Strongly Interacting Massive Particles with Yonit Hochberg and - - PowerPoint PPT Presentation
+ Strongly Interacting Massive Particles with Yonit Hochberg and Eric Kuflik
with Yonit Hochberg and Eric Kuflik
秋の学校「理論と観測から迫るダークマターの正体とその分布」 国立天文台 Nov 9, 2016
Hitoshi Murayama (Berkeley, Kavli IPMU)
東京大学 シンボルマーク+ロゴ タ イプ 新東大ブルー 基本形 漢字のみ 英語のみ 秋の学校「理論と観測から迫るダークマターの正体とその分布」 国立天文台 Nov 9, 2016 Hitoshi Murayama (Berkeley, Kavli IPMU)
東京大学 シンボルマーク+ロゴ タ イプ 新東大ブルー 基本形 漢字のみ 英語のみ http://nyti.ms/2ezzlp2
ELECTION 2016
Results Live Presidential Forecast Live Coverage Key States Electoral votes Fla. 29 Mich. 16 N.H. 4 N.C. 15 Pa. 20 Wis. 10 Va. 13 Ariz. 11 Colo. 9 Minn. 10 Clinton Trump Reporting 100% 94% 91% 100% 99% 99% 98% 83% 76% 92% Senate » House » Live Briefing
President » Full Results
Clinton Trump 2:33 AM ET 48% 47% 48% 47% 48% 46% 50% 45% 48% 47% 49% 48% 47% 51% 49% 49% 45% 50% 45% 45%
Dem. 47 Rep. 51 Dem. 174 Rep. 234
270 to win
fluctuations ~O(10–5) more-or-less scale invariant P(k) ∝ kns–1
gravitational attraction
everything between 0<z<1300
Planck Collaboration: Cosmological parameters
10
COSMOS HST (640 orbits: ~500hrs)
Conducting a major survey for 300 nights! First data release Feb 2017
dark matter map ~20 square degrees (2 hours of observation)
11
Now move forward to writing the 1st-year science papers with about 170
degrees
clusters used Projected mass density Radius of background galaxies from each cluster center preliminary
Search for MACHOs (Massive Compact Halo Objects) Large Magellanic Cloud
MACHO 95% cl 0.2 −6 −2 −8 −4 2 0.0 0.4 0.6 f = −7 EROS−2 + EROS−1 upper limit (95% cl) logM= 2log( /70d) tE
EROS collaboration astro-ph/0607207
fraction in the galaxy halo
(modified from Hu, Barkana, Gruzinov, astro-ph/0003365)
V = GN Mm r rB = 2 GNMm2
mass [GeV]
mirolensing etc to fluffy no good idea QCD axion
mass [GeV]
WIMP
Use the effective coupling
Leff ∼ e2 4⇡2 a fa ~ E · ~ B
4 ADMX QCD Axion SN 1987A Static EDM 1014 1012 1010 108 106 104 102 100 1020 1015 1010 105 102 104 106 108 1010 1012 1014 mass eV gd GeV2 frequency Hz
Budker et al arXiv:1306.6089
Heff (t) = −~ µ · ~ B − mu m2
const
sin(mat) × ~ sn · ~ E
SQUID pickup loop ~ Bext ~ M ~ E∗
nDM s = 4.4 × 10−10 GeV mDM hσ2→2vi ⇡ α2 m2 α ≈ 10−2 m ≈ 300 GeV
[GeV]
χ
M
1 10
2
10
3
10
]
2
χ
10
10
10
10
10
10
10
10
10
10
10
CMS, 90% CL, 8 TeV, 19.7 fb
CMS, 90% CL, 7 TeV, 5.0 fb
LUX 2013 s u p e r C D M S C D M S l i t e XENON100 COUPP 2012 SIMPLE 2012 CoGeNT 2011 CDMS II
CMS
Spin Independent
2Λ q)
µγ q )( χ
µγ χ ( Vector
3Λ 4
2)
ν µ a(G
sα χ χ Scalar
CMS, 90% CL, 8 TeV, 19.7 fb
]
2
χ
X E N O N 1 t
[GeV]
1
t ~
m
200 300 400 500 600 700 800 900
[GeV]
1
χ ∼
m
100 200 300 400 500 600
1χ ∼ W b →
1t ~ /
1χ ∼ t →
1t ~
1χ ∼ t →
1t ~
1χ ∼ W b →
1t ~
1χ ∼ c →
1t ~
=8 TeV, 20 fb s
t) < m
1χ ∼ ,
1t ~ m( ∆
W+ m
b) < m
1χ ∼ ,
1t ~ m( ∆ ) < 0
1χ ∼ ,
1t ~ m( ∆
1
χ ∼ t →
1
t ~ /
1
χ ∼ W b →
1
t ~ /
1
χ ∼ c →
1
t ~ /
1
χ ∼ b f f' →
1
t ~ production,
1
t ~
1
t ~
Status: ICHEP 2016
ATLAS Preliminary
1χ ∼ W b
1χ ∼ c
1χ ∼ b f f'
Observed limits Expected limits All limits at 95% CL
=13 TeV s [CONF-2016-077]
t0L 13.2 fb [CONF-2016-050]
t1L 13.2 fb [CONF-2016-076]
t2L 13.3 fb [1604.07773]
MJ 3.2 fb Run 1 [1506.08616]
CMS Exotica Physics Group Summary – ICHEP , 2016!
RS1(jj), k=0.1 RS1(γγ), k=0.1 1 2 3 4 coloron(jj) x2 coloron(4j) x2 gluino(3j) x2 gluino(jjb) x2 1 2 3 4RS Gravitons Multijet Resonances
SSM Z'(ττ) SSM Z'(jj) SSM Z'(ee)+Z'(µµ) SSM W'(jj) SSM W'(lv) 1 2 3 4 5Heavy Gauge Bosons
CMS Preliminary
LQ1(ej) x2 LQ1(ej)+LQ1(νj) β=0.5 LQ2(μj) x2 LQ2(μj)+LQ2(νj) β=0.5 LQ3(τb) x2 1 2 3 4Leptoquarks
e* (M=Λ) μ* (M=Λ) q* (qg) q* (qγ) f=1 1 2 3 4 5 6Excited Fermions
dijets, Λ+ LL/RR dijets, Λ- LL/RR 0 1 2 3 4 5 6 7 8 9 101112131415161718192021 ADD (γ+MET), nED=4, MD ADD (jj), nED=4, MS QBH, nED=6, MD=4 TeV NR BH, nED=6, MD=4 TeV String Scale (jj) 1 2 3 4 5 6 7 8 9 10Large Extra Dimensions
Compositeness
TeV TeV TeV TeV TeV TeV TeV13 TeV 8 TeV
LQ3(νb) x2 LQ3(τt) x2 LQ3(vt) x2 Single LQ1 (λ=1) Single LQ2 (λ=1) RS1(ee,μμ), k=0.1 SSM Z'(bb) b* QBH (jj), nED=4, MD=4 TeV ADD (j+MET), nED=4, MD ADD (ee,μμ), nED=4, MS ADD (γγ), nED=4, MS Jet Extinction Scale dimuons, Λ+ LLIM dimuons, Λ- LLIM dielectrons, Λ+ LLIM dielectrons, Λ- LLIM single e, Λ HnCM single μ, Λ HnCM inclusive jets, Λ+ inclusive jets, Λ- 1,000,000,001 1,000,000,001
1,000,000,002 1,000,000,000
1
2
us
ηDM=ηb=0 ηDM+ηb≠0 ηDM≠0 ηb≠0 ηDM=ηb=0 ηDM+ηb=0, ηDM=–ηb≠0 ηDM≠0 ηb≠0
mDM = nb nDM ΩDM Ωb mp ≈ 6 GeV × ηb ηDM mp ≈ Λe−8π2/g2
s(Λ)b0
mass [GeV]
mirolensing etc to fluffy no good idea QCD axion
mass [GeV]
asymmetric DM WIMP
“Cosmological Experiments in Superfluid Helium?”
H = −µ⇧ F 2 + F 2
z
a b m=0 m=0
H–1≈Tc–1|MPl/Tc|
dark matter!
ξ≈Tc–1|MPl/Tc|1/3
among dark matter
1 5 10 50
ν=0.70 ν=0.672 ν=0.625 ν=0.5
M (PeV)
100 0.5
1 10–4 10–2 102
ΩPDh2
WMAP
HM, Jing Shu
mass [GeV]
mirolensing etc to fluffy no good idea QCD axion
mass [GeV]
sterile neutrino asymmetric DM WIMP defects
Alexander Merle
Exclusi sion:'
[Canem*et*al.:*Phys.*Rev.*D87*(2013)*093006]*
DW'line' N1''''''''''ν+γ'
Exclusi sion:'
[Canem*et*al.:*Phys.*Rev.*D87*(2013)*093006]*
DW'line' N1''''''''''ν+γ' LyXα'bound'
[Boyarsky*et*al.:*JCAP* 0905*(2009)*012]*
Alexander Merle
mass [GeV]
mirolensing etc to fluffy no good idea QCD axion
mass [GeV]
gravitino sterile neutrino asymmetric DM WIMP defects
n3/2 s ∼ 10−12 TRH 1010GeV
10
10
10
10
10
10
1 1 10 10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
m3/2 (GeV) Tmax (GeV) 10
1
10
2
10
3
10
4
10
5
10
10
10
χ→ψµ+γ after the BBN Lyman α Forest Ωh2>1 95% C.L. B(ψµ→gg)=1 η=(6.1±0.3)×10–10 Ejet=m3/2/2 ~
Kawasaki, Kohri, Moroi, astro-ph/0408426 Viel et al, astro-ph/0501562 Moroi, HM, Yamaguchi, PLB303 (1993) 289 de Gouvêa, Moroi, HM, hep-ph/9701244
m2
3/2 =
1 3M 2
P l
✓ |F|2 + 1 2D2 ◆
φ0 ≈ T 2
eqM 3 P l
mφ !1/4 = (3 × 1011GeV) ✓ eV mφ ◆1/4
SUSY breaking (~TeV), modulus may be very light
comparable to the gravitino mass
can be dark matter (de Gouvêa, HM, Moroi, hep-ph/ 9701244)
Kusenko, Lowenstein, Yanagida
τ(φ → γγ) ∼ 1028sec ⇣ mφ 10keV ⌘−3 φ0 ≈ T 2
eqM 3 P l
mφ !1/4 = (3 × 1011GeV) ✓ eV mφ ◆1/4
SIMP
mass [GeV]
mirolensing etc to fluffy no good idea QCD axion
mass [GeV]
moduli w/ vector mediation gravitino sterile neutrino asymmetric DM WIMP defects non-thermal
nDM s = 4.4 × 10−10 GeV mDM
hσ2→2vi ⇡ α2 m2 α ≈ 10−2 m ≈ 300 GeV
hσ3→2v2i ⇡ α3 m5 m ≈ 300MeV α ≈ 4π
Hochberg, Kuflik, Volansky, Wacker arXiv:1402.5143
Back of the envelope calculation
Γann ' H|freezeout
mdmndm ∼ mpnb nb ∼ ηbs
H ' T 2 Mpl
Γann ' Teqα2 x3
F
H ' m2
dm
Mplx2
F
hσv2i3→2 ' α3 m5
dm
×mdm Γann ' T 2
eqα3
x4
F
Γann ' ndmhσv i2→2
hσv i2→2 ' α2 m2
dm
Γann ' n2
dmhσv2i3→2
s ' T 3 ηb ' Teq/mp
Eric Kuflik
, no input of scales or particle physics
A coincidence of scales
mdm ' α
eqMpl/x4 F
1
3
mdm ' α ⇥ 100 MeV α ∼ 1
Strongly interacting sub-GeV dark matter
xF ∼ 20 Eric Kuflik
52
From: Murayama Hitoshi <hitoshi@berkeley.edu> Subject: Re: model Date: April 28, 2014 at 21:31:38 PDT To: yonit.hochberg@berkeley.edu Bcc: Murayama Hitoshi <hitoshi@berkeley.edu> The absolutely SIMPlest is probably SU(2) gauge theory with six doublets = three
anomalous if gauged. The quark bilinear breaks it down to Sp(3), with 14 NGBs in the rank-two anti-symmetric tensor representation 14 of Sp(3). Because of the homotopy exact sequence, 0 = pi_5 (Sp(3)) —> pi_5 (SU(6))=Z —> pi_5 (SU(6)/Sp(3)) —> pi_4 (Sp(3))=Z2 —> pi_4 (SU(6))=0, we see that pi_5 (SU(6)/Sp(3)=Z and hence Wess-Zumino term is possible. This is of course expected because SU(6) is anomalous. Upon the common mass term, the entire 14-plet acquires the same mass. Because of the flavor quantum number, they are stable, and they have 2—>3 scattering because of the WZ term. SU(3) or SU(2), the remaining question is how to couple them to the Standard
that couples to quarks in the dark matter sector and Higgs in the Standard Model. Hitoshi 、 のメール： 、 のメール：
nDM s = 4.4 × 10−10 GeV mDM
+HM arXiv:1411.3727
scale is similar to QCD
QCD! Miracle3
LWZW = 8Nc 15⇡2f 5
π
✏abcde✏µνρσ⇡a@µ⇡b@ν⇡c@ρ⇡d@σ⇡e + O(⇡7) Lchiral = 1 16f 2
π
Tr∂µU †∂µU π5(G/H) 6= 0
(a) (b) (c)
425
D or D' (the curve 7 could continuously be looped around the sphere or turned inside out). Working with D' we would get
ia Aidx i =
, (9)
where a crucial minus sign on the right-hand side of (9) appears because ~, bounds D in a right-hand sense, but bounds D' in a left-hand sense. If we are to introduce the right-hand side of (8) or (9) in a Feynman path integral, we must require that they be equal. This is equivalent to
1 =exp(iafD+DF~jdY~iJ).
(10) Since D + D' is the whole two sphere S 2, and fs2F~jdE ij = 4~r, (10) is obeyed if and
product of electric and magnetic charges. Now let us return to our original problem. We imagine space-time to be a very large four-dimensional sphere M. A given non-linear sigma model field U is a mapping of M into the SU(3) manifold (fig. 2a). Since 7r4(SU(3)) = 0, the four-sphere in SU(3) defined by U(x) is the boundary of a five-dimensional disc Q. By analogy with the previous problem, let us try to find some object that can be integrated over Q to define an action functional. On the SU(3) manifold there is a unique fifth rank antisymmetric tensor w~jkt m that is invariant under SU(3)L × SU(3)R*. Analogous to the right-hand side of eq. (8), we define
F = fQwijkt m d.Y ijkt" . ( 11 )
* Let us first try to define w at U = 1; it can then be extended to the whole SU(3) manifold by an SU(3)L × SU(3)R transformation. At U= 1, w must be invariant under the diagonal subgroup of SU(3)L × SU(3) R that leaves fixed U = I. The tangent space to the SU(3) manifold at U = 1 can be identified with the Lie algebra of SU(3). So ~0, at U = 1, defines a fifth-order antisymmetrie invariant in the SU(3) Lie algebra. There is only one such invariant. Given five SU(3) generators A, B, C, D and E, the one such invariant is Tr ABCDE - Tr BA CDE + permutations. The SU(3)I~ × SU(3) R invariant w so defined has zero curl (c~iwjk/.,.+_ permutations=0) and for this reason (11) is invariant under infinitesimal variations of Q; there arises only the topological problem discussed in the text.
Witten
−1 2mQ Jijqiqj + h.c. Lquark = 1 4F a
µνF µνa + ¯
qii6Dqi
Lpion = 1 4Tr@µ⇡@µ⇡−m2
π
4 Tr⇡2 + m2
π
12f 2
π
Tr⇡4 − 1 6f 2
π
Tr
2Nc 15⇡2f 5
π
✏µνρσTr [⇡@µ⇡@ν⇡@ρ⇡@σ⇡] + O(⇡6)
−1 2mQµ3TrJΣ + h.c. − iNc
240π2 Z Tr(Σ†dΣ)5 LSigma = f 2
π
16Tr∂µΣ ∂µΣ†
(a) (b) (c)
425
D or D' (the curve 7 could continuously be looped around the sphere or turned inside out). Working with D' we would get
ia Aidx i =
, (9)
exp( ) exp( )
where a crucial minus sign on the right-hand side of (9) appears because ~, bounds D in a right-hand sense, but bounds D' in a left-hand sense. If we are to introduce the right-hand side of (8) or (9) in a Feynman path integral, we must require that they be equal. This is equivalent to
1 =exp(iafD+DF~jdY~iJ).
(10) Since D + D' is the whole two sphere S 2, and fs2F~jdE ij = 4~r, (10) is obeyed if and
product of electric and magnetic charges. Now let us return to our original problem. We imagine space-time to be a very large four-dimensional sphere M. A given non-linear sigma model field U is a mapping of M into the SU(3) manifold (fig. 2a). Since 7r4(SU(3)) = 0, the four-sphere in SU(3) defined by U(x) is the boundary of a five-dimensional disc Q. By analogy with the previous problem, let us try to find some object that can be integrated over Q to define an action functional. On the SU(3) manifold there is a unique fifth rank antisymmetric tensor w~jkt m that is invariant under SU(3)L × SU(3)R*. Analogous to the right-hand side of eq. (8), we define
F = fQwijkt m d.Y ijkt" . ( 11 )
* Let us first try to define w at U = 1; it can then be extended to the whole SU(3) manifold by an SU(3)L × SU(3)R transformation. At U= 1, w must be invariant under the diagonal subgroup of SU(3)L × SU(3) R that leaves fixed U = I. The tangent space to the SU(3) manifold at U = 1 can be identified with the Lie algebra of SU(3). So ~0, at U = 1, defines a fifth-order antisymmetrie invariant in the SU(3) Lie algebra. There is only one such invariant. Given five SU(3) generators A, B, C, D and E, the one such invariant is Tr ABCDE - Tr BA CDE + permutations. The SU(3)I~ × SU(3) R invariant w so defined has zero curl (c~iwjk/.,.+_ permutations=0) and for this reason (11) is invariant under infinitesimal variations of Q; there arises only the topological problem discussed in the text.
Sp(2), Nf = 2 Sp(4), Nf = 2 Sp(8), Nf = 2 Sp(16), Nf = 2
10-2 10-1 1 10 2 4 6 8 10 10-2 10-1 1 10 102 mπ [GeV] mπ/fπ SU(2Nf) / Sp(2Nf) σscatter/mπ [cm2/g]
mπ . 2πfπ
mπ fπ ∝ m3/10
π
σscatter mπ ∝ m−9/5
π
Solid curves: solution to Boltzmann eq. Dashed curves: along that solution
mπ . 2πfπ
mπ fπ ∝ m3/10
π
σscatter mπ ∝ m−9/5
π
Solid curves: solution to Boltzmann eq. Dashed curves: along that solution
SU(3), Nf = 3 SU(5), Nf = 3 SU(10), Nf = 3
10-2 10-1 1 10 2 4 6 8 10 10-2 10-1 1 10 102 mπ [GeV] mπ/fπ SU(Nf)×SU(Nf) / SU(Nf) (SU(Nf) broken) σscatter/mπ [cm2/g]
mπ . 2πfπ
mπ fπ ∝ m3/10
π
σscatter mπ ∝ m−9/5
π
Solid curves: solution to Boltzmann eq. Dashed curves: along that solution
SO(6)c, NF = 3 SO(10)c, NF = 3 SO(20)c, NF = 3 10-2 10-1 1 10 2 4 6 8 10 10-2 10-1 1 10 102 mπ [GeV] mπ/fπ SU(NF) / SO(NF) σscatter/mπ [cm2/g]
Abell 3827
σ m ≈ 1.5cm2 g = 0.27b 100MeV
Extremely we% measured cross-correlation of galaxy clusters and faint photometric galaxies First detection of the halo edge! The edge is sma%er than expected by about 20 percent (nomina%y 4-sigma confidence) Dark matter self-interactions(?!) Discussions with Dalal, Murayama and Matsumoto
SM et al (2016), ApJ
−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0r (Mpc/h)
−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0r (Mpc/h) Surface density of photometric galaxies around SDSS clusters
−1.8 −1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 r (Mpc/h) −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 r (Mpc/h) Surface density of photometric galaxies around SDSS clustersGradient
Expected
Astrophysics Particle
physics
NASA/ESA/T. Brown and J. Tumlinson (STScI)]
nominal boundary (rt ~ 76’), but more member stars actually exist inside/beyond this limit. Cumula=ve number of observable stars
Subaru/PFS enables us to measure a large number of stellar spectra over unprecedentedly wide outer areas, where DM largely dominates! ⇒ Best for studying the nature of DM
>800 stars observable
PFS FOV
Subaru/PFS Blue dots: spectroscopic targets in previous work (Walker+ 2009)
Sculptor
FoV for pervious survey
Stellar Velocity Data DM Gravita=onal Poten=al
DM Halo: J-factor =
Fit
Velocity data of >~ 800 stars enable to determine DM halo profiles very precisely! (number of stars) J-factor is determined very precisely! ⇒ nature of DM
Prime Focus Instrument Wide Field Corrector Wide Field Corrector Fiber Posi=oner (from boZom) Spectrograph Fiber Cable Metrology camera Wide Field Corrector
Prime Focus Spectrograph
67
be transferred to e±, γ
at some level
signal
excluded by structure formation, [de Laix, Scherrer and Schaefer, Astrophys. J. 452, 495 (1995)]
Tdm Tsm
Carlson, Hall and Machacek,
dark QCD with SIMP Standard Model
e−
+
γ χ
¯ χ
e−
+
γ χ
¯ χ
photon dark photon ✏γ 2cW BµνF µν
D
SU(2) gauge group with Nf=2 (4 doublets)
⊂ SO(2) ×SO(3) ⊂ SO(5)=Sp(4)
quarks
for co-annihilation
✏γ 2cW BµνF µν
D
SU(4)/Sp(4) = S5 (π++, π−−, π0
x, π0 y, π0 z)
(q+, q+, q−, q−)
10-1 1 101 102 103 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1
50 ab–1!
e− e+
γ χ
¯ χ
A0(⇤)
Eγ = √s 2 ✓ 1 − M 2
inv
s ◆
2 4 6 8
10-2 10-1 1 101 102
Eγ = √s 2 ✓ 1 − M 2
inv
s ◆
e− e+
γ χ
¯ χ
A0(⇤)
Yonit Hochberg, Eric Kuflik, HM
0.6 0.8 1.0 1.2 1.4 1.6
10-3 10-2 10-1 1 101
e− e+
γ χ
¯ χ
A0(⇤)
Yonit Hochberg, Eric Kuflik, HM
1 2 3 4 5 6 0.001 0.010 0.100 1 10 100 Minv [GeV] dσ /dMinv [fb/GeV] s = 10 GeV
Yonit Hochberg, Eric Kuflik, HM
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.001 0.010 0.100 1 10 100 1000 Minv [GeV] dσ /dMinv [fb/GeV] s = 5 GeV
Yonit Hochberg, Eric Kuflik, HM
V V ρ
× × =
V V = V V
× ×
ρn
X
n
inspired by AdS/CFT from string theory
1 0-40 c m2 1 0-40 c m2 1 0-41 c m2 1 0-41 c m2 1 0-42 c m2 1 0-42 c m2
10-1 1 101 102 103 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1
81