REVIEW
$Z^\prime$ models with less-minimal flavour violation
High Energy Physics - Phenomenology · Submitted 30 Sep 2019 · 132 references
Pith's verdict: A careful U(2)^3 derivation of Z' flavour couplings wrapped around a benchmark that only works if you add a second Z' to cancel the di-muon tails — worth reading for the derivation, not for the fit.
T0 · AI review
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Referee report
The paper
The paper claims
A single heavy Z′ boson, tied to the quark flavour symmetry that the Standard Model already almost respects, can account for three separate anomalies at once: the excess in direct CP violation in kaon decays, the long-standing B→Kπ pattern,
The reading
What carries the argument
The load-bearing device is the spurion expansion of the quark Yukawa matrices under $U(2)_Q imes U(2)_u imes U(2)_d$, in which the symmetry-breaking is carried by two-component spurions $Delta_{u,d}$ and $X_{t,b}$. Diagonalising these matrices perturbatively yields the left-handed rotation matrices $V_d$ and $V_u$ as products of three rotations, and hence the $Z^prime$ couplings in the interaction basis become expressions in CKM elements times the charge differences $X_Q = Q_{Q3}-Q_{Q1,2}$ and $X_{ud} = Q_{u1,2}-Q_{d1,2}$. The practical payoff is predictivity: the whole quark-flavour structure of the model collapses onto known CKM parameters plus $c_B$ and $alpha_B$, so a fit to one anomaly constrains the others. Isospin violation, parametrised by $X_{ud}$, is what makes $epsilon^prime/epsilon$ respond at all, and the paper derives the explicit threshold $|g^prime X_{ud}| gtrsim 1.26 imes (epsilon^prime/epsilon)_{mathrm{NP}}/10^{-3}$.
Extended reading notes
Core claim
The central claim is that $epsilon^prime/epsilon$, the $B o Kpi$ puzzle and $b o s ell^+ell^-$ data can be explained simultaneously by a single $Z^prime$ whose quark couplings are fixed by a $U(2)^3$ flavour symmetry up to two order-one parameters, a real factor $c_B$ and a phase $alpha_B$. The authors first show that the symmetry forces the $Z^prime$ couplings into a rigid form: the $s o d$ coupling is proportional to $c_B^2 X_Q V_{td}^* V_{ts}$ with its phase locked to the CKM phase, while the $b o s$ coupling carries the free phase $alpha_B$ through $c_B e^{i alpha_B} X_Q V_{ts}^* V_{tb}$. This is what makes the $epsilon_K$ bound survivable while $b o s$ CP violation stays adjustable. They then perform a combined fit including $epsilon^prime/epsilon$, $epsilon_K$, $B_d$–$bar B_d$ mixing, hadronic $B$ decays and $b o s ell^+ell^-$, and find that $alpha_B$ between about 2.5 and 3 with $c_B$ around 1.4 fits everything at $2sigma$. The same region predicts $langle A_8(B^0 o K^* mu mu)rangle_{[1.1,6]}$ between 0.015 and 0.03, a CP-violating observable in the muon channel that upcoming measurements can probe.
Load-bearing premise
The paper's simultaneous explanation only survives if a second neutral boson with flavour-universal left-handed quark couplings cancels the di-muon tail excess that the benchmark itself produces, and the authors state plainly that the interaction strength of about $(0.25/mathrm{TeV})^2$ is in conflict with LHC bounds before that cancellation is invoked.
Editorial extensions
If this is right
- The CP-violating observable $langle A_8(B^0 o K^* mu mu)rangle$ in the $q^2$ window $[1.1,6]$ GeV$^2$ is predicted in the range 0.015 to 0.03, within reach of planned Belle II and LHCb measurements.
- A common explanation of $epsilon^prime/epsilon$ and the $B o Kpi$ puzzle requires isospin-violating quark couplings that generate four-quark contact interactions of order $(0.15/mathrm{TeV})^2$, close to but still inside current LHC di-jet tail limits.
- Once $b o s ell^+ell^-$ is included, the implied two-quark–two-muon interaction strength of about $(0.25/mathrm{TeV})^2$ exceeds LHC di-muon bounds, so the minimal benchmark is in conflict with data unless a second neutral boson supplies destructive interference.
- The required charge assignments drive the $U(1)^prime$ gauge coupling to a Landau pole around 50 to 60 TeV, so the model as written cannot be extended far beyond the reach of the LHC without new matter or a changed ultraviolet completion.
- For the benchmark, the $K_L o pi^0 ar u u$ rate is reduced by roughly 75 percent (LFU scenario) or 30 percent ($L_mu-L_tau$ scenario) relative to the Standard Model prediction.
Reading between the lines
- The prediction for $langle A_8rangle$ is the cleanest near-term discriminator: if Belle II settles it near zero while $b o s ell^+ell^-$ anomalies persist, the specific phase structure $alpha_B in [2.5,3]$ that ties the hadronic and leptonic anomalies together would be disfavoured, even if a $Z^prime$ explanation of $b o s ell^+ell^-$ alone survived.
- The need for a second $Z^{primeprime}$ with flavour-universal left-handed quark couplings is a structural hint rather than a nuisance: it suggests the ultraviolet completion contains a product gauge group in which only one factor carries the $U(2)^3$-breaking charges, which is a concrete model-building target.
- Because the $s o d$ coupling phase is fixed by $V_{tb}V_{ts}^*$ while the $b o s$ phase is free, this framework predicts a correlated sign between new physics in $epsilon^prime/epsilon$ and in $B o Kpi$ that a future lattice-driven determination of $epsilon^prime/epsilon$ could confirm or break.
- A Landau pole at tens of TeV means the model is testable in the same energy window as its own inconsistency, so any direct evidence for the $Z^prime$ at the high-luminosity LHC would also sharpen what ultraviolet completion is required.
Original abstract
We study the phenomenology of simplified $Z^\prime$ models with a global $U(2)^3$ flavour symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. This flavour symmetry, known as less-minimal flavour violation, protects $\Delta F=2$ processes from dangerously large new physics (NP) effects, and at the same time provides a free complex phase in $b\to s$ transitions, allowing for an explanation of the hints for additional direct CP violation in kaon decays ($\epsilon^\prime/\epsilon$) and in hadronic $B$-decays ($B\to K\pi$ puzzle). Furthermore, once the couplings of the $Z^\prime$ boson to the leptons are included, it is possible to address the intriguing hints for NP (above the 5$\,\sigma$ level) in $b\to s \ell^+\ell^-$ transitions. Taking into account all flavour observables in a global fit, we find that $\epsilon^\prime/\epsilon$, the $B\to K\pi$ puzzle and $b\to s \ell^+\ell^-$ data can be explained simultaneously. Sizeable CP violation in $b\to s \ell^+\ell^-$ observables, in particular $A_8$, is predicted, which can be tested in the near future, and an explanation of the $B\to K\pi$ and $\epsilon^\prime/\epsilon$ puzzles leads to effects in di-jet tails at the LHC, that are not far below the current limits. Once $b\to s \ell^+\ell^-$ is included, cancellations in di-muon tails, possibly by a second $Z^\prime$, are required by LHC data.
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
We study the phenomenology of simplified $Z^\prime$ models with a global $U(2)^3$ flavour symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. This flavour symmetry, known as less-minimal flavour violation, protects $\Delta F=2$ processes from dangerously large new physics (NP) effects, and at the same time provides a free complex phase in $b\to s$ transitions, allowing for an explanation of the hints for additional direct CP violation in kaon decays ($\epsilon^\prime/\epsilon$) and in hadronic $B$-decays ($B\to K\pi$ puzzle). Furthermore, once the couplings of the $Z^\prime$ boson to the leptons are included, it is possible to address the intriguing hints for NP (above the 5$\,\sigma$ level) in $b\to s \ell^+\ell^-$ transitions. Taking into account all flavour observables in a global fit, we find that $\epsilon^\prime/\epsilon$, the $B\to K\pi$ puzzle and $b\to s \ell^+\ell^-$ data can be explained simultaneously. Sizeable CP violation in $b\to s \ell^+\ell^-$ observables, in particular $A_8$, is predicted, which can be tested in the near future, and an explanation of the $B\to K\pi$ and $\epsilon^\prime/\epsilon$ puzzles leads to effects in di-jet tails at the LHC, that are not far below the current limits. Once $b\to s \ell^+\ell^-$ is included, cancellations in di-muon tails, possibly by a second $Z^\prime$, are required by LHC data.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the phenomenology of simplified $Z^\prime$ models with a global $U(2)^3$ flavour symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. | contribution 0.98 | 0.83 | 0.03 | asserted 0.92 |
| s1 | This flavour symmetry, known as less-minimal flavour violation, protects $\Delta F=2$ processes from dangerously large new physics (NP) effects, and at the same time provides a free complex phase in $b\to s$ transitions, allowing for an explanation of the hints for additional direct CP violation in kaon decays ($\epsilon^\prime/\epsilon$) and in hadronic $B$-decays ($B\to K\pi$ puzzle). | background 0.37 | 0.17 | 0.18 | asserted 0.95 |
| s2 | Furthermore, once the couplings of the $Z^\prime$ boson to the leptons are included, it is possible to address the intriguing hints for NP (above the 5$\,\sigma$ level) in $b\to s \ell^+\ell^-$ transitions. | contribution 0.66 | 0.37 | 0.08 | hedged possibility 0.96 |
| s3 | Taking into account all flavour observables in a global fit, we find that $\epsilon^\prime/\epsilon$, the $B\to K\pi$ puzzle and $b\to s \ell^+\ell^-$ data can be explained simultaneously. | result 1.00 | 0.95 | 0.64 | asserted 1.00 |
| s4 | Sizeable CP violation in $b\to s \ell^+\ell^-$ observables, in particular $A_8$, is predicted, which can be tested in the near future, and an explanation of the $B\to K\pi$ and $\epsilon^\prime/\epsilon$ puzzles leads to effects in di-jet tails at the LHC, that are not far below the current limits. | result 0.88 | 0.85 | 0.19 | asserted 0.91 |
| s5 | Once $b\to s \ell^+\ell^-$ is included, cancellations in di-muon tails, possibly by a second $Z^\prime$, are required by LHC data. | result 0.87 | 0.71 | 0.08 | asserted 0.68 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:1910.00014 by the authors.
References
How the literature uses it
34 arXiv papers cite this in 38 sentences
Papers citing it · 21 sentences without a confident label
Compares with it 1 paper
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Early Dark Energy (EDE) [ref] typically produces power-law modifications with $ΔN_eff ∼0.3$–$0.5$, creating tension with the Planck temperature spectrum [ref] .
Doubly Logarithmic Corrections to Radiation Domination from CET {\Omega}: Theory and Planck/BBN Constraints · Comparison with Other Early-Universe Scenarios · 0.96
Cites it as background 15 papers
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Depending on the quark couplings involved, these $$ models can be classified into two categories: (i) The $$ boson has flavour-violating couplings to $b$ and $s$ quarks and the $b →s ℓ^+ ℓ^-$ transitions receive contributions from tree-level $$ exchange [ref] .
Explaining the $b \to s \ell^+ \ell^-$ anomalies in $Z^\prime$ scenarios with top-FCNC couplings · Introduction · 0.97
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Various $U(1)'$ gauge symmetry have been proposed to explain the NCBAs [ref] .
Explaining the $R_{K^{(*)}}$ anomalies in a Fundamental Composite Higgs Model with Gauged $U(1)_{SM_3-HB}$ · The $U(1)'$ gauge symmetry in fundamental composite Higgs models · 0.92
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As a prototypical-model (a partial list of references is [ref] ), we consider a $Z^'$ which dominantly couples to $b s$ and $μ^+ μ^-,$ via left-handed currents[Right-handed currents in the lepton-sector actually worsen the compatibility of $R_K^(*)$ explanation with the $ΔM_s$ (mass-differences of neutral $B$-mesons) measurement [ref] , since they demand a larger Wilson-coefficient.].
Probing the $R_{K^{(*)}}$ Anomaly at a Muon Collider · Introduction · 0.82
Discussion
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