dark matter phenomenology in scotogenic models

Dark matter phenomenology in scotogenic models

June 10th, 2021 — Institut für Theoretische Physik und Astronomie — Würzburg, Germany

Björn Herrmann

Laboratoire d’Annecy-le-Vieux de Physique Théorique (LAPTh)Univ. Grenoble Alpes — Univ. Savoie Mont Blanc — CNRS

Annecy — France

ONLINE SEMINAR

based mainly on work in collaboration with Maud Sarazin and Jordan Bernigaudto be published — arXiv:2107.0xyz

Motivation for scotogenic models

Review and introduction to T1-2A model

Phenomenology of the T1-2A model

Summary and perspectives

Dark matter phenomenology in scotogenic models

The Standard Model…

en.wikipedia.org/wiki/Standard_Model

http://en.wikipedia.org/wiki/Standard_Model

The Standard Model… and its shortcomings

Dark matter in the Universe…?

Hierarchy problem…?

Gauge coupling un

ification…?

Gravity…?

Neutrino masses…?

Lepton-flavour non-universality…?

Flavour problem…?

Dark matter in the Universe — relic abundance

x = m/T (time)

Y =

n/s

(abu

ndan

ce) Time evolution of number density of the relic

particle described by Boltzmann equation

small ⟨σannv⟩

large ⟨σannv⟩

dn

dt= �3Hn� h�annvi

�n2 � n

2eq

�

Prediction of dark matter relic density(if masses and interactions are known)

⌦�h2 =

m�n�

⇢crit⇠ 1

h�annvi

(dis)favoured parameter regions…?

⌦CDMh2 = 0.1199± 0.0022

Planck 2015

Dark matter candidate…? WIMP…?

Figure 1: Current (left) and future (right) 90% C.L. exclusion plots to the e↵ective WIMP–proton cross section �p ofEq. (13) for the SI interaction of Eq. (1) corresponding to the O1 operator in Eq.(3) for the isoscalar case cp

1=cn1. The

figure shows the constraints from the full set of experiments that we include in our analysis, which consists in the latestavailable data from 14 existing DM searches, and the estimated future sensitivity of 4 projected ones (LZ, PICO-500(C3F8), PICO-500 (CF3I) and COSINUS). The closed solid (red) contour represents the 5–sigma DAMA modulationamplitude region, while we indicate with DAMA0 the upper bound from the DAMA average count–rate. Notice thatafter the release of the DAMA/LIBRA-phase2 result [5] a spin–independent isoscalar (cn/cp=1) interaction does notprovide anymore a good fit to the modulation e↵ect, while it still does for di↵erent values of cn/cp and for other e↵ectivecouplings [44].

experiments, and the estimated future sensitivity of 4 projected ones. The details of our procedureto obtain the exclusion plots are provided in Appendix B.

The relative sensitivity of di↵erent detectors is determined by two elements: the thresholdsvth

min of di↵erent experiments expressed in terms of the WIMP incoming velocity, and the scalinglaw of the WIMP–nucleus cross section o↵ di↵erent targets.

The former element explains the steep rise of all the exclusion plot curves at low WIMPmasses, which corresponds to the case when vth

min approaches the value of the escape velocityin the lab rest frame, and is sensitive to experimental features close to the energy threshold thatare typically a↵ected by uncertainties, such as e�ciencies, acceptances and charge/light yields.With the assumptions listed in Appendix B, among the experiments included in our analysisthe ones with the lowest velocity thresholds turn out to be DS50, CRESST–II, CDMSlite andCDEX. In particular, for m�=1 GeV we have vth

min,DS 50 ' 450 km/s, vthmin,CRES S T�II ' 480 km/s

(for scatterings o↵ oxygen), vthmin,CDMS lite ' 910 km/s, vth

min,CDEX ' 1600 km/s. Assuming vlabesc '

782 km/s (see the previous Section) this implies that in our analysis only DS50 and CRESST-II(for e↵ective interactions for which argon and oxygen have a non–vanishing nuclear responsefunction) are sensitive to m� <⇠ 1 GeV. On the other hand CDMSlite and CDEX are sensitive toslightly higher masses (for instance, for m�=2 GeV vth

min,CDMS lite ' 460 km/s, vthmin,CDEX ' 850

km/s, while for m�=3 GeV vthmin,CDEX ' 580 km/s). The velocity threshold is a purely kinematical

feature that does not depend on the type of interaction and that favors experiments with the lowestvth

min at fixed m�.With the exception of very low masses, where the e↵ect of vth

min is dominant, the relativesensitivity of di↵erent detectors is determined by the scaling law of the WIMP–nucleus crosssection with di↵erent targets, which is the focus of our analysis. In particular the SI interaction(corresponding to the M e↵ective nuclear operator) favors heavy nuclei, so that the most stringent

8

Figure 1: Current (left) and future (right) 90% C.L. exclusion plots to the e↵ective WIMP–proton cross section �p ofEq. (13) for the SI interaction of Eq. (1) corresponding to the O1 operator in Eq.(3) for the isoscalar case cp

1=cn1. The

figure shows the constraints from the full set of experiments that we include in our analysis, which consists in the latestavailable data from 14 existing DM searches, and the estimated future sensitivity of 4 projected ones (LZ, PICO-500(C3F8), PICO-500 (CF3I) and COSINUS). The closed solid (red) contour represents the 5–sigma DAMA modulationamplitude region, while we indicate with DAMA0 the upper bound from the DAMA average count–rate. Notice thatafter the release of the DAMA/LIBRA-phase2 result [5] a spin–independent isoscalar (cn/cp=1) interaction does notprovide anymore a good fit to the modulation e↵ect, while it still does for di↵erent values of cn/cp and for other e↵ectivecouplings [44].

experiments, and the estimated future sensitivity of 4 projected ones. The details of our procedureto obtain the exclusion plots are provided in Appendix B.

The relative sensitivity of di↵erent detectors is determined by two elements: the thresholdsvth

min of di↵erent experiments expressed in terms of the WIMP incoming velocity, and the scalinglaw of the WIMP–nucleus cross section o↵ di↵erent targets.

The former element explains the steep rise of all the exclusion plot curves at low WIMPmasses, which corresponds to the case when vth

min approaches the value of the escape velocityin the lab rest frame, and is sensitive to experimental features close to the energy threshold thatare typically a↵ected by uncertainties, such as e�ciencies, acceptances and charge/light yields.With the assumptions listed in Appendix B, among the experiments included in our analysisthe ones with the lowest velocity thresholds turn out to be DS50, CRESST–II, CDMSlite andCDEX. In particular, for m�=1 GeV we have vth

min,DS 50 ' 450 km/s, vthmin,CRES S T�II ' 480 km/s

(for scatterings o↵ oxygen), vthmin,CDMS lite ' 910 km/s, vth

min,CDEX ' 1600 km/s. Assuming vlabesc '

782 km/s (see the previous Section) this implies that in our analysis only DS50 and CRESST-II(for e↵ective interactions for which argon and oxygen have a non–vanishing nuclear responsefunction) are sensitive to m� <⇠ 1 GeV. On the other hand CDMSlite and CDEX are sensitive toslightly higher masses (for instance, for m�=2 GeV vth

min,CDMS lite ' 460 km/s, vthmin,CDEX ' 850

km/s, while for m�=3 GeV vthmin,CDEX ' 580 km/s). The velocity threshold is a purely kinematical

feature that does not depend on the type of interaction and that favors experiments with the lowestvth

min at fixed m�.With the exception of very low masses, where the e↵ect of vth

min is dominant, the relativesensitivity of di↵erent detectors is determined by the scaling law of the WIMP–nucleus crosssection with di↵erent targets, which is the focus of our analysis. In particular the SI interaction(corresponding to the M e↵ective nuclear operator) favors heavy nuclei, so that the most stringent

8

XENON collaboration

Dark matter in the Universe — direct searches

Dark matter candidate…? WIMP…?

Direct Detection Direct Detection Methods and Technologies

Germanium Detectors

Figure : [KIP]

create electron hole pairs

collect charge

e.g. CoGeNT

Tobias Brueck Detection of WIMPs July 1, 2016 24

Viable regions of

parameter space

Figu

re: K

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onn

Uni

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Dire

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Dire

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Met

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2016

24

100 GeV — 2 TeV typical masses in scotogenic models

Neutrino masses and mixing

Mechanism for neutrino mass generation…?

νe νμ

ντ

ν1ν2ν3

= Vν

νeνμντ

= VPMNS

νeνμντ

VPMNS = V†ℓVν

𝓵k

νi

W±∝ (VPMNS)ik

S�`�K2i2` AMi2`p�H

�m212 [7.0; 7.84] · 10�23

m⌫2 [8.367; 8.854] · 10�12

�m213 [2.47; 2.57] · 10�21

m⌫3 [4.96; 5.07] · 10�11


✓12 [31.90; 34.98]

✓13 [8.33; 8.81]

✓23 [46.8; 51.6]

�CP [143; 251]

h�#H2 k, AMi2`p�Hb �i i?2 XXXW +QM}/2M+2 H2p2H 7Q` i?2 M2mi`BMQ K�bb2b �M/ KBtBM; T�`�K2@i2`b 2ti`�+i2/ 7`QK ;HQ#�H }ib Q7 2tT2`BK2Mi�H M2mi`BMQ /�i� (k8Ĝkd)X h?2 M2mi`BMQ K�bb2b�`2 ;Bp2M BM :2o- i?2 �M;H2b �M/ T?�b2b 2Mi2`BM; i?2 SJLa K�i`Bt �`2 ;Bp2M BM /2;`22bX

AM i?2 #�bBb r?2`2 i?2 +?�`;2/ H2TiQM umF�r� K�i`Bt Bb /B�;QM�H- i?2 KBtBM; K�i`BtU⌫ BM 1[X UjX3V Bb B/2MiB}2/ rBi? i?2 SQMi2+Q`pQ@J�FB@L�F�;�r�@a�F�i� USJLaV K�i`Bt(kj- k9)X h?2 H�ii2` +�M #2 2tT`2bb2/ �b i?2 T`Q/m+i

UPMNS =

0

B@1 0 0

0 c23 s230 �s23 c23

1

CA

0

B@c13 0 s13e�i�CP

0 1 0

�s13ei�CP 0 c13

1

CA

0

B@c12 s12 0

�s12 c12 0

0 0 1

1

CA

0

B@1 0 0

0 ei↵1 0

0 0 ei↵2

1

CA , UjXNV

r?2`2 ✓12- ✓13- �M/ ✓23 �`2 i?2 i?`22 M2mi`BMQ KBtBM; �M;H2b- �CP Bb i?2 CP @pBQH�iBM; .B`�+T?�b2- �M/ ↵1,2 �`2 irQ CP @pBQH�iBM; J�DQ`�M� T?�b2bX 1tT2`BK2Mi�H /�i�- K�BMHv 7`QKM2mi`BMQ Qb+BHH�iBQM K2�bm`2K2Mib- ;Bp2b �++2bb iQ i?2 /Bz2`2M+2b Q7 i?2 M2mi`BMQ K�bb2bb[m�`2/ �b r2HH �b iQ i?2 KBtBM; �M;H2b �M/ i?2 .B`�+ T?�b2 (k8Ĝkd)X aBM+2 BM i?2 T`2b2Mi+�b2- i?2 HB;?i2bi M2mi`BMQ `2K�BMb K�bbH2bb- i?2 2ti`�+i2/ K�bb b[m�`2/ /Bz2`2M+2b /B`2+iHvi`�MbH�i2 BMiQ BMi2`p�Hb 7Q` i?2 irQ `2K�BMBM; K�bb2b �b ;Bp2M BM h�#X kX q2 �HbQ b?Qr i?2BMi2`p�Hb 7Q` i?2 KBtBM; �M;H2b �M/ i?2 .B`�+ T?�b2X LQi2 i?�i i?2 J�DQ`�M� T?�b2b `2K�BMmM+QMbi`�BM2/ #v T`2b2Mi /�i�X

� aQì Qmi Lm@6Bi `272`2M+2b (k8Ĝkd) BM h�#H2 kX lb2 QMHv i?2 H�i2bi QM2 (kd)\ .Q r2 M22/i?2 Qi?2` QM2b\*QKTH2i2 +QM}/2M+2 H2p2H BM h�#H2 kX

6QHHQrBM; i?2 *�b�b@A#�``� T�`�K2i`Bx�iBQM (k3)- i?2 +QmTHBM;b gF �M/ g - r?B+? �`2`2bTQMbB#H2 7Q` i?2 ;2M2`�iBQM Q7 i?2 M2mi`BMQ K�bb2b- �`2 `2H�i2/ iQ i?2 T�`�K2i2`b 2Mi2`BM;1[X UjX3V i?`Qm;?

G = ULD�1/2L RD1/2

⌫ U⇤PMNS . UjXRyV

>2`2- D⌫ Bb � /B�;QM�H K�i`Bt +QMi�BMBM; i?2 M2mi`BMQ K�bb 2B;2Mp�Hm2b �M/ UPMNS Bbi?2 SJLa K�i`BtX h?2 K�i`B+2b DL �M/ UL `2H�i2 iQ i?2 HQQT BMi2;`�Hb 2p�Hm�i2/ BMi?2 K�bb 2B;2M#�bBb Ub22 6B;X 8V �M/ /2T2M/ QM i?2 T�`�K2i2`b `2H�i2/ iQ i?2 b+�H�` �M/72`KBQM b2+iQ`bX � /2i�BH2/ /Bb+mbbBQM Q7 i?2 M2mi`BMQ K�bb K�i`Bt �M/ i?2 *�b�b@A#�``�T�`�K2i`Bx�iBQM BM i?2 KQ/2H mM/2` +QMbB/2`�iBQM Bb ;Bp2M BM �TTbX � �M/ "X

Ai Bb BKTQì�Mi iQ MQi2 i?�i 1[X UjXRyV Bb #�b2/ QM i`22@H2p2H `2H�iBQMbX AM T�ìB+mH�`-i?2 /B�;QM�HBx�iBQM Q7 i?2 b+�H�` �M/ 72`KBQM b2+iQ`b 2Mi2`BM; i?2 K�i`B+2b DL �M/ UL Bb

Ĝ N Ĝ


�m212 [7.0; 7.84] · 10�23

m⌫2 [8.367; 8.854] · 10�12

�m213 [2.47; 2.57] · 10�21

m⌫3 [4.96; 5.07] · 10�11


✓12 [31.90; 34.98]

✓13 [8.33; 8.81]

✓23 [46.8; 51.6]

�CP [143; 251]



UPMNS =

0

B@1 0 0

0 c23 s230 �s23 c23

1

CA

0


0 1 0

�s13ei�CP 0 c13

1

CA

0

B@c12 s12 0

�s12 c12 0

0 0 1

1

CA

0

B@1 0 0

0 ei↵1 0

0 0 ei↵2

1

CA , UjXNV




G = ULD�1/2L RD1/2




Ĝ N Ĝ


�m212 [7.0; 7.84] · 10�23

m⌫2 [8.367; 8.854] · 10�12

�m213 [2.47; 2.57] · 10�21

m⌫3 [4.96; 5.07] · 10�11


✓12 [31.90; 34.98]

✓13 [8.33; 8.81]

✓23 [46.8; 51.6]

�CP [143; 251]



UPMNS =

0

B@1 0 0

0 c23 s230 �s23 c23

1

CA

0


0 1 0

�s13ei�CP 0 c13

1

CA

0

B@c12 s12 0

�s12 c12 0

0 0 1

1

CA

0

B@1 0 0

0 ei↵1 0

0 0 ei↵2

1

CA , UjXNV




G = ULD�1/2L RD1/2




Ĝ N Ĝ

NuF

it C

olla

bora

tion

2021

+ 2 Majorana phases…?

Extensions of the scotogenic type

νi νj

ϕ

χStandard Model + new scalars + new fermions— radiative generation of neutrino masses

“σκότος” —- “darkness”

“γεννώ” —- “generate”

symmetry— stable dark matter candidate (scalar or fermion)— implications on collider phenomenology

ℤ2

SM

SM

ϕ

χ

SM

SM

ϕ

ϕ

SM

SM

χ

χ

Verifiable radiative seesaw mechanism of neutrino mass and dark matter

Ernest Ma

Physics Department, University of California, Riverside, California 92521, USA

(Received 27 January 2006; published 14 April 2006)

Neutrino oscillations have established that neutrinos !i have very small masses. Theoretically, they are

believed to arise through the famous seesaw mechanism from their very heavy and unobservable Dirac

mass partners Ni. It is proposed here in a new minimal extension of the standard model with a second

scalar doublet ("! , "0) that the seesaw mechanism is actually radiative, and that Ni and ("! , "0) are

experimentally observable at the forthcoming Large Hadron Collider, with the bonus that the lightest of

them is also an excellent candidate for the dark matter of the Universe.

DOI: 10.1103/PhysRevD.73.077301

PACS numbers: 14.60.Pq, 95.35.+d

In the well-known canonical seesaw mechanism [1],

three heavy singlet Majorana neutrinos Ni (i " 1), 2, 3

are added to the standard model (SM) of elementary par-

ticles, so that

M#e;#;$$! " %MDM

%1N MT

D;(1)

where MD is the 3& 3 Dirac mass matrix linking the

observed neutrinos !% (% " e;#; $) to Ni, and MN is

the Majorana mass matrix of Ni. More generally [2], M!

comes from the unique dimension-five operator

L ! "fij!#!i&0 % li&!$#!j&

0 % lj&!$ ! H:c:; (2)

where (!i, li) are the usual left-handed lepton doublets

transforming as (2, %1=2) under the standard electroweak

SU#2$L&U#1$Y gauge group and #&! ;&0$ ' #2; 1=2$ is

the usual Higgs doublet of the SM. There are three and only

three tree-level realizations [3] of this operator, one of

which is of course the canonical seesaw mechanism.

There are also three generic mechanisms for obtaining

this operator in one loop [3]. Whereas the new particles

required in the three tree-level realizations are most likely

too heavy to be observed experimentally in the near future,

those involved in the one-loop realizations may in fact be

light enough to be detected, in forthcoming experiments at

the Large Hadron Collider (LHC), for example.

Consider the following minimal extension of the SM.

Under SU#2$L&U#1$Y& Z2, the particle content is given

by

#!i;li$'#2;%1=2;!$; lci'#1;1;!$; Ni'#1;0;%$;(3)

#&! ;&0$ ' #2; 1=2;!$; #"! ;"0$ ' #2; 1=2;%$: (4)

Note that the new particles, i.e. Ni and the scalar doublet

("! , "0), are odd under Z2. A previously proposed model

[4] of neutrino mass shares the same particle content of this

model, but the extra symmetry assumed there is global

lepton number, which is broken explicitly but softly by

the unique bilinear term #2"y"! H:c: in the Higgs po-

tential. Here, Z2 is an exact symmetry, in analogy with the

well-known R-parity of the minimal supersymmetric stan-

dard model (MSSM), hence this term is strictly forbidden.

As a result, "0 has zero vacuum expectation value and

there is no Dirac mass linking !i withNj. Neutrinos remain

massless at tree level as in the SM.

The Yukawa interactions of this model are given by

L Y " fij#&%!i!#&0li$lcj ! hij#!i"

0 % lj"!$Nj ! H:c:

(5)

In addition, the Majorana mass term

12MiNiNi! H:c:

and the quartic scalar term

12'5#"y"$

2 ! H:c:

are allowed. Hence the one-loop radiative generation of

M! is possible, as depicted in Fig. 1. This diagram was

discussed in Ref. [3], but without recognizing the crucial

role of the exact Z2 symmetry being considered here.

The immediate consequence of the exact Z2 symmetry

of this model is the appearance of a lightest stable particle

(LSP). This can be either bosonic, i.e. the lighter of the two

mass eigenstates of Re"0 and Im"0 , or fermionic, i.e. the

lightest mass eigenstate of N1;2;3. The latter possibility was

first proposed in a different model [5], where neutrino

masses are radiatively generated in three loops with the

addition of two charged scalar singlets.

FIG. 1. One-loop generation of neutrino mass.

PHYSICAL REVIEW D 73, 077301 (2006)

1550-7998=2006=73(7)=077301(3)$23.00077301-1

2006 The American Physical Society

First and simplest scotogenic model:

SM + scalar doublet + 3 fermionic singlets

Models with radiative neutrino masses and viable dark mattercandidatesDiego Restrepo⇤, Oscar Zapata†,

Instituto de Fısica, Universidad de Antioquia,Calle 70 No. 52-21, Medellın, Colombia

Carlos E. Yaguna‡Institut fur Theoretische Physik, Universitat Munster,

Wilhelm-Klemm-Straße 9, D-48149 Munster, GermanyOctober 14, 2013

AbstractWe provide a list of particle physics models at the TeV-scale that are compatible with

neutrino masses and dark matter. In these models, the Standard Model particle content is

extended with a small number ( 4) of scalar and fermion fields transforming as singlets,

doublets or triplets under SU(2), and neutrino masses are generated radiatively via 1-loop

diagrams. The dark matter candidates are stabilized by a Z2 symmetry and are in general

mixtures of the neutral components of such new multiplets. We describe the particle content

of each of these models and determine the conditions under which they are consistent with

current data. We find a total of 35 viable models, most of which have not been previously

studied in the literature. There is a great potential to test these models at the LHC not

only due to the TeV-scale masses of the new fields but also because about half of the viable

models contain particles with exotic electric charges, which give rise to background-free

signals. Our results should serve as a first step for detailed analysis of models that can

simultaneously account for dark matter and neutrino masses.1 IntroductionThe evidence for physics beyond the Standard Model rests on two pillars: neutrino masses

and dark matter, both solidly supported by the experimental data. Cosmological observations

show that about 25% of the energy-density of the Universe consists of a new form of matter

usually called dark matter [1, 2]. The elementary particle responsible for it should be neutral

and stable and, to be consistent with structure formation, it must behave as cold dark matter.

⇤[email protected]†[email protected]‡[email protected]

1

arX

iv:1

308.

3655

v2 [

hep-

ph]

11 O

ct 2

013

Classification of models w.r.t.particle content and topologies

JHEP 11 (2013) 011

The model T1-2A 1 2 F � S

SU(2)L 2 2 1 2 1

U(1)Y @R R y R y

h�#H2 R, �//BiBQM�H }2H/ +QMi2Mi Q7 i?2 KQ/2H hR@k�X

�i i?2 QM2 HQQT H2p2H �b r2HH �b i?2 bi�#BHBiv Q7 i?2 /�`F K�ii2` +�M/B/�i2X �HH bi�M/�`/KQ/2Hb }2H/b �`2 2p2M mM/2` i?2 KB``Q` bvKK2i`vX h?2 �//BiBQM�H }2H/ +QMi2Mi BM+Hm/BM;i?2B` `2bT2+iBp2 `2T`2b2Mi�iBQMb mM/2` SU(2)L⇥U(1)Y Bb bmKK�`Bx2/ BM h�#H2 RX �++Q`/BM;iQ i?2 +H�bbB}+�iBQM Q7 _27X (d)- i?Bb bT2+B}+ b+QiQ;2MB+ KQ/2H Bb H�#2HH2/ ǳhR@k�Ǵ- r?2`2i?2 ǳhRǴ `272`b iQ XXX- r?BH2 i?2 ǳk�Ǵ XXX h?2 ǳhR@kǴ iQTQHQ;v +Q``2bTQM/b iQ i?2 �//BiBQMQ7 irQ 72`KBQMb �M/ irQ b+�H�`bX h?2 ǳ�Ǵ K2�Mb i?�i i?2 KQ/2H Bb #mBHi rBi? irQ bBM;H2ib-QM2 72`KBQMB+ �M/ QM2 b+�H�`- �M/ irQ /Qm#H2ib- �HbQ QM2 72`KBQMB+ �M/ QM2 7`QK i?2 b+�H�`}2H/X

� _2+�HH r?v i?2 KQ/2H Bb /m##2/ ǴhR@k�Ǵ- b22 _27X (d)XXX

AM i?Bb a2+iBQM- r2 rBHH #`B2~v BMi`Q/m+2 i?2 /Bz2`2Mi b2+iQ`b- T`2b2Mi i?2 +Q``2bTQM/BM;G�;`�M;B�M- �M/ b2i i?2 MQi�iBQMX

kXR h?2 b+�H�` b2+iQ`h?2 b+�H�` b2+iQ` Q7 i?2 KQ/2H +QMbBbib Q7 i?2 ai�M/�`/ JQ/2H >B;;b /Qm#H2i H- i?2 �/@/BiBQM�H bBM;H2i S- �M/ i?2 �//BiBQM�H /Qm#H2i �X h?2v +�``v +?�`;2b �b ;Bp2M BM h�#H2RX lTQM 2H2+i`Qr2�F bvKK2i`v #`2�FBM;- i?2 /Qm#H2ib +�M #2 2tT�M/2/ BMiQ +QKTQM2Mib�++Q`/BM; iQ

H =

G+

1p2

⇥v + h0 + iG0

⇤!, � =

�+

1p2

⇥�0 + iA0

⇤!

. UkXRV

>2`2- h0 Bb i?2 ai�M/�`/@JQ/2H >B;;b #QbQM- G0 �M/ G+ �`2 i?2 :QH/biQM2 #QbQMb- �M/v =

p2hHi ⇡ 246 :2o /2MQi2b i?2 p�+mmK 2tT2+i�iBQM p�Hm2X JQ`2Qp2`- �0 �M/ A0 �`2

CP @2p2M �M/ CP @Q// M2mi`�H b+�H�`b- �M/ �+ Bb � +?�`;2/ b+�H�`X LQi2 i?�i i?2 �//BiBQM�Hb+�H�`b �`2 MQi >B;;b #QbQMb BM i?2 b2Mb2 Q7 bvKK2i`v #`2�FBM;- r2 b?�HH `272` iQ i?2KbBKTHv �b b+�H�`b i?`Qm;?Qmi i?2 T`2b2Mi T�T2`X

h?2 b+�H�` TQi2MiB�H Q7 i?2 KQ/2H Bb ;Bp2M #v

�Lscalar = µ2H

��H��2 + �H

��H��4 + 1

2µ2SS

2 + �4SS4 + µ2

�

��2 + �4�

��4 + 1

2�SS

2��H��2

+ ��

��2��H

��2 + �0�

��H�†��2 + 1

2�00�

n�H�†�2 + h.c.

o+ T

nSH�† + h.c.

o.

UkXkV

h?2 }`bi irQ i2`Kb �`2 i?2 mbm�H ai�M/�`/ JQ/2H T�`i `2H�i2/ iQ i?2 >B;;b /Qm#H2i H-rBi? i?2 K�bb T�`�K2i2` µ2

H �M/ i?2 >B;;b b2H7@+QmTHBM; �H X �7i2` 2H2+i`Qr2�F bvKK2i`v#`2�FBM;- �i i?2 i`22@H2p2H- i?2 mbm�H KBMBKBx�iBQM `2H�iBQM BM i?2 >B;;b b2+iQ`-

m2h0 = � 2µ2

H = 2�Hv2 , UkXjV

Ĝ j Ĝ

fermionic doublet + singlet

scalar doublet + singlet

−ℒscalar = μ2H H

2+λH H

4+

12

μ2SS2+λ4SS4+μ2

Φ Φ2+λ4Φ Φ

4+

12

λSS2 H2

+λΦ Φ2

H2+λ′ Φ HΦ†

2+

12

λ′ ′ Φ{(HΦ†)2 + h . c . }+T{SHΦ† + h . c . }

−ℒfermion = −i2 (Ψ1σμDμΨ1 + Ψ2σμDμΨ2) +

12

MFF2+MΨΨ1Ψ2+y1Ψ1HF+y2Ψ2HF + h . c .

−ℒint = giΨΨ2LiS+gi

FΦLiF+giRL c

RiΦ†Ψ1

23 parameters in model Lagrangian — need for an efficient parameter space study…

The model T1-2A — scalar sector

H =G+

1

2[v + h0 + iG0] Φ =

ϕ+

1

2[ϕ0 + iA0] S

ℳ2ϕ =

μ2S + 1

2 v2λS vT

vT μ2Φ + 1

2 v2λL

(ϕ01

ϕ02) = Uϕ ( S

ϕ0)

Higgs boson + 2 neutral scalars + 1 pseudoscalar + 1 charged scalar — mixing between scalar and doublet (for the neutral scalars) — one-loop corrections to the masses amount typically to a few percent

mNLOϕ0

1− mLO

ϕ01

mLOϕ0

1

The model T1-2A — fermion sector

ℳχ =MF vy1 vy2

y1 0 MΨ

y2 MΨ 0

χ01

χ02

χ03

= Uχ

FΨ1

Ψ2

3 neutral Majorana fermions + 1 charged fermion — mixing between scalar and doublet (for the neutral fermion) — one-loop corrections to the masses amount typically to a few percent

Ψ1 = (Ψ01

Ψ−1 ) Ψ2 =

−(Ψ−2 )†

(Ψ02)†

F

mNLOχ0

1− mLO

χ01

mLOχ0

1

Neutrino masses and coupling parameters

νi νj

ϕ0n

χ0k

νi νj

ϕ0n

χ0k

νi νj

ϕ0n

χ0k

giF gj

F giF gj

Ψ giΨ gj

Ψ

∼ gjF mFk

B0(0; mFk, mϕn

) giF 𝒢 = (g1

Ψ g2Ψ g3

Ψ

g1F g2

F g3F)ℳν = 𝒢t MLoop 𝒢

Neutrino mass matrix

MLoop 𝒢𝒢tmFk

16π2B0(0; mχk

, mϕn)gj

F giF

arX

iv:h

ep-p

h/01

0306

5v2

7 N

ov 2

001

Oscillating

neutrino

s andµ → e, γ

J.A. Casas1∗and A. Iba

rra1,2†

1 Instituto

de Estruc

turade la

Materia, CS

IC

Serrano 123,

28006 Madrid

2 Department o

f Physics,

Theoretic

al Physics

, Universi

ty of Oxford

1 KebleRoad

, OxfordOX1

3NP,Unit

ed Kingdom.

Abstrac

t

If neutrin

o massesand

mixings are

suitable to expla

in the atmospheric and

solarneut

rinofluxe

s, this am

ounts to

contributi

ons to FCN

C processes,

in par-

ticular µ

→ e, γ.If th

e theory is su

persymmetric

andthe o

riginof th

e massesis

a see-saw mechan

ism, weshow

thatthe pred

ictionfor BR(µ

→ e, γ)is in gen-

erallarge

r than the expe

rimentaluppe

r bound, e

specially if the

largest Yu

kawa

coupling

is O(1) andthe solar

dataare expla

inedby a large

angleMSW

ef-

fect,whic

h recent analy

ses suggest as the prefe

rredscena

rio.Our analy

sis is

bottom-up and complete

ly general, i

.e. itis ba

sed juston obser

vablelow-e

nergy

data. The

workgene

ralizes previ

ous results of the litera

ture,ident

ifying the

dominantcontr

ibutions.

Applicatio

n of the resul

ts to scenarios

withappr

oxi-

mate top-n

eutrino unifi

cation, lik

e SO(10)

models, rule

s outmost o

f them unles

s

the leptonic Yuka

wa matrices satis

fy verypreci

se requirements.

Otherpossi

ble

ways-out,

like gauge mediat

ed SUSYbreak

ing,are also

discussed.

March2001

IEM-FT-211/

01

OUTP-01

-11P

IFT-UAM

/CSIC-01

-08

hep-ph/01

03065

∗E-mail: alber

to@makok

i.iem.cs

ic.es

†E-mail: a.iba

rra@phys

ics.ox.a

c.uk

𝒢 = UL D−1/2L R D1/2

ν U*PMNS

Neutrino masses and mixing angles

Efficient parameter space exploration thanks to Casas-Ibarra parametrization

Rotation matrix

Nucl. Phys. B 618 (2001) 171

UL D−1/2L𝒢

The model T1-2A — recap

χ01 , χ0

2 , χ03 , χ±ϕ0

1 , ϕ02 , A0, ϕ±Standard Model + +

FermionsScalars

SQBMi n, ~✓n

✓n+1i = G

�✓ni ,

�✓K�ti � ✓KBM

i

��

Ln+1(~✓n+1, ~O)

µ < Ln+1(~✓n+1, ~O)

Ln(~✓n, ~O)6�BH, `2bi�ì �i n am++2bb, n ! n+ 1

µ 2 [0, 1]

6B;m`2 d, AHHmbi`�iBQM Q7 i?2 J*J* �H;Q`Bi?K miBHBx�iBQM


�H [0.1; 0.4]

µ2S - µ2

� [0.5⇥ 106; 4⇥ 106]

T [�1000; 1000]

��- �0�- �00

� [�2; 2]

�S - �4S - �4� [�2; 2]


MF - M [700; 2000]

y1- y2 [�1.2; 1.2]

giR Ui = 1, 2V [�1.2; 1.2]

g3R [�2.0; 2.0]

r [�1; 1]

h�#H2 j, AM/2T2M/2Mi BMTmi T�`�K2i2`b Q7 Qm` J*J* b+�MX AM �//BiBQM iQ i?2 K�tBKmKBMi2`p�Hb- r2 �HbQ BM/B+�i2 i?2 ǳDmKT bBx2Ǵ- �b r2HH �b i?2 mM/2`HvBM; `�M/QK /Bbi`B#miBQMX�HH /BK2MbBQM7mH [m�MiBiB2b �`2 ;Bp2M BM :2oX

�++Q`/BM; iQ i?2 J�`FQp *?�BM JQMi2 *�`HQ i2+?MB[m2- 2�+? T�`�K2i2` TQBMi Bb `�M@/QKHv +?Qb2M BM i?2 pB+BMBiv Q7 i?2 T`2pBQmb TQBMi- r?BH2 +2ì�BM Qp2`�HH HBKBib �`2 `2bT2+i2/�b ;Bp2M BM h�#bX j �M/ kX h?2 `2bmHiBM; p�Hm2b Q7 ~�pQm`- HQr@2M2`;v- �M/ /�`F K�ii2` `2@H�i2/ Q#b2`p�#H2 �`2 i?2M +QKT�`2/ iQ i?2 `2bT2+iBp2 2tT2`BK2Mi�HHv �HHQr2/ BMi2`p�Hb ;Bp2MBM h�#X 9 BM i2`Kb Q7 � HBF2HB?QQ/ p�Hm2X h?2 +?Qb2M TQBMi Bb i?2M �++2Ti2/ Q` `2D2+i2/ #�b2/QM i?2 +QKT�`BbQM rBi? i?2 HBF2HB?QQ/ Q7 i?2 T`2pBQmb TQBMiX

AM T`�+iB+2- 2�+? +QMbi`�BMi HBbi2/ BM h�#X 9 H2�/b iQ � HBF2HB?QQ/ p�Hm2 �bbQ+B�i2/ iQ i?2bT2+B}+ +QMbi`�BMi- i�FBM; BMiQ �++QmMi i?2 2tT2`BK2Mi�H mM+2ì�BMiv �i i?2 XXXW +QM}/2M+2

Ĝ Rk Ĝ


�m212 [7.0; 7.84] · 10�23

m⌫2 [8.367; 8.854] · 10�12

�m213 [2.47; 2.57] · 10�21

m⌫3 [4.96; 5.07] · 10�11


✓12 [31.90; 34.98]

✓13 [8.33; 8.81]

✓23 [46.8; 51.6]

�CP [143; 251]

h�#H2 k, AMi2`p�Hb �i i?2 XXXW +QM}/2M+2 H2p2H 7Q` i?2 M2mi`BMQ K�bb2b �M/ KBtBM; T�`�K2@i2`b 2ti`�+i2/ 7`QK ;HQ#�H }ib Q7 2tT2`BK2Mi�H M2mi`BMQ /�i� (keĜk3)X h?2 M2mi`BMQ K�bb2b�`2 ;Bp2M BM :2o- i?2 �M;H2b �M/ T?�b2b 2Mi2`BM; i?2 SJLa K�i`Bt �`2 ;Bp2M BM /2;`22bX

AM i?2 #�bBb r?2`2 i?2 +?�`;2/ H2TiQM umF�r� K�i`Bt Bb /B�;QM�H- i?2 KBtBM; K�i`BtU⌫ BM 1[X UjX3V Bb B/2MiB}2/ rBi? i?2 SQMi2+Q`pQ@J�FB@L�F�;�r�@a�F�i� USJLaV K�i`Bt(k9- k8)X h?2 H�ii2` +�M #2 2tT`2bb2/ �b i?2 T`Q/m+i

UPMNS =

0

B@1 0 0

0 c23 s230 �s23 c23

1

CA

0


0 1 0

�s13ei�CP 0 c13

1

CA

0

B@c12 s12 0

�s12 c12 0

0 0 1

1

CA

0

B@1 0 0

0 ei↵1 0

0 0 ei↵2

1

CA , UjXNV

r?2`2 ✓12- ✓13- �M/ ✓23 �`2 i?2 i?`22 M2mi`BMQ KBtBM; �M;H2b- �CP Bb i?2 CP @pBQH�iBM; .B`�+T?�b2- �M/ ↵1,2 �`2 irQ CP @pBQH�iBM; J�DQ`�M� T?�b2bX 1tT2`BK2Mi�H /�i�- K�BMHv 7`QKM2mi`BMQ Qb+BHH�iBQM K2�bm`2K2Mib- ;Bp2b �++2bb iQ i?2 /Bz2`2M+2b Q7 i?2 M2mi`BMQ K�bb2bb[m�`2/ �b r2HH �b iQ i?2 KBtBM; �M;H2b �M/ i?2 .B`�+ T?�b2 (keĜk3)X aBM+2 BM i?2 T`2b2Mi+�b2- i?2 HB;?i2bi M2mi`BMQ `2K�BMb K�bbH2bb- i?2 2ti`�+i2/ K�bb b[m�`2/ /Bz2`2M+2b /B`2+iHvi`�MbH�i2 BMiQ BMi2`p�Hb 7Q` i?2 irQ `2K�BMBM; K�bb2b �b ;Bp2M BM h�#X kX q2 �HbQ b?Qr i?2BMi2`p�Hb 7Q` i?2 KBtBM; �M;H2b �M/ i?2 .B`�+ T?�b2X LQi2 i?�i i?2 J�DQ`�M� T?�b2b `2K�BMmM+QMbi`�BM2/ #v T`2b2Mi /�i�X

� aQì Qmi Lm@6Bi `272`2M+2b (keĜk3) BM h�#H2 kX lb2 QMHv i?2 H�i2bi QM2 (k3)\ .Q r2 M22/i?2 Qi?2` QM2b\*QKTH2i2 +QM}/2M+2 H2p2H BM h�#H2 kX

6QHHQrBM; i?2 *�b�b@A#�``� T�`�K2i`Bx�iBQM (kN)- i?2 +QmTHBM;b gF �M/ g - r?B+? �`2`2bTQMbB#H2 7Q` i?2 ;2M2`�iBQM Q7 i?2 M2mi`BMQ K�bb2b- �`2 `2H�i2/ iQ i?2 T�`�K2i2`b 2Mi2`BM;1[X UjX3V i?`Qm;?

G = ULD�1/2L RD1/2




Ĝ N Ĝ

mν1= 0

𝒢 = (g1Ψ g2

Ψ g3Ψ

g1F g2

F g3F)

NuFit Collaboration 2021

Neutrino sector and related couplingsS�`�K2i2` AMi2`p�H

�m212 [7.0; 7.84] · 10�23

m⌫2 [8.367; 8.854] · 10�12

�m213 [2.47; 2.57] · 10�21

m⌫3 [4.96; 5.07] · 10�11


✓12 [31.90; 34.98]

✓13 [8.33; 8.81]

✓23 [46.8; 51.6]

�CP [143; 251]



UPMNS =

0

B@1 0 0

0 c23 s230 �s23 c23

1

CA

0


0 1 0

�s13ei�CP 0 c13

1

CA

0

B@c12 s12 0

�s12 c12 0

0 0 1

1

CA

0

B@1 0 0

0 ei↵1 0

0 0 ei↵2

1

CA , UjXNV




G = ULD�1/2L RD1/2




Ĝ N Ĝ


�m212 [7.0; 7.84] · 10�23

m⌫2 [8.367; 8.854] · 10�12

�m213 [2.47; 2.57] · 10�21

m⌫3 [4.96; 5.07] · 10�11


✓12 [31.90; 34.98]

✓13 [8.33; 8.81]

✓23 [46.8; 51.6]

�CP [143; 251]



UPMNS =

0

B@1 0 0

0 c23 s230 �s23 c23

1

CA

0


0 1 0

�s13ei�CP 0 c13

1

CA

0

B@c12 s12 0

�s12 c12 0

0 0 1

1

CA

0

B@1 0 0

0 ei↵1 0

0 0 ei↵2

1

CA , UjXNV




G = ULD�1/2L RD1/2




Ĝ N Ĝ


�m212 [7.0; 7.84] · 10�23

m⌫2 [8.367; 8.854] · 10�12

�m213 [2.47; 2.57] · 10�21

m⌫3 [4.96; 5.07] · 10�11


✓12 [31.90; 34.98]

✓13 [8.33; 8.81]

✓23 [46.8; 51.6]

�CP [143; 251]



UPMNS =

0

B@1 0 0

0 c23 s230 �s23 c23

1

CA

0


0 1 0

�s13ei�CP 0 c13

1

CA

0

B@c12 s12 0

�s12 c12 0

0 0 1

1

CA

0

B@1 0 0

0 ei↵1 0

0 0 ei↵2

1

CA , UjXNV




G = ULD�1/2L RD1/2




Ĝ N Ĝ

Parameters and constraints

μ eϕ−

χ0k

giF,Ψ,R gj

F,Ψ,R

γ

μ e

ϕ0n , A0

χ±

γ

giF,Ψ,R gj

F,Ψ,R

+ 2 “bubble” diagrams

μ → eγ

Dark matter annihilation

SM

SM

χ01

χ01

Z0 SM

SM

χ01

χ01

ϕ01,2

giF,Ψ,R

gjF,Ψ,R

+ 2 similar diagrams for scalar dark matter+ co-annihilation diagrams

Dark matter direct detection

h0

ϕ01

q

ϕ01

qZ0h0

χ01

q

χ01

qZ0

Parameters and constraints

P#b2`p�#H2 *QMbi`�BMi

mH 125.0± 3.0 :2o

⌦CDMh2 0.1198± 0.0042

"_Uµ� ! e��V < 4.2 · 10�13

"_U⌧� ! e��V < 3.3 · 10�8

"_U⌧� ! µ��V < 4.4 · 10�8

"_Uµ� ! e�e+e�V < 1.0 · 10�12

"_U⌧� ! e�e+e�V < 2.7 · 10�8

"_U⌧� ! µ�µ+µ�V < 2.1 · 10�8

"_U⌧� ! µ+e�e�V < 1.5 · 10�8

"_U⌧� ! µ�e+e�V < 2.1 · 10�8

"_U⌧� ! e+µ�µ�V < 1.7 · 10�8

"_U⌧� ! e�µ+µ�V < 2.7 · 10�8

P#b2`p�#H2 *QMbi`�BMi

"_UZ0 ! e±µ⌥V < 7.5 · 10�7

"_UZ0 ! e±⌧⌥V < 9.8 · 10�6

"_UZ0 ! µ±⌧⌥V < 1.2 · 10�5

"_U⌧� ! e�⇡0V < 8.0 · 10�8

"_U⌧� ! µ�⇡0V < 1.1 · 10�7

"_U⌧� ! e�⌘V < 9.3 · 10�8

"_U⌧� ! e�⌘0V < 1.6 · 10�7

"_U⌧� ! µ�⌘V < 6.5 · 10�8

"_U⌧� ! µ�⌘0V < 1.3 · 10�7

CRµ!eUhBV < 4.3 · 10�12

CRµ!eUS#V < 4.6 · 10�11

CRµ!eU�mV < 7.0 · 10�13

h�#H2 9, *QMbi`�BMib bi2KKBM; 7`QK >B;;b K�bb K2�bm`2K2Mi (\ )- /�`F K�ii2` `2HB+/2MbBiv (9y)- �b r2HH �b ~�pQm` �M/ HQr@2M2`;v T`2+BbBQM /�i� (\ )X AM Qm` b2imT- BMi2`p�Hb�`2 BKTH2K2Mi2/ mbBM; � :�mbbB�M 7mM+iBQM �i i?2 XXX +QM}/2M+2 H2p2H- r?BH2 mTT2` HBKBib�`2 BKTH2K2Mi2/ rBi? � bBM;H2@bB/2/ :�mbbB�M �HHQrBM; 7Q` � RyW mM+2ì�BMiv �i i?2 XXXH2p2HX

H2p2H �M/- B7 �p�BH�#H2- i?2 i?2Q`2iB+�H mM+2ì�BMivX h?2b2 BM/BpB/m�H HBF2HB?QQ/b �`2 i?2MKmHiBTHB2/ iQ Q#i�BM i?2 Qp2`�HH HBF2HB?QQ/ �bbQ+B�i2/ iQ i?2 T�`�K2i2` TQBMiX

� *QKTH2i2 `272`2M+2b BM h�#X 9X6BM�HHv- +QKTH2i2 +QM}/2M+2 H2p2Hb BM +�TiBQMX q?�i Bb i?2 2t�+i mH +QMbi`�BMi\

h?2 7QHHQrBM; bm#b2+iBQMb T`QpB/2 � KQ`2 /2i�BH2/ /Bb+mbbBQM Q7 i?2 b2i Q7 +?Qb2M BMTmiT�`�K2i2`b �b r2HH �b i?2 �TTHB2/ +QMbi`�BMibX

� *?2+F �M/ K2MiBQM +QMp2`;2M+2 +`Bi2`B� ¨ H� :2HK�M@_m#BM- b22 _27X (9R)\

9Xj AMTmi T�`�K2i2`b

PM2 T�`�K2i2` Q7 i?2 b+�H�` b2+iQ` Bb `2H�i2/ iQ i?2 ai�M/�`/ JQ/2H >B;;b /Qm#H2i- M�K2Hvi?2 +QmTHBM; �H X �Hi?Qm;? i?2 K�bb Q7 i?2 T?vbB+�H >B;;b #QbQM Bb 2tT2`BK2Mi�HHv }t2/-r2 p�`v i?Bb T�`�K2i2`- bBM+2 �i i?2 QM2@HQQT H2p2H +QMi`B#miBQMb BM+Hm/BM; i?2 �//BiBQM�H}2H/b K�v �Hi2` i?2 >B;;b K�bbX

h?2 �//BiBQM�H b+�H�`b �`2 T�`�K2i`Bx2/ #v i?2 K�bb T�`�K2i2`b M2S �M/ M2

� 7Q` i?2bBM;H2i �M/ /Qm#H2i- `2bT2+iBp2Hv- �M/ i?2 [m�ìB+ +QmTHBM;b �S - �4S - �4�- �0

�- �M/ �00�X h?Bb

b2+iQ` Bb +QKTH2i2/ #v i?2 i`BHBM2�` +QmTHBM; T�`�K2i2` T X

Ĝ Rj Ĝ

+ d

ark

mat

ter

dire

ct d

etec

tion

limits

(XEN

ON

-1T

)

Numerical evaluation — SARAH + SPheno Staub, Porod, Goodsell (2003-2021)

— micrOMEGAs Bélanger, Boudjema, Pukhov, Semenov et al. (2004-2021)

Parameter space exploration

23 free parameters in model Lagrangian + numerous constraints

— need for an efficient algorithm… — Markov Chain Monte Carlo

ℒn = Πiℒin = Πjℒj

n Πkℒkn

n

n + 1

intervals upper limits

e.g. , mh ΩCDMh2 e.g. , DDμ → eγ

ℒn+1 ℒn> accept new point (and iterate…)

accept new point with probability ℒn+1/ℒn

✓

✗

?

JHEP10(2018)055

Publishedfor SISSA by Springer

Received: April 11, 201

8

Revised: August 31, 201

8

Accepted: September 26, 2018

Published:October 8, 2018

A singlet doublet dark matter model with radiative

neutrino masses

Sonja Esch,a Michael Klasen

a and Carlos E. Yagunab

aInstitut furTheoretische

Physik, Westfalische Wilhelms-Universitat Munster,

Wilhelm-Klemm-Straße 9, D-48149 Munster, Germany

bUniversidadPedagogica

y Tecnologicade Colombia,

Avenida Central delNorte 39-115, 150

003 Tunja, Tunja, Boyaca, C

olombia

E-mail: sonja.esch@uni-muens

ter.de, michael.klase

[email protected],

[email protected]

Abstract: We present a detailed study of a combined singlet-doub

let scalar and singlet-

doublet fermion model for dark

matter. Thesemodels have o

nly been studied separately in

the past. We show that their combination allows for the radiative generation of neutrino

masses, but that it also implies the existence of lepton-fla

vour violating (LFV) proce

sses.

We first analyse the dark matter, neutrino mass and LFV aspects separately.

We then

perform two random scans for scalar dark matter imposing Higgs mass, relic density and

neutrino mass constraints, one over the full parameter space, t

he other over regions wher

e

scalar-fermion coannihilations become important. In the first case, a large part of the

new parameter space is excluded by LFV, and the remaining models will be probed by

XENONnT. In the second case, directdetection cross section

s are generally too small, but

a substantial part of the vi

able models will betested by future LFV

experiments. Possible

constraintsfrom the LHC are also discussed.

Keywords: Beyond Standard Model, Cosmology of Theoriesbeyond the SM, Neutrino

Physics

ArXiv ePrint: 1804.03384

Open Access, c© The Authors.

Article funded by SCOAP3 .

https://doi.org/10.1007

/JHEP10(2018)055

JHEP 10 (2018) 055

JHEP10(2018)055

Figure 15. Direct detection cross section of scalar singlet dark matter as a function of its mass andits correlation with the lepton-flavour violating branching ratio BR(µ → eγ) (colours). All pointsfulfill relic density as well as neutrino mass and mixing constraints.

limit the mixing in the scalar and fermion sectors by reducing the scan ranges of |λS |, A, |y1|and y2 to values below π ·10−4. This also enhances the annihilation into lepton final states.

After imposing all experimental constraints, including those on the direct detection

cross section and lepton-flavour violating processes, we obtain the scalar-fermion couplings

gij shown in figure 16. Since A, y1 and y2 are now all small, we can obtain viable neutrino

masses for sizeable values of gij . As figure 16 shows, at least one of these couplings must

be large, but they cannot be both large at the same time, which reflects the two rather

different neutrino mass differences. Due to the weaker limits on lepton-flavour violation

for processes involving the τ lepton, the values of g13 are less restricted than those of g11and g12. As the singlet scalar mass MS,S and with it the doublet fermion mass MD,F

increase, so must the couplings gij to compensate for the propagator suppression in the

neutrino mass loops. Conversely, as λ′′D and with it the doublet scalar mass splitting and

the neutrino masses increase (cf. eq. 4.6), the corresponding scalar-fermion couplings g2imust decrease for the neutrino masses to remain in the viable range (cf. figure 17). Since

dark matter is chosen to be mostly singlet-scalar-like, the impact of dark matter constraints

and lepton flavour violation bounds is much stronger for g1i than for g2i. The couplings

g2i are mostly associated with the scalar doublet and are mostly limited by neutrino mass

limits as indicated by figure 17, which shows the need for compensating small g21 by a

larger λ′′D. The possibility of co-annihilation between scalars and fermions allows to obtain

viable relic densities even though gij can be relatively small.

– 21 –

focus on scalar dark matter

neglect coupling gR

ΩCDMh2

MCMC — Constraints…

mh0 [GeV]

mϕ01

[GeV] g1R

and predictions

MCMC studywith a total of

~80 000 points

Coupling parameters| g

2 Ψ|

|g1Ψ |

BR

(μ→

eγ)

Couplings and mainly bound

by neutrino mass constraints(via Casas-Ibarra parametrization)

gF gΨ

| g2 R|

|g1R |

Couplings constrained by

lepton-flavour violating processes(in particular )

gR

μ → eγ

Dark matter mass and nature

χ01 (64%)

ϕ01 (32%)

A0 (4%)

mDM [GeV]

JHEP10(2018)055

Published

for SISSA by

Springer

Received: A

pril 11, 20

18

Revised: Au

gust 31, 20

18

Accepted:

September 26, 2

018

Published

: October 8, 20

18

A singlet dou

blet dark matter

modelwith

radiative

neutrino masses

SonjaEsch,

a Michael Klas

ena and Carlo

s E. Yaguna

b

a Institut fur

Theoretisch

e Physik, Westfal

ischeWilhelm

s-Universit

at Munster,

Wilhelm-Klem

m-Straße 9, D-

48149Munste

r, Germany

bUniversidad

Pedagogica

y Tecnologica

de Colombia,

Avenida Centr

al delNorte

39-115, 15

0003Tunja

, Tunja, Bo

yaca,Colom

bia

E-mail: sonja.es

ch@uni-m

uenster.

de, michae

l.klasen

@uni-mue

nster.de

,

cyaguna@

gmail.co

m

Abstract:

We present a detail

ed studyof a combined

singlet-dou

blet scalar

and singlet-

doublet fer

mion model for da

rk matter.These

modelshave

only beenstudie

d separately

in

the past.We show

thattheir

combination allow

s forthe radia

tive generation

of neutrino

masses,but t

hat italso implies

the existence of lep

ton-flavour

violating (LFV

) processes

.

We first analyse the dark

matter,neutr

ino mass and LFVaspec

ts separately.

We then

perform two rando

m scansfor sc

alar dark matter

imposing Higgs

mass, relic densi

ty and

neutrino mass co

nstraints, o

ne over the

full param

eter space,

the other o

ver regions

where

scalar-ferm

ion coannihilat

ions become importa

nt. In the first case,a large

partof th

e

new parameter space

is excluded by LFV,

and the remainingmodels

will be probe

d by

XENONnT.

In the second

case,direct

detection cross

sections are

generally too small, b

ut

a substantial

part of the

viablemodels

will be test

ed by futureLFV

experiments.

Possible

constraints

fromthe LHC

are also discussed.

Keywords: Beyon

d Standard Model,

Cosmology

of Theories

beyond the SM, Neu

trino

Physics

ArXiv ePrint: 1

804.03384

Open Access, c© The Auth

ors.

Article funde

d by SCOAP3 .

https://do

i.org/10.10

07/JHEP10

(2018)055

JHEP 10 (2018) 055

Scalar dark matter mainly singlet-like

Constraints prefer fermionic dark matter

with mχ01

∼ 1.0 − 1.2 TeV

(Co)annihilation channels — fermionic dark matter

mDM = mχ01

[GeV]

Ωχ0 1h2

χ02 , χ±

ϕ01 ϕ±

(mχ01

− M )/mχ01

χ01 ≈ F (singlet)

χ01 ≈ Ψ (doublet)

Dark matter fermion is mainly doublet-like — relic density governed by co-annihilations with other fermions — “correct” value achieved for mχ0

1∼ 1 − 1.2 TeV

Direct detection

XENON nT

χ01

ϕ01

A0

mDM [GeV]

σSI DM

−nu

cl.

[cm

2 ]

XENON 1T

Upcoming experiments will constrain mainly (doublet-like) scalar dark matter

Fermionic dark matter (especially the doublet) difficult to constrain — efficient co-annihilation around allows for small couplingsmDM 1 − 1.2 TeV

Particle masses for collider studies — scalars

ϕ01 ϕ0

2

A0 ϕ±

Particle masses for collider studies — fermions

χ01 χ0

2

χ03 χ±

Summary and outlook

Scotogenic models allow to generate neutrino masses while providing viable dark matter candidates

We have studied a rather generic scotogenic setup (T1-2A)

— Markov Chain Monte Carlo study

— Interesting dark matter phenomenology

— Specific mass configurations (especially in the fermion sector)

— Interesting collider phenomenology…?

— What about anomalous magnetic moment of the muon…?

— Leptogenesis…?

— Other scotogenic frameworks…?

dark matter phenomenology in scotogenic models

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