BBN-Implications from a metastable (sub)GeV-scale sector · Perimeter Institute with Maxim Pospelov GGI Dark Matter Workshop 2010, Florence Tuesday, June 15, 2010. Outline Part I

BBN-Implications from a metastable (sub)GeV-scale sector

Josef Pradler

Perimeter Institute

with Maxim Pospelov

GGI Dark Matter Workshop 2010, Florence

Tuesday, June 15, 2010

Outline

Part I

Part II

Big Bang Nucleosynthesis as a probe of New Physics

Based on [Pospelov, JP; Ann.Rev.Nucl.Part.Sci. 2010]

Metastable GeV-scale sector as a solution to the lithium problem

[Pospelov, JP; arXiv: 1006:xxxx]


Part I

Big Bang Nucleosynthesis as a probe of New Physics


Multipole moment l10 100 500 1000

Tem

pera

ture

Flu

ctua

tions

[K

2 ]

Angular Size

0

1000

2000

3000

4000

5000

6000

90° 2° 0.5° 0.2°

ΛCDM and Standard BBN (SBBN)

• Standard cosmological picture

=> WMAP: flat Universe filled with baryons, cold dark matter, a cosmological constant and neutrinos fits data

=> Baryon density known to better than 3% (at )z � few × 103

• Standard BBN: SM + GR

... or more precisely

[Dunkley et al., 2009]ηb(tCMB) = (6.225± 0.170)× 10−10


The Universe at the redshift of a billion:

basic assumptions for SBBN

• Universe is flat, spatially homogeneous and isotropic and dominated by radiation => GR:

(nn � np)|T�∆mnp=

12nb

H ≡ a

a=

�8πGNρ/3 � 1

2t

• Universe was “hot” enough T |init � ∆mnp = 1.293 MeV

• Particle content & their interactions given by the SM

nb

s(tBBN) =

nb

s(tCMB).




• Universe is flat, spatially homogeneous and isotropic and dominated by radiation => GR:

(nn � np)|T�∆mnp=

12nb

H ≡ a

a=

�8πGNρ/3 � 1

2t

• Universe was “hot” enough T |init � ∆mnp = 1.293 MeV

• Particle content & their interactions given by the SM

nb

s(tBBN) =

nb

s(tCMB).⇒ ηb(tCMB) as input: SBBN “parameter-free” theory




• tight kinetic coupling of nucleons/nuclei to the radiation field

dYi

dt= −H(T )T

dYi

dT=

�(ΓijYj + ΓiklYkYl + ...),

=> their abundances are found by solving the coupled set of integrated Boltzmann equations

Yi = ni/nb

Γij... generalized rates

=> nucleons/nuclei are approximately thermally distributed


6Li/H

N

7Li/H

7Be/H

3He/HT/H

D/H

Yp

H

SBBN f.o.

D b.n.

e± ann.n/p dec.! dec.

t/sec

T/keV

0.1 1 10 100 1000 104 105 106

1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

SBBN f.o.

D b.n.


T/keV1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14


SBBN predictions natural units: T9 ≡T

109 K


6Li/H

N

7Li/H

7Be/H

3He/HT/H

D/H

Yp

H

SBBN f.o.

D b.n.


t/sec

T/keV

0.1 1 10 100 1000 104 105 106

1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

SBBN f.o.

D b.n.


T/keV1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

p + n↔ D + γ



109 K


6Li/H

N

7Li/H

7Be/H

3He/HT/H

D/H

Yp

H

SBBN f.o.

D b.n.


t/sec

T/keV

0.1 1 10 100 1000 104 105 106

1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

SBBN f.o.

D b.n.


T/keV1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

p + n↔ D + γ



109 K

T9 ∼ 1


(selected) Light element observations I

• Deuterium:

- no known astrophysical source (=> monotonic evolution)

- recent FUSE measurements [Linsky et al., 2006]

wide dispersion in the local gas => potential D absorption on dust

- inference of primordial value from Quasar absorption systems recent obs.: [Pettini et al., 2008]

scatter may indicate underestimated systematics Q1243+3047

Q2206-199

SDSS1558-0331

Q0913+072

from [Olive, arXiv:1005.3955]



• Deuterium:






Q2206-199

SDSS1558-0331

Q0913+072


D/H|SBBN = (2.49 ± 0.17)× 10−5



• Deuterium:






Q2206-199

SDSS1558-0331

Q0913+072


D/H|SBBN = (2.49 ± 0.17)× 10−5 ✓


(selected) Light element observations II

• Lithium:

- produced in galactic cosmic rays => correlation with metallicity

- unlike deuterium, tiny lithium abundance forbids absorption measurements in extragalactic clouds

- measured in atmospheres of old, metal-poor halo stars (Pop II)

[Fields, Olive, 1999]


The Li-prediction in SBBN

6Li/H

N

7Li/H

7Be/H

3He/HT/H

D/H

Yp

H

SBBN f.o.

D b.n.


t/sec

T/keV

0.1 1 10 100 1000 104 105 106

1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

SBBN f.o.

D b.n.


T/keV1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

WMAP5 + new nuclear data on

7Li/H = (5.24± 0.7)× 10

−10

[Cyburt et al., 2008]

3He(α, γ)

7Be


The Li-prediction in SBBN

6Li/H

N

7Li/H

7Be/H

3He/HT/H

D/H

Yp

H

SBBN f.o.

D b.n.


t/sec

T/keV

0.1 1 10 100 1000 104 105 106

1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

SBBN f.o.

D b.n.


T/keV1000 100 10 1

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

3He +

4He→7

Be + γ

WMAP5 + new nuclear data on

7Li/H = (5.24± 0.7)× 10

−10

[Cyburt et al., 2008]

3He(α, γ)

7Be


10-5

-3.5 -3 -2.5 -2 -1.5 -1 -0.5

WMAP( )

( )

[Si/H] or [O/H]

D/H

Upper(1 )

Mean(1 )

Q1009+2956 (Bur98)

PKS 1937-1009 (Tyt96)

HS 0105+1619 (OMe01)

Q2206-199 (Pet01)

Q0347-383 (DOd01)

Q1243+3047 (Kir03)

10-10

10-9

-3.5 -3 -2.5 -2 -1.5 -1 -0.5[Fe/H]

Li/H

Adopted (95% c.l.)(Ryan et al. 2000)

WMAPRyan et al. (1999)Ryan et al. (2000)

Thevenin et al. (2001)Bonifacio et al. (2002)

[Coc et al., 2004]

7Li/H|obs = (1 ÷ 2.5)× 10

−10

• discrepancy between observations and prediction [Cyburt et al., 2008](4÷ 5)σ

SBBN

The Li-problem in SBBN

• NB: newest observations show metallicity dependence of Spite-plateau at lowest metallicities [Aoki et al., 2009; Sbordone et al. 2010, Asplund et al. 2010]


The Li-problem in SBBN #2?

• Lithium-6:

- Claim of (2σ) detections in 9 halo stars [Asplund et al., 2006]

6Li/7Li ∼ 5%

- Claim challenged [Cayrel et al., 2006]

=> Li-6 mimicked by convectivemotion of material

=> detections turn into upper limits


Light element predictions from helium to lithium span roughly 9 orders of magnitude in number

in qualitative agreement with observationsimpressive success of the hot Big Bang model

At least one quantitative problem: lithium

Solution may turn out to be of astrophysical origin but couldalso signal new physics operative during BBN


Generic ways to affect BBN

p,n Dp,n

DD2

DD1

T

He

He

Be

Li

3

7

4

7

He HeHe D

T D

Li p

3

3

D p

He n Be n

He T

3

4

7

4

7

D

Fig. from [Mukhanov, 2004]



p,n Dp,n

DD2

DD1

T

He

He

Be

Li

3

7

4

7

He HeHe D

T D

Li p

3

3

D p

He n Be n

He T

3

4

7

4

7

D


H

Change in timing



p,n Dp,n

DD2

DD1

T

He

He

Be

Li

3

7

4

7

He HeHe D

T D

Li p

3

3

D p

He n Be n

He T

3

4

7

4

7

D


H

Change in timing

X → γ/q...

�

non-equilibrium BBN



p,n Dp,n

DD2

DD1

T

He

He

Be

Li

3

7

4

7

He HeHe D

T D

Li p

3

3

D p

He n Be n

He T

3

4

7

4

7

D


H

Change in timing

X → γ/q...

�

non-equilibrium BBN

( X−)

catalyzedBBN


• defining moment in BBN: end of deuterium bottleneck

=> neutrons incorporated into helium

=> strong dependence of D and He4 on n/p - ratio

0.24 < Yp < 0.26

3He

4He 7Li

3He

D

4He

H

!!SM/!SM (T < 0.1 MeV)

!Y

/Y

SB

BN

10.80.60.40.20-0.2-0.4

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

0.24 < Yp < 0.26

3He

4He 7Li

3He

D

4He

H

!!SM/!SM (T < 0.1 MeV)

!Y

/Y

SB

BN

10.80.60.40.20-0.2-0.4

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

Generic ways to affect BBNTiming

“dark radiation”

HSBBN → H = HSBBN

�1 + ρdr/ρSM

can be translated into bound on Nν,eff


• defining moment in BBN: end of deuterium bottleneck

=> neutrons incorporated into helium

=> strong dependence of D and He4 on n/p - ratio

Generic ways to affect BBNTiming

7Li/HD/H

Yp

!Eb/Eb

!m

np/m

np

0.10.050-0.05-0.1

0.1

0.05

0

-0.05

-0.1

4!

10 !5

D/H

|SBBN

2!10 !

5

0.26

0.24 Yp|SBBN

10!10

10!10

2.5 ! 10!10

7Li/H|SBBN

“sliding couplings and mass scales”

exponential sensitivity to

- neutron/proton mass difference

- deuterium binding energy

for concrete realizations, see e.g. [Nollett, Lopez, 2002; Dimitriev et al., 2004;

Coc et al. 2007; Dent et al., 2007]


Generic ways to affect BBNNon-equilibrium BBN

• energy release during SBBN (mass conversion into nuclear binding energy)

=> marginal effect at ∼ 2 MeV/nucleon

• decays/annihilations of non-standard particles

=> a lot of work has been done!

T9 ∼ 1

e.g. [ ...., Kawasaki et al. 2004, Jedamzik 2006, Cyburt et al. 2009]

electromagnetic energy injection (“clean”)

hadronic energy injection (“messy”)

• relevant because of Dark Matter connection (residual DM annihilation)

primary decay/ann. channel


Electromagnetic energy injection

• rapid formation of em-cascade; “zeroth-generation” (IC and pair production)

pγ(Eγ) =

K0(Eγ/Elow)−1.5 for Eγ < Elow

K0(Eγ/Elow)−2.0 for Elow < Eγ < EC

0 for Eγ > EC

EC � m2e/22Tγ + γT → e− + e− :

• “break-out” photons can dissociate light elements

Tph �

7 keV for7Be + γ →3

He +4He (Eb = 1.59 MeV)

5 keV for D + γ → n + p (Eb = 2.22 MeV)

0.6 keV for4He + γ →4

He(T) + n(p) (Eb � 20 MeV)

[Protheroe, 1994]

[Kawasaki et al, 1994]


X

N

6Li/H|sec

6Li/H

(7Li+7Be)/H

D/H(3He+T)/H

Yp

T/keV100 10 1 0.1 0.01 0.001

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14


• Important secondary effect:

3H +

4He→6

Li + n

3He +

4He→6

Li + p;

[Dimopulous, 1988, Jedamzik, 2000]



• Important secondary effect:

3H +

4He→6

Li + n

3He +

4He→6

Li + p;

[Dimopulous, 1988, Jedamzik, 2000]

prim.+sec.prim.

6Li/H

10!13

10!12

10!11

10!10

!X/sec

" em

YX

/G

eV

101210111010109108107106105104

103

102

101

1

10!1

10!2

10!3

10!4

10!5

10!6

10!7


Generic ways to affect BBNCatalyzed BBN



quadrupole transitionheavily hindered



[Pospelov, J.P., Steffen 2008]


Part II

Metastable GeV-scale sector as a solution to the lithium problem


GeV-scale metastablestates X

Big BangNucleosynthesis

•

• light sector secluded from the SM => longevity of X SM

• recent attention in connectionwith cosmic ray anomalies(mediator physics)

mX ∼ O(MeV −GeV)

τX > 1 s→


Solving the Li-problem: mechanism

• inject “extra neutrons” at [Reno & Seckel 1988]T9 ∼ 0.5

7Be + n→7

Li→4He +

4He

proton burning

• classical BBN scenario with decaying X: extensive literature! e.g. [ ...., Kawasaki et al. 2004, Jedamzik 2006, Cyburt et al. 2009]

=> hadronic and electromagnetic cascades ( => “extra neutrons” )

=> large energy depositions hard to find “Li-sweet-spot” where all observational constraints respected

• => reduction of [Jedamzik 2004]nn/nb|T9∼0.5 = O(10−5) 7Be +7 LiO(1)

mX = O(100 GeV), e.g. �χ→ �G + SM


GeV-scale metastablestates X

...below the di-nucleon threshold

X → ll, π+π−, π0π0, K+K−, K0K0 . . .

• we get “extra neutrons” e.g. from

νe + p→ n + e+

”µ/νBBN” : µ− → e− + νe + νµ

”πBBN” : π− + p→ n + π0/n + γ


Pπp→n =

� ∞

tinj

exp(−Γπdec(t− tinj))Γπ

pdt � Γπpτπ± ∼ O(10−6)

πBBN : X → π+π−

• Hierarchy of scales H � Γπp � Γπ

dec � Γπstop.

Γπp = np�σv�πpn � (3× 102 s−1)

T 39 �σv�πpn

1 mb

• interconversion rate:p→ n

• efficiency of interconversion during pion lifetime:

injection of pions/baryon yields neutronsO(10) O(10−5)

T9 ∼ 0.5



• we need pion-nucleon, pion-He cross sections at threshold

=> can be extracted from measurements of the level widthsof pionic hydrogen and helium see e.g. review [Gasser, 2008]

• these cross sections receive Coulomb corrections

F (Z, v) � 2πη

1− e−2πη, η =

Zα

v

Γ1S = |ψ1S(0)|2(σv)0

=> win a factor Fpπ− � 2, F4Heπ− � 3.5 at T9 ∼ 0.5

�σiv� � F (Z, �v�)(σv)i



YX = 8, !X = 103 secX ! "+ + "!

6Li/H

"±

X

N

7Be/H

D/H

Yp

T9

1 0.1 0.01

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

YX = nX/nb



YX = 8, !X = 103 secX ! "+ + "!

6Li/H

"±

X

N

7Be/H

D/H

Yp

T9

1 0.1 0.01

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14

π− +4He→ T + n

n + p→ D + γ

YX = nX/nb



1011 ! (6Li/H)105 ! (D/H)

Yp

!

X " !+ + !!

0.26

0.25

66

4

3

2

!X/sec

YX

105104103102

100

10

1

!X/sec

YX

105104103102

100

10

1

7Li/H

!X/sec

YX

105104103102

100

10

1

!X/sec

YX

105104103102

100

10

1

YX = nX/nb



1011 ! (6Li/H)105 ! (D/H)

Yp

!

X " !+ + !!

0.26

0.25

66

4

3

2

!X/sec

YX

105104103102

100

10

1

!X/sec

YX

105104103102

100

10

1

7Li/H

!X/sec

YX

105104103102

100

10

1

!X/sec

YX

105104103102

100

10

1

π− +4He→ T + n

6Li

4He|bg+

D + γ → p + n

n + p→ D + γ

YX = nX/nb


• completely different hierarchy

• injected neutrinos redshift, oscillate and build up

=> in the numerical treatment we follow phase-space evolution

Γνp , Γν

stop � H

Pνp→n =

� ∞

tinj

Γνpdt =

13

Γνp(Tinj)

H(Tinj)∼ 2× 10−9

Γνp = npσ

νpn � 10−41 cm2 × npE2

ν

(10 MeV)2

ν/µBBN : X → µ+µ− → νe�s + . . .

• estimate on efficiency of interconversionp→ n

injection of muon decays/baryon yields neutronsO(10−5)O(104) decouples scenario from P ν

p→n << Pπp→n ν/µBBN πBBN


105 ! (D/H)Yp

!

X " µ+ + µ!

0.26

0.25

6

4

3

2 1

!X/sec

YX

104103102101

106

105

104

103

!X/sec

YX

104103102101

106

105

104

103

7Li/H

!X/sec

YX

104103102101

106

105

104

103

!X/sec

YX

104103102101

106

105

104

103

ν/µBBN : X → µ+µ− → νe�s + . . .


ν/µBBN : X → µ+µ− → νe�s + . . .

X

6Li/H

µ±

YX = 5 ! 104, !X = 8.5 ! 103 secX " µ+ + µ!

N

7Li/H

7Be/H

D/H

Yp

T9

1 0.1 0.01

1

10!2

10!4

10!6

10!8

10!10

10!12

10!14


A more comprehensive picture ...

• Stopping power of the plasma falls rapidly with temperature => pions poorly stopped for T9 � 0.35

100 MeV1 MeV

100 MeV1 MeV

10!31

103

!K±

!!±

Ein ! Elow :

"dec/"stop

T9

Ein

/M

eV

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

1000

100

10

1

⇒

Gas08Said

Brs06

!-resonance

!! + p ! !0 + n

E!/MeV

(!v

!)/

mb

300250200150100500

45

40

35

30

25

20

15

10

5

0

pion reactions enhanced



κ(Einπ , T ) ≡ Pp→n(Ein

π , T )Pp→n(T )

=1

τπ(σv)th

� ∞

0dt(σv)E(t) exp

�−

� t

0dt�

1τπγ(Eπ)

�.

! !P !

p!n(Ein, T )P !

p!n(Ethm, T )

! = 1

180 MeV

300 MeV

230 MeV

100 MeV

Ein = 10 MeV

T9

!

0.6 0.5 0.4 0.3 0.2 0.1

30

25

20

15

10

5

0

average along the “lifetime-trajectory of pions”

1011 ! (6Li/H)105 ! (D/H)

Yp

E! = 180MeV

X " !+ + !!

0.26

0.25

6

6

4

3

!X/sec

YX

105104103102

100

10

1

!X/sec

YX

105104103102

100

10

1

7Li/H

!X/sec

YX

105104103102

100

10

1

!X/sec

YX

105104103102

100

10

1

⇒∆− resonance



1011 ! (6Li/H)105 ! (D/H)

Yp

mX ! 2mK±

X " K+ + K!

6

0.26

0.25

6

4

3

!X/sec

YX

105104103102

102

101

1

10!1

!X/sec

YX

105104103102

102

101

1

10!1

7Li/H

!X/sec

YX

105104103102

102

101

1

10!1

!X/sec

YX

105104103102

102

101

1

10!1



• X decay to kaons; “s-quark exchange” reactions, e.g.

K− + p→ Σ±π∓, Σ0π0, Λπ0

K− + n→ Σ−π0, Σ0π−, Λπ−

1011 ! (6Li/H)105 ! (D/H)

Yp

mX ! 2mK±

X " K+ + K!

6

0.26

0.25

6

4

3

!X/sec

YX

105104103102

102

101

1

10!1

!X/sec

YX

105104103102

102

101

1

10!1

7Li/H

!X/sec

YX

105104103102

102

101

1

10!1

!X/sec

YX

105104103102

102

101

1

10!1


Examples of secluded sectors

α�, κ, mh� , and mV (V-portal),

LH−portal =12(∂µS)2 − V (S)− (λSS + AS)(H†

H).

A, λ, and m2S (S-portal)

• Higgs-portal (Singlet S) [McDonald 1994; Burgess et al 2001]

• Vector-portal (new broken by Higgs‘ ) [Holdom 1986]U(1)�

LV−portal = −14V 2

µν −κ

2FY

µνV µν + |Dµφ|2 − V (φ),

φ


Examples of secluded sectors

α�, κ, mh� , and mV (V-portal),

LH−portal =12(∂µS)2 − V (S)− (λSS + AS)(H†

H).

A, λ, and m2S (S-portal)

• Higgs-portal (Singlet S) [McDonald 1994; Burgess et al 2001]

• Vector-portal (new broken by Higgs‘ ) [Holdom 1986]U(1)�

Lint = −κ

2VµνFµν +

m2V

v� h�V 2µ +

m2V

v�2 h�2V 2µ −

m2h�

2v� h�3 − m2h�

8v�2 h�4.

φ


Consider V-portal

τV ≤ 0.05 s×�

10−10

κ

�2 �500 MeV

mV

�for mV � me.

V γ

τX ∼ 103 s


Consider V-portal

τV ≤ 0.05 s×�

10−10

κ

�2 �500 MeV

mV

�for mV � me.

V γ

“super-Wimp”regime

⇒ mV < mh�

κ � 10−12

Γprod(V )� H

τX ∼ 103 s


Consider V-portal

τV ≤ 0.05 s×�

10−10

κ

�2 �500 MeV

mV

�for mV � me.

V γ


⇒ mV < mh�

κ � 10−12

Γprod(V )� H

naturally long-lived h’

-mh! > mV :

h!V

V

! e!

mh! < mV :

h!f

f

! e!e2Q2f!

2"

1(4!)2

“Wimp” regime⇒ mh� < mV

[Batell et al., 2009]

τX ∼ 103 s


Consider V-portal

τV ≤ 0.05 s×�

10−10

κ

�2 �500 MeV

mV

�for mV � me.

V γ

τh� ∼ (103 ÷ 104) s×� α

α�

� �3.4× 10−5

κ

�4 �250 MeV

mh�

� � mV

500 MeV

�2.


⇒ mV < mh�

κ � 10−12

Γprod(V )� H

naturally long-lived h’

-mh! > mV :

h!V

V

! e!

mh! < mV :

h!f

f

! e!e2Q2f!

2"

1(4!)2

“Wimp” regime⇒ mh� < mV

[Batell et al., 2009]

τX ∼ 103 s


easily

h� + h� → V + V : Γ1 ∝ (α�)2κ0 exp(−mh�/T − 2∆m/T )

h� + V → l+l− : Γ2 ∝ α�ακ2 exp(−mh�/T −∆m/T )

h� + l± → V + l± : Γ3 ∝ α�ακ2 exp(−∆m/T ),

“Wimp” regime: h’

Yh� =

�10 (πBBN)104 (ν/µBBN)

[Credit: N. Weiner]

YX


easily

h� + h� → V + V : Γ1 ∝ (α�)2κ0 exp(−mh�/T − 2∆m/T )

h� + V → l+l− : Γ2 ∝ α�ακ2 exp(−mh�/T −∆m/T )

h� + l± → V + l± : Γ3 ∝ α�ακ2 exp(−∆m/T ),

“Wimp” regime: h’

Yh� =

�10 (πBBN)104 (ν/µBBN)

[Credit: N. Weiner]

“super-Wimp”: V

production peaks at => can only estimate

YV ∼ 0.3×�

103 sτV

� �GeVmV

�2 �40geff

�3/2

seems somewhat small for “pion-solution”, but...

mV ∼ ΛQCD

YX


Conclusions

• (sub-)GeV scale sector which decays at ~ 1000 sec can reconcile Li observations with BBN

=> long lived injected mesons

=> injected neutrinos (accumulative effect)

• not hard to construct a model

=> particularly motivated by galactic cosmic ray signals

• BBN has become a powerful toolbox to test and constrain new physics

=> every model must pass this cosmological consistency check


Documents

BBN-Implications from a metastable (sub)GeV-scale sector · Perimeter Institute with Maxim Pospelov GGI Dark Matter Workshop 2010, Florence Tuesday, June 15, 2010. Outline Part I