Composite Dark Matter and the Higgs - ectstar.eu · Composite Dark Matter and the Higgs...
Transcript of Composite Dark Matter and the Higgs - ectstar.eu · Composite Dark Matter and the Higgs...
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Composite Dark Matter and the Higgs
G.Cacciapaglia (IPNL)
14/9/2017 @ ETC* Trento
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Do we still need BSM?
�m2h ⇠ g2
16⇡2M2
NPh
We have a pretty good idea of the mechanism
But, we don’t know how to protect it:
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Do we still need BSM?
�m2h ⇠ g2
16⇡2M2
NPh
Compositeness is a way to dynamically protect the Higgs mechanism!
Compositeness scale
E
vSM ⇠ 246 GeV
⇤C ⇠ 4⇡vSM
Composite scalars
No scalars =
No hierarchy problem!
3 TeV
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Compositeness, and the Higgs boson
G ! HGoldstones include the longitudinal d.o.f. of W and Z
the Higgs is a heavy bound state (singlet under H)
QCD template:
⇡ pions
� sigma
HGSU(2)L ⇥ U(1)Y
U(1)em
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Compositeness, and the Higgs boson
G ! HGoldstones include the longitudinal d.o.f. of W and Z
the Higgs is a pseudo-Goldstone (pNGB)
QCD template:
⇡ pions
� sigma
HG
SU(2)L ⇥ U(1)Y
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Compositeness, and the Higgs boson
Strong dynamics
Electroweak gauging
It’s a story of alignment
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Compositeness, and the Higgs boson
sin ✓ ⇠ v
f
v ⇠ f
v ⌧ f
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The FCD approachDefine a confining gauge group (GTC)
Add in N fermions charged under the confining group GTC
Assign SM quantum numbers to the fermions (thus providing embedding in the global symmetry)
Couple them to SM fermions
G.C., F.Sannino 1402.0233
Guides EFT construction!
Lattice results can be used! See Enrico’s talk
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Models with a pion-Higgs allow a mass term for the fermions!
The FCD approach
m h i EW preserving vacuum
Gauge-invariant mass term
We will be interested in non-chiral theories (“real” in Roberto’s talk)
Good news for Lattice: chiral limit not needed!
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The FCD approach
GTC GF SM
RTC RF RSM
RTC is real: GF = h i ji
h i ji
h i jipseudo-real: GF =
complex: GF =
SU(N ) SU(N ) ! SO(N )
SU(2N ) SU(2N ) ! Sp(2N )
SU(N )2 SU(N )
2 ! SU(N )
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The FCD approach
coset GTC TF Higgs doublets
pNGBs
SU(4)/Sp(4) Sp(2N) fund 1 5
SU(5)/SO(5) SU(4) 6 1 14
SU(4)xSU(4)/SU(4)
SU(N) fund 2 15
SU(6)/Sp(6) Sp(2N) fund 2 14
Minimal!
G.C., T.Ma 1508.07014
G.C., M.Lespinasse in prep.
Dugan, Georgi, Kaplan 1985!!!
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vSM ⇠ f sin ✓
f
⇤ ⇠ 4⇡f
⇤flavour
100 GeV
1 TeV
10 TeV
100.000 TeV
EWSB
Condensation scale (extra pions)
Vector resonances, …
Flavour scale
} Conformal region
} Top partners?
Are large baryon anomalous dimensions consistent with CFT?
What are they composite of? (QCD colour…)
What generates the Yukawas?
The hot potato: flavour!
They might, or might not, play a role in the naturalness of the
pion-Higgs potential!
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Composite Dark Matter
Some pions may be stable due to residual unbroken global symmetries
Stable techni-baryons may give rise to asymmetric DM S.Nussinov
Phys.Lett. B165, 55 (1985)
See Michele’s talk
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Compositeness: DM and the Higgs!
HiggsDM ???
One dynamics to rule the all!
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SU(4)/Sp(4)?
LWZW =
d cos ✓
64⇡2
⌘
f
⇣g2 Wµ⌫
˜Wµ⌫ � g02Bµ⌫
˜Bµ⌫⌘
No linear couplings in the chiral Lagrangian, however it decays via the WZW interactions.
Frigerio, Pomarol, Riva, Urbano 1204.2808
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SU(4)/Sp(4)?
LWZW =
d cos ✓
64⇡2
⌘
f
⇣g2 Wµ⌫
˜Wµ⌫ � g02Bµ⌫
˜Bµ⌫⌘
✓ =⇡
2TC limit:
-1 1
In the TC limit, Sp(4) C U(1)em x U(1)DM
� =h+ i⌘p
2is charged under the unbroken U(1)DM,
and thus stable (TIMP).
Rhyttov, Sannino 0809.0713
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A composite 2HDMG.C., T.Ma 1508.07014
SU(4)⇥ SU(4) ! SU(4)
Complex bi-doublet (2HDM)
Triplet
SU(2)R Triplet
SU(3)HC
“QCD with 4 flavours”
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A composite 2HDMG.C., T.Ma 1508.07014SU(3)HC
⌃ = eif ⇧
Is it there a parity stabilising the pions?
⌃ ! P · ⌃T · P P =
✓�2 00 ��2
◆
s ! s
H1 ! H1
H2 ! �H2
� ! ��
N ! �N
}}
Mimics the minimal case
Dark Sector!
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A composite 2HDMG.C., T.Ma 1508.07014
h�Hi = hH1 + iH2i =✓
vei� 00 vei�
◆
⌃ =
✓cos ✓ 1 ei� sin ✓ 1
�ei� sin ✓ 1 cos ✓ 1
◆
Beta can be removed by an SU(4) rotation:
Beta = relative phase of the two T-quarks!
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A composite 2HDMG.C., T.Ma 1508.07014
Vtop
(✓) = �Ctf4
8|Yt|2 sin2 ✓ +
2p2|Yt|2 sin(2✓)
h1
f+
+4p2 Im(Y ⇤
DYt) sin ✓h2
f
+2p2 Re(Y ⇤
DYt) sin(2✓)A
0
f
+ 4 Im(Y ⇤T Yt) sin
2 ✓N
0
+�0
f+ . . .
�
Potential for theta
Set to zero by phase-shift
Custodial violating VEVs!!!
4 “Yukawa” couplings!
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A composite 2HDMG.C., T.Ma 1508.07014
Vtop
(✓) = �Ctf4
8|Yt|2 sin2 ✓ +
2p2|Yt|2 sin(2✓)
h1
f+
+4p2 Im(Y ⇤
DYt) sin ✓h2
f
+2p2 Re(Y ⇤
DYt) sin(2✓)A
0
f
+ 4 Im(Y ⇤T Yt) sin
2 ✓N
0
+�0
f+ . . .
�
Potential for theta
Set to zero by phase-shift
Custodial violating VEVs!!!
4 “Yukawa” couplings!
XX
X
DM parity!
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A composite 2HDM: spectrum
The spectrum essentially depends on 2 parameters:
A Yukawa coupling;
A mass difference.
� =m L �m R
m L +m R
ms =mh
sin ✓
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A composite 2HDM: spectrum
singlet
CP-odd
charged
neutral(DM?)
N
H2
�
F⇡ = 2p2f
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A composite 2HDM: Dark-Matter
G.C., T.Ma, Y.Wu, B.Zhang 1703.06903Relic abundance:
Excluded by
overclosure
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A composite 2HDM: Dark-Matter
Direct Detection G.C., T.Ma, Y.Wu, B.Zhang 1703.06903
[GeV]DMM500 1000 1500 2000 2500 3000
))2
/(c
m p
χS
I,σ(
10
log
49−
48−
47−
46−
45−
44−
43−
42− T/Y
0 TY
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
XENON-100XENON-1TPandaX-IILUX-2016LZ-projected
= 0.0δ
Thermal relic Fixing DM relic
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A composite 2HDM: Dark-Matter
G.C., T.Ma, Y.Wu, B.Zhang 1703.06903Combined bounds:
Excluded by DD
Excluded by DD
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Lattice results
Study QCD (i.e. SU(3) gauge theory) with 12 flavours.
4 flavours are light, with mass 8 flavours are heavy, with mass
ml
mH
A.Hasenfratz, C.Rebbi, O.Witzel 1609.01401, 1611.07427
UV IR
mlmH12 flavours 4 flavours
Conformal behaviour
Chiral sym. broken (Higgs)
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A.Hasenfratz, C.Rebbi, O.Witzel 1609.01401, 1611.07427
vector axial-vector
Lattice results
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A.Hasenfratz, C.Rebbi, O.Witzel 1609.01401, 1611.07427
vector axial-vector
No sign of resonances becoming lighter in the conformal limit!
Lattice results
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Summary
Simple composite models can contain a Dark pion (and the Higgs)
Thermal relic natural for moderate tuning
Testable @ Direct Detection, but no chance @ the LHC!
More work needed to explore models/theories -> FCD a precious guide + welcome Lattice results!
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Bonus tracks
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A composite 2HDM: EWPTs
Bounds similar to minimal cases.
G.C., T.Ma 1508.07014
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A composite 2HDM: Dark-Matter
Indirect Detection G.C., T.Ma, Y.Wu, B.Zhang 1703.06903
[GeV]DMM500 1000 1500 2000 2500 3000
))-1
s3
v>
/(c
mσ
(<1
0lo
g
28−
27−
26−
25−
24−
23− T/Y
0 TY
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fermi-LAT
H.E.S.S.
WW = 0.0δ
Thermal relic abundance
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A composite 2HDM: Dark-Matter
Indirect Detection G.C., T.Ma, Y.Wu, B.Zhang 1703.06903
Fixed DM relic abundance
[GeV]DMM500 1000 1500 2000 2500 3000
))-1
s3
v>
/(c
mσ
(<1
0lo
g
28−
27−
26−
25−
24−
23− T/Y
0 TY
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fermi-LAT
H.E.S.S.
WW = 0.0δ
[GeV]DMM500 1000 1500 2000 2500 3000
))-1
s3
v>
/(c
mσ
(<1
0lo
g
31−
30−
29−
28−
27−
26−
25−
24−
23− T/Y
0 TY
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
H.E.S.S.
tt = 0.0δ
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The hot potato: flavour!
vSM ⇠ f sin ✓
f
⇤ ⇠ 4⇡f
⇤flavour
100 GeV
1 TeV
10 TeV
100.000 TeV
EWSB
Condensation scale (extra pions)
Vector resonances, …
Scale of fermion mass generation
} How can this hierarchy be generated?
Lfermions
=1
⇤2
fl.
( )(qcLqR)
+1
⇤2fl.
(qcLqR)(qcLqR) +
1
⇤2fl.
( )2
Higgs
FCNCs Higgs mass
mtop
⇠ (4⇡f)3
⇤2
fl.
sin ✓
Too small!
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The hot potato: flavour!
vSM ⇠ f sin ✓
f
⇤ ⇠ 4⇡f
⇤flavour
100 GeV
1 TeV
10 TeV
100.000 TeV
EWSB
Condensation scale (extra pions)
Vector resonances, …
Scale of fermion mass generation
} Intermediate conformal
region
( ) ! OH
dim[OH ] = dH
1
⇤d�1fl.
OHqcLqR
effective Yukawa:
mtop
⇠✓4⇡f
⇤fl.
◆d�1
4⇡f sin ✓
d ⇠ 1.
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The hot potato: flavour!
vSM ⇠ f sin ✓
f
⇤ ⇠ 4⇡f
⇤flavour
100 GeV
1 TeV
10 TeV
100.000 TeV
EWSB
Condensation scale (extra pions)
Vector resonances, …
Light fermions
} Conformal region
Multi-scale model
mc ⇠✓4⇡f
⇤fl.
◆d�1
4⇡f sin ✓
⇠ 0.01 ) d ⇠ 1.5
Still, for the top, one would need:
⇤top
⇠ 4⇡f
⇤top
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The partial compositeness paradigm
1
⇤d�1fl.
OHqcLqR �m2H ⇠
✓4⇡f
⇤fl.
◆d�4
f2
dH > 1 dH2 > 4we assume:
Let’s postulate the existence of fermionic operators:
1
⇤dF�5/2fl.
(yL qLFL + yR qRFR)
f(yL qLQL + yR qRQR) yL/Rf ⇠✓4⇡f
⇤fl.
◆dF�5/2
4⇡fwith
This dimension is not related to the Higgs!
Both irrelevant if
Kaplan Nucl.Phys. B365 (1991) 259
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The partial compositeness paradigm
f(yL qLQL + yR qRQR)
Higgs
yL yR
QqL qR
mq ⇠ yLyRf2
M2Q
f sin ✓
MQ ⇠ f ) yL, yR ⇠ 1 MQ ⇠ 4⇡f ) yL, yR ⇠ 4⇡
Top can cancel top loop, PUVC