Axions TAE 2018 Javier Redondo Universidad de Zaragoza Max Planck Institute für Physik Overview - Strong CP problem - Axions - Axion Dark matter - Searching for axions in the sky in the lab Parity and Time reversal in particle physics (electroweak interactions) P-violation (Wu 56) T-violation (CPLEAR 90’s) R(K¯ 0 K0) R(K0 K¯ 0) ! − ! R(K¯ 0 K0)+R(K0 K¯ 0) 60% ! ! 40% ... but not in the strong interactions many theories based on SU(3)c (QCD) 1 ↵ = G Gµ⌫ + iq¯γµD q qmq¯ + s ✓G Gµ⌫ LQCD −4 µ⌫a a µ − 8⇡ µ⌫a a q X e P,T conserving P,T violating we tend to forget this ↵s µ⌫ ✓Gµ⌫aGa induces P and T (CP) violation ✓ 8⇡ / e ✓ ( ⇡, ⇡) infinitely versions of QCD... all are P,T violating 2 − Neutron EDM 15 Most important P, T violating observable dn ✓ (10− )e cm ⇠ ⇥ O ✓ (1) ⇠ O EDM violates P,T The theta angle of the strong interactions - The value of ✓ controls P,T violation in QCD ✓ ⇡ ⇡ − 0 n n n n¯ n¯ n¯ 10 Measured today ✓ < 10− | | (strong CP problem) Roberto Peccei and Helen Quinn 77 QCD vacuum energy minimised at theta = 0 - ... if ✓ ( t, x ) is dynamical field, relaxes to its minimum Energy generated by QCD! ✓ ⇡ ⇡ − 0 n n¯ 10 Measured today ✓ < 10− | | (strong CP problem) ain’t you forgetting something? P. Higgs and a new particle is born ... - if ✓ ( t, x ) is dynamical field Energy generated by QCD! ✓ ⇡ ⇡ − 0 Field Excitations around the vacuum are particles clears the strong CP problem it’s a higgslet! like my favorite soap S. Weinberg F. Wiczek and a new particle is born ... the axion - if ✓ ( t, x ) is dynamical field Energy generated by QCD! ✓ ⇡ ⇡ − 0 Field Excitations around the vacuum are particles clears the strong CP problem it’s a higgslet! like my favorite soap and a new scale sets the game, fa - kinetic term for ✓ requires a new scale Energy generated by QCD! ✓ = a/fa ⇡ ⇡ − 0 ↵ 1 = s G Gµ⌫ ✓ + (@ ✓)(@µ✓)f 2 L✓ 8⇡ µ⌫a a 2 µ a e ↵s µ⌫ a 1 µ ✓ = Gµ⌫aGa + (@µa)(@ a) L 8⇡ fa 2 e How to get the axion-term? - Peccei-Quinn idea: New symmetry, spontaneously broken Goldstone theorem: Global continuous symmetry SB -> massless boson Other terms that preserve the symmetry ✓<latexit sha1_base64="v5PgnYvWR82Fe3koxMBimu9WFQc=">AAACAXicZVBdSwJBFJ21L7Mvq4ceelkSIQhkV5PVN6GXHg3yA1yRu+Oog7MfzNwNRHzqp/QUFESv/Yye+jeN7hJZBwYO59zLnXO8SHCFlvVlZDY2t7Z3sru5vf2Dw6P88UlbhbGkrEVDEcquB4oJHrAWchSsG0kGvidYx5veLP3OA5OKh8E9ziLW92Ec8BGngFoa5M9cnDAEF0MzYVcuiGgCg3zBKlkrmP+JnZICSdEc5D/dYUhjnwVIBSjVs60I+3OQyKlgi5wbKxYBncKY9TQNwGeqP18FWJhFrQzNUSj1C9Bcqb835uArNfM9PekDTtRfbyn+eMW1Uziq9ec8iGJkAU0ujWJh6rzLOswhl4yimGkCVHL9WZNOQAJFXVpu1YJddpyqrcPX63WnWkmIVan9tNAul2w9dnddaNTSPrLknFyQS2IThzTILWmSFqFkQZ7IC3k1Ho1n4814T0YzRrpzStZgfHwDQxuW5g==</latexit> ✓ + ↵ f 2 ! µ V (✓)=0 ? = (@µ✓)(@ ✓)+... symmetry protects the mass and other non-derivativeinteractions <latexit sha1_base64="2EgSZUwzH769Fu8YlMr2aPyXvXM=">AAAB83icZVDLSgMxFM34rPVVdekmWAp1U2Zay7QLoeDGZQX7gHYomTTThmYeJHeEMvQzXAkK4tavceXfmE6HYvVA4HDOudyb40aCKzDNb2Nre2d3bz93kD88Oj45LZydd1UYS8o6NBSh7LtEMcED1gEOgvUjyYjvCtZzZ3dLv/fEpOJh8AjziDk+mQTc45SAlgbd8hCmDMj1rTkqFM2KmQL/J1ZGiihDe1T4Go5DGvssACqIUgPLjMBJiAROBVvkh7FiEaEzMmEDTQPiM+Uk6ckLXNLKGHuh1C8AnKq/JxLiKzX3XZ30CUzVX28prr3SxirwGk7CgygGFtDVJi8WGEK8LACPuWQUxFwTQiXXx2I6JZJQ0DXl0xasqm3XLf35ZrNp12srYtYa6xa61YqlYw83xVYj6yOHLtEVKiML2aiF7lEbdRBFIXpGr+jNiI0X4934WEW3jGzmAm3A+PwBtNOQ8w==</latexit> L<latexit sha1_base64="CW8R3SRExDnnmy3F8Tag6LOQ1AM=">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</latexit> 2 Quantum level .... If symmetry is color anomalous -> anomalous 2-gluon coupling g ↵s µ ?+=N GG✓ JA µ L<latexit sha1_base64="aO5/uQ+dMATmuMCc0an9Xdf9a6g=">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</latexit>sha1_base64="OBnuSyfyJRsY2XmuOu9Zpouqn/w=">AAAB2nicZVBNS8NAEJ3Urxqr1rOXxVLwVBIvehS8eKxgW6ENZbOZtEs3m7A7EUrpH/DiQRD/lyf/jdsPxLYPBh7vzTAzLy6UtBQEP15lb//g8Kh67J/U/NOz83qta/PSCOyIXOXmJeYWldTYIUkKXwqDPIsV9uLJw8LvvaKxMtfPNC0wyvhIy1QKTk5qD+uNoBUswXZJuCYNWGNY/x4kuSgz1CQUt7YfBgVFM25ICoVzf1BaLLiY8BH2HdU8QxvNlmfOWdMpCUtz40oTW6r/J2Y8s3aaxa4z4zS2295C/POaG6sovYtmUhcloRarTWmpGOVs8TRLpEFBauoIF0a6Y5kYc8MFuWh8F0K4/fIu6d60wqAVPgVQhUu4gmsI4Rbu4RHa0AEBCbzBhye9d+9zFVbFW6d2ARvwvn4BtGyKYg==</latexit>sha1_base64="xu7lVrBbe9sUQ2y+RLLOMb1WeZA=">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</latexit>sha1_base64="AyEeD4C75RC7Lv5x5KVJRw/A/f4=">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</latexit>sha1_base64="4Z1PoF/ocBEHZ14UY+Lmi/Vmsro=">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</latexit> 8⇡ @µJ5 q g N = number of quarks running ein the loop ~number of quarks charged under PQ symmetry a a ✓ ,N✓ fa = f/N <latexit sha1_base64="nPFp6+w9F4Rw8NXS5HEDWextpSo=">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</latexit> ⌘ f ⌘ fa ! Simple model KSVZ - Peccei-Quinn symmetry, color anomalous, spontaneously broken at fa 1 µ 4 2 2 = + iQDQ¯ + (@ σ)(@ σ⇤) (yQ¯ Q σ +h.c) λ σ + µ σ L LSM 2 µ − L R − | | | | a(x) i 2 σ(x)=⇢(x)e fa fa = µ /2λ a p f ~ 1 2 ↵s a - At energies below f a (SSB) (@a) + GG L22 8⇡ fa 0 e - At energies below ⇤ QCD , a ⌘ 0 ⇡ ⌘ ... mixing ~GeV − − − − 9 m⇡f⇡ 10 GeV axion mass ma 6meV ' fa ⇠ fa ¯ µ a ↵ µ⌫ a couplings a,I = cN,aNγ γ5N + caγ Fµ⌫ F + ... L fa 2⇡ fa XN nucleons ... photons ... e mesons ... ENERGY couplings - Shift symmetry allows some generic types of interactions 1 ↵ = (@ ✓)(@µ✓)f 2 + c [f¯γµγ f]@ ✓ E F F µ⌫ ✓ La 2 µ f 5 µ − 8⇡ µ⌫ Xf 1 µ gaγ µe⌫ 1 a = (@µa)(@ a)+ gaf [f¯γ5f]a Fµ⌫ F a (canonically normalised) g L 2 − 4 <latexit sha1_base64="n5NKewxQMcOKpnRbKoyS3uLKUYs=">AAACAHicZVDLSsNAFJ3UV62vqODGTbAUXJWktaTdVdy4rGAf0IQwmU7aoZNMmJkIJXbjp7gSFMStv+HKv3GahmL1wIXDOfdy7z1+TImQpvmtFTY2t7Z3irulvf2DwyP9+KQnWMIR7iJGGR/4UGBKItyVRFI8iDmGoU9x35/eLPz+A+aCsOhezmLshnAckYAgKJXk6WdjJ+YslsxwAg5Ras3TwLuee3rZrJoZjP/EykkZ5Oh4+pczYigJcSQRhUIMLTOWbgq5JIjieclJBI4hmsIxHioawRALN83unxsVpYyMgHFVkTQy9fdECkMhZqGvOkMoJ+KvtxBXXmVtlQyabkqiOJE4QstNQUIN9e8iDWNEOEaSzhSBiBN1rIEmUAUhVWalLAWrZtsNSz3farXsRn1JzHpzlUKvVrVU291Vud3M8yiCc3ABLoEFbNAGt6ADugCBR/AMXsGb9qS9aO/ax7K1oOUzp2AN2ucP16iWsg==</latexit> / fA Xf - Color anomaly breaks explicitly shift symmetry -> axione mass + interactions (EDM+...) 2 ↵ µ⌫ ↵s µ⌫ A 1 A 1 2 2 N heavy-Q N Gµ⌫ G ✓ Gµ⌫ G V (A) χQCD = mAA 8⇡ ⌘ 8⇡ fA ⇠ 2 fA 2 n o n o ✓ ◆ e e electron coupling nucleon coupling g [¯eγ e]a g [N¯γ N]a photon coupling ef 5 Nf 5 CP Neutron electric dipole gaγ µ⌫ 1 µ⌫ A Fµ⌫ F a [Fµ⌫ n¯σ γ5n] − 4 / mn fA FCNC e g f¯γ f 0 <latexit sha1_base64="1ET9KzK6JCVwe9/78vdm/P2WzZY=">AAACBHicZVDLSgNBEJyNrxhfUW96GQwhnsJuYkhyC3jxGME8IAlL72Q2GTKzu8zMCmEJePJTPAkK4tWf8OTfOHkgRutUVFXT3eVFnClt219WamNza3snvZvZ2z84PMoen7RVGEtCWyTkoex6oChnAW1ppjntRpKC8DjteJPrud+5p1KxMLjT04gOBIwC5jMC2khu9mzkJuD7hVnfA4l93B+BEOBWsF9wszm7aC+A/xNnRXJohaab/ewPQxILGmjCQameY0d6kIDUjHA6y/RjRSMgExjRnqEBCKoGyeKHGc4bZYj90BwRBhov1N8TCQilpsIzSQF6rP56c/HHy6+t0n5tkLAgijUNyHKTH3OsQzxvBA+ZpETzqSFAJDPHYjIGCUSb3jKLFpxStVpxzPP1er1aKS+JXa79tNAuFR0Tu73KNWqrPtLoHF2gS+SgKmqgG9RELUTQA3pCL+jVerSerTfrfRlNWauZU7QG6+Mb7XqXHQ==</latexit>