Phenomenological implication of Continuum Clockwork

Transcription

1 Phenomenological implication of Continuum Clockwork Chang Sub Shin (IBS-CTPU) Based on works with Kiwoon Choi, Sang Hui Im with Jinn-Ouk Gong with Kyu Jung Bae, Jeff Kost At IBS workshop Dec. 4, 018

2 Outline Idea of discrete clockwork - Clockwork axion - Clockwork photon Continuum limit of clockwork - Realization with 5d Geometry and Bulk/Boundary potentials Phenomenological application - Nontrivial wave-function renormalization - Inflation, baryogenesis and dark matter via rolling Continuum CW ALPs Conclusions 0

3 Idea of discrete clockwork mechanism

4 heavy axion direction KNP mechanism [Kim, Nilles, Peloso 04] Proposal to obtain a trans-planckian field excursion in the context of natural inflation! " +Λ $ cos :, = [0,] Introducing two axions with (Λ Λ)! " +! " +Λ $ cos 3 +Λ $ cos 3 light axion direction Integrating out a heavy mode: (1+1/9)! " +Λ $ cos 3 :, = 1+1/9 [0,3 1+1/9]

5 Extending KNP mechanism Adding one more axion : extending the axion period Λ $ cos(3 ) Λ $ cos(3 )+Λ $ cos(3 ) , = 1+1/9 [0,3 1+1/9], = 1+1/9+1/81 3 [0,3 1+1/9+1/81]

6 Clockwork axion [Choi, Kim, Yun 14] 89 Considering N+1 axions with 67 Λ $ cos(3 6 6: ) =>> =< 8 1+< 9 +, = 1+1/9 +1/9 8 8 [0, /9 +1/9 8 ] Exponential extending of the field excursion Exponential localization of the lightest mode at the last site 6 = < 6 A, =>> +heavy modes C D > EFF,@ A

7 Clockwork photon [Saraswat 16] Staring from gauged G 1 HG 1 (I " I "+J 9! " K,I " I " +J 9! " K ) with a bilinear Higgs field: L exp N(< K K ) L ( L = 0) 3 K unbroken G(1) IR " = I "+<I " 1+< G 1 L ( <, 1) G 1 broken G(1) K < I " I "

8 Clockwork photon [Giudice, McCullough 16] Clockwork U(1) can be constructed by introducing N+1 U(1) with N Higgs fields G 1 L ( <, 1) G 1 L G 1 ( <, 1) L W ( <, 1) G 1 L 8 G 1 8 ( <, 1) Unbroken G 1 ST gauge symmetry with I ST" Exponentially small unit charge ( < 98: J 1) I 6" = < 6 I ST" +heavy modes 1+< + < 8 J X 6 I 6 " Y6" A < 6 JX 6 " I 1+< + < 8 ST Y 6" (A)

9 Clockwork Goldstone [Feng, Shiu, Soler, Ye 14] Two Goldstone boson (, ), one combination absorbed by the broken U(1) vector field 3 uneaten Goldstone L ( <) G 1 L (1) Stuckelberg Goldstone A fundamental domain Each domains are connected by discrete gauge transformation

10 Clockwork Goldstone [Bonnefoy,Dudas, Pokorski ] Among N+1 Goldstones, N combinations are eaten by vector bosons for the broken U(1)s. L ( <) G 1 L (1, <) G 1 L L 89 (1, <) G 1 L ] ^ 8 _9^ (1, <) (1) Uneaten Goldstone mode: The Goldstone boson field period from is exponentially reduced as, = +< +< < + +< 8 +< +< 8 8 0, in a fundamental domain, 0,/ 1+< + +< 8 < 9(8:)

11 For the CW zero mode * Exponentially large (small) axion field period * Exponentially small U(1) unit charge Applications * Couplings of the lightest mode to operators at two different sites are hierarchically different Inflation, relaxion, QCD axion [Choi, Kim, Yun 14] [Higaki, Jeong, Kitajima, Takahashi 14,15,16] [Choi, Im 15] [Farina, Pappadopulo, Rompineve, Tesi 16] [Kaplan, Rattazzi 15] [Kehagias, Riotto 17] [Park, CSS 18] Gravity [Giudice, McCullough 16] Neutrino mass [Giudice, McCullough 16] [Hambye, Teresi, Tytgat 16] [Park, CSS 17] Flavors, etc.

12 Continuum limit of CW

13 Up to quadratic order CW mechanism up to quadratic order: r! " 6 1 rs 6: < Extension to a continuum limit: 6 (A) Φ(A,b) (cd 1) 1 lm h ib! "Φ +! q Φ c Φ c = < 1 e f C,g Physical interpretation: Nontrivial 5D background geometry 1 h ib jj k8! k Φ! 8 Φ Bulk and boundary mass terms in a flat 5D lm in =o $ W pq (ia " ia " +ib ) Φ o pq Φ [Giudice, McCullough 16] 1 lm h ib! kφ +c Φ +cφ (t b t b d ) [Craig, Garcia, Sutherland 17]

14 Continuum clockwork axion (1) Defining frame in 5D is important : Nontrivial 5D background geometry u 0, [Choi, Im, CSS 17] in =o $ W pq (ia " ia " +ib ) lm h ib j W u jk8! k u! 8 u +t b b jj+o 6 j 8 $@ A Flat zero mode profile along the 5 th dim in the 5D field basis Integrating out KK modes ( ST A u(a,b )) u A,b = ST A +o 9pq rkk modes w7 W 4c o plm 1! " ST + ST 8 jj+o A Axion decay constant : =>> ={ } W d plm W d However, s ~ ={ } s W plm d s W d No hierarchically different couplings between different branes =>> s ~ = s W

15 Continuum clockwork axion (1) axion graviton b =0 b =d lm =h ib j 1 c o plm/w d Warped large volume

16 Continuum clockwork axion () Defining frame in 5D is important : Bulk and boundary mass terms u 0, with a periodic ˆ(A) = ˆ(A + ) [Choi, Im, CSS 17] lm h ib W! " u +! q u c ˆ(u) +t b b u 8 jj+o A Ex) ˆ A =sina =A+@ A W Localized zero in the 5D field basis at different positions for different u e.g. at u =0,! q tu ctu (localized at b =d) at u =,! q tu+ctu (localized at b =0) Integrating out KK modes ( ST A (A,b )) ( ST,b )! " ST + ST 8 jj+o A Axion decay constant : =>> ( cd) W d. No exponentially large Hierarchically different couplings depending on the axion expectation value

17 Continuum clockwork axion () ST,b = /c tanhcd 1+ cosh cd cb cosh cd sinh (cd cb ) cosh cd cos ST 1 cosh cd cb cosh cd cos ST Nontrivial wave-function renormalization For c 0 ST,b d For cd 1 (atb =0) ST,b c(1+ o 9 plm cos ST ) W c exp cd,š ST =0 For cd 1 (atb =d) ST,b c(1+ o 9 plm +cos ST ) c exp cd,š ST =d

18 Continuum clockwork photon (1) In nontrivial 5D background G 1 :I k I k +! k K K(A,b) 0, [Choi, Im, CSS 17] lm h ib j 1 j k8 j ~ k~ 8 +t b b j $ 4J N o " (! " NI " ) Flat zero mode in the 5D field basis I " A,b =I ST" A +o 9pq w7kk modes Integrating out KK modes (I ST A I(A,b )) 3 8J c (o plm/w 1) ST " ST " + N "! " N I ST" Gauge coupling : J =>> o 9plm/W J c J / d However, for charged fields at a boundary p Π< k, p Πk o 9plm J m k k =>> No hierarchically different couplings for different branes

19 For 5D gauge symmetry, Continuum clockwork photon () bulk and boundary mass terms from the Stuckelberg kinetic term ( A,b +K) lm h ib 1 4J k8 s J! k I k Integrating out KK modes, For š =1: CW gauge symmetry realizes not as G 1 ST but as R ST from 5D G(1)! Massless s 1 š decoupled 1+ š s t b t b d [Choi, Im, CSS 17] 1 4 ST " s 1 š! " I ST" + N "! " N o 9Ÿ k (lm 9q ) I ST" Is it really OK? Well.. if starting from the 5D Higgs œ A,b = W 1+ ž,q > o 6 ž,q, s 1 š +š h(a)! " I ST" š 1: strong coupling regime (breakdown of perturbative theory) strongly disfavor

20 In nontrivial 5D background Continuum clockwork Goldstone [Choi 03] [Choi, Im, CSS 17] [Flacke, Gripaios, March-Russell, Maybury 06] lm h ib j 1 4J j k8 j ~ k~ 8 Opposite boundary condition I " b =0 =I " d =0: s w " =! " I! q I " Except zero-mode, all modes becomes massive vector bosons Integrating out KK modes, lm ST (A)=h ib I A,b =1 =0 I " w I (w) The zero mode kinetic term becomes L =>> = c 3J! " ST (1 o 9 plm/w ) Axion decay constant : =>> p s =>> s ~ o 9plm Similar to the masses of low KK modes ( =>> /s =1,, 1/ cd)

21 Continuum clockwork Goldstone Goldstone graviton b =0 b =d

22 (Generalized) Linear Dilaton The nontrivial 5D background [Antoniadis, Arvanitaki, Dimopoulos, Giveon 11] in =o $ W pq (ia " ia " +ib ) can be obtained from Linear Dilaton Model ( =1,Λ,Λ $ <0) lm h ib j o s W W d+s jk8! k ª! 8 ª Λ Λ $ t b t b d j In the Einstein frame, (š = / 4 3 ) lm h ib j s W [Choi, Im, CSS 17] W d s jk8! k ª! 8 ª o 9 Ÿ / W Λ o9ÿ / W Λ $ t b t b d j For 1(š 1), more general metric realized in =o q ia " ia " +o Ÿ q ib «= Λ 3(š 4)

23 KK spectrum and couplings (Generalized) Linear Dilaton [Choi, Im, CSS 17] s w s w s 1 š 1+š / LED 1 š 1+ š 1 (RS) ² w w

24 (Generalized) Linear Dilaton Can we realize š ³1? In heterotic M-theoryš 6is obtained [Im, Nilles, Olechowski ] From Sang Hui s talk slides

25 Phenomenological application of CCW axions

26 Nontrivial wave-function renormalization Deform the axionpotential ST,b! " ST +Λ $ cos ST = 1! " +Λ $ cos ST [] E.g. for b =d, ST ST =,d o plm 1 cd =3 cd =1 cd =0

27 Natural Cliff Inflation [Gong, CSS 17] The slope of the potential around the extremum is exponentially sensitive to cd. tanh Approximately, for e mπr >> 1 : same type of Higgs (R ) inflation with a much smaller f (<< MPl) Inflating.. end.. (m=0 : vanilla natural inflation) Slow role parameters: Observables Amplitude of the curvature perturbation:, spectral tilt: tensor to scalar ratio:

28 Natural Cliff Inflation [Gong, CSS 17] The slope of the potential around the extremum is exponentially sensitive to cd. ¹ D = = 1 1 s ~ h i e ¹ F º exp 6 s ~ PLANCK 013(015) m º1 =,» º 8 = s ~

29 Natural Cliff Inflation [Gong, CSS 17] The slope of the potential around the extremum is exponentially sensitive to cd. ¹ D = = 1 1 s ~ h i e ¹ F º exp 6 s ~ PLANCK 018 m º1 =,» º 8 = s ~

30 Natural Cliff Inflation [Gong, CSS 17] Inflation with a sub-planckian periodic potential can be achieved without tuning of initial position of 6. = = 1 ¹ 1 D s ~ h i exp 6 e s ~ ¹ F º m º1 =,» º 8 = s ~ Reheating can be done by boundary interactions between the inflaton and the photons in the SM.

31 Comparing with other deformed Natural Inf. Scalar potentials induced by an anomalous coupling between the inflaton and a confining large N pure Yang-Mills gauge group [Nomura et.al , ] 1! " ˆ¼½¾ () + 8 " " k N multi branches (tunneling is allowed), field independent coupling to the SM 1! " Λ $ (1 cos ST [])+ ST[] 8 " " k One branch, field dependent coupling to the SM : different (p)reheating history

32 Spontaneous baryogenesis and dark matter If the CCW axion couples to ªG À HG 1 Á gauge fields, [Bae, Kost, CSS ] 1! " Λ $ (1 cos ST [])+ ST[] 8 š ²²Â +š Ãà the rolling axion can generate a baryon asymmetry due to B+L anomaly! " Y Ä " = > 8 ² " ²Â" à " à " Most of baryon asymmetry is generated during this period Coherent oscillation gives the dark matter abundance?

33 ST 1/(1+e cos ST ) [Bae, Kost, CSS ] The Journey with the rolling axion (in the canonical field basis) Slow roll ( º 6w6, ~@(1)) Fast roll (Æ~@ 1, Δ 1) Tracker (e 1, º1/ ) Coherent oscillation ( e, º1/e )

34 ST 1/(1+e cos ST ) [Bae, Kost, CSS ] The Journey with the rolling axion (in the canonical field basis) Slow roll ( º 6w6, ~@(1)) Fast roll (Æ~@ 1, Δ 1) Tracker (e 1, º1/ ) L º! " ST ST 1 Λ$ ST = 1! "È e Λ $ o Ê /> See Jeff s talk Coherent oscillation ( e, º1/e ) L º! " ST e 1 Λ$ ST = 1! "È e Λ $ È

35 Conclusions Discrete clockwork has very special features Natural extension to the continuum limit via 5D theory construction shows similar feature (spectrum and couplings relative to different KK modes). However the global structure is quite different Continuum clockwork axion is an example to provide a nontrivial wave-function Inflation, baryogenesis and dark matter could be related with rolling axion with deformed potential by CCW mechanism