Charming new physics in rare B-decays and mixing?

1.1 MB·

by  Sebastian Jäger

IPPP/17/5
Charming new physics in rare B-decays and mixing?
Sebastian J¨ager and Kirsten Leslie
University of Sussex, Department of Physics and Astronomy, Falmer, Brighton BN1 9QH, UK∗
Matthew Kirk and Alexander Lenz
IPPP, Department of Physics, Durham University, Durham DH1 3LE, UK†
(Dated: January, 2017)
Weconductasystematicstudyoftheimpactofnewphysicsinquark-levelb→cc¯stransitionson
B-physics, in particular rare B-decays and B-meson lifetime observables. We find viable scenarios
whereasizableeffectinraresemileptonicB-decayscanbegenerated,compatiblewithexperimental
indications and with a possible dependence on the dilepton invariant mass, while being consistent
with constraints from radiative B-decay and the measured B width difference. We show how,
s
if the effect is generated at the weak scale or beyond, strong renormalisation-group effects can
7 enhance the impact on semileptonic decays while leaving radiative B-decay largely unaffected. A
1 good complementarity of the different B-physics observables implies that precise measurements of
0 lifetime observables at LHCb may be able to confirm, refine, or rule out this scenario.
2

n
a Rare B-decays are excellent probes of new physics at ate large shifts in the (low-energy) effective C9 coupling
J the electroweak scale and beyond, due to their strong from small b cc¯s couplings at a high scale without
1 suppression in the Standard Model (SM). Interestingly, conflicting wit→h the measured B¯ X γ decay rate [10].
s
3 experimentaldataonrarebranchingratios[1,2]andan- →

gular distributions for B K(∗)µ+µ− decay [2, 3] may
h] hint at a beyond-SM (BS→M) contact interaction of the CHARMING NEW PHYSICS SCENARIO
p form (s¯ γµb )(µ¯γ µ), which would destructively inter-
L L µ
-
p fere with the corresponding SM (effective) coupling C9 We consider a scenario where new physics enters
e [4], although the significance of the effect is somewhat through b cc¯s transitions. We refer to this as ‘charm-
h uncertain because of form-factor uncertainties as well as ing BSM’ →(CBSM) scenario. As long as the mass scale
[
uncertain long-distance virtual charm contributions [5]. M of new physics satisfies M mB, the modifications
(cid:29)
1 However, iftheBSMinterpretationiscorrect, itrequires to the b cc¯s transitions can be accounted for through
→
v reducing C by (20%) in magnitude. Such an effect a local effective Hamiltonian,
9
3 O
mightarisefromnewparticles(seee.g.[6]), whichmight
8 10
1 in turn be part of a more comprehensive new dynam- cc¯ = 4GFV∗V (cid:88)(CcQc+Cc(cid:48)Qc(cid:48)). (1)
9 ics. Noting that in the SM, about half of C9 comes from Heff √2 cs cb i i i i
i=1
0 (short-distance) virtual-charm contributions, in this let-
. ter we ask whether new physics affecting the quark-level Wechooseouroperatorbasisandrenormalisationscheme
1
0 b cc¯s transitions could cause the anomalies, affect- to agree with [11] upon the substitution d b, s¯ c¯,
7 ing→rare B-decays through a loop. The bulk of these ef- u¯ s¯. The first four local operators Qc rea→d →
→ i
1 fects would also be captured through an effective shift
v: ∆C9(q2), with a possible dependence on the dilepton Qc1 =(c¯iLγµbjL)(s¯jLγµciL), Qc2 =(c¯iLγµbiL)(s¯jLγµcjL),
Xi mass q2. At the same time, such a scenario offers the Qc =(c¯i bj)(s¯jci ), Qc =(c¯i bi )(s¯jcj ). (2)
exciting prospect of confirming the rare B-decay anoma- 3 R L L R 4 R L L R
r
a lies through correlated effects in hadronic B decays into The Qci(cid:48) are obtained by changing all the quark chirali-
charm, with “mixing” observables such as the B -meson ties. Weleaveadiscussionofsuch“right-handedcurrent”
s
width difference standing out as precisely measured [7] effectsforfuturework[12]anddiscardtheQc(cid:48)below. We
i
and under reasonable theoretical control. This is in con- split the Wilson coefficients into SM and BSM parts,
trast with the Z(cid:48) and leptoquark models usually con-
Cc(µ)=Cc,SM(µ)+∆C (µ), (3)
sidered, where correlated effects are typically restricted i i i
to other rare processes and are highly model-dependent.
where Cc,SM = 0 except for i = 1,2 and µ is the renor-
SpecificscenariosofhadronicnewphysicsintheBwidths i
malisation scale.
have been considered previously [8], while the possibility
of virtual charm BSM physics in rare semileptonic decay
hasbeenmentionedin[9]. Aswewillshow,viablescenar-
RARE B-DECAYS
ios exist, which can mimic a shift ∆C = (1) while
9
−O
being conistent with all other observables. In particu-
The leading-order (LO), one-loop CBSM effects in
lar, very strong renormalization-group effects can gener-
radiative and rare semileptonic decays may be ex-
2
b s b s ¯b s¯
c¯ ¯b ¯b
c¯
q γ
↓ q γ c c
µ+ µ µ+ ↓ µ s b s s
− −
FIG. 2. Leading Feynman diagrams for CBSM contribu-
FIG.1. LeadingFeynmandiagramsforCBSMcontributions tionstothewidthdifference∆Γ (left)andthelifetimeratio
s
to rare and semileptonic decays. With our choice of Fierz- τ(B )/τ(B ) (right).
s d
ordering, only the diagram on the left is relevant.
pressed through “effective” Wilson coefficient contribu-
tions∆Ceff(q2)and∆Ceff(q2)inaneffectivelocalHamil-
9 7 from a(z) and they introduce a sizable dependence on
tonian
the renormalisation scale µ and the charm quark mass.
rsl = 4GFV∗V (cid:0)Ceff(q2)Q +Ceff(q2)Q (cid:1),(4) Since a shift of ∆C7eff(q2) is strongly constrained by the
Heff − √2 ts tb 7 7γ 9 9V measured B Xsγ decay rate, we do not consider the
→
coefficients ∆C any further and focus on the four
5...10
where q2 is the dilepton mass and coefficients ∆C in the remainder, which do not con-
1...4
Q7γ = 1e6mπb2(s¯LσµνbR)Fµν, Q9V = 4απ(s¯LγµbL)((cid:96)¯γµ(cid:96)). ttrriibbuutteiontos cBan→beXismγpaotrt1a-nlotoifptohrednere.wHpihgyhseirc-sogrdenerercaotnes-
∆C attheweakscaleorbeyond,asistypicallyexpected.
i
For q2 small (in particular, well below the charm res- InthiscaselargelogarithmslnM/m occurandneedto
B
onances), ∆Ceff(q2) and ∆Ceff(q2) govern the theoreti- be resummed. We will return to this point below. For
9 7
cal predictions for both exclusive (B K(∗)(cid:96)+(cid:96)−,B ournumericalevaluation,weemploythecharmpolemass
s
→ →
φ(cid:96)+(cid:96)−, etc) and inclusive B X (cid:96)+(cid:96)− decay, up to in the h-function. Finally note that, had we chosen dif-
s
→
(α ) QCD corrections and power corrections to the ferent Fierz ordering in defining Qc, Fig. 1 (right), the
O s i
heavy-quark limit that we neglect in our leading-order constant terms in (5) and (6) would be different. This
analysis. Similarly, ∆Ceff(0) determines radiative B- implies a compensating scheme dependence in the value
7
decay rates. We will neglect the small CKM combina- C (M) in matching a given UV model to the effective
9
tion V∗V , implying V∗V = V∗V , and focus on weak hamiltonian.
us ub cs cb − ts tb
real (CP-conserving) values for the Cc. From the dia-
i
gram shown in Figure 1 (left) we then obtain
∆Ceff(q2)=(cid:18)C1 c C3c,4(cid:19)h 2Cc , 1 (5)
9 1,2− 2 − 9 3,4
∆Ceff(q2)= mc(cid:20)(cid:0)4Cc Cc (cid:1)y+4C5c,6−C7c,8(cid:21),(6)
7 m 9,10− 7,8 6
b
MIXING AND LIFETIME OBSERVABLES
with Cc =3∆Cc+∆Cc and the loop functions
x,y x y
4(cid:20) m2 2 (cid:21)
h(q2,m ,µ)= ln c +(2+z)a(z) z , (7) A distinctive feature of the CBSM scenario is that
c −9 µ2 − 3 −
nonzero ∆C affect not only radiative and rare semilep-
y(q2,mc,µ)=−13(cid:20)lnmµ22c − 32 +2a(z)(cid:21), (8) stoitnioicnsd.ecaWysih,ibleutthaelsothtreeoer-elteivceallhcaodnrtornoilcobve→r cec¯xsclutrsaivne-
b cc¯smodesisverylimitedatpresent,thedecaywidth
where a(z)=(cid:112)z 1 arctan√1 and z =4m2/q2. di→fference ∆Γ and the lifetime ratio τ(B )/τ(B ) stand
| − | z−1 c s s d
We note that only the four Wilson coefficients ∆C out as being calculable in a heavy-quark expansion [13],
1...4
enter ∆Ceff(q2). Conversely, ∆Ceff(q2) is given in terms seeFig.2. Forbothobservables,theheavy-quarkexpan-
9 7
oftheothersixWilsoncoefficients∆C . Theappear- siongivesrisetoanoperatorproductexpansioninterms
5...10
ance of a one-loop, q2-dependent contribution to Ceff is of local ∆B = 2 (for the width difference) or ∆B = 0
7
a novel feature in the CBSM scenario. Numerically, the (for the lifetime ratio) operators. The formalism is re-
loop function a(z) equals one at q2 = 0 and vanishes at viewed in elsewhere [14] and applies to both SM and
q2 = (2m )2. The constant terms and the logarithm ac- CBSM contributions. For the B width difference, we
c s
companying y(q2,m ) partially cancel the contribution have [15] ∆Γ = 2Γs,SM+Γcc¯ cosφs , where the phase
c s | 12 12| 12
3
φs is small. Neglecting the strange-quark mass, we find
12
(cid:112)
1 4x2
Γcc = G2(V∗V )2m2M f2 − c
12 − F cs cb b Bs Bs 576π ×
(cid:40)
(cid:104)
16(1 x2)(4Cc,2+Cc,2)+8(1 4x2)
− c 2 4 − c ×
(12Cc,2+8CcCc+2CcCc+3Cc,2) 192x2
1 1 2 3 4 3 − c×
(cid:105)
(3CcCc+CcCc+CcCc+CcCc) B+2(1+2x2)
1 3 1 4 2 3 2 4 c ×
(cid:41)
(4Cc,2 8CcCc 12Cc,2 3Cc,2 2CcCc+Cc,2)B˜(cid:48) , FIG.3. MixingobservablesversusraredecaysintheCBSM
2 − 1 2 − 1 − 3 − 3 4 4 S
scenario. Left: (∆C ,∆C ) plane, Right: (∆C ,∆C ) plane.
1 2 3 4
(9) In each case, all Wilson coefficients are renormalized at µ =
4.2GeVandthosenotcorrespondingtoeitheraxissettozero.
with xc =mc/mb. B, B˜S(cid:48) are defined through Themeasuredcentralvalueforthewidth difference isshown
asbrown(solid)linetogetherwiththe1σallowedregion. The
2
B (s¯ γ b )(s¯ γµb )B¯ = M2 f2 B, (10) lifetime ratio measurement is depicted as green (dashed) line
(cid:104) s| L µ L L L s(cid:105) 3 BS Bs and band. Overlaid are contours of ∆Ceff(5GeV2)=−1,−2
(cid:104)Bs|(s¯iLbjR)(s¯jLbiR)|B¯s(cid:105)= 112MB2sfB2sB˜S(cid:48), (11) (abslaccokm,pduatsehdedfr)omand(5∆).CT9effh(e2G∆eCVe2ff)==0−9c1o,n−t2ou(rreisd,shdoowttneda)s,
9
with values taken from [16]. For our numerical evalua- black solid line.
tion of Γcc, we split the Wilson coefficients according to
12
(3), subtract from the LO expression (9) the pure SM
RARE DECAYS VERSUS LIFETIMES -
contributionandaddtheNLOSMexpressionsfrom[17].
LOW-SCALE SCENARIO
In general, a modification of Γcc also affects the semi-
12
leptonic CP asymmetries. However, since we consider
We are now in a position to confront the CBSM sce-
CP-conserving new physics in this paper and since the
nario with rare decay and mixing observables, as long as
corresponding experimental uncertainties are still large,
we consider renormalization scales µ m . Then the
the semi-leptonic asymmetries will not lead to an addi- B
∼
logarithms inside the h-function entering (5) are small
tional constraint.
and our leading-order calculation should be accurate.
In a similar manner, for the the lifetime ratio we find
Such a scenario is directly applicable if the mass scale
(cid:18) (cid:19) (cid:18) (cid:19)
τ τ τ
Bs = Bs + Bs , (12) M ofthephysicsgeneratingthe∆Ci isnottoofarabove
τBd τBd SM τBd NP mB,suchthatln(M/mB)issmall. Fig.3(left)showsthe
where the SM contribution is taken from [18] and experimental 1σ allowed regions for the width difference
(cid:18)τ (cid:19) (cid:112)1 4x2 andlifetimeratio[20]inthe(∆C1,∆C2)plane. Thecen-
Bs =G2 V V 2m2M f2 τ − c tral values are attained on the brown (solid) and green
τBd NP F| cb cs| b Bs Bs Bs 144π × (dashed) curves, respectively. The measured lifetime ra-
(cid:40)
(cid:104) (cid:105) tio, which differs by about 2.5σ from the SM theoretical
(1−x2c) (4C1c,,22+C3c,,42)B1+6(4C2c,2+C4c,2)(cid:15)1 prediction,andthewidthdifferencemeasurementcannot
be simultaneously accommodated for any values of the
(cid:16) (cid:17)
12x2 Cc Cc B +6CcCc(cid:15) (1+2x2) Wilson coefficients, although each individually can, and
− c 1,2 3,4 1 2 4 1 − c × the agreement between the two might be improved with
(cid:41)
(cid:104) (cid:105) a small negative contribution ∆C . Also shown in the
(4Cc,2+Cc,2)B +6(4Cc,2+Cc,2)(cid:15) , (13) 1
1,2 3,4 2 2 4 2 plotarecontourlinesforthecontributiontotheeffective
semileptonic coefficient ∆Ceff(q2), both for q2 =2GeV2
subtracting the SM part and defining B , B , (cid:15) , (cid:15) as 9
1 2 1 2 and q2 = 5GeV2 We see that sizable negative shifts are
1
B (¯b γ s )(s¯ γµb )B = f2 M2 B , (14) possible while respecting the measured width difference.
(cid:104) s| L µ L L L | s(cid:105) 4 Bs Bs 1 For example, a shift ∆Ceff 1 as data may suggest
1 9 ∼ −
B (¯b s )(s¯ b )B = f2 M2 B , (15) could be achieved through ∆C1 0.5 alone, although
(cid:104) s| R L L R | s(cid:105) 4 Bs Bs 2 this slightly worsens the tension∼wi−th the measured life-
1
B (¯b γ TAs )(s¯ γµTAb )B = f2 M2 (cid:15) , (16) time ratio. Such a value for ∆C1 may well be consistent
(cid:104) s| L µ L L L | s(cid:105) 4 Bs Bs 1 with CP-conserving exclusive b cc¯s decay data, where
1 →
B (¯b TAs )(s¯ TAb )B = f2 M2 (cid:15) , (17) no accurate theoretical predictions exist. On the other
(cid:104) s| R L L R | s(cid:105) 4 Bs Bs 2 hand, ∆Ceff only exhibits a mild q2-dependence. Distin-
9
with values taken from [19]. We interpret the quark guishing this from possible long-distance contributions
masses as MS parameters at µ=4.2 GeV. would require substantial progress on the theoretical un-
4
derstanding of the latter. is the technically most challenging aspect of this work.
We can also consider other Wilson coefficients, such Ourcalculationemploysthe1PI(off-shell)formalismand
as the pair (∆C ,∆C ) (right panel in Fig. 3). A shift the method of [28] for computing UV divergences, which
3 4
∆Ceff 1 is equally possible and consistent with the involves an infrared-regulator mass and the appearance
9 ∼ −
widthdifference,requiringonly∆C 0.5. Itisinterest- of a set of gauge-non-invariant counterterms. The result
3
∼
ing to note that BSM contributions ∆C or ∆C generi- is
3 4
callyworsentheagreementwiththelifetimeratio,giving (cid:18) (cid:19)
416 224
a positive contribution. This suggests that the combina- γeff(0) = 0, ,0, (i=1,2,3,4).
tionofmixingmeasurementsmightdiscriminatebetween QciQ7 81 81 i
different CBSM scenarios. We will return to this point
We have not obtained the 2-loop mixing of Cc into C
below. We reiterate that, as explained before, B X γ 3,4 8g
s andsettheseanomalousdimensionelementstozero. For
→
is not affected in either scenario, at leading order.
the case of Cc where this mixing is known, the impact
1,2
ofneglectingγeff(0) on∆Ceff(µ)issmall(theonlychange
i8 7
HIGH-SCALE SCENARIO AND RGE in the matrix below being 0.19 0.18). We expect
− → −
a similarly small error in the case of Cc . Our stated
3,4
results for i = 1,2 agree with the results in [22, 25],
If the CBSM operators are generated at a high scale
which constitutes a cross-check of our calculation.
then large logarithms lnM/m generally require resum-
B
Solving the RGE for µ = M , µ = 4.2 GeV, and
mation, whichisachievedbyevolvingtheinitial(match- 0 W
α (M )=0.1181, results in a CBSM contribution
ing)conditionsC (µ M)toascaleµ M according s Z
i 0 B
∼ ∼
to the coupled renormalization-group equations (RGE)    
∆C (µ) 1.12 0.27 0 0
1
−  
µdCj(µ)=γ (µ)C (µ), (18) ∆C2(µ) −0.27 1.12 0 0  ∆C1(µ0)
dµ ij i ∆C3(µ)= 0 0 0.92 0 ∆C2(µ0).
∆C4(µ)  0 0 0.33 1.91 ∆C3(µ0)
   
wherethesumisoveralloperatorswith∆B =−∆S =1 ∆C7eff(µ) 0.02 −0.19 −0.01 −0.13 ∆C4(µ0)
flavor quantum numbers. (For a review of the formalism ∆C (µ) 8.48 1.96 4.24 1.91
9
− −
see [21].) A set of Wilson coefficients that contains C ,
7
C9, and C1c...4 and is closed under renormalization nec- A striking feature are the large coefficients in the ∆C9
essarily also contains four QCD-penguin coefficients CPi case,whichareO(1/αs)inthelogarithmiccounting. The
multiplying the operators P3...6 (we define them as in largestcoefficientsappearfor∆C1and∆C3,whichatthe
[22])andthechromodipolecoefficientC8g,resultinginan same time practically do not mix into C7eff. This means
11 11 anomalous-dimension matrix γ. It is convenient thatsmallvalues∆C1 0.1or∆C3 0.2cangenerate
to ×define a rescaled version Q˜9(µ) = (4π/αs(µ))Q9V(µ); ∆C9(µ) ∼ −1 while ha∼vin−g essentially∼no impact on the
then to leading order γ (µ)=α (µ)/(4π)γ(0), with con- B Xsγ decay rate. Conversely, values for ∆C2 or
ij s ij ∆C→that lead to ∆C 1 lead to large effects in Ceff.
stant γ(0). As is well known, this matrix is scheme- 4 9 ∼− 7
ij Just this is what in fact happens in the SM case, where
dependent already at LO [23]. A scheme-independent
Cc(µ ) = 1, inducing CLO(µ) = 1.96, close to half its
matrix γeff(0) can be achieved by replacing C and C 2 0 9
7 8 total value at NNLO, while the corresponding virtual-
by the scheme-independent combinations Ceff = C +
7 7 charmcontributiontoCeff exceedsthetotalSMvaluein
(cid:80) y C and Ceff = C +(cid:80) z C (respectively), where 7
i i i 8 8 i i i magnitude(duetodesctructiveinterferencewithvirtual-
sγ Q b = y sγ Q b , sg Q b = z sγ Q b , and
i i 7γ i i 8g top contributions).
(cid:104) | | (cid:105) (cid:104) | | (cid:105) (cid:104) | | (cid:105) (cid:104) | | (cid:105)
thesumsrunoverallfour-quarkoperators. Wefindthat
The situation in various two-parameter planes is de-
y and z vanish for Qc , leaving only the known co-
i i 1...4 picted in Figure 4, where the 1σ constraint from B
efficients y = ( 1/3, 4/9, 20/3, 80/9) and z = →
Pi − − − − i Pi Xsγ is shown as blue, straight bands. (We implement it
(1, 1/6,20, 10/3) (i = 3...6) [22]. Many of the ele-
i by splitting BR(B X γ) into SM and BSM parts and
men−tsofγeff(−0) areknown[11,23–26], exceptforγQeffci(Q0)7γ, employ the numeric→al ressult and theory error from [29]
γeff(0) , γeff(0), and γeff(0), for i = 3,4. The latter can for the former. The experimental result is taken from
QciQ8g QciPj QciQ˜9 [20].) The top row corresponds to Fig. 3, but contours
be read off from the logarithmic terms in (5), and the
of given ∆C lie much closer to the origin. In all panels,
mixing into P follows from substituting gauge coupling 9
i they pass through the region allowed by radiative decay,
and colour factors in diagram Figure 1 (left). This gives
leading to parallelogram-shaped regions covering the full
γ(0) =(cid:18) 8, 8,4,4(cid:19), γ(0) =(cid:18)0,4,0, 2(cid:19), range ( −2≤∆C9 ≤0 ). Clearly, generating ∆C9 ∼−1
QciQ˜9 −3 −9 3 9 i QciP4 3 −3 i wfrohmat∆lesCs2soalfoonre∆iCs r)u.leIdtios,uhtoawtehviegrh,psoigsnsiibfilceatnocege(nseormatee-
4
for i = 1,2,3,4, with the mixing into C vanishing. itjointlythrough∆C and∆C (bottom-rightplot);this
P3,5,6 2 4
The leading mixing into Ceff arises at two loops [27] and entails a cancellation between contributions to Ceff.
7 7
5
0.4 0.4 0 -1 -2
0.2 0.2
) )
W W
(MC2 0.0 (MC4 0.0
Δ Δ
-0.2 -0.2
-0.4 -2 -1 0 -0.4
-0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4
ΔC1(MW) ΔC3(MW)
0.4 0.4 FIG. 5. Future prospects for mixing observables. Dashed:
contoursofconstantwidthdifference,dotted: contoursofcon-
0.2 0.2 stant lifetime ratio. See text for discussion.
) )
W W
(MC3 0.0 (MC4 0.0
Δ Δ wecannotnecessarilyexpectaconsistentregioninanyof
-0.2 -0.2
ourtwo-parameterplanes. Onecouldalsoconsiderthree
-0.4 -2 -1 0 -0.4 -2 -1 0 or all four ∆Ci simultaneously.
-0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4
ΔC1(MW) ΔC1(MW)
PROSPECTS AND SUMMARY
0.4 0.4 -2
0.2 -2 0.2 The preceding discussion suggests that better knowl-
()MCW3 0.0 -1 ()MCW4 0.0 -1 eBdRge(Bof wiXdtshγ),dimffearyenhcaeveanthdelpifoettiemnteiarlattoiod,isacsriwmeilnlaates
Δ 0 Δ beween→different CBSM scenarios, or rule them out alto-
-0.2 -0.2
gether, subject to the stated caveats. This is illustrated
0
-0.4 -0.4 inFig.5,showingcontourvaluesforbothmixingobserv-
-0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4 ables. In each panel, the solid (brown and green) con-
ΔC2(MW) ΔC2(MW) tours correspond to the SM central values of the width
difference and lifetime ratio (respectively). The spac-
FIG. 4. Mixing observables versus rare decays, for ∆C
i
ing of the accompanying contours is such that the area
renormalized at µ = M . Color coding as in Figure 3,
0 W
B →X γ constraintshowninaddition(straightbluebands). between any two neighbouring contours corresponds to
s
a prospective 1σ-region, assuming a combined (theoreti-
cal and experimental) error on the lifetime ratio of 0.001
and a combined error on ∆Γ of 5%. The assumed fu-
s
Thewidthdifference(brownsolidlinesandbands)con- tureerrorsareambitiousbutseemfeasiblewithexpected
strains all scenarios. In all but the (∆C2,∆C4) case it experimental and theoretical progress. Overlaid is the
aisndcoinnsitshteen(t∆wCi1t,h∆bCo2th) arnaddi(a∆tivCe2,d∆ecCa3y)acnadses∆iCt9na=rro−w1s, (dciuscrrriemntin)aBtio→n bXestγweceonnstthreaitnwt.oTscheenafirgiuorseminadyicinatdeesedthbaet
down the allowed regions further. possible, as well as independent evidence for a (CBSM-
The measured lifetime ratio, which is about 2.5σ induced)effectin∆C , althoughthissomewhatdepends
9
from the SM prediction, can be accommodated in the ontheeventualvaluesofthemixingobservables. Further
(∆C ,∆C ), (∆C ,∆C ), and (∆C ,∆C ) scenarios, progress on B X γ in the Belle II era would provide
1 2 2 3 2 4 s
→
though it is never consistent with more than one of complementary information.
the other three observables (including ∆C ). The In summary, we have given a comprehensive anal-
9
(∆C ,∆C ) scenario can reproduce the lifetime ratio ysis of BSM effects in partonic b cc¯s transitions
3 4
→
only for values outside the plot region (and inconsis- (CBSM scenario) in the CP conserving case, focusing
tent with radiative decay), while the (∆C ,∆C ) and on those observables that can be computed in a heavy-
1 3
(∆C ,∆C )scenarioscannotaccommodatevaluesbelow quark expansion, considering both low and high new
1 4
about0.999atall. Wecautionthatthelifetimeratiocon- physics mass scales. In both cases, an effect in rare
straintdependsratherstronglyonthecharmquarkmass semileptonic B-decays of the type and size hinted at
scheme (not included in the error band). This would be by current LHCb and B-factory data can be generated,
resolved by higher-order calculations. The lifetime ra- while satisfying the constraint from inclusive B X γ.
s
→
tio could be affected by BSM contributions in τ that The effect can originate from different combinations of
Bd
do not affect the other observables, and Ceff could be b cc¯s operators. The required Wilson coefficients are
7 →
affected by additional short-distance contributions, such so small that constraints from B-decays into charm are
6
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