REVIEW
Minimal flavour violation and beyond: Towards a flavour code for short distance dynamics
High Energy Physics - Phenomenology · Submitted 7 Dec 2010 · 276 references
Pith's verdict: A solid, useful map of the BSM flavour landscape whose one new idea — the 3x3 flavour code — is honestly bounded and, by the author's own admission, not yet discriminating enough to carry much weight.
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Referee report
The paper
The paper claims
Buras proposes a 3×3 'flavour code matrix' that gives each extension of the Standard Model a compact code, so that models with the same code can be told apart by the same handful of measurements.
The reading
What carries the argument
The flavour code matrix. Its rows encode where flavour and CP violation come from: the CKM matrix alone (MFV), new complex flavour structures (BMFV), or phases that carry no flavour (FBPs). Its columns encode the Lorentz structure of the new charged currents: left-handed, right-handed, or scalar. The matrix is meant to be read together with the 'DNA' tables of Section 5.13, which record for each model whether a given observable can show large, moderate or no visible new-physics effect, and with the correlation tables collected in Table 4. The mechanism that makes the grid non-trivial is that the Lorentz structure of the new operators is not a detail: operators with a $(bar s gamma_mu P_L d)(bar s gamma_mu P_R d)$ or $(bar s P_L d)(bar s P_R d)$ shape mix under QCD with large anomalous dimensions and have chirally enhanced hadronic matrix elements in the kaon system, so models with right-handed currents and models with only left-handed ones have qualitatively different reach in $S_{psiphi}$ even when both are non-MFV.
Extended reading notes
Core claim
The paper's own statement of its contribution is that, having surveyed the flavour phenomenology of a dozen extensions of the Standard Model, it proposes a coding system in the form of a $3times3$ matrix that helps distinguish between them. The rows are MFV, non-MFV (labelled BMFV) and flavour-blind phases; the columns are left-handed, right-handed and scalar currents. A model is characterised by which cells of this grid are occupied, and the paper fills in codes for CMFV, 2HDM with MFV and flavour-blind phases, the Littlest Higgs model with T-parity, the Standard Model with a sequential fourth generation, the flavour-blind MSSM, left-handed-dominated supersymmetric flavour models, the right-handed MFV effective framework, a Randall-Sundrum model with custodial protection, the abelian and non-abelian supersymmetric flavour models, and a supersymmetric $SU(5)$ GUT with right-handed neutrinos. Two structural claims come with the grid: the cell combining MFV with right-handed currents is always empty, because MFV forces such currents to be suppressed by quark mass ratios; and the coordinates are chosen so that the operator content that drives the phenomenology — in particular the scalar operator $Q^{LR}_2$, whose large anomalous dimension and chirally enhanced matrix elements make it the engine of large $S_{psiphi}$ — is at least partially captured. The author is explicit that the scheme is a first step, not a finished classification.
Load-bearing premise
The load-bearing premise is that three coordinates — MFV, non-MFV and flavour-blind phases, crossed with left-handed, right-handed and scalar currents — carry enough information to separate models, and the paper's own tables give identical codes to models whose predictions differ, which the author acknowledges by saying the scheme cannot yet fully depict all properties of a given model.
Editorial extensions
If this is right
- If the grid is the right set of coordinates, then a measurement of $S_{psiphi}$ well above its Standard Model value of about 0.04 already selects a region of the grid, and the accompanying predictions for $B_{s,d}to mu^+mu^-$ and $Kto pi nu barnu$ follow from the code rather than from a parameter scan.
- In the large-$S_{psiphi}$ regime the paper expects the abelian supersymmetric flavour model and the 2HDM with MFV and flavour-blind phases to push $B_{s,d}to mu^+mu^-$ toward the then-current upper bound of roughly $3times10^{-8}$, the fourth-generation model to reach only $(6-9)times10^{-9}$, and the Randall-Sundrum model to stay Standard-Model-like.
- Because the 2HDM with MFV and flavour-blind phases ties the two mixing phases by $phi_{B_d} approx (m_d/m_s) phi_{B_s} approx phi_{B_s}/17$ when the phases sit in the Yukawa couplings, a large $S_{psiphi}$ forces a definite downward shift in $S_{psi K_S}$ and raises the predicted $epsilon_K$ toward its measured value, softening the tension between $epsilon_K$, $S_{psi K_S}$ and $|V_{ub}|$.
- If the grid is complete in the sense claimed, no model can occupy the MFV/right-handed cell, so any future signal of a right-handed charged current at a strength not suppressed by $m_s/m_b$, $m_d/m_b$ or $m_d/m_s$ would be a signal of physics outside the MFV row entirely.
- The programme sets a concrete experimental shopping list: $S_{psiphi}$, $B_{s,d}to mu^+mu^-$, $K^+to pi^+ nu barnu$ and $K_Lto pi^0 nu barnu$ first, then $S_{phi K_S}$, $S_{eta' K_S}$, the angular observables in $Bto K^*ell^+ell^-$, the lepton-flavour-violating rates and the hadronic electric dipole moments.
Reading between the lines
- The grid is a compression scheme, and its value can be measured by how often it fails: the paper's own tables give the Littlest Higgs model with T-parity and the fourth-generation model the same code, yet their $B_sto mu^+mu^-$ reach differs by roughly a factor of three, so the code as it stands is not a sufficient statistic for the predictions.
- A natural next step the paper does not take is to make the code quantitative — to attach, for each occupied cell, the size of the coefficient multiplying the corresponding operator, so that two models with the same occupancy but different Wilson coefficients are no longer conflated.
- The scheme suggests a decision procedure for the coming decade: rather than fitting each model to the data, measure the small set of observables that probe individual cells and read off the occupancy directly, treating a filled MFV/right-handed cell or an empty scalar column as a sharp discriminant.
- If the correlation between $S_{psiphi}$ and hadronic electric dipole moments in the 2HDM with flavour-blind phases is confirmed, then the grid acquires a column that the current tables leave largely blank, since electric dipole moments probe flavour-diagonal CP violation rather than flavour-changing currents.
Original abstract
This decade should provide the first definitive signals of New Physics (NP) beyond the Standard Model (SM) and the goal of these lectures is a review of flavour physics in various extensions of the SM that have been popular in the last ten years. After an overture, two pilot sections and a brief summary of the structure of flavour violation and CP violation in the SM, we will present the theoretical framework for weak decays that will allow us to distinguish between different NP scenarios. Subsequently we will present twelve concrete BSM models summarizing the patterns of flavour violation characteristic for each model. In addition to models with minimal flavour violation (MFV) accompanied by flavour blind phases we will discuss a number of extensions containing non-MFV sources of flavour and CP violation and, in particular, new local operators originating in right-handed charged currents and scalar currents. Next we will address various anomalies in the data as seen from the point of view of the SM that appear very natural in certain extensions of the SM. In this presentation selected superstars of this field will play a very important role. These are processes that are very sensitive to NP effects and which are theoretically clean. Particular emphasis will be put on correlations between various observables that could allow us to distinguish between various NP scenarios. Armed with this knowledge we will propose a coding system in a form of a 3*3 matrix which helps to distinguish between various extensions of the SM. Finding which flavour code is chosen by nature would be an important step towards the fundamental theory of flavour. We give several examples of flavour codes representing specific models.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
This decade should provide the first definitive signals of New Physics (NP) beyond the Standard Model (SM) and the goal of these lectures is a review of flavour physics in various extensions of the SM that have been popular in the last ten years. After an overture, two pilot sections and a brief summary of the structure of flavour violation and CP violation in the SM, we will present the theoretical framework for weak decays that will allow us to distinguish between different NP scenarios. Subsequently we will present twelve concrete BSM models summarizing the patterns of flavour violation characteristic for each model. In addition to models with minimal flavour violation (MFV) accompanied by flavour blind phases we will discuss a number of extensions containing non-MFV sources of flavour and CP violation and, in particular, new local operators originating in right-handed charged currents and scalar currents. Next we will address various anomalies in the data as seen from the point of view of the SM that appear very natural in certain extensions of the SM. In this presentation selected superstars of this field will play a very important role. These are processes that are very sensitive to NP effects and which are theoretically clean. Particular emphasis will be put on correlations between various observables that could allow us to distinguish between various NP scenarios. Armed with this knowledge we will propose a coding system in a form of a 3*3 matrix which helps to distinguish between various extensions of the SM. Finding which flavour code is chosen by nature would be an important step towards the fundamental theory of flavour. We give several examples of flavour codes representing specific models.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This decade should provide the first definitive signals of New Physics (NP) beyond the Standard Model (SM) and the goal of these lectures is a review of flavour physics in various extensions of the SM that have been popular in the last ten years. | background 0.78 | 0.06 | 0.05 | asserted 0.70 |
| s1 | After an overture, two pilot sections and a brief summary of the structure of flavour violation and CP violation in the SM, we will present the theoretical framework for weak decays that will allow us to distinguish between different NP scenarios. | method 0.48 | 0.16 | 0.02 | asserted 0.81 |
| s2 | Subsequently we will present twelve concrete BSM models summarizing the patterns of flavour violation characteristic for each model. | contribution 0.86 | 0.29 | 0.04 | asserted 0.92 |
| s3 | In addition to models with minimal flavour violation (MFV) accompanied by flavour blind phases we will discuss a number of extensions containing non-MFV sources of flavour and CP violation and, in particular, new local operators originating in right-handed charged currents and scalar currents. | contribution 0.87 | 0.20 | 0.04 | asserted 0.83 |
| s4 | Next we will address various anomalies in the data as seen from the point of view of the SM that appear very natural in certain extensions of the SM. | contribution 0.84 | 0.14 | 0.03 | asserted 0.74 |
| s5 | In this presentation selected superstars of this field will play a very important role. | method 0.57 | 0.09 | 0.02 | asserted 0.96 |
| s6 | These are processes that are very sensitive to NP effects and which are theoretically clean. | method 0.49 | 0.07 | 0.03 | asserted 0.97 |
| s7 | Particular emphasis will be put on correlations between various observables that could allow us to distinguish between various NP scenarios. | method 0.62 | 0.20 | 0.06 | hedged possibility 0.96 |
| s8 | Armed with this knowledge we will propose a coding system in a form of a 3*3 matrix which helps to distinguish between various extensions of the SM. | contribution 0.84 | 0.67 | 0.18 | asserted 0.83 |
| s9 | Finding which flavour code is chosen by nature would be an important step towards the fundamental theory of flavour. | interpretation 0.75 | 0.06 | 0.23 | asserted 0.77 |
| s10 | We give several examples of flavour codes representing specific models. | contribution 0.89 | 0.80 | 0.07 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
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Figures
Figures reproduced from arXiv:1012.1447 by the authors.
References
How the literature uses it
38 arXiv papers cite this in 60 sentences
Papers citing it · 22 sentences without a confident label
Builds on it 1 paper
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In Section [ref], the main section of this writing, we will have a first look at the modifications of the results of all models considered in [ref] , adding few models that have been analysed by us since then.
BSM models facing the recent LHCb data: A first look · Introduction · 0.88
Uses its method or tool 2 papers
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The reason why we can at all make any statements about the changes in predictions of various models without basically performing any new numerical analysis is that the strategy of the analyses discussed in [ref] was to present the predictions for various observables as functions of $S_ψϕ$.
BSM models facing the recent LHCb data: A first look · Introduction · 0.86
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To this end it will be useful to adopt the notations of [ref] .
Patterns of Flavour Violation in Models with Vector-Like Quarks · Implications for the down-quark sector · 0.88
Uses its data or values 12 papers
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In this study we will adopt the value given in [ref] for the $CP$-averaged SM branching ratio and, following [ref] , take $_SM=3.5×10^-9$ for the value rescaled by the effects of $B_s-B̅_s$ oscillations (time averaged).
Two ultimate tests of constrained supersymmetry · in the MSSM · 1.00
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Heavily suppressed in the SM partially due to helicity conservation, the decay $B_s^0→μ^+μ^-$ is predicted by Buras [ref] to have a branching fraction, after a correction due to the relatively large size of $ΔΓ_s$, of $(3.5±0.2)×10^-9$ [ref] .
New physics from flavour · $B_s^0→μ^+μ^-$ · 0.95
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A good example of this is the decay $B_s →μ^+ μ^-$, where the experimental upper bound on $BR(B_s →μ^+ μ^-)$ has been recently improved to $4.5 ×10^-9$ [ref] against a SM prediction of $(3.2 ±0.2) ×10^-9$ [ref] .
How Constrained is the cMSSM? · The Model and its Constraints · 0.95
Compares with it 2 papers
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This updates the estimate $(3.2±0.2)×10^-9$ in Ref. [ref] , where $ΔΓ_s$ effects where not included and other input, in particular the value of $τ_B_s$, was different than now.
Probing New Physics with the B_s to {\mu}+ {\mu}- Time-Dependent Rate · The Branching Ratio · 0.87
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They differ only marginally from those quoted in [ref] and given in ([ref]) and ([ref]).
BSM models facing the recent LHCb data: A first look · Introduction · 0.91
Cites it as background 14 papers
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Finally, our strategy won't be to repeat any details of the models considered here, because in [ref] a rather compact presentation of most of them can be found.
BSM models facing the recent LHCb data: A first look · Introduction · 0.90
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Due to the GIM [ref] mechanism this structure has automatically profound implications for the pattern of FCNC processes that seems to be in remarkable accordance with the present data within theoretical and experimental uncertainties [ref] , bearing in mind certain anomalies [ref] , in particular in CP-violating observables which are discussed below.
Delta F = 2 observables and B -> X_q gamma decays in the Left-Right Model: Higgs particles striking back · Introduction · 0.90
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A summary of these studies before 2011 with brief descriptions of all these models can be found in [ref] .
Flavour Visions · Anatomies of explicit models · 0.91
What it cites · 318 sentences without a confident label
Contests 2 papers
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The universality hypothesis of $φ_B_s=φ_B_d$ in [ref] was clearly ad hoc.
Correlations among new CP violating effects in Delta F = 2 observables · The $ε_K-S_ψK_S$ Anomaly · contest 0.81
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The universality hypothesis of $φ_B_s=φ_B_d$ in [ref] was clearly ad hoc.
Probing New Physics through B Mixing: Status, Benchmarks and Prospects · The $ε_K-S_ψK_S$ Anomaly · contest 0.81
Builds on 2 papers
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While in [ref] only the case of FBPs in Yukawa interactions has been considered, in [ref] these considerations have been extended to include also the FBPs in the Higgs potential.
Higgs-mediated FCNCs: Natural Flavour Conservation vs. Minimal Flavour Violation · Preliminaries · 0.94
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While in [ref] only the case of FBPs in Yukawa interactions has been considered, in [ref] these considerations have been extended to include also the FBPs in the Higgs potential.
EDMs vs. CPV in B_{s,d} mixing in two Higgs doublet models with MFV · Preliminaries · 0.94
Uses the method or tool of 1 paper
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In order to see what is here involved we follow a compact formulation of Gino Isidori [ref] .
B physics in the LHC era · Minimal Flavour Violation · 0.85
Uses data or values from 9 papers
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The recent inclusion of LD effects in $ImM_12$ modified this estimate to $κ_ε=0.94±0.02$ [ref] .
On epsilon_K beyond lowest order in the Operator Product Expansion · The $ε_K-S_ψK_S$ Anomaly · 0.87
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Very recently also NNLO-QCD corrections to the QCD factor $η_ct$ in $ε_K$ [ref] have been calculated enhancing the value of $ε_K$ by $3%$.
Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution · The $ε_K-S_ψK_S$ Anomaly · 0.83
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The main reasons for this tension are on the one hand a decreased value of the relevant non-perturbative parameter $B̂_K=0.724±0.008±0.028$ [ref] [Interestingly this value is very close to $B̂_K=0.75$ obtained in the large-N limit of QCD [ref] .
Neutral kaon mixing from 2+1 flavor Domain Wall QCD · The $ε_K-S_ψK_S$ Anomaly · 0.96
Compares with 9 papers
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As stressed in the point 1 of the previous subsection none of the models discussed in [ref] was able to simultaneously account for the current data for $S_ψϕ$ and $S_ϕK_S$, in contrast to the $SSU(5)_RN$ model discussed here.
Anatomy and Phenomenology of FCNC and CPV Effects in SUSY Theories · Supersymmetric $SU(5)$ GUT with RH neutrinos (RN): $SSU(5)_RN$ · 0.97
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In the second non abelian $SU(3)$ model by Antusch, King and Malinsky (AKM) [ref] analyzed by us the RH contributions are CKM-like but new LH contributions in contrast to the RVV2 model can be suppressed arbitrarily at the high scale.
Solving the SUSY Flavour and CP Problems with SU(3) Family Symmetry · Supersymmetric Flavour Models (SF) · 0.86
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The patterns of flavour violation in the RVV2 model and in the $SSU(5)_RN$ has some similarities but as we emphasized in Section 5 also few striking difference have been identified in [ref] .
Footprints of SUSY GUTs in Flavour Physics · Examples of Flavour Code Matrices (FCM) · 0.87
Cites as support 9 papers
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Yet, it is a fact, as pointed out and analyzed recently in particular in [ref] , that the presence of right-handed currents could either remove or significantly weaken some of these tensions, especially in the case of $|V_ub|$.
Effects of right-handed charged currents on the determinations of |V_ub| and |V_cb| · The Minimal Effective Model with Right-handed Currents:RHMFV · 0.98
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Yet, it is a fact, as pointed out and analyzed recently in particular in [ref] , that the presence of right-handed currents could either remove or significantly weaken some of these tensions, especially in the case of $|V_ub|$.
Left-right mixing on leptonic and semileptonic $b\to u$ decays · The Minimal Effective Model with Right-handed Currents:RHMFV · 0.98
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Therefore as pointed out in [ref] in the $2HDM_MFV$ the best agreement with the data is obtained by having these phases both in Yukawa interactions and the Higgs potential, which is to be expected in any case.
EDMs vs. CPV in B_{s,d} mixing in two Higgs doublet models with MFV · $S_ψϕ≈0.25$ · 0.96
Cites as background 101 papers
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The simplest class of extensions of the SM are models with Constrained Minimal Flavour Violation (CMFV) [ref] .
Minimal Flavour Violation Waiting for Precise Measurements of Delta M_s, S_{psi phi}, A^s_SL, |V_ub|, gamma and B^0_{s,d} -> mu+ mu- · Master Formula for Weak Decays · 0.97
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The simplest class of extensions of the SM are models with Constrained Minimal Flavour Violation (CMFV) [ref] .
Minimal Flavour Violation · Master Formula for Weak Decays · 0.97
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The simplest class of extensions of the SM are models with Constrained Minimal Flavour Violation (CMFV) [ref] .
Universal Unitarity Triangle and Physics Beyond the Standard Model · Master Formula for Weak Decays · 0.97
Discussion
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