Non-perturbative beyond the Standard Model physics Enrico Rinaldi - PowerPoint PPT Presentation

“Stealth Dark Matter” model [LSD collab., arxiv:1503.04203] • The field content of the model Field SU ( N ) D (SU (2) L , Y ) Q ! ! F u consists in 8 Weyl fermions +1 / 2 1 F 1 = ( 2 , 0) N F d − 1 / 2 1 ! ! F u +1 / 2 • Dark fermions interact with the SM 2 F 2 = ( 2 , 0) N F d − 1 / 2 2 Higgs and obtain current/chiral F u ( 1 , +1 / 2) +1 / 2 N 3 masses F d ( 1 , − 1 / 2) − 1 / 2 N 3 F u ( 1 , +1 / 2) +1 / 2 N 4 F d ( 1 , − 1 / 2) − 1 / 2 N • Introduce vector-like masses for 4 dark fermions that do not break EW symmetry L ⊃ + y u 14 ✏ ij F i 1 H j F d 4 + y d 14 F 1 · H † F u 4 − y d 23 ✏ ij F i 2 H j F d 3 − y u 23 F 2 · H † F u • Diagonalizing in the mass 3 + h.c. eigenbasis gives 4 Dirac fermions • Assume custodial SU(2) symmetry arising when u ↔ d

“Stealth Dark Matter” model [LSD collab., arxiv:1503.04203] • The field content of the model Field SU ( N ) D (SU (2) L , Y ) Q ! ! F u consists in 8 Weyl fermions +1 / 2 1 F 1 = ( 2 , 0) N F d − 1 / 2 1 ! ! F u +1 / 2 • Dark fermions interact with the SM 2 F 2 = ( 2 , 0) N F d − 1 / 2 2 Higgs and obtain current/chiral F u ( 1 , +1 / 2) +1 / 2 N 3 masses F d ( 1 , − 1 / 2) − 1 / 2 N 3 F u ( 1 , +1 / 2) +1 / 2 N 4 F d ( 1 , − 1 / 2) − 1 / 2 N • Introduce vector-like masses for 4 dark fermions that do not break EW symmetry L ⊃ + y u 14 ✏ ij F i 1 H j F d 4 + y d 14 F 1 · H † F u 4 − y d 23 ✏ ij F i 2 H j F d 3 − y u 23 F 2 · H † F u • Diagonalizing in the mass 3 + h.c. eigenbasis gives 4 Dirac fermions 1 F j L ⊃ M 12 ✏ ij F i 2 − M u 34 F u 3 F d 4 + M d 34 F d 3 F u 4 + h.c. • Assume custodial SU(2) symmetry arising when u ↔ d

“Stealth Dark Matter” model [LSD collab., arxiv:1503.04203] • The field content of the model Field SU ( N ) D (SU (2) L , Y ) Q ! ! F u consists in 8 Weyl fermions +1 / 2 1 F 1 = ( 2 , 0) N F d − 1 / 2 1 ! ! F u +1 / 2 • Dark fermions interact with the SM 2 F 2 = ( 2 , 0) N F d − 1 / 2 2 Higgs and obtain current/chiral F u ( 1 , +1 / 2) +1 / 2 N 3 masses F d ( 1 , − 1 / 2) − 1 / 2 N 3 F u ( 1 , +1 / 2) +1 / 2 N 4 F d ( 1 , − 1 / 2) − 1 / 2 N • Introduce vector-like masses for 4 dark fermions that do not break EW symmetry L ⊃ + y u 14 ✏ ij F i 1 H j F d 4 + y d 14 F 1 · H † F u 4 − y d 23 ✏ ij F i 2 H j F d 3 − y u 23 F 2 · H † F u • Diagonalizing in the mass 3 + h.c. eigenbasis gives 4 Dirac fermions 1 F j L ⊃ M 12 ✏ ij F i 2 − M u 34 F u 3 F d 4 + M d 34 F d 3 F u 4 + h.c. • Assume custodial SU(2) symmetry y u 14 = y d y u 23 = y d M u 34 = M d arising when u ↔ d 14 23 34

Colliders SUSY Stealth LSP heavier superpartners scalar baryon baryon excited resonances Collider searches dominated by light meson production and decay. Missing energy signals largely absent! Stealth DM at colliders ρ VS. Π s Plot by G. Kribs

Colliders baryon excited Missing energy signals largely absent! SUSY resonances Collider searches dominated by light meson production and decay. scalar baryon superpartners heavier LSP Stealth Stealth DM at colliders ρ VS. Π s Plot by G. Kribs Signatures are not dominated by missing energy: DM is not the • lightest particle! The interactions are suppressed (form factors)

Colliders Stealth LSP heavier superpartners scalar baryon baryon excited resonances Collider searches dominated by light meson production and decay. Missing energy signals largely absent! SUSY Stealth DM at colliders ρ VS. Π s Plot by G. Kribs Signatures are not dominated by missing energy: DM is not the • lightest particle! The interactions are suppressed (form factors) Light meson production and decay give interesting signatures: • the model can be constrained by collider limits

Lattice Stealth DM 0.8 • Non-perturbative lattice Ê Ê 0.7 calculations of the spectrum spin 2 Ê Ê Ê Ê Ê Ê Ê spin 1 Ê 0.6 Ê confirm that lightest baryon Ê Ê Ê spin 0 Ê has spin zero 0.5 aM 0.4 • The ratio of pseudoscalar Ê 0.3 V Ê Ê Ê Ê Ê (PS) to vector (V) is used as Ê 0.2 PS Ê Ê Ê probe for different dark 0.1 0.50 0.55 0.60 0.65 0.70 0.75 fermion masses m PS ê m v • The meson to baryon mass • Study systematic effects ratio allows us to translate due to lattice discretization LEPII bounds on charged and finite volume due to the meson to LEP bounds on relative unfamiliar nature of composite bosonic dark the system matter [LSD collab., Phys. Rev. D89 (2014) 094508]

Lattice Stealth DM 0.8 • Non-perturbative lattice Ê Ê 0.7 calculations of the spectrum spin 2 Ê Ê Ê Ê Ê Ê Ê spin 1 Ê 0.6 Ê confirm that lightest baryon Ê Ê baryons Ê spin 0 Ê has spin zero 0.5 aM 0.4 • The ratio of pseudoscalar Ê 0.3 V Ê Ê Ê Ê Ê (PS) to vector (V) is used as Ê 0.2 PS Ê Ê Ê probe for different dark 0.1 0.50 0.55 0.60 0.65 0.70 0.75 fermion masses m PS ê m v • The meson to baryon mass • Study systematic effects ratio allows us to translate due to lattice discretization LEPII bounds on charged and finite volume due to the meson to LEP bounds on relative unfamiliar nature of composite bosonic dark the system matter [LSD collab., Phys. Rev. D89 (2014) 094508]

Lattice Stealth DM 0.8 • Non-perturbative lattice Ê Ê 0.7 calculations of the spectrum spin 2 Ê Ê Ê Ê Ê Ê Ê spin 1 Ê 0.6 Ê confirm that lightest baryon Ê Ê baryons Ê spin 0 Ê has spin zero 0.5 aM 0.4 • The ratio of pseudoscalar Ê 0.3 V Ê Ê Ê Ê Ê (PS) to vector (V) is used as Ê 0.2 mesons PS Ê Ê Ê probe for different dark 0.1 0.50 0.55 0.60 0.65 0.70 0.75 fermion masses m PS ê m v • The meson to baryon mass • Study systematic effects ratio allows us to translate due to lattice discretization LEPII bounds on charged and finite volume due to the meson to LEP bounds on relative unfamiliar nature of composite bosonic dark the system matter [LSD collab., Phys. Rev. D89 (2014) 094508]

Lattice Stealth DM 0.8 • Non-perturbative lattice Ê Ê 0.7 calculations of the spectrum spin 2 Ê Ê Ê Ê Ê Ê Ê spin 1 Ê 0.6 Ê confirm that lightest baryon Ê Ê baryons Ê spin 0 Ê has spin zero 0.5 aM 0.4 • The ratio of pseudoscalar Ê 0.3 V Ê Ê Ê Ê Ê (PS) to vector (V) is used as Ê 0.2 mesons PS Ê Ê Ê probe for different dark 0.1 0.50 0.55 0.60 0.65 0.70 0.75 fermion masses m PS ê m v • The meson to baryon mass • Study systematic effects ratio allows us to translate due to lattice discretization LEPII bounds on charged and finite volume due to the meson to LEP bounds on relative unfamiliar nature of composite bosonic dark the system matter [LSD collab., Phys. Rev. D89 (2014) 094508]

“How dark is Stealth DM?” Interactions of dark fermions with Higgs + Interactions of dark baryon with photon through form factors hf ¯ • dimension 4 ➥ Higgs exchange f [LSD collab., arxiv:1503.04205] (¯ χσ µ ν χ ) F µ ν • dimension 5 ➥ magnetic dipole Λ dark (¯ χχ ) v µ ∂ ν F µ ν • dimension 6 ➥ charge radius Λ 2 dark (¯ χχ ) F µ ν F µ ν • dimension 7 ➥ polarizability Λ 3 dark [LSD collab., arxiv:1503.04203]

“How dark is Stealth DM?” Interactions of dark fermions with Higgs + Interactions of dark baryon with photon through form factors hf ¯ • dimension 4 ➥ Higgs exchange f [LSD collab., arxiv:1503.04205] (¯ χσ µ ν χ ) F µ ν spin 0 • dimension 5 ➥ magnetic dipole Λ dark (¯ χχ ) v µ ∂ ν F µ ν • dimension 6 ➥ charge radius Λ 2 dark (¯ χχ ) F µ ν F µ ν • dimension 7 ➥ polarizability Λ 3 dark [LSD collab., arxiv:1503.04203]

“How dark is Stealth DM?” Interactions of dark fermions with Higgs + Interactions of dark baryon with photon through form factors hf ¯ • dimension 4 ➥ Higgs exchange f [LSD collab., arxiv:1503.04205] (¯ χσ µ ν χ ) F µ ν spin 0 • dimension 5 ➥ magnetic dipole Λ dark (¯ χχ ) v µ ∂ ν F µ ν custodial SU(2) • dimension 6 ➥ charge radius Λ 2 dark (¯ χχ ) F µ ν F µ ν • dimension 7 ➥ polarizability Λ 3 dark [LSD collab., arxiv:1503.04203]

“How dark is Stealth DM?” Interactions of dark fermions with Higgs + Interactions of dark baryon with photon through form factors hf ¯ • dimension 4 ➥ Higgs exchange f [LSD collab., arxiv:1503.04205] (¯ χσ µ ν χ ) F µ ν spin 0 • dimension 5 ➥ magnetic dipole Λ dark (¯ χχ ) v µ ∂ ν F µ ν custodial SU(2) • dimension 6 ➥ charge radius Λ 2 dark (¯ χχ ) F µ ν F µ ν • dimension 7 ➥ polarizability Λ 3 dark [LSD collab., arxiv:1503.04203]

Computing polarizability c F e 2 χ ? χ F µ ↵ F ⌫ ↵ v µ v ⌫ m 3 � χ χ p 0 p q = k 0 − k = p − p 0 ` ` − q k 0 k k + ` Nucleus Nucleus

Computing polarizability c F e 2 χ ? χ F µ ↵ F ⌫ ↵ v µ v ⌫ m 3 � χ χ p 0 p Lattice q = k 0 − k = p − p 0 ` ` − q k 0 k k + ` Nucleus Nucleus

Computing polarizability c F e 2 χ ? χ F µ ↵ F ⌫ ↵ v µ v ⌫ m 3 � χ χ p 0 p Lattice q = k 0 − k = p − p 0 ` ` − q Nuclear Physics k 0 k k + ` Nucleus Nucleus

[Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) [LSD collab., arxiv:1503.04203] 094505 and Phys. Rev. D81 (2010) 054502] Lattice: Polarizability of DM 32 3 x64 quenched lattices (large volume) one lattice spacing and two masses (matched) • Background field method: 40 sources on 200 independent configurations multi-exponential fits with 3 states for the baryon 0 . 93 response of neutral baryon SU(4) 0 . 92 E to external electric field E B 0 . 91 E 0 0 . 90 0 . 89 • Measure the shift of the 0 . 000 0 . 005 0 . 010 0 . 015 0 . 020 0 . 025 0 . 030 0 . 67 E SU(3) baryon mass as a function 0 . 66 0 . 65 E of E B E 0 0 . 64 0 . 63 0 . 62 E B, 4 c = m B + 2 C F |E| 2 + O 0 . 61 E 4 � � 0 . 00 0 . 01 0 . 02 0 . 03 0 . 04 E 0 . 05 SU(3) 0 . 00 − 0 . 05 2 C F − µ B 2 ✓ ◆ |E| 2 + O − 0 . 10 E 4 � � E B, 3 c = m B + Z r Z r − 0 . 15 8 m 3 − 0 . 20 B − 0 . 25 − 0 . 30 − 0 . 35 0 . 00 0 . 01 0 . 02 0 . 03 0 . 04 Z r = E µ B ( E ) E E 2 m 2 precise lattice results B

[Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) [LSD collab., arxiv:1503.04203] 094505 and Phys. Rev. D81 (2010) 054502] Lattice: Polarizability of DM 32 3 x64 quenched lattices (large volume) one lattice spacing and two masses (matched) • Background field method: 40 sources on 200 independent configurations multi-exponential fits with 3 states for the baryon 0 . 93 response of neutral baryon SU(4) 0 . 92 E to external electric field E B 0 . 91 E 0 0 . 90 0 . 89 • Measure the shift of the 0 . 000 0 . 005 0 . 010 0 . 015 0 . 020 0 . 025 0 . 030 0 . 67 E SU(3) baryon mass as a function 0 . 66 0 . 65 E of E B E 0 0 . 64 0 . 63 0 . 62 E B, 4 c = m B + 2 C F |E| 2 + O 0 . 61 E 4 � � 0 . 00 0 . 01 0 . 02 0 . 03 0 . 04 E 0 . 05 SU(3) 0 . 00 − 0 . 05 2 C F − µ B 2 ✓ ◆ |E| 2 + O − 0 . 10 E 4 � � E B, 3 c = m B + Z r Z r − 0 . 15 8 m 3 − 0 . 20 B − 0 . 25 − 0 . 30 − 0 . 35 0 . 00 0 . 01 0 . 02 0 . 03 0 . 04 Z r = E µ B ( E ) E E 2 m 2 precise lattice results B

[Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) [LSD collab., arxiv:1503.04203] 094505 and Phys. Rev. D81 (2010) 054502] Lattice: Polarizability of DM 32 3 x64 quenched lattices (large volume) one lattice spacing and two masses (matched) • Background field method: 40 sources on 200 independent configurations multi-exponential fits with 3 states for the baryon 0 . 93 response of neutral baryon SU(4) 0 . 92 E to external electric field E B 0 . 91 E 0 0 . 90 0 . 89 • Measure the shift of the 0 . 000 0 . 005 0 . 010 0 . 015 0 . 020 0 . 025 0 . 030 0 . 67 E SU(3) baryon mass as a function 0 . 66 0 . 65 E of E B E 0 0 . 64 0 . 63 0 . 62 E B, 4 c = m B + 2 C F |E| 2 + O 0 . 61 E 4 � � 0 . 00 0 . 01 0 . 02 0 . 03 0 . 04 E 0 . 05 SU(3) 0 . 00 − 0 . 05 2 C F − µ B 2 ✓ ◆ |E| 2 + O − 0 . 10 E 4 � � E B, 3 c = m B + Z r Z r − 0 . 15 8 m 3 − 0 . 20 B − 0 . 25 − 0 . 30 − 0 . 35 0 . 00 0 . 01 0 . 02 0 . 03 0 . 04 Z r = E µ B ( E ) E E 2 m 2 precise lattice results B

[Detmold, Tiburzi & Walker-Loud, Phys. Rev. D79 (2009) [LSD collab., arxiv:1503.04203] 094505 and Phys. Rev. D81 (2010) 054502] Lattice: Polarizability of DM 32 3 x64 quenched lattices (large volume) one lattice spacing and two masses (matched) • Background field method: 40 sources on 200 independent configurations multi-exponential fits with 3 states for the baryon 0 . 93 response of neutral baryon SU(4) 0 . 92 E to external electric field E B 0 . 91 E 0 0 . 90 0 . 89 • Measure the shift of the 0 . 000 0 . 005 0 . 010 0 . 015 0 . 020 0 . 025 0 . 030 0 . 67 E SU(3) baryon mass as a function 0 . 66 0 . 65 E of E B E 0 0 . 64 0 . 63 0 . 62 E B, 4 c = m B + 2 C F |E| 2 + O 0 . 61 E 4 � � 0 . 00 0 . 01 0 . 02 0 . 03 0 . 04 E 0 . 05 SU(3) 0 . 00 − 0 . 05 2 C F − µ B 2 ✓ ◆ |E| 2 + O − 0 . 10 E 4 � � E B, 3 c = m B + Z r Z r − 0 . 15 8 m 3 − 0 . 20 B − 0 . 25 − 0 . 30 − 0 . 35 0 . 00 0 . 01 0 . 02 0 . 03 0 . 04 Z r = E µ B ( E ) E E 2 m 2 precise lattice results B

Nuclear: Rayleigh scattering O M M M • it is hard to extract the momentum dependence of this nuclear form factor γ γ • similarities with the double-beta decay nuclear matrix element could suggest large uncertainties ~ orders of A A A magnitude f A = h A | F µ ν F µ ν | A i • to asses the impact of uncertainties on F the total cross section we start from naive dimensional analysis F ∼ 3 Z 2 α M A f A F M A R • we allow a “magnitude” factor to F change from 0.3 to 3 *� 2 + σ ' µ 2 c F e 2 � n χ f A � � [Pospelov & Veldhuis, Phys. Lett. B480 (2000) 181] � � F π A 2 m 3 [Weiner & Yavin, Phys. Rev. D86 (2012) 075021] � � χ [Frandsen et al., JCAP 1210 (2012) 033] [Ovanesyan & Vecchi, arxiv:1410.0601]

Nuclear: Rayleigh scattering O M M M • it is hard to extract the momentum dependence of this nuclear form factor γ γ • similarities with the double-beta decay nuclear matrix element could suggest large uncertainties ~ orders of A A A magnitude f A = h A | F µ ν F µ ν | A i • to asses the impact of uncertainties on F the total cross section we start from naive dimensional analysis F ∼ 3 Z 2 α M A f A F M A R • we allow a “magnitude” factor to F change from 0.3 to 3 *� 2 + σ ' µ 2 c F e 2 � n χ f A � � [Pospelov & Veldhuis, Phys. Lett. B480 (2000) 181] � � F π A 2 m 3 [Weiner & Yavin, Phys. Rev. D86 (2012) 075021] � � χ [Frandsen et al., JCAP 1210 (2012) 033] [Ovanesyan & Vecchi, arxiv:1410.0601]

Nuclear: Rayleigh scattering O M M M • it is hard to extract the momentum dependence of this nuclear form factor γ γ • similarities with the double-beta decay nuclear matrix element could suggest large uncertainties ~ orders of A A A magnitude f A = h A | F µ ν F µ ν | A i • to asses the impact of uncertainties on F the total cross section we start from naive dimensional analysis F ∼ 3 Z 2 α M A f A F M A R • we allow a “magnitude” factor to F change from 0.3 to 3 *� 2 + σ ' µ 2 c F e 2 � n χ f A � � [Pospelov & Veldhuis, Phys. Lett. B480 (2000) 181] � � F π A 2 m 3 [Weiner & Yavin, Phys. Rev. D86 (2012) 075021] � � χ [Frandsen et al., JCAP 1210 (2012) 033] [Ovanesyan & Vecchi, arxiv:1410.0601]

[LSD collab., arxiv:1503.04203] Stealth DM polarizability n χ ( M A 144 πα 4 µ 2 F ) 2 σ nucleon ( Z, A ) = Z 4 [ c F ] 2 A 2 m 6 χ R 2 �� × �� - �� �� - ������� ����� ������� ( �� � ) �� × �� - �� �� × �� - �� �� × �� - �� �� × �� - �� �� × �� - �� �� × �� - �� �� �� ��� ��� ���� ���� � � ( ��� )

[LSD collab., arxiv:1503.04203] Stealth DM polarizability n χ ( M A 144 πα 4 µ 2 F ) 2 σ nucleon ( Z, A ) = Z 4 [ c F ] 2 LUX exclusion A 2 m 6 χ R 2 bound for spin- independent cross �� × �� - �� section �� - ������� ����� ������� ( �� � ) �� × �� - �� �� × �� - �� �� × �� - �� �� × �� - �� �� × �� - �� �� × �� - �� �� �� ��� ��� ���� ���� � � ( ��� )

[LSD collab., arxiv:1503.04203] Stealth DM polarizability n χ ( M A 144 πα 4 µ 2 F ) 2 σ nucleon ( Z, A ) = Z 4 [ c F ] 2 LUX exclusion A 2 m 6 χ R 2 bound for spin- independent cross �� × �� - �� section �� - ������� ����� ������� ( �� � ) �� × �� - �� �� × �� - �� �� × �� - �� �� × �� - �� Coherent neutrino �� × �� - �� scattering background �� × �� - �� �� �� ��� ��� ���� ���� � � ( ��� )

[LSD collab., arxiv:1503.04203] Stealth DM polarizability n χ ( M A 144 πα 4 µ 2 F ) 2 σ nucleon ( Z, A ) = Z 4 [ c F ] 2 LUX exclusion A 2 m 6 χ R 2 bound for spin- independent cross �� × �� - �� section �� - ������� ����� ������� ( �� � ) �� × �� - �� �� × �� - �� �� × �� - �� LEPII bound on �� × �� - �� charged mesons Coherent neutrino �� × �� - �� scattering background �� × �� - �� �� �� ��� ��� ���� ���� � � ( ��� )

[LSD collab., arxiv:1503.04203] Stealth DM polarizability n χ ( M A 144 πα 4 µ 2 F ) 2 σ nucleon ( Z, A ) = Z 4 [ c F ] 2 LUX exclusion A 2 m 6 χ R 2 bound for spin- independent cross �� × �� - �� section �� - ������� ����� ������� ( �� � ) �� × �� - �� �� × �� - �� �� × �� - �� LEPII bound on �� × �� - �� charged mesons Coherent neutrino �� × �� - �� scattering background �� × �� - �� �� �� ��� ��� ���� ���� � � ( ��� ) lowest allowed direct detection cross-section for composite dark matter theories with EW charged constituents

Stealth DM polarizability 10 1 C [from arxiv:1307.5458] D D M A 10 2 M S I C l i ( 2 ) 0 1 2 t e ( 10 3 2 CoGeNT 0 1 (2012) 3 WIMP nucleon cross section pb ) 10 4 CDMS Si (2013) SIMPLE (2012) 10 5 COUPP (2012) DAMA ZEPLIN-III (2012) CRESST 10 6 CDMS II Ge (2009) ) 1 1 Xenon100 (2012) 0 2 ( S S 10 7 I E W L E D E O C H E LUX (2013) R E N T 10 8 7 Be N E Neutrinos U E T R T T R I A C N I N S O G 8 B 10 9 Neutrinos 10 10 C OHE R E NT NEU 10 11 N O SC AT TER ING T R I 10 12 E U s N o n T r i N t u E e R N E B H N O C S D d n a T R c G i r 10 13 I N e h p I R s N O E T o A T m t S C A 10 14 1 10 100 1000 10 4 WIMP Mass GeV c 2

Stealth DM polarizability 10 1 C [from arxiv:1307.5458] D D M A 10 2 M S I C l i ( 2 ) 0 1 2 t e ( 10 3 2 CoGeNT 0 1 (2012) 3 WIMP nucleon cross section pb ) 10 4 CDMS Si (2013) SIMPLE (2012) 10 5 COUPP (2012) DAMA ZEPLIN-III (2012) CRESST 10 6 CDMS II Ge (2009) ) 1 1 Xenon100 (2012) 0 2 ( S S 10 7 I E W L E �� �� - �� D E O C �� ������� ����� ������� ���� �� �� � H E LUX (2013) R E N T 10 8 7 Be N �� �� - �� E Neutrinos U E T R T T R I A C N I N S O G 8 B 10 9 �� �� - �� Neutrinos 10 10 �� �� - �� C OHE R E NT NEU 10 11 N O SC AT TER ING �� �� - �� T R I 10 12 E U s N o n T r i N t u �� �� - �� E e R N E B H N O C S D d n a T R c G i r 10 13 I N e h p I R s N O E T o A T m t S C A �� �� - �� 10 14 �� �� ��� ��� ���� ���� 1 10 100 1000 10 4 � �� ��� WIMP Mass GeV c 2 Direct detection signal is below the neutrino coherent scattering background for M B >1TeV

Concluding remarks • Composite dark matter is a viable interesting possibility with rich phenomenology • Lattice methods can help in calculating direct detection cross sections and production rates at colliders. Direct phenomenological relevance. • Dark matter constituents can carry electroweak charges and still the stable composites are currently undetectable. Stealth cross section.

[Berkowitz, Bucho ff , Rinaldi, arxiv:1505.07455, PRD] Part II • General features of axions as a solution of the Strong CP problem • Current physical constraints on axion models’ parameters based on dark matter interpretation • GOAL : Lower bound on the axion mass using lattice QCD as input to axion cosmology based on work with Evan Berkowitz and Michael Buchoff

[Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791] [Preskill, Wise & Wilczek, Phys Lett B 120 (1983) 127-132] Axion dark matter • Axions were originally proposed to deal with the Strong CP Problem • They also form a plausible DM candidate • The axion energy density requires non-perturbative QCD input • Being sought in ADMX (LLNL, UW) & CAST-IAXO (CERN) with large discovery potential in the next few years Ω tot = 1.000(7) • Requiring Ω a ≤ Ω CDM yields a lower PDG 2014 bound on the axion mass today

[Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791] [Preskill, Wise & Wilczek, Phys Lett B 120 (1983) 127-132] Axion dark matter • Axions were originally proposed to deal with the Strong CP Problem • They also form a plausible DM candidate • The axion energy density requires non-perturbative QCD input • Being sought in ADMX (LLNL, UW) & Lattice Field Theory Methods CAST-IAXO (CERN) with large discovery potential in the next few years Ω tot = 1.000(7) • Requiring Ω a ≤ Ω CDM yields a lower PDG 2014 bound on the axion mass today

“Strong CP” problem 1 • QCD has a parameter, θ 32 ⇡ 2 ✏ µ νρσ F µ ν F ρσ L QCD 3 ✓ • Controls QCD CP violation 1 Z d 4 x ✏ µ νρσ F µ ν F ρσ ∈ Z • Topological Q = 32 ⇡ 2 e iS ∝ e iQ θ • θ can take any value in (- π , π ]

“Strong CP” problem 1 • QCD has a parameter, θ 32 ⇡ 2 ✏ µ νρσ F µ ν F ρσ L QCD 3 ✓ • Controls QCD CP violation 1 Z d 4 x ✏ µ νρσ F µ ν F ρσ ∈ Z • Topological Q = 32 ⇡ 2 e iS ∝ e iQ θ • θ can take any value in (- π , π ] • Neutron EDM ≲ 3 10 -26 e cm [Baker et al., PRL 97, 131801 (2006) / hep-ex/0602020] • ⟹ | θ | ≲ 10 -10

“Strong CP” problem 1 • QCD has a parameter, θ 32 ⇡ 2 ✏ µ νρσ F µ ν F ρσ L QCD 3 ✓ • Controls QCD CP violation 1 Z d 4 x ✏ µ νρσ F µ ν F ρσ ∈ Z • Topological Q = 32 ⇡ 2 e iS ∝ e iQ θ • θ can take any value in (- π , π ] • Neutron EDM ≲ 3 10 -26 e cm [Baker et al., PRL 97, 131801 (2006) / hep-ex/0602020] Why is θ so • ⟹ | θ | ≲ 10 -10 small?

[Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791] Axions as a solution • Couple to topological charge ✓ a ◆ L axions = 1 1 2 ( @ µ a ) 2 + + ✓ 32 ⇡ 2 ✏ µ νρσ F µ ν F ρσ f a • Otherwise have shift symmetry a → a + α • Amenable to effective theory treatment V e ff ⇠ cos ( θ + c h a i ) • Axion mass from instantons effects a = ∂ 2 F � m 2 a f 2 � � ∂θ 2 � θ =0

[Peccei & Quinn: PRL 38 (1977) 1440, PR D16 (1977) 1791] Axions as a solution • Couple to topological charge ✓ a ◆ L axions = 1 1 2 ( @ µ a ) 2 + + ✓ 32 ⇡ 2 ✏ µ νρσ F µ ν F ρσ f a • Otherwise have shift symmetry a → a + α • Amenable to effective theory treatment QCD V e ff ⇠ cos ( θ + c h a i ) Topological Susceptibility • Axion mass from instantons effects a = ∂ 2 F � m 2 a f 2 � � ∂θ 2 � θ =0

Current axion constraints [ADMX Website]

Current axion constraints Over-closure constraint on axion mass [ADMX Website]

Current axion constraints • Two main models for light axions predict axion coupling to photons [KSVZ & DFSZ] • m a (f a ) is the only free parameter Over-closure constraint on • experiments look for a → γγ transitions axion mass • parameter space bound by astrophysical and cosmological constrains [ADMX Website]

The over-closure bound High temperature arguments imply χ vanishes as T → ∞ Sketches kindly provided by E. Berkowitz

The over-closure bound High temperature arguments imply χ vanishes as T → ∞ m 2 a f 2 a = χ Sketches kindly provided by E. Berkowitz

The over-closure bound High temperature arguments imply χ vanishes as T → ∞ m 2 a f 2 a = χ Universe cools as it expands Sketches kindly provided by E. Berkowitz

The over-closure bound High temperature arguments imply χ vanishes as T → ∞ m 2 a f 2 a = χ Universe cools as it expands Axions feel their mass when 3H ~ m a H: Hubble constant Sketches kindly provided by E. Berkowitz

The over-closure bound High temperature arguments imply χ vanishes as T → ∞ m 2 a f 2 a = χ Universe cools as it expands Axions feel their mass when 3H ~ m a T 1 ≈ 5.5 T c H: Hubble constant Sketches kindly provided by E. Berkowitz

The over-closure bound Axions feel their mass when 3H ~ m a T 1 ≈ 5.5 T c from models Sketches kindly provided by E. Berkowitz

The over-closure bound Axions feel their mass when 3H ~ m a T 1 ≈ 5.5 T c from models Axions continue to get heavier until the QCD phase transition Sketches kindly provided by E. Berkowitz

The over-closure bound Axions feel their mass when 3H ~ m a T 1 ≈ 5.5 T c from models Axions continue to get heavier until the QCD phase transition ρ ( t ) R 3 m a ( t ) = # axions in a fixed comoving volume Sketches kindly provided by E. Berkowitz

The over-closure bound Axions feel their mass when 3H ~ m a T 1 ≈ 5.5 T c from models Axions continue to get heavier until the QCD phase transition ρ ( t ) R 3 m a ( t ) = # axions in a fixed comoving volume energy density per co-moving volume is NOT invariant because the mass changes with time! Sketches kindly provided by E. Berkowitz

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound • Value of ρ when oscillations start ρ < Ω CDM = 0 . 12 given by FRW equations, EOM ρ c and m a (T) • χ PT today yields • m a (T) is provided by models. Note: assume PQ-symmetry is intact during inflation

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound • Value of ρ when oscillations start ρ < Ω CDM = 0 . 12 given by FRW equations, EOM ρ c and m a (T) • χ PT today yields • m a (T) is provided by models. Note: assume PQ-symmetry is intact during inflation

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound • Value of ρ when oscillations start ρ < Ω CDM = 0 . 12 given by FRW equations, EOM ρ c and m a (T) • χ PT today yields • m a (T) is provided by models. Note: assume PQ-symmetry is intact during inflation

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound • Value of ρ when oscillations start ρ < Ω CDM = 0 . 12 given by FRW equations, EOM ρ c and m a (T) • χ PT today yields • m a (T) is provided by models. f a ≤ (2.8 ± 2) 10 11 GeV m a ≥ 21 ± 2 μ eV Note: assume PQ-symmetry is intact during inflation

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound • Value of ρ when oscillations start ρ < Ω CDM = 0 . 12 given by FRW equations, EOM ρ c and m a (T) • χ PT today yields • m a (T) is provided by models. f a ≤ (2.8 ± 2) 10 11 GeV m a ≥ 21 ± 2 μ eV ( ± uncontrolled systematic) Note: assume PQ-symmetry is intact during inflation

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound [ADMX Website]

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound Wantz & Shellard IILM [ADMX Website]

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound Wantz & Shellard IILM systematic uncertainty? [ADMX Website]

[Wantz & Shellard, arXiv:0910.1066] State-of-the-art bound Wantz & Shellard IILM systematic uncertainty? Reliance on models is unnecessary: we can calculate m a2 f a2 from lattice QCD [ADMX Website]

Lattice results 0.45 ⌦ Q 2 ↵ � � χ = lim 0.4 Definition of Q N � V V →∞ Globally fit integer 64 � � � 80 � 0.35 96 � 144 � � � � � 0.3 � 1 / 4 / T c � � � � 0.25 � � � � � � 0.2 � � 0.15 � 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 2.3 2.4 2.5 T / T c

Lattice results 0.45 ⌦ Q 2 ↵ � � χ = lim 0.4 Definition of Q N � V V →∞ Globally fit integer 64 � � � 80 � 0.35 96 � 144 � � � � � 0.3 � 1 / 4 / T c � � � � 0.25 � � � � � � 0.2 � � 0.15 � • previous calculations stop at T/T c = 1.3 [arxiv:hep-lat/0203013] 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 2.3 2.4 2.5 T / T c • high precision data and careful systematic study

Model and extrapolation C χ = 0.5 N � T 4 ( T/T c ) n DIGM fit + statistical error 64 � c Systematic fitting error 80 � � � 96 � 0.4 144 � � � � � � 1 / 4 / T c � � 0.3 � �� �� �� �� 0.2 �� � � � 0.1 0. 1. 2. 3. 4. 5. 6. T / T c

Model and extrapolation C χ = 0.5 N � T 4 ( T/T c ) n DIGM fit + statistical error 64 � c Systematic fitting error 80 � � � 96 � 0.4 144 � � � � � � 1 / 4 / T c � � 0.3 � �� �� �� �� 0.2 �� � � � 0.1 • asymptotic large-T susceptibility in the DIGM model 0. 1. 2. 3. 4. 5. 6. [Gross&Ya ff e, RevModPhys.53.43] T / T c • fits lattice data of 𝜓 remarkably well for all temperatures

Axion oscillations f a [GeV] DIGM fit 9 H 2 f 2 a = m 2 a f 2 9 H 2 f a 2 / T c 4 , f a = 10 10 GeV a = χ 9 H 2 f a 2 / T c 4 , f a = 10 11 GeV 10 - 4 9 H 2 f a 2 / T c 4 , f a = 10 12 GeV 10 10 � / T c4 10 - 6 10 11 10 - 8 10 12 10 - 10 5 10 15 20 25 30 T / T c

Axion oscillations f a [GeV] DIGM fit 9 H 2 f 2 a = m 2 a f 2 9 H 2 f a 2 / T c 4 , f a = 10 10 GeV a = χ 9 H 2 f a 2 / T c 4 , f a = 10 11 GeV 10 - 4 9 H 2 f a 2 / T c 4 , f a = 10 12 GeV 10 10 � / T c4 10 - 6 10 11 10 - 8 10 12 10 - 10 5 10 15 20 25 30 T / T c T 1 (f a =10 10 )

Axion oscillations f a [GeV] DIGM fit 9 H 2 f 2 a = m 2 a f 2 9 H 2 f a 2 / T c 4 , f a = 10 10 GeV a = χ 9 H 2 f a 2 / T c 4 , f a = 10 11 GeV 10 - 4 9 H 2 f a 2 / T c 4 , f a = 10 12 GeV 10 10 � / T c4 10 - 6 10 11 10 - 8 10 12 10 - 10 5 10 15 20 25 30 T / T c T 1 (f a =10 10 ) T 1 (f a =10 11 )

Axion oscillations f a [GeV] DIGM fit 9 H 2 f 2 a = m 2 a f 2 9 H 2 f a 2 / T c 4 , f a = 10 10 GeV a = χ 9 H 2 f a 2 / T c 4 , f a = 10 11 GeV 10 - 4 9 H 2 f a 2 / T c 4 , f a = 10 12 GeV 10 10 � / T c4 10 - 6 10 11 10 - 8 10 12 10 - 10 5 10 15 20 25 30 T / T c T 1 (f a =10 10 ) T 1 (f a =10 11 ) T 1 (f a =10 12 )

Axion oscillations 40 T 1 Uncertainty 30 T 1 / T c 20 10 10 9 10 10 10 11 10 12 10 13 f a [ GeV ]

Axion energy density ρ ( t ) R 3 m a ( t ) = # axions in a fixed comoving volume

Axion energy density ✓ R ( T 1 ) ◆ 3 ρ ( T γ ) = ρ ( T 1 ) m a ( T γ ) T γ = 2 . 73K m a ( T 1 ) R ( T γ )

Axion energy density ✓ R ( T 1 ) ◆ 3 ρ ( T γ ) = ρ ( T 1 ) m a ( T γ ) T γ = 2 . 73K m a ( T 1 ) R ( T γ ) √ χ m a ( T 1 ) = T 1 = T 1 ( f a ) f a

Axion energy density ✓ R ( T 1 ) ◆ 3 ρ ( T γ ) = ρ ( T 1 ) m a ( T γ ) T γ = 2 . 73K m a ( T 1 ) R ( T γ ) √ χ m a ( T 1 ) = T 1 = T 1 ( f a ) f a m a ( T γ ) = 1 √ m u m d from χ PT f π m π m u + m d f a

Axion energy density ✓ R ( T 1 ) ◆ 3 ρ ( T γ ) = ρ ( T 1 ) m a ( T γ ) T γ = 2 . 73K m a ( T 1 ) R ( T γ ) √ χ m a ( T 1 ) = T 1 = T 1 ( f a ) f a m a ( T γ ) = 1 √ m u m d from χ PT f π m π m u + m d f a R ( T ) from cosmology

Axion energy density ✓ R ( T 1 ) ◆ 3 ρ ( T γ ) = ρ ( T 1 ) m a ( T γ ) T γ = 2 . 73K m a ( T 1 ) R ( T γ ) √ χ m a ( T 1 ) = T 1 = T 1 ( f a ) f a m a ( T γ ) = 1 √ m u m d from χ PT f π m π m u + m d f a R ( T ) from cosmology ρ ( T 1 ) = 1 2 m 2 a f 2 a θ 2 θ 1 random: PQ breaks after inflation 1

Axion energy density ✓ R ( T 1 ) ◆ 3 ρ ( T γ ) = ρ ( T 1 ) m a ( T γ ) T γ = 2 . 73K m a ( T 1 ) R ( T γ ) √ χ m a ( T 1 ) = T 1 = T 1 ( f a ) f a m a ( T γ ) = 1 √ m u m d from χ PT f π m π m u + m d f a R ( T ) from cosmology ρ ( T 1 ) = 1 2 m 2 a f 2 a θ 2 θ 1 random: PQ breaks after inflation 1 = π 2 θ 2 ⌦ ↵ 1 3