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Two Notions of Naturalness For almost 40 years, the requirement that models of BSM physics be natural has heavily inuenced model-building in high-energy physics. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 1 / 60 The expectation of a natural solution to the hierarchy problem was probably the most popular argument for expecting new particles at the LHC. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 2 / 60 The Standard Model reigns supreme. As of today, the LHC has discovered no evidence for SUSY or any other mechanism for naturally stabilizing the weak scale. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 4 / 60 As of today, the LHC has discovered no evidence for SUSY or any other mechanism for naturally stabilizing the weak scale. The Standard Model reigns supreme. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 4 / 60 This has left many people in the HEP community unsure about how to proceed. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 5 / 60 Now What? Aspen 2013 - Higgs Quo Vadis Nathan Seiberg IAS TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA AA If neither supersymmetry nor any other sort of natural solution...appears in the data...[t]his would...give theorists a strong incentive to take the ideas of the multiverse more seriously. – Nima Arkani-Hamed (2012) Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 8 / 60 If the electroweak symmetry breaking scale is anthropically xed, then we can give up the decades long search for a natural solution to the hierarchy problem. – Steven Weinberg (2007) The principle of Naturalness, which has been guiding beyond the Standard Model (BSM) physics for several decades, is now in question, and the possibility that the electroweak (EW) scale is tuned by environmental selection in a multiverse looks increasingly alluring. – Asimina Arvanitaki et al. (2014) Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 10 / 60 There is already ongoing activity on how the concept of naturalness could be reshaped in post-natural times...The most daring approach of this kind is based on a multiverse populated by eternal ination, in conjunction with the idea that fundamental parameters may not necessarily be god-given numbers, but dynamical variables that take dierent values in a landscape of vacuum states. – Gian Francesco Giudice (2017) Others have presented a multiverse as providing a new framework in which we can embed (and perhaps answer) the problems of naturalness that have plagued us since the 1970s. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 11 / 60 Others have presented a multiverse as providing a new framework in which we can embed (and perhaps answer) the problems of naturalness that have plagued us since the 1970s. There is already ongoing activity on how the concept of naturalness could be reshaped in post-natural times...The most daring approach of this kind is based on a multiverse populated by eternal ination, in conjunction with the idea that fundamental parameters may not necessarily be god-given numbers, but dynamical variables that take dierent values in a landscape of vacuum states. – Gian Francesco Giudice (2017) Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 11 / 60 My aim in this talk is to distinguish two notions of naturalness now in play in BSM physics. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 12 / 60 This notion is an “autonomy of scales” requirement: low-energy physics should not depend too sensitively on high-energy physics. The rst notion is the best way to understand the general principle that we’ve been calling “naturalness” since the 1970s. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 13 / 60 The rst notion is the best way to understand the general principle that we’ve been calling “naturalness” since the 1970s. This notion is an “autonomy of scales” requirement: low-energy physics should not depend too sensitively on high-energy physics. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 13 / 60 It has culminated in the relatively recent notion of “stringy” or “landscape” naturalness. The second notion is a related, but distinct, statistical notion that began to come to prominence in the mid-90s. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 14 / 60 The second notion is a related, but distinct, statistical notion that began to come to prominence in the mid-90s. It has culminated in the relatively recent notion of “stringy” or “landscape” naturalness. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 14 / 60 Claim: The latter is not just a re-casting of the former. The two are distinct principles with distinct motivations. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 15 / 60 – Victor Weisskopf (1939) The recognition that there is something perverse about elementary scalar particles goes back at least to Victor Weisskopf: Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 17 / 60 The recognition that there is something perverse about elementary scalar particles goes back at least to Victor Weisskopf: – Victor Weisskopf (1939) Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 17 / 60 It is interesting to note that there are no weakly coupled scalar particles in nature; scalar particles are the only kind of free particles whose mass term does not break either an internal or a gauge symmetry. This discussion can be summarized by saying that mass or symmetry-breaking terms must be “protected” from large corrections at large momenta due to various interactions (electromagnetic, weak, or strong)...This requirement means that weak interactions cannot be mediated by scalar particles. – Kenneth G. Wilson (1971) This perversity became widely recognized as a problem through the 1970s as the EFT understanding caught on. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 18 / 60 This perversity became widely recognized as a problem through the 1970s as the EFT understanding caught on. It is interesting to note that there are no weakly coupled scalar particles in nature; scalar particles are the only kind of free particles whose mass term does not break either an internal or a gauge symmetry. This discussion can be summarized by saying that mass or symmetry-breaking terms must be “protected” from large corrections at large momenta due to various interactions (electromagnetic, weak, or strong)...This requirement means that weak interactions cannot be mediated by scalar particles. – Kenneth G. Wilson (1971) Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 18 / 60 Physicists have characterized the nature of the perversity in many ways. • The elementary scalar mass divergences quadratically! • No custodial symmetry protects the their masses from large radiative corrections! • All parameters should be of order 1! • The theory is ne-tuned! • The Standard Model is displeasing to my aesthetic taste! Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 19 / 60 Eective eld theory suggests this shouldn’t happen. The most well-motivated characterization is that light elementary scalars are perverse because their masses are very sensitive to the structure of the theory at high energies. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 20 / 60 The most well-motivated characterization is that light elementary scalars are perverse because their masses are very sensitive to the structure of the theory at high energies. Eective eld theory suggests this shouldn’t happen. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 20 / 60 Eective eld theory and RG methods are built on the assumption that one can analyze a physical process “one scale at a time”. ...that doesn’t help me to deal with the question of how to actually generate a workable renormalization group transformation...By 1971 I was ready to say: I’m going to divide the whole momentum continuum and to divide it up into slices so that their average momenta are separated by a factor of 2 and I’m going to try to make the simplest approximations I can, based on separating low momentum from high momentum at least qualitatively. – Kenneth Geddes Wilson (2002) Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 21 / 60 The RG tells us that given a high-energy theory, we can do the path integral over the high-energy degrees of freedom to produce a low-energy theory. The high energy physics contributes to low-energy scattering only by modifying the couplings of the low-energy theory (usually logarithmically) and through small corrections to the low-energy Green’s functions. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 22 / 60 [Naturalness] is the consequence of a reasonable criterion that assumes the lack of special conspiracies between phenomena occurring at very dierent length scales. It is deeply rooted in our description of the physical world in terms of eective theories. – Gian Francesco Giudice (2013) Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 23 / 60 Naturalness requires a more stringent autonomy of scales than we are strictly licensed to expect. Caveat 1: Nothing in the EFT machinery puts any bounds on the radiative corrections to the couplings. Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 24 / 60 Caveat 1: Nothing in the EFT machinery puts any bounds on the radiative corrections to the couplings.
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