A CLOCKWORK WIMP · 2018. 11. 21. · Université Libre de Bruxelles Belgium Universidad Técnica...

A CLOCKWORK WIMP

Michel H.G. Tytgat Université Libre de Bruxelles

Belgium

Universidad Técnica Federico Santa María Valparaiso, Chile, 8-12 January 2018

The Clockwork Mechanism illustrated

Construction of a Clockwork wimp

Majorana neutrino masses

Relation to dimension deconstruction

Conclusions

PLAN

Based on arXiv:1612.06411, in collaboration with Thomas Hambye and Daniele Teresi

ON SCALES AND MASSES

Weinberg operator ⟶ L breaking scale

Proton decay ⟶ GUT scale

Axion ⟶ PQ symmetry breaking scale

Quantum gravity ⟶ Planck scale…

but MASS ≠ SCALE

new physics (local) ⟶ effective operators ⟶ new scale

⇤⌫ ⇠ MR

y2MP ⇠ Ms

gsG�1/2

F ⇠ MW

gFermi Weinberg Planck

THE CLOCKWORK MECHANISM

The Clockwork is a possible mechanism to generate small numbers

out of a theory with O(1) parameters

or large effective scales (e.g. ) out of

dynamics at much lower energies (e.g. TeV)

We are often reluctant to introduce small parameters(even if natural in the sense of ’t Hooft)

Kaplan & Ratazzi (2015); Choi & Im (2015) ; Giuidice & McCullough (2016)

reading experimentally accessible energies…

large scale physics : large mass or tiny coupling?⇤ ⇠ M

yx

MP


Grand Goal : Addressing the Hierarchy ProblemGuidice & McCullough (2016)


More prosaically, a framework for model builders….


hierarchy problem Guidice & McCullough (2016)

low scale invisible axion Guidice & McCullough (2016); Farina et al (2016)

inflation Kehagias & Riotto (2016)

neutrino physics Hambye, Teresi & MT (2016); Carena et al (2017); Ibarra et al (2017)

sugra Antoniadis, Delgado, Markou & Pokorski (2016)

dark matter Hambye, Teresi & MT (2016) (this talk)

…

THE CLOCKWORK MECHANISM ILLUSTRATED

Scalar Clockwork

××× × ×× ××�0 �1 �k ⇠ ei�k/f. . . . . . �N

L =f2

2

NX

k=0

|@�k|2 �m2f2

2

N�1X

k=0

(�†k�

qk+1 + h.c.)


××× × ×× ××�0 �1 �k ⇠ ei�k/f. . . . . . �N

Guidice & McCullough (2016)

q > 1

L =f2

2

NX

k=0

|@�k|2 �m2f2

2

N�1X

k=0

(�†k�

qk+1 + h.c.)

G = U0(1)⌦ U1(1)⌦ . . .⌦ UN (1) �! U(1)m2 6= 0

one massless + N massive modes

�m2

2

N�1X

0

(�k � q�k+1)2 + . . .


××× × ×× ××�0 �1 �k ⇠ ei�k/f. . . . . . �N

q > 1

M2 = m2

0

BBBBBBB@

1 �q 0 . . . 0�q 1 + q2 �q . . . 00 �q 1 + q2 �q 0...

......

. . ....

�q 1 + q2 �q0 0 0 . . . �q q2

1

CCCCCCCA

M2'(0) = 0 �! '(0) ⇠ �0 + �1/q + . . .+ �N/qN

q > 1 ! qN � 1massless mode

localized towards site k=0

�m2

2

N�1X

0

(�k � q�k+1)2 + . . . �!


××× × ×× ××�0 �1 �k ⇠ ei�k/f. . . . . . �N

plot from Farina et al (2016)

(1� q)2

(1 + q)2

m2(k)

m2

(q = 3, N = 20)

k

N + 1

one massless mode

N massive modes(clockwork gears)


plot from Farina, Pappadopulo, Rompineve & Tesi (2016)

k

N + 1

'(k) =NX

n=0

a(k)n �n

a(k)n=12

Clockwork Gears have unsuppressed

overlap (eventually coupling) at all sites!

p2/(N + 1)

�p

2/(N + 1)


××× × ×× ×. . .

massless mode localized towards

site k=0 L � �N

FGG̃ �!

N = 15, q = 3 �! qNF ⇠ 1010✓

F

TeV

◆GeV

e.g.

'(0)

qNFGG̃

�0 �1 �N'(0) ⇠ — SM

thus large effective scale!

tiny coupling!


WIMP abundance from thermal freeze-out

A CLOCKWORK WIMP ?

h�vi ⇠ ↵2

M2mass in hundreds of GeV-TeV range

WIMP abundance from thermal freeze-out

A CLOCKWORK WIMP ?

h�vi ⇠ ↵2

M2mass in hundreds of GeV-TeV range

WIMP stability in general protected by a symmetry

SUSY, SO(10), exact gauge symmetry, accidental symmetry (like the proton),…

e.g. a Majorana SU(2) 5-plet (aka Minimal Dark Matter)

⌧ ⇠ ⇤4

M5⇤ & 1016GeVpossible decay through

dim-6 op.a large, difficult

to test scale

CAN WE STABILIZE A WIMP THROUGH THE CLOCKWORK MECHANISM ?

A CLOCKWORK WIMP - CONSTRUCTION

×× × ×× ×. . .R0 L1R1 RNLN

×

Si ⇠ (1,�1) under U(1)Li+1 ⇥ U(1)Ri

Ci ⇠ (1,�1) under U(1)Li ⇥ U(1)Ri

{complex scalars

chiral chain

basic ingredients:

One chiral chain (L and R Weyl spinors)+ 2 N complex scalars (spurions and/or dynamical)

The construction goes through 4 steps


×× × ×× ×. . .R0 L1R1 RNLN

L � �mNX

i=1

�L̄iRi�1 � qL̄iRi

�+ h.c.

×

Si ⇠ (1,�1) under U(1)Li+1 ⇥ U(1)Ri

Ci ⇠ (1,�1) under U(1)Li ⇥ U(1)Ri

{complex scalars

chiral chain

rem: these fields are spurions in the original frameworkthey are dynamical in our case

U(1)R

one massless mode

step 1: break the chiral symmetries

⇢m ! yShSiimq ! yChCii

×× × ×× ×. . .R0 L1R1 RNLN

L � �mNX

i=1


�+ h.c.


N ⇡ R0 +1

qR1 +

1

q2R2 + . . .+

1

qNRN

(n) ⇡ 1pN

X

k

[O(1)Lk +O(1)Rk]

massless chiral mode

N Dirac gearsmass ~ q m

×

i.e. pretty much like the scalar clockwork

L � �mNX

i=1


�+ h.c.� 1

2mN R̄c

0R0

×× × ×× ×. . .R0 L1R1 RNLN

L � �mNX

i=1


�+ h.c.


×

step 2: break the residual chiral symmetry

i.e.

give a mass to the state N

L � �mNX

i=1


�+ h.c.� 1

2mN R̄c

0R0

×× × ×× ×. . .R0 L1R1 RNLN

L � �mNX

i=1


�+ h.c.

⇠ mN/m

⇠ q � 1

⇠ q + 1


mN = 0

⇠ q � 1

⇠ q + 1

(q = 10, N = 15,mN = 0) (q = 10, N = 15,mN = 5m)

×

L � �mNX

i=1


�+ h.c.� 1

2mN R̄c

0R0

×× × ×× ×. . .R0 L1R1 RNLN

L � �mNX

i=1


�+ h.c.

⇠ mN/m

⇠ q � 1

⇠ q + 1


⇠ q � 1

⇠ q + 1(q = 10, N = 15,mN = 5m)clockwork mechanism

unaffected providedmN . qm

Hambye, Teresi & MT (2016)

one light & localized mode

N gears with O(1) couplings{(pseudo-Dirac if ) q � mN/m

×

L � �mNX

i=1


�+ h.c.� 1

2mN R̄c

0R0

×× × ×× ×. . .R0 L1R1 RNLN

×

L � �mNX

i=1


�+ h.c.

— SM


�y(L̄SM H̃RN + h.c.)

step 3: couple the chain to the SM

L � �mNX

i=1


�+ h.c.� 1

2mN R̄c

0R0

×× × ×× ×. . .R0 L1R1 RNLN

×

L � �mNX

i=1


�+ h.c.


— SM


step 3: couple the chain to the SM

N ⇡ R0 +1

qR1 +

1

q2R2 + . . .+

1

qNRN ! L � � y

qNL̄SM H̃N + h.c.

tiny coupling


L � �mNX

i=1


�+ h.c.� 1

2mN R̄c

0R0

×× × ×× ×. . .R0 L1R1 RNLN

×

L � �mNX

i=1


�+ h.c.

— SM

& 1026sec

e.g.

(gamma’s, etc.)

q2N & 1052⇣ mN

100GeV

⌘y2


�(N ! ⌫h, ⌫Z, lW ) ⇠ mN

8⇡

y2

q2NL � �y

qNL̄SM H̃N + h.c.

The N mode is unstable but lifetime

if (q = 10, N = 26, y = 1)

L � �mNX

i=1


�+ h.c.� 1

2mN R̄c

0R0

×× × ×× ×. . .R0 L1R1 RNLN

×

L � �mNX

i=1


�+ h.c.

— SM

NN ! hh, hZ, ll̄, . . . / y4

q4N

i.e. quite suppressed…

but rate


last (but not the least) step: abundance from thermal freeze-out?


×× × ×× ×. . .R0 L1R1 RNLN

×— SM

A CLOCKWORK WIMP - AT LAST

�SB

Higgs portal

A CLOCKWORK WIMP - AT LAST

L � �⇠Sjp2S1 ̄jPRN + h.c.

⇠Sj ⇡r

2

N + 1sin

✓j⇡

N + 1

◆yS ⇠j ⇡ ✓S⇠

Sj

� ⇠jp2h ̄jPRN + h.c.

NN $ S1S1, S1h, hh, . . . ! / ⇠2S (⇠2) =NX

j=1

|⇠Sj |2 ⇡ y2S (✓S)2

O(1) couplings, the N could be a WIMP!

N

j

with and

S1 hX✓S

A CLOCKWORK WIMP - TO RECAP

Abundance

(secluded scenario) (Higgs portal scenario)

annihilation through thechiral gears

h�vi ⇠ 3 · 10�26cm3s�1


L � mNp2m

⇠

q2N̄ cN h+ h.c.Diagonal coupling to Higgs

(taking into account the pseudo-Dirac nature of the clockwork gears)

Abundance


Nh

⌫

1

qNsuppressed by the chiral chain


h�vi ⇠ 3 · 10�26cm3s�1

Stability/decay


L � mNp2m

⇠

q2N̄ cN h+ h.c.Diagonal coupling to Higgs

(taking into account the pseudo-Dirac nature of the clockwork gears)

Abundance


Stability/decay h

⌫

1

qNsuppressed by the chiral chain


h�vi ⇠ 3 · 10�26cm3s�1

R0 ×× ××1/q

A CLOCKWORK WIMP — SECLUDED SCENARIO

black solid: yS requiredfor ⌦dm ⇡ 0.25

blue solid: LUX16 exclusions (below lines)

red dashed: Xenon1T reach

Higgs mediated / (✓S/q)2

A CLOCKWORK WIMP — HIGGS PORTAL SCENARIO

black solid: requiredfor ⌦dm ⇡ 0.25

blue solid: LUX16 exclusions (below lines)

yS✓S

✓S . 0.4pN

A CLOCKWORK WIMP — BASIC PHENOIndirect detection p-wave annihilation, but decay into

monochromatic neutrinos N ! h⌫e.g. El Aisati, Gustafsson & Hambye (2015)


monochromatic neutrinos N ! h⌫

Collider searches j in the hundred GeV/TeV range, coupled via

yL̄SMHRN with sizable and j � RNy

observable pseudo-Dirac sterile RH neutrinos!

e.g. El Aisati, Gustafsson & Hambye (2015)


monochromatic neutrinos N ! h⌫

Collider searches j in the hundred GeV/TeV range, coupled via

yL̄SMHRN with sizable and j � RNy

|✓l |2 ⌘ y2v2/(2m2 ) . 10�3EWPT:

BR(µ ! e�) ⇠ 10�3|✓e |2|✓µ |2 . 10�13LFV:

L conserving searches: m . 200 GeV

300 fb�1withL violating searches: m . 300GeVmN . m

300 fb�1withDas, Dev & Okada (2014)

Deppisch, Dev & Pilaftsis (2015)

assu

min

gsi

ngle

sta

teap

prox

imat

ion

e.g. El Aisati, Gustafsson & Hambye (2015)

large mixing h-S in scenario B ✓S . 0.3� 0.4 (direct or EWPT)e.g. Falkowski, Gross & Lebedev (2015)

observable pseudo-Dirac sterile RH neutrinos!

A CLOCKWORK WIMP IS POSSIBLE

CLOCKWORK MAJORANA NEUTRINO MASS

×× × ×× ×

. . .R0 L1R1 RNLN

×— SM

another chain…

Majorana mass

SM neutrinos

Majorana character has to go throughthe whole chain


(q = 10, N = 7,M = 1TeV)

but need one per SM neutrino mass!

Smaller chain than for DM stability

m⌫ ⇠ y2v2

qNM

See also Carena, Li, Machado, Machado & Wagner (2017); Ibarra, Kushwaha & Vempati (2017)

(i.e. at least 2 chains for neutrino, one for the DM…)

LOT OF FIELDS, WITH VERY SPECIFIC COUPLINGS…

A CLOCKWORK WIMP FROM DECONSTRUCTION

our Lagrangian is related to a discretized flat 5th dimension


L5 � ̄(i / !@ �M) = i ̄�µ@µ +

1

2

�L̄@ZR� @ZL̄R

��ML̄R+ h.c.

�(Z)

2) naive discretization ⇒ fermion doubling

⇒ add a Wilson term

3) Dirichlet condition L(0) = 0 R0⇒ surviving chiral mode

L �N�1X

i=0

1

aL̄i+1Ri �

NX

i=1

✓1

a+M

◆L̄iRi

4) Standard Model degrees of freedom at (~ braneworld)Z = ⇡R

qN =

✓1 +

⇡RM

N

◆N

! e⇡RMqmm

{�a

2@Z ̄@Z a =

⇡R

N! 0with lattice spacing

1)

well-defined continuum limit

1/M ⌧ ⇡R

MORE ON DECONSTRUCTION

Clockwork (CW) scalar ☞ Linear Dilaton (LD)Giuidice & McCullough (2016)

LargeExtraDim < CW/LD < Randall-Sundrum

warped, conformally flat 5D

M2P / RM3

5

Giuidice, Kats, McCullough, Torre & Urbano (2017)

hierarchy from volume

hierarchy from warping


Clockwork (CW) scalar ☞ Linear Dilaton (LD)Giuidice & McCullough (2016)

LargeExtraDim < CW/LD < Randall-Sundrum

warped, conformally flat 5D

hierarchy from

volume & warping


M2P / RM3

5

hierarchy from volume

hierarchy from warping


Clockwork (CW) scalar ☞ Linear Dilaton (LD)

KK graviton → γγ


CONCLUSIONS

We have built a clockwork WIMP It is accidentally stable (not protected by a symmetry)

Its decay is mediated by the very same degrees of freedom that determine its abundance (it’s a WIMP)

These many degrees of freedom lie in the 100 GeV-TeV range

They could be seen @ LHC as sterile RHN

There are also (possibly) plenty of scalars to search for @ LHC

It is also a framework for low scale SM neutrino Majorana mass and potentially for much of BSM physics

The clockwork could be seen as a (discrete) spatial dimensionMay lead to unusual signatures, which are worth being studied further

ON SCALES AND MASSES

new physics (local) ⟶ effective operators ⟶ new scale

following Giuidice & McCullough see also Brodsky & Hoyer

L ⇠ M4

g2�! [�] =

M

g, [ ] =

M3/2

g

O =1

⇤d�4�nB nF �! ⇤ =

M

gnB+nF �2

d�4

a mass

a scale

⇤⌫ ⇠ MR

y2MP ⇠ Ms

gsG�1/2

F ⇠ MW

gFermi Weinberg Planck

A CLOCKWORK WIMP · 2018. 11. 21. · Université Libre de Bruxelles Belgium Universidad Técnica...

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Transcript of A CLOCKWORK WIMP · 2018. 11. 21. · Université Libre de Bruxelles Belgium Universidad Técnica...