Enhancement of Neutralino Dark Matter Annihilation from Electroweak CorrectionsF

Enhancement of Neutralino Dark Matter Annihilation from

Electroweak Corrections

Francesca Calore

in collaboration with Torsten Bringmann

II Institute for Theoretical Physics, University of Hamburg, Germany MITP Workshop "Cosmic Rays and Photons from

Dark Matter Annihilation: Theoretical issues"

Neutralino DM Annihilation

Velocity suppression: if present the S-wave dominates the cross section

Helicity suppression: for a fermionic Majorana DM candidate the S-wave annihilation into light fermion- antifermion pairs is

h ^ann v i = a + bv ² + O(v ⁴ )

The lifting of the helicity suppression via radiative corrections is possible

/ m

/m

Radiative corrections

Electromagnetic Corrections :

emission of an additional photon

FSR: logarithmic enhancement of collinear photons

VIB: spectral features at high energies from di-boson and co- annihilation channel

Electroweak Corrections :

emission of W, Z

more stable particles in the low- energy tail of the spectrum;

multi-messenger signal

lifting of the helicity suppression from VIB and ISR; FSR

logarithmic enhancement

! f ¯ F V ⇠⇠ _{V = , Z, W} ^±

Bringmann et al., 2008

EW Radiative Corrections

Motivation: relevance of EW corrections in modeling the predicted DM fluxes

EW Radiative Corrections

Motivation: relevance of EW corrections in modeling the predicted DM fluxes Current literature:

specific models corresponding to some MSSM neutralino limit (i.e. bino, wino, higgsino)

Kachelrieß et al., 2009 Bell et al., 2011

Garny et al., 2011, 1012

EW Radiative Corrections

Motivation: relevance of EW corrections in modeling the predicted DM fluxes Current literature:

specific models corresponding to some MSSM neutralino limit (i.e. bino, wino, higgsino)

rather model-independent approach (effective field theory operators)

Ciafaloni et al., 2010, 2011, 2012 PPPC4DMID

EW Radiative Corrections

Motivation: relevance of EW corrections in modeling the predicted DM fluxes Current literature:

specific models corresponding to some MSSM neutralino limit (i.e. bino, wino, higgsino)

rather model-independent approach (effective field theory operators)

Novelty of this work: first fully general calculation for MSSM neutralino DM, keeping

all relevant diagrams

the full mass dependence of fermions, gauge bosons and other involved particles.

“s − channel”

VIB FSR ISR

˜ χ⁰₁

˜

χ⁰₁ F¯

V f

F¯

˜ χ⁰₁

˜ χ⁰₁

V

f V

˜ χ⁰₁

˜ χ⁰₁

f

F¯

f

F¯

˜ χ⁰₁

˜ χ⁰₁

V F¯

˜ V χ⁰₁

˜ χ⁰₁

f

“t/u − channel” ^{χ˜ V}

01

˜ χ⁰₁

f

F¯

f˜_i f˜j

f˜_i

f˜_i

f˜_i f˜i

V f

F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰_n/ ˜χ^±_n

f

V F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰₁

F¯ f

V f

V F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰_n/ ˜χ^±_n

˜ χ⁰_n/ ˜χ^±_n

˜ χ⁰_n/ ˜χ^±_n

The Method

generation of diagrams (46) with FeynArts for the

process: ^{! f ¯ F V}

Virtual Internal Bremsstrahlung

“s − channel”

VIB FSR ISR

˜ χ⁰₁

˜

χ⁰₁ F¯

V f

F¯

˜ χ⁰₁

˜ χ⁰₁

V

f V

˜ χ⁰₁

˜ χ⁰₁

f

F¯

f

F¯

˜ χ⁰₁

˜ χ⁰₁

V F¯

˜ V χ⁰₁

˜ χ⁰₁

f

“t/u − channel” ^{χ˜ V}

01

˜ χ⁰₁

f

F¯

f˜_i f˜j

f˜_i

f˜_i

f˜_i f˜i

V f

F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰_n/ ˜χ^±_n

f

V F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰₁

F¯ f

V f

V F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰_n/ ˜χ^±_n

˜ χ⁰_n/ ˜χ^±_n

˜ χ⁰_n/ ˜χ^±_n

The Method

generation of diagrams (46) with FeynArts for the

process: ^{! f ¯ F V}

Final State Radiation

“s − channel”

VIB FSR ISR

˜ χ⁰₁

˜

χ⁰₁ F¯

V f

F¯

˜ χ⁰₁

˜ χ⁰₁

V

f V

˜ χ⁰₁

˜ χ⁰₁

f

F¯

f

F¯

˜ χ⁰₁

˜ χ⁰₁

V F¯

˜ V χ⁰₁

˜ χ⁰₁

f

“t/u − channel” ^{χ˜ V}

01

˜ χ⁰₁

f

F¯

f˜_i f˜j

f˜_i

f˜_i

f˜_i f˜i

V f

F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰_n/ ˜χ^±_n

f

V F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰₁

F¯ f

V f

V F¯

˜ χ⁰₁

˜ χ⁰₁

˜ χ⁰_n/ ˜χ^±_n

˜ χ⁰_n/ ˜χ^±_n

˜ χ⁰_n/ ˜χ^±_n

The Method

generation of diagrams (46) with FeynArts for the

process: ^{! f ¯ F V}

Initial State Radiation

generation of diagrams with FeynArts

computation of the total squared matrix element in the limit

S-wave projector

kinematics: only two independent variables

“ helicity amplitudes method” extended to three-body final state

1

P

v ! 0

The Method

Edsjo&Gondolo,1997

S-Wave Initial State Projector

DM Majorana fermion annihilating in the zero-velocity limit acts as a pseudo-scalar decaying particle

Initial State S-Wave projector: only the pseudo-scalar current and the temporal component of the vector current lead to non-

vanishing contributions

in the CM system

Lorentz invariant expression P

= S(⇤)(P

)

S

(⇤) =

(m (p

p

)/2)

p 2

(P

)

=

m (1

)

p 2

“ Helicity amplitudes method”

(p

) (p

) ! f(k

) ¯ F (k

)V (k

)

M / ¯v

(p

) (

)

u

(p

)¯ u

(k

) (

)

v

(k

)✏

(k

)

(¯ u

v)

= X

↵...

⇣ C

(s⁰, ⁰)

e

...e

⌘

s⁰, ⁰ s,

typical s-channel matrix element structure

1

P

1 4

X

r,s,r⁰,s⁰,

M

2

⌘ 1 4

X

h,

X

diag.

M

2

Total Squared Matrix

The Method

generation of diagrams with FeynArts

computation of the total squared matrix element in the limit

numerical implementation in DarkSUSY:

squared matrix element differential cross section

spectra of final state particles spectra of final stable particles

v ! 0

The importance of s-channel resonances

s-channel VIB/ISR

s- and t-channel FSR

X = h, H, A, H

, Z, W

F¯

˜ V χ⁰₁

˜ χ⁰₁

f

V

˜ χ⁰₁

˜ χ⁰₁

f

F¯

˜ χ⁰_n/ ˜χ^±_n

X X

X

˜ χ⁰₁

˜ χ⁰₁

V f

F¯

X

D

(q) / ((p k

)

m

)

' (4m

+ m

4m E

m

)

D

(q) / ((p k

)

m

)

' (4m

4m E

)

E

' m (1 + m

m

4m

)

E

' m

Results: final state particles spectra

m = 233.3 GeV

Z

/(1 Z

) = 220 m

= 238.9 GeV m = 1210.8 GeV

m

= 532.2 GeV m

= 124.4 GeV

s-channel resonances

Z

= 3.55 · 10

An MSSM example PRELIMINARY

PRELIMINARY

z

= 0.998 z

= 0.952

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10² 10³ 10⁴ 10⁵

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 dN V/dz

z

ccZ bbZ

10^-1 10⁰

10^-1 10⁰

dN f/dz

z

ccZ bbZ

z

⌘ E

m = 1 + m

m

4m

z

= 1

dN

dE = dN

dE + dN

dE + dN

dE

m = 233.3 GeV

Z

/(1 Z

) = 220 m

= 238.9 GeV

Results: total photon yield

A cMSSM example

10^-2 10^-1 10⁰ 10¹

10^-3 10^-2 10^-1 10⁰

x2 dN/dx

x

Sec + EM Sec + EM + EW

PRELIMINARY

dN

dx

= m

; x =

Conclusions and Outlook

first fully general computation of EW corrections for MSSM neutralino all the diagrams are included (s-, t- and u- channel)

implementation in DarkSUSY

enhancement in co-annihilation region due to the lifting of the helicity suppression

importance of resonances in the s-channel diagrams

an extended scan over cMSSM and MSSM models is running and almost complete

enhancement mechanisms ?

relevance for the low-energy spectra ?

viable models as new benchmark for ID DM ?

not only gamma-rays...

Backup slides

DM Majorana fermion annihilating in the zero-velocity limit acts as a pseudo-scalar decaying particle

P = ( 1)

= 1

C = +1

(¯ u v)

= (¯ u

v

u ¯ v )

p 2 (1)

(¯ u v)

= u ¯ v

(2)

(¯ u v)

= (¯ u

v

+ ¯ u v )

p 2 (3)

(¯ u v)

= u ¯

v (4)

⌘

Definition of helicity states in terms of 4-component spinors with helicity +/-:

where

Kinematical boundaries x

= m

m

x

= (4 + m

m

(m

+ m

)

m

)/4 x

= m

m

x

= (4 + m

m

(m

+ m

)

m

)/4

Results: total photon yield (II)

MSSM example

PRELIMINARY

10^-3 10^-2 10^-1 10⁰

10^-3 10^-2 10^-1 10⁰

x2 dN/dx

x

Sec + EM Sec + EM + EW

***** MODEL A *****

Neutralino mass: 1210.8; Gaugino Fraction: 3.55 ·10

v

= 8.08 ·10

v

= 1.50 ·10

2.04 ·10

4.71 ·10

1.53 ·10

2.60 ·10

5.25 ·10

4.13 ·10

1.27 ·10

3.6 ·10

***** MODEL B *****

Neutralino mass: 233.26; Gaugino Fraction: 0.995 v

= 8.50 ·10

v

= 2.43 ·10

1.69 ·10

5.13 ·10

1.89 ·10

1.23 ·10

1.12 ·10

1.12 ·10

6.32 ·10

1.04 ·10

[units of cm

s

]

Results: final state particles spectra

m = 233.3 GeV

Z

/(1 Z

) = 220 m

= 238.9 GeV m = 1210.8 GeV

m

= 532.2 GeV m

= 124.4 GeV

s-channel resonances

Z

= 3.55 · 10

An MSSM example PRELIMINARY

PRELIMINARY

z

= 1 z

= 0.998

z

= 0.949 z

= 0.952

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10² 10³ 10⁴ 10⁵

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 dN V/dz

z

ccZ bbZ

10^-1 10⁰

10^-1 10⁰

dN f/dz

z

ccZ bbZ

z

⌘ E

m = 1 + m

m

4m

The Method

|M|

d( v)

dE

dE

= 1 16 m

1

(2⇡)

|M|

dN

dE

= 1

v

Z

E_p0^min(E_p)

d( v)

dE

dE

dE

dN

dE

= X

p=F,f,V

Z

E_p^min

1 2

dN

dE

dN

dE

dE

Squared matrix

element

The Method

|M|

d( v)

dE

dE

= 1 16 m

1

(2⇡)

|M|

dN

dE

= 1

v

Z

E_p0^min(E_p)

d( v)

dE

dE

dE

dN

dE

= X

p=F,f,V

Z

E_p^min

1 2

dN

dE

dN

dE

dE

Differential

cross section

The Method

|M|

d( v)

dE

dE

= 1 16 m

1

(2⇡)

|M|

dN

dE

= 1

v

Z

E_p0^min(E_p)

d( v)

dE

dE

dE

dN

dE

= X

p=F,f,V

Z

E_p^min

1 2

dN

dE

dN

dE

dE

Spectra of final

state particles

The Method

|M|

d( v)

dE

dE

= 1 16 m

1

(2⇡)

|M|

dN

dE

= 1

v

Z

E_p0^min(E_p)

d( v)

dE

dE

dE

dN

dE

= X

p=F,f,V

Z

E_p^min

1 2

dN

dE

dN

dE

dE

Spectra of final

stable particles