On the importance of electroweak corrections for B anomalies
Received: May
On the importance of electroweak corrections for B
Ferruccio Feruglio 0 2
Paride Paradisi 0 2
Andrea Pattori 0 1
Zurich 0
Switzerland 0
0 Via Marzolo 8, I-35131 Padova , Italy
1 Physik-Institut, Universitat Zurich
2 Dipartimento di Fisica e Astronomia \G. Galilei", Universita di Padova
3 Sezione di Padova
The growing experimental indication of Lepton Flavour Universality Violation (LFUV) both in charged- and neutral-current semileptonic B-decays, has triggered many theoretical interpretations of such non-standard phenomena. Focusing on popular scenarios where the explanation of these anomalies requires New Physics at the TeV scale, we emphasise the importance of including electroweak corrections to obtain trustable predictions for the models in question. We nd that the most important quantum e ects are the modi cations of the leptonic couplings of the W and Z vector bosons and the generation of a purely leptonic e ective Lagrangian. Although our results do not provide an inescapable no-go theorem for the explanation of the B anomalies, the tight experimental bounds on
Phenomenological Models
Z-pole observables and decays challenge an explanation of the current non-standard data. We illustrate how these e ects arise, by providing a detailed discussion of the running and matching procedure which is necessary to derive the low-energy e ective Lagrangian.
1 Introduction 2
Theoretical framework
2.1
Electroweak renormalization group ow
2.1.1
2.1.2
Rotation to the mass basis
Modi ed Z and W couplings
2.2
2.3
E ective theory below t, W and Z thresholds
E ective theory below the electroweak breaking scale
3
Observables
3.1
The B anomalies 3.2 Tree-level semileptonic phenomenology { 1 {
B ! K``
Introduction
The search for lepton
avour universality violation (LFUV) represents one of the most
powerful tool to unveil New Physics (NP) phenomena, as the Standard Model (SM) predicts
negligible LFUV e ects. Interestingly enough, in the last few years, hints of large LFUV
in semi-leptonic B decays were observed by various experimental collaborations both in
charged-current as well as neutral-current transitions. In particular, the statistically most
signi cant results are accounted for by the following observables:
(1.1)
(1.2)
(1.3)
(1.4)
RD=` = B(B ! D
RD=` = B(B ! D
B(B ! D ` )exp=B(B ! D ` )SM
B(B ! D` )exp=B(B ! D` )SM
)exp=B(B ! D
)SM = 1:34
0:17 ;
)exp=B(B ! D
)SM = 1:23
where ` = e; , which follow from the HFAG averages [1] of Babar [2], Belle [3], and LHCb
data [4], combined with the corresponding theory predictions [5, 6], and
RK=e = B(B ! K
RK=e = B(B ! K
)exp
)exp
B(B ! K ee)exp q22[1:1;6]GeV
B(B ! Kee)exp q22[1;6]GeV
based on combination of LHCb data [7, 8] with the SM expectation RK=(e ) = 1:00
Moreover, there are additional tensions between the SM predictions and
experimental data in b ! s`` di erential observables, though large non-perturbative
effects can be invoked to explain the observed anomaly [11{15]. Yet, it is interesting that
the whole set of b ! s`` data could be reconciled with the theory predictions assuming
some NP contributions exclusively in the muonic channels, see e.g. refs. [16{22]. In the
recent literature, many studies focused on the experimental signatures implied by the
solution of these anomalies in speci c scenarios, including kaon observables [23, 24], kinematic
distributions in B decays [25{35], the lifetime of the Bc
meson [36],
and
leptonic
decays [37], tau lepton searches [38, 39] and dark matter [40, 41].
These anomalies have also triggered many theoretical speculations about the
possible NP scenarios at work. Of particular interest are those attempting to a simultaneous
explanation of both charged- and neutral-current anomalies. Such a task can be most
naturally achieved assuming that NP intervenes through e ective 4-fermion operators involving
left-handed currents, (sL
bL)( L
L) and (cL
bL)( L
L), which are related by the
SU(2)L gauge symmetry [42]. In this setup, a necessary requirement is that NP couples
much more strongly to the third generation than to the rst two, since (cL
bL)( L
L)
is already generated at the tree level in the SM while (sL
bL)( L
L) is loop-induced.
Such a requirement is automatically accomplished if NP is coupled, in the interaction basis,
only to the third fermion generation, couplings to lighter generations being generated by
the misalignment between the mass and the interaction bases through small avour mixing
angles [43]. In this case LFUV is expected to be associated with lepton avour violating
{ 2 {
(LFV) phenomena. Another possibility consists in NP coupling to di erent fermion
generations proportionally to the charged lepton mass squared [44]. In this case LFUV does
not necessarily imply LFV at an observable level, if also NP preserves the lepton family
numbers in the limit of massless neutrinos.
In ref. [45], electroweak corrections for B anomalies has been analyzed, focusing on a
class of semilept (...truncated)