Gauged U(1) clockwork Hyun Min Lee Chung-Ang University, Korea Based on arxiv: 1708.03564 Workshop on the Standard Model and Beyond Corfu, Greece, Sept 2-10, 2017.
Outline Introduction & motivation Gauged U(1) clockwork Examples: DM mediator, B-meson decays Conclusions Taken from Giudice, McCollough
Intensity vs energy frontiers Complementary direct probes for new physics with light particles or heavy particles. [SHiP physics case, 1504.04855]
New physics at weak scales Two hierarchically different masses: Planck scale vs weak scale in SM + GR. New symmetry protects Higgs mass against large quantum corrections and predicts new particles with sizable couplings at weak scale. No direct hint yet for new physics at weak scales.
New physics below weak scale QCD axion, sterile neutrinos, new long-range force, self-interacting dark matter, etc. New particles could be produced at low-energy experiments, such as ADMX, Belle-II, SHiP, etc. How new physics couples so weakly to the SM? Portal models: Higgs, Z, neutrino, axion, etc H 2 O new, F µ F 0µ, NO new a ALP F µ F µ, [Ilten et al, 2016]
Flavors of the SM The quark mixing in the SM well parametrized and no FCNC at tree level due to GIM mechanism. But, we don t know the origin of neutrino masses and flavor structure. Flavor violation is a precise probe of new physics at high scales, complementary to direct searches at the LHC
Beyond WIMP DM Various evidences for dark matter from galaxy rotation curves, CMB, and gravitational lensing, etc. No direct evidence for WIMP DM light or heavy? Simulation with CDM (cusp) overshoots galaxy rotation curves. (small-scale problems) self-interacting DM? CDM
Clockwork mechanism Multiple copies of symmetries are broken down to one symmetry by nearest neighbor interactions. L = 1 2 NX j=0 @ µ j @ µ j m 2 2 X ( j q j+1 ) 2, N 1 j=0 M 2 = { Zero mode: localized at j=0 for q>1 by mass protected by remaining symmetry, j =0 1 2 N 1 N N = 1 q N 1 = = 1 q N 0 1/q j e jka ; j! j + c q j.
Effective couplings Effective couplings of massless mode depend on the locations of external fields. L int = l O ext, l(x) = N 0 q l 0(x)+ NX k=1 a lk k(x). j =0 1 2 N 1 N l k zero mode massive O ext 0 { e.g. QCD axion: O ext = 1 f QCD G µ Gµ : L e = 1 f e 0G µ Gµ, [Kaplan, Rattazzi, 2015] l = N f e = q N f QCD f QCD. Large effective decay constant
UV-complete scalar CW Continuum limit: (x, y) = j (x), y= ja,(y = R Na) L = 1 NX @ µ j @ µ m 2 NX 1 j ( j q j+1 ) 2, 2 2 j=0 j=0 Z R apple 1 L = dy 0 2 (@ µ ) 2 1 2 (@ y + k ) 2 a! 0, m!1; Z ma! 1,q! 1. + dy (y R) O ext a : lattice distance [Giudice, McCollough, 2016] 5d dilaton background: = e ky, S = ky dilaton" Z R apple Z 1 + dy (y R)e 1 2 L S 5d = dy e S O ext, 2 @ M @ M KK reduction 0 0 e ky, n cos ny R zero mode massive kr n sin ny R, KK mass
Applications & generalization Axion-like scalars V = 4 1 NX 1 j=0 cos j f q V e = 4 2 cos j+1 f 0 f e + [Nilles, Kim, Peloso, 2014; Choi, Im, 2015; Kaplan, Rattazzi, 2015] + 4 N 2 cos f, f e = q N f. +, 1 2 See also K. Choi s talk! Fields with other spins Fermion clockwork Tensor clockwork Vector clockwork [Giudice, McCollough, 2016] e.g. neutrino masses spin-2 graviton topic of this talk!
Gauged U(1) clockwork N+1 local U(1) s broken down to U(1) by link fields: U(1) 0 U(1) 1 U(1) N! U(1) [HML, 2017] A 0 A 2 µ A 1 µ µ A N µ 2 A N µ 1 A N µ 0 1 N 2 N 1 =(1, q) h i i = 1 p 2 f Similar localization of massless mode at j=0 for q>1. Each U(1) gauge boson is expanded as A j µ(x) = N 0 q j Ã0 µ(x)+ NX a jk à j µ(x). k=1
Couplings to external fields Fermion interactions Boson interactions milicharge effective couplings : Remaining U(1) gauge boson has a naturally small mass due to extra Higgs field with milicharge.
UV-complete U(1) CW 5d kinetic term for Higgs requires new link fields S j. A 0 A 2 µ A 1 µ µ A N µ 2 A N µ 1 A N µ 0 1 N 2 N 1 ( =(1, q 1,q) ) ( ) hs j i =! f h j i = 1 p 2 (f + h j )e i j/f 5d limit is U(1) with dilaton coupling + decoupled Higgs. L 5d = Z R 0 dy e S apple 1 4 F MNF MN
U(1) as dark matter mediator Clockwork for an anomaly-free U(1) has interactions to dark matter χ at j=0 and SM fermions f at j=n. L Z 0 = q g Z 0 µ A 0 µ q f q Z 0 f µ fa N µ O dark j =0 1 2 N 1 N f apple M O SM f
U(1) as dark matter mediator DM annihilation DM self-scattering DM-nucleon scattering f Z 0 Z 0 f f f e 2k R M 2 0 + F 1(k R) k 2 suppressed 2! = q4 g 4 Z 0 m 2 F 1 (x) = sinh x x cosh x 4 sinh 2, x 4 1 M 2 0 + F 2(k R) k 2 large self-scattering F 2 (x) = 2 f p,n = c p,n q g 2 Z 0 sinh x cosh x x 1, x 1 1 4, x 1 4 sinh 2 x e 2k R. M 2 0 suppressed + F 1(k R) k 2
Self-interacting dark matter [Tulin, Yu, 2017] Z 0 DM self-interactions can solve small-scale problems at galaxies. self-scattering sub-gev dark matter or Sommerfeld effects
SIMP mechanism Self-scattering vs 3 2 annihilation Number-changing DM self-interactions [Carlson,Machacek, Hall (1992); Hochberg et al(2014); S-M Choi, HML (2015)] DM DM DM DM DM DM 2 e self = 2 e m 2 DM R = g DM e 3/2 x (2 ) 3/2 f Relic density: =0.1b e x f DM mdm 100 MeV 3 e DM DM h e vi = n DM h v 2 i = R self = 10 12 b Boltzmann-suppressed small annihilation Strongly Interacting Massive Particles (SIMP)
U(1) -mediated dark matter Z 0 Z 0 Z 0 Z 0 3 2 process (cf. J. Cline et al, 1702.07716) forbidden channels m <m Z 0 Large self-interaction & thermal freeze-out. [S.-M. Choi, Y.-J. Kang, HML, 2016] f Z 0 f 2 2 scattering for kinetic equilibrium & DM-electron scattering
B-meson decays from U(1) B-meson 2-3σ anomalies at LHCb might hint at violation of lepton flavor universality. B +! K + l + l B 0! K 0 l + l [June 24, 2014] [April 18, 2017] Minimal choice for bottom quark and non-lfu: U(1) B3 L 3 + lepton flavor mixing or mixing with U(1)Lµ L [Alonso et al, 2017] [Bian, Choi, Kang, HML, 2017]
U(1) clockwork & B-decays U(1) B-L clockwork with first two families and third family localized at different sites. x Effective family-dependent B-L: U(1) B3 L 3 [U(1) B L ] N+1 y 3rd F j =0 1 2 N 1 N 1st, 2nd F, B-meson G-fit: [Crivellin et al, 2017]
Model constraints LHC dimuon searches: b + xg Z 0 xg Z 0 g b b Neutrino trident production (CHARM-II, CCFR, NuTeV) < 1.45(2 ) m Z 0 yg Z 0 > 554 GeV. cf. similar bounds from tau decay.
Parameter space Lepton couplings gz 'y 4 3 2 1 σ(pp Z')xBR(Z' μ + μ - )(fb), m Z' =500GeV τ-decay ν-trident (g-2) μ 5fb 10fb [Bian, Choi, Kang, HML, 2017] C μ 9 1fb 0 0.00 0.01 0.02 0.03 0.04 0.05 g Z' x Quark couplings ATLAS-CONF-2017-027 LHC dimuon and tau decay/neutrino scattering are complementary in constraining B/L charges.
Conclusions Clockwork mechanism can explain effective small or large couplings due to the localization of fields, without a hierarchy of couplings. Scalar clockwork based on shift symmetry might allows for a common existence of QCD and large effective decay constants for axion. Gauged U(1) clockwork provides a mechanism to generate hierarchical gauge couplings, identified with a 5d massless U(1) with dilaton background. We showed examples with DM mediators and flavor-dependent U(1) for B-meson anomalis.