Tevpa 2017.Pdf

東京大学 2004.2.12 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 TeV frontier in particle astrophysics

Hitoshi Murayama (Berkeley, Kavli IPMU) TeVPA 2017, Columbus, Aug 11, 2017 東京大学 2004.2.12 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 sub-GeV frontier in particle astrophysics

Hitoshi Murayama (Berkeley, Kavli IPMU) TeVPA 2017, Columbus, Aug 11, 2017

+Yonit Hochberg, Eric Kuﬂik

matter

Ωm changes the overall heights of the peaks matter

Ωm changes the overall heights of the peaks nDM 10 GeV =4.4 10 WIMP Miracles ⇥ mDM DM SM

DM SM

“weak” coupling correct abundance “weak” mass scale

Miracle2 nDM 10 GeV =4.4 10 WIMP Miracles ⇥ mDM DM SM ↵2 2 2v h ! i⇡m2 2 ↵ 10 ⇡ m 300 GeV DM SM ⇡

“weak” coupling correct abundance “weak” mass scale

Miracle2 sociology

• Particle physicists used to think sociology

• Particle physicists used to think • need to solve problems with the SM sociology

• Particle physicists used to think • need to solve problems with the SM • hierarchy problem, strong CP, etc sociology

• Particle physicists used to think • need to solve problems with the SM • hierarchy problem, strong CP, etc • it is great if a solution also gives dark matter candidate as an option sociology

• Particle physicists used to think • need to solve problems with the SM • hierarchy problem, strong CP, etc • it is great if a solution also gives dark matter candidate as an option • big ideas: supersymmetry, extra dim sociology

-36 -36

superCDMS ] 10 ] 10

CDMSlite 2 CMS 2 CMS 10-37 10-37

-38 -38 SIMPLE 2012 direct detection 10 CMS, 90% CL, 7 TeV, 5.0 fb-1 10 - COUPP 2012+ 10-39 10-39 W CMS, 90% CL, 8 TeV, 19.7 fb-1 Super-K W µ -1 -40 (χγ χ)(qγ q) -40 CMS, 90% CL, 7 TeV, 5.0 fb µ - 10 10 +W CoGeNT 2011 Λ2 IceCube W -41 Vector -41 CMS, 90% CL, 8 TeV, 19.7 fb-1 10 SIMPLE 2012 10 (χγ γ χ)(qγ µγ q) 10-42 10-42 µ 5 5 Axial-vector operator 2 COUPP 2012 Λ -43 -43 10 CDMS II 10 χχα (Ga )2 -1 XENON1t s µν CMS, 90% CL, 8 TeV, 19.7LHC fb -44 -44 10 3 10 4Λ XENON100 -Nucleon Cross Section [cm -45 Scalar -Nucleon Cross Section [cm -45 χ 10 LUX 2013 χ 10 Spin Dependent Spin Independent 10-46 10-46 1 10 102 103 1 10 102 103 Mχ [GeV] Mχ [GeV] Figure 5: Upper limits on the DM-nucleon cross section, at 90% CL, plotted against DM particle mass and compared with previously published results. Left: limits for the vector and scalar operators from the previous CMS analysis [10], together with results from the CoGeNT [60], SIMPLE [61], COUPP [62], CDMS [63, 64], SuperCDMS [65], XENON100 [66], and LUX [67] collaborations. The solid and hatched yellow contours show the 68% and 90% CL contours + respectively for a possible signal from CDMS [68]. Right: limits for the axial-vector operator e from the previous CMS analysis [10], together with results from the SIMPLE [61], COUPP [62], γSuper-K from [69], dSph and IceCube [70] collaborations.

Figure 6: Observed limits on the mediator mass divided by coupling, M/pgcgq, as a function of the mass of the mediator, M, assuming vector interactions and a dark matter mass of 50 GeV (blue, ﬁlled) and 500 GeV (red, hatched). The width, G, of the mediator is varied between M/3 and M/8p. The dashed lines show contours of constant coupling pgcgq.

K = s /s of 1.4 for d = 2, 3 , 1.3 for d = 4, 5 , and 1.2 for d = 6 [71]. Figure 7 shows 95% NLO LO { } { } CL limits at LO, compared to published results from ATLAS, LEP, and the Tevatron. Table 7 shows the expected and observed limits at LO and NLO for the ADD model. Figure 8 shows the expected and observed 95% CL limits on the cross-sections for scalar un- ~~ ~ 0 ~ 0 ~ 0 ~ 0 t t production, t → b f f' χ∼ / t → c χ∼ / t → W b χ∼ / t → t χ∼ Status: ICHEP 2016 1 1 1 1 1 1 1 1 1 1 600

ATLAS Preliminary s=13 TeV ~ 0 ~ 0 -1 t → t ∼χ / t → W b ∼χ t0L 13.2 fb [CONF-2016-077] [GeV] 1 1 1 1 0 1 ~ 0 -1 ∼ χ t → t ∼χ t1L 13.2 fb [CONF-2016-050] 500 1 1 m ~ 0 t → W b ∼χ -1 1 1 t2L 13.3 fb [CONF-2016-076] ~ 0 -1 t → c ∼χ MJ 3.2 fb [1604.07773] 1 1 s=8 TeV, 20 fb-1 Run 1 [1506.08616] 400 Observed limits Expected limits All limits at 95% CL

300 W t

+ m 0 ) < m b 0 ) < 0 ∼ 1 ,χ ∼ 1 χ ~ t 1 , 0 ) < m ~ t 1 ∼χ 1 m( ~ , m( t 1 ∆ ∆ 0 m( c ∼ ∆ 200 χ1

0 b f f' ∼ χ1

100 13 TeV 8 TeV LQ1(ej) x2 LQ1(ej)+LQ1(νj) β=0.5 0 coloron(jj) x2 W b ∼ LQ2(μj) x2 χ1 LQ2(μj)+LQ2(νj) β=0.5 coloron(4j) x2 LQ3(τb) x2 Leptoquarks Multijet LQ3(νb) x2 gluino(3j) x2 LQ3(τt) x2 Resonances LQ3(vt) x2 gluino(jjb) x2 0 Single LQ1 (λ=1) 200 300 400 500 600 700 800 900Single LQ2 (λ=1) 0 1 2 3 4 TeV 0 1 2 3 4 TeV ~ ADD (γ+MET), nED=4, MD m [GeV] RS Gravitons ADD (jj), nED=4, MS t1 RS1(jj), k=0.1 RS1(γγ), k=0.1 QBH, nED=6, MD=4 TeV RS1(ee,μμ), k=0.1 NR BH, nED=6, MD=4 TeV

0 1 2 3 4 TeV String Scale (jj) QBH (jj), nED=4, MD=4 TeV CMS Preliminary ADD (j+MET), nED=4, MD no sign of ADD (ee,μμ), nED=4, MS Large Extra Heavy Gauge ADD (γγ), nED=4, MS Dimensions SSM Z'(ττ) Jet Extinction Scale Bosons SSM Z'(jj) 0 1 2 3 4 5 6 7 8 9 10 new physics SSM Z'(ee)+Z'(µµ) TeV SSM W'(jj) dijets, Λ+ LL/RR SSM W'(lv) dijets, Λ- LL/RR SSM Z'(bb) dimuons, Λ+ LLIM that explains 0 1 2 3 4 5 TeV dimuons, Λ- LLIM dielectrons, Λ+ LLIM Excited dielectrons, Λ- LLIM e* (M=Λ) Fermions single e, Λ HnCM μ* (M=Λ) single μ, Λ HnCM Compositeness q* (qg) hierarchy problem! inclusive jets, Λ+ q* (qγ) f=1 b* inclusive jets, Λ- 0 1 2 3 4 5 6 TeV 0 1 2 3 4 5 6 7 8 9 1011121314151617181920TeV21 CMS Exotica Physics Group Summary – ICHEP, 2016! recent thinking recent thinking

• dark matter deﬁnitely exists recent thinking

• dark matter deﬁnitely exists • hierarchy problem may be optional? recent thinking

• dark matter deﬁnitely exists • hierarchy problem may be optional? • need to explain dark matter on its own recent thinking

• dark matter deﬁnitely exists • hierarchy problem may be optional? • need to explain dark matter on its own • perhaps we should decouple these two recent thinking

• dark matter deﬁnitely exists • hierarchy problem may be optional? • need to explain dark matter on its own • perhaps we should decouple these two • do we really need big ideas like SUSY? recent thinking

1050 1040 1030 1020 1010

100 10–10 10–20 10–30 mass [GeV]

1050 etc mirolensing 1040 1030 1020 1010

100 10–10 10–20 10–30 mass [GeV]

1050 etc mirolensing 1040 1030 1020 1010

100 10–10

10–20

–30 10 to ﬂuffy to mass [GeV]

1050 etc mirolensing 1040 1030 no good idea good no 1020 1010

100 10–10

10–20

–30 10 to ﬂuffy to mass mass [GeV] [GeV]

1050 etc mirolensing 106 1040 1030 no good idea good no 1020 100 1010

100 10–10

10–20

–30 10–10 10 to ﬂuffy to

mass mass [GeV] [GeV] defects

1050 etc mirolensing 106 non-thermal 1040

10 WIMP asymmetric DM asymmetric no good idea good no 1020 100 1010 gravitino

100 sterile neutrino sterile 10–10 vector vector mediation 10–20 w/ moduli

10–30 10–10 to ﬂuffy to axion QCD

QCD axion to ﬂuffy

10 10

–30 –10

moduli w/ –20 mediation

vector

10 –10

sterile neutrino

10 0

gravitino 10

10 10

0 SIMP 20

asymmetric DM no good idea WIMP 10

10 40

non-thermal

10 10

6 mirolensing etc 50 defects [GeV] [GeV] mass mass Seminar in Berkeley Strongly Interacting Massive Particle (SIMP)

Yonit Hochberg nDM 10 GeV =4.4 10 Miracles s ⇥ mDM DM SM ↵2 2 2v h ! i⇡m2 2 ↵ 10 ⇡ m 300 GeV DM SM ⇡ WIMP miracle! nDM 10 GeV =4.4 10 Miracles s ⇥ mDM DM SM ↵2 2 2v h ! i⇡m2 2 ↵ 10 ⇡ m 300 GeV DM SM ⇡ WIMP miracle!

DM DM

DM DM nDM 10 GeV =4.4 10 Miracles s ⇥ mDM DM SM ↵2 2 2v h ! i⇡m2 2 ↵ 10 ⇡ m 300 GeV DM SM ⇡ WIMP miracle!

DM DM 3 2 ↵ 3 2v h ! i⇡m5 DM ↵ 4⇡ ⇡ m 300MeV DM DM ⇡ nDM 10 GeV =4.4 10 Miracles s ⇥ mDM DM SM ↵2 2 2v h ! i⇡m2 2 ↵ 10 ⇡ m 300 GeV DM SM ⇡ WIMP miracle!

DM DM 3 2 ↵ 3 2v h ! i⇡m5 DM ↵ 4⇡ ⇡ m 300MeV DM DM ⇡ SIMP miracle! nDM 10 GeV =4.4 10 Miracles s ⇥ mDM DM SM ↵2 2 2v h ! i⇡m2 2 ↵ 10 ⇡ m 300 GeV DM SM ⇡ WIMP miracle!

DM DM 3 2 ↵ 3 2v h ! i⇡m5 DM ↵ 4⇡ Hochberg, Kuﬂik, ⇡ Volansky, Wacker m 300MeVarXiv:1402.5143 DM DM ⇡ SIMP miracle! LEE-WEINBERG FREEZE-OUT Back of the envelope calculation H ann ' |freezeout T 2 H ann ndm v 2 2 ' Mpl ' h i ! ↵2 mdmndm mpnb v ⇠ 2 2 2 h i ! ' mdm

nb ⌘bs ⇠ Eric Kuﬂik ⌘ T /m s T 3 b ' eq p ' 2 2 Teq↵ mdm ann 3 H 2 ' xF ' MplxF 3→2 LEE-WEINBERG FREEZE-OUT Back of the envelope calculation H ann ' |freezeout T 2 H ann ndm v 2 2 ' Mpl ' h i ! ↵2 mdmndm mpnb v ⇠ 2 2 2 h i ! ' mdm

nb ⌘bs ⇠ Eric Kuﬂik ⌘ T /m s T 3 b ' eq p ' 2 2 Teq↵ mdm ann 3 H 2 ' xF ' MplxF 3→2 LEE-WEINBERG FREEZE-OUT Back of the envelope calculation H ann ' |freezeout T 2 2 2 H ann ndm v 3 2 ' Mpl ' h i ! ↵2 mdmndm mpnb v ⇠ 2 2 2 h i ! ' mdm

nb ⌘bs ⇠ Eric Kuﬂik ⌘ T /m s T 3 b ' eq p ' 2 2 Teq↵ mdm ann 3 H 2 ' xF ' MplxF 3→2 LEE-WEINBERG FREEZE-OUT Back of the envelope calculation H ann ' |freezeout T 2 2 2 H ann ndm v 3 2 ' Mpl ' h i !

3 2 ↵ mdmndm mpnb v ⇠ 3 2 5 h i ! ' mdm

nb ⌘bs ⇠ Eric Kuﬂik ⌘ T /m s T 3 b ' eq p ' T 2 ↵3 m2 eq H dm ann ' x4 m ' M x2 F ⇥ dm pl F nDM 10 GeV =4.4 10 SIMPlest Miracles ⇥ mDM

• Not only the mass scale is similar to QCD DM DM • dynamics itself can be QCD! Miracle3 DM • DM = pions = qq¯ • e.g. SU(4)/Sp(4) = S5 DM DM 1 µ chiral = 2 Tr@ U †@µU L 16f⇡ 8N = c ✏ ✏µ⌫⇢⇡a@ ⇡b@ ⇡c@ ⇡d@ ⇡e + O(⇡7) LWZW 15⇡2f 5 abcde µ ⌫ ⇢ ⇡ ⇡ (G/H) =0 5 6 nDM 10 GeV =4.4 10 SIMPlest Miracles ⇥ mDM

• Not only the mass scale is similar to QCD DM DM • dynamics itself can be QCD! Miracle3 DM • DM = pions = qq¯ • e.g. SU(4)/Sp(4) = S5 DM DM 1 µ = Tr@ U †@ U Lchiral 16f 2 µ +HM ⇡ arXiv:1411.3727 8N = c ✏ ✏µ⌫⇢⇡a@ ⇡b@ ⇡c@ ⇡d@ ⇡e + O(⇡7) LWZW 15⇡2f 5 abcde µ ⌫ ⇢ ⇡ ⇡ (G/H) =0 5 6 SIMPlest Miracle

• SU(2) gauge theory with four doublets • SU(4)=SO(6) ﬂavor symmetry • ⟨qi qj⟩≠0 breaks it to Sp(2)=SO(5) • coset space SO(6)/SO(5)=S5 5 • π5(S )=ℤ ⇒ Wess-Zumino term μνρσ a b c d e • �WZ=εabcde ε π ∂μπ ∂νπ ∂ρπ ∂σπ SIMPlest Miracle

E. Witten / Global aspects of current algebra 425 • SU(Nc) gauge theory • π5(SU(Nf))=ℤ (Nf ≥3)

Sp(Nc) gauge theory • (a) (b) (c) Fig. 1. A particle orbit 3' on the two-sphere (part (a)) boundsWitten the discs D (part (b)) and D' (part (c)). • π5(SU(2Nf)/Sp(Nf))=ℤ (Nf≥2) D or D' (the curve 7 could continuously be looped around the sphere or turned inside out). Working with D' we would get • SO(Nc) gauge theory exp(ia Aidx i ) = exp( , ) (9) π5(SU(Nf)/SO(Nf))=ℤ (Nf≥3) • 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 also, non-abelian right-handvector bosonsside of (8) or(vector (9) in a Feynman SIMP) path integral, we must require that they +S-M Choi, HM beLee, equal. Y. This Mambrini, is equivalent M.to Pierre 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 only if c~ is an integer or half-integer. This is Dirac~s quantization condition for the 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. LAGRANGIANS

Quark theory

1 1 = F a F µ⌫a +¯q iDq m J ijq q + h.c. Lquark 4 µ⌫ i 6 i 2 Q i j

Sigma theory

2 iN f⇡ µ 1 3 c 5 = Tr@ ⌃ @ ⌃† mQµ TrJ⌃+h.c. E.Tr( Witten⌃ /† dGlobal⌃) aspects of current algebra 425 Sigma 16 µ 240⇡2 L 2 Z Pion theory

(a) (b) (c) 2 2 1 m m Fig.1 1. A particle orbit 3' on the two-sphere (part (a)) bounds the discs D (part (b)) and D' (part (c)). = Tr@ ⇡@µ⇡ ⇡ Tr⇡2 + ⇡ Tr⇡4 Tr ⇡2@µ⇡@ ⇡ ⇡@µ⇡⇡@ ⇡ Lpion 4 µ 4 12f 2 6f 2 µ µ ⇡ D or ⇡D' (the curve 7 could continuously be looped around the sphere or turned 2Nc µ⌫⇢ inside out).6 Working with D' we would get + 2 5 ✏ Tr [⇡@µ⇡@⌫ ⇡@⇢⇡@⇡]+ (⇡ ) 15⇡ f⇡ O exp(ia Aidx i ) = exp( , ) (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)

F = fQwijkt m d.Y ijkt" . ( 11 )

Quark theory

1 1 = F a F µ⌫a +¯q iDq m J ijq q + h.c. Lquark 4 µ⌫ i 6 i 2 Q i j

Sigma theory

2 iN f⇡ µ 1 3 c 5 = Tr@ ⌃ @ ⌃† mQµ TrJ⌃+h.c. E.Tr( Witten⌃ /† dGlobal⌃) aspects of current algebra 425 Sigma 16 µ 240⇡2 L 2 Z Pion theory

1 =exp(iafD+DF~jdY~iJ). (10)

F = fQwijkt m d.Y ijkt" . ( 11 )

SU(2Nf )/Sp(2Nf ) 10 102

10 ] g / m⇡ . 2⇡f⇡ 2 6 cm Sp(2), N = 2 [

π f f / 1 π π Sp(4), Nf = 2 m / m 4 Sp(8), Nf = 2

Sp(16), Nf = 2 scatter 10-1 σ 2

0 10-2 10-2 10-1 1 10

mπ [GeV]

m⇡ 3/10 m⇡ Solid curves: solution to Boltzmann eq. f⇡ / scatter 9/5 m⇡ Dashed curves: along that solution m⇡ / The Results

SU(2Nf )/Sp(2Nf ) 10 102

10 ] g / m⇡ . 2⇡f⇡ 2 6 cm Sp(2), N = 2 [

π f f / 1 π π Sp(4), Nf = 2 m / m 4 Sp(8), Nf = 2

Sp(16), Nf = 2 scatter 10-1 σ 2

0 10-2 10-2 10-1 1 10

mπ [GeV]

m⇡ 3/10 m⇡ Solid curves: solution to Boltzmann eq. f⇡ / scatter 9/5 m⇡ Dashed curves: along that solution m⇡ / The Results

SU(Nf )×SU(Nf )/SU(Nf )(SU(Nf ) broken) 10 102

10 ] g / m⇡ . 2⇡f⇡ 2

6 cm [ π f / SU(3), Nf = 3 1 π π m / m 4 SU(5), Nf = 3 SU(10), Nf = 3 scatter

10-1 σ 2

0 10-2 10-2 10-1 1 10

mπ [GeV]

m⇡ 3/10 m⇡ Solid curves: solution to Boltzmann eq. f⇡ / scatter 9/5 m⇡ Dashed curves: along that solution m⇡ / The Results

SU(NF)/SO(NF) 10 102

8 10 ] g

m⇡ 2⇡f⇡ /

. 2 6 cm [ π f / SO(6)c, NF = 3 1 π π m / m SO(10) , N = 3 4 c F

SO(20) , N = 3 scatter

c F σ 10-1 2

0 10-2 10-2 10-1 1 10

mπ [GeV]

m⇡ 3/10 m⇡ Solid curves: solution to Boltzmann eq. f⇡ / scatter 9/5 m⇡ Dashed curves: along that solution m⇡ / self interaction

• σ/m~cm2/g~10–24cm2 / 300MeV • ﬂattens the cusps in NFW proﬁle • actually desirable for dwarf galaxies?

cm2 0.27b 1.5 = m ⇡ g 100MeV if totally decoupled

Tdm

Carlson, Hall and Machacek, Astrophys. J. 398, 43 (1992) Tsm

• 3→2 annihilations without heat exchange is excluded by structure formation, [de Laix, Scherrer and Schaefer, Astrophys. J. 452, 495 (1995)] communication

DM DM • 3 to 2 annihilation DM • excess entropy must be transferred to e±, γ DM DM • need communication at some level • leads to experimental signal communication

DM DM • 3 to 2 annihilation DM • excess entropy must be transferred to e±, γ DM DM • need communication at some level DM DM • leads to experimental signal

SM entropy SM vector portal

2 2 photon dark QCDe e (iv) g (the coupling(iv) g of(the the coupling mediator of to the DM). mediator to DM). Standard Model with SIMP dark In most of theIn parameter most of the space parameter only restricted space only combi- restricted combi- nations of thesenations four parameters of these four are parameters relevant for are relevantpro- for pro- + + photon duction in e eduction collisions; in e wee describecollisions; this we in describe more detail this in more detail + ( ) + ( ) e A0 ⇤ e A0 ⇤ in Sec. III. Thein spin Sec. and III. TheCP properties spin and CP of theproperties mediator of the mediator ¯ ¯ and DM particlesand also DM have particles a (very) also limited have a (very)e↵ect on limited their e↵ect on their production rates,production but will rates, have abut more will significant have a more e↵ect significant e↵ect ✏ FIG. 1: +E/ productionFIG. 1: + channelsE/ production for LDM channels coupled for through LDM coupledonµ⌫ through comparisonson to comparisons other experimental to other constraints, experimental as constraints, will as will a light mediator.a lightLeft: mediator.ResonantLeft: ⌥(3SResonant) production, ⌥(3S followed)B production,µ⌫ FD followed 2cW the couplings ofthe the couplings mediator of to the other mediator SM particles. to other SMFor particles. For by decay to by+ decay through to + an on- through or o↵-shell an on- mediator. or o↵-shellthe mediator. rest of thethe paper, rest the of the “dark paper, matter” the “dark particle, matter”, can particle, , can Right: The focusRight: of thisThe paper focus – of non-resonant this paper – non-resonant+ pro- + pro- + + be taken to representbe taken any to hidden-sector represent any state hidden-sector that couples state that couples duction in e eductioncollisions, in e throughe collisions, an on- through or o↵-shell an on- light or o↵-shell light ( ) ( ) to the mediatorto and the mediator is invisible and in detectors;is invisible in in particu- detectors; in particu- mediator alsoA0 ⇤ .mediator (Noteaxion thatA portal:0 ⇤ in. this (Note paper,+Katelin that the in this symbol Schutz, paper,A0 theis Robert symbol A 0 McGeheeis in preparation used for vector,used pseudo-vector, for vector, scalar,pseudo-vector, and pseudo-scalar scalar, and me- pseudo-scalarlar, it me- does notlar, have it does to be not a (dominant) have to be a component (dominant) of component of diators.) diators.) the DM. the DM. The simplest exampleThe simplest of such example a setup of is such DM a that setup does is DM that does not interact withnot interact the SM withforces, the but SM that forces, nevertheless but that nevertheless a mono-photona triggermono-photon during trigger the entire during course the of entire data coursehas of interactions data has with interactions ordinary with matter ordinary through matter a hidden through a hidden taking. taking. photon. In thisphoton scenario,. In the thisA scenario,0 is the massive the A0 is mediator the massive mediator The rest of theThe paper rest is of organized the paper as is follows. organized In Sec. as follows. II of In a Sec. broken II Abelianof a broken gauge Abelian group, U gauge(1)0,inthehidden group, U(1)0,inthehidden we give a briefwe theoretical give a brief overview theoretical of LDM overview coupled of LDMsector, coupled and hassector, a small and kinetic has a mixing, small kinetic"/ cos mixing,✓W ,with"/ cos ✓W ,with through a lightthrough mediator. a light Sec. mediator. III contains Sec. a III more contains de- aSM more hypercharge, de- SMU hypercharge,(1)Y [42–44,U 56,(1) 60–62].Y [42–44, SM 56, fermions 60–62]. SM fermions tailed discussiontailed of the discussion production of the of production such LDM at of low-such LDMwith at charge low- qiwithcouple charge to theqi coupleA0 with to coupling the A0 with strength coupling strength + + energy e e colliders.energy e Ine Sec.colliders. IV we describe In Sec. IV the weBA describeBAR thege B=A"BeqARi. Thege variables= "eqi." The, g variables, m, and"m, gA0,arem, the and freemA0 are the free search [37], andsearch extend [37], the and results extend to the place results constraints to place constraintsparameters ofparameters the model. of We the restrict model. We restrict on LDM. In Sec.on LDM. V we In compare Sec. V our we results compare to our existing results to existing constraints suchconstraints as LEP, rare such decays, as LEP, beam-dump rare decays, exper- beam-dump exper- g < p4⇡, g(perturbativity) < p4⇡, (perturbativity)(1) (1) iments, and directiments, detection and direct experiments. detection In experiments. Sec. VI we In Sec. VI we + + estimate the reachestimate of a the similar reach search of a similar in a future searche ine a futurein ordere e to guaranteein order calculability to guarantee of calculability the model. of Such the a model. Such a collider such ascollider Belle II. such We as conclude Belle II. in We Sec. conclude VII. A shortin Sec. VII.constraint A short is alsoconstraint equivalent is also to equivalentimposing toA0 /m imposingA0 . 1 A0 /mA0 . 1 appendix discussesappendix the constraints discusses the on constraints invisibly decaying on invisiblywhich decaying is necessarywhich for is the necessaryA0 to have for the a particleA0 to have descrip- a particle descrip- hidden photonshidden for some photons additional for some scenarios. additional scenarios. tion. We willtion. refer in We the will following refer in to the this following restriction to this as restriction as the “perturbativity”the “perturbativity” constraint. constraint. In this paper,In we this discuss paper, this we prototype discuss this model prototype as well model as well II. LIGHT DARKII. LIGHT MATTER DARK WITH MATTER A LIGHT WITH A LIGHTas more generalas LDM more models general with LDM vector, models pseudo-vector, with vector, pseudo-vector, MEDIATOR MEDIATOR scalar, and pseudo-scalarscalar, and pseudo-scalar mediators. We mediators. stress that We in stress that in UV completeUV models, complete scalar models, and pseudo-scalar scalar and pseudo-scalar medi- medi- A LDM particle,A LDM in a hidden particle, sector in a that hidden couples sector weakly that couplesators weakly genericallyators couple generically to SM couple fermions to SMthrough fermions mix- through mix- to ordinary matterto ordinary through matter a light, through neutral a light, boson neutral (the bosoning with (the a Higgsing with boson, a Higgs and consequently boson, and theirconsequently cou- their cou- mediator), ismediator), part of many is part well-motivated of many well-motivated frameworks frameworkspling to electronspling is to proportional electrons is to proportional the electron to Yukawa, the electron Yukawa, 6 6 + + g y 3 g10 y. As3 a result,10 . low-energy As a result,e low-energye col- e e col- that have receivedthat significant have received theoretical significant and theoretical experimen- and experimen-e / e ⇠ ⇥ e / e ⇠ ⇥ tal attention intal recent attention years, in see recent e.g. years, [38–55] see and e.g. refer- [38–55]liders and refer- are realisticallyliders are unlikely realistically to be unlikely sensitive to to be them. sensitive to them. ences therein.ences A light therein. mediator A light may mediator play a significant may play a significantNonetheless, sinceNonetheless, more intricate since more scalar intricate sectors scalar may al- sectors may al- role in settingrole the in DM setting relic densitythe DM [56, relic 57], density or in [56, alle- 57], orlow in for alle- significantlylow for larger significantly couplings, larger we include couplings, them we for include them for viating possibleviating problems possible with problems small-scale with structure small-scale in structurecompleteness. in completeness. ⇤CDM cosmology⇤CDM [58, cosmology 59]. [58, 59]. For simplicityFor we consider simplicity only we fermionic consider only LDM, fermionic as the LDM, as the The hidden sectorThe may hidden generally sector may contain generally a multitude contain of a multitudedi↵erences of betweendi↵erences fermion between and scalar fermion production and scalar are production are states with complicatedstates with interactions complicated among interactions themselves. among themselves.very minor. Wevery do minor. not consider We do models not consider with a models t-channel with a t-channel However, forHowever, the context for of the this context paper, of it this is su paper,cient it ismediator sucient (suchmediator as light (such neutralino as light production neutralino through production through to characterizeto it characterize by a simple it model by a with simple just model two parti-with justselectron two parti- exchange).selectron In exchange). these, the In mediator these, the would mediator be would be cles, the DM particlecles, the DMand particle the mediator andA the0 (which, mediator withA0 (which,electrically with chargedelectrically and so charged could not and be so light. could not be light. abuse of notation,abuse may of notation, refer to a may generic refer (pseudo-)vector, to a generic (pseudo-)vector, or (pseudo-)scalar,or (pseudo-)scalar, and does not and necessarily does not indicate necessarily a indicate a III. PRODUCTIONIII. PRODUCTION OF LIGHT DARK OF LIGHT MATTER DARK MATTER hidden photon),hidden and four photon), parameters: and four parameters: + + AT e e COLLIDERSAT e e COLLIDERS (i) m (the DM(i) mass)m (the DM mass) Fig. 1 illustratesFig. the 1 illustrates production the of production + E/ events of at+ E/ events at (ii) mA0 (the mediator(ii) mA0 (the mass) mediator mass) + + low-energy e elow-energy colliderse ine LDM colliders scenarios. in LDM The scenarios. chan- The chan- (iii) ge (the coupling(iii) ge of(the the coupling mediator of to the electrons) mediator to electrons)nel shown on thenel left shown of Fig. on the 1 is left the of resonant Fig. 1 is production the resonant production Kinetically mixed U(1)

• e.g., the SIMPlest model SU(4)/Sp(4) = S5 SU(2) gauge group with Nf=2 (4 doublets) • gauge U(1)=SO(2) (q+,q+,q ,q ) ⊂ SO(2) ×SO(3) ⊂ SO(5)=Sp(4) ++ 0 0 0 • maintains degeneracy of (⇡ ,⇡,⇡x,⇡y,⇡z ) quarks • near degeneracy of pions ✏ for co-annihilation µ⌫ Bµ⌫ FD 2cW 1

10-1

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10-8 10-1 1 101 102 103 e+ e– colliders

50 ab–1! e+ e– colliders

50 ab–1!

e (iv) g (the coupling of the mediator to DM). In most of the parameter space only restricted combi- nations of these four parameters are relevant for pro- + duction in e e collisions; we describe this in more detail + ( ) e A0 ⇤ in Sec. III. The spin and CP properties of the mediator ¯ and DM particles also have a (very) limited e↵ect on their production rates, but will have a more significant e↵ect FIG. 1: +E/ production channels for LDM coupled through on comparisons to other experimental constraints, as will a light mediator. Left: Resonant ⌥(3S) production, followed the couplings of the mediator to other SM particles. For by decay to + through an on- or o↵-shell mediator. the rest of the paper, the “dark matter” particle, , can Right: The focus of this paper – non-resonant + pro- + be taken to represent any hidden-sector state that couples duction in e e collisions, through an on- or o↵-shell light ( ) to the mediator and is invisible in detectors; in particu- mediator A0 ⇤ . (Note that in this paper, the symbol A0 is used for vector, pseudo-vector, scalar, and pseudo-scalar me- lar, it does not have to be a (dominant) component of diators.) the DM. The simplest example of such a setup is DM that does not interact with the SM forces, but that nevertheless a mono-photon trigger during the entire course of data has interactions with ordinary matter through a hidden taking. photon. In this scenario, the A0 is the massive mediator The rest of the paper is organized as follows. In Sec. II of a broken Abelian gauge group, U(1)0,inthehidden we give a brief theoretical overview of LDM coupled sector, and has a small kinetic mixing, "/ cos ✓W ,with through a light mediator. Sec. III contains a more de- SM hypercharge, U(1)Y [42–44, 56, 60–62]. SM fermions tailed discussion of the production of such LDM at low- with charge qi couple to the A0 with coupling strength + energy e e colliders. In Sec. IV we describe the BABAR ge = "eqi. The variables ", g, m, and mA0 are the free search [37], and extend the results to place constraints parameters of the model. We restrict on LDM. In Sec. V we compare our results to existing constraints such as LEP, rare decays, beam-dump exper- g < p4⇡, (perturbativity) (1) iments, and direct detection experiments. In Sec. VI we + estimate the reach of a similar search in a future e e in order to guarantee calculability of the model. Such a collider such as Belle II. We conclude in Sec. VII. A short constraint is also equivalent to imposing A0 /mA0 . 1 appendix discusses the constraints on invisibly decaying which is necessary for the A0 to have a particle descrip- hidden photons for some additional scenarios. tion. We will refer in the following to this restriction as the “perturbativity” constraint. In this paper, we discuss this prototype model as well II. LIGHT DARK MATTER WITH A LIGHT as more general LDM models with vector, pseudo-vector, MEDIATOR scalar, and pseudo-scalar mediators. We stress that in UV complete models, scalar and pseudo-scalar medi- A LDM particle, in a hidden sector that couples weakly ators generically couple to SM fermions through mix- to ordinary matter through a light, neutral boson (the ing with a Higgs boson, and consequently their cou- mediator), is part of many well-motivated frameworks pling to electrons is proportional to the electron Yukawa, 6 + g y 3 10 . As a result, low-energy e e col- that have received significant theoretical and experimen- e / e ⇠ ⇥ tal attention in recent years, see e.g. [38–55] and refer- liders are realistically unlikely to be sensitive to them. ences therein. A light mediator may play a significant Nonetheless, since more intricate scalar sectors may al- role in setting the DM relic density [56, 57], or in alle- low for significantly larger couplings, we include them for viating possible problems with small-scale structure in completeness. ⇤CDM cosmology [58, 59]. For simplicity we consider only fermionic LDM, as the The hidden sector may generally contain a multitude of di↵erences between fermion and scalar production are states with complicated interactions among themselves. very minor. We do not consider models with a t-channel However, for the context of this paper, it is sucient mediator (such as light neutralino production through to characterize it by a simple model with just two parti- selectron exchange). In these, the mediator would be cles, the DM particle and the mediator A0 (which, with electrically charged and so could not be light. abuse of notation, may refer to a generic (pseudo-)vector, or (pseudo-)scalar, and does not necessarily indicate a III. PRODUCTION OF LIGHT DARK MATTER hidden photon), and four parameters: + AT e e COLLIDERS (i) m (the DM mass) Fig. 1 illustrates the production of + E/ events at (ii) mA0 (the mediator mass) + low-energy e e colliders in LDM scenarios. The chan- (iii) ge (the coupling of the mediator to electrons) nel shown on the left of Fig. 1 is the resonant production e+ e– colliders

50 ab–1!

e (iv) g (the coupling of the mediator to DM). In most of the parameter space only restricted combi- nations of these four parameters are relevant for pro- + 2 ductionps in e e collisions;M we describe this in more detail + ( ) inv e A0 ⇤ E in= Sec. III. The1 spin and CP properties of the mediator ¯ and DM2 particles also haves a (very) limited e↵ect on their production✓ rates, but will have◆ a more significant e↵ect FIG. 1: +E/ production channels for LDM coupled through on comparisons to other experimental constraints, as will a light mediator. Left: Resonant ⌥(3S) production, followed the couplings of the mediator to other SM particles. For by decay to + through an on- or o↵-shell mediator. the rest of the paper, the “dark matter” particle, , can Right: The focus of this paper – non-resonant + pro- + be taken to represent any hidden-sector state that couples duction in e e collisions, through an on- or o↵-shell light ( ) to the mediator and is invisible in detectors; in particu- mediator A0 ⇤ . (Note that in this paper, the symbol A0 is used for vector, pseudo-vector, scalar, and pseudo-scalar me- lar, it does not have to be a (dominant) component of diators.) the DM. The simplest example of such a setup is DM that does not interact with the SM forces, but that nevertheless a mono-photon trigger during the entire course of data has interactions with ordinary matter through a hidden taking. photon. In this scenario, the A0 is the massive mediator The rest of the paper is organized as follows. In Sec. II of a broken Abelian gauge group, U(1)0,inthehidden we give a brief theoretical overview of LDM coupled sector, and has a small kinetic mixing, "/ cos ✓W ,with through a light mediator. Sec. III contains a more de- SM hypercharge, U(1)Y [42–44, 56, 60–62]. SM fermions tailed discussion of the production of such LDM at low- with charge qi couple to the A0 with coupling strength + energy e e colliders. In Sec. IV we describe the BABAR ge = "eqi. The variables ", g, m, and mA0 are the free search [37], and extend the results to place constraints parameters of the model. We restrict on LDM. In Sec. V we compare our results to existing constraints such as LEP, rare decays, beam-dump exper- g < p4⇡, (perturbativity) (1) iments, and direct detection experiments. In Sec. VI we + estimate the reach of a similar search in a future e e in order to guarantee calculability of the model. Such a collider such as Belle II. We conclude in Sec. VII. A short constraint is also equivalent to imposing A0 /mA0 . 1 appendix discusses the constraints on invisibly decaying which is necessary for the A0 to have a particle descrip- hidden photons for some additional scenarios. tion. We will refer in the following to this restriction as the “perturbativity” constraint. In this paper, we discuss this prototype model as well II. LIGHT DARK MATTER WITH A LIGHT as more general LDM models with vector, pseudo-vector, MEDIATOR scalar, and pseudo-scalar mediators. We stress that in UV complete models, scalar and pseudo-scalar medi- A LDM particle, in a hidden sector that couples weakly ators generically couple to SM fermions through mix- to ordinary matter through a light, neutral boson (the ing with a Higgs boson, and consequently their cou- mediator), is part of many well-motivated frameworks pling to electrons is proportional to the electron Yukawa, 6 + g y 3 10 . As a result, low-energy e e col- that have received significant theoretical and experimen- e / e ⇠ ⇥ tal attention in recent years, see e.g. [38–55] and refer- liders are realistically unlikely to be sensitive to them. ences therein. A light mediator may play a significant Nonetheless, since more intricate scalar sectors may al- role in setting the DM relic density [56, 57], or in alle- low for significantly larger couplings, we include them for viating possible problems with small-scale structure in completeness. ⇤CDM cosmology [58, 59]. For simplicity we consider only fermionic LDM, as the The hidden sector may generally contain a multitude of di↵erences between fermion and scalar production are states with complicated interactions among themselves. very minor. We do not consider models with a t-channel However, for the context of this paper, it is sucient mediator (such as light neutralino production through to characterize it by a simple model with just two parti- selectron exchange). In these, the mediator would be cles, the DM particle and the mediator A0 (which, with electrically charged and so could not be light. abuse of notation, may refer to a generic (pseudo-)vector, or (pseudo-)scalar, and does not necessarily indicate a III. PRODUCTION OF LIGHT DARK MATTER hidden photon), and four parameters: + AT e e COLLIDERS (i) m (the DM mass) Fig. 1 illustrates the production of + E/ events at (ii) mA0 (the mediator mass) + low-energy e e colliders in LDM scenarios. The chan- (iii) ge (the coupling of the mediator to electrons) nel shown on the left of Fig. 1 is the resonant production 5 3 10 ● ● 10 ● ● ● ● ● ● ● ● ● ● 2 ● 10 ● 4 ● ● 10 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 10 ● ● ● ● ● 3 10 ● 1 ●●

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Discovery of these states at LHC is therefore difficult. May explain null results. Roni Harnik and Zackaria Chacko, JHU workshop 2017 in Budapest Twin Higgs • degenerate u, d, s, c, b, no CKM mixing • SU(5) ﬂavor symmetry • Make all leptons > GeV • charged pions don’t decay by W-boson • hyper charge assignment: Y–(B–L)/2 • anomaly-free • all quarks and leptons have charge ±1/2 • neutral pions don’t decay into γ γ Twin Higgs • degenerate u, d, s, c, b, no CKM mixing • SU(5) ﬂavor symmetry • Make all leptons > GeV • charged pions don’t decay by W-boson • hyper charge assignment: Y–(B–L)/2 • anomaly-free • all quarks and leptons have charge ±1/2 • neutral pions don’t decay into γ γ Can solve hierarchy problem, too1 Conclusion

• surprisingly an old theory for dark matter • SIMP Miracle3 • mass ~ QCD • coupling ~ QCD • theory ~ QCD • can solve problem with DM proﬁle • very rich phenomenology • Exciting dark spectroscopy • May also solve the hierarchy problem