Fermionic DM Higgs Portal! An EFT approach
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1 Fermionic DM Higgs Portal An EFT approach Michael A. Fedderke University of Chicago Based on [hep-ph] (MF, Chen, Kolb, Wang) Unlocking the Higgs Portal ACFI, UMass, Amherst May 014
2 01 discovery of (a) ~15GeV Higgs boson natural motivation for exploring Higgs Portal (HP) couplings L H H O New 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 [Djouadi, et al.] [Lopez-Honorez, Schwetz, Zupan] [Greljo, et al.] [De Simone, Giudice, Strumia]
3 Dimension 5 fermionic DM (WIMP) Higgs portal with scalar (CP-even) and pseudoscalar (CP-odd) couplings L = L SM + (i/@ M 0 ) + H H Singlet fermion 1 (Majorana: ) p (1, 1, 0) c c 5 5 i 5 Convenient re-parametrisation L = L SM + (i/@ M 0 ) + 1 H H (cos +sin i 5 ) Good for numerical parameter scan Mixes up suppression scales (NB for judging unitarity bounds) 3
4 Standard lore for WIMP direct detection bounds The `pseudoscalar (C)P-odd H H i 5 coupling is momentum-transfer suppressed = velocity suppressed ( ) for elastic scattering. Only the scalar (C)P-even H H coupling is relevant. Direct detection bounds strong. v 10 6 Pseudoscalar coupling strongly favoured ( / ) However 4
5 after EWSB, L i/@ + 1 apple M 0 hvi Chiral rotation to real-mass basis. Modifies the couplings and mass. cos +sin i 5 cos +sin i 5 hvih + 1 h L i/@ M + 1 hvih + 1 h applecos +sin i 5,. Scalar cos = M 0 M apple cos hvi sin = M Pseudoscalar 0 M 0 M sin M = s M 0 hvi hvi cos + sin 5
6 after EWSB, L i/@ + 1 apple M 0 hvi Chiral rotation to real-mass basis. Modifies the couplings and mass. cos +sin i 5 cos +sin i 5 hvih + 1 h L i/@ M + 1 hvih + 1 h applecos +sin i 5,. Scalar cos = M 0 M apple cos hvi sin = M Pseudoscalar 0 M 0 M sin M = s M 0 hvi hvi cos + sin 6
7 Motivates a parameter scan of the low energy Lagrangian considering both couplings: L i/@ M + 1 hvih + 1 h applecos +sin i 5 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. M/T F 0 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
8 Motivates a parameter scan of the low energy Lagrangian considering both couplings: L i/@ M + 1 hvih + 1 h applecos +sin i 5 Analysis: WIMP freeze-out used to fix (M, ) parameter space constrained by Invisible Higgs width LUX direct detection bounds 8
9 Annihilation cross-sections Only look at -body decays; 3- and 4-body decays phase-space suppressed. Only tree level. Channels: χ h(k) χ hh h(k) χ f f f(k) + k k h (P ) [hhh] h (P ) [hf f] h(k ) v h(k ) χ v f(k ) χ χ χ ZZ Z ν (k) O( 1 ) χ W + W W ν (k) h (P ) [hzz] µν h (P ) [hw W ] µν χ v Z µ (k ) χ v W +µ (k ) 9
10 Also have O( ) contributions to hh via t- and u- channel diagrams Higher order χ v h(k) - effects are generally small +k k - expect other corrections at same order from neglected operators χ h(k ) We ignore these. (see backup) v In the NR limit ( ) s 4M + M v relevant for freeze-out away from thresholds BR( χχ ab) hh W + W Z 0 Z 0 f f f and resonances. 10
11 Most of the annihilation (except contact) through s- channel Higgs. Scale as h 1 m h/s +(m h h /s) i 1 DM contribution to the Higgs width very important for : M <m h h = MeV Huge compared to SM width s 1TeV 1 Will return to this for constraints 4M m h apple 1 4M m h cos (for ; halved for Majorana) 11
12 Gondolo and Gelmini, Nucl. Phys. B360 (1991) Srednicki, Watkins and Olive, Nucl. Phys. B310 (1988) 693. Kolb and Turner, The Early Universe (Westview),1994. WIMP relic density from Boltzmann Equation ṅ +3Hn = h v Møller i n n EQ Numerical solution, using full thermal averaging (important near resonances and below thresholds) h v Møller i = 8M 4 TK (M/T ) 1 Z 1 4M (s) (s 4M ) p sk 1 ( p s/t ) ds Defining Y = n/s, = 1 self-conjugate DM non-self-conjugate DM Ms 0 c Y 1 Use DM h to fix. Planck =0.1186(31) Planck Collaboration, [hep-ph] 1
13 EFT suppression scale for correct relic abundance 1.0 < hvi 10 Scalar 4 Majorana Majorana < hvi Λ [GeV] cos ξ Ωh = Ωh = cos ξ 0.4 Λ [GeV] Λ [GeV] 0.6 cos ξ Ωh = = M 103 v Pseudo scalar v v =M Now fix the suppression scale at this value. 13
14 EFT suppression scale for correct relic abundance L 1.0 < hvi 3 hv ih + h O hvi 1 1 (H H ) O 3 10 Scalar 4 Majorana Majorana < hvi Λ [GeV] cos ξ Ωh = Ωh = cos ξ 0.4 Λ [GeV] Λ [GeV] 0.6 cos ξ Ωh = = M 103 v Pseudo scalar v v =M Now fix the suppression scale at this value. 14
15 Invisible width constraint Already noted that invisible width SM width Recent limits on Higgs width - Global fits to Higgs data Belanger et. al., [hep-ph] B inv h SM + h apple 95% confidence for fit with SM couplings fixed (floating). - CMS analysis of on-shell vs. off-shell Higgs production and decay h, tot apple 17.4MeV h ZZ llll, 95% confidence. CMS-PAS-HIG and Caola and Melnikov, [hep-ph] 15
16 Resulting limits on the DM mass M & GeV Invisible BR [Belanger, et al.] Couplings fixed to SM Invisible BR [Belanger, et al.] Couplings floating Direct limit [CMS] Majorana (Practically independent of S/PS nature: larger for PS, but less phase-space suppression) 16
17 Direct detection Agrawal et. al., [hep-ph] Spin-independent Higgs mediated t-channel elastic scattering on nucleons Leads to the SI cross-section N SI L X Nuclear matrix element q m q direct detection Le = 1 f N M N µ N X q=u,d,s m h f (N) Tq hvi h qq + 1 [cos +sin i 5 ] hvi h. fn + 9 f (N) TG X q 1 m h apple m q qq [cos +sin i 5 ]. cos + 1 µ N M e.g. Hill, Solon, [hep-ph] Ellis, Ferstl, Olive, hep-ph/ MN 0.33GeV pion scattering 0.30M N 0.8GeV lattice 0km/s 10 3 c WIMP-nucleon reduced mass 17
18 Direct detection Limits from LUX LUX Collaboration, [astro-ph.co] and DMTools (dmtools.brown.edu) cos ξ < hvi Excluded 95% 90% SI /σlux 95% CL UL σ χn cos ξ < hvi Majorana Majorana Excluded 95% 90% SI /σlux 95% CL UL σ χn Ωh = Ωh = Pion scattering matrix element 18
19 Direct detection Limits from LUX LUX Collaboration, [astro-ph.co] and DMTools (dmtools.brown.edu) cos ξ < hvi Excluded 95% 90% SI /σlux 95% CL UL σ χn cos ξ < hvi Majorana Majorana Excluded 95% 90% SI /σlux 95% CL UL σ χn Ωh = Ωh = Lattice matrix element; limits somewhat weaker 19
20 Combined Limits < hvi <M < hvi Majorana Majorana <M < M < M cos ξ cos ξ Ωh = Direct detection constraints LUX Collaboration, [astro-ph.co] Ωh = Higgs width constraints Belanger, et. al [hep-ph] Pion scattering matrix elements 0
21 Combined Limits < hvi <M < hvi Majorana Majorana <M < M < M cos ξ cos ξ Ωh = Direct detection constraints LUX Collaboration, [astro-ph.co] Ωh = Higgs width constraints Belanger, et. al [hep-ph] Lattice matrix elements 1
22 Other limits (I) Indirect detection: fairly weak. Only marginally constraining once (large) astrophysical uncertainties are factored in, and then only for dominantly pseudoscalar coupling. based on Fermi-LAT data Galactic Centre gamma rays.. H H i 5 ~40GeV ~11GeV ~0GeV NFW Einasto =1. NFWc ( ) MF, Kolb, Lin, Wang, [hep-ph]
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. V h j χ MET q V h χ MET χ V j χ q.. V 3
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 [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. 4
25
26 BACKUP B1
27 B Annihilation Cross-sections I f (s; M,m 0 )= 1 3 M r 4M s r M s 4M r 1 4m 0 s f (s; M,m 0 ) f (s; M,m 0 ) 1 4 X spins 1 4 Z d M f 8 1 4m Z /s + 1m4 Z /s ZZ = 1 4 s cos 1 4M /s +sin " # 1 m h /s + m h h /s >< >: 1 4m W /s + 1m4 W /s W + W 1 4m f /s 4m f /s f f " 1+m h /s + # m h h /s hh.
28 Annihilation Cross-sections II f (s; M,m 0 )= 1 3 M r 4M s r M s 4M r 1 4m 0 s f (s; M,m 0 ) hh (s; M,m h )= 1 4 s 1+m h /s + 1 m h /s + hm h /s applecos hm h /s 1 4M +sin s + Mhvi cos 3 1 m 1+m h /s h /s + apple m h /s + 8M s cos + m h s hm h /s hm h /s tanh 1 1 m h /s hvi 4 4 apple M s 1 4m h s + hvi4 1 m h 4 1 s tanh 1 + m4 h s 1 apple 1 1 m h /s 4m h s 1 apple 16M 4 s cos 4 + M s + 6m4 h s + 16M s 1 1 m h s 4m h s cos 1 + cos 3M 4 s (s; M,m h ) + 3m4 h s cos 4 q (1 4M /s)(1 4m h /s) B3
29 B4 Effects of the neglected O( ) terms π π ξ 3π 4 π π 4 Ωh = (Λ with H.O.T.) / (Λ without H.O.T.) cos ξ 3π 4 π π 4 Ωh = Without
30 B5 Effects of the neglected O( ) terms π π ξ 3π 4 π π 4 Ωh = (Λ with H.O.T.) / (Λ without H.O.T.) ξ 3π 4 π π 4 Ωh = With
31 Solution for at low mass ( M < M <m h ) Typically get two solutions. 1 h 1 m h/s +(m h h /s) i A + B/ 4 One has (much) smaller than the other. We always take the larger value = more conservative..0 M = 30 GeV ξ = π/ Majorana Ωh / Λ [GeV] B6
32
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