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Lattice Field Theory Beyond the Standard Model

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Lattice Field Theory Beyond the Standard Model Ethan T. Neil (Colorado) Lattice field theory for the USQCD Collaboration beyond the Standard Model LQCD-ext III Scientific Review July 9, 2019 Outline of talk 1. Motivation and overview 2. Background: the “theory space” of strongly- coupled gauge interactions 3. Science drivers for lattice BSM 4. USQCD science highlights 5. Conclusion "2 Lattice BSM Ethan Neil (Colorado) 1. Motivation/overview "3 Lattice BSM Ethan Neil (Colorado) Motivation • There are many motivations for studying models of new physics Beyond the Standard Model (BSM). Some excerpts from the P5 report:! • “Dark matter is presumed to consist of one or more kinds of new particles…”! • “What is the origin of neutrino mass?”! • “…Is there one Higgs particle or many? Is the new particle really fundamental, or is it composed of others?”! • Perturbative extensions of the SM are nice for the theorist, but sometimes physics is strongly coupled, e.g. QCD!! • If BSM physics is strongly coupled, lattice can give physics information that is otherwise inaccessible. "4 Lattice BSM Ethan Neil (Colorado) What kinds of BSM models? Composite Higgs: new strongly- coupled sector at the electroweak scale; Higgs is a composite bound state. (W/Z, top often have some composite part too.) Composite dark matter: dark “hidden sector” which is strongly coupled. Can appear naturally with composite Higgs or GUT theories. Supersymmetry (SUSY): hypothetical symmetry relating bosons to fermions. Supersymmetric SM requires SUSY breaking, where strong coupling can be relevant. "5 Lattice BSM Ethan Neil (Colorado) What kinds of BSM models? Composite Higgs: new strongly- coupled sector at the electroweak scale; Higgs is a composite bound state. (W/Z,Strongly-coupled top often have some quantum field theory! Exploringcomposite the rich part dynamics too.) of QFT at strong coupling cuts across all models; lattice is the only available non-perturbative definition Composite dark matter: dark We learn about strong dynamics from“hidden lattice, sector” even which if BSM is strongly model X is ruled out. (Like exploring QCDcoupled. at non-physical Can appear quark naturally mass.) with composite Higgs or GUT theories. Need to develop tools for studying strongly-coupled QFT now, to Supersymmetry (SUSY): hypotheticalbe ready symmetry for possible relating discovery at the LHC or elsewhere! bosons to fermions. Supersymmetric SM requires SUSY breaking, where strong coupling can be relevant. "6 Lattice BSM Ethan Neil (Colorado) 2. Background: “theory space” "7 Lattice BSM Ethan Neil (Colorado) Exploring the theory space (diagram: SU(Nc) gauge with Nf fermions in fundamental irrep) Asymptotic freedom lost Veneziano limit ’t Hooft limit Aside from specific models, lattice can give non-perturbative insight into the broader space of gauge-fermion theories, which exhibits: • rich phase structure (IR-conformal phase transition), • emergent dynamics (4d conformal field theories), • well-established trends (the ’t Hooft and Veneziano large-N limits.) "8 Lattice BSM Ethan Neil (Colorado) Aside: the infrared-conformal phase @g β(g) = β g3 β g5 ... • Many theories in the space are “cousins” @(log µ) 0 1 of QCD: color charges confine into a <latexit sha1_base64="x7iVdOTwx2gX945bZFO2B/3dQ3c=">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</latexit> ⌘ − − − spectrum of “hadron” bound states. g(μ) β(g) • In the infrared-conformal phase, gauge β<latexit sha1_base64="yhqvFEclCQYuLV3jW0qbr/ypGzs=">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</latexit> 0 > 0, β1 < 0 coupling g will approach an “infrared ∗ g fixed point”, freezing at some g=g*>0. g g∗ • This freezing restores scale invariance - UV IR we recover a conformal field theory (CFT). CFTs have a unique “spectrum” of operator anomalous dimensionsμ ; no confined bound states. β<latexit sha1_base64="F9GCYezBYc89cJMcBoh87xdbxnI=">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</latexit> 0 > 0, β1 > 0 • These CFTs can appear in many models of new physics, but only with broken scale invariance, since our world isn’t conformal! Still, learning about the symmetric limit is useful and important. (Analogous to supersymmetric BSM models: SUSY must be broken, but it’s still useful to describe the physics.) "9 Lattice BSM Ethan Neil (Colorado) Modeling the theory space • If we have models like ’t Hooft large-N expansion available, why do we need lattice? • Lattice gives quantitative information in a vast space for which we have only one real-world example (QCD). Allows us to: • Test and validate models of theory space • Search for novel phenomena that might require new models • Fill in details that the models don’t provide • Analogous to the Wigner-Eckart theorem in quantum mechanics. Symmetry gives us a big part of the story, but we still have to calculate the reduced matrix elements to make concrete predictions! (k) (k) j0,m0 Tˆ j, m = jk; mq jk; j0m0 j0 Tˆ j h<latexit sha1_base64="76a/0lM/jYQUnvndK/GVVjXXAco=">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</latexit> | q | i h | ih || || i "10 Lattice BSM Ethan Neil (Colorado) What about e$ective theories? • We can take a more bottom-up approach and say: just identify the right effective field theory (EFT) for collider physics, dark matter detection, etc. • Nothing wrong with this approach, but using only the EFT has limited predictive power: need to fix many (infinite!) low-energy constants from experiment. • Plus, EFT comes with an energy cutoff: fine for working in the low-energy limit at the threshold of discovery, but many details of the full theory are out of reach. • EFT + lattice allows analytic calculation but many LECs are determined from a handful of underlying UV parameters - best of both worlds! - t C ) C . 4 f. Leff , 3 tC4 WHY Luv = a tb "11 Lattice BSM Ethan Neil (Colorado) Example: electromagnetic polarizability of “dark baryons” (LSD Collaboration, arXiv:1503.04205) • “Stealth DM” model based on LUX direct-detection bound ) -�� SU(4) gauge group, with lightest � ��×�� �� ( baryon as dark matter! ��×��-�� -�� “Stealth DM” • Dark quarks carry electric charge, ��×�� polarizability but the baryon is net neutral; ��×��-�� LEP bound on (from lattice) symmetry —> leading interaction charged stealth ��×��-�� is EM polarizability - EFT operator mesons ��×��-�� ������� ����� ������� ���� �� - ��×��-�� �� �� �� ��� ��� ���� ���� mM (GeV)(GeV) • But EFT doesn’t tell us CF… ���BB(���) cosmic background with four quarks in a baryon, � CF may be heavily suppressed • Lattice calculation reveals no suppression if the quarks pair up into relative to SU(3); direct detection can dipoles due to Fermi statistics. probe the stealth model up to ~ TeV scale. "12 Lattice BSM Ethan Neil (Colorado) (see also: LatKMI Collaboration, arXiv:1305.6006 and 1403.5000) Example: emergence of a light scalar particle LSD Collaboration, arXiv:1601.04027 LatHC Collaboration, arXiv:1605.08750 σ π π σ • In QCD (and similar theories), pions are the lightest hadronic states by far, due to their pseudo- Goldstone boson nature. • But lattice studies in multiple theories (left: SU(3) Nf=8, right: SU(3) Nf=2 “sextet” irrep) revealed a surprising light 0++ scalar state as light as the pions! • This state has the same quantum numbers as the Higgs boson, and has been speculated to be a pseudo-dilaton associated with closeness to the IR-conformal transition. "13 Lattice BSM Ethan Neil (Colorado) 3. Science drivers for lattice BSM "14 Lattice BSM Ethan Neil (Colorado) Science drivers: questions for lattice model builders Concrete science goals which are driving our lattice investigations in the near term, divided by topic area. *: new questions added this year. 1)
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