Phenomenological constraints on broken R parity symmetry in supersymmetry models

This is Chemtob's 2004 survey of indirect bounds on R-parity-violating couplings, and the honest summary is that it is a well-organized catalogue rather than a source of new results. It does the catalogue job well: 48 couplings sorted against the processes that constrain them, the bilinear/spontaneous-breaking option cleanly separated from the trilinear one, and the closing sections on RGE running and cosmology give the reader a place to start on questions the bound tables do not answer. The four-way split into hadron flavor, lepton flavor, lepton number and baryon number is the right organizing principle and I have used it. The effective Lagrangians in Eqs. 3, 41 and 42 and the one-loop neutrino mass formula in Eq. 33 are standard and correctly assembled. The author is also candid about the earlier EDM bounds in Refs. [155, 173] being invalid, which is the right way to handle it. The genuinely new content is thin: a corrected CKM unitarity formula in §3.1.2 that restores the quadratic coupling products dropped by Ledroit and Sajot, and updated top-mass entries in the epsilon and neutron-EDM estimates. That is worth having but it is not a review's reason for existing. On soft spots: the stress-test note lands. Several of the strongest entries — Eqs. 24, 25 and the neutron EDM bound in Eq. 28 — are derived explicitly in the m_squark >> m_W, m_t limit and then quoted at the 100 GeV reference mass, where that limit is marginal. The author flags in §1.3 that scaling differs between tree and loop mechanisms but does not flag that specific entries sit outside their derivation's domain. That is a correctness risk on individual numbers, not on the headline order-of-magnitude claim, which survives. The single-coupling-dominance worry is already acknowledged in §1.3 and §1.4, so I would not press it as a discovery. The 1998 PDG vintage is stated in §1.5 and is a product of its time. Who should read it: anyone entering RPV phenomenology who needs the map, and anyone writing a bound table who wants a checklist. Do not copy the numbers without going back to the cited sources — several entries are garbled in the text as presented. This deserves a referee, mainly to check the catalogue entries against their sources and to force the heavy-sfermion-limit issue into the open.

The central claim is the §1.3 statement that bounds are typically [λ, λ', λ''] < [O(10^-1) – O(10^-2)] × (m̃/100 GeV), with the linear mass scaling 'strictly holding in tree level type mechanisms.' The reader's weakest_assumption — single-coupling dominance and its basis dependence — is explicitly acknowledged in §1.3 and §1.4 and is built into the claim's own wording ('bounds derived under the single coupling constant dominance hypothesis'), so it does not land on the claim as stated. The narrower, less-acknowledged soft spot is the reference-mass convention. Several of the strongest entries are derived in an explicit heavy-sfermion limit: §3.3.1 states the K–K̄ effective Lagrangian is valid 'in the limit of large scalar superpartners masses, m_q >> m_W, m_q >> m_t,' and Eqs. 24–25 and the neutron-EDM bound in Eq. 28 inherit that limit. Yet the catalogue quotes these at m̃ = 100 GeV, where m̃ ≈ m_t and the decoupling/logarithmic approximations used to obtain the coefficients are marginal. The paper acknowledges in §1.3 that scaling is non-uniform between tree and loop mechanisms, but does not flag that specific entries are evaluated outside the domain of their derivation. This affects individual numbers by factors of a few, not the order-of-magnitude headline, so it is a correctness risk on the catalogue rather than on the central claim.

The paper is a 2004 review whose load-bearing assertion is a hedged order-of-magnitude statement about the size of RPV couplings implied by existing data. The reader's weakest_assumption (single-coupling dominance plus basis dependence) is a real feature of the catalogue, but the paper states it plainly in §1.3–1.4 and the claim is phrased conditionally on it, so attacking it does not land on the claim as written. The reader's inference that the bounds 'remove the naturalness argument for exact R parity' is somewhat stronger than the paper's own text: the classic proton-decay naturalness argument turns on the product of a baryon-number-violating and a lepton-number-violating coupling being far below 10^-1, not on individual couplings being below unity, and the paper does not claim otherwise. The one concern I can raise that is concrete, technical, and not fully acknowledged is the uniform application of the 100 GeV reference mass to bounds derived in the m̃ >> m_W, m_t limit (Eqs. 24, 25, 28). That is a correctness risk on individual catalogue entries, not on the headline claim, and it does not move the verdict. The paper's other candid limitations — 1998 PDG vintage (§1.5), the invalidity of earlier EDM bounds in Refs. [155, 173], the basis ambiguity — are acknowledged rather than buried, and the standard formulas I can check (Eqs. 3, 33, 40, 41) follow from the stated assumptions. I therefore recommend UNCHANGED, with the mass-limit consistency check as the one verification step worth running before the catalogue numbers are reused verbatim.

If the headline scaling holds, no RPV coupling can be order unity with superpartners at the electroweak scale, which removes the naturalness motivation for exact R parity and confines any broken-R-parity model to a constrained corner of parameter space. The review's value lies in the breadth and internal cross-linking of the catalogue, in the explicit statement of the single-coupling-dominance hypothesis and its basis dependence (§1.3, §1.4), and in the basis-independent treatment of bilinear parameters via the alignment condition μα ∝ vα (§2.2.1). It also ships falsifiable predictions that can be tested independently of the catalogue: the transverse muon polarization P_T(K_μ2γ) < 10^-2 (§3.3.2), the neutrino transition moment μ_{νeνμ} ≈ (10^-11 – 10^-10) μ_B (§3.4.2), and the phase difference Δφ ≃ O(1) between B_d → φK_S and B_d → J/ψK_S (§3.3.4). The original electroweak-fit analysis in §3.1.2, which converts the m_W and sin²θ_W inputs into a bound on λ12k, is a genuine contribution rather than a compilation entry.

Supersymmetric extensions of the Standard Model usually assume an exact R parity, a discrete symmetry that forbids renormalizable couplings letting quarks and leptons interact with their scalar superpartners. Chemtob asks what happens if that symmetry is only approximate, and answers by cataloguing, process by process, the indirect limits that low- and intermediate-energy experiments already place on the 48 possible R-parity-violating couplings. The headline number is that, with superpartners at 100 GeV, essentially every coupling is pushed below $O(10^{-1})$ to $O(10^{-2})$ times $(m/100~GeV)$, with the linear mass scaling holding for tree-level mechanisms. If that is right, no R-parity-violating coupling can be of order unity at the electroweak scale, so the familiar naturalness argument for exact R parity loses its force and any broken-R-parity model is squeezed into a narrow corner of parameter space.

What carries the argument. The machinery that carries the argument is the effective four-fermion Lagrangian obtained by integrating out a single sfermion, whose coefficients scale as $lambda^2/m_{tilde f}^2$, together with the single-coupling-dominance hypothesis: each bound is derived by switching on one R-parity-violating coupling at a time and setting the rest to zero, with all superpartner masses fixed at a reference 100 GeV. A ubiquitous technical ingredient is the redefinition of the Fermi constant by sfermion exchange, $G_F to G_F(1 + r_{12k}(tilde e_{kR}))$ with $r_{ijk} = (m_W^2/g_2^2 m_{tilde e_k}^2)|lambda_{ijk}|^2$, which propagates into every charged- and neutral-current observable and makes the bounds on $lambda_{12k}$ from muon decay, CKM unitarity, and atomic parity violation correlated rather than independent.

Core claim. The paper's central claim is a quantitative one: the existing body of precision, rare-decay, mixing, neutrino and cosmological data is already sufficient to bound the R-parity-violating Yukawa couplings to a characteristic size of order $10^{-1}$ to $10^{-2}$ for 100 GeV superpartners, with the bound scaling linearly with the superpartner mass in tree-level processes. Chemtob builds this claim by surveying, in a single systematic framework, three families of constraints: the bilinear and spontaneously broken options (where sneutrino vacuum expectation values, majoron emission from stars, and the Z invisible width do the work), the trilinear couplings $lambda$, $lambda'$, $lambda''$ as tested by charged- and neutral-current universality, atomic parity violation, neutral meson mixing, rare leptonic and semileptonic decays, and neutrino masses, and finally the renormalization-group and cosmological/astrophysical constraints. A secondary but load-bearing observation is that bounds on products of two couplings are generally stronger than the product of the corresponding single-coupling bounds, so flavour-changing processes such as $K$-$bar K$ and $B$-$bar B$ mixing constrain pairs of couplings at the $10^{-8}$ to $10^{-9}$ level, and some individual entries are far tighter still, notably $|lambda'_{333}| < 6 times 10^{-6}$ from the cosmological limit on the sum of light neutrino masses.

The premise it rests on. Every bound in the catalogue assumes that one R-parity-violating coupling dominates at a time, with all superpartner masses fixed at 100 GeV and the couplings written in a chosen field basis, so a pair of non-zero couplings that cancels in an observable would evade the quoted limits entirely.

Exact R parity stops being justifiable on naturalness grounds: if every coupling must sit below roughly 0.1 at 100 GeV, an approximate symmetry suppresses proton decay and flavour violation as effectively as an exact one.

Broken R parity survives as a neutrino-mass mechanism only in narrow windows, since the cosmological sum-of-masses limit forces $|lambda'_{333}| < 6 times 10^{-6}$ and comparable entries, requiring the soft chirality-mixing squark terms to be correspondingly tuned.

The lightest supersymmetric particle decays, the defining signature of broken R parity, are suppressed in the surviving parameter regions, so prompt-LSP-decay searches at colliders probe mostly the already-excluded corner.

Flavour-changing explanations of B-meson decay anomalies must live at the edge of the quadratic bounds, since $K$-$bar K$ and $B$-$bar B$ mixing constrain the relevant coupling products to $10^{-8}$ to $10^{-9}$.

Any relaxation of the bounds is proportional to the superpartner mass, so the tightness of the catalogue is itself a statement about where supersymmetry must sit, not only about R parity.

The one-at-a-time table is structurally weaker than a global fit: because two non-zero couplings can cancel in an observable, the interesting question is which combinations of the 48 parameters survive jointly, and a likelihood over the full parameter space would say more than the per-coupling entries.

Because every bound scales with the sfermion mass, a discovery of multi-TeV superpartners would relax the entire catalogue proportionally, so these constraints are better read as a joint probe of the supersymmetry scale and R parity than as a verdict on R parity alone.

The basis dependence the author flags in the introduction means bounds quoted in the mass basis and in the gauge basis are not directly comparable; a future measurement interpreted in one basis should be re-expressed in the other before it is used to exclude a model.

The neutrino-mass entry, many orders tighter than the generic $10^{-1}$, is the most fragile item in the table: it inherits its strength from a cosmological input, so it moves with that input rather than with any laboratory measurement.

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