Two Notions of Naturalness

Home , Gian Francesco Giudice, Riccardo Barbieri

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?

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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.

– 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.

Naturalness requires a more stringent autonomy of scales than we are strictly licensed to expect.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 24 / 60 Indeed, one plausible diagnosis for the diculty with constructing a satisfactory measure of naturalness is that it runs afoul of an Aristotelian dictum:

It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits.

– Aristotle (∼ 340 BCE)

Caveat 2: This is not a precise criterion. It is a somewhat loose physical heuristic.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 25 / 60 Caveat 2: This is not a precise criterion. It is a somewhat loose physical heuristic.

Indeed, one plausible diagnosis for the diculty with constructing a satisfactory measure of naturalness is that it runs afoul of an Aristotelian dictum:

It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits.

– Aristotle (∼ 340 BCE)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 25 / 60 This is capable of underwriting several popular but prima facie less plausible readings of naturalness.

Nevertheless, understanding naturalness as a prohibition on “undue” sensitivity of low-energy physics to high-energy physics provides a plausible physical justication for many of the characterizations of the perversity of elementary scalars.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 26 / 60 Nevertheless, understanding naturalness as a prohibition on “undue” sensitivity of low-energy physics to high-energy physics provides a plausible physical justication for many of the characterizations of the perversity of elementary scalars.

This is capable of underwriting several popular but prima facie less plausible readings of naturalness.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 26 / 60 One often hears that naturalness problems have something to do with the fact that dimensionless parameters in an EFT should be of order one.

We naturally expect that dimensionless ratios of parameters in our theories should be of order unity, where the phrase “order unity” is interpreted liberally between friends, say anywhere from 10−2 or 10−3 to 102 or 103. – Tony Zee (2010)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 27 / 60

For a given physical process, one would can estimate (at tree-level) the contribution of an operator in an EFT based more or less entirely on the scales involved in the problem.

The demand that dimensionless parameters in an EFT be of order one is best understood as an expectation of the separation of scales.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 29 / 60 The demand that dimensionless parameters in an EFT be of order one is best understood as an expectation of the separation of scales.

For a given physical process, one would can estimate (at tree-level) the contribution of an operator in an EFT based more or less entirely on the scales involved in the problem.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 29 / 60 In a simple scalar EFT with a cuto Λ and dimensionless couplings gn, one can estimate the tree-level contribution of an operator On to a scattering process as

E n−2 E n O → g or O → g n n Λ n n Λ

where E is the scattering energy.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 30 / 60 Dimensionless couplings that are 1 or 1 drag an operator away from the energy scale where it naturally lives.

One should not have to set any of the gn in a way that articially amplies or suppresses an operator’s contribution to processes at a scale E.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 31 / 60 One should not have to set any of the gn in a way that articially amplies or suppresses an operator’s contribution to processes at a scale E.

Dimensionless couplings that are 1 or 1 drag an operator away from the energy scale where it naturally lives.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 31 / 60 Perhaps the most common way of characterizing the perversity of elementary scalars is to say that they require ne-tuning.

Fine; the problem isn’t the size of the dimensionless parameters. The problem is that they are ne-tuned.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 32 / 60 Fine; the problem isn’t the size of the dimensionless parameters. The problem is that they are ne-tuned.

Perhaps the most common way of characterizing the perversity of elementary scalars is to say that they require ne-tuning.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 32 / 60 2 2 X 2 mphys = mbare + Mi + logarithms i

Scalar masses receive quadratic corrections from every heavy particle to which they couple.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 33 / 60 Scalar masses receive quadratic corrections from every heavy particle to which they couple.

2 2 X 2 mphys = mbare + Mi + logarithms i

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 33 / 60 2 One must choose mbare at the cuto scale very delicately in order to cancel the radiative corrections and reproduce the measured physical mass of the scalar.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 34 / 60 A model is ne-tuned if a plot of its allowed parameter space makes you wanna puke.

– David Kaplan (2007)

...the extremely delicate adjustment of parameters needed to answer such basic questions seems incredibly implausible...It is as though we see a pencil standing on its tip in the middle of a table.

– Nima Arkani-Hamed (2012)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 35 / 60 ...the extremely delicate adjustment of parameters needed to answer such basic questions seems incredibly implausible...It is as though we see a pencil standing on its tip in the middle of a table.

– Nima Arkani-Hamed (2012)

A model is ne-tuned if a plot of its allowed parameter space makes you wanna puke.

– David Kaplan (2007)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 35 / 60 Original attempts to make this nausea precise were justied by an appeal to the autonomy of scales in EFT.

Let us nally spend a word on the signicance of the “naturalness” criterion that we are employing...There is no known example of cancellation between a quadratic divergence in the low energy theory and contributions from shorter distances.

– Riccardo Barbieri & Gian Francesco Giudice (1988)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 36 / 60 Following Barbieri & Giudice, one can construct “sensitivity parameters” which capture how sensitive certain low energy parameters, like the mass of the Z boson, are to variations in some set of high energy parameters ai.

a ∂M2 ∆ = i Z i 2 MZ ∂ai

with the sensitivity of a model given by ∆ ≡ max(∆i).

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 37 / 60 General strategy for this in HEP: • Pick a model (e.g. Standard Model) • Select low-energy parameter(s) (e.g. the W or Z mass) • Select high-energy parameters (e.g. parameters related to SUSY-breaking) • Take derivatives of low-energy parameters w.r.t. high-energy parameters • Dene the amount of “tuning” in the model as the maximum value of the derivatives.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 38 / 60 As opposed to, say, the proton mass.

Although one has to make somewhat arbitrary choices in this process, these measures can plausibly be justied within the EFT framework insofar as they aim to precisify the sense that elementary scalar masses are “unduly” sensitive to high energy physics.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 39 / 60 Although one has to make somewhat arbitrary choices in this process, these measures can plausibly be justied within the EFT framework insofar as they aim to precisify the sense that elementary scalar masses are “unduly” sensitive to high energy physics.

As opposed to, say, the proton mass.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 39 / 60 However, in the mid-1990s these sensitivity measures began to be re-interpreted as measures of probability: a model was more “natural” if and only if it was more “likely”.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 40 / 60 [The Barbieri & Giudice measure] is really a measure of sensitivity, and sensitivity does not automatically translate into ne tuning.

···

We construct a family of quantitative measures of ne tuning. [...] Our purpose is twofold. First, we wish to systematically clarify what measures of ne tuning best quantify our intuitive notion of naturalness and how these measures should be normalized. Second, we wish to make explicit the inherent, discretionary assumptions present in any standard that quanties naturalness.

– Greg Anderson & Diego Castano (1995)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 41 / 60 ...ne tuning may also be characterised by instability. It is this instability which the traditional measure is exploiting. Instead we wish to construct a tuning measure which determines how rare or atypical certain physical scenarios are.

– Peter Athron & David Miller (2007)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 42 / 60 These have taken on a life of their own, departing from the original physical motivation for naturalness.

For example, they commonly assign a high degree of ne-tuning to the QCD scale ΛQCD, a paradigmatically natural scale hierarchy.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 43 / 60 It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits.

– Aristotle (∼ 340 BCE)

So it is clear that measures of tuning have no intrinsic meaning...One frequently comes across models that are constructed using a legalistic interpretation of naturalness that fails an intuitive sni test. I would prefer we exercise our physical judgment when weighing naturalness. Perhaps a reasonable criterion in the context of model-building is to ask if the IR theory is a generic function of the UV parameters, but not commit overly much to specic measures.

– Nathaniel Craig (2014)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 44 / 60 So it is clear that measures of tuning have no intrinsic meaning...One frequently comes across models that are constructed using a legalistic interpretation of naturalness that fails an intuitive sni test. I would prefer we exercise our physical judgment when weighing naturalness. Perhaps a reasonable criterion in the context of model-building is to ask if the IR theory is a generic function of the UV parameters, but not commit overly much to specic measures.

– Nathaniel Craig (2014)

It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits.

– Aristotle (∼ 340 BCE)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 44 / 60 The rise in the probabilistic or statistical interpretation of naturalness has culminated in proposals to re-cast naturalness in the landscape.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 45 / 60

If the property in question is common among these “anthropically acceptable” vacua then the property is natural. By common I mean that some non-negligible fraction of the vacua have the required property. If however, the property is very rare, even among this restricted class, then it should be deemed unnatural. – Leonard Susskind (2004)

If all the multiverse does is allow for the existence of a region that resembles our own, it adds nothing to our understandings...instead, the possible epistemological role of the multiverse is to explain why our observed parameters are natural.

– Sean Carroll (2006)

An eective eld theory (or specic coupling, or observable) T1 is more natural in string theory than T2, if the number of phenomenologically acceptable vacua leading to T1 is larger than the number leading to T2. – Michael Douglas (2004)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 47 / 60 If all the multiverse does is allow for the existence of a region that resembles our own, it adds nothing to our understandings...instead, the possible epistemological role of the multiverse is to explain why our observed parameters are natural.

– Sean Carroll (2006)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 47 / 60 An eective eld theory (or specic coupling, or observable) T1 is more natural in string theory than T2, if the number of phenomenologically acceptable vacua leading to T1 is larger than the number leading to T2. – Michael Douglas (2004)

– Sean Carroll (2006) Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 47 / 60 The general strategy is to begin with a large set of vacua across which parameters are allowed to vary.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 48 / 60 • “phenomenologically acceptable” (restrict attention to EFTs with d = 4, no unbroken SUSY, at least 3 generations, etc.) • “anthropically acceptable” (restrict attention to EFTs with values of parameters that do not rule out observers)

One then typically oers some selection criteria that justies restricting attention to a subset of vacua.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 49 / 60 One then typically oers some selection criteria that justies restricting attention to a subset of vacua.

• “phenomenologically acceptable” (restrict attention to EFTs with d = 4, no unbroken SUSY, at least 3 generations, etc.) • “anthropically acceptable” (restrict attention to EFTs with values of parameters that do not rule out observers)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 49 / 60 Most likely = Most (landscape) natural

Having done that, one places some measure of probability on the selected vacua and determines which EFTs are most likely in this landscape.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 50 / 60 Having done that, one places some measure of probability on the selected vacua and determines which EFTs are most likely in this landscape.

Most likely = Most (landscape) natural

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 50 / 60 In the absence of other candidate solutions to the problem, we might even turn this around and call these ideas evidence for the hypothesis that we are in a compactication with many hidden sectors. – Michael Douglas (2004)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 51 / 60 This pattern of unnaturalness in three dierent arenas, cosmology, nuclear physics, and electroweak symmetry breaking, provides evidence for the multiverse, since each problem may be easily solved by environmental selection.

– Lawrence Hall and Yasunori Nomura (2008) It may even be reasonable to invest time in understanding what parameter ranges are hospitable to human life in order to focus our attention on some subset of the vacua.

It seems eminently reasonable to see whether “most” vacua in the landscape reproduce the general structure of the Standard Model and whether certain ranges of parameters are more prevalent than others.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 53 / 60 It seems eminently reasonable to see whether “most” vacua in the landscape reproduce the general structure of the Standard Model and whether certain ranges of parameters are more prevalent than others.

It may even be reasonable to invest time in understanding what parameter ranges are hospitable to human life in order to focus our attention on some subset of the vacua.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 53 / 60 My claim is that solving these problems does not amount to solving the naturalness problem that we began with in the 1970s.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 54 / 60 One way of seeing this is that weak-scale SUSY – the dominant natural solution to the hierarchy problem – need not be “stringy natural”!

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 55 / 60 This is an extremely strong constraint which very much disfavors the natural solutions to the hierarchy problem...perhaps we should not be too bothered by this, but we should ask for some more fundamental reason why ΛSUSY ∼ 30 − 100 TeV. Later we are going to argue this from stringy naturalness...

– Michael Douglas (2012)

Are the vacua with anthropically small enough cosmological constants and Higgs masses numerically dominated by low-energy supersymmetry or by supersymmetry breaking at very high energy scales? In other words is low energy supersymmetry breaking natural? My conclusion...is that the most numerous “acceptable vacua” do not have low energy supersymmetry. Phenomenological supersymmetry appears to be unnatural.

– Leondard Susskind (2004)

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 56 / 60 Whether a model is “stringy” natural depends wholly on the distribution of vacua; the “stringy naturalness” of a model is extrinsic to the model itself.

Understood in the previous “autonomy of scales” sense, the naturalness of a model was an intrinsic property of the model.

More generally, it is not surprising that what the two criteria count as “natural” can and will come apart.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 57 / 60 More generally, it is not surprising that what the two criteria count as “natural” can and will come apart.

Whether a model is “stringy” natural depends wholly on the distribution of vacua; the “stringy naturalness” of a model is extrinsic to the model itself.

Understood in the previous “autonomy of scales” sense, the naturalness of a model was an intrinsic property of the model.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 57 / 60

As attention is increasingly directed toward the possibility that we inhabit a multiverse, one should be aware that attempts to re-cast the traditional naturalness criterion in a statistical setting are not conservative embeddings.

In the context of a landscape we nd the meaning, motivation, and possible solutions to problems of naturalness altered considerably from our original starting point.

Traditionally, the best motivation for taking problems of naturalness seriously has been that they violate intuitions about the autonomy of scales derived from the EFT framework.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 59 / 60 Traditionally, the best motivation for taking problems of naturalness seriously has been that they violate intuitions about the autonomy of scales derived from the EFT framework.

In the context of a landscape we nd the meaning, motivation, and possible solutions to problems of naturalness altered considerably from our original starting point.

Porter Williams (University of Pittsburgh) Two notions of naturalness February 28, 2018 59 / 60 References

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