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Weak mixing angle at low energies
High Energy Physics - Phenomenology · Submitted 14 Sep 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting value of the low-energy weak mixing angle is sin^2 theta_W (0) = 0.23867 +- 0.00016.
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The abstract, sentence by sentence
We determine the weak mixing angle in the MS-bar scheme at energy scales relevant for present and future low energy electroweak measurements. We relate the renormalization group evolution of the weak mixing angle to the corresponding evolution of the QED coupling and include higher-order terms in alpha_s and alpha that had not been treated in previous analyses. We also up-date the analysis of non-perturbative hadronic contributions and argue that the associated uncertainty is small compared to anticipated experimental errors. The resulting value of the low-energy weak mixing angle is sin^2 theta_W (0) = 0.23867 +- 0.00016.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We determine the weak mixing angle in the MS-bar scheme at energy scales relevant for present and future low energy electroweak measurements. | contribution 1.00 | 0.95 | 0.09 | asserted 0.99 |
| s1 | We relate the renormalization group evolution of the weak mixing angle to the corresponding evolution of the QED coupling and include higher-order terms in alpha_s and alpha that had not been treated in previous analyses. | contribution 0.56 | 0.92 | 0.04 | asserted 1.00 |
| s2 | We also up-date the analysis of non-perturbative hadronic contributions and argue that the associated uncertainty is small compared to anticipated experimental errors. | contribution 0.81 | 0.86 | 0.04 | asserted 0.76 |
| s3 | The resulting value of the low-energy weak mixing angle is sin^2 theta_W (0) = 0.23867 +- 0.00016. | result 1.00 | 0.95 | 0.92 | asserted 1.00 |
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The paper
Original abstract
We determine the weak mixing angle in the MS-bar scheme at energy scales relevant for present and future low energy electroweak measurements. We relate the renormalization group evolution of the weak mixing angle to the corresponding evolution of the QED coupling and include higher-order terms in alpha_s and alpha that had not been treated in previous analyses. We also up-date the analysis of non-perturbative hadronic contributions and argue that the associated uncertainty is small compared to anticipated experimental errors. The resulting value of the low-energy weak mixing angle is sin^2 theta_W (0) = 0.23867 +- 0.00016.
Human review
References
How later papers used it
73 later papers cite it
5 later papers by other authors are listed below: 4 used its method or tool and 1 used its data or values.
Uses its method or tool 4 of 7 papers with this label
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To do so, an $$ definition of the EW mixing angle $$ [ref] , where $μ$ is chosen as the invariant mass of the final state leptons $μ=$, is considered.
Probing the Weak Mixing Angle at high energies at the LHC (2022) · Introduction · 0.93
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Implemented the shift of the MS-bar sine of the weak mixing angle using the evolution formula obtained in this paper.
Notes on interplay of the QCD and EW perturbative corrections to the pole-running top-quark mass ratio (2022) · 1.00 · paraphrased: the licence does not allow quoting
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We follow Ref. [ref] , which introduced the effective weak mixing angle $sin^2θ_W^eff(Q^2)$, such that at $Q^2=0$, we have
Measuring the weak mixing angle at SBND (2024) · Neutrino electron elastic scattering · 0.99
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Followed the convention in this paper for renormalizing the Lagrangian parameters e and sin^2 theta_w in the MS-bar scheme.
Probing the weak mixing angle at high energy (2023) · 0.98 · paraphrased: the licence does not allow quoting
Uses its data or values 1 of 28 papers with this label
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The weak charge $Q_Wβ^2$ is expressed in terms of the proton number ($Z$), neutron number ($N$), standard vector coupling constants $g_p^V=1/2-2sin^2θ_W$[We use the low energy value $sin^2θ_W$ = 0.2387 [ref] for the analysis.], $g_n^V=-1/2$ and the NC NSI parameters $ε_αβ^uV$ and $ε_αβ^dV$, as [equation]
CP-Violating and Charged Current Neutrino Non-standard Interactions in CE$\nu$NS (2021) · Fluxes with CC NSI, Cross Section with NC NSI and the Expected Energy Spectrum · 1.00
How the literature uses it
67 arXiv papers cite this in 109 sentences
Papers citing it · 59 sentences without a confident label
Contests it 1 paper
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We fill this gap and correct the previously used prescription of Ref. [ref] .
Matching the Weak Mixing Angle at Low Energies · Motivation and Introduction · contest 0.92
Uses its method or tool 7 papers
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The impact of hadronic uncertainties is discussed by using the framework of threshold quark masses introduced in Refs. [ref] .
Hadronic effects in M{\o}ller scattering at NNLO · Introduction · 0.98
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To do so, an $$ definition of the EW mixing angle $$ [ref] , where $μ$ is chosen as the invariant mass of the final state leptons $μ=$, is considered.
Probing the Weak Mixing Angle at high energies at the LHC · Introduction · 0.93
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The shift of the $$-scheme sine of the weak mixing angle from the initial normalization at $μ^2=M^2_Z$ to $μ^2=M^2_t$ is implemented by us with the help of the evolution formula, obtained in [ref] : [equation]
Notes on interplay of the QCD and EW perturbative corrections to the pole-running top-quark mass ratio · One-loop analysis · 1.00
Uses its data or values 27 papers
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The $A_LR$ asymmetry has been measured at low $Q^2 = 0.026$ GeV$^2$ in the SLAC–E158 experiment [ref] , with the result [equation] leading to a determination of the weak mixing angle of $sin^2 θ_W^eff = 0.2403 ±0.0013$ [ref] , which is $1.25σ$ higher than the SM prediction [ref] , $sin^2 θ^eff_W = 0.23867$.
Alternative $Z'$ Bosons in $E_6$ · Low Energy Constraints on $E_6$ · 0.93
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where $Q_i$ is the electric charge of the particle in units of the proton charge, $N_c = 3$ is the number of colors in QCD, $Π̂_3 γ^(3)(0; μ)$ is a nonperturbative current-current charge-isospin correlator in the theory with $n_f=3$ quark flavors estimated as $Π̂_3 γ^(3) = (1±0.2) Π̂_γγ^(3)$ [ref] with the charge-charge correlator evaluated from the experimental data on hadron production $Π̂_γγ^(3)(0; μ= 2 GeV) = 3.597(21)$ [ref] .
Flavor-dependent radiative corrections in coherent elastic neutrino-nucleus scattering · Four-fermion effective field theory and radiative corrections · 0.98
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To evaluate non-perturbative hadronic contributions, we take the charge-charge correlation function at $Q^2=0$, i.e. $Π̂_γγ^(3) ( 0; μ= 2 GeV ) = 3.597(21)$, from the data-driven analysis of [ref] and determine its $Q^2$ dependence in the theory with three quark flavors using the alphaQED2025 package [ref] .
Radiative corrections in neutral-current (anti)neutrino elastic scattering at $\text{GeV}$ energies I: Nucleon targets · Non-perturbative light-quark contributions · 0.96
Compares with it 2 papers
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The remainder is determined from the photon self energy and the $γZ$ mixing, and we find the explicit, final expression for the effective electromagnetic coupling constant in the LEFT in terms of the SM \(\)-renormalized coupling, [equation] or [equation] Equation [ref] is identical to the matching condition found in Ref. [ref] and its scale-independent part was used in Refs. [ref] to match the running fine structure constant at the $W$ threshold.
Matching the Weak Mixing Angle at Low Energies · Effective Low-Energy Theory · 0.95
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This value of the weak mixing angle, Eq. ([ref]), and the Standard Model prediction [ref]
Probing nonstandard interactions with reactor neutrinos · Weak mixing angle and effective electron neutrino charge radius · 0.83
Cites it as support 2 papers
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Here we have assumed that $sin^2θ_W$ is independent of the transfer momentum, which is consistent with SM expectation [ref] , for the range of interest.
First constraint on the weak mixing angle using direct detection experiments · Neutrino event rate · 0.96
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There is however an interesting observation that allows for the following simplification: for the renormalization scales ($q_max$) that matter in the calculation of WIMP discovery limits ($q_max≲200$MeV), the weak mixing angle RGE evolution (in the SM) is rather flat [ref] .
Impact of COHERENT measurements, cross section uncertainties and new interactions on the neutrino floor · Impact of nuclear form factor and weak mixing angle uncertainties · 0.98
Cites it as background 6 papers
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This can be defined either as an effective parameter which absorbs certain momentum-dependent higher-order corrections [ref] or in a framework with $$ renormalization as the solution of a renormalization group equation (RGE), often denoted $sin^2θ̂_W(μ)$ [ref] .
Matching the Weak Mixing Angle at Low Energies · Motivation and Introduction · 0.89
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For example, in the modified minimal subtraction scheme [ref] , $0.8MS$, the weak mixing angle is [equation] where $g$ and $g'$ are the $SU(2)_L$ and $U(1)_Y$ gauge coupling constants, respectively, and $μ$ is the scale of the physical process under consideration.
Measuring the Weak Mixing Angle in the DUNE Near Detector Complex · Introduction · 0.92
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For example, Refs. [ref]
Unparticle Searches Through Low Energy Parity Violating Asymmetry · Introduction · 0.93
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