REVIEW
The R-Parity Violating Minimal Supergravity Model
High Energy Physics - Phenomenology · Submitted 17 Sep 2003 · 112 references
Pith's verdict: A solid, double-checked RPV RGE paper whose real contribution is the full flavour-dependent one-loop running and the first explicit neutrino-mass bounds on λ and λ′; the abstract's 'five orders of magnitude' is a single-benchmark number, not a model-class statement.
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Referee report
The paper
The paper claims
A single non-zero R-parity-violating coupling at the unification scale is enough to generate a neutrino mass, and the observed neutrino mass bound then caps that coupling far below previously published limits.
The reading
What carries the argument
The machinery is the coupled one-loop renormalization group flow of the full R-parity-violating model, combined with an iterative minimization of the five-neutral-scalar potential. The flow equations for the $kappa_i$ and for the soft bilinear terms $tilde{D}_i$ are structurally different, so alignment present at the unification scale is lost at the weak scale; that misalignment is precisely what feeds the neutrino mass. The minimization is done by writing the neutral scalars as $h_2^0 = x_2 + i y_2$ and $tilde{nu}_alpha = r_alpha + i t_alpha$, fixing $tan beta = v_u/v_d$ so that it matches the R-parity-conserving definition, solving a quadratic for $mu$, then for $tilde{B}$, then a linear system for the sneutrino vevs $v_i$, and iterating to convergence. This is what lets the authors compute the neutrino mass and the sparticle spectrum from the same six inputs at the unification scale: $M_0$, $M_{1/2}$, $A_0$, $tan beta$, the sign of $mu$, and one non-zero R-parity-violating coupling.
Extended reading notes
Core claim
The central claim is that neutrino masses are not an optional extra in R-parity-violating supergravity but a compulsory consequence of it, and therefore a bound. Starting from $kappa_i = tilde{D}_i = 0$ at the unification scale, the authors show through Eqs. (28) and (29) that the anomalous dimension mixing the lepton doublets with $H_1$ is proportional to $Y_E Lambda_E + Y_D Lambda_D$; any non-zero $lambda$ or $lambda'$ combined with $mu(M_X) neq 0$ therefore generates non-zero $kappa_i$ at the weak scale. Those $kappa_i$, together with the sneutrino vacuum expectation values $v_i$ obtained from minimizing the potential, give the neutrino-neutralino mixing entry in the $7 times 7$ mass matrix, and Eq. (86) turns it into one massive neutrino, $m_nu approx -16 pi alpha_{GUT} sum_i Lambda_i^2 / (5 M_{1/2})$ with $Lambda_i = v_i - v_d kappa_i/mu$. Imposing $sum m_{nu_i} < 0.71$ eV from WMAP plus 2dFGRS then bounds the couplings: for SPS1a the strongest entries are around $3 times 10^{-6}$ at the unification scale for $lambda'_{333}$, against limits of order $10^{-1}$ to $10^{-3}$ from earlier direct searches. The paper also derives a separate no-tachyon bound on the same couplings, and reports that the lightest supersymmetric particle is a stau, selectron, or sneutrino over substantial regions of no-scale parameter space rather than the neutralino.
Load-bearing premise
The bounds are computed at one benchmark parameter point, and the paper's own scan shows the same bound shifting by roughly two orders of magnitude elsewhere in parameter space, so the headline factor describes that point rather than the model as a whole.
Editorial extensions
If this is right
- Any measurement of a lepton-number-violating coupling above the tabulated values, at a spectrum close to the benchmark, would conflict with the cosmological neutrino mass bound unless the model's parameters are moved substantially.
- Because the bound scales with the logarithm of the unification scale squared, the same argument gives weaker limits in models with lower mediation scales, and stronger ones as the mediation scale rises.
- The lightest supersymmetric particle need not be the neutralino, so missing-transverse-energy searches lose their universality and multilepton, multi-tau, and detached-vertex signatures become the discriminating channels.
- A stau lightest supersymmetric particle that does not couple to the dominant R-parity-violating operator decays through a four-body mode with a macroscopic lifetime, giving a displaced vertex.
- The neutrino mass and the sneutrino-antisneutrino mass splitting are of the same order in these models, so searches for like-sign dileptons from sneutrino mixing probe the same parameters.
Reading between the lines
- The quoted five-orders-of-magnitude improvement is a statement about one benchmark point; since the paper's own scan shows the $lambda'_{333}$ bound moving by about two orders of magnitude across the no-scale slice, a fair public summary should attach the number to SPS1a rather than to the model class.
- The comparison to earlier limits also crosses mass points, because the older bounds assume sfermions near 100 GeV while the benchmark has squarks several times heavier and the bounds scale with sfermion mass; a like-for-like comparison would narrow the headline factor.
- If the same RGE chain were run in a gauge-mediated model with a much lower messenger scale, the induced neutrino mass would shrink and the coupling limits would relax, which makes the argument a probe of the mediation scale as much as of R-parity violation.
- The assumption that $kappa_i$ and $tilde{D}_i$ vanish together at unification is motivated but not forced; a departure from it would shift the induced neutrino mass and hence every bound in the tables.
Original abstract
We present the minimal supersymmetric standard model with general broken R-parity, focusing on minimal supergravity (mSUGRA). We discuss the origins of lepton number violation in supersymmetry. We have computed the full set of coupled one-loop renormalization group equations for the gauge couplings, the superpotential parameters and for all the soft supersymmetry breaking parameters. We provide analytic formule for the scalar potential minimization conditions which may be iterated to arbitrary precision. We compute the low-energy spectrum of the superparticles and the neutrinos as a function of the small set of parameters at the unification scale in the general basis. Specializing to mSUGRA, we use the neutrino masses to set new bounds on the R-parity violating couplings. These bounds are up-to five orders of magnitude stricter than the previously existing ones. In addition, new bounds on the R-parity violating couplings are also derived demanding a non-tachyonic sneutrino spectrum. We investigate the nature of the lightest supersymmetric particle and find extensive regions in parameter space, where it is not the neutralino. This leads to a novel set of supersymmetric signatures, which we classify.
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 present the minimal supersymmetric standard model with general broken R-parity, focusing on minimal supergravity (mSUGRA). We discuss the origins of lepton number violation in supersymmetry. We have computed the full set of coupled one-loop renormalization group equations for the gauge couplings, the superpotential parameters and for all the soft supersymmetry breaking parameters. We provide analytic formule for the scalar potential minimization conditions which may be iterated to arbitrary precision. We compute the low-energy spectrum of the superparticles and the neutrinos as a function of the small set of parameters at the unification scale in the general basis. Specializing to mSUGRA, we use the neutrino masses to set new bounds on the R-parity violating couplings. These bounds are up-to five orders of magnitude stricter than the previously existing ones. In addition, new bounds on the R-parity violating couplings are also derived demanding a non-tachyonic sneutrino spectrum. We investigate the nature of the lightest supersymmetric particle and find extensive regions in parameter space, where it is not the neutralino. This leads to a novel set of supersymmetric signatures, which we classify.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present the minimal supersymmetric standard model with general broken R-parity, focusing on minimal supergravity (mSUGRA). | contribution 0.97 | 0.84 | 0.05 | asserted 0.96 |
| s1 | We discuss the origins of lepton number violation in supersymmetry. | background 0.64 | 0.50 | 0.03 | unclear 0.52 |
| s2 | We have computed the full set of coupled one-loop renormalization group equations for the gauge couplings, the superpotential parameters and for all the soft supersymmetry breaking parameters. | method 0.78 | 0.97 | 0.04 | asserted 1.00 |
| s3 | We provide analytic formule for the scalar potential minimization conditions which may be iterated to arbitrary precision. | method 0.55 | 0.96 | 0.04 | asserted 0.61 |
| s4 | We compute the low-energy spectrum of the superparticles and the neutrinos as a function of the small set of parameters at the unification scale in the general basis. | contribution 0.50 | 0.96 | 0.08 | asserted 1.00 |
| s5 | Specializing to mSUGRA, we use the neutrino masses to set new bounds on the R-parity violating couplings. | result 0.51 | 0.96 | 0.31 | asserted 1.00 |
| s6 | These bounds are up-to five orders of magnitude stricter than the previously existing ones. | result 0.88 | 0.82 | 0.27 | asserted 0.99 |
| s7 | In addition, new bounds on the R-parity violating couplings are also derived demanding a non-tachyonic sneutrino spectrum. | result 0.73 | 0.96 | 0.09 | asserted 1.00 |
| s8 | We investigate the nature of the lightest supersymmetric particle and find extensive regions in parameter space, where it is not the neutralino. | result 0.94 | 0.97 | 0.17 | asserted 1.00 |
| s9 | This leads to a novel set of supersymmetric signatures, which we classify. | result 0.41 | 0.94 | 0.17 | asserted 0.99 |
What was examined, and what was not
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Figures
Showing 6 of the paper's 8 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0309196 by the authors.
References
How the literature uses it
67 arXiv papers cite this in 203 sentences
Papers citing it · 133 sentences without a confident label
Contests it 1 paper
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Note that the bounds in Ref. [ref] were also obtained for a less restrictive cosmological bound of $∑m_ν_i < 0.71 eV$ [Ref. [ref] did not calculate the dominant loop contributions to the neutrino mass matrix.
Bounds on R-parity Violating Couplings at the Grand Unification Scale from Neutrino Masses · Comparison with Previous Results · contest 0.75
Builds on it 1 paper
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We go beyond this and also consider a scalar tau LSP [ref] .
A Simple Baryon Triality Model for Neutrino Masses · Introduction · 0.84
Uses its method or tool 6 papers
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We employ the full set of renormalization group equations (RGEs) at one loop [ref] in order to obtain the $B_3$ SSM spectrum and the neutrino masses at the electroweak scale ($M_EW$).
Bounds on R-parity Violating Couplings at the Grand Unification Scale from Neutrino Masses · Introduction · 0.97
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Rather, we use custom programs to solve the one-loop RG equations [ref] of the RPV-MSSM between $M_SUSY$ and $M_GUT$.
Baryonic R-parity violation and its running · Numerical procedures and mass spectrum · 0.96
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We have employed the one-loop contributions from gauge interactions [ref] , as well as the B$_3$ leading interaction
Sneutrino as Lightest Supersymmetric Particle in B3 mSUGRA Models and Signals at the LHC · $A_0$ Dependence · 0.93
Uses its data or values 6 papers
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The least constrained couplings of the $L_i L_j E̅_k$ operators, Eq. ([ref]), are [ref] [equation] where the bounds apply at $M_Z$.
All Possible Lightest Supersymmetric Particles in R-Parity Violating Minimal Supergravity Models · Non-$χ̃_1^0$ LSPs via LLE · 0.92
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Demanding that this neutrino mass is smaller than the cosmological bound on the sum of neutrino masses, determined by the combination of the WMAP data [ref] and the 2dFGRS data [ref] , [equation] results in upper bounds on $'_ijk|_GUT$, which were calculated in Ref. [ref] for the parameter point SPS1a [ref] .
Sneutrino as Lightest Supersymmetric Particle in B3 mSUGRA Models and Signals at the LHC · Bounds from Tree Level Neutrino Masses · 0.91
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The black region corresponds to excluded parameter points, with tachyons [ref] or which violate the Higgs mass or stau mass bounds from LEP [Following Ref. [ref] we use the lower stau mass bound from LEP obtained in the $R$-parity conserving limit, because LEP did not explore the possibility of a stau LSP decaying via a four-body decay.], $m_h^0>90$–$114.4$ GeV [ref] , depending on the SUSY parameters [In order to calculate the correct Higgs mass bound we used the respective routine implemented in SOFTSUSY.], and $m_τ̃_1>86$ GeV [ref] .
Stau as the Lightest Supersymmetric Particle in R-Parity Violating SUSY Models: Discovery Potential with Early LHC Data · Discovery Potential with early LHC Data · 0.90
Compares with it 1 paper
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In Sec. [ref], we first compare our bounds with those given in Ref. [ref] , where the mSUGRA parameters of the benchmark point SPS1a [ref] (in addition to $Λ$) were used.
Bounds on R-parity Violating Couplings at the Grand Unification Scale from Neutrino Masses · Bounds on Trilinear $B_3$ Couplings from $ν$–Masses · 0.99
Cites it as support 3 papers
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Within a baryon triality supergravity model the largest neutrino mass is naturally small [ref] .
A Simple Baryon Triality Model for Neutrino Masses · Introduction · 0.98
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This solution has an additional feature, it naturally leads to small neutrino masses [ref] , as experimentally observed [ref] .
Single Slepton Production in association with a single Top Quark at the Tevatron and LHC · Introduction · 0.98
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Furthermore as argued in Ref. [ref] , at the unification scale the $_i$ can be set to zero.
The ABC of RPV III: Classification of R-parity Violating Signatures from LQD Couplings and their Coverage at the LHC · Introduction · 0.98
Cites it as background 40 papers
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For detailed phenomenological studies, the $B_3$ mSUGRA model was proposed in Ref. [ref] .
Sneutrino as Lightest Supersymmetric Particle in B3 mSUGRA Models and Signals at the LHC · $B_3$ mSUGRA Model · 0.93
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In the B$_3$ mSUGRA model [ref] there are six free parameters at the unification scale ($M_GUT$) [equation] Here $M_0, M_1/2$ are the universal supersymmetry breaking scalar and gaugino masses, respectively. $A_0$ is the universal supersymmetry breaking scalar trilinear coupling and $tanβ$ is the ratio of the two vacuum expectation values. $sgn(μ)= ±1$ is the sign of the Higgs mixing parameter.
Stau as the Lightest Supersymmetric Particle in R-Parity Violating SUSY Models: Discovery Potential with Early LHC Data · Motivation · 0.97
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A more generic version of the MSSM, therefore, contains $R$-parity violating (RPV) terms [ref] , which can lead to generation of light neutrino masses and mixings naturally [ref] .
Markov Chain Monte Carlo analysis to probe trilinear $R$-parity violating SUSY scenarios and possible LHC signatures · Introduction · 0.81
Discussion
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