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The rare decays B --> K(*) anti-K(*) and R-parity violating supersymmetry

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Rumin Wang, G. R. Lu, En-Ke Wang, Ya-Dong Yang

High Energy Physics - Phenomenology · Submitted 12 Mar 2006 · 30 references

Pith's verdict: Useful RPV bounds and interesting CP predictions, but the advertised fL conclusion is not supported because VV annihilation amplitudes are dropped.

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arXiv IDhep-ph/0603088 (version 2)
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CitationEn-Ke Wang, G. R. Lu, Rumin Wang, Ya-Dong Yang. "The rare decays B --> K(*) anti-K(*) and R-parity violating supersymmetry." arXiv:hep-ph/0603088 (2006). https://pith.science/paper/ZORRIG5X
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The paper

The paper claims

This paper claims that R-parity-violating supersymmetry can strongly alter the rates and CP asymmetries of rare B-to-K-anti-K decays while barely moving the K* anti-K* polarizations, and it derives new coupling bounds from current data.

The reading

This paper tries to establish that R-parity-violating supersymmetry leaves a specific fingerprint in the rare decays $B\to K^{(*)} \bar K^{(*)}$. These are pure penguin $b\to d s\bar s$ transitions, and the paper shows that the five relevant product couplings can boost some still-unmeasured branching ratios by one or two orders of magnitude and drive direct CP asymmetries to values as large as about $\pm 0.99$. The same calculation finds that the longitudinal polarization fractions of $B\to K^*\bar K^*$ move only from about 0.9 to a range 0.59--0.97, so these modes stay longitudinally dominated even when RPV effects are large. From the current B-factory data the authors derive new upper limits on the couplings, three of which are stronger than earlier bounds. If real, the predictions give experimenters concrete windows to look in: measured rates, asymmetries, and polarizations in these channels would confirm or rule out this scenario.

What carries the argument

The machinery is QCD factorization for the hadronic matrix elements supplemented by a set of tree-level four-fermion operators from an R-parity-violating superpotential. The paper writes the total amplitude as $A = A_{\rm SM}^f + A_{\rm SM}^a + A_{\not R_p}$, where the RPV part is built from five complex product couplings $\lambda''_{i23}\lambda''^*_{i12}$, $\lambda'_{i13}\lambda'^*_{i22}$, $\lambda'_{i22}\lambda'^*_{i31}$, $\lambda'_{i12}\lambda'^*_{i32}$, and $\lambda'_{i23}\lambda'^*_{i21}$, each carrying a weak phase $\phi_{\not R_p}$; these couplings enter through $1/m_{\tilde f}^2$ propagator factors with QCD running factors, and are convoluted with the same form factors, decay constants, and next-to-leading-order coefficients $a_i$ and $b_i$ as the SM amplitude. This lets one scan the coupling magnitudes and phases against the measured branching ratios and the one measured CP asymmetry, producing the allowed regions and the predictions.

Extended reading notes

Core claim

The central claim is that the R-parity-violating part of the amplitude, built from tree-level sfermion exchange with complex couplings $\lambda''\lambda''^*$ or $\lambda'\lambda'^*$, can interfere with the SM penguin amplitude strongly enough to change the branching ratios and direct CP asymmetries of $B\to K^{(*)}\bar K^{(*)}$ by large factors, while barely touching the longitudinal polarization of the two vector modes. Concretely, with one 100 GeV sfermion at a time, the fits give $|\lambda''_{i23}\lambda''^*_{i12}| \le 2.9\times10^{-3}$ and $|\lambda'_{i13}\lambda'^*_{i22}| \le 2.2\times10^{-3}$, with the latter two $\lambda'$ products tighter than previously published limits. Using these constrained ranges, the unmeasured branching ratios are predicted to span roughly $5\times10^{-9}$ to $2\times10^{-5}$, direct CP asymmetries may reach $\pm 0.99$ in some modes, and $f_L(B\to K^{*+}\bar K^{*0}, K^{*0}\bar K^{*0})$ stays between 0.59 and 0.97. The paper states this as a testable separation: RPV can make the rates and asymmetries look very non-standard, yet the $K^*\bar K^*$ channels still look longitudinally polarized.

Load-bearing premise

The load-bearing premise is that one sfermion with mass 100 GeV contributes at a time, so each of the five RPV coupling products is constrained independently; if multiple sfermion exchanges interfere, the upper limits and the predicted ranges in Table III no longer follow directly from the data.

Editorial extensions

If this is right

  • Unmeasured modes get concrete target windows: for example, $B(B\to K^{*+}\bar K^{*0})$ is predicted below about $2\times10^{-5}$, below the current upper limit, so a future measurement inside that window would be consistent with these RPV couplings.
  • Direct CP asymmetries in several modes can be far larger than the SM's small values; for $B^0_d\to K^{*0}\bar K^0$ the allowed range reaches $\pm 0.99$, so a large observed asymmetry in these pure-penguin decays would point to new CP-violating phases of the RPV type.
  • The longitudinal polarization fractions $f_L$ for $B\to K^*\bar K^*$ remain in roughly 0.59--0.97 under all five couplings, so a measured suppression of $f_L$ would disfavor this simple one-coupling-at-a-time RPV explanation.
  • The bounds scale as $(m_{\tilde f}/100\,\mathrm{GeV})^2$, so the same constraints translate immediately to heavier sfermions by weakening the limits quadratically.
  • Improved measurements of the already-seen modes, such as $B^+\to K^+\bar K^0$ and its CP asymmetry, will directly shrink the currently allowed coupling bands.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The one-sfermion-at-a-time assumption means the bounds are per-product rather than global; a combined fit allowing several sfermions to interfere could either loosen or tighten the limits, and would be the natural next step.
  • Because the same five products also feed other $b\to d s\bar s$ observables, such as $\phi\pi^0$ modes and $B_s$ decays, a global fit across channels could sharpen the discrimination.
  • The near-independence of $f_L$ is itself a diagnostic: models that explain polarization puzzles generally need right-handed currents or new tensor operators, whereas RPV here changes rates and CP asymmetries while leaving the helicity structure nearly SM-like, so a future experiment seeing both large CP violation and SM-like $f_L$ would point toward scalar-exchange new physics.
Original abstract

We study the branching ratios, the direct CP asymmetries in $B\to K^{(*)}\bar{K}^{(*)}$ decays and the polarization fractions of $B\to K^{*}\bar{K}^{*}$ decays by employing the QCD factorization in the minimal supersymmetric standard model with R-parity violation. We derive the new upper bounds on the relevant R-parity violating couplings from the latest experimental data of $B\to K^{(*)}\bar{K}^{(*)}$, and some of these constraints are stronger than the existing bounds. Using the constrained parameter spaces, we predict the R-parity violating effects on the other quantities in $B\to K^{(*)}\bar{K}^{(*)}$ decays which have not been measured yet. We find that the R-parity violating effects on the branching ratios and the direct $CP$ asymmetries could be large, nevertheless their effects on the longitudinal polarizations of $B\to K^{*}\bar{K}^{*}$ decays are small. Near future experiments can test these predictions and shrink the parameter spaces.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,543 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.40 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.22 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the branching ratios, the direct CP asymmetries in $B\to K^{(*)}\bar{K}^{(*)}$ decays and the polarization fractions of $B\to K^{*}\bar{K}^{*}$ decays by employing the QCD factorization in the minimal supersymmetric standard model with R-parity violation. We derive the new upper bounds on the relevant R-parity violating couplings from the latest experimental data of $B\to K^{(*)}\bar{K}^{(*)}$, and some of these constraints are stronger than the existing bounds. Using the constrained parameter spaces, we predict the R-parity violating effects on the other quantities in $B\to K^{(*)}\bar{K}^{(*)}$ decays which have not been measured yet. We find that the R-parity violating effects on the branching ratios and the direct $CP$ asymmetries could be large, nevertheless their effects on the longitudinal polarizations of $B\to K^{*}\bar{K}^{*}$ decays are small. Near future experiments can test these predictions and shrink the parameter spaces.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the branching ratios, the direct CP asymmetries in $B\to K^{(*)}\bar{K}^{(*)}$ decays and the polarization fractions of $B\to K^{*}\bar{K}^{*}$ decays by employing the QCD factorization in the minimal supersymmetric standard model with R-parity violation. contribution 0.93 0.94 0.06 asserted 0.94
s1 We derive the new upper bounds on the relevant R-parity violating couplings from the latest experimental data of $B\to K^{(*)}\bar{K}^{(*)}$, and some of these constraints are stronger than the existing bounds. result 0.92 0.95 0.29 asserted 1.00
s2 Using the constrained parameter spaces, we predict the R-parity violating effects on the other quantities in $B\to K^{(*)}\bar{K}^{(*)}$ decays which have not been measured yet. contribution 0.78 0.92 0.10 asserted 0.99
s3 We find that the R-parity violating effects on the branching ratios and the direct $CP$ asymmetries could be large, nevertheless their effects on the longitudinal polarizations of $B\to K^{*}\bar{K}^{*}$ decays are small. result 1.00 0.95 0.63 hedged possibility 0.81
s4 Near future experiments can test these predictions and shrink the parameter spaces. future work 0.98 0.13 0.09 hedged possibility 0.85

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from analysis of existing data 0.75.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. The next to leading order nonfactorizable contributions to the coefficients a p i
Figure 2. The weak annihilation contributions to the coefficients b p i . where the effective parameters a p i including nonfactorizable corrections at order of αs. They are calculated from the vertex corrections, the hard spectator scattering, and the QCD penguin contributions, which are shown in Fig.1. The parameters b p i are calculated from the weak annihilation contributions as shown in Fig.2. Under the naive factorization (NF) approach, the factorized matrix element is given by AM1M2 ≡ hM2|(¯q2γµ(1 − γ5)q3)|0ihM1|( ¯bγµ (1 − γ5)q1)|Bi. (4) In term of the decay constant and form f
Figure 3. Sleptons exchanging diagrams for nonleptonic B decays. uj dk ˜di um dn λ ′′ jki λ ′′∗ mni dj dk u˜i dm dn λ ′′ ijk λ ′′∗ inm
Figure 4. Squarks exchanging diagrams for nonleptonic B decays. From Eq.(8), we can obtain the following four fermion effective Hamiltonian due to the sleptons exchange as shown in Fig.3 H ′6Rp 2u−2d = X i λ ′ ijmλ ′∗ ikl 2m2 e˜Li η −8/β0 ( ¯dmγ µPRdl)8(¯ukγµPLuj )8, H ′6Rp 4d = X i λ ′ ijmλ ′∗ ikl 2m2 ν˜Li η −8/β0 ( ¯dmγ µPRdl)8( ¯dkγµPLdj )8. (9) The four fermion effective Hamiltonian due to the squarks exchanging as shown in Fig.4 are H ′′6Rp 2u−2d = X n λ ′′ iknλ ′′∗ jln 2m2 d˜n η −4/β0 nh(¯uiγ µPRuj )1( ¯dkγµPRdl)1 − (¯uiγ µPRuj )8( ¯dkγµPRd
Figure 5. The allowed parameter spaces for the relevant RPV couplin
Figure 6. The effects of RPV coupling λ ′′ i23λ ′′∗ i12 in B → K(∗)K¯ (∗) decays. 28
Figure 7. The effects of RPV coupling λ ′ i13λ ′∗ i22 in B → K(∗)K¯ (∗) decays. 29
Figure 8. The effects of RPV coupling λ ′ i22λ ′∗ i31 in B → K(∗)K¯ (∗) decays. 30
Figure 9. The effects of RPV coupling λ ′ i12λ ′∗ i32 in B → K(∗)K¯ (∗) decays
Figure 10. The effects of RPV coupling λ ′ i23λ ′∗ i21 in B → K(∗)K¯ (∗) decays. 31

Figures reproduced from arXiv:hep-ph/0603088 by the authors.

References
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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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