REVIEW
Right-handed neutrinos and the CDF II anomaly
High Energy Physics - Phenomenology · Submitted 9 Apr 2022 · 56 references
Pith's verdict: A timely, honest application of the known non-unitarity framework to CDF II; the physics is standard but the fit is done properly, and the main caveat is a framing choice in the abstract rather than an error.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
Right-handed neutrinos, integrated out to a single dimension-six operator, make the neutrino mixing matrix slightly non-unitary, which raises the predicted W-boson mass toward the CDF II value without violating lepton-flavour universality.
The reading
What carries the argument
The load-bearing object is the non-unitarity matrix $eta$, defined by $N_{alpha i} = (delta_{alphaeta} - eta_{alphaeta})U_{eta i}$, where $U$ is the unitary rotation diagonalizing the Weinberg operator and $eta = c_{d=6} v^2/4$. Its diagonal entries are the only quantities that enter the electroweak observables: $eta_{ee} + eta_{mumu}$ controls the shift in the Fermi constant and hence in $M_W$; the same combination appears in the invisible Z width through $N_ u$; and the universality ratios $R_P^{alpha/eta}$ constrain the difference through $(1-eta_{mumu})/(1-eta_{ee})$. What makes the mechanism work is that $eta$ is positive semi-definite when it comes from right-handed neutrino Yukawa couplings, so the W-mass prediction can only move upward, in the direction CDF II indicates.
Extended reading notes
Core claim
The claim is that right-handed neutrinos supply a single, economical origin for the CDF II W-mass anomaly. Integrating out the heavy states generates $O_{d=6} = i/2 (Y_ u Y_ u^dagger / Lambda^2)(H^dagger l_L) slashed{partial} (l_L^dagger H)$, which after electroweak symmetry breaking shifts the PMNS matrix to $N = (1-eta)U$ with $eta = Y_ u Y_ u^dagger v^2/(4 Lambda^2)$ Hermitian and positive semi-definite. Because the same lepton vertex appears in muon decay, the extracted Fermi constant relates to the true one by $G_F = G_mu (1 + eta_{ee} + eta_{mumu})$, and the W-mass prediction rises accordingly. Fitting the CDF II value $M_W = 80.4335(94)$ GeV along with pion, kaon and tau universality ratios gives an excellent fit, $chi^2/mathrm{ndof} = 3.3/2$, with $eta_{ee} approx eta_{mumu} approx 3 imes 10^{-3}$, and the resulting $N_ u = 3 - 4eta_{ au au} - eta_{ee} - eta_{mumu}$ also sits comfortably with the LEP invisible width. Including the $\beta$- and kaon-decay determinations of $V_{ud}$ and $V_{us}$ destroys the fit, with $chi^2/mathrm{ndof} = 40.1/7$ and a p-value of $1.3 imes 10^{-6}$, because a positive semi-definite $eta$ can only worsen the Cabibbo anomaly. The authors are explicit that a common explanation of both anomalies is in tension, and that the Cabibbo-anomaly branch of their fit requires $eta_{mumu} < 0$, which right-handed neutrinos alone cannot produce.
Load-bearing premise
The positive result rests on dropping the beta- and kaon-decay constraints from the fit, so the good agreement with CDF II and with lepton universality holds only if the Cabibbo angle anomaly has some other, separate origin.
Editorial extensions
If this is right
- If the fit is right, the heavy neutrinos mix with $ u_e$ and $ u_mu$ at the few-percent level, about $0.07$ in amplitude, which for order-one Yukawa couplings places the heavy states near the TeV scale and within reach of future collider searches.
- The invisible Z width should read $N_ u = 3 - 4eta_{ au au} - eta_{ee} - eta_{mumu}$, slightly below three, consistent with the LEP value of $2.9963(74)$.
- Lepton-flavour-universality ratios in pion, kaon and tau decays constrain only the difference $eta_{ee} - eta_{mumu}$, so the fit naturally prefers the two diagonal entries to be nearly equal.
- A common origin for the W-mass anomaly and the Cabibbo angle anomaly is ruled out within this operator: the positive semi-definiteness of $eta$ forces the Cabibbo fit into the wrong direction, so a joint explanation needs additional new physics beyond right-handed neutrinos.
Reading between the lines
- A future Z-pole run with a Tera-Z sample would measure $N_ u$ to a precision that tests the same $eta_{ee} + eta_{mumu}$ combination independently of the hadronic form-factor uncertainties that dominate the kaon extraction.
- If the CDF II W mass is not confirmed by later measurements, the surviving branch of this analysis is the Cabibbo-anomaly one, which needs $eta_{mumu} < 0$ and therefore cannot come from right-handed neutrinos alone; the scenario then becomes a discriminator between the two anomalies rather than a bridge between them.
- Direct searches for heavy neutral leptons with percent-level mixing in both the electron and muon channels would be the sharpest independent check, since the fit requires the two mixings to be comparable rather than hierarchical.
- The same non-unitarity shifts the weak mixing angle extracted from parity-violating measurements, which the authors deliberately exclude here; folding those in would tighten the allowed band on $eta_{ee} + eta_{mumu}$ and could sharpen or close the CDF II window.
Original abstract
We point out that right-handed neutrinos can resolve the tension between the latest CDF II measurement of the $W$-boson mass, $M_W$, and the standard model. Integrating out the new states yields a single $d=6$ operator, which induces a deviation from unitarity in the PMNS matrix. This alters the extraction of the Fermi constant from muon decay and increases the prediction for $M_W$, in line with the CDF II result. Non-unitarity of the PMNS matrix would also affect beta, meson, and tau decays. We find that the CDF II value for $M_W$ can be explained without conflicting with lepton flavour universality constraints or the invisible decay width of the $Z$. However, the so-called Cabibbo angle anomaly is worsened if right-handed neutrinos are the origin of the $d=6$ operator. The situation improves if the operator coefficient is left unconstrained, implying additional sources of new physics, but a common explanation of both anomalies is in tension with universality bounds.
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 point out that right-handed neutrinos can resolve the tension between the latest CDF II measurement of the $W$-boson mass, $M_W$, and the standard model. Integrating out the new states yields a single $d=6$ operator, which induces a deviation from unitarity in the PMNS matrix. This alters the extraction of the Fermi constant from muon decay and increases the prediction for $M_W$, in line with the CDF II result. Non-unitarity of the PMNS matrix would also affect beta, meson, and tau decays. We find that the CDF II value for $M_W$ can be explained without conflicting with lepton flavour universality constraints or the invisible decay width of the $Z$. However, the so-called Cabibbo angle anomaly is worsened if right-handed neutrinos are the origin of the $d=6$ operator. The situation improves if the operator coefficient is left unconstrained, implying additional sources of new physics, but a common explanation of both anomalies is in tension with universality bounds.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We point out that right-handed neutrinos can resolve the tension between the latest CDF II measurement of the $W$-boson mass, $M_W$, and the standard model. | contribution 0.59 | 0.84 | 0.83 | hedged possibility 0.63 |
| s1 | Integrating out the new states yields a single $d=6$ operator, which induces a deviation from unitarity in the PMNS matrix. | result 0.46 | 0.75 | 0.06 | asserted 1.00 |
| s2 | This alters the extraction of the Fermi constant from muon decay and increases the prediction for $M_W$, in line with the CDF II result. | result 0.56 | 0.61 | 0.22 | asserted 1.00 |
| s3 | Non-unitarity of the PMNS matrix would also affect beta, meson, and tau decays. | interpretation 0.79 | 0.15 | 0.04 | asserted 0.74 |
| s4 | We find that the CDF II value for $M_W$ can be explained without conflicting with lepton flavour universality constraints or the invisible decay width of the $Z$. | result 0.99 | 0.92 | 0.43 | asserted 0.90 |
| s5 | However, the so-called Cabibbo angle anomaly is worsened if right-handed neutrinos are the origin of the $d=6$ operator. | limitation 0.59 | 0.57 | 0.11 | asserted 0.97 |
| s6 | The situation improves if the operator coefficient is left unconstrained, implying additional sources of new physics, but a common explanation of both anomalies is in tension with universality bounds. | interpretation 0.55 | 0.65 | 0.23 | asserted 0.82 |
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
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:2204.04559 by the authors.
References
How the literature uses it
65 arXiv papers cite this in 74 sentences
Papers citing it · 40 sentences without a confident label
Uses its data or values 1 paper
-
To be mentioned is the new measurement from the CDF II collaboration of the $W$-gauge boson mass [ref] , that exceeds the SM prediction by approximately $7σ$ (but not confirmed by the last ATLAS result [ref] ): assuming that the CDF II result is correct, different explanations have been proposed to account for the deviation from the SM prediction, from tree-level modification of the muon decay induced by exotic leptons (see for example Refs. [ref] ), to loop quantum corrections to the two-point functions of the SM gauge bosons (see for example Refs. [ref] ).
Flavour and Higgs physics in $Z_2$-symmetric 2HD models near the decoupling limit · Introduction · 0.85
Cites it as support 1 paper
-
As it is pointed out in [ref] , the insertion of right-handed neutrinos in the model produces a positive definite $η$ matrix which is a necessary condition to explain the CDF-measurement of the W-boson mass.
Sterile neutrinos, $0\nu\beta\beta$ decay and the W-boson mass anomaly in a Flipped $SU(5)$ from F-theory · A possible interpretation of the CDF measurement of the W-mass · 0.98
Cites it as background 32 papers
-
There have been many attempts to resolve the W mass anomaly, see e.g. [ref] .
Constraints from New CDF II W-Boson Mass On Top-Bottom Seesaw and the TopFlavor Models · Introduction · 0.99
-
Recently, several novel physics models, including the : Two-Higgs doublet model [ref] , Higgs triplet model [ref] , supersymmetry [ref] , leptoquark model [ref] , seesaw mechanism [ref] , vector-like leptons and/or vector-like quarks [ref] and other SM extensions [ref] are proposed to explain the W boson mass anomaly.
Consistency of New CDF-II W Boson Mass with 123-Model · Introduction · 0.97
-
Various BSM models have been studied to explain the new oblique parameters [ref] .
CDF $W$ boson mass and muon $g-2$ in type-X two-Higgs-doublet model with a Higgs-phobic light pseudoscalar · Introduction · 0.93
What it cites · 49 sentences without a confident label
Uses data or values from 2 papers
-
Data coming from pion, kaon, and tau lepton decays constrain ratios of $η$ elements [ref] : (1-η_μμ/1-η_ee)_π= 1.0010(9), (1-η_μμ/1-η_ee)_K= 0.9978(18),
Testing Lepton Flavor Universality with Pion, Kaon, Tau, and Beta Decays · Introduction · 0.97
-
The correlation matrix among the kaon decay observables from [ref] has also been taken into account.
Experimental determination of $V_{us}$ from kaon decays · Introduction · 0.86
Cites as background 4 papers
-
This is the case of the Inverse [ref] or Linear [ref] Seesaw mechanisms.
Novel Supersymmetric SO(10) Seesaw Mechanism · Introduction · 0.89
-
In the canonical type-I Seesaw mechanism [ref] , where the lightness of neutrino masses derives from the hierarchy between the Dirac and Majorana masses, the $d=6$ operator will be highly suppressed, making its phenomenological impact negligible.
Complex Spinors and Unified Theories · Introduction · 0.97
-
The Standard Model of particle physics (SM) is an extremely successful theory, having made countless predictions that have been experimentally verified, the crowning achievement being the discovery of the Higgs boson a decade ago [ref] .
Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC · Introduction · 0.95
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.