1

73. Production and Decay of b-flavored Hadrons

73. Production and Decay of b-flavored Hadrons
Revised March 2024 by P. Eerola (Research Council of Finland), M. Kreps (Warwick U.) and Y.
Kwon (Yonsei U., Seoul).
The b quark belongs to the third generation of quarks and is the weak–doublet partner of thet quark. The existence of the third–generation quark doublet was proposed in 1973 by Kobayashi
and Maskawa [1] in their model of the quark mixing matrix (“CKM” matrix), and confirmed four
years later by the first observation of a bb meson [2]. In the KM model, CP violation is explained
within the Standard Model (SM) by an irreducible phase of the 3 × 3 unitary matrix. The regularpattern of the three lepton and quark families is one of the most intriguing puzzles in particle
physics. The existence of families gives rise to many of the free parameters in the SM, including
the fermion masses, and the elements of the CKM matrix.
Since the b quark is the lighter element of the third–generation quark doublet, the decays ofb-flavored hadrons occur via generation-changing processes through CKM matrix. Because of this,and the fact that the CKM matrix is close to a 3 × 3 unit matrix, many interesting features suchas loop and box diagrams, flavor oscillations, as well as large CP asymmetries, can be observed in
the weak decays of b-flavored hadrons.
The CKM matrix is parameterized by three real parameters and one complex phase. This
complex phase is the source of CP violation in B meson decays in the Standard Model. A crucial
milestone was the first observation of CP violation in the B meson system in 2001, by the BaBar [3]and Belle [4] collaborations. They measured a large value for the parameter sin 2β (= sin 2φ1 ) [5],almost four decades after the discovery of a small CP asymmetry in neutral kaons. A more detailed
discussion of the CKM matrix and CP violation can be found elsewhere in this Review [6, 7].
The structure of this mini-review is organized as follows. After a discussion of b-quark production and current results on spectroscopy, we discuss lifetimes of b-flavored hadrons. We thendiscuss some basic properties of B-meson decays, followed by summaries of dominant hadronic, rare0
hadronic, and electroweak penguin decays of B-mesons. There are separate mini-reviews for B 0 –B
mixing [8] and the extraction of the CKM matrix elements Vcb and Vub from B-meson decays [9] inthis Review.

73.1 Production and spectroscopy
The bound states of a b antiquark and a u, d, s, or c quark are referred to as the Bu (B + ),Bd (B 0 ), Bs (Bs0 ), and Bc (Bc+ ) mesons, respectively. The Bc+ is the heaviest of the ground–stateb-flavored mesons, and the most difficult to produce: it was observed for the first time in thesemileptonic mode by CDF in 1998 [10], but its mass was accurately determined only in 2006, fromthe fully reconstructed mode Bc+ → J/ψπ + [11]. Many exclusive decay channels can now be used
for the accurate mass measurements, given the large statistics available at the LHC. Currently themost precise measurement is made by LHCb and yields m(Bc+ ) = 6274.47±0.27±0.17 MeV/c2 [12],combining Bc+ → J/ψπ + , Bc+ → J/ψπ + π − π + , Bc+ → J/ψpp̄π + , Bc+ → J/ψDs+ , Bc+ → J/ψD0 K +and Bc+ → Bs0 π + decay modes.
The first excited meson is called the B ∗ meson, while B ∗∗ is the generic name for the fourorbitally excited (L = 1) B-meson states that correspond to the P -wave mesons in the charmsystem, D∗∗ . Excited states of the Bs0 meson are similarly named Bs∗ and Bs∗∗ .
Of the possible bound bb states, the Υ (nS) and χbJ (nP ) states are well studied. The pseudoscalar ground state ηb has been observed for the first time by BaBar [13] indirectly throughthe decay Υ (3S) → γηb , and then confirmed by Babar in Υ (2S) decays [14] and CLEO in Υ (3S)
decays [15]. The most accurate mass and width measurements come now from Belle, using deS. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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73. Production and Decay of b-flavored Hadrons

cays Υ (5S) → hb (1P )π + π − , hb (1P ) → γηb (1S) [16], Υ (4S) → ηhb (1P ), hb (1P ) → γηb (1S)[17], and Υ (2S) → γηb (1S) [18]. Belle has also reported first evidence for the ηb (2S) in thehb (2P ) → ηb (2S)γ transition [16]. In addition, Belle has observed Tbb̄1 (10610) (was Zb (10610))
and Tbb̄1 (10650) (was Zb (10650)) states in the processes Υ (5S) → Υ (nS)π + π − (n = 1, 2, 3) andΥ (5S) → hb (mP )π + π − (m = 1, 2) [19]. These Tbb̄1 states are observed to decay to Υ (nS)π ± andhb (mP )π ± , hence electrically charged and do not belong to ordinary q q̄ mesons. For classificationand naming of these and other states, see Ref. [20].
Experimental studies of b decays have been performed in e+ e− collisions at the Υ (4S) (ARGUS,
CLEO, Belle, BaBar) and Υ (5S) (CLEO, Belle) resonances. The e+ e− → bb production crosssection at the Υ (4S) (Υ (5S)) resonance is about 1.1 nb (0.3 nb). The full data samples of BaBar
and Belle are 560 fb−1 and 1020 fb−1 , respectively, of which 433 fb−1 and 710 fb−1 are at the Υ (4S)0resonance. Since the Υ (4S) decays dominantly to a pair of B mesons (either B + B − or B 0 B ), a
precise knowledge of the energy-momentum of one B meson (the ‘tagging B’) enables deducing theproperties of the other B (the ‘signal B’). This property has been exploited by both BaBar andBelle, in particular, to measure inclusive decay modes as well as final states with missing neutrinos.
The Belle II experiment at SuperKEKB has started recording data in 2019, and the experimenthas so far collected about 428 fb−1 of data by summer 2022, when their long shutdown 1 started.
Of collected data, 363 fb−1 is at the Υ (4S) resonance. At the Z resonance (SLC, LEP) all speciesof b-flavored hadrons could be studied for the first time. The e+ e− → bb production cross-section
at the Z resonance is about 6.6 nb.
High-energy pp̄ (Tevatron) and pp collisions (LHC) produce b-flavored hadrons of all species with√large cross-sections. At the Tevatron ( s = 1.96 TeV) the visible cross section σ(pp → bX, |η| < 1)
is about 30 µb. CDF and D0 experiments at the Tevatron have accumulated by the end of theirrunning about 10 fb−1 each.
√At the LHC pp collider at s = 7 − 13 TeV, the visible b-hadron cross section at the LHCb
experiment with pseudorapidity acceptance 2 < η < 5 has been measured to be ∼ 72 µb at 7 TeV
and ∼ 144 µb at 13 TeV [21] (cross section at 13 TeV corrected in Erratum). LHCb has collected
about 1 fb−1 at 7 TeV, 2 fb−1 at 8 TeV, and close to 5.9 fb−1 at 13 TeV during LHC Runs 1√
and 2. CMS and ATLAS have collected each about 5 fb−1 of data at s = 7, 20 fb−1 at 8 TeV
and about 150 fb−1 at 13 TeV during LHC Runs 1 and 2. The latest LHC Run 3 at 13.6 TeV
started in summer 2022, with upgraded detectors. By the time of the writing (March 2024), LHC
has delivered about 70 fb−1 to ATLAS and CMS experiments, and about 300 pb−1 to the LHCb
experiment with major detector upgrades.
In hadron collisions, production happens as bb pairs via leading order flavor creation or higher
order processes such as gluon–splitting. Single b-quarks can be produced by flavor excitation. The
total b-production cross section is an interesting test of our understanding of leading and higher
order QCD processes. With a wealth of measurements at LHC and at Tevatron (see Ref. [21]and references therein), and improved calculations [22], there is a reasonable agreement between
measurements and predictions.
Each quark of a bb pair produced in hadron collisions hadronizes separately and incoherently
from the other, but it is still possible to obtain a statistical indication of the charge of a produced b/b
quark (“flavor tag” or “charge tag”) from the accompanying particles produced in the hadronization
process, or from the decay products of the other quark. The momentum spectrum of produced
b-quarks typically peaks near the b-quark mass, and extends to much higher momenta, droppingby about a decade for every ten GeV. Typical decay lengths are of the order of a centimeter at 13
TeV pp collisions; the resolution for the decay vertex must be more precise than this to resolve thefast oscillations of Bs0 mesons.
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73. Production and Decay of b-flavored Hadrons

In e+ e− colliders, since the B mesons are very slow in the Υ (4S) rest frame, asymmetric beamenergies are used to boost the decay products to allow time-dependent measurements that are
crucial for the study of CP violation. At KEKB, the boost was βγ = 0.43, while PEP-II used aslightly larger boost, βγ = 0.55. The typical B-meson decay length is dilated from ≈ 20 µm to≈ 200 µm. At SuperKEKB the boost is lower, βγ = 0.28, which puts more demanding requirementson the track reconstruction precision at Belle II to reach a resolution in decay time measurements
similar to Belle. The two B mesons produced in Υ (4S) decay are in a coherent quantum state, whichmakes it easier than in hadron collisions to infer the charge state of one B meson from observationof the other; however, the coherence also requires determination of the decay time of both mesons,rather than just one, in order to perform time–dependent CP –violation measurements. For Bs0 ,which can be produced at Υ (5S) the situation is less favourable, as boost is not high enough toprovide sufficient time resolution to resolve the fast Bs0 oscillations.
For the measurement of branching fractions, the initial composition of the data sample must be0
known. The Υ (4S) resonance decays predominantly to B 0 B and B + B − ; the current experimental
upper limit for non-BB decays of the Υ (4S) is less than 4% at the 95% confidence level (CL) [23].
The observed modes of this category are decays to lower Υ states and a pion pair, η, or η 0 , measured
branching fractions being of order 10−4 − 10−5 [24], and decays to hb (1P )η with branching fractionof order 10−3 [17].
The ratio f+ /f0 of the fractions of charged to neutral B productions from Υ (4S) decays has beenmeasured by CLEO, BaBar, and Belle in various ways. They typically use pairs of isospin-related
decays of B + and B 0 , such that it can be assumed that Γ (B + → x+ ) = Γ (B 0 → x0 ). In this way,
the ratio of the number of events observed in these modes is proportional to (f+ τ+ )/(f0 τ0 ) [25].
BaBar has also performed an independent measurement of f0 with a different method that does
not require isospin symmetry or the value of the lifetime ratio, based on the number of eventswith one or two reconstructed B 0 → D∗− `+ ν decays [26]. The combined result, from the current
average of τ+ /τ0 , is f+ /f0 = 1.058 ± 0.024 [27]. The result is consistent within 2.4σ with equal0
production of B + B − and B 0 B pairs, and we assume f+ /f0 = 1 in this mini-review except where
explicitly stated otherwise. This assumption is also supported by the near equality of the B + andB 0 masses: our fit yields m(B 0 ) = 5279.72 ± 0.08 MeV/c2 , m(B + ) = 5279.41 ± 0.07 MeV/c2 , andm(B 0 ) − m(B + ) = 0.31 ± 0.05 MeV/c2 .
Data collected at the Υ (5S) resonance gave CLEO, Belle and BaBar access to Bs0 decays. In
Υ (5S) decays there are seven possible final states including a pair of non-strange B mesons and 0,∗000
1 or 2 pions, and three final states with a pair of strange B mesons (Bs∗0 B s , Bs∗0 B s , and Bs0 B s ).
The fraction of events with a pair of Bs0 mesons over the total number of events with a pair of∗0 ∗0b-flavored hadrons has been measured to be fs [Υ (5S)] = 0.199+0.030−0.029 [28], of which 88% is Bs B̄s0
events. However, the small boost of Bs mesons produced in this way prevents resolution of theirfast oscillations for time-dependent measurements; these are only accessible in hadron collisions (orat the Z peak).
In high-energy collisions, the produced b or b̄ quarks can hadronize with different probabilities
into the full spectrum of b-hadrons, either in their ground or excited states. The hadronization does
not have to be identical in pp or pp collisions and in Z decay, because of the different momentum
distributions of the b-quark in these processes; the sample used in the pp measurements has momenta
close to the b mass, rather than mZ /2 in Z decay. The available data from Tevatron and LHC showthat the production fractions fd , fu , fs , and fbaryon of B 0 , B + , Bs0 , and b baryons, respectively,of weakly decaying b hadrons depend on the kinematics of the produced b hadron. Recently
LHCb experiment found evidence for dependence of b-quark hadronization on multiplicity in pp
0collisions [29]. The production fractions of b hadrons are discussed in more detail in the B 0 – B
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473. Production and Decay of b-flavored Hadrons

mixing section in this Review [8].
Excited B-meson states have been thoroughly studied by CLEO, LEP, CUSB, D0 and CDF(an admixture of B mesons) and LHCb (B ∗+ -meson). The current world average of the B ∗ –B
mass difference is 45.21 ± 0.21 MeV/c2 . Excited Bs∗ -meson states have observed in Υ (5S) decays
by CUSB, CLEO and Belle.
For orbitally excited B(s) meson states, with relative angular momentum L=1 of the two quarks,
there exist four states (J, jq ) = (0, 1/2), (1, 1/2), (1, 3/2), (2, 3/2), where jq is the total angularmomentum of the light u, d or s quark and J is the total angular momentum of the B meson. These∗∗ mesons. The j = 1/2 states are named B ∗states are collectively called as B(s)q(s)0 (J = 0) and B(s)1∗(J = 1) mesons, while the states with jq = 3/2 are named B(s)1 (J = 1) and B(s)2(J = 2) mesons.
The states with jq = 1/2 can decay through an S-wave transition and are expected to have a large
width, but the jq = 3/2 states are narrow D-wave decays. Evidence for B ∗∗ production has been
initially obtained at LEP as a broad Bπ resonance [30] or a B + K − enhancement [31]. Detailed
results have been obtained for the narrow states B1 (5721)0,+ and B2 (5747)0,+ at the Tevatronand by LHCb, and clear enhancements compatible with the higher mass states BJ (5840)0,+ and
BJ (5970)0,+ have been observed [32]. Also the narrow Bs∗∗ states Bs1 (5830)0 and Bs2 (5840)0 havebeen measured at the CDF [32], LHCb [33], and CMS [34].
Excited states of Bc+ mesons will provide important information about the strong potential. A+
Bc π + π − resonance has been observed for the first time by ATLAS [35]. The mass of the resonancehas been measured precisely by CMS and LHCb as 6871.2 ± 1.0 MeV/c2 [36]. The resonance may
be interpreted as the second S-wave state of the Bc+ meson, Bc+ (2S), but the quantum numbers
are to be confirmed.
Baryon states containing a b quark are labeled according to the same scheme used for non-bbaryons, with the addition of a b subscript [20]. The first observed b baryon was the Λ0b (quark
composition udb). Thanks to the large samples accumulated at the Tevatron and specially at
the LHC many new b baryons have been found. The masses of all these new baryons have beenmeasured to a precision of a few MeV/c2 , and found to be in agreement with predictions from
Heavy Quark Effective Theory (HQET).
Clear signals of four strongly–decaying baryon states, Σb+ , Σb∗+ (uub), Σb− , Σb∗− (ddb) havebeen obtained by CDF [37] and LHCb [38]. LHCb has also observed two new mass peaks in theΛ0b π ± systems, consistent with single resonances and named as Σb± (6097) [38]. The nature of theseresonances is, however, not yet clear. The isodublet of strange b baryons Ξb0 (usb) and Ξb± (dsb) has
been observed by CDF and D0 [39]. Masses, lifetimes, and branching ratios have been accurately
measured by LHCb [40–42] and CDF [43]. LHCb has also measured several parameters sensitive to
P and CP violation [42,44]. Other observed Ξb baryons are spin-3/2 states Ξb (5945)0 (Ξb∗0 ) [45,46],Ξb∗ (5955)− [46,47] and Ξb (6100)− [46,48], a spin-1/2 state Ξb0 (5935)− [46,47], and resonance statesΞb− (6227) [41, 49], Ξb0 (6327) [50] and Ξb0 (6333) [50]. The doubly–strange bottom baryon Ωb− hasbeen observed first by D0 and CDF [51]. Mass and mean life have been measured precisely by
LHCb [52] and CDF [43]. LHCb has also observed four excited Ωb− states Ωb− (6316), Ωb− (6330),Ωb− (6340) and Ωb− (6350) [53].
The so-called exotic states have raised a lot of interest recently. While many exotic states wereseen in the charm sector, in bottom sector there are fewer seen. The D0 Collaboration claimed anarrow state X(5568) decaying into a Bs0 π ± final state [54]. While this would be an interesting
addition to the observed states as the first exotic state with constituent quarks with four different
flavours (b, s, u, d), analysis by LHCb yields negative result [55]. Also CMS finds no such astate [56].
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73. Production and Decay of b-flavored Hadrons

573.2 Lifetimes
Precise lifetimes are key in extracting the weak parameters that are important for understanding0
the role of the CKM matrix in CP violation, such as the determination of Vcb and Bs0 –B s mixing
parameters. In the naive spectator model, the heavy-flavored hadrons can decay only via theexternal spectator mechanism, and thus, the lifetimes of all mesons and baryons containing b quarks
would be equal. Non–spectator effects, such as the interference between contributing amplitudes,
modify this simple picture and give rise to a lifetime hierarchy for b-flavored hadrons similar tothe one in the charm sector. However, since the lifetime differences are expected to scale as 1/m2Q ,where mQ is the mass of the heavy quark, the variations in the b system are expected to be only
10% or less [57, 58]. We expect:τ (B + ) ≥ τ (B 0 ) ≈ τ (Bs0 ) > τ (Λ0b )  τ (Bc+ ) .

(73.1)For the Bc+ , both quarks decay weakly, so the lifetime is much shorter.
Measurements of the lifetimes of the different b-flavored hadrons thus provide a means to determine the importance of non-spectator mechanisms in the b sector. Availability of large samples offully–reconstructed decays of different b-hadron species has resulted in precise measurements withsmall statistical and systematic uncertainties (∼1%). The world averages given in Table 73.1 havebeen determined by the Heavy Flavor Averaging Group (HFLAV) [59].
Table 73.1: Summary of the world-average b-hadron lifetime measurements. For the Bs0 lifetimes, see text below.
Particle
B+
B0
Bs0
0
BsL
0
BsH
+
Bc
Λ0b
Ξb−
Ξb0
Ωb−

Lifetime [ps]1.638 ± 0.004
1.517 ± 0.004
1.520 ± 0.005
1.429 ± 0.006
1.623 ± 0.008
0.510 ± 0.009
1.471 ± 0.009
1.572 ± 0.040
1.480 ± 0.030+0.181.64−0.17

The Bs0 lifetime in Table 73.1 is defined as 1/Γs , where Γs is the average width of the light (L)and heavy (H) mass eigenstates, (ΓL + ΓH )/2. In the absence of CP violation, the light (heavy) Bs0
mass eigenstate is the CP -even (CP -odd) eigenstate. Thus, the lifetime of the light (heavy) mass
eigenstate can be measured from CP -even (odd) final states. The lifetimes can also be obtained
from time-dependent angular analysis of Bs0 → J/ψφ decays.
The short Bc+ lifetime is in good agreement with predictions [60]. With large samples of Bc+
mesons at the LHC precision on the lifetimes can still improve. The measurement using semileptonic
decays gives τBc+ = 0.509 ± 0.008 ± 0.012 ps [61] while using decays Bc+ → J/ψπ + yields τBc+ =0.5134 ± 0.0110 ± 0.0057 ps [62]. Each of these is more precise than the combination of all previous
experiments.
The recent Λ0b lifetime measurements from LHC experiments and CDF are precise and favour
lifetime close to the lifetime of B 0 meson, in agreement with theory.
For precision comparisons with theory, lifetime ratios are more sensitive. Experimentally it is
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found [59]:73. Production and Decay of b-flavored Hadrons

τBs0
τB +
= 1.076 ± 0.004 ,= 1.002 ± 0.004 ,
τB 0
τB 0
τΛ0
b
= 0.969 ± 0.006 ,τB 0

while recent Heavy Quark Expansion (HQE) predictions give [58]:
τBs0
τB +
= 1.04+0.05= 1.001 ± 0.002 ,−0.01 ± 0.02 ± 0.01 ,
τB 0
τB 0
τΛ0
b

τB 0

= 0.935 ± 0.054.

The ratio of B + to B 0 lifetimes has a precision of better than 1%, and is significantly different from
1.0, in agreement with predictions [57]. The ratio of Bs0 to B 0 lifetimes is expected to be very close
to 1.0.
For a detailed discussion on neutral B 0 and Bs0 oscillation and relevant CP violation measurements see Ref. [8].

73.3 Features of decays
The ground states of b-flavored hadrons decay via weak interactions. In most decays of theb-flavored hadrons, where the b-quark is accompanied by lighter partner quarks (d, u, s, or c), thedecay modes are well described by the decay of the b quark (spectator model) [63]. The dominant
decay mode of a b quark is b → cW ∗− (referred to as a “tree” or “spectator” decay), where thevirtual W materializes either into a pair of leptons `ν̄ (“semileptonic decay”), or into a pair ofquarks which then hadronizes. The transition b → u is suppressed by |Vub /Vcb |2 ∼ (0.1)2 relative
to b → c transitions. The decays in which the spectator quark combines with one of the quarks
from W ∗ to form one of the final state hadrons are suppressed by a factor ∼ (1/3)2 , because thecolors of the two quarks from different sources must match (“color–suppression”).
Semileptonic B decays B → Xc `ν and B → Xu `ν provide an excellent way to measure the magnitude of the CKM elements |Vcb | and |Vub | respectively, because the strong interaction effects aremuch simplified due to the two leptons in the final state. Both exclusive and inclusive decays can beused with dominant uncertainties being complementary. For exclusive decay analysis, knowledge ofthe form factors for the exclusive hadronic system Xc(u) is required. For inclusive analysis, it is usually necessary to restrict the available phase-space of the decay products to suppress backgrounds;
subsequently uncertainties are introduced in the extrapolation to the full phase-space. Moreover,restriction to a small corner of the phase-space may result in breakdown of the operator-productexpansion scheme, thus making theoretical calculations unreliable. A more detailed discussion of
B semileptonic decays and the extraction of |Vcb | and |Vub | is given elsewhere in this Review [9].
While traditionally B 0 and B + decays were used, over time also other B hadron studies became
available. Most notably, determination of of |Vub | using Λ0b → pµ− ν̄µ decays by LHCb [64] was more
precise than expected. Besides, there have been measurements of inclusive semileptonic decay ratesof Bs0 [65] and Bc+ [66] mesons. One of the latest additions in this area is the observation of theBs0 → K − µ+ νµ decays by LHCb using only a fraction of their available data [67].
On the other hand, hadronic B decays are complicated because of strong interaction effects
caused by the surrounding cloud of light quarks and gluons. While this complicates the extractionof CKM matrix elements, it also provides a great opportunity to study perturbative and nonperturbative QCD, hadronization, and Final State Interaction (FSI) effects.
Many aspects of B decays can be understood through the Heavy Quark Effective Theory(HQET) [68]. This has been particularly successful for semileptonic decays. For further discussion
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73. Production and Decay of b-flavored Hadronsof HQET, see for instance Ref. [69]. For hadronic decays, one typically uses effective Hamiltonian calculations that rely on a perturbative expansion with Wilson coefficients. In addition, someform of the factorization hypothesis is commonly used, where, in analogy with semileptonic decays,
two-body hadronic decays of B mesons are expressed as the product of two independent hadronic
currents, one describing the formation of a charm meson (in case of the dominant b → cW ∗− decays), and the other describing the hadronization of the remaining ud (or cs) system from the virtualW − . Qualitatively, for B decays with a large energy release, e.g. b → uW ∗− transitions, the ud pair
(produced as a color singlet) travels fast enough to leave the interaction region without influencing
the meson containing the spectator quark. This is known to work well for the dominant spectator
decays [70]. There are several common implementations of these ideas for hadronic B decays, themost common of which are QCD factorization (QCDF) [71], perturbative QCD (pQCD) [72], andsoft collinear effective theory (SCET) [73].
The transitions b → s and b → d are flavor-changing neutral-current (FCNC) processes. Although they are not allowed in the SM as a tree-process, they can occur via loop diagrams (denoted “penguin” decays). The rates for b → s penguin decays are comparable to the CKMsuppressed b → u tree processes. Pure-penguin decays were first established by the observation of B → K ∗ (892)γ [74]. Penguin processes involving b → d transitions are further suppressed by CKM, and have been observed for B → (ρ/ω)γ decays [75, 76]. LHCb has observed ab → d penguin transition in the B + → π + µ+ µ− mode and measured its branching fraction to be(1.83 ± 0.24 ± 0.05) × 10−8 [77].
Other decay processes discussed in this Review include W –exchange (a W is exchanged between
initial–state quarks), penguin annihilation (the gluon from a penguin loop attaches to the spectator
quark, similar to an exchange diagram), and pure–annihilation (the initial quarks annihilate to a
virtual W , which then decays). Some observed decay modes such as B 0 → Ds− K + , may beinterpreted as evidence of a W -exchange process [78]. The evidence for the purely leptonic decay
B + → τ + ν from Belle [79] and BaBar [80] is the first sign of a pure annihilation decay. The average
branching fraction is (1.09 ± 0.24) × 10−4 , which is somewhat larger than, though consistent with,the value expected in the SM. A substantial region of parameter space of charged Higgs mass vs.
tan β is excluded by the measurements of this mode. A dedicated discussion of purely leptonic
decays of charged pseudoscalar mesons is given elsewhere in this Review [81].

73.4 Dominant hadronic decays
Most of the hadronic B decays involve b → c transition at the quark level, resulting in acharmed hadron or charmonium in the final state. Other types of hadronic decays are very rare
and will be discussed separately in the next section. The experimental results on hadronic B decays
have steadily improved over the years, and the measurements have reached sufficient precision tochallenge our understanding of the dynamics of these decays. With good particle detection andhadron identification capabilities of B-factory detectors, a substantial fraction (roughly on theorder of a few per mill) of hadronic B decay events can be fully reconstructed. In particular,
good performances for detecting π 0 and other neutral particles helped Belle and BaBar to make0
comprehensive measurements of the decays B → D(∗)0 h0 [82], where h0 stands for light neutral0mesons such as π 0 , η ( ) , ρ0 , ω. The measurements are being complemented by LHCb, in decays likeB 0 → D0 π + π − [83], where no neutral particles reconstruction is needed. These decays proceed
through color-suppressed diagrams, hence they provide useful tests on the factorization models.
Because of the kinematic constraint of Υ (4S) → B B̄, the energy sum of the final-state particles
of a B meson decay is always equal to one half of the total energy in the center of mass frame.
As a result, the two variables, ∆E (energy difference) and MB (B candidate mass with a beamenergy constraint) are very effective for reducing combinatorial background both from Υ (4S) and13th September, 2024

873. Production and Decay of b-flavored Hadrons

e+ e− → q q̄ continuum events. In particular, the energy-constraint in MB improves the signal
resolution by almost an order of magnitude.
The kinematically clean environment of B meson decays provides an excellent opportunity tosearch for new states. For instance, quark-level b → cc̄s decays have been used to search for new
charmonium and charm-strange mesons and study their properties in detail. While narrow charm∗ (2317) [84] and D (2460) [85] were discovered by BaBar and CLEO, respectively,
strange states Ds0
s1∗ (2317)
the properties of these new states were revealed by studying the B meson decays, B → DDs0
and B → DDs1 (2460) by Belle [86] and BaBar [87]. Another example is Dalitz plot analysis of decay
Bs0 → D̄0 K − π + in which the decay to spin-3 resonance was observed for the first time [88]. Oneof the most significant improvements in the past decade is establishment of decays B + → D0 K +0and B + → D0 K ∗ (892)+ with D0 decaying to final state common to D0 and D [89]. This allows+3.3
direct determination of CKM angle γ(= φ3 ) to be 65.9−3.5 .
Information on Bs0 , Bc+ and Λ0b decays have been remarkably improved with recent studies of(∗)+ (∗)−
large samples from LHCb. Noticeable additions in Bs include decay modes to Ds Ds , D̄0 K̄ 0 ,
(∗)+
(∗)−
decays were first observed by CDF [90], followed by Belleand J/ψ K̄ ∗ (892)0 . The Bs0 → Ds Ds(∗)+ (∗)−[91]. LHCb has improved the precision with B(Bs0 → Ds Ds ) = (3.07±0.22±0.33)% [92], which(∗)+ (∗)−
decays do not saturate the CP -even modes of the Bs decays. The
suggests that Bs0 → Ds Ds000
Bs → D̄ K̄ decay occurs mostly via a color-suppressed tree diagram, and has a small theoreticaluncertainty in the SM, thus this mode can significantly improve the determination of the CP violation angle φs . LHCb has observed this decay and the branching fraction is (4.3±0.5±0.7)×10−4[93]. The Bs0 → J/ψ K̄ ∗ (892)0 decay can be used to constrain the penguin pollution in determining
φs . LHCb has updated the branching fraction and measured the CP asymmetries of this decay,
thereby constraining the penguin pollution in φs [94], although a much more stringent constraint
on penguin pollution can come from B 0 → J/ψρ0 which has been observed by BaBar [95] and
LHCb [96]. The Bc+ → Bs0 π + decay is unique as the only observed mode of b-flavored hadron decays
where the partner quark decays (c in this case) while the b quark remains a spectator. LHCb has
observed this mode [97] and measured B(Bc+ → Bs0 π + )/B(Bc+ → J/ψπ + ) = (91±10±8±3) [98]. In(∗)+
addition, LHCb [99] and ATLAS [100] have measured Bc+ → J/ψDs , which, by comparing with
+ − −Bc+ → Bs0 π + , provides a ratio of exclusive b → c and c → s decays of Bc+ . For Λ0b → Λ+c π π π[101], not only the total rate is measured, but also structure involving decays through excited Λcand Σc baryons.
In addition, a variety of exotic particles that do not fit the conventional meson spectroscopy havebeen discovered in B decays. Belle found the X(3872) state by studying B + → J/ψπ + π − K + [102],
which was confirmed by CDF [103], D0 [104] and BaBar [105]. Production of X(3872) has beenstudied by the LHC experiments, LHCb [106], CMS [107] and ATLAS [108].
A charged charmonium-like state X(4430)± that decays to ψ(2S)π ± was observed by Belle in
B → ψ(2S)Kπ ± [109]. Since it is charged, it could not be an ordinary charmonium state. A highstatistics study by LHCb confirmed the existence of the X(4430)± in decays B → ψ(2S)Kπ ± [110],demonstrated its resonance character by studying the phase motion, unambiguously determined
its spin-parity, and saw evidence for another state. In a Dalitz plot analysis of B̄ 0 → J/ψK − π +[111], Belle has found another state, labeled as X(4200)+ in this Review, adding to the list of
exotic charged charmonium-like states. In an amplitude analysis of the decay Λ0b → J/ψpK − ,LHCb observed exotic structures, labeled as Pc (4380)+ and Pc (4450)+ in this Review, in the J/ψpchannel [112]. The subsequent analysis with significantly increased statistics observed additional
state and resolved the peak at 4450 MeV/c2 as being due to the two states close in the mass [113].
The structure in the J/ψp channel was also seen in the Bs0 → J/ψpp decays [114] and in the J/ψΛ
channel in B + → J/ψΛp and Ξb− → J/ψΛK − decays [115]. They are referred to as charmonium13th September, 2024

973. Production and Decay of b-flavored Hadrons

pentaquark states. More detailed discussions of exotic meson-like states and pentaquarks are given
elsewhere in this Review [116].

73.5 Rare hadronic decays
All B-meson decays that do not occur through the b → c transition are usually called rare
B decays. These include both semileptonic and hadronic b → u decays that are suppressed atleading order by the small CKM matrix element Vub , as well as higher-order b → s(d) processes
such as electroweak and gluonic penguin decays. In this section, we review hadronic rare B decays,
while electroweak penguin decays and others are discussed in the next.
Charmless B meson decays into two-body hadronic final states such as B → ππ and Kπ
are experimentally clean, and provide good opportunities to probe new physics and search forindirect and direct CP violations. Since the final state particles in these decays tend to have larger
momenta than average B decay products, the event environment is cleaner than for b → c decays.
Branching fractions are typically around 10−5 . Over the past decade, many such modes have been
observed not only by e+ e− collider experiments such as BaBar and Belle, but also by hadroncollider experiments such as CDF (pp̄) and LHCb (pp). In the latter cases, huge data samples ofthe modes with all charged final-state particles have been reconstructed by triggering on the impact
parameter of the charged tracks. This has also allowed observation of charmless decays of the Bs ,in final states such as φφ [117], K + K − [118, 119], and K − π + [119, 120], and of charmless decays ofthe Λ0b baryon [120]. The large samples available at LHCb experiment allow to perform also timedependent CP violation measurements [121]. Charmless Bs modes are related to corresponding B 0
modes by U-spin symmetry, and are determined by similar amplitudes. Combining the observablesfrom Bs0 and B 0 modes is a further way of eliminating hadronic uncertainties and extracting relevant
CKM information [122].
Because of relatively high-momenta for final state particles, the dominant source of backgroundin e+ e− collisions is q q̄ continuum events; sophisticated background suppression techniques exploiting event shape variables are essential for these analyses. In hadron collisions, the dominantbackground comes from QCD or partially reconstructed heavy flavors, and is similarly suppressedby a combination of kinematic and isolation requirements. The results are in general consistentamong the experiments.
Most rare decay modes including B 0 → K + π − have contributions from both b → u tree andb → sg penguin processes. If the size of the two contributions are comparable, the interference
between them may result in direct CP violation, seen experimentally as a charge asymmetry in the
decay rate measurement. BaBar [123], Belle [124], CDF [118], and LHCb [121, 125] have measured
the direct CP violating asymmetry in B 0 → K + π − decays. Direct CP violation has been observedin this decay with a significance of more than 5σ. The world average value of the asymmetry
is now rather precise, ACP (K + π − ) = −0.0834 ± 0.0032. The CP asymmetry in B + → K + π 0
mode has been measured by BaBar [126], *Belle [124] and LHCb [127] with the average value
ACP (K + π 0 ) = 0.030 ± 0.013. These two asymmetries differ significantly, in contrast to a naive
expectation based on simplified picture in the SM. For more detailed tests, there are sum rules [128]that relate the decay rates and decay-rate asymmetries between the four Kπ charge states. A crucial
ingredient of the sum rule test is ACP (K 0 π 0 ). Currently, measured values are reported by both
BaBar [129] and Belle [130]. Using the ACP (K 0 π 0 ) value of Ref. [130], Belle reports the sum rule
test result that is consistent with zero within 1.9σ [124]. With the future improvements via Belle II
and upgraded LHCb, the measurements are expected to become precise enough to shape a definite
conclusion. The CP asymmetry in the π + K − mode has also been measured in Bs0 decays, by
CDF [118] and LHCb [121, 125]. The combined value is ACP (Bs0 → π + K − ) = 0.224 ± 0.012.
In addition to B(s) → Kπ modes, significant (> 3σ) non-zero CP asymmetries have been
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73. Production and Decay of b-flavored Hadrons

measured in several other rare decay modes: ACP (B + → ρ0 K + ) = 0.37 ± 0.10 [131], ACP (B + →ηK + ) = −0.37 ± 0.08 [132], ACP (B 0 → ηK ∗0 ) = 0.19 ± 0.05 [133], and ACP (B + → f2 (1270)K + ) =−0.68+0.19−0.17 [131]. In at least the first two cases, a large direct CP violation might be expected since
the penguin amplitude is suppressed so the tree and penguin amplitudes may have comparable
magnitudes. There are also measurements by LHCb of CP asymmetries in several 3-body modes:
ACP (B + → π + π − π + ) = 0.057 ± 0.013, ACP (B + → K + π − π + ) = 0.027 ± 0.008, ACP (B + →K + K − π + ) = −0.122 ± 0.0021, and ACP (B + → K + K − K + ) = −0.033 ± 0.008 [134]. Many of theseanalyses now include Dalitz plot treatments with many intermediate resonances.
00
BaBar [135] and Belle [124, 136] have observed the decays B + → K K + and B 0 → K 0 K .
0The world-average branching fractions are B(B 0 → K 0 K ) = (1.21 ± 0.16) × 10−6 and B(B + →0
K K + ) = (1.31 ± 0.17) × 10−6 . These are the first observations of hadronic b → d transitions,with significance bigger than 5σ for all four measurements. CP asymmetries have been measured
for these modes, but with large errors. LHCb has observed B 0 → K + K − mode which occurs
via a weak-annihilation process and is the rarest hadronic B-meson decay thus far observed, with
B(B 0 → K + K − ) = (7.80 ± 1.52) × 10−8 [137]. Bs0 → K + K − decay mode, which occurs mostly
via b → s penguin process, has been observed by Belle [138], CDF [139] and LHCb [119]. The
average branching fraction is B(Bs0 → K + K − ) = (26.6 ± 2.2) × 10−6 . Belle has also observed0
Bs0 → K 0 K [140] which also occurs via b → s penguin transition in the SM. This was recently
confirmed by LHCb [141]. The average branching fraction is (1.76 ± 0.31) × 10−5 .
The decay B 0 → π + π − can be used to extract the CKM angle α (for details see elsewhere inthis Review [142]). This is complicated by the presence of significant contributions from penguin
diagrams. An isospin analysis [143] can be used to untangle the penguin complications. The
decay B 0 → π 0 π 0 is crucial in this analysis. Both BaBar and Belle have observed B 0 → π 0 π 0 ,with a mild tension in the measured branching fractions: (1.83 ± 0.25) × 10−6 for BaBar [123] and(1.31±0.26)×10−6 for Belle [144]. It turns out that the amount of penguin pollution in the B → ππsystem is rather large. In the past few years, measurements in the B 0 → ρρ system have produced
more precise values of α, since penguin amplitudes are generally smaller for decays with vector
mesons. An important ingredient in the analysis is the B 0 → ρ0 ρ0 branching fraction. The averageof measurements from BaBar [145] and Belle [146] yields a branching fraction of (0.96±0.15)×10−6 .
This is only 3% of the ρ+ ρ− branching fraction, much smaller than the corresponding ratio (& 20%)in the ππ system.
Since B → ρρ has two vector mesons in the final state, the CP eigenvalue of the final state
depends on the longitudinal polarization fraction fL for the decay. Therefore, a measurement of
fL is needed to extract the CKM angle α. Both BaBar and Belle have measured fL for the decays
ρ+ ρ− [147] and ρ+ ρ0 [148] and in both cases the measurements show fL > 0.9, making a complete
angular analysis unnecessary. In B 0 → ρ0 ρ0 , fL is measured by BaBar [145], Belle [146] and+0.08
LHCb [149], with the average value being 0.71−0.09.
By analyzing the angular distributions of the B decays to two vector mesons, we can learn
a lot about both weak- and strong-interaction dynamics in B decays. Decays that are penguindominated surprisingly have values of fL near 0.5. The list of such decays has now grown to include
B → φK ∗ (892), B → ρK ∗ (892), and B → ωK ∗ (892). The reasons for this "polarization puzzle"
are not fully understood. A detailed description of the angular analysis of B decays to two vector
mesons can be found in a separate mini-review [150] in this Review .

73.6 Electroweak penguin decays
Electroweak penguin decays are one-loop FCNC decays proceeding through penguin or box
Feynman diagrams with final state including real photon or pair of leptons. Such decays were firstobserved by CLEO experiment when it observed decay B → K ∗ (892)γ [74]. Since then significant
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amount of experimental information was obtained. Branching fractions for these decays are 10−5 orless, which makes them excellent candidates for searches for new physics beyond SM. Often several
observables are available, which allows for stringent tests of the SM.
Starting with radiative decays, experimentally easiest to study are exclusive decays with a fullyreconstructed final state. The best studied decay in this class is B → K ∗ (892)γ seen by CLEO,
Belle, BaBar experiments [151, 152] with world average branching fraction B(B 0 → K ∗ (892)0 γ) =(41.8 ± 2.5) × 10−6 . Decays through several other kaon resonances such as B → K1 (1270)γ,K2∗ (1430)γ, etc. were studied at B-factories [153, 154]. It is worth to mention decay B + →K + π + π − γ for which besides measurements of the branching fraction [154,155] one can also use theangular distribution to access photon polarization. Such a measurement was done by the LHCb
experiment, which was able to clearly demonstrate that the photon in B + → K + π + π − γ decay ispolarized [156]. Unfortunately given non-trivial hadronic structure, more work is needed before
turning this into test of the SM. The exclusive radiative decays Bs0 → φγ was seen by the Belle and
LHCb experiments [157] with an average branching fraction of (3.4 ± 0.4) × 10−5 and more recently
also decay Λb → Λγ was observed by LHCb [158].
Compared to b → sγ, the b → dγ transitions such as B → ργ, are suppressed by the CKM
elements ratio |Vtd /Vts |2 . Both Belle and BaBar have observed these decays [75, 76]. The world
average B(B → (ρ, ω)γ) = (1.30 ± 0.23) × 10−6 . This can be used to calculate |Vtd /Vts | [159]; the+0.033measured values are 0.195+0.025−0.024 from Belle [75] and 0.233−0.032 from BaBar [76].
The observed radiative penguin branching fractions can constrain a large class of SM extensions[160]. However, due to the uncertainties in the hadronization, only the inclusive b → sγ rate canbe reliably compared with theoretical calculations. This rate can be measured from the endpointof the inclusive photon spectrum in B decay. By combining the measurements of B → Xs γfrom the CLEO, BaBar, and Belle experiments [161, 162], HFLAV obtains the average: B(B →Xs γ) = (3.49 ± 0.19) × 10−4 [59] for Eγ ≥ 1.6 GeV, averaging over B + and B 0 . Consistent but
less precise results have been reported by ALEPH for inclusive b–hadrons produced at the Z,
which includes also contribution from Bs0 and Λ0b hadrons. Using the sum of seven exclusive final
states, the BaBar experiment measured the branching fraction of inclusive b → dγ decays to be(9.2 ± 2.0 ± 2.3) × 10−6 [163]. The measured branching fraction can be compared to theoretical
calculations. Recent calculations of B(b → sγ) at NNLO level predict for the Eγ ≥ 1.6 GeV valuesof (3.36 ± 0.23) × 10−4 for b → sγ and (1.68 ± 0.17) × 10−5 for b → dγ decays [164].
The CP asymmetry in b → sγ is extensively studied theoretically both in the SM and beyond[165]. According to the SM, the CP asymmetry in b → sγ is smaller than 1%, but some non-SM
models allow significantly larger CP asymmetry (∼ 10%) without altering the branching fraction.
The current world average is ACP = 0.015 ± 0.011, again dominated by BaBar and Belle [166, 167].
In addition to the CP asymmetry, BaBar and Belle also measured the isospin asymmetry ∆0− =−0.005 ± 0.020 in b → sγ measured using sum of exclusive decays [166, 168]. An alternative
measurement using full reconstruction of the companion B in the hadronic decay modes yields a
consistent, but less precise result [169]. Both Belle and BaBar experiments measured the isospin
asymmetry in exclusive B → K ∗ (892)γ decay with average of 6.3 ± 1.7% [152] and therefore
providing evidence for the non-zero isospin asymmetry.
In addition, experiments have measured the inclusive photon energy spectrum for b → sγ,
and by analyzing the shape of the spectrum they obtain the first and second moments for photon
energies. Belle has measured these moments covering the widest range in the photon energy (1.7 <Eγ < 2.8 GeV) [162]. The measurement by BaBar has slightly smaller range with lower limit at
1.8 GeV [170]. These results can be used to extract non-perturbative HQET parameters that areneeded for precise determination of the CKM matrix element Vub (see further discussion elsewherein this Review [171]).
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Additional information on FCNC processes can be obtained from b → s`+ `− decays. These
processes are studied as a function of dilepton invariant mass squared, q 2 . Different q 2 regions are
sensitive to different physics. Starting at the very low q 2 decays exhibit sensitivity to the same
physics as the radiative decays. Then for the q 2 in region 1.1 to 6.0 GeV2 /c4 the SM and new
physics have best chance to compete. At the high q 2 above the ψ(2S) mass, the interference of SM
and new physics is to some extend complementary to that in lower q 2 . Regions around J/ψ andψ(2S) is normally excluded from measurements as these are dominated by the b → c transitions tocharmonia. For exclusive decays, theory predictions require calculations of hadronic form factors.
With current theory predictions, the most useful are measurements within the q 2 regions 1.1 to
6.0 GeV2 /c4 and from 16.0 GeV2 /c4 up to the kinematic limit. From this reason in the listing weprovide results mainly in those two regions.
Similar as for radiative decays, also for the b → s`+ `− decays the inclusive measurements provide
some benefits. Both Belle and BaBar performed such measurement without reconstructing hadronicpart exclusively and measure a branching fraction of (5.8 ± 1.3) × 10−6 [172]. Unfortunately thismeasurement is not trivially possible at hadron colliders and also does not easily allow the angular
distributions of the decay products to be exploited. One alternative is to extract information on
the inclusive decay as sum of exclusive decays. Such a measurement was performed by Belle [173],
but in this case the difficulty lies in extrapolation for the missing hadronic states.
Turning to the exclusive decays, the initial measurements performed by B-factories typicallyaveraged between charged and neutral B mesons as well as between e+ e− and µ+ µ− finals states.
The experiments CDF, LHCb, ATLAS and CMS are much better suited for the µ+ µ− finals statescompared to the e+ e− final states. As such most measurements at hadron colliders are done onlywith µ+ µ− pairs and by separating charged and neutral B mesons. Recently, however, with muchincreased statistics, LHCb measured several final states with e+ e− , to make a series of tests of e/µ
universality in B → K (∗) `+ `− decays. At hadron colliders other b hadrons are produced and as such
CDF and LHCb experiments did observe also Bs0 → φµ+ µ− [174, 175], Λ0b → Λµ+ µ− [174, 176] andΛ0b → pK − µ+ µ− decays [177]. The averages of the total branching fractions integrated over wholeq 2 regions are (5.6 ± 0.6) × 10−7 for B + → K + e+ e− , (4.53 ± 0.35) × 10−7 for B + → K + µ+ µ− ,−6 for B 0 → K ∗ (892)0 e+ e− and (0.94 ± 0.05) × 10−6 for B 0 → K ∗ (892)0 µ+ µ−(1.03+0.19−0.17 ) × 10
decays [178–182]. The total branching fractions for Bs0 → φµ+ µ− and Λ0b → Λµ+ µ− decays are(8.4 ± 0.4) × 10−7 [174, 175, 183] and (1.08 ± 0.28) × 10−6 [174, 176] respectively. With increased
precision of B 0 → K ∗ (892)0 `+ `− decay, there is a question on what fraction of the seen branching
fraction is due to the K ∗ (892)0 resonance and what fraction is due to the Kπ in s-wave. This has
been studied by LHCb which found that the Kπ in s-wave fraction varies between 1% and about
10% depending on the q 2 region [182]. It should be noted, that for all relevant B meson decays thebranching fractions so far studied are consistently below the SM expectation.
In the b → s`+ `− decays angular distributions offer rich source of information. The full angular analysis was performed for decays B + → K + `+ `− , B 0 → K 0 `+ `− , B + → K ∗ (892)+ `+ `− ,B 0 → K ∗ (892)0 `+ `− , Bs0 → φµ+ µ− and Λ0b → Λµ+ µ− decays [184–192]. An attempt to increase
sensitivity to the NP was made by constructing observables, which have reduced theory uncertainties and measurements of these are done. Most notably the observable called P50 [193] shows adiscrepancy with the SM in the q 2 region which is highly sensitive to new physics [186–188]. Measurements of the CP asymmetries [177, 178, 181, 194, 195] and the isospin asymmetry [179–181, 194]
were also performed. All these measurements are well consistent with the small ACP and small
isospin asymmetry expected in the SM [196]. With statistics available at the LHC, the measurement of phase difference between long- and short-distance contribution in B + → K + µ+ µ− decays
became possible [197].
With the data samples available at LHC, the lepton universality in b → s`+ `− can be tested.
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While in the SM decays to electron-positron and muon pairs are expected to be same up to small
corrections due to the different masses of leptons, in extensions of the SM this does not have to hold.
The angular analysis of B 0 → K ∗ (892)0 e+ e− decays was performed by LHCb at low dilepton invariant masses [198] and Belle in several regions over whole q 2 range [188]. The LHCb measurement
yields the most stringent constraint on the photon polarization. The result on lepton universality
test which over past few years attracted most attention is the ratio of branching fractions between
B + → K + µ+ µ− and B + → K + e+ e− and between B 0 → K ∗ (892)0 µ+ µ− and B 0 → K ∗ (892)0 e+ e−
decays [179, 199]. The measurements by LHCb showed mild discrepancy from the SM, with significance of 3.1 σ for B + → K + `+ `− and about 2.4 σ for B 0 → K ∗ (892)0 `+ `− . The latest analysis
in Ref. [200] identified previously missed hadronic misidentification background. With better handling of such background the results are now consistent with the SM. LHCb experiment performed
similar test with Λ0b → pK − `+ `− decays [201], B 0 → KS0 `+ `− and B + → K ∗ (892)+ `+ `− [202].
While b → d`+ `− decays are further suppressed, they recently became accessible. Signals wereobserved for B + → π + µ+ µ− [77], B 0 → π + π − µ+ µ− [203] and Λ0b → pπ − µ+ µ− [204] decays.
∗
Search for the Bs0 → K (892)0 µ+ µ− at LHCb is complicated by large background from B 0 →K ∗ (892)0 µ+ µ− and current significance for the decay is 3.4σ [205]. The total branching fractions
are only quantities measured and these are about 2 × 10−8 for the meson decays and about 7 × 10−8
for the Λ0b decay.
A closely related process is B → Xs νν. Since the neutrinos are not detected, the final state isa strange hadron system Xs plus missing energy-momentum. Depending on Xs , the SM branching
fraction is O(10−6 ). New physics effects beyond SM, e.g. those from dark sector models cangreatly enhance the yield of Xs plus missing energy. BaBar [206], Belle [207], and Belle II [208]have searched for these decays and determined the upper limits in the range O(10−5 ).
0 → e+ e− and µ+ µ− are interesting since they only proceed at second
Finally the decays B(s)order in weak interactions in the SM, but may have large contributions from supersymmetricloops, proportional to (tan β)6 . First limits were published more than 30 years ago and since thenexperiments at Tevatron, B-factories and LHC gradually improved those and effectively excluded
whole models of new physics and significantly constrained allowed parameter space of others. For
the decays to µ+ µ− , Tevatron experiments pushed the limits down to roughly factor of 5-10 above
the SM expectation [209]. The long journey in the search for these decays culminated in 2012, when
first evidence for Bs0 → µ+ µ− decay was seen [210]. Subsequently, LHC experiments ATLAS [211],
CMS [212] and LHCb [213] observed statistically significant signal for Bs0 → µ+ µ− decay. The
average branching fraction is found to be (3.01 ± 0.435) × 10−9 . In experiments at hadron colliders
searches for B 0 → µ+ µ− decays are performed at the same time. The B(B 0 → µ+ µ− ) is extracted−9in simultaneously with B(Bs0 → µ+ µ− ) and is found to be (0.07+0.13−0.11 ) × 10 . The limits for the
+
−
−9
−9
0
e e modes are: < 9.4 × 10 and < 2.5 × 10 , respectively, for Bs and B 0 [214]. The searches
for decays to τ + τ − are more challenging with current best limits of B(B 0 → τ + τ − ) < 2.1 × 10−3
and B(Bs0 → τ + τ − ) < 6.8 × 10−3 at 95% C.L. [215]. All existing measurements of B 0 and Bs0
decays to same flavour dilepton pair is consistent with SM expectation [216]. With Bs0 → µ+ µ−
decay observed, it was suggested that the effective lifetime is useful further test of the decay [217].
Attempt was made by LHCb and CMS experiments, but its precision is not yet sufficient to provide
test of the SM [212, 213]. It will take couple of years until interesting precision is reached. The
searches were also performed for lepton flavour violating decays to two leptons with best limits ine± µ∓ channel, where limits are < 1.3 × 10−9 for B 0 and < 6.3 × 10−9 for Bs0 , at 95% confidence
level [218].
Several theory groups performed global analysis of electroweak decays concluding that significant tension between data and SM is present [219]. The tension can be relieved by new physics
beyond SM. For more detailed reviews see e.g. Ref. [220].
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73.7 Summary and Outlook
The study of B mesons continues to be one of the most productive fields in particle physics.
With the two asymmetric B-factory experiments Belle and BaBar, we now have a combined data
sample of well over 1 ab−1 . CP violation has been firmly established in many decays of B mesons.
Evidence for direct CP violation has been observed. Many rare decays resulting from hadronicb → u transitions and b → s(d) penguin decays have been observed, and the emerging patternis still full of surprises. Despite the remarkable successes of the B-factory experiments, many
fundamental questions in the flavor sector remain unanswered.
At Fermilab, CDF and D0 each has accumulated about 10 fb−1 , which is the equivalent of about
12
10 b-hadrons produced. In spite of the low trigger efficiency of hadronic experiments, a selectionof modes have been reconstructed in large quantities, giving a start to a program of studies on Bs
and b-flavored baryons, in which a first major step has been the determination of the Bs oscillation
frequency.
As Tevatron and B-factories finished their data taking few year ago, the experiments at the
LHC have become very active. LHCb has collected about 1 fb−1 at 7 TeV, 2 fb−1 at 8 TeV, andclose to 5.9 fb−1 at 13 TeV during LHC Runs 1 and 2. CMS and ATLAS have collected each about√
5 fb−1 of data at s = 7 TeV, 20 fb−1 at 8 TeV and about 150 fb−1 at 13 TeV during LHC Runs
1 and 2. The latest LHC Run 3 at 13.6 TeV started in summer 2022, with upgraded detectors.
By the time of the writing (summer 2023), LHC has delivered about 70 fb−1 to ATLAS and CMS
experiments. LHCb, which is dedicated to the studies of b- and c-hadrons, has a data sample that isfor many decays larger than the sum of all previous experiments. With it, we are entering to regimeof precision physics even for many rare decays, which allows much more detailed measurements.
The Belle II experiment at the SuperKEKB has started recording data in 2019 and has bysummer 2022 collected about 428 fb−1 of data, when their long shutdown 1 started. The aim toincrease sample to ∼ 50 ab−1 will make it possible to explore the indirect evidence of new physics
beyond the SM in the heavy-flavor particles (b, c, and τ ), in a way that is complementary to the
LHC. The LHCb Collaboration is commissioning upgrade of its detector and is planning on nominal
running from 2024. The aim of the upgrade was to increase flexibility of the trigger, which willallow about a factor of five increase in instantaneous luminosity and of about a factor of two in
efficiencies on triggering on purely hadronic decays. The plan is to integrate about 50 fb−1 of data
during LHC runs 3 and 4.
These experiments promise a rich spectrum of rare and precise measurements that have thepotential to fundamentally affecting our understanding of the SM and CP -violating phenomena.
References[1] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).
[2] S. W. Herb et al., Phys. Rev. Lett. 39, 252 (1977).
[3] B. Aubert et al. (BaBar), Phys. Rev. Lett. 87, 091801 (2001), [hep-ex/0107013].
[4] K. Abe et al. (Belle), Phys. Rev. Lett. 87, 091802 (2001), [hep-ex/0107061].
[5] Currently two different notations (φ1 , φ2 , φ3 ) and (α, β, γ) are used in the literature for CKM
unitarity angles. In this mini-review, we use the latter notation following the other minireviews in this Review. The two notations are related by φ1 = β, φ2 = α and φ3 = γ.
[6] See the “CP Violation in Meson Decays” by D. Kirkby and Y. Nir in this Review.
[7] See the “CKM Quark Mixing Matrix," by A. Cecucci, Z. Ligeti, and Y. Sakai, in this Review.
0[8] See the note on “B 0 – B mixing,” by O. Schneider in this Review.
[9] See the “Determination of |Vcb | and |Vub |,” by R. Kowalewski and T. Mannel in this Review.
13th September, 2024

15

73. Production and Decay of b-flavored Hadrons[10] F. Abe et al. (CDF), Phys. Rev. Lett. 81, 2432 (1998), [hep-ex/9805034]; F. Abe et al. (CDF),
Phys. Rev. D58, 112004 (1998), [hep-ex/9804014].
[11] A. Abulencia et al. (CDF), Phys. Rev. Lett. 96, 082002 (2006), [hep-ex/0505076].
[12] R. Aaij et al. (LHCb), JHEP 07, 123 (2020), [arXiv:2004.08163].
[13] B. Aubert et al. (BaBar), Phys. Rev. Lett. 101, 071801 (2008), [Erratum: Phys. Rev. Lett.
102, 029901 (2009)], [arXiv:0807.1086].
[14] B. Aubert et al. (BaBar), Phys. Rev. Lett. 103, 161801 (2009), [arXiv:0903.1124].
[15] G. Bonvicini et al. (CLEO), Phys. Rev. D81, 031104 (2010), [arXiv:0909.5474].
[16] R. Mizuk et al. (Belle), Phys. Rev. Lett. 109, 232002 (2012), [arXiv:1205.6351].
[17] U. Tamponi et al. (Belle), Phys. Rev. Lett. 115, 14, 142001 (2015), [arXiv:1506.08914].
[18] B. Fulsom et al. (Belle), Phys. Rev. Lett. 121, 232001 (2018), [arXiv:1807.01201].
[19] A. Bondar et al. (Belle), Phys. Rev. Lett. 108, 122001 (2012), [arXiv:1110.2251].
[20] See the note on “Naming scheme for hadrons,” by M. Roos and C.G. Wohl in this Review.
[21] R. Aaij et al. (LHCb), Phys. Rev. Lett. 118, 5, 052002 (2017), [Erratum: Phys. Rev. Lett.
119, 169901 (2017)], [arXiv:1612.05140].
[22] M. Cacciari et al., JHEP 10, 137 (2012), [arXiv:1205.6344]; B. A. Kniehl et al., Phys. Rev.
D84, 094026 (2011), [arXiv:1109.2472]; M. Cacciari, M. L. Mangano and P. Nason, Eur.
Phys. J. C75, 12, 610 (2015), [arXiv:1507.06197].
[23] B. Barish et al. (CLEO), Phys. Rev. Lett. 76, 1570 (1996).
[24] E. Guido et al. (Belle), Phys. Rev. Lett. 121, 062001 (2018), [arXiv:1803.10303]; E. Guido
et al. (Belle), Phys. Rev. D96, 052005 (2017), [arXiv:1707.04973]; A. Sokolov et al. (Belle),
Phys. Rev. D79, 051103 (2009), [arXiv:0901.1431]; B. Aubert et al. (BaBar), Phys. Rev.
D78, 112002 (2008), [arXiv:0807.2014].
[25] J. P. Alexander et al. (CLEO), Phys. Rev. Lett. 86, 2737 (2001), [hep-ex/0006002]; S. B.
Athar et al. (CLEO), Phys. Rev. D66, 052003 (2002), [hep-ex/0202033]; N. C. Hastings
et al. (Belle), Phys. Rev. D67, 052004 (2003), [hep-ex/0212033].
[26] B. Aubert et al. (BaBar), Phys. Rev. Lett. 95, 042001 (2005), [hep-ex/0504001].
[27] Y. Amhis et al. (HFLAV), Eur. Phys. J. C77, 12, 895 (2017), [arXiv:1612.07233].
[28] Y. S. Amhis et al. (HFLAV), Eur. Phys. J. C 81, 3, 226 (2021), [arXiv:1909.12524].
[29] R. Aaij et al. (LHCb) (2022), [arXiv:2204.13042].
[30] P. Abreu et al. (DELPHI), Phys. Lett. B345, 598 (1995).
[31] R. Akers et al. (OPAL), Z. Phys. C66, 19 (1995).
[32] T. A. Aaltonen et al. (CDF), Phys. Rev. D90, 1, 012013 (2014), [arXiv:1309.5961]; R. Aaij
et al. (LHCb), JHEP 04, 024 (2015), [arXiv:1502.02638].
[33] R. Aaij et al. (LHCb), Phys. Rev. Lett. 110, 15, 151803 (2013), [arXiv:1211.5994].
[34] A. M. Sirunyan et al. (CMS), Eur. Phys. J. C78, 939 (2018), [arXiv:1809.03578].
[35] G. Aad et al. (ATLAS), Phys. Rev. Lett. 113, 21, 212004 (2014), [arXiv:1407.1032].
[36] A. Sirunyan et al. (CMS), Phys. Rev. Lett. 122, 132001 (2019), [arXiv:1902.00571]; R. Aaij
et al. (LHCb), Phys. Rev. Lett. 122, 232001 (2019), [arXiv:1904.00081].
[37] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 99, 202001 (2007), [arXiv:0706.3868]; T. Aaltonen
et al. (CDF), Phys. Rev. D85, 092011 (2012), [arXiv:1112.2808].
[38] R. Aaij et al. (LHCb), Phys. Rev. Lett. 122, 012001 (2019), [arXiv:1809.07752].
13th September, 2024

16

73. Production and Decay of b-flavored Hadrons[39] V. M. Abazov et al. (D0), Phys. Rev. Lett. 99, 052001 (2007), [arXiv:0706.1690]; T. Aaltonen
et al. (CDF), Phys. Rev. Lett. 99, 052002 (2007), [arXiv:0707.0589].
[40] R. Aaij et al. (LHCb), Phys. Rev. Lett. 113, 032001 (2014), [arXiv:1405.7223]; R. Aaij et al.
(LHCb), Phys. Lett. B736, 154 (2014), [arXiv:1405.1543]; R. Aaij et al. (LHCb), Phys. Rev.
D89, 3, 032001 (2014), [arXiv:1311.4823]; R. Aaij et al. (LHCb), Phys. Rev. Lett. 113, 24,242002 (2014), [arXiv:1409.8568]; R. Aaij et al. (LHCb), Phys. Rev. Lett. 115, 24, 241801(2015), [arXiv:1510.03829]; R. Aaij et al. (LHCb), Phys. Rev. Lett. 118, 7, 071801 (2017),[arXiv:1612.02244]; R. Aaij et al. (LHCb), Phys. Lett. B722, 265 (2017), [arXiv:1701.05274];
R. Aaij et al. (LHCb), JHEP 02, 98 (2018), [arXiv:1711.05490]; R. Aaij et al. (LHCb), Phys.
Rev. D99, 052006 (2019), [arXiv:1901.07075]; R. Aaij et al. (LHCb), Phys. Rev. Lett. 124,
11, 111802 (2020), [arXiv:1912.02110].
[41] R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 103, 012004 (2021), [arXiv:2010.14485],
URL https://link.aps.org/doi/10.1103/PhysRevD.103.012004.
[42] R. Aaij et al. (LHCb), Phys. Rev. D104, 052010 (2021), [arXiv:2104.15074].
[43] T. A. Aaltonen et al. (CDF), Phys. Rev. D89, 7, 072014 (2014), [arXiv:1403.8126].
[44] R. Aaij et al. (LHCb), JHEP 08, 039 (2018), [arXiv:1805.03941]; R. Aaij et al. (LHCb), Eur.
Phys. J. C 79, 9, 745 (2019), [arXiv:1903.06792]; R. Aaij et al. (LHCb), Eur. Phys. J. C79,
9, 745 (2019), [arXiv:1903.06792].
[45] S. Chatrchyan et al. (CMS), Phys. Rev. Lett. 108, 252002 (2012), [arXiv:1204.5955]; R. Aaij
et al. (LHCb), JHEP 1605, 161 (2016), [arXiv:1604.03896].
[46] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 131, 171901 (2023), [arXiv:2307.13399],
URL https://link.aps.org/doi/10.1103/PhysRevLett.131.171901.
[47] R. Aaij et al. (LHCb), Phys. Rev. Lett. 114, 062004 (2015), [arXiv:1411.4849].
[48] A. M. Sirunyan et al. (CMS Collaboration), Phys. Rev. Lett. 126, 252003 (2021),[arXiv:2102.04524], URL https://link.aps.org/doi/10.1103/PhysRevLett.126.252003.
[49] R. Aaij et al. (LHCb), Phys. Rev. Lett. 121, 072002 (2018), [arXiv:1805.09418].
[50] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 128, 162001 (2022), [arXiv:2110.04497],
URL https://link.aps.org/doi/10.1103/PhysRevLett.128.162001.
[51] V. M. Abazov et al. (D0), Phys. Rev. Lett. 101, 232002 (2008), [arXiv:0808.4142]; T. Aaltonen
et al. (CDF), Phys. Rev. D80, 072003 (2009), [arXiv:0905.3123].
[52] R. Aaij et al. (LHCb), Phys. Rev. Lett. 110, 18, 182001 (2013), [arXiv:1302.1072]; R. Aaij
et al. (LHCb), Phys. Lett. B736, 154 (2014), [arXiv:1405.1543]; R. Aaij et al. (LHCb), Phys.
Rev. D93, 9, 092007 (2016), [arXiv:1604.01412]; R. Aaij et al. (LHCb), Phys. Rev. D104,
L091102 (2021), [arXiv:2107.03419].
[53] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 124, 082002 (2020), [arXiv:2001.00851],
URL https://link.aps.org/doi/10.1103/PhysRevLett.124.082002.
[54] V. M. Abazov et al. (D0), Phys. Rev. Lett. 117, 2, 022003 (2016), [arXiv:1602.07588]; V. M.
Abazov et al. (D0), Phys. Rev. D97, 092004 (2018), [arXiv:1712.10176].
[55] R. Aaij et al. (LHCb), Phys. Rev. Lett. 117, 15, 152003 (2016), [Addendum: Phys. Rev.
Lett.118,no.10,109904(2017)], [arXiv:1608.00435].
[56] A. Sirunyan et al. (CMS), Phys. Rev. Lett. 120, 202005 (2018), [arXiv:1712.06144].
[57] C. Tarantino, Eur. Phys. J. C33, S895 (2004), [hep-ph/0310241]; F. Gabbiani, A. I. Onishchenko and A. A. Petrov, Phys. Rev. D70, 094031 (2004), [hep-ph/0407004]; F. Gabbiani,
A. I. Onishchenko and A. A. Petrov, Phys. Rev. D68, 114006 (2003), [hep-ph/0303235].
13th September, 2024

17

73. Production and Decay of b-flavored Hadrons[58] A. Lenz, Int. J. Mod. Phys. A30, 10, 1543005 (2015), [arXiv:1405.3601].
[59] Y. S. Amhis et al. (Heavy Flavor Averaging Group, HFLAV), Phys. Rev. D 107, 5, 052008(2023), [arXiv:2206.07501].
[60] C.-H. Chang et al., Phys. Rev. D64, 014003 (2001), [hep-ph/0007162]; V. V. Kiselev, A. E.
Kovalsky and A. K. Likhoded, Nucl. Phys. B585, 353 (2000), [hep-ph/0002127]; A. Yu.
Anisimov et al., Phys. Lett. B452, 129 (1999), [hep-ph/9812514]; M. Beneke and G. Buchalla,
Phys. Rev. D53, 4991 (1996), [hep-ph/9601249].
[61] R. Aaij et al. (LHCb), Eur. Phys. J. C74, 5, 2839 (2014), [arXiv:1401.6932].
[62] R. Aaij et al. (LHCb), Phys. Lett. B742, 29 (2015), [arXiv:1411.6899].
[63] The Bc is a special case, where a weak decay of the c quark is also possible, but the spectatormodel still applies.
[64] R. Aaij et al. (LHCb), Nature Phys. 11, 743 (2015), [arXiv:1504.01568].
[65] J. P. Lees et al. (BaBar), Phys. Rev. D85, 011101 (2012), [arXiv:1110.5600]; C. Oswald
et al. (Belle), Phys. Rev. D87, 7, 072008 (2013), [Erratum: Phys. Rev. D90, 119901(2014)], [arXiv:1212.6400]; C. Oswald et al. (Belle), Phys. Rev. D92, 7, 072013 (2015),[arXiv:1504.02004].
[66] T. A. Aaltonen et al. (CDF), Phys. Rev. D93, 5, 052001 (2016), [arXiv:1601.03819].
[67] R. Aaij et al. (LHCb), Phys. Rev. Lett. 126, 8, 081804 (2021), [arXiv:2012.05143].
[68] B. Grinstein, Nucl. Phys. B339, 253 (1990); H. Georgi, Phys. Lett. B240, 447 (1990); A. F.
Falk et al., Nucl. Phys. B343, 1 (1990); E. Eichten and B. R. Hill, Phys. Lett. B234, 511(1990).
[69] “Heavy-Quark and Soft-Collinear Effective Theory" by C.W. Bauer and M. Neubert in thisReview.
[70] M.
Neubert,“Aspects
of
QCD
Factorization,”
hep-ph/0110093, Proceedings of HF9, Pasadena (2001) and references therein; Z. Ligeti, M. E. Lukeand M. B. Wise, Phys. Lett. B507, 142 (2001), [hep-ph/0103020].
[71] M. Beneke et al., Phys. Rev. Lett. 83, 1914 (1999), [hep-ph/9905312]; M. Beneke et al.,Nucl. Phys. B591, 313 (2000), [hep-ph/0006124]; M. Beneke et al., Nucl. Phys. B606, 245(2001), [hep-ph/0104110]; M. Beneke and M. Neubert, Nucl. Phys. B675, 333 (2003), [hepph/0308039].
[72] Y.-Y. Keum, H.-n. Li and A. I. Sanda, Phys. Lett. B504, 6 (2001), [hep-ph/0004004]; Y. Y.
Keum, H.-N. Li and A. I. Sanda, Phys. Rev. D63, 054008 (2001), [hep-ph/0004173]; Y.-Y.
Keum and H.-n. Li, Phys. Rev. D63, 074006 (2001), [hep-ph/0006001]; C.-D. Lu, K. Ukai and
M.-Z. Yang, Phys. Rev. D63, 074009 (2001), [hep-ph/0004213]; C.-D. Lu and M.-Z. Yang,
Eur. Phys. J. C23, 275 (2002), [hep-ph/0011238].
[73] C. W. Bauer, S. Fleming and M. E. Luke, Phys. Rev. D63, 014006 (2000), [hep-ph/0005275];
C. W. Bauer et al., Phys. Rev. D63, 114020 (2001), [hep-ph/0011336]; C. W. Bauer and
I. W. Stewart, Phys. Lett. B516, 134 (2001), [hep-ph/0107001].
[74] R. Ammar et al. (CLEO), Phys. Rev. Lett. 71, 674 (1993).
[75] N. Taniguchi et al. (Belle), Phys. Rev. Lett. 101, 111801 (2008), [Erratum: Phys. Rev. Lett.
101, 129904 (2008)], [arXiv:0804.4770].
[76] B. Aubert et al. (BaBar), Phys. Rev. D78, 112001 (2008), [arXiv:0808.1379].
[77] R. Aaij et al. (LHCb), JHEP 10, 034 (2015), [arXiv:1509.00414].
13th September, 2024

18

73. Production and Decay of b-flavored Hadrons[78] P. Krokovny et al. (Belle), Phys. Rev. Lett. 89, 231804 (2002), [hep-ex/0207077]; B. Aubert
et al. (BaBar), Phys. Rev. Lett. 98, 081801 (2007), [hep-ex/0604012].
[79] B. Kronenbitter et al. (Belle), Phys. Rev. D92, 5, 051102 (2015), [arXiv:1503.05613]; I. Adachi
et al. (Belle), Phys. Rev. Lett. 110, 13, 131801 (2013), [arXiv:1208.4678].
[80] J. P. Lees et al. (BaBar), Phys. Rev. D88, 3, 031102 (2013), [arXiv:1207.0698]; B. Aubert
et al. (BaBar), Phys. Rev. D81, 051101 (2010), [arXiv:0912.2453].
[81] See the “Leptonic decays of charged pseudoscalar mesons,” by R. Briere, J. Rosner, S. Stone,
and R. Van de Water, in this Review.
[82] J. P. Lees et al. (BaBar), Phys. Rev. D84, 112007 (2011), [Erratum: Phys. Rev. D87, 039901(2013)], [arXiv:1107.5751]; S. Blyth et al. (Belle), Phys. Rev. D74, 092002 (2006), [hepex/0607029].
[83] R. Aaij et al. (LHCb), Phys. Rev. D 92, 3, 032002 (2015), [arXiv:1505.01710].
[84] B. Aubert et al. (BaBar), Phys. Rev. Lett. 90, 242001 (2003), [hep-ex/0304021].
[85] D. Besson et al. (CLEO), Phys. Rev. D68,
Rev.D75,119908(2007)], [hep-ex/0305100].

032002 (2003),[Erratum:Phys.

[86] P. Krokovny et al. (Belle), Phys. Rev. Lett. 91, 262002 (2003), [hep-ex/0308019]; Y. Mikami
et al. (Belle), Phys. Rev. Lett. 92, 012002 (2004), [hep-ex/0307052].
[87] B. Aubert et al. (BaBar), Phys. Rev. Lett. 93, 181801 (2004), [hep-ex/0408041].
[88] R. Aaij et al. (LHCb), Phys. Rev. Lett. 113, 162001 (2014), [arXiv:1407.7574].
[89] R. Aaij et al. (LHCb), JHEP 12, 141 (2021), [arXiv:2110.02350]; F. Abudinén et al. (Belle,
Belle-II), JHEP 02, 063 (2022), [Erratum: JHEP 12, 034 (2022)], [arXiv:2110.12125].
[90] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 108, 201801 (2012), [arXiv:1204.0536].
[91] S. Esen et al. (Belle), Phys. Rev. D87, 3, 031101 (2013), [arXiv:1208.0323].
[92] R. Aaij et al. (LHCb), Phys. Rev. D93, 9, 092008 (2016), [arXiv:1602.07543].
[93] R. Aaij et al. (LHCb), Phys. Rev. Lett. 116, 16, 161802 (2016), [arXiv:1603.02408].
[94] R. Aaij et al. (LHCb), JHEP 11, 082 (2015), [arXiv:1509.00400].
[95] B. Aubert et al. (BaBar), Phys. Rev. D76, 031101 (2007), [arXiv:0704.1266].
[96] R. Aaij et al. (LHCb), Phys. Rev. D90, 1, 012003 (2014), [arXiv:1404.5673].
[97] R. Aaij et al. (LHCb), Phys. Rev. Lett. 111, 18, 181801 (2013), [arXiv:1308.4544].
[98] R. Aaij et al. (LHCb), JHEP 07, 066 (2023), [arXiv:2210.12000].
[99] R. Aaij et al. (LHCb), Phys. Rev. D87, 11, 112012 (2013), [Addendum: Phys. Rev. D89,019901 (2014)], [arXiv:1304.4530].
[100] G. Aad et al. (ATLAS), Eur. Phys. J. C76, 1, 4 (2016), [arXiv:1507.07099]; G. Aad et al.
(ATLAS), JHEP 08, 087 (2022), [arXiv:2203.01808].
[101] R. Aaij et al. (LHCb), Phys. Rev. D84, 092001 (2011), [Erratum:
Phys.
Rev.D85,039904(2012)], [arXiv:1109.6831]; T. Aaltonen et al. (CDF), Phys. Rev. D85, 032003(2012), [arXiv:1112.3334].
[102] S. K. Choi et al. (Belle), Phys. Rev. Lett. 91, 262001 (2003), [hep-ex/0309032].
[103] D. Acosta et al. (CDF), Phys. Rev. Lett. 93, 072001 (2004), [hep-ex/0312021].
[104] V. M. Abazov et al. (D0), Phys. Rev. Lett. 93, 162002 (2004), [hep-ex/0405004].
[105] B. Aubert et al. (BaBar), Phys. Rev. D71, 071103 (2005), [hep-ex/0406022].
[106] R. Aaij et al. (LHCb), Eur. Phys. J. C72, 1972 (2012), [arXiv:1112.5310].
13th September, 2024

19

73. Production and Decay of b-flavored Hadrons[107] S. Chatrchyan et al. (CMS), JHEP 04, 154 (2013), [arXiv:1302.3968].
[108] M. Aaboud et al. (ATLAS), JHEP 01, 117 (2017), [arXiv:1610.09303].
[109] S. K. Choi et al. (Belle), Phys. Rev. Lett. 100, 142001 (2008), [arXiv:0708.1790]; R. Mizuket al. (Belle), Phys. Rev. D80, 031104 (2009), [arXiv:0905.2869].
[110] R. Aaij et al. (LHCb), Phys. Rev. Lett. 112, 22, 222002 (2014), [arXiv:1404.1903]; R. Aaij
et al. (LHCb), Phys. Rev. D92, 11, 112009 (2015), [arXiv:1510.01951].
[111] K. Chilikin et al. (Belle), Phys. Rev. D90, 11, 112009 (2014), [arXiv:1408.6457].
[112] R. Aaij et al. (LHCb), Phys. Rev. Lett. 115, 072001 (2015), [arXiv:1507.03414].
[113] R. Aaij et al. (LHCb), Phys. Rev. Lett. 122, 22, 222001 (2019), [arXiv:1904.03947].
[114] R. Aaij et al. (LHCb), Phys. Rev. Lett. 128, 6, 062001 (2022), [arXiv:2108.04720].
[115] R. Aaij et al. (LHCb), Phys. Rev. Lett. 131, 3, 031901 (2023), [arXiv:2210.10346]; R. Aaij
et al. (LHCb), Sci. Bull. 66, 1278 (2021), [arXiv:2012.10380].
[116] See the “Non-q q̄ mesons,” by C. Amsler and C. Hanhart, and “Pentaquarks,” by M. Karliner
and T. Skwarnicki, in this Review.
[117] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 107, 261802 (2011), [arXiv:1107.4999]; R. Aaij
et al. (LHCb), JHEP 10, 053 (2015), [arXiv:1508.00788].
[118] T. A. Aaltonen et al. (CDF), Phys. Rev. Lett. 113, 24, 242001 (2014), [arXiv:1403.5586].
[119] R. Aaij et al. (LHCb), JHEP 10, 037 (2012), [arXiv:1206.2794].
[120] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 103, 031801 (2009), [arXiv:0812.4271].
[121] R. Aaij et al. (LHCb), Phys. Rev. D 98, 3, 032004 (2018), [arXiv:1805.06759]; R. Aaij
et al. (LHCb), JHEP 12, 155 (2019), [arXiv:1907.10003]; R. Aaij et al. (LHCb) (2023),[arXiv:2304.06198].
[122] R. Fleischer, Phys. Lett. B459, 306 (1999), [hep-ph/9903456]; D. London and J. Matias,
Phys. Rev. D70, 031502 (2004), [hep-ph/0404009].
[123] J. P. Lees et al. (BaBar), Phys. Rev. D87, 5, 052009 (2013), [arXiv:1206.3525].
[124] Y. T. Duh et al. (Belle), Phys. Rev. D87, 3, 031103 (2013), [arXiv:1210.1348].
[125] R. Aaij et al. (LHCb), JHEP 03, 075 (2021), [arXiv:2012.05319].
[126] B. Aubert et al. (BaBar), Phys. Rev. D76, 091102 (2007), [arXiv:0707.2798].
[127] R. Aaij et al. (LHCb), Phys. Lett. B 726, 646 (2013), [arXiv:1308.1277]; R. Aaij et al. (LHCb),
Phys. Rev. Lett. 126, 9, 091802 (2021), [arXiv:2012.12789].
[128] M. Gronau and J. L. Rosner, Phys. Rev. D71, 074019 (2005), [hep-ph/0503131]; M. Gronau,
Phys. Lett. B627, 82 (2005), [hep-ph/0508047].
[129] B. Aubert et al. (BaBar), Phys. Rev. D 79, 052003 (2009), [arXiv:0809.1174].
[130] M. Fujikawa et al. (Belle), Phys. Rev. D 81, 011101 (2010), [arXiv:0809.4366].
[131] B. Aubert et al. (BaBar), Phys. Rev. D78, 012004 (2008), [arXiv:0803.4451]; A. Garmash
et al. (Belle), Phys. Rev. Lett. 96, 251803 (2006), [hep-ex/0512066].
[132] C. T. Hoi et al. (Belle), Phys. Rev. Lett. 108, 031801 (2012), [arXiv:1110.2000]; B. Aubert
et al. (BaBar), Phys. Rev. D80, 112002 (2009), [arXiv:0907.1743].
[133] B. Aubert et al. (BaBar), Phys. Rev. Lett. 97, 201802 (2006), [hep-ex/0608005]; C. H. Wanget al. (Belle), Phys. Rev. D75, 092005 (2007), [hep-ex/0701057].
[134] R. Aaij et al. (LHCb), Phys. Rev. D90, 11, 112004 (2014), [arXiv:1408.5373]; C.-L. Hsu et al.
(Belle), Phys. Rev. D 96, 3, 031101 (2017), [arXiv:1705.02640].
13th September, 2024

20

73. Production and Decay of b-flavored Hadrons[135] B. Aubert et al. (BaBar), Phys. Rev. Lett. 97, 171805 (2006), [hep-ex/0608036].
[136] K. Abe et al. (Belle), Phys. Rev. Lett. 98, 181804 (2007), [hep-ex/0608049].
[137] R. Aaij et al. (LHCb), Phys. Rev. Lett. 118, 8, 081801 (2017), [arXiv:1610.08288].
[138] C. C. Peng et al. (Belle), Phys. Rev. D82, 072007 (2010), [arXiv:1006.5115].
[139] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 106, 181802 (2011), [arXiv:1103.5762].
[140] B. Pal et al. (Belle), Phys. Rev. Lett. 116, 16, 161801 (2016), [arXiv:1512.02145].
[141] R. Aaij et al. (LHCb), Phys. Rev. D 102, 1, 012011 (2020), [arXiv:2002.08229].
[142] See the “Determination of CKM angles from B hadrons,” by T. Gershon, M. Kenzie, and K.
Trabelsi, in this Review.
[143] M. Gronau and D. London, Phys. Rev. Lett. 65, 3381 (1990).
[144] T. Julius et al. (Belle), Phys. Rev. D96, 3, 032007 (2017), [arXiv:1705.02083].
[145] B. Aubert et al. (BaBar), Phys. Rev. D78, 071104 (2008), [arXiv:0807.4977].
[146] P. Vanhoefer et al. (Belle), Phys. Rev. D89, 072008 (2014), [Addendum: Phys. Rev. D89
119903 (2014)], [arXiv:1212.4015].
[147] B. Aubert et al. (BaBar), Phys. Rev. D76, 052007 (2007), [arXiv:0705.2157]; P. Vanhoefer
et al. (Belle), Phys. Rev. D 93, 3, 032010 (2016), [Addendum: Phys.Rev.D 94, 099903 (2016)],[arXiv:1510.01245].
[148] B. Aubert et al. (BaBar), Phys. Rev. Lett. 102, 141802 (2009), [arXiv:0901.3522]; J. Zhang
et al. (Belle), Phys. Rev. Lett. 91, 221801 (2003), [hep-ex/0306007].
[149] R. Aaij et al. (LHCb), Phys. Lett. B747, 468 (2015), [arXiv:1503.07770].
[150] See the “Polarization in B Decays,” by A. Gritsan in this Review.
[151] T. E. Coan et al. (CLEO), Phys. Rev. Lett. 84, 5283 (2000), [hep-ex/9912057].
[152] B. Aubert et al. (BaBar), Phys. Rev. Lett. 103, 211802 (2009), [arXiv:0906.2177];
T. Horiguchi et al. (Belle), Phys. Rev. Lett. 119, 19, 191802 (2017), [arXiv:1707.00394].
[153] B. Aubert et al. (BaBar), Phys. Rev. D70, 091105 (2004), [hep-ex/0409035]; S. Nishida et al.
(Belle), Phys. Lett. B610, 23 (2005), [hep-ex/0411065]; B. Aubert et al. (BaBar), Phys. Rev.
D74, 031102 (2006), [hep-ex/0603054].
[154] H. Yang et al. (Belle), Phys. Rev. Lett. 94, 111802 (2005), [hep-ex/0412039].
[155] B. Aubert et al. (BaBar), Phys. Rev. Lett. 98, 211804 (2007), [Erratum: Phys. Rev.
Lett.100,199905(2008)], [hep-ex/0507031]; P. del Amo Sanchez et al. (BaBar), Phys. Rev.
D93, 5, 052013 (2016), [arXiv:1512.03579].
[156] R. Aaij et al. (LHCb), Phys. Rev. Lett. 112, 16, 161801 (2014), [arXiv:1402.6852].
[157] J. Wicht et al. (Belle), Phys. Rev. Lett. 100, 121801 (2008), [arXiv:0712.2659]; D. Dutta
et al. (Belle), Phys. Rev. D91, 1, 011101 (2015), [arXiv:1411.7771]; R. Aaij et al. (LHCb),
Nucl. Phys. B867, 1 (2013), [arXiv:1209.0313].
[158] R. Aaij et al. (LHCb), Phys. Rev. Lett. 123, 3, 031801 (2019), [arXiv:1904.06697].
[159] A. Ali, E. Lunghi and A. Ya. Parkhomenko, Phys. Lett. B595, 323 (2004), [hep-ph/0405075];
P. Ball, G. W. Jones and R. Zwicky, Phys. Rev. D75, 054004 (2007), [hep-ph/0612081].
[160] J. L. Hewett, Phys. Rev. Lett. 70, 1045 (1993), [hep-ph/9211256].
[161] S. Chen et al. (CLEO), Phys. Rev. Lett. 87, 251807 (2001), [hep-ex/0108032]; J. P. Lees et al.
(BaBar), Phys. Rev. D86, 112008 (2012), [arXiv:1207.5772].
13th September, 2024

21

73. Production and Decay of b-flavored Hadrons[162] A. Limosani et al. (Belle), Phys. Rev. Lett. 103, 241801 (2009), [arXiv:0907.1384]; T. Saito
et al. (Belle), Phys. Rev. D91, 5, 052004 (2015), [arXiv:1411.7198].
[163] P. del Amo Sanchez et al. (BaBar), Phys. Rev. D82, 051101 (2010), [arXiv:1005.4087].
[164] M. Misiak et al., Phys. Rev. Lett. 114, 22, 221801 (2015), [arXiv:1503.01789]; M. Czakon
et al., JHEP 04, 168 (2015), [arXiv:1503.01791]; R. Bause et al., Eur. Phys. J. C 83, 5, 419(2023), [arXiv:2209.04457].
[165] L. Wolfenstein and Y. L. Wu, Phys. Rev. Lett. 73, 2809 (1994), [hep-ph/9410253]; G. M.
Asatrian and A. Ioannisian, Phys. Rev. D54, 5642 (1996), [hep-ph/9603318]; M. Ciuchini, E. Gabrielli and G. F. Giudice, Phys. Lett. B388, 353 (1996), [Erratum: Phys.
Lett.B393,489(1997)], [hep-ph/9604438]; S. Baek and P. Ko, Phys. Rev. Lett. 83, 488 (1999),[hep-ph/9812229]; A. L. Kagan and M. Neubert, Phys. Rev. D58, 094012 (1998), [hepph/9803368]; K. Kiers, A. Soni and G.-H. Wu, Phys. Rev. D62, 116004 (2000), [hepph/0006280].
[166] S. Watanuki et al. (Belle), Phys. Rev. D 99, 3, 032012 (2019), [arXiv:1807.04236].
[167] J. P. Lees et al. (BaBar), Phys. Rev. D90, 9, 092001 (2014), [arXiv:1406.0534].
[168] B. Aubert et al. (BaBar), Phys. Rev. D72, 052004 (2005), [hep-ex/0508004].
[169] B. Aubert et al. (BaBar), Phys. Rev. D77, 051103 (2008), [arXiv:0711.4889].
[170] J. P. Lees et al. (BaBar), Phys. Rev. Lett. 109, 191801 (2012), [arXiv:1207.2690].
[171] See the “Semileptonic b-Hadron Decays, Determination of Vcb , Vub ,” by T. Mannel and P.
Urquijo in this Review.
[172] M. Iwasaki et al. (Belle), Phys. Rev. D72, 092005 (2005), [hep-ex/0503044]; J. P. Lees et al.
(BaBar), Phys. Rev. Lett. 112, 211802 (2014), [arXiv:1312.5364].
[173] Y. Sato et al. (Belle), Phys. Rev. D93, 3, 032008 (2016), [Addendum:
Rev.D93,no.5,059901(2016)], [arXiv:1402.7134].

Phys.

[174] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 107, 201802 (2011), [arXiv:1107.3753].
[175] R. Aaij et al. (LHCb), JHEP 07, 084 (2013), [arXiv:1305.2168]; R. Aaij et al. (LHCb), JHEP
09, 179 (2015), [arXiv:1506.08777].
[176] R. Aaij et al. (LHCb), Phys. Lett. B725, 25 (2013), [arXiv:1306.2577].
[177] R. Aaij et al. (LHCb), JHEP 06, 108 (2017), [arXiv:1703.00256].
[178] B. Aubert et al. (BaBar), Phys. Rev. Lett. 102, 091803 (2009), [arXiv:0807.4119].
[179] S. Choudhury et al. (BELLE), JHEP 03, 105 (2021), [arXiv:1908.01848].
[180] R. Aaij et al. (LHCb), JHEP 06, 133 (2014), [arXiv:1403.8044].
[181] J. T. Wei et al. (Belle), Phys. Rev. Lett. 103, 171801 (2009), [arXiv:0904.0770].
[182] R. Aaij et al. (LHCb), JHEP 11, 047 (2016), [Erratum:[arXiv:1606.04731].

JHEP 04, 142 (2017)],[183] R. Aaij et al. (LHCb), Phys. Rev. Lett. 127, 15, 151801 (2021), [arXiv:2105.14007].
[184] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 108, 081807 (2012), [arXiv:1108.0695].
[185] R. Aaij et al. (LHCb), JHEP 05, 082 (2014), [arXiv:1403.8045].
[186] A. M. Sirunyan et al. (CMS), Phys. Lett. B 781, 517 (2018), [arXiv:1710.02846].
[187] R. Aaij et al. (LHCb), Phys. Rev. Lett. 125, 1, 011802 (2020), [arXiv:2003.04831].
[188] S. Wehle et al. (Belle), Phys. Rev. Lett. 118, 11, 111801 (2017), [arXiv:1612.05014].
[189] M. Aaboud et al. (ATLAS), JHEP 10, 047 (2018), [arXiv:1805.04000].
13th September, 2024

22

73. Production and Decay of b-flavored Hadrons[190] R. Aaij et al. (LHCb), Phys. Rev. Lett. 126, 16, 161802 (2021), [arXiv:2012.13241].
[191] R. Aaij et al. (LHCb), JHEP 11, 043 (2021), [arXiv:2107.13428].
[192] R. Aaij et al. (LHCb), JHEP 09, 146 (2018), [arXiv:1808.00264].
[193] S. Descotes-Genon et al., JHEP 01, 048 (2013), [arXiv:1207.2753].
[194] J. P. Lees et al. (BaBar), Phys. Rev. D86, 032012 (2012), [arXiv:1204.3933].
[195] R. Aaij et al. (LHCb), JHEP 09, 177 (2014), [arXiv:1408.0978].
[196] J. Lyon and R. Zwicky, Phys. Rev. D88, 9, 094004 (2013), [arXiv:1305.4797].
[197] R. Aaij et al. (LHCb), Eur. Phys. J. C77, 3, 161 (2017), [arXiv:1612.06764].
[198] R. Aaij et al. (LHCb), JHEP 12, 081 (2020), [arXiv:2010.06011].
[199] R. Aaij et al. (LHCb), Phys. Rev. Lett. 122, 19, 191801 (2019), [arXiv:1903.09252]; R. Aaij
et al. (LHCb), JHEP 08, 055 (2017), [arXiv:1705.05802]; R. Aaij et al. (LHCb), Nature Phys.
18, 3, 277 (2022), [arXiv:2103.11769]; A. Abdesselam et al. (Belle), Phys. Rev. Lett. 126, 16,161801 (2021), [arXiv:1904.02440].
[200] R. Aaij et al. (LHCb), Phys. Rev. Lett. 131, 5, 051803 (2023), [arXiv:2212.09152].
[201] R. Aaij et al. (LHCb), JHEP 05, 040 (2020), [arXiv:1912.08139].
[202] R. Aaij et al. (LHCb), Phys. Rev. Lett. 128, 19, 191802 (2022), [arXiv:2110.09501].
[203] R. Aaij et al. (LHCb), Phys. Lett. B743, 46 (2015), [arXiv:1412.6433].
[204] R. Aaij et al. (LHCb), JHEP 04, 029 (2017), [arXiv:1701.08705].
[205] R. Aaij et al. (LHCb), JHEP 07, 020 (2018), [arXiv:1804.07167].
[206] J. P. Lees et al. (BaBar), Phys. Rev. D 87, 11, 112005 (2013), [arXiv:1303.7465].
[207] J. Grygier et al. (Belle), Phys. Rev. D 96, 9, 091101 (2017), [Addendum: Phys. Rev. D97,
099902 (2018)], [arXiv:1702.03224].
[208] F. Abudinén et al. (Belle-II), Phys. Rev. Lett. 127, 18, 181802 (2021), [arXiv:2104.12624].
[209] T. Aaltonen et al. (CDF), Phys. Rev. Lett. 107, 191801 (2011), [Addendum: Phys. Rev. Lett.
107, 239903 (2011)], [arXiv:1107.2304]; V. M. Abazov et al. (D0), Phys. Rev. D87, 7, 072006(2013), [arXiv:1301.4507].
[210] R. Aaij et al. (LHCb), Phys. Rev. Lett. 110, 2, 021801 (2013), [arXiv:1211.2674].
[211] M. Aaboud et al. (ATLAS), JHEP 04, 098 (2019), [arXiv:1812.03017].
[212] A. M. Sirunyan et al. (CMS), JHEP 04, 188 (2020), [arXiv:1910.12127].
[213] R. Aaij et al. (LHCb), Phys. Rev. Lett. 118, 19, 191801 (2017), [arXiv:1703.05747]; R. Aaij
et al. (LHCb), Phys. Rev. Lett. 128, 4, 041801 (2022), [arXiv:2108.09284].
[214] R. Aaij et al. (LHCb), Phys. Rev. Lett. 124, 21, 211802 (2020), [arXiv:2003.03999].
[215] R. Aaij et al. (LHCb), Phys. Rev. Lett. 118, 25, 251802 (2017), [arXiv:1703.02508].
[216] C. Bobeth et al., Phys. Rev. Lett. 112, 101801 (2014), [arXiv:1311.0903].
[217] K. De Bruyn et al., Phys. Rev. Lett. 109, 041801 (2012), [arXiv:1204.1737]; A. J. Buras et al.,JHEP 07, 77 (2013), [arXiv:1303.3820].
[218] R. Aaij et al. (LHCb), JHEP 03, 078 (2018), [arXiv:1710.04111].
[219] J. Aebischer et al., Eur. Phys. J. C 80, 3, 252 (2020), [arXiv:1903.10434]; F. Beaujean,
C. Bobeth and D. van Dyk, Eur. Phys. J. C74, 2897 (2014), [Erratum: Eur. Phys. J. C74,3179 (2014)], [arXiv:1310.2478]; M. Algueró et al., JHEP 07, 096 (2019), [arXiv:1902.04900];
M. Algueró et al., Eur. Phys. J. C 79, 8, 714 (2019), [Addendum: Eur.Phys.J.C 80,
13th September, 2024

23

73. Production and Decay of b-flavored Hadrons
511 (2020)], [arXiv:1903.09578]; M. Algueró et al., Eur. Phys. J. C 82, 4, 326 (2022),[arXiv:2104.08921]; A. Arbey et al., Phys. Rev. D 100, 1, 015045 (2019), [arXiv:1904.08399];
W. Altmannshofer and P. Stangl, Eur. Phys. J. C 81, 10, 952 (2021), [arXiv:2103.13370];
T. Hurth et al., Phys. Lett. B 824, 136838 (2022), [arXiv:2104.10058].

[220] T. Blake, G. Lanfranchi and D. M. Straub, Prog. Part. Nucl. Phys. 92, 50 (2017),[arXiv:1606.00916]; J. Albrecht, S. Reichert and D. van Dyk, Int. J. Mod. Phys. A 33, 1830016(2018), [arXiv:1806.05010]; J. Albrecht, D. van Dyk and C. Langenbruch, Prog. Part. Nucl.
Phys. 120, 103885 (2021), [arXiv:2107.04822].

13th September, 2024