Table Of Content

IPPP/17/5 Charming new physics in rare B-decays and mixing? Sebastian Jäger 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 contributions∆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 (theoretical 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 not effective, particularly in the high-scale case, where arXiv:1309.2466 [hep-ph]; R. Gauld, F. Goertz, and large renormalization-group enhancements are present. U. Haisch, JHEP 01, 069 (2014), arXiv:1310.1082 [hep- A more precise measurement of mixing observables, at ph]; A. J. Buras, F. De Fazio, and J. Girrbach, JHEP02,112(2014),arXiv:1311.6729[hep-ph]; W.Alt- a level achievable at LHCb, may be able to confirm (or mannshofer, S. Gori, M. Pospelov, and I. Yavin, rule out) the CBSM scenario, and to discriminate be- Phys. Rev. D89, 095033 (2014), arXiv:1403.1269 [hep- tweendifferentBSMcouplings. Finally,letusstressthat ph]; G. Hiller and M. Schmaltz, Phys. Rev. D90, allCBSMeffectsarelepton-flavour-universal. Inparticu- 054014 (2014), arXiv:1408.1627 [hep-ph]; B. Gripaios, lar,iftheCBSMscenarioindeedaccountsforthebulkof M.Nardecchia, andS.A.Renner,JHEP05,006(2015), the rare B decay anomalies, the true value of the lepton arXiv:1412.1791 [hep-ph]; A. Crivellin, G. D’Ambrosio, flavouruniversalityparameterR shouldbemuchcloser and J. Heeck, Phys. Rev. Lett. 114, 151801 (2015), K arXiv:1501.00993 [hep-ph]; I. de Medeiros Varzielas to one than current experimental central values [30] sug- and G. Hiller, JHEP 06, 072 (2015), arXiv:1503.01084 gest. Withthestatedcaveats, ourconclusionsarerather [hep-ph]; A. Crivellin, G. D’Ambrosio, and J. Heeck, model-independent. It would be interesting to construct Phys. Rev. D91, 075006 (2015), arXiv:1503.03477 [hep- concrete realisations of the CBSM scenario. ph]; D. Becirevic, S. Fajfer, and N. Kosnik, Phys. Rev. D92, 014016 (2015), arXiv:1503.09024 [hep-ph]; We would like to thank C. Bobeth, P. Gambino, M. A. Celis, J. Fuentes-Martin, M. Jung, and H. Sero- Gorbahn, and in particular M. Misiak for discussions. dio, Phys. Rev. D92, 015007 (2015), arXiv:1505.03079 This work was supported by an IPPP Associateship. [hep-ph]; R. Alonso, B. Grinstein, and J. Martin Ca- SJ and KL acknowledge support by STFC consolidated malich, JHEP 10, 184 (2015), arXiv:1505.05164 [hep- grantST/L000504/1,anSTFCstudentship,andaWeiz- ph]; G. Bélanger, C. Delaunay, and S. Westhoff, Phys. Rev. D92, 055021 (2015), arXiv:1507.06660 [hep- mann Institute “Weizmann-UK Making Connections” ph]; A. Falkowski, M. Nardecchia, and R. Ziegler, grant. AL and MK are supported by the STFC IPPP JHEP11,173(2015),arXiv:1509.01249[hep-ph]; B.Gri- grant. paios, M. Nardecchia, and S. A. Renner, JHEP 06, 083 (2016), arXiv:1509.05020 [hep-ph]; M. Bauer and M. Neubert, Phys. Rev. Lett. 116, 141802 (2016), arXiv:1511.01900 [hep-ph]; S. Fajfer and N. Kosnik, Phys.Lett.B755,270(2016),arXiv:1511.06024[hep-ph]; ∗ [email protected] S.M.Boucenna,A.Celis,J.Fuentes-Martin,A.Vicente, † [email protected] and J. Virto, JHEP 12, 059 (2016), arXiv:1608.01349 [1] R. Aaij et al. (LHCb), JHEP 06, 133 (2014), [hep-ph]; P. Arnan, L. Hofer, F. Mescia, and A. Criv- arXiv:1403.8044 [hep-ex]. ellin, (2016), arXiv:1608.07832 [hep-ph]; D. Becirevic, [2] R. Aaij et al. (LHCb), JHEP 09, 179 (2015), S.Fajfer,N.Kosnik, andO.Sumensari,Phys.Rev.D94, arXiv:1506.08777[hep-ex]; V.Khachatryanetal.(CMS), 115021 (2016), arXiv:1608.08501 [hep-ph]; A. Crivellin, Phys.Lett.B753,424(2016),arXiv:1507.08126[hep-ex]. J.Fuentes-Martin,A.Greljo, andG.Isidori,Phys.Lett. [3] J.P.Leesetal.(BaBar),Phys.Rev.D93,052015(2016), B766, 77 (2017), arXiv:1611.02703 [hep-ph]. arXiv:1508.07960[hep-ex]; J.T.Weietal.(Belle),Phys. [7] G. Aad et al. (ATLAS), JHEP 08, 147 (2016), Rev.Lett.103,171801(2009),arXiv:0904.0770[hep-ex]; arXiv:1601.03297[hep-ex]; V.Khachatryanetal.(CMS), T. Aaltonen et al. (CDF), Phys. Rev. Lett. 108, 081807 Phys. Lett. B757, 97 (2016), arXiv:1507.07527 [hep-ex]; (2012), arXiv:1108.0695 [hep-ex]; R. Aaij et al. (LHCb), R. Aaij et al. (LHCb), Phys. Rev. Lett. 114, 041801 JHEP02,104(2016),arXiv:1512.04442[hep-ex]; A.Ab- (2015), arXiv:1411.3104 [hep-ex]; JHEP 04, 114 (2014), desselam et al. (Belle), in Proceedings, LHCSki 2016 - arXiv:1402.2554 [hep-ex]. A First Discussion of 13 TeV Results: Obergurgl, Aus- [8] C. Bobeth, U. Haisch, A. Lenz, B. Pecjak, and tria,April10-15,2016 (2016)arXiv:1604.04042[hep-ex]; G. Tetlalmatzi-Xolocotzi, JHEP 06, 040 (2014), S. Wehle et al. (Belle), (2016), arXiv:1612.05014 [hep- arXiv:1404.2531 [hep-ph]; C. Bobeth, M. Gor- ex]. bahn, and S. Vickers, Eur. Phys. J. C75, 340 [4] F. Beaujean, C. Bobeth, and D. van Dyk, Eur. (2015), arXiv:1409.3252 [hep-ph]; J. Brod, A. Lenz, Phys. J. C74, 2897 (2014), [Erratum: Eur. Phys. G.Tetlalmatzi-Xolocotzi, andM.Wiebusch,Phys.Rev. J.C74,3179(2014)], arXiv:1310.2478 [hep-ph]; W. Alt- D92, 033002 (2015), arXiv:1412.1446 [hep-ph]; C. W. mannshofer and D. M. Straub, Eur. Phys. J. C75, 382 Bauer and N. D. Dunn, Phys. Lett. B696, 362 (2011), (2015), arXiv:1411.3161 [hep-ph]; S. Descotes-Genon, arXiv:1006.1629 [hep-ph]. L. Hofer, J. Matias, and J. Virto, JHEP 06, 092 [9] J.LyonandR.Zwicky, (2014),arXiv:1406.0566[hep-ph]. (2016), arXiv:1510.04239 [hep-ph]; T. Hurth, F. Mah- [10] S. Chen et al. (CLEO), Phys. Rev. Lett. 87, 251807 moudi, and S. Neshatpour, Nucl. Phys. B909, 737 (2001), arXiv:hep-ex/0108032 [hep-ex]; K. Abe et al. (2016), arXiv:1603.00865 [hep-ph]. (Belle), Phys. Lett. B511, 151 (2001), arXiv:hep- [5] S. Ja¨ger and J. Martin Camalich, JHEP 05, 043 ex/0103042 [hep-ex]; B. Aubert et al. (BaBar), Phys. (2013), arXiv:1212.2263 [hep-ph]; Phys. Rev. D93, Rev. D77, 051103 (2008), arXiv:0711.4889 [hep-ex]; 014028 (2016), arXiv:1412.3183 [hep-ph]; M. Ciuchini, A. Limosani et al. (Belle), Phys. Rev. Lett. 103, M.Fedele,E.Franco,S.Mishima,A.Paul,L.Silvestrini, 241801 (2009), arXiv:0907.1384 [hep-ex]; J. P. Lees and M. Valli, JHEP 06, 116 (2016), arXiv:1512.07157 et al. (BaBar), Phys. Rev. Lett. 109, 191801 (2012), [hep-ph]. arXiv:1207.2690 [hep-ex]; Phys. Rev. D86, 112008 [6] A. J. Buras and J. Girrbach, JHEP 12, 009 (2013), (2012), arXiv:1207.5772 [hep-ex]; Phys. Rev. D86, 7 052012 (2012), arXiv:1207.2520 [hep-ex]; T. Saito et al. arXiv:hep-ph/0110124 [hep-ph]. (Belle),Phys.Rev.D91,052004(2015),arXiv:1411.7198 [20] Y. Amhis et al., (2016), arXiv:1612.07233 [hep-ex]. [hep-ex]. [21] G.Buchalla,A.J.Buras, andM.E.Lautenbacher,Rev. [11] A.J.Buras,M.Misiak, andJ.Urban,Nucl.Phys.B586, Mod.Phys.68,1125(1996),arXiv:hep-ph/9512380[hep- 397 (2000), arXiv:hep-ph/0005183 [hep-ph]. ph]. [12] S.Ja¨ger,M.Kirk,A.Lenz, andK.Leslie,inpreparation. [22] K. G. Chetyrkin, M. Misiak, and M. Munz, [13] V. A. Khoze and M. A. Shifman, Sov. Phys. Usp. 26, Phys. Lett. B400, 206 (1997), [Erratum: Phys. 387 (1983); M. A. Shifman and M. B. Voloshin, Sov. Lett.B425,414(1998)], arXiv:hep-ph/9612313 [hep-ph]. J. Nucl. Phys. 41, 120 (1985), [Yad. Fiz.41,187(1985)]; [23] M. Ciuchini, E. Franco, G. Martinelli, L. Reina, and I. I. Y. Bigi, N. G. Uraltsev, and A. I. Vain- L. Silvestrini, Phys. Lett. B316, 127 (1993), arXiv:hep- shtein, Phys. Lett. B293, 430 (1992), [Erratum: Phys. ph/9307364 [hep-ph]; Phys. Lett. B334, 137 (1994), Lett.B297,477(1992)], arXiv:hep-ph/9207214 [hep-ph]. arXiv:hep-ph/9406239[hep-ph]; M.Ciuchini, E.Franco, [14] A. Lenz, (2014), arXiv:1405.3601 [hep-ph]. L. Reina, and L. Silvestrini, Nucl. Phys. B421, 41 [15] M. Artuso, G. Borissov, and A. Lenz, Rev. Mod. Phys. (1994), arXiv:hep-ph/9311357 [hep-ph]. 88, 045002 (2016), arXiv:1511.09466 [hep-ph]. [24] M. K. Gaillard and B. W. Lee, Phys. Rev. Lett. 33, 108 [16] S. Aoki et al., Eur. Phys. J. C74, 2890 (2014), (1974); G.AltarelliandL.Maiani,Phys.Lett.B52,351 arXiv:1310.8555 [hep-lat]. (1974); F. J. Gilman and M. B. Wise, Phys. Rev. D20, [17] M. Beneke, G. Buchalla, and I. Dunietz, 2392(1979); M.A.Shifman,A.I.Vainshtein, andV.I. Phys. Rev. D54, 4419 (1996), [Erratum: Phys. Zakharov, Sov. Phys. JETP 45, 670 (1977), [Zh. Eksp. Rev.D83,119902(2011)], arXiv:hep-ph/9605259 [hep-ph]; Teor. Fiz.72,1275(1977)]. A. S. Dighe, T. Hurth, C. S. Kim, and T. Yoshikawa, [25] F. J. Gilman and M. B. Wise, Phys. Rev. D21, 3150 Nucl. Phys. B624, 377 (2002), arXiv:hep-ph/0109088 (1980). [hep-ph]; M. Beneke, G. Buchalla, C. Greub, A. Lenz, [26] B. Guberina and R. D. Peccei, Nucl. Phys. B163, 289 andU.Nierste,Phys.Lett.B459,631(1999),arXiv:hep- (1980). ph/9808385 [hep-ph]; M. Beneke, G. Buchalla, A. Lenz, [27] S. Bertolini, F. Borzumati, and A. Masiero, Phys. Rev. andU.Nierste,Phys.Lett.B576,173(2003),arXiv:hep- Lett. 59, 180 (1987); B. Grinstein, R. P. Springer, and ph/0307344[hep-ph]; M.Ciuchini,E.Franco,V.Lubicz, M. B. Wise, Phys. Lett. B202, 138 (1988); Nucl. Phys. F. Mescia, and C. Tarantino, JHEP 08, 031 (2003), B339, 269 (1990); M. Misiak, Phys. Lett. B269, 161 arXiv:hep-ph/0308029[hep-ph]; A.LenzandU.Nierste, (1991). JHEP 06, 072 (2007), arXiv:hep-ph/0612167 [hep-ph]. [28] K.G.Chetyrkin,M.Misiak, andM.Munz,Nucl.Phys. [18] E.Franco,V.Lubicz,F.Mescia, andC.Tarantino,Nucl. B518, 473 (1998), arXiv:hep-ph/9711266 [hep-ph]. Phys.B633,212(2002),arXiv:hep-ph/0203089[hep-ph]. [29] M. Misiak et al., Phys. Rev. Lett. 114, 221801 (2015), [19] D. Becirevic, Proceedings, 2001 Europhysics Conference arXiv:1503.01789 [hep-ph]. on High Energy Physics (EPS-HEP 2001): Budapest, [30] R. Aaij et al. (LHCb), Phys. Rev. Lett. 113, 151601 Hungary, July 12-18, 2001, PoS HEP2001, 098 (2001), (2014), arXiv:1406.6482 [hep-ex].