Explaining $h\to\mu^\pm\tau^\mp$, $B\to K^* \mu^+\mu^-$ and $B\to K \mu^+\mu^-/B\to K e^+e^-$ in a two-Higgs-doublet model with gauged $L_\mu-L_\tau$

1.6 MB·English

by  Andreas Crivellin

CERN-PH-TH-2015-001
ULB-TH/14-26
Explaining h → µ±τ∓, B → K∗µ+µ− and B → Kµ+µ−/B → Ke+e−
in a two-Higgs-doublet model with gauged L −L
µ τ
Andreas Crivellin,1 Giancarlo D’Ambrosio,1,2 and Julian Heeck3
1CERN Theory Division, CH–1211 Geneva 23, Switzerland
2INFN-Sezione di Napoli, Via Cintia, 80126 Napoli, Italy
3Service de Physique Th´eorique, Universit´e Libre de Bruxelles,
Boulevard du Triomphe, CP225, 1050 Brussels, Belgium
The LHC observed so far three deviations from the Standard Model (SM) predictions in flavour
observables: LHCb reported anomalies in B →K∗µ+µ− and R(K)=B →Kµ+µ−/B →Ke+e−
while CMS found an excess in h→µτ. We show, for the first time, how these deviations from the
SMcanbeexplainedwithinasinglewell-motivatedmodel: atwo-Higgs-doubletmodelwithgauged
L −L symmetry. Wefindthat,despitetheconstraintsfromτ →µµµandB –B mixing,onecan
µ τ s s
explainh→µτ,B →K∗µ+µ− andR(K)simultaneously,obtaininginterestingcorrelationsamong
the observables.
I. INTRODUCTION inducedbyasingleoperatoruptodim-6andBr[h→µτ]
5 can easily be up to 10% taking into account this op-
1 So far, the LHC completed the SM by discovering erator only [23–28]. However, it is in general difficult
0
the last missing piece, the Brout–Englert–Higgs parti- to get dominant contributions to this operator in a UV
2
cle [1, 2]. Furthermore, no significant direct evidence complete model, as for example in models with vector-
ar for physics beyond the SM has been found, i.e. no new like leptons [29]. Therefore, among the several attempts
M particles were discovered. However, the LHC did ob- to explain this h → µτ observation [30–34], most of
servethree’hints’fornewphysics(NP)intheflavorsec- them are relying on models with extended Higgs sec-
0 tor, which are sensitive to virtual effects of new parti- tors. One solution employs a two-Higgs-doublet model
1 cles and can be used as guidelines towards specific NP (2HDM) with gauged Lµ−Lτ [35].
h] mKoµd+eµls−:/Bh →→ Kµτe,+Be−.→ItKis∗µth+eµr−ef,oraenidntRer(eKst)in=g tBo e→x- eraTl:henaobteolinalnysiysmthmisetarynUan(1o)mLµa−lyL-τfreiseingtloerbeasltisnygminmgeetrny-
p amine if a specific NP model can explain these three within the SM [36–38], it is also a good zeroth-order ap-
- anomalies simultaneously, predicting correlations among proximationforneutrinomixingwithaquasi-degenerate
p
them. mass spectrum, predicting a maximal atmospheric and
e
h LHCbreporteddeviationsfromtheSMpredictions[3, vanishing reactor neutrino mixing angle [39–41]. Break-
[ 4] (mainly in an angular observable called P(cid:48) [5]) in ing Lµ−Lτ is mandatory for a realistic neutrino sector,
B →K∗µ+µ− [6] with a significance of 2–3σ de5pending and such a breaking can also induce charged LFV pro-
2
on the assumptions of hadronic uncertainties [7–9]. This cesses, such as τ →3µ [42, 43] and h→µτ [35].
v
3 discrepancycanbeexplainedinamodelindependentap- Supplementing the model of Ref. [35] with the in-
9 proachbyratherlargecontributionstotheWilsoncoeffi- ducedZ(cid:48) quarkcouplingsofRef.[15]canresolveallthree
9 cientC [10–12],i.e.anoperator(sγ P b)(µγαµ),which anomalies from above. Interestingly, the semileptonic B
9 α L
0 canbeachievedinmodelswithanadditionalheavyneu- decays imply lower limit on g(cid:48)/MZ(cid:48), which allows us to
0 tralZ(cid:48) gaugeboson[13–15]. Furthermore, LHCb[16]re- set a lower limit on τ →µµµ, depending on h→µτ.
.
1 centlyfoundindicationsfortheviolationofleptonflavour
0 universality in
5 II. THE MODEL
1 B →Kµ+µ−
R(K)= =0.745+0.090±0.036, (1)
v: B →Ke+e− −0.074 Our model under consideration is a 2HDM with a
Xi which disagrees from the theoretically rather clean SM gauged U(1)Lµ−Lτ symmetry [35]. The Lµ−Lτ symme-
prediction RSM =1.0003±0.0001 [17] by 2.6σ. A possi- try with the gauge coupling g(cid:48) is broken spontaneously
ar bleexplanatiKonisagainaNPcontributingtoCµµ involv- by the vacuum expectation value (VEV) of a scalar Φ
9
ing muons, but not electrons [18–20]. Interestingly, the with QΦ =1, leading to the Z(cid:48) mass
Lµ−Lτ
value for C required to explain R(K) is of the same
9 √
order as the one required by B → K∗µ+µ− [8, 21]. m = 2g(cid:48)(cid:104)Φ(cid:105)≡g(cid:48)v , (3)
Z(cid:48) Φ
In Ref. [15], a model with gauged muon minus tauon
number (Lµ−Lτ) was proposed in order to explain the and Majorana masses for the right-handed neutrinos1.
B →K∗µ+µ− anomaly.
Two Higgs doublets are introduced which break the
Concerning Higgs decays, CMS recently measured a electroweak symmetry: Ψ with QΨ1 = −2 and Ψ
lepton-flavour violating (LFV) channel [22] 1 Lµ−Lτ 2
Br[h→µτ]=(cid:0)0.89+0.40(cid:1)%, (2)
−0.37
whichdisagreesfromtheSM(wherethisdecayisforbid- 1 Active neutrino masses are generated via seesaw with close-to-
den) by about 2.4σ. Such LFV SM Higgs couplings are maximalatmosphericmixingandquasi-degeneratemasses[35].
2
with QΨ2 =0. Therefore, Ψ gives masses to quarks models(asidefromthekineticZ–Z(cid:48) mixing, whichisas-
Lµ−Lτ 2
and leptons while Ψ couples only off-diagonally to τµ: sumed to be small). Following Ref. [15], we introduce
1
heavy vector-like quarks, i.e. Q ≡ (U ,D ), Dc, Uc
L L L R R
LY ⊃ −(cid:96)fYi(cid:96)δfiΨ2ei−ξτµ(cid:96)3Ψ1e2 (4) and their chiral partners Q˜R ≡ (U˜R,D˜R), D˜Lc, U˜Lc, with
−Q YuΨ˜ u −Q YdΨ d +h.c.. vector-like mass terms
f fi 2 i f fi 2 i
m Q Q˜ +m D˜ D +m U˜ U +h.c., (9)
Q L R D L R U L R
Here Q ((cid:96)) is the left-handed quark (lepton) doublet, u
(e) is the right-handed up-quark (charged-lepton) and and Lµ−Lτ charges +1 (i.e. QDLµR−Lτ =QULRµ−Lτ =−1),
d the right-handed down quark while i and f label the coupling them to the Z(cid:48) boson. Yukawa-like couplings
three generations. The scalar potential is the one of a involvingtheheavyvector-quarks,thelightchiralquarks
U(1)-invariant 2HDM [44] with additional couplings to and Φ
the SM-singlet Φ, which most importantly generates the
3
doublet-mixing term Φ(cid:88)(cid:16)D˜ YQP d +U˜ YQP u (cid:17) (10)
R j L j R j L j
j=1
V(Ψ ,Ψ ,Φ) ⊃ 2λΦ2Ψ†Ψ →λv2Ψ†Ψ ≡m2Ψ†Ψ ,
1 2 2 1 Φ 2 1 3 2 1 3
+Φ†(cid:88)(cid:16)D˜ YDP d +U˜ YUP u (cid:17)+h.c.
that induces a small vacuum expectation value for L j R j L j R j
Ψ [35]. We define tanβ =(cid:104)Ψ (cid:105)/(cid:104)Ψ (cid:105) and α is the usual j=1
1 2 1
mixing angle between the neutral CP-even components theninducecouplingsoftheSMquarkstotheZ(cid:48) onceΦ
of Ψ and Ψ (see for example [44]). We neglect the acquiresitsVEV.Thus,integratingouttheheavyvector-
1 2
additional mixing of the CP-even scalars with Re[Φ]. likequarksgivesrisetoeffectiveZ(cid:48)d¯d couplings[45,46]
i j
Quarksandgaugebosonshavestandardtype-I2HDM of the form
couplings to the scalars. The only deviations are in the g(cid:48)(cid:0)d¯γµP d Z(cid:48)ΓdL+d¯γµP d Z(cid:48)ΓdR(cid:1), (11)
lepton sector: while the Yukawa couplings Y(cid:96)δ of Ψ i L j µ ij i R j µ ij
i fi 2
are forced to be diagonal due to the Lµ−Lτ symmetry, with hermitian matrices ΓdL that are related to the vec-
ij
ξ gives rise to an off-diagonal entry in the lepton mass
τµ tor quark masses m and Yukawa couplings YQ,D,U
Q,D,U
matrix:
as follows [15]:
 
m(cid:96)fi = √v yes0inβ yµs0inβ 00 . (5) ΓdijR (cid:39)−2vmΦ22 (YiDYjD∗), ΓdijL (cid:39) 2vmΦ22 (YiQYjQ∗), (12)
2 0 ξ cosβ y sinβ D Q
τµ τ
which holds in the approximation |ΓqR/L|(cid:28)1.3
It is this τ–µ entry that leads to the LFV couplings of h ij
and Z(cid:48) of interest to this letter. The lepton mass basis
is obtained by simple rotations of (µR,τR) and (µL,τL) III. FLAVOUR OBSERVABLES
with the angles θ and θ , respectively:
R L
We will now recall the necessary formula in the region
v tanθ m
sinθ (cid:39) √ ξ cosβ, L = µ (cid:28)1. (6) of interest (i.e. small θ ) considering only the processes
R 2mτ τµ tanθR mτ giving to most relevantRbounds on our model, i.e. B –B¯
s s
mixing, neutrino trident production and τ →3µ.
Theangleθ isautomaticallysmallandwillbeneglected
L
in the following.2 A non-vanishing angle θ not only
R
gives rise to the LFV decay h→µτ due to the coupling
A. h→µτ
m cos(α−β)
τ sin(θ )cos(θ )τ¯P µh≡Γh τ¯P µh,
v cos(β)sin(β) R R R τµ R The branching ratio for h→µτ reads
in the Lagrangian, but also leads to off-diagonal Z(cid:48) co(u7)- Br[h→µτ](cid:39) 8πmΓh (cid:12)(cid:12)Γhτµ(cid:12)(cid:12)2, (13)
SM
plings to right-handed leptons
whereΓ (cid:39)4.1MeVisthedecaywidthintheSMfora
SM
(cid:18) (cid:19) (cid:18) (cid:19) 125 GeV Higgs [47] and Γh is defined in Eq. (7). Com-
cos2θ sin2θ µ τµ
g(cid:48)Zν(cid:48) (µ,τ) sin2θR −cos2Rθ γνPR τ , (8) paring this to Eq. (2) one sees that both sinθR (cid:54)= 0
R R
and cos(α − β) (cid:54)= 0 are required to explain the CMS
excess [35].
whiletheleft-handedcouplingsaretoagoodapproxima-
tion flavour conserving. In order to explain the observed
anomaliesintheB mesondecays,acouplingoftheZ(cid:48) to
quarksisrequiredaswell,notinherentlypartofL −L
µ τ
3 ComparedtoRef.[15], thevector-likequarksalsohaveYukawa
couplings yΨ1 to the Lµ−Lτ-charged scalar doublet Ψ1. This
inducesasmalladditionalmassmixingamongtheheavyquarks,
andalsoacouplingtohsuppressedbyyΨ1cos(α−β). Weassume
2 ChoosingQLµ−Lτ =+2forΨ2wouldessentiallyexchangeθL↔ these couplings yΨ1 to be small to avoid large contributions to
θR [35],withlittleimpactonourstudy. gg→handh→γγ.
3
tan Β (cid:61)10 yellow andtan Β (cid:61)50 blue 7
0.15 g' mQ(cid:61)mZ' g'
(cid:72) (cid:76) (cid:72) (cid:76) (cid:72) (cid:76) (cid:72) (cid:76) mZ' 2 Σ
6 Bsmixing 15 (cid:144) (cid:144) C 9
(cid:61) (cid:76)
(cid:72)
7TeV 5 mQ
sinΘ (cid:61)0.05
R
0.10 ΜΤ V (cid:68)
ΘsinR (cid:72)(cid:76) 1Σh(cid:174) 2Σh(cid:174)ΜΤ g'TeZ' 34 (cid:144)(cid:64) C 9 1 Σ(cid:72) (cid:76) (cid:72) (cid:76)C9 2(cid:72)Σ (cid:76)
m sinΘ (cid:61)0.02
5TeV R
0.05
2
(cid:72) (cid:76)
ΜΤ
h (cid:174) (cid:174) ΜΤ 1 Τ(cid:174)3ΜforsinΘR (cid:61)0.005
1Σ Σ h m g'(cid:61)3TeV
2 Z' neutrino trident product(cid:72)ion(cid:76)
0.00 0
(cid:45)0.4 (cid:45)0.2 0(cid:144).0 0.2 0.4 0.00 0.01 0.02 0.03 0.04
cos Α(cid:45)Β (cid:71)dL
23
FIG. 1: Left: Allowed regions in the cos(α−β)–sin(θ ) plane. The blue (light blue) region corresponds to the 1σ (2σ)
(cid:72) (cid:76) R
region of the CMS measurement of h → µτ for tanβ = 50; yellow stands for tanβ = 10. The (dashed) red contours mark
deviations of h→ττ by 10% compared to the SM for tanβ =50 (10). The vertical green lines illustrate the naive LHC limit
|cos(α−β)|<∼0.4, horizontal lines denote the 90% C.L. limit on τ →3µ via Z(cid:48) exchange.
Right: AllowedregionsintheΓd23L–mZ(cid:48)/g(cid:48) planefromB →K∗µ+µ− andR(K)(yellow)andBs mixing(blue). ForBs mixing
(light) blue corresponds to (mQ = 15mZ(cid:48)/g(cid:48)) mQ = mZ(cid:48)/g(cid:48). The horizontal lines denote the lower bounds on mZ(cid:48)/g(cid:48) from
τ →3µ for sin(θ )=0.05, 0.02, 0.005. The gray region is excluded by NTP.
R
B. Lepton decays suppressed Cµτ). C(cid:48)ee is not affected, which natu-
9 9
rally generates violations of lepton flavour universality
in B →Kµ+µ−/B →Ke+e−. We find
WhiletheHiggscontributionstoτ →µµµandτ →µγ
turn out to be very small in most regions of parameter
space[35]duetothesmallleptonmassesinvolved,theZ(cid:48) g(cid:48)2 π 1
cθo2n/tvr4ib.uTtihoensbrtaonτch→ing3µratciaonisbegisvieznabblye [42] and restrict C9((cid:48))µµ (cid:39) √2m2Z(cid:48) αGFVtbVt∗sΓd23L(R), (15)
R Φ
m5 g(cid:48)4 where we set cos(2θR)=1. As already noted in Ref. [10,
Br[τ →3µ](cid:39) τ sin2(2θ ), (14) 51]Cµµ <0andC(cid:48)µµ =0givesagoodfittodata. Using
512π3Γ m4 R 9 9
τ Z(cid:48) the global fit of Ref. [8] we see that at (1σ) 2σ level
which has to be compared to the current upper limit
of 2.1 × 10−8 at 90% C.L. [48] obtained by Belle. A −0.5(−0.8)≥ReC9µµ ≥(−1.6) −2.0. (16)
combination with data from BaBar [49] gives an even
strongerlimitof1.2×10−8at90%C.L.[50],tobeusedin Interestingly, the regions for Cµµ required by R(K) and
9
the following. For small θR, the branching ratio for τ → B →K∗µ+µ−lieapproximatelyinthesameregion. Fur-
µγ is proportional to the same combination θ2/v4, but thermore, a good fit to the current data does not even
R Φ
highly suppressed by 2α/π, and hence not as restrictive. requireC(cid:48)µµ [8], soweneglectitinthefollowingforsim-
9
plicity. This can be achieved in the limit m (cid:29) m ,
D Q
resulting in ΓdL (cid:29) ΓdR. We will also assume our Cµµ
9
C. B →K∗µ+µ− and B →Kµ+µ−/B →Ke+e− to be real for simplicity. Note that our model predicts
the decay B → Kµτ (recently discussed in Refs. [52])
to be suppressed by θ2 compared to B → Kµµ, while
Both B → K∗µ+µ− and R(K) are sensitive to the R
B →Kµe and B →Kτe are forbidden.
Wilson coefficients C((cid:48))µµ and C((cid:48))µµ.4 While in our
9 10
model the contribution to C is suppressed by sin(2θ )
10 R
(or even sin(2θ )), the Wilson coefficients Cµµ and C(cid:48)µµ
L 9 9
with muons are generated (as well as Cττ and the θ
9 R D. B –B mixing
s s
TheinteractionsofZ(cid:48) andΦrelevantforB →Kµ+µ−
4 ForconventionsseeRefs.[8,19]. also contribute to Bs–Bs mixing [15]. For mD (cid:29) mQ,
4
we get cosΑ(cid:45)Β (cid:61)0.2
0.10
(cid:18) (cid:19)
(cid:0)ΓdL(cid:1)2 1+ 1 g(cid:48)2m2Q (cid:72) (cid:76)
M12 (cid:39)1+ 23 16π2 m2Z(cid:48) . (17)
M1S2M 64gπ242mm2W2Zg(cid:48)(cid:48)2(Vt∗sVtb)2S0 0.08 ction 1Σtahn(cid:174)ΒΜ(cid:61)Τ2fo5r Σ (cid:76)
u 1
We require the NP contribution to be less than 15% in d (cid:72)
order to satisfy the experimental bounds [15]. Due to 0.06 pro (cid:72) (cid:76) C9
(cid:76)
thedominanceofthevector-quarkQwecanexpressΓdL R t &
23 Θ n
dbioruenctdlsyintermsofC9µµ fromEq.(15)andfindtheupper sin 0.0(cid:72)4 otride tan Β (cid:61)50 ixing
mZ(cid:48)/g(cid:48) <3.2TeV/|C9µµ|, mQ <41TeV/|C9µµ|. (18) utrin (cid:72) (cid:76) Bms
Combining Eq. (18) with Eq. (16) then gives an upper 0.02 ne tan Β (cid:61)85
bound of m /g(cid:48) <4TeV (6.5TeV) at 1σ (2σ).
Z(cid:48) (cid:72) (cid:76) Τ (cid:174) 3 Μ future Τ (cid:174) 3Μ
0.00
E. Neutrino trident production 0 1 2 3 4 5
m g' TeV
The most stringent bound on flavour-diagonal Z(cid:48) cou- Z'
plings to muons arises from neutrino trident production
(NTP) ν N →ν Nµ+µ− [15, 53]: FIG. 2: Allowed regions in the(cid:144) m(cid:64)Z(cid:48)/g(cid:48)–(cid:68)sin(θR) plane: the
µ µ horizontal stripes correspond to h → µτ (1σ) for tanβ =
85, 50, 25andcos(α−β)=0.2,(light)bluestandsfor(future)
1+(cid:16)1+4s2 +8 g(cid:48)2 m2W(cid:17)2 τ →3µ limits at 90% C.L. The gray regions are excluded by
σNTP (cid:39) W MZ2(cid:48) g22 . (19) NTP or Bs–Bs mixing in combination with the 1σ range for
σNSMTP 1+(1+4s2W)2 C9 (see Eq. (18)).
Seeingasourregionofinterestisinthesmallθ regime,
R
the NTP bound is basically independent of the angle we focus on the limit M → ∞ (i.e. C(cid:48) → 0) we find
D 9
θ . Taking only the CCFR data [54], we get roughly that unless ΓdL is rather large, B → K∗µ+µ− can be
R 23
mZ(cid:48)/g(cid:48) >∼ 550GeV at 95% C.L. Compared to τ → µµµ explained without violating bounds from Bs–B¯s. Only a
thetridentneutrinoboundonlydominatesforverysmall very small ΓdL independent region is excluded by NTP.
23
valuesofθR,roughlywhenθR <∼10−3(seeFig.2(right)). In addition, bounds from τ → 3µ depending on sin(θR)
For m >m , the LHC constraints from the process can be obtained.
Z(cid:48) Z
pp → µµZ(cid:48) → 4µ (or 3µ plus missing energy) [55] are Concerning τ → 3µ, future sensitivities down to
currently weaker than NTP [15], but will become com- Br[τ →3µ] (cid:39) 10−9 seem feasible [61] and will cut deep
petitive with higher luminosities [56–58]. into our parameter space (see Fig. 2). Using the 1σ lim-
its on h → µτ to fix θ and B mixing with C to fix
R s 9
m /g(cid:48) – as well as the LHC limit |cos(α−β)| < 0.4 –
Z(cid:48)
F. Phenomenological analysis we can obtain a lower limit on the rate τ →3µ
Concerning the phenomenological consequences of of Br[τ →3µ]>∼3.8×10−8(10/tanβ)2, (20)
our model, let us first consider the implications of h → which implies tanβ >∼ 18 with current data [50] and
µτ. In the left plot of Fig. 1 we show the regions in the tanβ >∼ 61 if branching ratios down to 10−9 can be
cos(α−β)–sin(θR) plane which can explain h → µτ at probed in the future. This is the main prediction of our
the 1σ and 2σ level for different values of tanβ. Mea- simultaneous explanation of h→µτ, B →K∗µ+µ− and
surements of the h couplings to vector bosons require R(K).
|cos(α − β)| <∼ 0.4 [59, 60] while the Higgs effects in Finally, weremarkthataZ–Z(cid:48) mixingangleθZZ(cid:48) [45]
τ → 3µ and τ → µγ are typically negligible [35]. As is induced by the VEV of Ψ [35]
1
a side effect, the h → µτ rate also implies a change in
the h → ττ rate, although this is negligible in regions g v2cos2β (cid:18) 20 (cid:19)2(cid:18) TeV (cid:19)2
|g(cid:48)θ |(cid:39) 1 (cid:39)10−4 ,
with small θR. In addition we show the regions com- ZZ(cid:48) m2Z(cid:48)/g(cid:48)2 tanβ mZ(cid:48)/g(cid:48)
patible with τ → 3µ for various values of mZ(cid:48)/g(cid:48). Note (21)
that g(cid:48) <∼ 0.3 in order to avoid a Landau pole below the
Planckscale. Insummary,smallvaluesofθ canexplain which leads to small shifts in the vector couplings of Z
R
the CMS h → µτ excess for moderate to large values of to muons and taus
tanβ for cos(α−β)(cid:39)0.1. gZ(µµ,ττ)(cid:39)−1/2+2s2 ±g(cid:48)θ /(g/c ), (22)
In the right plot of Fig. 1 we examine which regions in V W ZZ(cid:48) W
parameter space can account for B → K∗µ+µ− taking and thus ultimately to lepton non-universality [43]. For
into account the constraints from B –B¯ mixing. Since the values of interest to our study (see Fig. 2), and in
s s
5
the limit m (cid:28) m , the shift is automatically small presentboundsforlargetanβ inwideragesofparameter
Z Z(cid:48)
enough to satisfy experimental bounds and leads to tiny space. Interestingly, B →K∗µ+µ− and R(K) combined
branching ratios Z → µτ below 10−8 (for θ < 0.1). with B –B put a upper limit on m /g(cid:48) resulting in a
R s s Z(cid:48)
Note that the couplings to electrons and quarks remain lower limit on τ → 3µ if Br[h → µτ] (cid:54)= 0: for lower val-
unaffected. Form (cid:29)m ,theρparameterisenhanced uesoftanβ thecurrentexperimentalboundsarereached
Z(cid:48) Z
by [45] and future sensitivities will allow for a more detailed ex-
ploration of the allowed parameter space. The possible
(cid:18)θ (cid:19)2(cid:16)m (cid:17)2 range for the L −L breaking scale further implies the
ρ−1(cid:39)1.2×10−4 ZZ(cid:48) Z(cid:48) , (23) µ τ
10−3 TeV masses of the Z(cid:48) and the right-handed neutrinos to be
at the TeV scale, potentially testable at the LHC with
and is therefore compatible with electroweak precision interestingadditionalconsequencesforLFVobservables.
data (ρ − 1 < 9 × 10−4 at 2σ [62]) for the parameter
space studied in this letter.
Acknowledgments
IV. CONCLUSIONS
A. Crivellin is supported by a Marie Curie Intra-
In this letter we showed for the first time that all European Fellowship of the European Community’s 7th
three LHC anomalies in the flavour sector can be ex- Framework Programme under contract number PIEF-
plained within a single well-motivated model: A 2HDM GA-2012-326948. G. D’Ambrosio acknowledges the
withagaugedL −L symmetryandeffectiveZ(cid:48)s¯bcou- partial support my MIUR under the project number
µ τ
plings induced by heavy vector-like quarks. Except for 2010YJ2NYW.TheworkofJ.Heeckisfundedinpartby
the τ–µ couplings, the Higgs sector resembles the one IISN and by Belgian Science Policy (IAP VII/37). We
of a 2HDM of type-I. Therefore, the constraints from thank Gian Giudice for useful discussions. We are grate-
h decays or LHC searches for A0 → τ+τ− are rather fultoWolfgangAltmannshoferandDavidStraubforuse-
weak and h → µτ can be easily explained in a wide fuldiscussionsandadditionalinformationconcerningthe
parameter space. The model can also account for the model-independent fit to Cµµ and C(cid:48)µµ.
9 9
deviations from the SM in B → K∗µ+µ− and naturally Note added: duringthepublicationprocessofthisletter,
leads to the right amount of lepton-flavour-universality CMS has released its final analysis of the h→µτ search
violating effects in R(K). Due to the small values of the as a preprint [63], resulting in slightly changed values –
τ–µ mixing angle θ , sufficient to account for h → µτ, Br[h → µτ] = (cid:0)0.84+0.39(cid:1)% – which have however only
R −0.37
the Z(cid:48) contributions to τ → 3µ are not in conflict with a small impact on our study.
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