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A Comparative Study of the Decays $B \to (K,K^*) \ell^+ \ell^-$ in Standard Model and Supersymmetric Theories

High Energy Physics - Phenomenology · Submitted 4 Oct 1999 · 73 references

Pith's verdict: The real contribution is Eq. (4.32): the FB-asymmetry zero in B → K*ℓℓ becomes a form-factor-free relation between short-distance coefficients, and that is what later work picked up.

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arXiv IDhep-ph/9910221 (version 2)
Pith ID5SO6UL7T, Pith's permanent record of this paper and its review
CitationA. Ali (DESY, G. Hiller (SLAC), Hamburg), L.T. Handoko (DESY, Patricia Ball (CERN). "A Comparative Study of the Decays $B \to (K,K^*) \ell^+ \ell^-$ in Standard Model and Supersymmetric Theories." arXiv:hep-ph/9910221 (1999). https://pith.science/paper/5SO6UL7T
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The paper

The paper claims

The dilepton forward-backward asymmetry in $B^*$ decays has a zero whose position barely depends on hadronic form factors, so measuring it tests the Standard Model against supersymmetry.

The reading

The paper asks whether the rare decays $B^0$ into a $K$ or $K^*$ plus a lepton pair can be turned into a clean test of physics beyond the Standard Model. Its answer is yes, and the cleanest handle is the forward-backward asymmetry in $B^0$ into $K^*$ plus two muons: the lepton emitted forward versus backward relative to the $B$ direction. The authors compute the relevant hadronic form factors with light-cone QCD sum rules, including next-to-leading radiative corrections and twist-4 corrections, then propagate those form factors through the decay distributions in the Standard Model and in four supersymmetric scenarios. The central observation is that the dilepton mass at which the asymmetry crosses zero is almost insensitive to the form factors, because in the large-energy limit the ratios $T_2/A_1$ and $T_1/V$ lose their hadronic dependence, leaving a relation between the short-distance coefficients $C_7^{eff}$ and $C_9^{eff}$. That turns a hadronically messy exclusive decay into a short-distance measurement comparable in cleanliness to the inclusive $B^0$ into $X_s$ dilepton decay, and it lets existing data on $B^0$ into $X_s$ photon and the $B^0$ into $K^*$ dimuon upper limit constrain the coefficients of the underlying effective theory.

What carries the argument

The load-bearing device is the zero of the forward-backward asymmetry in $B^0$ into $K^*$ lepton pairs, defined as the dilepton invariant mass ${s}_0$ where $dA_{FB}/d{s}$ changes sign. The differential asymmetry is proportional to $C_{10}$ times a combination $Re(C_9^{eff}) V A_1 + hat m_b {s} C_7^{eff}[V T_2 (1-hat m_{K^*}) + A_1 T_1 (1+hat m_{K^*})]$, so its zero is set by a ratio of Wilson coefficients dressed by ratios of form factors. The large-energy relations make those form-factor ratios universal, which is what converts a hadronic nuisance into a short-distance observable. Supporting machinery: light-cone QCD sum rule form factors with radiative and twist-4 corrections, parametrized as $F({s}) = F(0) exp(c_1 {s} + c_2 {s}^2 + c_3 {s}^3)$ with central, maximum and minimum parameter sets; two treatments of the long-distance charm-loop contribution to $C_9^{eff}$, a Breit-Wigner resonance ansatz with fudge factors fitted to $B^0$ into $K^{(*)}$ charmonium data, and a dispersion relation built from hadronic cross-section data; and a table of coefficients expressing the partially integrated branching ratios and asymmetry as quadratics in $C_7^{eff}$, $C_9$ and $C_{10}$.

Extended reading notes

Core claim

The paper's central claim is that the forward-backward asymmetry in $B^0$ into $K^*$ lepton pairs is a precision test of the Standard Model, because its zero is nearly free of form-factor uncertainty. Using the large-energy effective theory relations $T_2/A_1 = (1+hat m_{K^*})/(1+hat m_{K^*}^2-{s}) (1-{s}/(1-{s}m_{K^*}^2))$ and $T_1/V = 1/(1+hat m_{K^*})$, the condition for the asymmetry to vanish collapses from a form-factor-dependent equation to $Re(C_9^{eff}({s}_0)) = -2 hat m_b {s}_0 C_7^{eff} (1-{s}_0)/(1+hat m_{K^*}^2-{s}_0)$. In the Standard Model with the stated inputs this gives ${s}_0 = 2.88^{+0.44}_{-0.28}$ GeV$^2$, with the form-factor error contributing only about one percent. The asymmetry also has a sharp qualitative signature: it vanishes below the charmonium resonances only if $C_7^{eff}$ and $Re(C_9^{eff})$ have opposite signs, as in the Standard Model and low-$tan beta$ supergravity, whereas the large-$tan beta$ supergravity solutions that survive the $B^0$ into $X_s$ photon bound flip the sign of $C_7^{eff}$ and leave the asymmetry negative with no zero at all. Alongside this, the authors use the $B^0$ into $X_s$ photon bound and the CDF upper limit on $B^0$ into $K^*$ dimuons to carve allowed regions in the $C_9$-$C_{10}$ plane, and find that the most aggressive flavor-violating supersymmetric enhancement scenarios are already excluded by those limits.

Load-bearing premise

The argument leans on the charm-loop contribution to the effective coefficient $C_9^{eff}$ being modeled well enough by the two competing prescriptions, and on the large-energy relations between form factors holding at the few-GeV dilepton masses where the asymmetry zero sits.

Editorial extensions

If this is right

  • A measurement of the zero of the forward-backward asymmetry in $B^0$ into $K^*$ dimuons near 2.9 GeV$^2$ would confirm the Standard Model coefficient ratio, while a zero at a different mass or no zero at all below the charmonium resonances would point to a new-physics contribution to $C_7^{eff}$ or $C_9^{eff}$.
  • The large-$tan beta$ supergravity solutions compatible with the $B^0$ into $X_s$ photon rate predict a positive $C_7^{eff}$, hence an asymmetry that stays negative below the $J/psi$ and dilepton spectra enhanced by up to a factor of two relative to the Standard Model, which the stated experimental reach should separate from the Standard Model band.
  • The existing CDF upper limit on $B^0$ into $K^*$ dimuons already excludes the most aggressive flavor-violating supersymmetric enhancement points, so the $C_9$-$C_{10}$ plane is constrained by data rather than only by theory.
  • The tabulated coefficients for partially integrated rates and asymmetry let any model specified by three real coefficients be checked against a forthcoming measurement without recomputing form factors.
  • If the asymmetry zero behaves as predicted, the exclusive channel delivers short-distance information at a precision competitive with the inclusive $B^0$ into $X_s$ dilepton decay, where the analogous condition is $Re(C_9^{eff}({s}_0)) = -2{s}_0 C_7^{eff}$.

Reading between the lines

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

  • Because the zero depends on the ratio $C_7^{eff}/Re(C_9^{eff})$ and on the quark mass rather than on hadronic details, a future lattice determination of the same form-factor ratios at low recoil would provide an independent cross-check of the large-energy relations, and any disagreement would shift the extracted coefficient ratio rather than merely widen an error bar.
  • The same logic should transfer to $B_s$ into phi lepton pairs and to $B^0$ into $K^*$ tau pairs, with the caveat the authors note that the tau channel has no asymmetry zero by kinematics and that neutral Higgs exchange, neglected here, could matter there.
  • If the asymmetry in the dimuon channel is measured to match the Standard Model, the remaining room in the $C_9$-$C_{10}$ plane will be squeezed mainly by the $B^0$ into $K^*$ dimuon rate, so the asymmetry and the rate together act as two nearly orthogonal constraints on the same two coefficients.
  • The paper's treatment of the charmonium region means that a claimed sign flip of $C_{10}$, which reverses the asymmetry sign without touching the dilepton spectra, would be hardest to confirm precisely where the long-distance modeling is weakest, so a measurement of the asymmetry integrated only below the $J/psi$ would be the sharper discriminator.
Original abstract

Using improved theoretical calculations of the decay form factors in the Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B \to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard model (SM) and a number of popular variants of the supersymmetric (SUSY) models. Theoretical precision on the differential decay rates and FB-asymmetry is estimated in these theories taking into account various parametric uncertainties. We show that existing data on $B \to X_s \gamma$ and the experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+ \mu^-)$ provide interesting bounds on the coefficients of the underlying effective theory. We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. In particular, the presently allowed large-$\tan \beta$ solutions in SUGRA models, as well as more general flavor-violating SUSY models, yield FB-asymmetries which are characteristically different from the corresponding ones in the SM.

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, 4,649 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.31 · human participants 0.01 · controlled comparison 0.66 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.77 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Using improved theoretical calculations of the decay form factors in the Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B \to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard model (SM) and a number of popular variants of the supersymmetric (SUSY) models. Theoretical precision on the differential decay rates and FB-asymmetry is estimated in these theories taking into account various parametric uncertainties. We show that existing data on $B \to X_s \gamma$ and the experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+ \mu^-)$ provide interesting bounds on the coefficients of the underlying effective theory. We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. In particular, the presently allowed large-$\tan \beta$ solutions in SUGRA models, as well as more general flavor-violating SUSY models, yield FB-asymmetries which are characteristically different from the corresponding ones in the SM.

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 Using improved theoretical calculations of the decay form factors in the Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B \to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard model (SM) and a number of popular variants of the supersymmetric (SUSY) models. contribution 0.96 0.92 0.06 asserted 0.93
s1 Theoretical precision on the differential decay rates and FB-asymmetry is estimated in these theories taking into account various parametric uncertainties. method 0.50 0.82 0.04 asserted 0.99
s2 We show that existing data on $B \to X_s \gamma$ and the experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+ \mu^-)$ provide interesting bounds on the coefficients of the underlying effective theory. result 0.86 0.69 0.08 asserted 0.88
s3 We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. interpretation 0.98 0.37 0.57 hedged possibility 0.80
s4 In particular, the presently allowed large-$\tan \beta$ solutions in SUGRA models, as well as more general flavor-violating SUSY models, yield FB-asymmetries which are characteristically different from the corresponding ones in the SM. result 0.93 0.73 0.30 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.85 · evidence from simulation or computation 0.95.

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. LCSR form factors with theoretical uncertainties for the B → K transition as a function of sˆ. Solid, dotted and dashed curves correspond to f+, fT , f0, respectively. Renormal￾ization scale for fT is µ = mb. (a) (b)
Figure 2. LCSR form factors with theoretical uncertainties for the B → K∗ transition as a function of sˆ. In (a), the solid, dotted, dashed and short long dashed curves correspond to V, A0, A1, A2 and in (b), the solid, dotted and dashed curves correspond to T1, T2, T3, respec￾tively. Renormalization scale for Ti is µ = mb. 9
Figure 3. Theoretical expectations for the exclusive decay branching ratios B(B → K∗ ℓ +ℓ −), B(B → Kℓ+ℓ −), ℓ ± = e ±, µ±, τ ±, calculated in the LCSR method in the SM. For the sake of completeness, we also give the branching ratios for the inclusive decays B → Xsℓ +ℓ − and B → Xdℓ +ℓ − in the SM, including the CKM dependence of the latter. Experimental upper limits (at 90% C.L.) are also shown: solid squares are from the charged B+ decays (and charge conjugate), circles from the decays of B0 (and charge conjugate), and the empty squares are from the inclusive decays, averaged over th
Figure 4. The dilepton invariant mass distribution in B → Kµ+µ − decays, using the form factors from LCSR as a function of s. Solid curve: SD + LD using Ref. [29], dashed curve: SD + LD using Ref. [28]; dotted: pure SD; long-short dashed curve: SD + LD using Ref. [29] with C7 eff = −C7 eff SM. (a) (b)
Figure 5. The dilepton invariant mass distribution (a), and the normalized FB-asymmetry (b) in B → K∗µ +µ − decays, using the form factors in LCSR as a function of s in the SM. Solid curves: SD + LD according to Ref. [29], dashed curves: SD + LD using Ref. [28]; dotted: pure SD; long-short dashed curves: SD + LD using Ref. [29] with C7 eff = −C7 eff SM. 20
Figure 6. The dilepton invariant mass distribution in B → Kµ+µ − decays, using the form factors from LCSR as a function of s. All resonant cc¯ states are parametrized as in Ref. [29]. The solid line represents the SM and the shaded area depicts the form factor-related uncer￾tainties. The dotted line corresponds to the SUGRA model with R7 = −1.2, R9 = 1.03 and R10 = 1. The long-short dashed lines correspond to an allowed point in the parameter space of the MIA-SUSY model, given by R7 = −0.83, R9 = 0.92 and R10 = 1.61. The corresponding pure SD spectra are shown in the lower part of the plot
Figure 7. The dilepton invariant mass distribution in B → K∗µ +µ − decays, using the form factors from LCSR as a function of s. All resonant cc¯ states are parametrized as in Ref. [29]. The legends are the same as in
Figure 8. The normalized forward-backward asymmetry in B → K∗µ +µ − decay as a function of s, using the form factors from the LCSR approach. All resonant cc¯ states are parametrized as in Ref. [29]. The solid line denotes the SM prediction. The dotted (long-short dashed) lines correspond to the SUGRA (the MIA-SUSY) model, using the parameters given in Eq. (6.4) (Eq. (6.10)) with the upper and lower curves representing the C7 eff < 0 and C7 eff > 0 case, respectively. The dashed curves indicating a positive asymmetry for large s correspond to the MIA-SUSY models using the parameters given in E
Figure 9. Bounds on the coefficients C9(mB) and C10 resulting from the experimental upper bound B(B0 → K∗0µ +µ −) < 4.0 × 10−6 (at 90% C.L.) [34] and C7 eff(µ = 4.8 GeV) = −0.249 from the bounds given in Eq. (6.1).The SM-point and two representative points in the SUSY￾MIA approach from Ref. [23] are also shown. The three curves correspond to using the central values of the form factors (solid curve), the minimum (outer dashed curve) and maximum (inner dashed curve) allowed values discussed in Sec. 3. −15 −5 5 15 −15 −5 5 15 C9 C10 C7 eff > 0 MIAbest enh

Showing 9 of the paper's 12 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/9910221 by the authors.

References
How later papers used it

95 later papers cite it

Evidence: substantial. 83 of the citing papers share no author with it, and 23 of those carry a confident label from Pith's citation classifier.

Pith read 34 of the 164 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Builds on it 1 of 2 papers with this label
Uses its method or tool 2 of 12 papers with this label
Uses its data or values 5 of 10 papers with this label · 1 by the same authors

By the same authors

How the literature uses it

90 arXiv papers cite this in 158 sentences

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

Papers citing it · 95 sentences without a confident label

Builds on it 2 papers
Uses its method or tool 12 papers
Uses its data or values 9 papers
Compares with it 7 papers
Cites it as support 2 papers
Cites it as background 21 papers

Discussion

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