 0 c Values in GeV

43 Inflation too brief H 2 >N e Can the scanning continue after inflation ends?

44 Inflation too brief H 2 >N e Can the scanning continue after inflation ends? Yes! *but before SM reheats

45 Scanning after inflation Hubble decreases /H increases Scanning very fast once: H. 2

46 Scanning after inflation M P < < v5 µ 4 s T 8 & v 5 µ 4 sm P µ s < 40 TeV f f 0 c Values in GeV

47 Conlusions Particle production is an efficient mechanism to both dissipate energy and to select small Higgs mass Qualitatively new approach to relaxion It can work without super planckian field excursions and with normal amounts of inflation The scanning can happen after inflation