Weakly Interacting Stable Pions Yang Bai

Theoretical Physics Department, Fermilab

Santa Fe 2010 Summer Workshop

JHEP 1002, 049 arXiv:1003.3006 arXiv:1005.0008

Richard Hill Patrick Fox Adam Martin Univ. of Chicago Fermilab Fermilab Outline

• The dark matter motivation • Review properties of pions in the SM • Stable “new” pion • Collider signatures of topological “new” pion • Conclusions

2 Matter Pie of Our Universe

Ordinary Matter 16.8%

Dark Matter 83.2% From WMAP

3 The WIMP “Miracle”

χ¯ f¯ χ¯ f¯

χ χ f f

χ¯ f¯

Kolb, Turner

χ f

1 Relic Abundance Ω σ v − DM ∼ A WIMP • “WIMP Miracle” relates the DM relic abundance to the DM annihilation cross section. 2 1 mχ Ω σ v − DM ∼ A ∼ g4 • Three conditions to have a viable thermal DM candidate. • DM is stable: requires an unbroken discrete or continuous symmetry. • DM interacts with SM particles: requires DM charged under SM gauge symmetries or via Higgs portal. • Not to overclose the universe and not ruled out by the current direct detection experiments.

5 Discrete and Continuous Symmetries in the SM • Parity, Charge Conjugation, Time Reversal • Baryon number and lepton number

6 Pions in the Standard Model

SU(3)c SU(2)W U(1)Y

(uL, dL) 3 2 1/6 two ﬂavors

uR 3 1 2/3

dR 3 1 -1/3 Chiral symmetry is spontaneously broken gs gets strong at ΛQCD 1 GeV ∼ SU(2) SU(2) L × R u¯ u + d¯ d =0 L R L R ⇓ SU(2)V

+ 0 Three pions are generated: π , π− and π

SU(2) U(1) U(1) W × Y → em 7 The Discovery of Charged Pion

• Prediction of pion existence: Yukawa ’1935 • Detected in cosmic rays captured in photographic emulsion: Cecil Powell et al. ’1947 • Produced at Univ. of California’s cyclotron in ’1948

8 The Discovery of Neutral Pion

• At the Univ. of California’s cyclotron in ’1950 • In cosmic-ray balloon experiments at Bristol Univ. in ’1950

Nov. 2009, LHC

9 G-parity in the SM

10 Deﬁnition of the G-parity

G = exp[iπI ] C 2

a a a a π τ C π (τ )∗ −→

iπI 2 a a a a S e 2 = iσ S†τ S = (τ )∗ S†(τ )∗S = τ ≡ − −

a a G a a a a π τ π S† (τ )∗ S = π τ −→ −

0 G 0 G π π π± π± −→ − −→ −

11 G-parity in the SM

Lee, Yang 1956’

12 G-parity is broken in the SM • The G-parity in the SM is broken by the chiral weak interaction and nonzero hypercharges of quarks.

a a = ψ† σ¯ (i∂ + + W τ )ψ + ψ† σ (i∂ + )ψ L L i · A ij L j R i · A R i

G 2 2 ψ ( iσ )(σ ) ψ∗ , L i −→ − ij R j G 2 2 ψ (iσ )(σ ) ψ∗ , R i −→ ij L j G a a C = A (t )∗ , A −→ A − a a G a a 2 a a 2 W τ (W τ )C = σ (W τ )σ −→

a a = ψ† σ¯ (i∂ + + W τ )ψ + ψ† σ (i∂ + )ψ L R i · A ij R j L i · A L i G-parity is broken. Pion-number is not conserved.

13 Decay of Charged Pions

µ+

π+ W +

νµ

mπ+ = 139.6 MeV mµ+ = 105.7 MeV

G2 f 2m2 (m2 m2 )2 + + F π µ π − µ 17 Γ(π µ νµ) = 3 = 2.6 10− GeV → 16πmπ ×

8 τ = 2.6 10− s ×

14 Decay of Neutral Pion

π0 Z

0 mπ = 135.0 MeV e−

2 2 2 0 + GF fπmemπ 21 4 Γ(π e e−) = = 3.4 10− GeV τ = 2.0 10− s → 16π × ×

15 Chiral Anomaly

5,a ¯ a Jµ = ψγµγ5τ ψ Classically Conserved

[Adler and Bell, Jackiw’1969] broken at quantum level γ

5,3 Jµ 2 µ 5,3 Nc e µν ρσ ∂ Jµ = = 2 µνρσF F γ A − 48π

0 π α2m3 0 0 π matches experimental data π γγ Γ(π 2γ) = 3 2 fπ A ⇒ → → 64π fπ Why not to use the G-parity to explain the stability of the dark matter particle? Dark Matter Sector

Dark QCD dark quarks, dark pions, dark baryons, ...

dark G-parity is unbroken

dark pion is the LGP Dark QCD

Introduce a new QCD-like strong dynamical gauge group with a conﬁnement scale at TeV

Λ 1 GeV QCD ∼ To keep the dark G-parity: • Make “dark quarks” vector-like under SU(2) weak gauge interaction. • Choose zero hypercharge for “dark quarks”.

19 New G-parity Odd Pions

SU(N)h SU(3)c SU(2)W U(1)Y ψˆL,R N 1 2 0

SU(2) SU(2) L × R ⇓ SU(2)V = SU(2)W

quark-level pion-level

G 2 ψˆ S ψˆC = S i γ ψˆ∗ −→ G b b G b b b b a a Aˆ T (Aˆ T )C = Aˆ (T )∗ Π Π −→ − −→ − W a G W a −→ Πa : (3) S = iτ 2 0 Stable

20 General Weak Representations Richard Hill, YB 1005.0008 SU(N)h SU(3)c SU(2)W U(1)Y ψL,R N 1 2j + 1 0

SU(2j + 1) SU(2j + 1) U(1) SU(2j + 1) U(1) L × R × B → V × B [I, G] = 0 pions ...... � 2j �10 1400 � (2j + 1)2 1 = (2J + 1) �9 � 8�

− � � � J=1 � �7 � 1000 6� GeV

� � � 2 2 2 �

J 5 M J C (J) g f 2 2 Π � � � Π 4� ∼ M 600 � � � �3 � � � �2 weak SU(2) is 200 1� � � � 0 unbroken G�odd G�even 21 General Weak Representations

W W Π2 Π2

W W 3 3 Π 2 Π Π2 Π

1 Π1 Π

(3M) (1M ) 2 5 5 4 J J 2 Γ(Π Π + 2W ) α m /(4π) f Π Π − + W + W → ∼ 2 Π Π →

2 Γ(Π(2M)) α2m3 /(4π)3f 2 Π ∼ 2 Π Π W

22 Lightest G-odd particle

From electromagnetic radiative corrections

2 2 θW m (JQ) m (J0) α Q m sin Π − Π ≈ 2 W 2

Especially m (1 1) m (10) 170 MeV Π ± − Π ≈ 2 (1 1) (10) 4GF 2 2 2 2 Γ(Π ± Π + π±) = ∆ ∆ m f → π − π π The charged parts have decay length: cτ 5 cm ≈ behave as a long-lived charged particle at colliders

The current constraints set mΠ1 > 88 GeV

Π10 is the LGP

23 Relic Abundance and Detection

Annihilation Cross section: 4 0 0 g2 σ(Π Π W W ) 4π m2 → ≈ Π To satisfy the relic abundance m 1 2 TeV Π ∼ −

Not to over-close the universe 0.1 mΠ 1 TeV

Π0 Π0

Π−

W + W + Direct Detection 45 2 10− cm

A Z+1N

A A ZN ZN 24 Resonant Effects 0 Π0 Π Patrick Fox, YB JHEP 1002, 049

Π−

W + γ γ + · · · W

A Z+1N

A A ZN ZN The typical binding energy is O(10) MeV

If the mass splitting, ∆ = mΠ mΠ0 = O(10 MeV) − − abc a b c for example, add the operator Π Π (H†t H) The resonance effects become important

DAMA/LIBRA results can be explained

25 Binding Energy is Element Dependent Patrick Fox, YB CDMS ZEPLIN XENON JHEP 1002, 049

A 23 28 74 127 129 133 184 Z N 11Na 14Si 32Ge 53 I 54 Xe 55 Cs 74 W A 23 28 74 127 129 133 184 Z+1N 12Mg 15P 33As 54 Xe 55 Cs 56 Ba 75 Re ∆m (MeV) 3.8 13.8 2.1 0.15 0.7 0.01 1.0

Sn (MeV) 13.1 14.5 8.0 7.3 9.6 7.2 6.5

Eb (MeV) 5.8 7.5 13.5 19.1 19.4 19.6 23.3

DAMA KIMS CRESST • The rDM can reconcile the apparent contradiction between DAMA and other experiments like CDMS, XENON, KIMS, ZEPLIN and CRESST. 26 Discussions

• The G-parity is unbroken from all renormalizable operators. • Two dim-ﬁve operators violate G-parity: ˆ¯ µν ˆ a ¯ a Bµν ψσ ψ/ΛUV H†t HψˆJ ψˆ/ΛUV • Introducing a Peccei-Quinn symmetry, the LGP can still have a lifetime longer than the age of our universe. • Hidden sector baryons are also stable. However, they only contribute a very small fraction of the dark matter density:

ΩB σv Π 2 2 4π α 10− Ω ∼ σv ∼ 2 ∼ Π B

27 Extension to Color SU(3) Richard Hill, YB 1005.0008

SU(N)h SU(3)c SU(2)W U(1)Y ψL,R N 8 2 0 only possible for real representation

8 8 = 8 + 10 + 10 + 1 + 8 + 27 × A A A S S S 800

27, 3 � � � � 27, 1 600 � 10, 3 � 10, 3 � 10, 1 � 10, 1 � � � � �� 8, 3 � �8, 3 �� GeV 400 8, 1 8, 1 � � � � � � � � � � � � M � � � � � 200 � � 1, 3 � �

0 G�odd G�even 28 Topological Pions vector-like representation: [Kilic, Okui, Sundrum: 0906.0577]

+ A case study at colliders Π(8,3)

1.0

They only decay via anomalies 0.8 �A,0 � g Z

0.6 Ratio gA 0.4 �A,0 � g Γ A,0 Branching Π 0.2

0.0 γ Z 100 120 140 160 180 200

M�A,0 GeV

� � Width: (1 MeV) 29 O Topological Pions

pair produced at colliders 105

104 + � q∗ q Z q e e− at D0 fb

� → → � 1000 A,0 �

A,0 100 �

�� 10 q∗ q γ at CDF p → p �

Σ 1 Tevatron �1.96 TeV di-photon resonance search 0.1 [D0: 0901.1887] 100 200 300 400 500

M�A,0 GeV

� �

30 Reconstruction

100 pT > 30 GeV M A,0 �180 GeV H > 180 GeV � T Tevatron � 5 fb�1 80 GeV 60 10 �

40 Events

0 0 50 100 150 200 250 300

Mj�Γ GeV

BG: n j + 2 γ BG: n j + 1 γ + jet fakes � � ATLAS physics TDR 31 Discovery Potential Martin and YB: 1003:3006

100 � 1 � fb � 10

1 luminosity

0.1 Tevatron � 1.96 TeV discovery 0.01 LHC � 7 TeV

5Σ LHC � 14 TeV 0.001 200 250 300 350 400 450 500

M�A,0 GeV

1 2 p > MΠ/3 , p > MΠ/6 , HT > max(� �MΠ , 3 MΠ 600 GeV) T T −

32 Conclusions

• An unbroken and nontrivial discrete symmetry emerges in a class of models with vector-like SM gauging of fermions with QCD-like strong dynamics. • The dark matter particle, LGP, could be a stable pion emerges in this class of models. • The mechanism leads to testable and distinct dark matter and LHC phenomenologies.

• New pions decaying into gluon plus photon (anomaly induced) may be found with the early data of the LHC.