SUSY-QCD corrections to (co)annihilation and their impact ...bib-pubdb1.desy.de/record/140659/files/SeminarBonn.pdf · 1 Relic density prediction 2 DM@NLO - an extension for numerical

SUSY-QCD corrections to (co)annihilation andtheir impact on the relic density.

Julia Harz, DESY Hamburgin collaboration with B. Herrmann, M. Klasen, K. Kovarik and Q. Le Boulc’h

Theoretisches Seminar, Bonn

3.12.2012

Relic density predictionDM@NLO - an extension for numerical relic density calculators

Phenomenology of neutralino-stop coannihilationAnalytical discussion

Results

Overview

1 Relic density prediction

2 DM@NLO - an extension for numerical relic density calculators

3 Phenomenology of neutralino-stop coannihilation

4 Analytical discussion

5 Results

Julia Harz SUSY-QCD corrections to (co)annihilation 1 / 37



Results

Overview





5 Results




Results

Constraining the SUSY parameter spaceNeutralino - LSP and cold dark matter candidate

Interplay between LHC and PLANCKdata will be even more interesting

Particle physics bounds

Collider searchese.g.mχ0

1> 46 GeV , mt > 95.7 GeV

PDG (2012)

Precision measurementse.g.Br(b → sγ) = (3.55±0.26) ·10−4

HFAG collaboration (2010)

Cosmology bounds

7 year data of WMAP⇒ Ωh2 = 0.1123± 0.035

WMAP collaboration (2011)




Results

Calculating the relic density

Today’s number density can be calculated via Boltzmann equation.

dndt

= −3Hn − 〈σeff v〉(

n2 − n2eq

)σ cross section of annihilation andcoannihilation

〈σeff v〉 =∑

ij

〈σijvij〉neq

i

neq

neqj

neq withneq

i

neq ∝ exp[−(mi −mχ)

T

]

Coannihilation...gets important, when masses of LSP and NLSP almost degenerate

K. Griest, D. Seckel. Phys. Rev. D 43 (1991) 10, 3191-3203




Results

Calculating the relic density

On the basis of the number density one can calculate the relic density.

ΩCDM h2 =mχn0

ρC∝ 1〈σv〉

Public computational programs (e.g.):

DarkSUSYGondolo, Edsjö, Ullio, Bergström, Bringmann et al. [astro-ph/0406204]

MicrOMEGAsBélanger, Boudjema, Pukhov et al. [hep-ph/1004.1092]

SuperIso RelicArbey, Mahmoudi [hep-ph/0906.0369]




Results

Theoretical uncertainties in the relic density prediction

In cosmology

Choice of cosmological modelHamann, Hannestad, et.al. (2006) [hep-ph/0611582]

Variation in Hubble expansionrateArbey, Mahmoudi (2008) [hep-ph/0803.0741]

In particle physics

Precision of massesAllanach, Kraml, Porod (2003) [hep-ph/0302102]

Uncertainties of spectrum calculatorsBélanger, Kraml, Pukhov (2005) [hep-ph/0502079]

Precision in the calculation of(co)annihilation cross sectionBaro, Boudjema, Semenov (2007) [hep-ph/0710.1821]

Current status in calculating the relic density:

Calculation in public programs only on effective tree level

Current theoretical uncertainties bigger than future precision of PLANCK

Significant impact of NLO-corrections on the relic density




Results

Current packages at next-to-leading order

- electroweak corrections

Huge number of processes and NLO-diagrams

Automatized calculation

Interface to micrOMEGAshttp://code.sloops.free.fr

- strong corrections

SUSY-QCD corrections to (co)annihilationprocesses

Efficient infrared treatment (dipole subtractionmethod)

Interface to micrOMEGAs (and DarkSUSY inthe future)

http://dmnlo.hepforge.org




Results

Overview





5 Results




Results

DM@NLO - relic density including QCD corrections

SPhenocalculation of sparticle masses,mixings & precision observables

W. Porod.

?

Inputsetting parameters for cMSSM,

pMSSM,...

MicrOMEGAsintegration of Boltzmann equation,

etc.G. Bélanger, F. Boudjema, A. Pukhov, A. Semenov.

relevant CalcHEP cross sectionsare replaced by DM@NLO calculat-ed NLO cross sections

?

CalcHEPcalculation of (co)annihilation

processes at tree levelA. Pukhov, A. Belyaev, N. Christensen.

-

Outputneutralino relic density

DM@NLOcalculation of cross sections @

NLO level for relevant processesJ.Harz, B. Herrmann, M. Klasen, K. Kovarik, Q. Le Boulc’h.

-

http://projects.hepforge.org/dmnlo Julia Harz SUSY-QCD corrections to (co)annihilation 9 / 37



Results

Impact of SUSY-QCD-corrections to annihilation

Example: Dominant Z-exchange

Enhancement of annihilation crosssection into quarks by 50 % throughQCD-corrections

Reduction of the predicted relicdensity

Significant shift of the WMAPfavoured region

10˜

10˜

q

qH0k

10˜

10˜

q

qZ0

10˜

10˜

q

qqi˜

10˜

10˜

q

qqi˜

tan β = 10, A0 = 0,m0 = 1500,M2 = 600, µ > 0Herrmann, Klasen, Kovarik (2009), arXiv:0907.0030 [hep-ph].

⇒ Effect of corrections to the relic density lager than currentexperimental uncertainties!

B. Herrmann, M. Klasen, K. Kovarik




Results


Example: Dominant Z-exchange

Enhancement of annihilation crosssection into quarks by 50 % throughQCD-corrections

Reduction of the predicted relicdensity

Significant shift of the WMAPfavoured region

10˜

10˜

q

qH0k

10˜

10˜

q

qZ0

10˜

10˜

q

qqi˜

10˜

10˜

q

qqi˜

tan β = 10, A0 = 0,m0 = 1500,M2 = 600, µ > 0Herrmann, Klasen, Kovarik (2009), arXiv:0907.0030 [hep-ph].

⇒ Effect of corrections to the relic density lager than currentexperimental uncertainties!

B. Herrmann, M. Klasen, K. Kovarik




Results


Extension: annihilation of other gauginos

Especially relevant for wino- orhiggsino-like neutralinos

Realisation e.g. in pMSSM

Generalisation of neutralinoannihilation code

Addition of few new contributionsconcerning charginos

χ0/± χ0/±

χ0/± χ0/± χ0/± χ0/±q q q q

q q q q

Z0 H0i

q q

γ W± H±

χ0/±

χ0/±q q

q χ0/±

χ0/± q

q

χ+

χ− q

AbdusSalam, Allanach and Quevedo, Phys. Rev. D 81 (2012).

B. Herrmann, M. Klasen, K. Kovarik, M. Meinecke (in progress).




Results

Coannihilation with Squarks

Contribution if squarks and neutralinoalmost degenerate

Dominant in different regions ofparameter space

Extendable to coannihilation ofgauginos with sfermions in general

0

100

200

300

400

500

600

700

800

900

1000

1100

Mas

s/

GeV

h0

A0H0

H±

qR

qL

b1

b2

t1

νL

˜R

˜L

τ1ντ

τ2

g

χ01

χ02 χ±

1

χ03

χ04 χ±

2

t2

J.H., B. Herrmann, M. Klasen, K. Kovarik, Q. Le Boulc’h (in progress)




Results

Overview





5 Results




Results

Phenomenology of neutralino-stop coannihilationFrom particle physics point of view

light stops interesting regarding collider phenomenology

large stop splitting interesting for Higgs mass around 125 GeV

m2h ≈ M2

Z cos2 2β +3g2m4

t

8π2m2W

[ln(

M2SUSY

m2t

)+

X 2t

M2SUSY

(1− X 2

t

12M2SUSY

)]with Xt ≡ At − µ/ tanβ and MSUSY =

√mt1

mt2

max contribution from stop mixing obtained for |Xt |/MSUSY =√

6(m2

q10

0 m2q2

)= U†q

(M2

Q + m2t + M2

Z c2β(T 3q −Qqs2

w ) mtXt

mtXt M2˜tR

+ m2t + M2

Z c2βQqs2w

)Uq

From cosmology point of view

Neutralino-stop coannihilation can contribute significantly to σeff




Results

Phenomenology of neutralino-stop coannihilationStudy of phenomenological MSSM with 8 free parameters (pMSSM8)

random scan of 1 200 000 points

parameter range:

200 GeV ≤ M1 ≤ 1000 GeV

500 GeV ≤ Mq1,2 ,M ˜ ≤ 4000 GeV

500 GeV ≤ Mq3 ≤ 2500 GeV

100 GeV ≤ mA ≤ 2000 GeV

2 ≤ tanβ ≤ 50

|µ| ≤ 3000 GeV

|Tt | ≤ 5000 GeV

χn0˜

qi˜

q’

φq

χn0˜

qi¯

q’

φ

qj˜χn0˜

qi¯

q’

φχk0˜

χn0˜

qi˜

q’

Vq

χn0˜

qi¯

q’

V

qj˜χn0˜

qi¯

q’

Vχk0˜

with φ = h0, H0, A0, H± , V = Z0, W± , (γ), (g)

Constraints:

0.0773 ≤Ωχh2 ≤ 0.1473

120 GeV ≤mh0 ≤ 130 GeV

2.5× 104 ≤BR(b → sγ) ≤ 4.6× 104




Results

Phenomenology of neutralino-stop coannihilationAll points with coannihilation:

h0, H0, A0, H±, Z0, W±, γ, g




Results

Phenomenology of neutralino-stop coannihilationCut on Higgs mass:

h0, H0, A0, H±, Z0, W±, γ, g




Results

Phenomenology of neutralino-stop coannihilationCut on Higgs mass and relic density:

h0, H0, A0, H±, Z0, W±, γ, g




Results

Phenomenology of neutralino-stop coannihilation:Cut on Higgs mass, relic density and b → sγ:

h0, H0, A0, H±, Z0, W±, γ, g




Results

Phenomenology of neutralino-stop coannihilationFurther study of 3 different scenarios:

M1 Mq1,2Mq3

M ˜ At mA µ tanβI 306.7 2037.7 709.7 1499.3 1806.5 1495.6 2616.1 9.0II 469.7 1261.2 905.3 1963.2 1515.5 1343.1 725.9 18.3III 314.9 2870.5 763.6 2417.7 1877.5 386.0 2301.5 10.3

χ01 t1 → th0 χ0

1 t1 → tH0 χ01 t1 → tZ 0 χ0

1 t1 → bW + sumI 38.6% – 3.4% 5.9% 47.9%II 26.5% – 11.6% 3.7% 41.8%III 14.0% 20.5% 1.2% 2.1% 37.8%

mχ01

mt1mh0 Ωχh2

I 306.9 350.5 124.44 0.124II 466.4 511.8 124.05 0.145III 317.0 371.4 123.43 0.102




Results

Phenomenology of neutralino-stop coannihilationContribution of different channels for studied scenarios

M1 Mq1,2Mq3

M ˜ At mA µ tan βI 306.7 2037.7 709.7 1499.3 1806.5 1495.6 2616.1 9.0II 469.7 1261.2 905.3 1963.2 1515.5 1343.1 725.9 18.3III 314.9 2870.5 763.6 2417.7 1877.5 386.0 2301.5 10.3




Results

Phenomenology of neutralino-stop coannihilationContribution of different channels for studied scenarios

M1 Mq1,2Mq3

M ˜ At mA µ tan βI 306.7 2037.7 709.7 1499.3 1806.5 1495.6 2616.1 9.0II 469.7 1261.2 905.3 1963.2 1515.5 1343.1 725.9 18.3III 314.9 2870.5 763.6 2417.7 1877.5 386.0 2301.5 10.3




Results

Overview





5 Results




Results

Full next-to-leading order calculation for coannihilation

Virtual corrections

q

q

q

g

q

q

qj˜

g

qi˜

qi˜

qi˜

g

qi˜

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qi˜ qj˜

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gV, H

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qj˜

qk˜

gV, H

qi˜

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q

gV, H

qi˜

qj˜

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Real emission

χn0˜

qi˜

q

V, H

g

qj˜q

χn0˜

qi˜

q

V, H

g

q

q

χn0˜

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q

g

V, H

q

q

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V, H

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χm˜

qj˜

χn0˜

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V, H

q

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χm˜q

χn0˜

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q

V, H

g

qj˜

qj˜

χn0˜

qi˜

q

g

V, H

qj˜

qj˜

χn0˜

qi˜

q

g

V, H

qj˜q

χn0˜

qi˜

q

g

V

qj˜




Results

Virtual corrections and renormalizationMixed DR-OS-scheme

input parameters: mMSb ,mOS

t ,ADRb ,ADR

t ,mOSb1,mOS

b2,mOS

t1

treat mt ,mt1,mt2

,mb1,mb2

in OS-schememb,At ,Ab in DR-scheme

renormalization of squark mixing matrizes before rotation→ counter term for mixing angle δθ appears(

cos θq sin θq− sin θq cos θq

)(m2q1

00 m2

q2

)(cos θq − sin θqsin θq cos θq

)=(

M2Q + m2

q + M2Z c2β(T 3

q − Qqs2w ) mq(Aq − µ∗κ)

mq(Aq − µκ) M2qR

+ m2q + M2

Z c2βQqs2w

)

in interaction eigenstates five soft parameters: M2Q ,M

2tR,M2

bR,At ,Ab

in mass eigenstates six parameters: mt1,mt2

, θt ,mb1,mb2

, θb→ choose mt2

as dependent parameter




Results

Virtual corrections and renormalization

Mixed DR-OS-scheme

Important issue by calculating counterterm δθ:choose θ such that

δθ =1

m2q1−m2

q2

· 1cos2 θ − sin2 θ

remains stable→ θ 6= 0→ θ 6= π/4




Results

Virtual corrections and renormalizationContribution of different virtual corrections:




Results

Real corrections and infrared treatment

Phase-space-slicing

σNLO =

∫2→3

dσR +

∫2→2

dσV

σbrems2→3 (λ) = σsoft (∆E , λ) + σhard (∆E)

M =i(2p − k)µεµ(k)

(p − k)2 −m2

(−igsT a)A0(p − k)

M = −(gsT a) ε.p

p.kM0 with kµ pµ

(dσdΩ

)soft

= −(

dσdΩ

)0× g2

s CF

(2π)3

∫|~k|≤∆E

d3k2ω

−2k1.p2

(p2.k)(k1.k)




Results


Phase-space-slicing

σNLO =

∫2→3

dσR +

∫2→2

dσV



(p − k)2 −m2


M = −(gsT a) ε.p

p.kM0 with kµ pµ

(dσdΩ

)soft

= −(

dσdΩ

)0× g2

s CF

(2π)3

∫|~k|≤∆E

d3k2ω

−2k1.p2

(p2.k)(k1.k)




Results


Phase-space-slicing

σNLO =

∫2→3

dσR +

∫2→2

dσV



(p − k)2 −m2


M = −(gsT a) ε.p

p.kM0 with kµ pµ

(dσdΩ

)soft

= −(

dσdΩ

)0× g2

s CF

(2π)3

∫|~k|≤∆E

d3k2ω

−2k1.p2

(p2.k)(k1.k)




Results

Real corrections and infrared treatmentTest of cut off independence:




Results

Real corrections and infrared treatmentContribution of 2→ 3 processes:




Results

Special treatment: on-shell propagatorsDiagram subtraction scheme

Internal top quark in real gluon emission can become on-shellCareful treatment to prevent double-counting

χ01 t1 −→ W + b g|on−shell top =⇒ (χ0

1 t1 → t g)× (t → W +b)

modelling with Breit-Wigner distribution retains interferences withnon-resonant terms

|Msubtr|2 =m2

topΓ2top

(p2top −m2

top)2 + m2topΓ2

top×∣∣Mres

∣∣2∣∣∣on−shell top

χ10˜

t1˜

b

W

g

t

t

χ10˜

t1˜

b

W

g

t1˜t




Results

Overview





5 Results




Results

Impact of SUSY-QCD-corrections to cross sectionScenario II

χ01 t1 → th0 χ0

1 t1 → tH0 χ01 t1 → tZ 0 χ0

1 t1 → bW + sumII 26.5% – 11.6% 3.7% 41.8%




Results

Impact of SUSY-QCD-corrections to cross sectionScenario I & III

χ01 t1 → th0 χ0

1 t1 → tH0 χ01 t1 → tZ 0 χ0

1 t1 → bW + sumI 38.6% – 3.4% 5.9% 47.9%

III 14.0% 20.5% 1.2% 2.1% 37.8%




Results

Impact on the relic densityReduction of relic density through next-to-leading order calculation

WithΩCDM h2 =

mχn0

ρC∝ 1〈σv〉

relic density gets shift of ≈ 10 %




Results

Impact on relic densityShift of WMAP favoured region of parameter space




Results

Impact on the relic densityReduction of relic density through next-to-leading order calculation




Results

Impact on relic densityShift of WMAP favoured region of parameter space




Results

Outlook

DM@NLO will correct further processesin the futureExample scenario I:

38.56% χ01 t1 → t h

19.81% χ01 χ

01 → t t

14.09% t1 ¯t1 → h h8.01% χ0

1 t1 → G t5.92% χ0

1 t1 → W + b3.37% χ0

1 t1 → Z t

Ongoing work for gluon final states→ sizeable corrections expected(Freitas)

Ongoing work for other processes(e.g. t1¯t1 → h h)

Freitas (2007), arXiv:0705.4027v2 [hep-ph].




Results

Conclusion

Public codes do not take into account full NLOcorrections

DM@NLO will contain SUSY-QCD corrections toGaugino annihilation and Neutralino-Squarkcoannihilation

sizeable corrections expected and thus an impacton the relic density prediction

Package DM@NLO allows to link SUSY-QCDcorrections to the public codes

→ Code will be public available!http://dmnlo.hepforge.org

q

q

q

g

q

q

qj˜

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qi˜

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qi˜

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qk˜

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q

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qi˜

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ql˜




Results


Documents

SUSY-QCD corrections to (co)annihilation and their impact ...bib-pubdb1.desy.de/record/140659/files/SeminarBonn.pdf · 1 Relic density prediction 2 DM@NLO - an extension for numerical