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Hierarchy of Hierarchies Hierarchy of HIerarchies Michael Dine Department of Physics University of California, Santa Cruz Northeastern University, in Honor of Pran Nath, May, 2019 Michael Dine Hierarchy of HIerarchies Princeton, 1982 Remember preprints? I won’t forget the arrival of a preprint at IAS by Arnowitt, Chamseddine and Nath, explaining how to think about supersymmetry and its breaking within the framework of supergravity. It was not aligned with my thinking at that moment, and I was very skeptical. On point after point, I was sure that they could not be correct, and each time, after some thought, I realized they were. That paper changed my understanding not just of supergravity but of the role of effective field theory in understanding loow energy effective field theory. From that time on, Pran has been a leader in the subject of supersymmetry, its phenomenology, and the study of its emergence in low energy effective field theories, and I want to acknowledge my debt to Pran today. Michael Dine Hierarchy of HIerarchies VOLUME 49, NUMBER 14 PHYSICAL REVIEW LETTERS $ QCTOBER 1982 symmetry. Brodsky, to be published. (11) I ocal gauge theory exposes an intimate 4Apart from the (p. q) ~ factors the convection terms relationship between internal symmetry and space- are of order q while in the usual cases the spin and contact terms are linear in When Dirac or vector time. Null zones, including the ancient dipole re- q. particles encounter a derivative coupling involving sult, show another face of this relationship, lead- their own field, quadratic terms appear and generally ing to more equations involving the internal vari- these violate the theorem. An important exception ables (e.g. , charge) and space-time (e.g. , mass- occurs for the Y~&g-Mills vertex, where a cancellation es and angles). occurs due to the cyclic nature of the gauge coupling. One of us (R.W.B.) is grateful for the hospitality ~The appearance of the current differences is easy of the theory group at Fermilab and for the sup- to understand by a complementary version of the theo- port of the National Science Foundation. We are rem. Namely, suppose that all of the j;/p; q factors were then vanishes charge conserva- indebted to Ken Kowalski for his help with phys- equal, M~(Vz) by tion, if we define all particles as outgoing. and his suggestions for the manuscript. ics D. R. Yennie, Lectures on Strong and E/ectxomag- netic Interactions (Brandeis, Massachusetts, 1963); J. D. Jackson, C/assica/ E/ect~odynamics (Wiley, New &'~On leave from Stanford Linear Accelerator Center, York, 1975), Chap. 14 and 15. Stanford University, Stanford, Cal. 94305. YR. W. Brown, D. Sahdev, and K. O. Mikaelian, Phys. & ~On leave from Case Western Reserve University, Rev. D 20, 1164 (1979). Cleveland, Ohio 44106. K. O. Mikaelian, M. A. Samuel, and D. Sahdev, Phys. We mean by this that the couplings involve no deriva- Rev. Lett. 43, 746 (1979). tives of Dirac fields and at most single derivatives of C. J. Goebel, F. Halzen, and J. P. Leveille, Phys. scalar and vector fields. Products of single derivatives Rev. D 23, 2682 (1981). Equation (8) can be shown to of distinct scalar fields are allowed. All vector deriva- agree with the factorization formula of this reference tive couplings must be of the Yang-Mills trilinear vari- for @=3, ety or products thereof. Such couplings include all re- Zhu Dorgpei, Phys. Rev. D 22, 2266 (1980). normalizable theories of current physical interest as "V. Bargmann, L. Michel, and V. L. Telegdi, Phys. weIl as an infinite class of nonrenormalizable theories Rev. Lett. 2, 435 (1959); S. J. Brodsky and J. R. Pri- corresponding to unrestricted numbers of fields. mack, Ann. Phys. (N.Y.) 52, 315 (1969). 2Attachments are made onto all charged lines and ' C. H. Llewellyn-Smith, Phys. Lett. 46B, 233 onto vertices with derivative couplings (seagulls). (1973); J. M. Cornwall, D. N. Levin, and T. Tiktopou- 3A much more detailed discussion will be presented los, Phys. Rev. Lett. 30, 1268 (1978), and 31, 572(E) elsewhere: R. W. Brown, K. L. Kowalski, and S. J. (1973). Locally Snpersymmetric Grand Unification A. H. Chamseddine, R. Arnowitt, and Pran Nath Department of Physics, Northeastern University, Boston, Massachusetts OZ115 (Received 12 July 1982) A locally supersymmetric grand unification program is proposed which couples the N = 1 supergravity multiplet to an arbitrary grand unified gauge group with any number of left-handed chiral multiplets and a gauge vector multiplet. A specific model is dis- cussed where it is shown that not only do the gravitational interactions eliminate the degeneracy of the vacuum state encountered in global supersymmetry, but simultaneous- ly they can. break both supersymmetry and SU(2) (3 U(1) down to a residual SU(3)'(m U(1) symmetry at 300 GeV. PA CS numbers: 12.10.En Recently much interest has been devoted to paper we propose a new type of supersymmetric supersymmetric grand unified theories. ' ' All grand unified model based on local supersym- existing supersymmetric grand unified models metry. We consider here N =1 supergravity' are based on global supersymmetry. In such coupled to left-handed chiral scalar' and gauge theories it is generally easy to break spontaneous- multiplets. ' We will see that the supergravity ly the internal, e.g. , SU(5), symmetry, but more couplings automatically produce a spontaneous difficult to break supersymmetry itself. In this breaking which removes the degeneracy of the 970 1982 The American Physical Society Michael Dine Hierarchy of HIerarchies The present moment: May, 2019 We have been obsessed with three hierarchy problems for several decades. 1 The weak scale hierarchy 2 The cosmological constant problem 3 The strong CP problem Michael Dine Hierarchy of HIerarchies There are other problems, which might fit in this list: Origin of the dark matter. Could be tied to one of the other problems (e.g. WIMPs in susy, axions for strong CP). Inflation: slow roll requires surprisingly light fields; possibly new, finely tuned scale; fine tuning to obtain sufficiently flat potential. Perhaps supersymmetry or compositeness? Alternatively, these might introduce their own independent hierarchies. We will not focus on these in this talk. Michael Dine Hierarchy of HIerarchies For each of these problems, proposed solutions: 1 Weak scale hierarchy: supersymmetry, dynamical electroweak symmetry breaking (technicolor, and variations), warped spaces, little Higgs, twin Higgs; dynamical explanations (“relaxion") 2 The strong CP problem: axions, mu = 0, Spontaneous CP violation (Nelson-Barr mechanism) 3 Cosmological constant problem: anthropic explanation, others(?) Michael Dine Hierarchy of HIerarchies Hierarchical ordering of hierarchies: Operator dimension. Lower dimension ) more finely tuned: 1 Cosmological constant: Dimension 0 2 Higgs mass: Dimension 2 3 FF~: Dimension 4 Michael Dine Hierarchy of HIerarchies Anthropic Hierarchy Given that the anthropic principle has raised its ugly head, it’s interesting to consider: which of these problems might most plausibly be solved by anthropic considerations: Ranking of problems by their potential anthropic significance: 1 Cosmological constant: must be small (everything else fixed) to satisfy the most primitive conditions for intelligent observers (existence of structure in the universe) 2 Weak scale hierarchy: might be solved anthropically, perhaps by demand of details required for carbon-based life (e.g. stellar processes) (Dimopoulos et al: “atomic principle") 3 θ: Hard to see significant consequence for existence of observers. θ ∼ 0:1 little consequence for stellar processes, nuclear physics,...(Ubaldi). I will discuss a recent suggestion of Kaloper/Terning. Michael Dine Hierarchy of HIerarchies Experimental Access to Natural Solutions Again, a hierarchy of how accessible these problems and their natural solutions might be to experimental test: 1 Cosmological constant: no compelling natural solution. Not clear what to search for. 2 Weak scale hierarchy: If susy, and if not significantly tuned, accessible to accelerators. At this point, much of parameter space excluded. Higgs mass troubling. In a simple-minded approach, points to scale of order 30 TeV or so. Probably have to live with significant tuning if SUSY plays any role. Alternatives to SUSY don’t fare much better. 3 Strong CP: Challenging. If dark matter produced in simplest cosmology, may be accessible to ADMX, other experiments. Lighter axions: proposals for search strategies. ADMX; other proposed searches will gradually sweep out parts of the parameter space. Michael Dine Hierarchy of HIerarchies Outline and plan: 1 The biggest problem: the c.c. Landscape/anthropic solutions. 2 Challenges to the traditional view of the electroweak hierarchy. Frame mainly in terms of supersymmetry. 3 Supersymmetry in a landscape – arguments against. 4 Supersymmetry in a landscape – an argument for. 5 Strong CP: a challenge to the landscape program Michael Dine Hierarchy of HIerarchies The Cosmological Constant Problem Within our hierarchy of hierarchies, the cosmological constant problem stands at the top. Because it involves contributions to the unit operator, it exhibits the most severe tuning. Because without (unbroken) supersymmetry, no known symmetry protects the cosmological constant, no (compelling) natural solution has been put forward. With supersymmetry, vanishing cosmological constant results from supersymmetry if: 1 Supersymmetry is unbroken 2 There is an unbroken R symmetry. In nature, supersymmetry is clearly badly broken. It is hard to see how supersymmetry can account naturally for a cosmological constant as small as we observe. Michael Dine Hierarchy of HIerarchies Anthropic solution of the cosmological constant: Weinberg with some updating Suppose the underlying theory (string theory(?)) possesses a vast number of (metastable) ground states. Among these, the cosmological constant is a random variable. Other constants of nature also presumably vary (“scan"). Consider that set where all other constants are as we observe, but the c.c. varies. Somehow (cosmologically) the universe samples all of these “vacua". Michael Dine Hierarchy of HIerarchies Weinberg (1987): Most of these universes will not contain intelligent observers.
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