WISPy dark matter from the top down Mark D. Goodsell LPTHE - PowerPoint PPT Presentation

Introduction ALPs Vector dark matter Other WISPy dark matter from the top down Mark D. Goodsell LPTHE

Introduction ALPs Vector dark matter Other Introduction • Reminder of the motivations for WISPs • Misalignment production of WISPy dark matter • Cosmological constraints • Motivation for WISPs in string theory • What properties we might expect ...

Introduction ALPs Vector dark matter Other Axions, ALPs, and Hidden Photons Axions/ALPs: • Periodic fields: φ i ∼ φ i + 2 πf i • Pseudo-Nambu Goldstone bosons of some symmetry • Most important couplings are to QCD (for axion), photons and electrons g 2 e 2 G µν − C iγγ L ⊃ − a F µν + C ei 32 π 2 G µν ˜ 32 π 2 φF µν ˜ 3 eγ µ γ 5 e∂ µ φ i ¯ f a f i 2 f i • Constrained f a � 10 9 GeV, upper bound of 10 12 GeV in absence of dark matter dilution mechanism Hidden photons: • Extend the (MS)SM by at least one U ( 1 ) gauge (super)field: b − θ M L ⊃ χ ab 2 F a µν F µν 8 π 2 F a µν ˜ F µν χ ab λ a σ µ ∂ µ λ b + h . c . ) b + ( i ˜

Introduction ALPs Vector dark matter Other Bottom-up motivation for WISPs For anyone who was asleep yesterday and/or has wandered in to the wrong meeting – many different experiments: • Haloscopes • Helioscopes • Dish antennae • Beam dumps – e.g. the SHiP experiment! • Light shining through walls • Molecular interferometry and of course cosmic searches such as isocurvature and tensor modes, rotation of CMB polarisation, ... • Opportunity to probe weak couplings or very high energy scales!

Introduction ALPs Vector dark matter Other ALPs

Introduction ALPs Vector dark matter Other ALPs: Bottom-up motivation L ⊃ − g 2 e 2 C iγ a C a 3 F µν + C ie 3 F b 3, µν ˜ F b , µν a i F µν ˜ eγ µ γ 5 e∂ µ a i , − ¯ 3 32 π 2 32 π 2 f a f a i 2 f a i • Axion as solution to strong CP problem! • Misalignment dark matter! • For a light ALP( < 10 − 9 eV) anomalous transparency of the universe for VHE gamma rays f i /C iγ ∼ 10 8 GeV • ... and for same value of f i /C iγ , steps is power spectrum at critical energy of 100 GeV, hinting at m ALP ∼ 10 − 9 ÷ 10 − 10 eV. • X-ray hint of ALPs from the Coma cluster (Conlon, Marsh, Powell, ...) f a � 10 10 GeV � 0.5 /∆N eff C aγ • (Now in doubt) solution to non-standard energy loss of white dwarfs f i /C ie ≃ ( 0.2 ÷ 2.6 ) × 10 9 GeV • These are compatible (need C iγ /C ie � 10 ) and could be searched for in future experiments!!

Introduction ALPs Vector dark matter Other Misalignment dark matter • An axion or ALP is a periodic field: it can take any initial value in [ 0, 2 πf a ] since the potential energy in the field is negligible compared to energies in early universe. • During inflation any scalar field will undergo quantum fluctuations of magnitude H I H I 2 π → σ Θ = 2 πf a • At later times, the scalar field behaves classically with equation of motion φ + 3 H ˙ ¨ φ + m 2 φ φ = 0 • While 3 H > m , the field is damped and retains its initial vev. • When 3 H = m , it starts to oscillate and will behave like a bath of particles; the a θ 2 which starts to red-shift like energy stored in the field is 1 2 m 2 φ 2 0 ∼ 1 2 m 2 a f 2 matter ∝ a − 3 . • One complication: for the QCD axion, the mass decreases rapidly as the temperature increases; instanton calculations give m u m d m s Λ 9 QCD → m a ∼ T − 4 V inst ∼ ( πT ) 8

Introduction ALPs Vector dark matter Other ALP vs axion dm • So for the QCD axion we find � 7 / 6 � θ a � 2 Ω a h 2 � f a 0.112 ≃ 6 × 10 12 GeV π • While for an ALP we find � 2 � θ a � m a i � 2 Ω a h 2 � 1 / 2 � f a i 0.112 ≃ 1.4 × × 10 11 GeV eV π This means that the parameter space can be very different: • For the QCD axion we are restricted by dark matter at high f a • The QCD axion always mixes with pions and therefore has restrictions coming from nucleon couplings • It will always have a minimal coupling to electrons and photons coming from this too (more later) which bound f a � 10 9 GeV. • For an ALP , we have no such restrictions except that it should not couple strongly to QCD! • In fact we have a “maximum” allowed coupling to the photon: C a i g iγ ≡ α α � 2 π f a i 2 πf a i • Gives the lifetime of � − 2 � m a i � � − 3 64 π g iγ ≃ 1.3 × 10 25 s τ a i = g 2 iγ m 3 10 − 10 GeV − 1 eV a i

Introduction ALPs Vector dark matter Other DM constraints EBL Axion models ALPS - 6 HB CAST + Sumico - 9 Log 10 g [ GeV - 1 ] τ ALP < 10 17 s γ - burst 1987a x ion Haloscope Optical - 12 Searches m 1 > 3H ( T eq ) m 1 / m 0 =( Λ / T ) β - 15 X - Rays EBL Standard ALP CDM ( m 1 = m 0 ) - 18 - 8 - 5 - 2 1 4 7 Log 10 m ϕ [ eV ]

Introduction ALPs Vector dark matter Other Cosmological constraints There are important cosmological constraints: • Black hole superradiance m a > 3 × 10 − 11 eV (or � 10 − 21 eV) ([ Arvanitaki, Dubovsky ’10]) • Isocurvature – since the axion is effectively massless during inflation its fluctuations correspond to isocurvature, and there are strong constraints: P II β iso = P RR + P II < 0.035 (Planck 2015) • We know that P RR = 2.196 + 0.051 − 0.060 is the amount of primordial fluctuations � Ω a i � 2 P II ≃ 4 σ 2 θ P RR θ 2 Ω m � Ω m � 2 → H I < 2.8 × 10 − 5 θf a i Ω a i � f a � 0.408 → H I < 0.9 × 10 7 GeV QCD axion 10 11 • Also have the constraint from non-observation of tensor modes that 2 H 2 r = P TT /P RR < 0.11 and P TT = I P giving π 2 M 2 H I < 8.3 × 10 13 GeV

Introduction ALPs Vector dark matter Other ALPs in IIB strings � K αβ � � � dc α + M P dc β + M P S ⊃ − π A i q iα ∧ ⋆ π A j q jβ 8 r iα c α tr ( F ∧ F ) − r iα τ α 1 + tr ( F i ∧ ⋆ F i ) . 4 πM P 4 πM P • Axions periodic fields, c α → c α + M P , T α = τ α + ic α ∼ T α + iM P • Decay constants determined by diagonalising ( K 0 ) αβ ≡ ∂ 2 (− 2 log V ) : ∂ τα ∂ τβ f α ≡ M P � λ α , a α ∼ a α + 2 πf α 4 π • Canonically normalise the axion fields αδ ′ = λ − 1 C γ ′ α K αβ C T C γ ′ α C T c α = 2 a γ C βα , βδ ′ = δ γ ′ δ ′ , γ ′ δ γ ′ δ ′ , • Read off couplings to gauge groups: � 1 / 2 f a j M P = 1 U ( 1 ) SU ( N ) . × r jα C T 1 C ji 8 π αi

Introduction ALPs Vector dark matter Other The LARGE Volume Scenario • Type IIB string theory, Complex structure moduli stabilised at SUSY value by three-form fluxes, gives superpotential W 0 • Volume of Calabi-Yau in “swiss-cheese” form V = τ 3 / 2 − τ 3 / 2 − h ( τ i ) s b • Or K 3 -fibration: V = τ 1 / 2 b ′ τ b − τ 3 / 2 − h ( τ i ) s • → Instanton/gaugino condensate generate contribution to superpotential W ⊃ Ae − aτ s , but typically only need one or two! (c.f. KKLT) � � • Kähler potential with α ′ corrections K ⊃ − 2 log ℜ ( τ b ) 3 / 2 + ξ/ 2 , needs h 2,1 > h 1,1 • Volume, τ b stabilised at exponentially large value: V ∼ 10 6 for GUT, ∼ 10 14 for intermediate scale strings, ∼ 10 30 for TeV strings • Small cycle τ s stabilised at aτ s ∼ log V • AdS vacuum with ✘✘ SUSY , small uplift required to dS by anti-branes, D-terms, ✘ F-terms, instantons at quivers ... • (MS)SM realised on D 7 branes on collapsed cycles τ a ∼ 0 (Quiver locus) or � 1 (Geometric regime)

Introduction ALPs Vector dark matter Other The LVS axiverse • For LARGE volume scenario (LVS) need W = W 0 + Ae − aτ dP , W 0 ∼ 1 • τ dP is a diagonal del Pezzo blow-up → removes issue of chirality. • Do not need other NP effects: others can be fixed by D-terms, α ′ and g s effects - open ( V ∼ W 2 V 3 ) and closed ( V ∼ W 2 0 V 4 ) string loops. 0 • Non-vanishing D -terms are dangerous ( V ∼ V − 2 ) but are useful for stabilising cycles relative to each other 1 4 π V q aj t j = 0 → linear combination fixed ξ a = • Each NP term in superpotential and each linearly independent D-term eats one axion • In scenario where LARGE cycle unwrapped/no D-term, have at least n ax = h 1,1 − 1 − d � 1 light axions • Generically this number may be large, particularly if many unwrapped cycles. • Since further single instanton/gaugino condensate contributions may not be generic → very light axions → ALPs.

Introduction ALPs Vector dark matter Other Swiss cheeses

Introduction ALPs Vector dark matter Other Decay constants We expect � M P /τ α non − local axion √ f α ∼ M s ∼ M P / V local axion � � τ 3 / 2 − τ 3 / 2 = τ b ∼ V 2 / 3 and 1 we have 4 πg − 2 e.g. for V = √ s b b 9 2 V − 4 / 3 V − 5 / 3 � � K 0 ∼ V − 5 / 3 V − 1 √ M P M P M P 3 1 M s Have f a b = τ b ≃ 4 π V 2 / 3 , f a s = √ V ≃ . √ √ 4 π 6 ( 2 τ s ) 1 / 4 4 πτ 1 / 4 4 π s L ⊃ c b c s g 2 g 2 b tr ( F b ∧ F b ) + s tr ( F s ∧ F s ) M P M P τ 3 / 4 � � � � � 1 � s ≃ O a b + O a s tr ( F b ∧ F b ) M P V 1 / 2 M P � � � � � � 1 1 + O a b + O a s tr ( F s ∧ F s ) . M P τ 3 / 4 M s s M P • Non-local ALPs can have small decay constants, e.g. V 2 / 3 , but the couplings to matter are always � M P suppressed • If we want ALPs in the classic axion window, they need to be “local,” and have an intermediate string scale: f i ∼ M s ∼ M P V , V ∼ 10 15 . √ • To have an axion and ALP , need several intersecting local cycles