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New properties of "standard model effective field theory"

  1. May 10, 2015 #1
    Holomorphy without Supersymmetry in the Standard Model Effective Field Theory

    Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar
    (Submitted on 2 Sep 2014 (v1), last revised 6 Nov 2014 (this version, v2))
    The anomalous dimensions of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) respect holomorphy to a large extent. The holomorphy conditions are reminiscent of supersymmetry, even though the SMEFT is not a supersymmetric theory.

    One-loop non-renormalization results in EFTs
    J. Elias-Miro, J. R. Espinosa, A. Pomarol
    (Submitted on 22 Dec 2014 (v1), last revised 17 Feb 2015 (this version, v2))
    In Effective Field Theories (EFTs) with higher-dimensional operators many anomalous dimensions vanish at the one-loop level for no apparent reason. With the use of supersymmetry, and a classification of the operators according to their embedding in super-operators, we are able to show why many of these anomalous dimensions are zero. The key observation is that one-loop contributions from superpartners trivially vanish in many cases under consideration, making supersymmetry a powerful tool even for non-supersymmetric models. We show this in detail in a simple U(1) model with a scalar and fermions, and explain how to extend this to SM EFTs and the QCD Chiral Langrangian. This provides an understanding of why most "current-current" operators do not renormalize "loop" operators at the one-loop level, and allows to find the few exceptions to this ubiquitous rule.

    Non-renormalization Theorems without Supersymmetry
    Clifford Cheung, Chia-Hsien Shen
    (Submitted on 7 May 2015)
    We derive a new class of one-loop non-renormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and anti-holomorphic weights, (w,wbar)=(n−h,n+h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator Oi can only be renormalized by an operator Oj if wi≥wj and wbari≥wbarj, absent non-holomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally.
  2. jcsd
  3. May 10, 2015 #2
    is Holomorphy without Supersymmetry a proposed resolution of higgs hierarchy without susy?
  4. May 11, 2015 #3


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    Hi Mitchell, I hope you discuss the general significance of these papers. I'm curious about this.
    Incidentally here is Clifford Cheung's Inspire profile:

    Here's the record for the Alonso Jenkins Manohar paper:
    Here are a couple of author profiles:
    Last edited: May 11, 2015
  5. May 11, 2015 #4


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    So the significance is that if a new candidate supersymmetric particle is found at the LHC, SMEFT is claimed to also be able to explain it?
  6. May 13, 2015 #5
    SMEFT is a framework for discussing BtSM physics without specifying the new fields and their interactions. It's like Fermi's theory of the weak interaction - in reality two fermions exchange a weak boson, but Fermi didn't know that detail and describes them as meeting at a point and interacting directly. SMEFT adds to the SM Lagrangian, new interactions of the SM fields that would be induced by unknown intermediate fields.

    Then, when the quantum mechanics of these extra effective interactions is worked out, and specifically the way that they vary with the energy scale considered, you find interdependence. To say how effective interaction A varies, you use a linear combination of effective interactions B, C, D... as a correction or addition to A.

    This is called operator mixing and it's an aspect of renormalization. But operator mixing is not total; sometimes the contribution of B to the corrected A is simply zero. A proof of this is called a non-renormalization theorem. Most such theorems apply specifically to supersymmetric theories, and often derive from their special complex-analytic properties.

    In the first paper, a mysterious pattern of non-renormalization relations - a lack of operator mixing - was discovered among the algebraic terms in SMEFT that have a "mass dimension" of 6. The "mass dimension" has nothing to do with particle mass or physical dimensions, it's about dimensional analysis, the number of factors of mass, length, and time appearing in a physical quantity - here, it's the quantities appearing in the SMEFT Lagrangian, like (random example) "scalar times derivative of a tensor, squared". The higher the mass dimension of such an effective interaction, the smaller its effect on low-energy physics. Also, operator mixing makes a further contribution to the effective mass dimension; this correction is called the anomalous dimension.

    The first paper speculated that the lack of mixing - which was found by brute calculation - was due to an unnoticed holomorphy in SMEFT, similar to that in a supersymmetric theory. The second paper was able to derive much of the operator mixing pattern, by adding supersymmetry. But the third paper was finally able to explain it all without supersymmetry, by factorizing the relevant Feynman diagrams and showing that some the sub-diagrams evaluated equal to zero. However, even this third paper uses techniques and perspectives that owe a lot to the study of SUSY theories.
  7. May 15, 2015 #6


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    I was expecting some cancellation depending of the number of generations, but nope :-(
  8. May 18, 2015 #7


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    I find this to be really exciting stuff that could harbor new breakthroughs. Any time that you find out that hidden symmetry in equations makes them far more tractable than they seem, and makes the results you are observing far more natural than they would appear at first glance, is a big deal.

    I also continue to be intrigued by the notion that something like "supersymmetry" the relationship may be present already in the Standard Model, without having to put in extra particles and forces by hand as conventional SUSY theories do (making it far more baroque), for reasons that a cryptic (i.e. unknown because they are hidden from what we know) in our current description of the Standard Model. This finding tends to support that intuition.
  9. May 25, 2015 #8
    So the pattern seen is in the distribution of "renormalizability" across the possible combinations of SM interactions and the energy scale. And renormalizability, or lack thereof is somehow down to the "dimensionality" of the interaction?
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