Flavoured B − L symmetry: from B decays to dark matter(arXiv:1705.03858)

Peter Cox1, Rodrigo Alonso2, Chengcheng Han1, Tsutomu T. Yanagida1

1Kavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa, Chiba 277-8583, Japan2CERN, Theoretical Physics Department, CH-1211 Geneva 23, Switzerland

Motivation

A well-motivated extension of the Standard Model is the addition of 3 right-handedneutrinos, which allows for the generation of small neutrino masses via the seesawmechanism, and the observed baryon asymmetry through leptogenesis.

This model possesses an exact B − L global symmetry in the limit of vanishingMajorana masses. It is natural to promote such a global symmetry to a local one;however the large RH neutrino masses needed for leptogenesis then lead to a very highbreaking scale for the B − L symmetry.

However, two superheavy RH neutrinos are sufficient for both seesaw and leptogenesis.It is therefore interesting to consider the possibility that a flavoured B − L gaugesymmetry could survive at low energies (∼ TeV). The third RH neutrino is then lightand can provide a dark matter candidate.

U(1)(B−L)3Model

We introduce a flavoured B − L gauge symmetry under which only the 3rd generationfermions are charged. The SM quarks and leptons take the following U(1)(B−L)3charges in flavour space:

T q =1

3

0 0 00 0 00 0 1

T l =

0 0 00 0 00 0 −1

The U(1) symmetry is vectorial, with the same charges for LH and RH fields, and isanomaly free. The SM Higgs is taken to be neutral under U(1)(B−L)3

.

RH Neutrino Dark Matter

I The third RH neutrino obtains a Majorana mass upon spontaneous breaking ofU(1)(B−L)3

by a scalar, φ (+2).

I Imposing an additional Z2 symmetry renders ν3R stable, and a viable dark matter

candidate.

I Z2 symmetry is further motivated by structure of the neutrino mass matrix.

I Produced via thermal freeze-out; annihilation through U(1)(B−L)3gauge interactions:

ν3R

ν3R

Z ′

φ

Z ′ν3R

ν3R

Z ′

Z ′

ν3R

ν3R

f

f̄

Z ′

Figure: All regions satisfy correct relicdensity. Coloured regions are excludedby experiment, and dark (light) greyregions by perturbative unitarity(perturbativity up to MPl).

I Direct detectionGenerally suppressed due to Majorana dark matter and no Z ′ coupling to lightquarks. However, can have a significant cross-section via φ-Higgs mixing.

I Indirect detectionAnnihilation cross-section is velocity-suppressed over much of the parameter space.ν3Rν

3R → φZ ′ is s-wave and can be probed with future gamma-ray experiments.

I LHC searchesSmall production cross-section, b̄b→ Z ′. Strongest bound is from Z ′→ ττ .

I Electroweak precisionKinetic mixing between Z ′ and Z is strongly constrained.Non-zero mixing is generated by RGE evolution, even if vanishing at high scales.

I PerturbativityPerturbative unitarity excludes large dark matter and Z ′ masses. Bounds becomesignificantly stronger if requiring perturbativity of couplings up to MPl.

Anomalies in b→ sµµ

Recently, there have been several intriguing hints of lepton flavour universality (LFU)violation in B decays. Measurements by LHCb [1, 2] of the theoretically clean ratios

R(∗)K =

Γ(B → K(∗)µ+µ−

)Γ(B → K(∗)e+e−

)show a deficit with respect to the SM prediction, leading to a combined tension withthe SM of around 4σ.

It is well-known that this tension can be alleviated via a new physics contribution tothe effective operators:

Ol9 =

α

4π(s̄γµ bL)

(l̄γµl

)Ol

10 =α

4π(s̄γµ bL)

(l̄γµγ

5l)

Heff = −4GF√2VtbV

∗ts

(C l

9Ol9 + C l

10Ol10

)0 1 2 3 4 5 6

q2 [GeV2/c4]

0.0

0.2

0.4

0.6

0.8

1.0

RK∗0

LHCb

LHCb

BIP

CDHMV

EOS

flav.io

JC

Flavour Phenomenology

I Z ′ interactions are generally not flavour diagonal after rotation to the mass basis.

I Can be additional mixing angles involving the 3rd generation, beyond those presentin VCKM and UPMNS.

I To explain the LFU anomalies, two new angles (θl, θq) are sufficient:

UeL = R23(θl), UνL = R23(θl)UPMNS, UdL = R23(θq), UuL = R23(θq)V†CKM

Figure: Best-fit region to theLFU anomalies (solid/dashedlines). Shaded regions areexcluded by existingmeasurements at 95% CL.

I LFU anomaliesIntegrating out Z ′ gives a contribution to the Wilson coefficients:

δCµ9 = −δCµ

10 = − π

α√

2GFVtbV ∗ts

g2sθqcθqs2θl

3m2Z ′

The best-fit region to the b→ sµµ anomalies is δCµ9 ∈ [−0.81 − 0.48] [3].

Can be explained with Z ′ masses O(TeV) and sθl ≈ 1.

I Meson mixingStrongest constraints on this model are from the mass difference in Bs − B̄s mixing.

I B decaysBs→ µµ: affected by δCµ

10; measured value consistent with both SM and best-fitregion for the anomalies.B → K(∗)νν̄: contribution guaranteed by SU(2)L gauge invariance, but existingbounds are sub-dominant.

I Lepton flavour violationStrongest bounds are from τ → 3µ. Constrains mixing angle in the lepton sector θl,and disfavours maximal mixing.

I LHC Z ′ searchesImportant bounds from Z ′→ µµ searches, but generally weaker than in othermodels. A light Z ′ below LHC searches also remains a possibility.

References

[1] R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. 113 (2014) 151601 [arXiv:1406.6482 [hep-ex]].

[2] R. Aaij et al. [LHCb Collaboration], arXiv:1705.05802 [hep-ex].

[3] W. Altmannshofer, P. Stangl and D. M. Straub, arXiv:1704.05435 [hep-ph].