Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻

The fully differential angular distribution for the rare flavor-changing neutral current decay Bd⁰ → K*⁰( → K⁻π⁺)e⁺e⁻ is studied. The emphasis is placed on accurate treatment of the contribution from the processes Bd⁰ → K*⁰( → K⁻π⁺)V with intermediate vector resonances V = ρ(770), ω(782), φ(1020), J...

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Дата:	2012
Автори:	Korchin, A.Yu., Kovalchuk, V.A., Lazarenko, D.O.
Формат:	Стаття
Мова:	English
Опубліковано:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2012
Назва видання:	Вопросы атомной науки и техники
Теми:	Section C. Theory of Elementary Particles. Cosmology
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/107061
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Цитувати:	Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻ / A.Yu. Korchin, V.A. Kovalchuk, D.O. Lazarenko // Вопросы атомной науки и техники. — 2012. — № 1. — С. 166-170. — Бібліогр.: 12 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

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spelling	irk-123456789-1070612016-10-13T03:02:16Z Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻ Korchin, A.Yu. Kovalchuk, V.A. Lazarenko, D.O. Section C. Theory of Elementary Particles. Cosmology The fully differential angular distribution for the rare flavor-changing neutral current decay Bd⁰ → K⁰( → K⁻π⁺)e⁺e⁻ is studied. The emphasis is placed on accurate treatment of the contribution from the processes Bd⁰ → K⁰( → K⁻π⁺)V with intermediate vector resonances V = ρ(770), ω(782), φ(1020), J/ψ, ψ(2S), … decaying into the e⁺e⁻ pair. The two versions of the vector-meson-dominance model for the transition Vγ are used and tested. The branching ratio, longitudinal polarization fraction of the K⁰ meson, transverse asymmetry AT⁽²⁾ and forward-backward asymmetry are compared with data from BaBar and CDF, and predictions for experiments at LHCb and B factories are made. Изучено полное дифференциальное угловое распределение редкого распада Bd⁰ → K⁰( → K⁻π⁺)e⁺e⁻, индуцированного нейтральным током, изменяющим аромат. Акцентировано внимание на аккуратном рассмотрении вкладов от процессов Bd⁰ → K⁰( → K⁻π⁺)V с промежуточными векторными резонансами V = ρ(770), ω(782), φ(1020), J/ψ, ψ(2S),…, распадающимися на e⁺e⁻ -пару. Использованы две версии модели векторной доминантности для перехода Vγ. Относительная вероятность распада, доля продольной поляризации K⁰ мезона, поперечная асимметрия AT⁽²⁾ и асимметрия "вперед-назад'' сравниваются с данными BaBar и CDF, а также выполнены предсказания для экспериментов LHCb и B-фабрик. Досліджено повний диференційний кутовий розподіл рідкого розпаду Bd⁰ → K⁰( → K⁻π⁺)e⁺e⁻, індукованого нейтральним струмом, який змінює аромат. Акцентовано увагу на акуратному розгляді вкладів від процесів Bd⁰ → K⁰( → K⁻π⁺)V з проміжними векторними резонансами V = ρ(770), ω(782), φ(1020), J/ψ, ψ(2S),…, які розпадаються на e⁺e⁻ -пару. Використані дві версії моделі векторної домінантності для переходу Vγ. Відносна ймовірність розпаду, частка повздовжньої поляризації K⁰ мезона, поперечна асиметрія AT⁽²⁾ та асиметрія "вперед-назад'' порівнюються з даними BaBar та CDF, а також виконані передбачення для експериментів LHCb та B-фабрик. 2012 Article Angular distribution and asymmetries in flavor-changing neutral-current decay B → K l⁺ l⁻ / A.Yu. Korchin, V.A. Kovalchuk, D.O. Lazarenko // Вопросы атомной науки и техники. — 2012. — № 1. — С. 166-170. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 13.20.He, 13.25.Hw, 12.40.Vv http://dspace.nbuv.gov.ua/handle/123456789/107061 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Section C. Theory of Elementary Particles. Cosmology Section C. Theory of Elementary Particles. Cosmology
spellingShingle	Section C. Theory of Elementary Particles. Cosmology Section C. Theory of Elementary Particles. Cosmology Korchin, A.Yu. Kovalchuk, V.A. Lazarenko, D.O. Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻ Вопросы атомной науки и техники
description	The fully differential angular distribution for the rare flavor-changing neutral current decay Bd⁰ → K⁰( → K⁻π⁺)e⁺e⁻ is studied. The emphasis is placed on accurate treatment of the contribution from the processes Bd⁰ → K⁰( → K⁻π⁺)V with intermediate vector resonances V = ρ(770), ω(782), φ(1020), J/ψ, ψ(2S), … decaying into the e⁺e⁻ pair. The two versions of the vector-meson-dominance model for the transition Vγ are used and tested. The branching ratio, longitudinal polarization fraction of the K*⁰ meson, transverse asymmetry AT⁽²⁾ and forward-backward asymmetry are compared with data from BaBar and CDF, and predictions for experiments at LHCb and B factories are made.
format	Article
author	Korchin, A.Yu. Kovalchuk, V.A. Lazarenko, D.O.
author_facet	Korchin, A.Yu. Kovalchuk, V.A. Lazarenko, D.O.
author_sort	Korchin, A.Yu.
title	Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻
title_short	Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻
title_full	Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻
title_fullStr	Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻
title_full_unstemmed	Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻
title_sort	angular distribution and asymmetries in flavor-changing neutral-current decay b → k* l⁺ l⁻
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2012
topic_facet	Section C. Theory of Elementary Particles. Cosmology
url	http://dspace.nbuv.gov.ua/handle/123456789/107061
citation_txt	Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻ / A.Yu. Korchin, V.A. Kovalchuk, D.O. Lazarenko // Вопросы атомной науки и техники. — 2012. — № 1. — С. 166-170. — Бібліогр.: 12 назв. — англ.
series	Вопросы атомной науки и техники
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first_indexed	2025-07-07T19:26:38Z
last_indexed	2025-07-07T19:26:38Z
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fulltext	ANGULAR DISTRIBUTION AND ASYMMETRIES IN FLAVOR-CHANGING NEUTRAL-CURRENT DECAY B → K∗ l+ l− A.Yu. Korchin1∗, V.A. Kovalchuk1, D.O. Lazarenko2 1National Science Center “Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine 2Université Paris-Sud 11, 91405 Orsay Cedex, France (Received November 1, 2011) The fully differential angular distribution for the rare flavor-changing neutral current decay B̄0 d → K̄∗0 (→ K− π+) e+ e− is studied. The emphasis is placed on accurate treatment of the contribution from the processes B̄0 d → K̄∗0 (→ K− π+)V with intermediate vector resonances V = ρ(770), ω(782), φ(1020), J/ψ, ψ(2S), . . . decaying into the e+e− pair. The two versions of the vector-meson-dominance model for the transition V γ are used and tested. The branching ratio, longitudinal polarization fraction of the K̄∗0 meson, transverse asymmetry A (2) T and forward-backward asymmetry are compared with data from BaBar and CDF, and predictions for experiments at LHCb and B factories are made. PACS: 13.20.He, 13.25.Hw, 12.40.Vv 1. INTRODUCTION The investigation of rare B decays induced by the flavor-changing neutral current (FCNC) transitions b → s and b → d represents an important test of the standard model (SM) and its extensions (see [1] for a review). Among the rare decays, the process b → s�+�−, where the virtual photon is converted to the lepton pair, is of considerable interest. In this decay the an- gular distributions and lepton polarizations can probe the chiral structure of the matrix element [1] and thereby effects of the new physics (NP) beyond the SM. In order to unambiguously measure effects of NP in the observed process B̄0 d → K̄∗0 (→ K− π+) �+ �−, mediated by b → s�+�− decay, one needs to calcu- late the SM predictions with a high accuracy. The amplitude in the SM consists of the short-distance (SD) and long-distance (LD) contributions. The for- mer are expressed in terms of the Wilson coefficients Ci calculated in perturbative QCD up to a certain or- der in αs(μ); they carry information on processes at energy scales ∼ mW , mt. The LD effects describing the hadronization process are expressed in terms of matrix elements of several b → s operators between the initial B and the K∗ final state. These hadronic matrix elements are parameterized in terms of form factors that are calculated in various approaches (see, e.g. [2]). The additional LD effects, originating from inter- mediate vector resonances ρ(770), ω(782), φ(1020), J/ψ(1S), ψ(2S),. . ., in general, may complicate theo- retical interpretation and make it more model depen- dent. The vector resonances modify the amplitude and thus may induce, for example, the right-handed currents which are absent in the SM. In the present paper we extend calculations of [3] to the whole region of dilepton invariant mass up to mmax ee = mB − mK∗ = 4.39 GeV. The effec- tive SM Hamiltonian with the Wilson coefficients in the next-to-next-to-leading order (NNLO) approxi- mation is applied. The LD effects mediated by the resonances, i.e. B̄0 → K̄∗0V → K̄∗0e+e− with V = ρ(770), ω(782), φ(1020), J/ψ, ψ(2S), . . ., are included explicitly in terms of the helicity amplitudes of the decays B̄0 → K̄∗0V . The information on the latter is taken from experiments if available; other- wise it is taken from theoretical predictions. 2. ANGULAR DISTRIBUTIONS AND AMPLITUDES FOR THE B̄0 d → K̄∗0 e+ e− DECAY The decay B̄0 d → K̄∗0 e+ e−, with K̄∗0 → K−π+ on the mass shell, is completely described by four in- dependent kinematic variables: the electron-positron pair invariant-mass squared, q2, and the three angles θl, θK , φ. In the helicity frame (Fig. 1), the angle θl (θK) is defined as the angle between the directions of motion of e+ (K−) in the γ∗ (K̄∗0) rest frame and the γ∗ (K̄∗0) in the B̄0 d rest frame. The azimuthal angle φ is defined as the angle between the decay planes of γ∗ → e+ e− and K̄∗0 → K−π+ in the B̄0 d rest frame. The fully differential angular distribution ∗Corresponding author E-mail address: korchin@kipt.kharkov.ua 166 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2012, N 1. Series: Nuclear Physics Investigations (57), p. 166-170. in these coordinates is given by W (q̂2, θl, θK , φ) ≡ d4 Γ dq̂2d cos θl d cos θKdφ / dΓ dq̂2 = 9 64 π 9∑ k=1 αk(q2)gk(θl, θK , φ) , (1) where gk are the angular and αk are the amplitude terms, q̂2 ≡ q2/m2 B, mB is the mass of the B0 d meson, and dΓ dq̂2 = mB N 2q̂2 √ λ̂ (\|A0\|2 + \|A‖\|2 + \|A⊥\|2 ) . (2) φ θK θl K0 _ B _ d 0 γ K- π+ e+ e- Fig. 1. Definition of helicity angles θl, θK , and φ, for the decay B̄0 d → K̄∗0 e+ e− We have neglected the electron mass me, and A0L(R), A‖L(R) and A⊥L(R) are the complex decay amplitudes of the three helicity states in the transver- sity basis, λ̂ ≡ λ(1, q̂2, m̂2 K∗) = (1 − q̂2)2 − 2(1 + q̂2)m̂2 K∗ + m̂4 K∗ , m̂K∗ ≡ mK∗/mB, where mK∗ is the mass of the K∗0 meson, and N = \|VtbV ∗ ts\| GFm 2 Bαem 32 π2 √ 3 π . Here, Vij are the Cabibbo-Kobayashi-Maskawa ma- trix elements [4, 5], GF is the Fermi coupling con- stant, αem is the electromagnetic fine-structure con- stant. Next, we implement the effects of LD contribu- tions from the decays B̄0 d → K̄∗0 V , where V = ρ0 , ω , φ , J/ψ(1S) , ψ(2S) , . . . mesons, followed by V → e+ e− in the decay B̄0 d → K̄∗0 e+ e− (Fig. 2). B̄0 d K̄∗0 e+ e− B̄0 d K̄∗0 V e+ e−γ Fig. 2. Nonresonant and resonant contributions to the decay amplitude We apply vector-meson dominance (VMD) ap- proach. In general, the V γ transition can be in- cluded into consideration using various versions of VMD model. In the “standard” version (see, e.g. [6], chapter 6), the V γ transition vertex can be written as 〈γ(q); μ\|V (q); ν 〉 = −efVQVmV g μν , (3) where gμν is the metric tensor, QV is the effective electric charge of the quarks in the vector meson: Qρ = 1√ 2 , Qω = 1 3 √ 2 , Qφ = −1 3 , QJ/ψ = Qψ(2S) = . . . = 2 3 . (4) The decay constants of neutral vector mesons fV can be extracted from their electromagnetic decay width. This version of VMD model will be called VMD1. A more elaborate model (called hereafter VMD2) orig- inates from Lagrangian LγV = −e 2 Fμν ∑ V fVQV mV Vμν , (5) where Vμν ≡ ∂μVν − ∂νVμ and Fμν ≡ ∂μAν − ∂νAμ is the electromagnetic field tensor. Based on VMD approach, we obtain the total am- plitude including nonresonant and resonant parts, A0L,R = 1 2 m̂K∗ √ q̂2 ( C0(q2) ( Ceff 9V ∓ C10A + 2m̂b ( Ceff 7γ − C′ eff 7γ ) κ0(q2) ) + 8π2 ∑ V CVD −1 V (q̂2) (( 1 − q̂2 − m̂2 K∗ ) SV1 + λ̂ SV2 2 )) , (6) A‖L,R = −√ 2 ( C‖(q2) ( Ceff 9V ∓ C10A + 2 m̂b q̂2 ( Ceff 7γ − C′ eff 7γ ) κ‖(q2) ) + 8π2 ∑ V CVD −1 V (q̂2)SV1 ) , (7) A⊥L,R = √ 2λ̂ ( C⊥(q2) ( Ceff 9V ∓ C10A + 2 m̂b q̂2 ( Ceff 7γ + C′ eff 7γ ) κ⊥(q2) ) + 4π2 ∑ V CVD −1 V (q̂2)SV3 ) , (8) where the form factors enter as C0(q2) = (1 − q̂2 − m̂2 K∗)(1 + m̂K∗)A1(q2) − λ̂ A2(q2) 1 + m̂K∗ , (9) C‖(q2) = (1 + m̂K∗)A1(q2), (10) C⊥(q2) = V (q2) 1 + m̂K∗ , (11) κ0(q2) ≡ ( (1 − q̂2 + 3m̂2 K∗)(1 + m̂K∗)T2(q2) − λ̂ 1 − m̂K∗ T3(q2) )( (1 − q̂2 − m̂2 K∗) × (1 + m̂K∗)2A1(q2) − λ̂ A2(q2) )−1 , (12) κ‖(q2) ≡ T2(q2) A1(q2) (1 − m̂K∗), (13) 167 κ⊥(q2) ≡ T1(q2) V (q2) (1 + m̂K∗). (14) In the above formulas the definition m̂b ≡ mb(μ)/mB is used, and A1(q2), A2(q2), V (q2), T1(q2), T2(q2), T3(q2) are the B → K∗ transition form factors, de- fined in [2]. Furthermore, DV (q̂2) = q̂2 − m̂2 V + im̂V Γ̂V (q̂2) is the usual Breit-Wigner function for the V meson resonance shape with the energy-dependent width ΓV (q2) [Γ̂V (q̂2) = ΓV (q2)/mB], m̂V ≡ mV /mB, Γ̂V ≡ ΓV /mB, mV (ΓV ) is the mass (width) of a V meson, and CV = QVmV fV q2 (VMD1) , CV = QV fV mV (VMD2) . (15) In Eqs. (6)-(8), SVi (i = 1, 2, 3) are the invariant amplitudes of the decay B0 d → K∗0 V . The energy-dependent widths of light vector res- onances ρ, ω and φ are chosen as in Ref. [3]. The up-dated branching ratios for resonances decays to different channels are taken from [7]. For the cc̄ reso- nances J/ψ, ψ(2S), . . . we take the constant widths. In order to calculate the resonant contribution to the amplitude of the B̄0 d → K̄∗0 e+ e− decay, one has to know the amplitudes of the decays B̄0 d → K̄∗0 ρ, B̄0 d → K̄∗0 ω, B̄0 d → K̄∗0 φ, B̄0 d → K̄∗0 J/ψ, B̄0 d → K̄∗0 ψ(2S), . . . At present the amplitudes of the B̄0 d → K̄∗0 φ, B̄0 d → K̄∗0 J/ψ, B̄0 d → K̄∗0 ψ(2S) decays are known from experiment [7], therefore, we use these amplitudes for calculation of invariant amplitudes. For the light resonances ρ and ω we use the theoret- ical prediction [8] for the decay amplitudes. At the same time, we are not aware of a similar prediction for the higher cc̄ resonances, such as ψ(3770) an so on, therefore we do not include contribution of these resonances to amplitudes in our calculation. The SM Wilson coefficients have been obtained in [9] at the scale μ = 4.8 GeV to NNLO accuracy. In the nu- merical estimations, we use the form factors from the light-cone sum rules (LCSR) calculation [2]. 3. RESULTS In Figs. 3 we present results for the dependence on the dilepton invariant mass squared of the differ- ential branching ratio, dB dq̂2 = τB dΓ dq̂2 , (16) the longitudinal polarization fraction of K∗ meson, fL = \|a0\|2 , (17) the forward-backward asymmetry AFB = −3 2 Re(a‖L a∗⊥L − a‖R a∗⊥R) , (18) Fig. 3. Solid line corresponds to the SM calculation without resonances taken into account. Dashed and dotted lines are calculated with account of resonances in the VMD1 and VMD2 model respectively 168 and the coefficient A (2) T ≡ a⊥ − a‖ a⊥ + a‖ , (19) for the B̄0 d → K̄∗0 e+ e− decay. Here aia ∗ j ≡ aiL(q2)a∗jL(q2) + aiR(q2)a∗jR(q2) (20) and aiL(R) ≡ AiL(R)√∑ j \|Aj \|2 , (21) i, j = (0, ‖,⊥), τB is the lifetime of a B0 d meson. The data from Belle [10] and CDF [11, 12] are shown by the circles and boxes respectively. The interval of q2 is taken from (30 MeV)2 up to (mB − mK∗)2 ≈ 19.22 GeV2. The phase δV0 is chosen zero for all res- onances except the φ meson, for which δφ0 = 2.82 rad is taken from experiment. As it is seen from the figures, VMD1 and VMD2 give different prediction for observables in the region of small q2 ≤ 2 GeV2 while at bigger values of q2 they yield similar results. Note that the difference between predictions of these two models is especially large for the high-lying cc̄ resonances. The experimental uncertainties are still large, nevertheless the version VMD2 seems more preferable as compared with data for the differential branching ratio and longitudinal polarization fraction. 4. CONCLUSIONS The rare FCNC decay B̄0 d → K̄∗0 (→ K− π+) e+ e− has been studied in the whole region of electron- positron invariant masses up to mB − mK∗ . The fully differential angular distribution over the three angles and dilepton invariant mass for the four-body decay B̄0 d → K− π+ e+ e− is analyzed. We defined a convenient set of asymmetries which allows one to extract them from measurement of the angular distri- bution once sufficient statistics is accumulated. We performed calculations of differential branching, po- larization fractions of K∗ meson and asymmetries. These asymmetries may have sensitivity to various effects of the NP, although in order to see signatures of these effects, the resonance contribution should be accurately evaluated. Contribution from intermediate vector resonances in the process B̄0 d → K̄∗0 (→ K− π+)V with V = ρ(770), ω(782), φ(1020), J/ψ, ψ(2S) decaying into the e+e− pair has been taken into account. Dif- ferent aspects of treatment of this LD contribution have been studied. The important aspect is the choice of the VMD model, describing the V γ∗ transition. We used two variants of the VMD model, called here VMD1 and VMD2 versions. Based on comparison of calculation for the differential branching ratio, longitudinal po- larization fraction and forward-backward asymmetry with the data from Belle and CDF, we can conclude that the VMD2 version is somewhat more preferable. For the vertex B̄0 d → K̄∗0 V we used an off-mass- shell extension of the helicity amplitudes describing production of on-shell vector mesons. For the latter the experimental information is used if available, and otherwise theoretical predictions. All asymmetries are calculated and the resonance contributions are studied. The coefficient A(2) T take sizable value at large mee, while in the wide region of invariant masses this observable is small. Ac- count of resonances changes this asymmetry, mainly in the vicinity of the resonance positions, i.e. at mee ≈ mV . In general, this observable is important in view of its sensitivity to the chiral-odd dipole tran- sition bL → sR + γR and thereby to the effects of the NP which are related to the right-handed currents. Calculations performed in the present work may be useful for experiments aiming at search of effects of the NP in the decay B̄0 d → K̄∗0 (→ K− π+) �+ �−. References 1. M. Antonelli et al. Flavor Physics in the Quark Sector // Phys. Rep. 2010, v. 494, p. 197-414. 2. P. Ball and R. Zwicky. Bd,s → ρ, ω,K∗, φ Decay Form Factors from Light-Cone Sum Rules Revis- ited // Phys. Rev. 2005, v. D71, 014029, 26 p. 3. A.Yu. Korchin and V.A. Kovalchuk. Contribu- tion of low-lying vector resonances to polarization observables in B̄0 d → K̄∗0 e+ e− decay // Phys. Rev. 2010, v. D82, 034013, 12 p. 4. N. Cabibbo. Unitary symmetry and leptonic de- cays // Phys. Rev. Lett. 1963, v. 10, p. 531-533. 5. M. Kobayashi and T. Maskawa. CP-violation in the renormalizable theory of weak interaction // Prog. Theor. Phys. 1973, v. 49, p. 652-657. 6. R.P. Feynman. Photon-hadron interactions. Rea- ding, Massachusets: W.A. Benjamin, Inc., 1972, 282 p. 7. K. Nakamura et al. Review of particle physics // J. Phys. G. 2010, v. 37, 075021, 1422 p. 8. C.H. Chen. Polarizations of two vector mesons in B decays // arXiv : 0601019v2[hep-ph]. 2006, 13 p. 9. W. Altmannshofer, P. Ball, A. Bharucha et al. Symmetries and Asymmetries of B → K∗μ+μ− Decays in the Standard Model and Beyond // J. High Energy Phys. 2009, v. 01, 019, 58 p. 10. J.-T. Wei et al. Measurement of the Differen- tial Branching Fraction and Forward-Backword Asymmetry for B → K(∗)l+l−// Phys. Rev. Lett. 2009, v. 103, 171801, 7 p. 11. T. Aaltonen et al. Observation of the Bary- onic Flavor-Changing Neutral Current Decay Λ0 b → Λμ+μ− // arXiv : 1107.3753v1[hep-ex]. 2011, 7 p. 12. T. Aaltonen et al. Measurements of the Angular Distributions in the Decays B → K(∗)μ+μ− at CDF // arXiv : 1108.0695v1[hep-ex]. 2011, 7 p. 169 �� B → K∗ l+ l−� � �� B̄0 d → K̄∗0 (→ K− π+) e+ e−� �� B̄0 d → K̄∗0 (→ K− π+)V � � �� V = ρ(770)� ω(782)� φ(1020)� J/ψ, ψ(2S), . . . � �� e+e− �� !� � V γ� "�� K̄∗0 �� A (2) T � �� #�� $ � �� %&%&' � ()� � �� +�� ,-(. � % ��/ �� B → K∗ l+ l−� � �� 0�� 1 �� 1�� 1 1 �� B̄0 d → K̄∗0 (→ K− π+) e+ e−� 1� �� 1��2 � �� 1 �� 1� �1 � ��1� B̄0 d → K̄∗0 (→ K− π+)V � � ��1�� V = ρ(770)� ω(782)� φ(1020)� J/ψ, ψ(2S), . . . � ��1 �� e+e− �� 3�� 1 �1 �� 14 �� 1 �� 4 ��1��1 � �� !� � V γ� 31 �� 1 �1�� 4 �� 14 K̄∗0 �� 1� A (2) T �� 1� #�� $ �� 1�� %&%&' �� ()� � �� 1 �� /�� 1� ,-(. �� % ��/ �� 567

Angular distribution and asymmetries in flavor-changing neutral-current decay B → K* l⁺ l⁻

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