Fermionic DM Higgs Portal An EFT approach Michael A. Fedderke - - PowerPoint PPT Presentation

Fermionic DM Higgs Portal An EFT approach

Michael A. Fedderke

University of Chicago

Based on 1404.2283 [hep-ph] (MF , Chen, Kolb, Wang)

Unlocking the Higgs Portal ACFI, UMass, Amherst 2 May 2014

2

2012 discovery of (a) ~125GeV Higgs boson natural motivation for exploring Higgs Portal (HP) couplings

• One avenue for particle DM to couple to SM
• This talk

Bottom-up EFT analysis of the allowed parameter space for the lowest dimension ‘scalar’ and ‘pseudoscalar’ HP couplings of fermionic WIMP DM in light of recent experimental limits.

• (See also results in Xiao-Gang He’s talk yesterday for scalar DM case)
• Previous similar work

1112.3299 [Djouadi, et al.] 1203.2064 [Lopez-Honorez, Schwetz, Zupan] 1309.3561 [Greljo, et al.] 1402.6287 [De Simone, Giudice, Strumia]

L ⊃ H†H ONew

3

Dimension 5 fermionic DM (WIMP) Higgs portal with scalar (CP-even) and pseudoscalar (CP-odd) couplings

• Singlet Dirac fermion

(Majorana: )

• Convenient re-parametrisation
• Good for numerical parameter scan

Mixes up suppression scales (NB for judging unitarity bounds)

χ →

1 √ 2χ

χ ∼ (1, 1, 0) L = LSM + ¯ χ(i/ ∂ − M0)χ + H†H ⇣

c1 Λ1 ¯

χχ + c5

Λ5 ¯

χiγ5χ ⌘ L = LSM + ¯ χ(i/ ∂ − M0)χ + 1 ΛH†H (cos θ ¯ χχ + sin θ ¯ χiγ5χ)

4

Standard lore for WIMP direct detection bounds

• The `pseudoscalar’ (C)P-odd coupling

is momentum-transfer suppressed = velocity suppressed ( ) for elastic scattering.

• Only the ‘scalar’ (C)P-even coupling is

relevant.

• Direct detection bounds strong.
• Pseudoscalar coupling strongly favoured ( )
• However…

H†H ¯ χχ H†H ¯ χiγ5χ v2 ∼ 10−6 θ ∼ π/2

5

…after EWSB,

• Chiral rotation to real-mass basis.
• Modifies the couplings and mass.

L ¯ χi/ ∂χ ¯ χMχ + Λ−1 ✓ hvih + 1 2h2 ◆  cos ξ ¯ χχ + sin ξ ¯ χiγ5χ

• ,

cos ξ = M0 M  cos θ hvi2 2ΛM0

• sin ξ = M0

M sin θ

L ¯ χi/ ∂χ  M0 ¯ χχ hvi2 2Λ ✓ cos θ ¯ χχ + sin θ ¯ χiγ5χ ◆ + Λ−1 ✓ cos θ ¯ χχ + sin θ ¯ χiγ5χ ◆ ✓ hvih + 1 2h2 ◆ .

M = s✓ M0 hvi2 2Λ cos θ ◆2 + ✓hvi2 2Λ ◆2 sin2 θ

Scalar Pseudoscalar

6

…after EWSB,

• Chiral rotation to real-mass basis.
• Modifies the couplings and mass.

L ¯ χi/ ∂χ ¯ χMχ + Λ−1 ✓ hvih + 1 2h2 ◆  cos ξ ¯ χχ + sin ξ ¯ χiγ5χ

• ,

cos ξ = M0 M  cos θ hvi2 2ΛM0

• sin ξ = M0

M sin θ

L ¯ χi/ ∂χ  M0 ¯ χχ hvi2 2Λ ✓ cos θ ¯ χχ + sin θ ¯ χiγ5χ ◆ + Λ−1 ✓ cos θ ¯ χχ + sin θ ¯ χiγ5χ ◆ ✓ hvih + 1 2h2 ◆ .

M = s✓ M0 hvi2 2Λ cos θ ◆2 + ✓hvi2 2Λ ◆2 sin2 θ

Scalar Pseudoscalar

Motivates a parameter scan of the low energy Lagrangian considering both couplings:

• For the purposes of low energy phenomenology,

need not explicitly account for the rotation: so long as the WIMP DM freezes out after the EW phase transition ( ) don’t need to compute relevant observables above EWSB scale.

• It is however still important in relating low energy

limits to the gauge-invariant EFT operators, and the EFT to some renormalizable model of the HP.

• 7

L ¯ χi/ ∂χ ¯ χMχ + Λ−1 ✓ hvih + 1 2h2 ◆  cos ξ ¯ χχ + sin ξ ¯ χiγ5χ

• M/TF ∼ 20

Motivates a parameter scan of the low energy Lagrangian considering both couplings:

• Analysis:
• WIMP freeze-out used to fix

parameter space constrained by Invisible Higgs width LUX direct detection bounds

8

L ¯ χi/ ∂χ ¯ χMχ + Λ−1 ✓ hvih + 1 2h2 ◆  cos ξ ¯ χχ + sin ξ ¯ χiγ5χ

• Λ

(M, ξ)

9

Annihilation cross-sections

• Only look at 2-body decays; 3- and 4-body decays

phase-space suppressed. Only tree level.

• Channels:

⟨v⟩ f(k) ¯ f(k′) [hf ¯ f] ∆h(P 2) χ ¯ χ ⟨v⟩ W −ν(k) W +µ(k′) [hWW]µν ∆h(P 2) χ ¯ χ ⟨v⟩ Zν(k) Zµ(k′) [hZZ]µν ∆h(P 2) χ ¯ χ

h(k′) h(k) + k ↔ k′ [hhh] h(k) h(k′) ⟨v⟩ ∆h(P 2) χ ¯ χ χ ¯ χ

O(Λ−1) hh f ¯ f ZZ W +W −

Also have contributions to via - and - channel diagrams

• Higher order
• effects are generally small
• expect other corrections at same
• rder from neglected operators

We ‘ignore’ these. (see backup)

• In the NR limit

( ) relevant for freeze-out away from thresholds and resonances.

10

101 102 103 M [GeV] 10−4 10−3 10−2 10−1 100 BR(¯ χχ → ab)

hh W +W − Z0Z0

• f f ¯

f

O(Λ−2) hh

h(k) h(k′) h(k′) ⟨v⟩ ⟨v⟩ ¯ χ χ +k ↔ k′

s ≈ 4M 2 + M 2v2 t u

Most of the annihilation (except contact) through s- channel Higgs. Scale as

• DM contribution to the Higgs width very important

for :

• (for Dirac; halved for Majorana)
• Will return to this for constraints…

11

Γh→¯

χχ =

• 3.034 × 102 MeV
• ×

✓1 TeV Λ ◆2 s 1 − 4M 2 m2

h

 1 − 4M 2 m2

h

cos2 ξ

• 2M < mh

Huge compared to SM width

σ ∼ h 1 − m2

h/s

2 + (mhΓh/s)2i−1

WIMP relic density from Boltzmann Equation

• Numerical solution, using full thermal averaging

(important near resonances and below thresholds)

• Defining ,
• Use to fix .

12

˙ n + 3Hn = hσvMølleri ⇥ n2 n2

EQ

⇤

hσvMølleri = ⇥ 8M 4TK2

2(M/T)

⇤−1 Z ∞

4M 2 σ(s) (s 4M 2) ps K1(ps/T) ds

Y = n/s Ω = ⇢ 1 self-conjugate DM 2 non-self-conjugate DM

• × Ms0

ρc Y∞ ΩDMh2

• Planck = 0.1186(31)

Λ

Gondolo and Gelmini, Nucl. Phys. B360 (1991) 145-179. Srednicki, Watkins and Olive, Nucl. Phys. B310 (1988) 693. Kolb and Turner, The Early Universe (Westview),1994. Planck Collaboration, 1303.5076 [hep-ph]

EFT suppression scale for correct relic abundance

• Now fix the suppression scale at this value.

13

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Dirac

⟨v⟩ 103 104 Λ [GeV]

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Majorana

⟨v⟩ 103 104 Λ [GeV] 101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Dirac

⟨v⟩ 103 104 Λ [GeV]

Λ < hvi

Λ = M Λ = 2M

Dirac Majorana

Scalar Pseudo- scalar

Λ < hvi

EFT suppression scale for correct relic abundance

• Now fix the suppression scale at this value.

14

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Dirac

⟨v⟩ 103 104 Λ [GeV]

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Majorana

⟨v⟩ 103 104 Λ [GeV] 101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Dirac

⟨v⟩ 103 104 Λ [GeV]

Λ < hvi

Dirac Majorana

Scalar Pseudo- scalar

L

1 Λ

3 (H

†

H)

2

O

χ

• h

v i

2

Λ

2

1 Λ

⇥ hvih +

3 2

h

2

⇤ O

χ

Λ < hvi

Λ = M Λ = 2M

15

Invisible width constraint

• Already noted that invisible width SM width
• Recent limits on Higgs width
• Global fits to Higgs data Belanger et. al., 1306.2941 [hep-ph]
• @ 95% confidence
• for fit with SM couplings fixed (floating).
• CMS analysis of on-shell vs. off-shell Higgs

production and decay

• @ 95% confidence.

h → ZZ → llll, llνν

• Binv ≡

Γh→¯

χχ

ΓSM + Γh→¯

χχ

≤ 0.19(0.38) Γh, tot ≤ 17.4MeV

CMS-PAS-HIG-14-002 and Caola and Melnikov, 1307.4935 [hep-ph]

16

Resulting limits on the DM mass

• (Practically independent of S/PS nature: larger for

PS, but less phase-space suppression)

Invisible BR [Belanger, et al.]

• Couplings fixed

to SM Invisible BR [Belanger, et al.]

• Couplings floating

Direct limit [CMS]

• —

Dirac

56.8 56.2 55.7

Majorana

55.3 54.6 53.8

M & GeV

Λ

17

Direct detection

• Spin-independent Higgs mediated -channel elastic

scattering on nucleons

• Leads to the SI cross-section
• Nuclear matrix element

t

L X

q

mq hvi h ¯ qq + Λ−1 [cos ξ ¯ χχ + sin ξ ¯ χiγ5χ] hvi h.

− → Ldirect detection

eff

⊃ − X

q

1 m2

h

mq Λ ¯ qq [cos ξ ¯ χχ + sin ξ ¯ χiγ5χ] .

σχN

SI

= 1 π ✓µχN m2

h

◆2 ✓fN Λ ◆2  cos2 ξ + 1 2 ⇣µχN M ⌘2 ν2

χ

• Ellis, Ferstl, Olive, hep-ph/0001005

Agrawal et. al., 1003.1912 [hep-ph] e.g. Hill, Solon, 1111.0016 [hep-ph]

fN ≡ MN ✓ X

q=u,d,s

f (N)

T q + 2 9f (N) T G

◆ ≈ ⇢ 0.35MN ≈ 0.33GeV pion scattering 0.30MN ≈ 0.28GeV lattice

νχ ∼ 220km/s ∼ 10−3c

WIMP-nucleon reduced mass

18

Direct detection Limits from LUX

• Pion scattering matrix element

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Majorana

10−4 10−3 10−2 10−1 100 101

σχN

SI /σLUX 95% CL UL

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Dirac

10−4 10−3 10−2 10−1 100 101

σχN

SI /σLUX 95% CL UL

Dirac Majorana

Excluded Excluded

9 5 % 9 5 % 9 % 9 %

LUX Collaboration, 1310.8214 [astro-ph.CO] and “DMTools” (dmtools.brown.edu)

Λ < hvi Λ < hvi

Direct detection Limits from LUX

• Lattice matrix element; limits somewhat weaker

19

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Majorana

10−4 10−3 10−2 10−1 100 101

σχN

SI /σLUX 95% CL UL

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Dirac

10−4 10−3 10−2 10−1 100 101

σχN

SI /σLUX 95% CL UL

Dirac Majorana

Excluded Excluded

9 5 % 9 5 % 90% 9 %

LUX Collaboration, 1310.8214 [astro-ph.CO] and “DMTools” (dmtools.brown.edu)

Λ < hvi Λ < hvi

20

Combined Limits

• Pion scattering matrix elements

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Dirac

40 90 10−3 10−2 10−1

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Majorana

40 90 10−3 10−2 10−1

Dirac Majorana

Λ < hvi Λ < hvi

Λ < 2M Λ < 2M

Direct detection constraints LUX Collaboration, 1310.8214 [astro-ph.CO] Higgs width constraints Belanger, et. al. 1306.2941 [hep-ph]

Λ < M Λ < M

21

Combined Limits

• Lattice matrix elements

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Dirac

40 90 10−3 10−2 10−1

101 102 103 M [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 cos2 ξ

Ωh2 = 0.1186

Majorana

40 90 10−3 10−2 10−1

Dirac Majorana

Λ < 2M Λ < 2M

Direct detection constraints LUX Collaboration, 1310.8214 [astro-ph.CO] Higgs width constraints Belanger, et. al. 1306.2941 [hep-ph]

Λ < hvi Λ < hvi

Λ < M Λ < M

“ …..” Other limits (I) Indirect detection: fairly weak. Only marginally constraining once (large) astrophysical uncertainties are factored in, and then only for dominantly pseudoscalar coupling.

• 22

MF , Kolb, Lin, Wang, 1310.6047 [hep-ph]

H†H ¯ χiγ5χ

Galactic Centre gamma rays

NFW Einasto NFWc ( )

γ = 1.2

~11GeV ~20GeV ~40GeV

based on Fermi-LAT data

23

Other limits (II)

• Direct collider searches via ‘VBF MET’ (two forward

tagging jets and large MET) or mono-X and MET. Have not examined reach in any detail, but expect to be challenging searches due to large SM backgrounds.

• MET

j j χ ¯ χ h V V V V h χ ¯ χ MET q ¯ q ..

24

Conclusions

• Completed a full bottom-up EFT analysis of the scalar and

pseudoscalar dimension 5 fermionic Higgs portal

• EWSB generates a scalar coupling if pure pseudoscalar above

EW phase transition… NB for direct detection.

• Scan of low-energy (post-EWSB) parameter space:
• All scenarios strongly ruled out by invisible Higgs width (and

possibly DD) for DM particles lighter than ~55-56GeV.

• Scalar portal always strongly ruled out by direct detection,

except near Higgs resonance see also Lopez-Honorez, et. al 1203.2064 [hep-ph]

• Mostly pseudoscalar portal still allowed by direct detection,

with larger scalar admixture for larger mass

• I.e. the usual lore, but i.t.o. low energy parameters; need to

translate into limits on Lagrangian above EW PT

• Other limits (ID, collider) possible, but expected to be weaker.

BACKUP

B1

Annihilation Cross-sections I

Σf(s; M, m0) ≡ 1 4 X

spins

· 1 4π Z dΩ |Mf|2 = 1 4 s Λ2 cos2 ξ

• 1 − 4M 2/s
• + sin2 ξ

"✓ 1 − m2

h/s

◆2 + ✓ mhΓh/s ◆2#2 × 8 > > > > > > > > > > < > > > > > > > > > > :

• 1 − 4m2

Z/s + 12m4 Z/s2

ZZ 2

• 1 − 4m2

W /s + 12m4 W /s2

W +W ✓ 1 − 4m2

f/s

◆✓ 4m2

f/s

◆ f ¯ f "✓ 1 + 2m2

h/s

◆2 + ✓ mhΓh/s ◆2# hh .

σf(s; M, m0) = 1 32πM 2 r 4M 2 s r M 2 s − 4M 2 r 1 − 4m02 s Σf(s; M, m0)

B2

Annihilation Cross-sections II

σf(s; M, m0) = 1 32πM 2 r 4M 2 s r M 2 s − 4M 2 r 1 − 4m02 s Σf(s; M, m0)

Σhh(s; M, mh) = 1 4 s Λ2 ✓ 1 + 2m2

h/s

◆2 + ✓ Γhmh/s ◆2 ✓ 1 m2

h/s

◆2 + ✓ Γhmh/s ◆2  cos2 ξ ✓ 1 4M 2 s ◆ + sin2 ξ

• + 2Mhvi2 cos ξ

Λ3 ✓ 1 m2

h/s

◆✓ 1 + 2m2

h/s

◆ + ✓ Γhmh/s ◆2 ✓ 1 m2

h/s

◆2 + ✓ Γhmh/s ◆2 ⇥  1 + 1 β ✓ 1 8M 2 s cos2 ξ + 2m2

h

s ◆ tanh−1 ✓ β 1 2m2

h/s

◆ hvi4 2Λ4 M 2 s ✓ 1 4m2

h

s ◆ + m4

h

s2 −1 16M 4 s2 cos4 ξ + 2M 2 s ✓ 1 4m2

h

s

• 1 + cos2 ξ

◆ + 3m4

h

s2

• + hvi4

Λ4 β−1 ✓ 1 2m2

h

s ◆−1  1 4m2

h

s + 6m4

h

s2 + 16M 2 s ✓ 1 m2

h

s ◆ cos2 ξ 32M 4 s2 cos4 ξ

• ⇥ tanh−1

✓ β 1 2m2

h/s

◆ B3

β(s; M, mh) ≡ q (1 − 4M 2/s) (1 − 4m2

h/s)

101 102 103 M [GeV]

π 4 π 2 3π 4

π ξ

Ωh2 = 0.1186

Dirac

0.7 0.8 0.9 1.0 1.1 1.2 1.3 (Λ with H.O.T.) / (Λ without H.O.T.) 101 102 103 M [GeV]

π 4 π 2 3π 4

π cos2 ξ

Ωh2 = 0.1186

Dirac

Effects of the neglected terms

O(Λ−2)

Without

ξ

B4

101 102 103 M [GeV]

π 4 π 2 3π 4

π ξ

Ωh2 = 0.1186

Dirac

101 102 103 M [GeV]

π 4 π 2 3π 4

π ξ

Ωh2 = 0.1186

Dirac

0.7 0.8 0.9 1.0 1.1 1.2 1.3 (Λ with H.O.T.) / (Λ without H.O.T.)

With Effects of the neglected terms

O(Λ−2)

B5

Solution for at low mass ( )

• Typically get two solutions.
• One has (much) smaller than the other.

We always take the larger value = more conservative.

50 100 150 200 Λ [GeV] 0.5 1.0 1.5 2.0 Ωh2 / 0.1186 M = 30 GeV — ξ = π/2 — Majorana

Λ Λ M ∗ < 2M < mh

B6

σ−1 ∼ Λ2 h 1 − m2

h/s

2 + (mhΓh/s)2i ∼ Λ2 ⇥ A + B/Λ4⇤