gilad perez moriond

Relaxion phenomenology

Gilad Perez

Weizmann

MORIOND EW

Mar. 2017

Outline

♦ How to search for relaxions: the various fronts.

2

♦ Summary.

♦ Relaxion, a new approach to ameliorate the Higgs fine tuning.

♦ Relaxion couplings to Standard Model (SM) fields.

The main ideaGraham, Kaplan & Rajendran (15)

Relaxion’s physicsGraham, Kaplan & Rajendran (15)

♦ A dynamical solution/amelioration of the Higgs fine-tuning problem:

(i) Add a scalar (relaxion) Higgs dependent mass: .�⇤2 � g2�2

�H†H

µ2(�)

� roles till µ2changes sign ) hHi 6= 0 ) stops rolling.(ii)

V (�)

�

�

U(1) toy model, symmetric phase

77

V (H) = �µ2H†H + �(H†H)2

For further use, consider the following toy model, of a global U(1) sym’:

µ2 < 0 ) trivial case:

H ! ei✓H(invariant under: , ) � > 0

V (H)

H

Both Lagrangian & Higgs VEV (ground state) respect the symmetry, .

♦

hHi = 0

µ2(�) = 0

Relaxion mechanismGraham, Kaplan & Rajendran (15)



�H†H

µ2(�)

(ii) � roles till µ2flips sign) hHi 6= 0 ) backreaction stops � .

V (�)

�

�

µ2(�) = 0




�H†H

µ2(�)


V (�)

�

�


77

V (H) = �µ2H†H + �(H†H)2




V (H)

H


♦

hHi = 0

µ2(�) = 0




�H†H

µ2(�)


V (�)

��


77

V (H) = �µ2H†H + �(H†H)2




V (H)

H


♦

hHi = 0

µ2(�) = 0




�H†H

µ2(�)


V (�)

�

� U(1) toy model, broken phase

78

V (H) = �µ2H†H + �(H†H)2


Higgs VEV (ground state) breaks the symmetry, => .

♦

hHi = v 6= 0

µ2 > 0 ) at present: V (H)

H

V (H)

H

mW,Z 6= 0

µ2(�) = 0




�H†H

µ2(�)


V (�)

�


78

V (H) = �µ2H†H + �(H†H)2



♦

hHi = v 6= 0


H

V (H)

H

mW,Z 6= 0hHi = v 6= 0

µ2(�) = 0

evolution ends




�H†H

µ2(�)


V (�)

�


78

V (H) = �µ2H†H + �(H†H)2



♦

hHi = v 6= 0


H

V (H)

H

mW,Z 6= 0hHi = v 6= 0

µ2(�) = 0

evolution ends

Roughly ⇤/v . n1/4 ⇠ (fUV/fIR)1/4 ⇠ 3

Nclock

/4 .

For v ⌧ ⇤ progress achieved.

Relaxion basic properties

12

♦ Focus shifts from Higgs dynamics to relaxion one: different pheno’, no partners (stops/t’, gauginos/KK Z’s …)

♦ Solution 1: raise cutoff but only up to O(few TeV), solving the little

♦ Solution 2: multi-site realization => clockworking. (see talk by M. McCullough)Choi, Kim & Yun (14); Choi & Im; Kaplan & Rattazzi (15)

Gupta, Komargodski, GP & Ubaldi (15)

♦ In terms of local QFT: construction is non-generic & challenging.

♦ Cosmology of framework is also non-trivial, not discussed. (requires full talk)see e.g.: Espinosa et al.; Choi, Kim & Sekiguchi; Kobayashi, Seto, Shimomura & Urakawa; Di Chiara et al.; Jaeckel, Mehta & Witkowski; Patil & Schwaller; Hardy …

hierarchy problem, say with stops at ~10 TeV. Gupta, Komargodski, GP & Ubaldi (15); for SUSY realization see: Batell, Giudice & McCullough (15)

“Generic” relaxion pheno’

13

(i) Backreaction is directly transmit to relaxion potential: Yields Higgs-relaxion mixing. . Flacke, Frugiuele, Fuchs, Gupta & GP; Choi & Im (16)

�

f(W,Z)µ⌫(W̃ , Z̃/�̃)µ⌫Requires coupling to EW gauge, .

Hook & Marques-Tavares (16)

Graham, Kaplan & Rajendran (15)

(ii) Backreaction is via induction of W/Z masses which are produced.

Friction via particle production:

♦ Consider 2 typical approaches and properties:

Friction via Hubble during inflation:

Relaxion pheno’ (focusing mostly on relaxion Higgs mixing)

14

♦ The relaxion Higgs mixings is:

♦ The relaxion mass is:

sin ✓ ⇠ M̃2v

m2hf

⇠ 10�1 ⇥

M̃

100GeV

!2

⇥ 1TeV

f.

m� ⇠ M̃v

f⇠ 10GeV ⇥ M̃

100GeV⇥ 1TeV

f.

✓⇠ sin ✓ ⇥ m2

h

M̃

◆

Flacke, Frugiuele, Fuchs, Gupta & GP (16)

Flacke, Frugiuele, Fuchs, Gupta & GP (16)

♦ Consider 2 “generic” properties:

(i) Higgs-relaxion mixing; (ii) coupling to EW gauge, . �

f(W,Z)µ⌫(W̃ , Z̃/�̃)µ⌫

Flacke, Frugiuele, Fuchs, Gupta & GP; Choi & Im (16) Hook & Marques-Tavares (16)

(more generally

˜M j/2v2�j/2/f , j = 2� 4)

15

Illustration: how to search for a relaxion?

10-16 10-12 10-6 10-2 1 102

10-2

10-4

10-10

10-18

10-26

10-38

Energy Frontier:Colliders, LEP, LHC, FCC …

Intensity Frontier:Colliders

astro’, cosmology

Precision frontier:Fifth force exp’

m�[GeV]

sin2 ✓ [or (v/f)2]

Figure 4. Constraints on the relaxion-Higgs mixing sin2 ✓ for relaxions with m� between 5GeVand 90GeV from LEP and the LHC: 4-fermion final states from Higgs strahlung at LEP (green,labelled as LEP hZ); Higgs decays to NP with BR(� ! NP) 20% at the LHC (purple, solid) aswell as a projection for BR(� ! NP) 10% (purple, dashed); explicit searches for h ! �� withfinal states 4⌧ (dark blue, dotted, m� < 10GeV, Run 3 projection) and 2µ2b (dark blue, dotted,m� > 25GeV, Run 3 projection). Contours for ⇤br = 120 GeV (gray, dashed for j = 2; brown,dashed for j = 1), f = mh and f = 1TeV (black for j = 2, brown for j = 1).

6 Cosmological and astrophysical probes of relaxion-Higgs mixing

As discussed in the previous section, laboratory measurements can probe a significant region

of the relaxion parameter space. However, in the sub-MeV region, before the fifth force

experiments start to gain sensitivity in the sub-eV region, a large portion of the parameter

space is left unconstrained. In this section we show how astrophysical and cosmological

probes can explore part of this region of the parameter space, as shown in Fig. 5, and

also provide relevant bounds if the relaxion mass is in the MeV-GeV range (also shown

in Fig. 3). In order to identify the part of the parameter space most relevant for relaxion

models and to gain an understanding of the theory contours in Fig. 5, we refer the reader

to the discussion at beginning of Sec. 5.

– 27 –

C A S I M I R

EqP

ISqL

Λtp<2 TeV

f>M P

l

f=M P

l

f=10

14GeV

Λ br=0.99

(Λ br)max

Λ br=5GeV

10-16 10-14 10-12 10-10 10-8

1.×10-38

1.×10-34

1.×10-30

1.×10-26

1.×10-22

mϕ [GeV]

sin2θ

Figure 2. Constraints on the relaxion-Higgs mixing sin2 ✓ for light relaxions with m� between10�16 GeV and 10�7 GeV. Fifth-force experiments (orange) probe the lightest mass range viathe equivalence principle (labelled as EqP), the inverse square law (ISqL) and the Casimir e↵ect(Casimir). Contours of constant ⇤br (gray) for ⇤br = 0.99(⇤br)max

' 104GeV (gray, thick, solid),⇤br = ⇤⇤

br ' 74GeV and ⇤br/(⇤br)max

= 10�1, 10�2, 10�3 (gray, dashed). Contours of constantf = M

Pl

, 1016 GeV, 1014 GeV (black, solid), the area of f > MPl

is shaded in dark gray. The lightgray region below the dotted gray line corresponds to trans-Planckian field excursions �� > M

Pl

for ⇤ = 5TeV.

5.2 Relaxion masses between the MeV- and the weak scale

Let us now study the region of parameter space where the relaxion mass is above the

electron threshold and thus it can decay into SM fermions. Furthermore, as shown in

Fig. 1(b), in this region the relaxion has a shorter lifetime and can be directly searched for

in laboratory facilities. Let us further distinguish two sub-regions based on the di↵erent

relevant probes. The bounds in the MeV-5GeV mass range are presented in Fig. 3 including

also astrophysical and cosmological constraints which will be discussed in the next section.

Fig. 4 presents the bound in GeV region.

5.2.1 The 1MeV - 5GeV range

This region of the parameter space is well covered by rare K- and B-meson decays at

proton beam dump and flavour experiments. Crucial for both kinds of experiments is

the possibility of producing a relaxion in rare decays of K- and B-mesons. In flavour

– 21 –

BBN

ηB

SN1987a

Neff

EBL

CMB-y

CMB-μ

GC-e

GC-γ

Λbr=0.99

(Λbr)max

f=10

10GeV

Pixie

f=10

6 GeV

f=mh

Λbr=1GeV

10-7 10-6 10-5 10-4 0.001 0.01 0.110-23

10-21

10-19

10-17

10-15

10-13

10-11

10-9

mϕ [GeV]

sin2θ

Figure 5. Cosmological and astrophysical bounds on s✓ and m� from 100 eV to 0.3GeV: globularcluster via coupling to electrons (blue) or coupling to photons (turquoise), supernova 1987a (lightblue), extragalactic background light (EBL, yellow), CMB y-distortion (light green) and µ-distortion(green), entropy injection �S/S bounded by the baryon-to-photon ratio ⌘B (orange) and by N

e↵

(pink), BBN (red). The light gray band indicates the possible range of s✓ for j = 1, i.e. theQCD case. The gray lines (from top to bottom) are contours of constant ⇤br = 0.99(⇤br)max

(thick, solid), ⇤⇤br, 0.01GeV (dashed). The black lines (from left to right) are contours of constant

f = 1010 GeV, 106 GeV (thin) and f = Mh (thick).

n = 3N = 330; as indicated in the figure these values can be easily rescaled for other values

of n or N .

The overview presented in Fig. 6 shows that large areas in the ⇤br � f plane are

already well covered by existing experimental and observational probes, or instance the

high-f region up to MPl

is probed by the fifth force experiments, on the other hand the

cosmological, astrophysical, beam dump and collider observables constrain lower values of

f . We see that in the above f ranges, the region with electroweak scale ⇤br is practically

completely ruled out apart from small gaps that still remain. We also show in Fig. 6 how

some of these gaps in parameter space might be covered soon by future experiments such as

SHiP, NA62 and PIXIE. However, the region between f ⇠ 1010GeV and 1014GeV which

corresponds to relaxion masses between 0.1 eV and 1 keV, is currently hardly constrained

by data.

For any f (or m�) value, all the constraints can be evaded for su�ciently small ⇤br

– 36 –

one of the most promising regions for rare K-decay measurements to probe new physics.

For instance the CERN experiment NA62 will improve the present limit on invisible K-

decays by almost an order of magnitude. They expect to see 90 SM signal events and 20

background events in two years [48]. Using only this information about the total rate and

no information about the di↵erential distribution of the SM and background events, we

show a conservative estimate of the 95% CL excluded region in light blue in Fig. 3 where

we have assumed a 10% theoretical error [49]. The gap in the excluded region is again due

to the veto around the charged pion mass, 100MeV . m� . 160MeV [48].

Finally for GeV scale masses we see from Fig. 3 that some regions of the parameter

space are bounded by LEP and LHC searches that we describe in detail in the next section.

B→K+inv

B0 →K0*μμ

K→π+inv

K→π+inv

K→πμ

μKL→

π0ll

B→K (*) ll Belle

B→Kμμ LHCb

NA62

CHARM

SHiP

Λbr=0.99

(Λbr)max

f=106 GeV

f=104 GeV

f=mh

cτ=2 m

Λbr=10GeV

Seaquest

NA62 BD

LEP hZ

LHC h→ϕϕ→4μ

SN1987a

τ=1 s

NeffηB

2m

μ

0.001 0.01 0.1 1 5

10-12

10-10

10-8

10-6

10-4

10-2

mϕ [GeV]

sin2

θ

Figure 3. Constraints on the relaxion-Higgs mixing sin2 ✓ for relaxions with m� between MeV andGeV. The laboratory probes include: proton beam dump experiments (red for CHARM, light redfor the projected sensitivity for SHIP, SeaQuest and NA62 possible run in beam dump mode), K-meson decays (blue, projection from NA62 in a lighter shade of blue), B-meson decays (turquoise),LHC search for h ! 4µ (light blue) and LEP (green). Astrophysical and cosmological probesinclude the Supernova 1987a (pale violet, labelled as SN), ⌘b (orange) and N

e↵

( pink). Contoursfor ⇤br = 0.99(⇤br)max

' 104GeV (gray, thick, solid), ⇤br = 10GeV (gray, dashed), f/GeV =106, 104, 125 (black, solid) are presented. The vertical light gray line corresponds to the contourfor the relaxion mass at the muon threshold; the yellow contour corresponds to c⌧ = 2 m and thepurple one to ⌧ = 1s.

– 24 –

16

Current-near-future constraintsFlacke, Frugiuele, Fuchs, Gupta & GP (16)

10-2

10-4

10-10

10-18

10-26

10-38

10-16 10-12 10-6 10-2 1 102

sin2 ✓

m�[GeV]

Relaxion-beams, relaxion flavor

17

♦ Depending on the mixing parameter the relaxion can be copiously produced at colliders; especially for simpler models \w not-so-large cutoff.

♦ Lifetime - typically it is stable blow the muon threshold:

had

c

2m

cm

2mmsin2

1

10-3

10-6

10-9

0.001 0.01 0.1 1 5

10-10

10-5

1

105

1010

1015

M [GeV]

c[m

]

Relaxion lifetime

Flacke, Frugiuele, Fuchs, Gupta & GP, preliminary.

Clarke, Foot & Volkas (13)

Relaxion parameter space: M̃, f

5thforce

-LHC-LEP

LHCb

B, KCHARM

SN

S/S

CMB

EBL

M ˜>M ˜max

M= eV

meV

eV

keV

MeV

GeV

tP=145GeV,

cq=107 GeV

tP=2TeV,

cq=108 GeV

tP=2TeV,

cq=108 GeV

10-3 10-2 10-1 100 101 102

103

106

109

1012

1015

101840 35 30 25 20

M˜[GeV]

f[GeV]

N

Elina Fuchs (Weizmann) | Atomic BSM | Relaxion | 9

= 100 TeV

18

5th force exp. (orange), EBL (blue), cosmological entropy injection (pink), supernova (red), CHARM (dark blue), rare B- and K-decays (light blue), LHCb (turquoise), LEP (green). The vertical gray band indicates exclusion due to M ̃ > M ̃max. The light gray, dotted lines correspond to ∆φ = MPl with Λ = 5 TeV (upper), Λ = 100 TeV (lower). The dashed, gray lines show the classical- vs.-quantum condition for Λ = 100 TeV (upper), Λ = 105 TeV. The thin, black lines indicate Mφ from 10−15 GeV (uppermost) to 1 GeV (lowest) with a spacing factor of 103 .

More about the big picture

Zooming on region \w low cutoff: simple construction; lots of progress can be made;and, relevant to intensity frontier.

Batell, M. Pospelov, and A. Ritz (09); Clarke, Foot & Volkas (13); Essig, et al. (13); Piazza & Pospelov (10); Dolan, Kahlhoefer, McCabe, Schmidt-Hoberg (14); Krnjaic (15); Dolan et al, (14); Alekhin, et al. SHIP (15)…

Flacke, F

rugiuele, Fuchs, G

upta & GP, preliminary.

19

Relaxion beams, relaxion flavor

Flacke, Frugiuele, Fuchs, Gupta & GP (16).

NOT FOR DISTRIBUTION JHEP_021P_0317 v1

BK+

inv

B0

K0*

K+

inv K

+in

v

KKL

0ll

B K(*) ll Belle

B K LHCbB0

K 0*LHCb

CHARM

SHiP

br=0.9

9( br

)max

f=10

6 GeV

f=10

4 GeV

f=mh

c =2m

br=10

GeV

LEP hZ

LHC h 4

SN1987a

=1 s

NeffB

2m

NA62 (our estimate)

SeaQ

uest

0.001 0.01 0.1 1 5

10-12

10-10

10-8

10-6

10-4

10-2

m [GeV]

sin

2

Figure 3. Constraints on the relaxion-Higgs mixing sin2 ✓ for relaxions with m� between MeVand 5GeV. The laboratory probes include: proton beam dump experiments (red for CHARM, lightred for the projected sensitivity for SHIP and SeaQuest), K-meson decays (blue, our conservativeprojection from NA62 in a lighter shade of blue), B-meson decays (turquoise), LHC search forh ! 4µ (light blue) and LEP (green). Astrophysical and cosmological probes include the Supernova1987a (pale violet, labelled as SN), ⌘b (orange) and N

e↵

( pink). Contours for ⇤br = 0.99⇤max

br '104GeV (gray, thick, solid), ⇤br = 10GeV (gray, dashed), f/GeV = 106, 104, 125 (black, solid) arepresented. Here ⇤max

br is the upper bound on ⇤br arising from the requirement of a non-tachyonic �in Eq. (3.12) for sin(�

0

/f) = 1/p2. The vertical light gray line corresponds to the contour for the

relaxion mass at the muon threshold; the yellow contour corresponds to c⌧ = 2m and the purpleone to ⌧ = 1 s.

to the visible decay channels of the Higgs boson to SM particles. While such a dilu-

tion of the visible decay channels may be compensated by increased scaling factors of the

couplings [57], this is not the case in Higgs portal models (like the relaxion case we are

considering) where the Higgs boson couplings are universally suppressed by cos ✓ with re-

spect to their SM values. This configuration with one universal coupling modifier and

non-standard decay channels has been considered in Ref. [57]. Therefore we apply their

upper limit on the Higgs branching ratio to non-standard channels from a fit to the data

of ATLAS and CMS at 8TeV with HiggsSignals [58]:

BR(h ! NP) 20% at 95% CL . (5.12)

– 23 –

20

Energy frontier, LEP, LHC …

To summarise, Fig. 4 visualises that the bounds from LEP and the LHC are comple-

mentary in the sense that LEP is more constraining on sin2 ✓ for m� <25 GeV whereas

the indirect constraint from the bound on the decay width into NP final states at the LHC

sets a stronger constraint for m� >25 GeV. Again we show contours of constant ⇤br and f

which, as we already mentioned, have been obtained by exact diagonalisation of the mass

matrices in Appendix A and B. We show the contours for ⇤br = 120 GeV for j = 2 (gray,

dashed) and j = 1 (brown, dashed), f = mh and f = 1TeV for both the j = 2 (black) and

the j = 1 case (brown).

Figure 4. Constraints on the relaxion-Higgs mixing sin2 ✓ for relaxions with m� between 5GeVand 90GeV from LEP and the LHC: 4-fermion final states from Higgs strahlung at LEP (green,labelled as LEP hZ); Higgs decays to NP with BR(� ! NP) 20% at the LHC (purple, solid) aswell as a projection for BR(� ! NP) 10% (purple, dashed); explicit searches for h ! �� withfinal states 4⌧ (dark blue, dotted, m� < 10GeV, Run 3 projection) and 2µ2b (dark blue, dotted,m� > 25GeV, Run 3 projection). Contours for ⇤br = 120 GeV (gray, dashed for j = 2; brown,dashed for j = 1), f = mh and f = 1TeV (black for j = 2, brown for j = 1).

6 Cosmological and astrophysical probes of relaxion-Higgs mixing

As discussed in the previous section, laboratory measurements can probe a significant region

of the relaxion parameter space. However, in the sub-MeV region, before the fifth force

experiments start to gain sensitivity in the sub-eV region, a large portion of the parameter

– 25 –


Relaxion pheno’ & Higgs/Z factories

21

♦ Rescaling LEP to FCCee \w O(107 Higgses) & O(1013 Zs).

Flacke, Frugiuele, Fuchs, Gupta, GP & Schlaffer (in preparations)

m�♦ Higgs prod’: simple models: triple couplings only function of : potentially exclude/discover heavy relaxion region above 10 GeV.

♦ Also, can constrain direct the scale f via coupling�

f(W,Z)µ⌫(W̃ , Z̃/�̃)µ⌫

robust operator, as in particle production mixing \w Higgs & digamma is small.Hook & Marques-Tavares (16)

♦ 3-body decay of off-shell Z, very strong bound on mixing angles.

Bounds from Higgs untagged decay

22

♦ Rescaling LEP to FCCee \w O(106 Higgses) => improvement of 2 orders of magnitude in the constrain on the mixing2 angle!


our strategy: relaxion bound (m�

, sin2 ✓, f) from the new 3-body decay of an

on-shell Z:

��tot

Z

= �(Z ! Z⇤� ! ff̄�) + �(Z ! ff̄ ! ff̄�) , (6)

where in the second term the contribution from f = b dominates.

2 Bound from H ! inv

FCCee benchmark: Atps = 240GeV, Higgs bosons are predominantly

produced in Higgs strahlung o↵ a Z with �(ps = 240GeV) ' 230 fb [7, 8, 9]

whereas the the production via VBF is negligible. If we require 107 Higgs events,

we need Lint

⌘RLdt ' 43 ab�1.

Comparison of bounds on untagged Higgs decays Estimations can be

found in the Higgs WG report [10].

Colliderps L

int

[fb�1] BR(H ! untagged) Ref.

LHC 7� 8TeV 22 0.2 [11, 12]

LHC 7� 14TeV 300 0.089 [11]

HL-LHC 7� 14TeV 3000 0.05 [11]

ILC 250GeV 250 9 · 10�3 [10]

FCCee 240GeV 104 1.9 · 10�3 [10]

FCCee 240GeV 4.3 · 104 9 · 10�4 [10, 7, 8]

References

[1] T. Flacke, C. Frugiuele, E. Fuchs, R. S. Gupta, and G. Perez,

“Phenomenology of relaxion-Higgs mixing,” arXiv:1610.02025

[hep-ph].

[2] A. Freitas, “Higher-order electroweak corrections to the partial widths

and branching ratios of the Z boson,” JHEP 04 (2014) 070,

arXiv:1401.2447 [hep-ph].

2

our strategy: relaxion bound (m�

, sin2 ✓, f) from the new 3-body decay of an

on-shell Z:

��tot

Z

= �(Z ! Z⇤� ! ff̄�) + �(Z ! ff̄ ! ff̄�) , (6)

where in the second term the contribution from f = b dominates.

2 Bound from H ! inv

FCCee benchmark: Atps = 240GeV, Higgs bosons are predominantly

produced in Higgs strahlung o↵ a Z with �(ps = 240GeV) ' 230 fb [7, 8, 9]

whereas the the production via VBF is negligible. If we require 107 Higgs events,

we need Lint

⌘RLdt ' 43 ab�1.

Comparison of bounds on untagged Higgs decays Estimations can be

found in the Higgs WG report [10].

Colliderps L

int

[fb�1] BR(H ! untagged) Ref.

LHC 7� 8TeV 22 0.2 [11, 12]

LHC 7� 14TeV 300 0.089 [11]

HL-LHC 7� 14TeV 3000 0.05 [11]

ILC 250GeV 250 9 · 10�3 [10]

FCCee 240GeV 104 1.9 · 10�3 [10]

FCCee 240GeV 4.3 · 104 9 · 10�4 [10, 7, 8]

References

[1] T. Flacke, C. Frugiuele, E. Fuchs, R. S. Gupta, and G. Perez,

“Phenomenology of relaxion-Higgs mixing,” arXiv:1610.02025

[hep-ph].

[2] A. Freitas, “Higher-order electroweak corrections to the partial widths

and branching ratios of the Z boson,” JHEP 04 (2014) 070,

arXiv:1401.2447 [hep-ph].

2

. arXiv:1310.8361

Relaxion pheno’ & Higgs factories

23


Figure 1: Bounds on sin2 ✓ and m�

from the upper limit on the untagged

branching ratio of the Higgs boson, here H ! ��. Current (solid, blue

area) and projected (blue, dash-dotted) exclusion from the LHC. Pro-

jection for the ILC withps = 250GeV, L

int

= 250 fb�1 and the FCCee

with 4IP,ps = 240GeV and L

int

= 10 ab�1, 43 ab�1.

[3] A. Freitas, “Numerical multi-loop integrals and applications,” Prog. Part.

Nucl. Phys. 90 (2016) 201–240, arXiv:1604.00406 [hep-ph].

[4] M. Reece, “Physics at a Higgs Factory,” Int. J. Mod. Phys. A31 no. 33,

(2016) 1644003, arXiv:1609.03018 [hep-ph].

[5] A. Falkowski, C. Gross, and O. Lebedev, “A second Higgs from the Higgs

portal,” JHEP 05 (2015) 057, arXiv:1502.01361 [hep-ph].

3

preliminary

Relaxion pheno’ from Z factory

24


0.01 0.05 0.10 0.50 1 5 10

0.2

0.4

0.6

0.8

1.0

m [GeV]

arb

itrary

units

Z ff (normalized)

mixing

dual

2 3 4 5 6 7 8

-12

-10

-8

-6

-4

-2

0

Log[F

GeV]

Log[s

in2

]

# with m =0 GeV from 1013 Z events

1010

108

106

104

102

100

LEP rescaled

preliminary

preliminary

♦ Probing on shell Z decay to Z*( f f )+relaxion._

Conclusions

25

♦ Relaxion, new approach to hierarchy problem.

♦ Interesting new theoretical challenges (unlike SUSY/compositeness).

♦ Cosmology/particle production very interesting, not discussed…

♦ Discuss some phenomenological aspects and search strategies.

Backups

26

Relaxion’s basic structure

27

Choi, Kim & Yun (2014) Choi & Im; Kaplan & Rattazzi; Gupta, Komargodski, GP & Ubaldi (15)

♦ QFT consistent constructions are of the form:

(M ⇠ ⇤)

.

♦ It implies that generically:

(i) CP violation is spontaneously induced (problematic for axion-relaxion models);

(ii) Higgs-relaxion mixing is induced:

V (�, H) = H†H[⇤

2�M2cos(�/f)]+r⇤2M2

cos(�/f)+H†H ˜M2cos(n�/f)

V 0(�⇤, v) = 0 ) r⇤4

sin(�⇤/f) ' v2n ˜M2sin(n�⇤/f) ) �⇤ is generic.

Vmix

⇠ nvM̃2

fsin(n�⇤/f)⇥H�

phys

' r⇤4

vfsin(�⇤/f)⇥H�

phys

.

(GKR: g ⇠ M/f)}

28

Relaxion beams, relaxion flavor

BK+inv

B0K0*

K+inv K

+inv

KKL

0ll

B K(*)ll Belle

B K LHCb

NA62

CHARM

SHiP

M˜ =0

.99M˜

max

f=106 GeV

c=2mm

f=104 GeV

f=mh

c =2m

M˜ =2

-3/4 M˜

h

M˜ =1

GeV

Seaquest

NA62 BD

SN

S/S

0.005 0.050 0.500 510

-13

10-11

10-9

10-7

10-5

10-3

M [GeV]

sin2

E787/E949


gilad perez moriond

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