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Next to Minimal Flavor Violation

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Kaustubh Agashe, Michele Papucci, Gilad Perez, Dan Pirjol

High Energy Physics - Phenomenology · Submitted 13 Sep 2005 · 64 references

Pith's verdict: The operator classification and the RS1 mapping are the durable parts; the ΔF=2 bound is defensible but the abstract's 'arbitrary phase' overstates the quoted fit, and the b→s half is conditional on Z-alignment.

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arXiv IDhep-ph/0509117 (version 2)
Pith ID4BNLZYPU, Pith's permanent record of this paper and its review
CitationDan Pirjol, Gilad Perez, Kaustubh Agashe, Michele Papucci. "Next to Minimal Flavor Violation." arXiv:hep-ph/0509117 (2005). https://pith.science/paper/4BNLZYPU
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The paper

The paper claims

New physics at the TeV scale can still make up roughly a third of the Standard Model's meson-mixing amplitude, with an arbitrary CP phase, without contradicting current B-factory data.

The reading

The paper asks whether the scale of new physics that stabilizes the electroweak scale can be the same as the scale that mediates flavor violation, a coincidence that the standard minimal-flavor-violation story forbids. It defines a wider class of models, called next-to-minimal flavor violation, in which new physics couples dominantly to the third generation of quarks and is only slightly misaligned with the Yukawa matrices, so that the severe kaon constraints tied to the first two generations are evaded while the new physics sits at a few TeV. The concrete question is then quantitative: how large a new-physics contribution to $K$--$K$, $B$--$B$ and $B_s$--$B_s$ mixing, with any phase, can present data tolerate? The authors answer with a global fit and find that contributions of order 30 to 40 percent of the Standard Model amplitude are still allowed, so the usual claim that a successful unitarity-triangle fit rules such models out is premature. They then extend the analysis to $b to s$ decays, using two hadronic models to gauge the theory error, and argue that correlating the mixing and decay observables is the sharpest near-term probe.

What carries the argument

The organizing object is the NMFV flavor structure: new physics is assumed to respect, to leading order, a $U(2)_Q times U(2)_d times U(2)_u times U(1)_3$ subgroup of the Standard Model quark flavor group, so that in a special interaction basis the new four-fermion operators involve only third-generation quarks, for example $c_3 (bar Q_3 Q_3)^2 / Lambda_{rm NMFV}^2$. Rotating to the mass basis with a CKM-like left-handed down-quark unitary matrix $D_L$ turns this into flavor-changing operators suppressed by $(D_L^* )_{3i} (D_L)_{3j}$, which gives kaon mixing a $lambda^5$ suppression and $B$ mixing a $lambda^3$ suppression. With $Lambda_{rm NMFV} sim 2$--$3$ TeV these land at the size of the Standard Model top-loop contribution. The second piece of machinery is the $(h_X, sigma_X)$ parameterization, which reduces any set of new $Delta F = 2$ operators to a single magnitude and phase per meson system because no strong phases enter; the third is the assumption that new physics in $Delta F = 1$ enters only left-handed operators aligned with the Standard Model $Z$ penguin, which makes the $b to s$ and mixing phases the same and hence correlated.

Extended reading notes

Core claim

The central claim is that a new-physics contribution to $Delta F = 2$ processes of roughly 30 to 40 percent of the Standard Model one, with an essentially arbitrary CP phase, survives the post-2005 data. The authors parameterize the new physics in each meson system by a magnitude $h_X$ and a phase $sigma_X$ relative to the Standard Model amplitude, so that the mixing observables become $Delta m_d = |1 + h_d e^{2i sigma_d}|, Delta m_d^{rm SM}$ and $S_{psi K} = sin[2beta + arg(1 + h_d e^{2i sigma_d})]$, with analogous expressions in the kaon and $B_s$ systems. Fitting to the CKMfitter inputs they report $h_d = 0$--$0.4$ for $2sigma_d$ between $pi$ and $2pi$, and $h_K = 0$--$0.6$ with $sigma_K$ over essentially the full physical range, while the $B_s$ system remains unconstrained because only a lower bound on $Delta m_s$ exists. Before the 2004 results the same analysis allowed new physics comparable to or larger than the Standard Model; the improvement since then has turned a coincidence question into a mild fine-tuning question, but has not closed the window. The authors stress that the allowed region is set mainly by theory errors in $Delta m_d$ and $|V_{ub}|$ and by the small number of independent observables, not by experimental precision.

Load-bearing premise

The size of the allowed new-physics contribution is measured against a Standard Model mixing amplitude fixed by $rho$ and $eta$ extracted from tree-level observables such as $S_{rho rho}$ and the $B to DK$ asymmetry, and the paper's own footnote states that this extraction assumes electroweak penguin contributions can be neglected, an assumption justified in the Standard Model but not model-independently.

Editorial extensions

If this is right

  • The flavor-violation scale and the electroweak-stabilization scale need not be separated, so a broad class of supersymmetric alignment models, non-abelian flavor models, little-Higgs models and warped extra-dimension models remain viable at a few TeV.
  • A measured $Delta m_s$ together with $S_{psi phi}$ would convert the currently unconstrained $B_s$ system into a sharp test, since the same phase that fits the $b to s$ anomalies predicts a definite correlation with $B_s$ mixing.
  • The $b to s$ anomalies in $S_{phi K_S}$ and $S_{eta' K_S}$ can be accommodated by a new-physics $Z$-penguin contribution of the same order as the Standard Model one, consistently with the $B to K pi$ branching ratios and direct CP asymmetries.
  • In this framework the tightest future constraint on the new degrees of freedom needed for electroweak stabilization is expected to come from flavor physics rather than from electroweak precision tests.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the allowed $h_d$ window is really set by the theory error on $Delta m_d$ and $|V_{ub}|$, then lattice and continuum improvements on the $B$ bag parameter and on $|V_{ub}|$ are as valuable for this program as new B-factory statistics, a priority the paper notes but does not quantify.
  • The same third-generation-coupling logic applies to leptons: a NMFV-like structure in the charged-lepton or neutrino sector would predict new physics in $tau$ and $B to tau nu$ observables at a level comparable to one-loop Standard Model contributions, which is a natural place to look next.
  • Because the framework ties the $Delta F = 1$ and $Delta F = 2$ phases together, an eventual discrepancy between the phase preferred by $b to s$ penguins and the phase preferred by $B_s$ mixing would be a clean signal that the third-generation dominance assumption, rather than the data, is what fails.
Original abstract

The flavor structure of a wide class of models, denoted as next to minimal flavor violation (NMFV), is considered. In the NMFV framework, new physics (NP), which is required for stabilization of the electroweak symmetry breaking (EWSB) scale, naturally couples (dominantly) to the third generation quarks and is quasi-aligned with the Yukawa matrices. Consequently, new sources of flavor and CP violation are present in the theory, mediated by a low scale of few TeV. However, in spite of the low flavor scale, the most severe bounds on the scale of NP are evaded since these are related to flavor violation in the first two generations. Instead, one typically finds that the NP contributions are comparable in size to SM loop processes. We argue that, in spite of the successful SM unitary triangle fit and contrary to the common lore, such a sizable contribution to Delta F=2 processes of ~ 40% (with arbitrary phase) compared to SM is presently allowed since B-factories are only beginning to constrain these models. Thus, it is very interesting that in the NMFV models one is not forced to separate the scale of NP related to EWSB and the scale of flavor violation. We show briefly that this simple setup includes a wide class of supersymmetric and non-supersymmetric models all of which solve the hierarchy problem. We further discuss tests related to Delta F=1 processes, in particular the ones related to b -> s transition. The b -> s processes are computed using two different hadronic models to estimate the uncertainties involved. In addition, we derive constraints on the NP from B -> Kpi data using only SU(3) flavor symmetry and minimal dynamical assumptions. Finally we argue that in many cases correlating Delta F=2 and Delta F=1 processes is a powerful tool to probe our framework.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 9,008 input tokens, $0.0004 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.94 · compares with prior results 0.69 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The flavor structure of a wide class of models, denoted as next to minimal flavor violation (NMFV), is considered. In the NMFV framework, new physics (NP), which is required for stabilization of the electroweak symmetry breaking (EWSB) scale, naturally couples (dominantly) to the third generation quarks and is quasi-aligned with the Yukawa matrices. Consequently, new sources of flavor and CP violation are present in the theory, mediated by a low scale of few TeV. However, in spite of the low flavor scale, the most severe bounds on the scale of NP are evaded since these are related to flavor violation in the first two generations. Instead, one typically finds that the NP contributions are comparable in size to SM loop processes. We argue that, in spite of the successful SM unitary triangle fit and contrary to the common lore, such a sizable contribution to Delta F=2 processes of ~ 40% (with arbitrary phase) compared to SM is presently allowed since B-factories are only beginning to constrain these models. Thus, it is very interesting that in the NMFV models one is not forced to separate the scale of NP related to EWSB and the scale of flavor violation. We show briefly that this simple setup includes a wide class of supersymmetric and non-supersymmetric models all of which solve the hierarchy problem. We further discuss tests related to Delta F=1 processes, in particular the ones related to b -> s transition. The b -> s processes are computed using two different hadronic models to estimate the uncertainties involved. In addition, we derive constraints on the NP from B -> Kpi data using only SU(3) flavor symmetry and minimal dynamical assumptions. Finally we argue that in many cases correlating Delta F=2 and Delta F=1 processes is a powerful tool to probe our framework.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The flavor structure of a wide class of models, denoted as next to minimal flavor violation (NMFV), is considered. contribution 0.72 0.60 0.03 asserted 0.86
s1 In the NMFV framework, new physics (NP), which is required for stabilization of the electroweak symmetry breaking (EWSB) scale, naturally couples (dominantly) to the third generation quarks and is quasi-aligned with the Yukawa matrices. background 0.48 0.20 0.09 asserted 0.97
s2 Consequently, new sources of flavor and CP violation are present in the theory, mediated by a low scale of few TeV. result 0.50 0.18 0.07 asserted 0.99
s3 However, in spite of the low flavor scale, the most severe bounds on the scale of NP are evaded since these are related to flavor violation in the first two generations. result 0.71 0.24 0.16 asserted 1.00
s4 Instead, one typically finds that the NP contributions are comparable in size to SM loop processes. result 0.84 0.58 0.09 asserted 0.75
s5 We argue that, in spite of the successful SM unitary triangle fit and contrary to the common lore, such a sizable contribution to Delta F=2 processes of ~ 40% (with arbitrary phase) compared to SM is presently allowed since B-factories are only beginning to constrain these models. result 0.55 0.44 0.52 asserted 0.63
s6 Thus, it is very interesting that in the NMFV models one is not forced to separate the scale of NP related to EWSB and the scale of flavor violation. interpretation 0.91 0.45 0.40 asserted 0.92
s7 We show briefly that this simple setup includes a wide class of supersymmetric and non-supersymmetric models all of which solve the hierarchy problem. contribution 0.71 0.91 0.10 asserted 1.00
s8 We further discuss tests related to Delta F=1 processes, in particular the ones related to b -> s transition. contribution 0.94 0.82 0.04 asserted 0.80
s9 The b -> s processes are computed using two different hadronic models to estimate the uncertainties involved. method 1.00 0.91 0.02 asserted 0.99
s10 In addition, we derive constraints on the NP from B -> Kpi data using only SU(3) flavor symmetry and minimal dynamical assumptions. method 0.65 0.94 0.04 asserted 1.00
s11 Finally we argue that in many cases correlating Delta F=2 and Delta F=1 processes is a powerful tool to probe our framework. interpretation 0.51 0.60 0.21 asserted 0.53

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from argument 0.60.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1: The constraint on the
Figure 2. FIG. 2: Left: The allowed range for
Figure 3. FIG. 3: Left: The allowed range for
Figure 4. FIG. 4: The constraint on the
Figure 5. FIG. 5: Left: The allowed range for
Figure 6. FIG. 6: The allowed range for
Figure 7. FIG. 7: The constraints on
Figure 8. FIG. 8: The constraints on
Figure 9. FIG. 9: The allowed range for
Figure 10. FIG. 10: The allowed range for
Figure 11. FIG. 11: The allowed values of
Figure 12. FIG. 12: The allowed values

Figures reproduced from arXiv:hep-ph/0509117 by the authors.

References
How the literature uses it

47 arXiv papers cite this in 79 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 55 sentences without a confident label

Uses its method or tool 1 paper
Uses its data or values 1 paper
  • A more reasonable approach might be to estimate the sum of the different contributions via a “random walk” approach, which will increase the amplitude by factor of roughly $√(N/2)$, where $N$ is the number of independent terms.] for $C_4^K$, requiring that the NP contribution to $||$ is 60% of the experimental value [ref] and evaluating the resulting suppression scale [ref] and the quark masses [ref] at 5 TeV leads to [equation] for $β=1$.

    Combining Direct & Indirect Kaon CP Violation to Constrain the Warped KK Scale · RS Contributions to $$ and $b→sγ$ · 0.86

Compares with it 2 papers
  • The scenario we are considering has some similarities with the Next-to-MFV framework of Ref. [ref] , where flavoured couplings induced by New Physics(NP) are “quasi-aligned” to the SM Yukawas, and where the NP couples “dominantly” to the third generation.

    Solving the flavour problem with hierarchical fermion wave functions · Introduction · 0.92

  • It should also be pointed out that NLMFV differs from the next-to-MFV framework [ref] , since the latter exhibits additional spurions at low energy.

    TASI 2009 Lectures - Flavor Physics · General MFV · 0.93

Cites it as support 2 papers
  • However, due to various symmetries (approximate flavor or analog of GIM mechanism of the SM [ref] and custodial isospin [ref] ), we can show that gauge KK masses as small as $∼3$ TeV are consistent with oblique electroweak (EW) data [ref] (we comment on non-oblique effects such as $Zb b̅$ below) and FCNC's [ref] .[ See references [ref] for other studies of FCNC's in such frameworks.

    LHC Signals for Warped Electroweak Neutral Gauge Bosons · SM in bulk · 0.97

  • Flavor-changing neutral currents are not bad in TC2 because topcolor only couples to top, at leading order, so it naturally falls into next-to-minimal flavor violation [ref] .

    Top condensation as a motivated explanation of the top forward-backward asymmetry · Conclusion · 0.99

Cites it as background 17 papers
  • Specifically, it has been shown that warped geometry provides an automatic built-in GIM mechanism which suppresses tree-level flavor changing neutral currents [ref] .

    5D UED: Flat and Flavorless · Flavor constraints · 0.83

  • However, once the fermion wave functions are required to be close to flat, the traditional anarchic RS approach to flavor [ref] (where fermion wave function overlaps generate fermion mass hierarchies and also give a protection called RS-GIM against FCNC's [ref] ) can no longer be applied.

    A Flavor Protection for Warped Higgsless Models · Introduction · 0.89

  • Specific assumptions on the flavour structure of NP, for example Minimal [ref] or Next-to-Minimal [ref] Flavour Violation (MFV or NMFV), correspond to particular choices of the $F_i$ functions, as detailed below.

    Model-independent constraints on Delta F=2 operators and the scale of New Physics · Introduction · 0.87

Discussion

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