What can PAMELA and Fermi/LAT tell us about MSSM?

B. Bajc

What can PAMELA and Fermi/LAT tell us about MSSM? Borut Bajc

J. Stefan Institute, Ljubljana, Slovenia

BB, Enkhbat, Ghosh, Senjanović, Zhang, 10

MPI Heidelberg, 2010

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Outline

• Introduction • Dark matter in MSSM (the old paradigm) • Dark matter after PAMELA and Fermi/LAT • Neutrino mass in MSSM • Who is the dark matter in MSSM? • Constraints for MSSM parameters • Tests/consequences of gravitino DM • Conclusion


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Introduction

The SM very successful, except for two things (right now) • dark matter (DM) • neutrino masses

Some physics beyond the SM thus needed


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A very appealing candidate is the Minimal Supersymmetric Standard Model (MSSM):

• resolves (or better, stabilizes) the hierarchy problem m2H

≈

m2H,0

α 2 + m 4π SU SY

SUSY does not automatically give (the doublet-triplet problem) m2H,0 ≈ m2H but once this is done the correction is small providing m2SU SY ≈ m2H,0 MPI Heidelberg, 2010

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• it improves the running of the gauge couplings to reach a one-step unification running of gauge couplings in the MSSM 1.2

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1

0.8

0.8

0.6

0.6

gi

gi

running of gauge couplings in the SM 1.2

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0.2

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0 2

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6

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10 log10 (E/GeV)

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0 2

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10 log10 (E/GeV)

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Dimopoulos, Raby, Wilczek, 81 Iba˜ nez, Ross, 81 Einhorn, Jones, 82 Marciano, Senjanović, 82 MPI Heidelberg, 2010

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• in many of its versions it has a DM candidate (to be considered soon) • in some of its versions it can accomodate nonzero neutrino masses (to be considered soon)


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Dark matter in MSSM (the old paradigm)

Dark matter must • live enough to be seen today as almost stable

τDM > life of the universe • have the right density for

mDM nDM ≈ 5 ρvisible


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In the MSSM that means that either • have a relatively good approximate R-parity =⇒ the lightest supersymmetric partner (LSP) relatively long-lived • two dark matter candidates: neutralino (mixture of neutral higgsinos and neutral wino and bino) or sneutrino

or • gravitino the lightest superpartner • long lived because of gravitational interactions


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Dark matter after PAMELA and Fermi/LAT What is PAMELA? • it is a satellite based experiment, measuring and distinguishing electrons, positrons, protons, antiprotons • it was believed we knew and understood the abundance of these particles in cosmic rays • it was a surprise to find out an increase of the measured positron to electron fluxes ratio: it started at ≈ 10 GeV and became 10× bigger than the expected theoretical background at ≈ 100 GeV • NO such increase was found in the antiproton vs proton fluxes MPI Heidelberg, 2010

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What is Fermi/LAT? • Fermi is recently launched Gamma-Ray Space Telescope • LAT stands for its main detector, the Large Area Telescope • It was originally designed to measure gamma rays, but it can probe also electrons/positrons up to 1 TeV. • it was found that the electron + positron flux is larger than the theoretical expectations in the region 50 GeV< ∼E < ∼ 1 TeV (with a factor up to ≈ 2)


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There are some candidates for describing these discrepancies with astrophysics (for example pulsars), but nothing conclusive

Let us assume that it is particle physics that explains the DM and its decay explains PAMELA and/or Fermi/LAT


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Two main consequences follow from here • the DM candidate should be heavy enough: mDM > ∼ few hundred GeV mDM > ∼ few TeV

(from PAMELA) (from Fermi/LAT)

• the interaction that makes the DM candidate decay must be leptophilic • ΓDM ≈ 10−50 GeV


(τDM ≈ 1026 s)

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Neutrino mass in MSSM There is no way to describe neutrino mass using only the d.o.f. of the renormalizable standard model. Always possible to write down the d = 5 Weinberg operator

L = Yij

Li HHLj M

After hHi = v one gets the mass v2 mν = Y M This not very useful: it tells us that new degrees if freedom at the scale M have been integrated out. This term is a remnant of the UV completion. MPI Heidelberg, 2010

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Can we describe the neutrino mass in MSSM without any new physics in the UV? Yes, enough to break the lepton number (i.e. R-parity). In general R-parity violating couplings are

1 1 00 c c c c 0 c 0 W = + λ QLd + u d d + µ LHu λLLe λ R 2 2 λ, λ0 , µ0 break lepton number λ00 break baryon number


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Experimental constraints: • proton decay

λ0 λ00 . 10−27

mde 2 300GeV Smirnov, Vissani, 96

• neutron-antineutron oscillation m 2 m 0 1/2 χ e 00 −7 −8 de λ . (10 − 10 ) 100GeV 100GeV Zwirner, 83 Dimopoulos, Hall, 87 Hinchliffe, Kaeding, 93 Babu, Mohapatra, 01 MPI Heidelberg, 2010

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All we need is a small enough λ00 . Assuming for example λ 6= 0: hHi

˜ L

L

e˜c

ec

L

L

hHi

mν '


λ2 (m2è)LR mτ 16π 2 m2e `

(m2è)LR = A` vd − µ∗ yτ vu

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Similar result for internal quarks and squarks with • λ → λ0 • extra factor 3 (= NC )


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Last possibility is the tree order contribution due to h˜ νi = 6 0 vev: ˜ hLi

L

˜ hLi

χ ˜0

L

g 2 h˜ ν i2 mν ' mχ˜0 Notice that h˜ ν i ∝ µ0 MPI Heidelberg, 2010

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Who is the dark matter in MSSM? R couplings 6= 0 =⇒ neutralinos decay too fast =⇒ gravitino the only DM candidate (decay suppressed by 1/MP l )

L

=

−√

1 2MPl

i ¯ a µ νρ a χ ¯L γ µ γ ν Dν φ − √ λ γ σ Fνρ ψµ + h.c. 4 2

ψµ . . . gravitino (χL , φ) . . . chiral multiplet a (λa , Fµν ) . . . vector multiplet


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Which are the gravitino decay modes? Depending on its mass • 2-body decay modes: ψµ → W ` ψµ → Zν ψµ → γν ψµ → H 0 ν ... • 3-body decay modes ψµ → `+ `0− ν

⇐= MUST DOMINATE !

ψµ → q q¯0 `/ν ... MPI Heidelberg, 2010

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Constraints for MSSM parameters Nothing original in considering gravitino DM candidate to explain PAMELA and/or Fermi/LAT. Many different works so far: Takayama , Yamaguchi, 00 Covi, Grefe, Ibarra, Tran, 09 Hamaguchi, Takahashi, Yanagida, 09 Chen, Mohapatra, Nussinov, Zhang, 09 Ishiwata, Matsumoto, Moroi, 09 Buchmuller, Ibarra, Shindou, Takayama, Tran, 09 Bomark, Lola, Osland, Raklev, 09 What is new here is describing at the same time neutrino mass and DM data. MPI Heidelberg, 2010

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ψµ → `+ `0− ν

main decay mode

• Γ2 (ψµ ) Γ3 (ψµ ) • λ0 λ

(2-body less than 3-body)

(3-body with quarks less than 3-body with leptons)

Since Γ2 (ψµ → νγ) ∝ µ02 , among R parameters λ, λ0 , µ0 =⇒ only λ important


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Constraints we will take:

0.03 eV . mν . 0.3 eV 10−51 GeV . Γ3 . 10−49 GeV Γ2 . Γ3 /10 λ2 . 4π

(ν mass) (PAMELA/Fermi-LAT) (leptophilic DM) (perturbativity bound)

What do they mean for the MSSM parameters?


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mν

' 10−2 λ

2 (m ) m 2 è LR τ

m2e `

Γ2

3 2 2 m (m ) LR e 3/2 ' 10−7 λ2 ` 4 2 me MPl `

Γ3

3 4 m m 3/2 3/2 ' 10−6 λ2 4 2 me MPl `

From these tree level (Γ3 ) and 1-loop (Γ2 , mν ) expressions and previous constraints some inequalities follow


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From mν , Γ2 , Γ3 and Γ2 < Γ3 /10 =⇒lower bound on slepton mass:

−1/2 m 5/2 m 1/2 Γ3 3/2 ν mè & 600 TeV 400 GeV 0.1eV 10−49 GeV

From Γ3 and λ2 < 4π =⇒ upper bound on slepton mass:

−1/4 7/4 m Γ3 3/2 mè . 104 TeV 400 GeV 10−51 GeV


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From mν , Γ2 and (Γ2 < Γ3 /10)=⇒ upper bound on gravitino mass: 2 2 m 3 m 2 λ Γ3 0.1eV 3/2 3/2 1+ .2 3 TeV 3 TeV 4π 10−49 GeV mν

For λ2 = 4π, Γ3 = 10−49 GeV, mν = 0.03 eV: m3/2 . 5TeV


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(PAMELA: m3/2 > ∼ 300 GeV

Fermi/LAT: m3/2 > ∼ 2 TeV)

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Log10 @m GeVD

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Fit only PAMELA positron excess (m3/2 > ∼ few hundred GeV) • m3/2 = 400 GeV • τ3/2 = 2.3 × 1026 sec (Γ3/2 = 0.3 × 10−50 GeV) • mν = 0.2 eV (best fit)

0.1

+

(e )/[

+

(e )+

-

(e )]

• m2è/λ ' 1.3 × 107 TeV2

0.01 1

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A


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This fit is valid for different values of (m2è)LR and λ providing we are in the white region below (for example): m32 =400 GeV, Hm slepton 2 LLR =H200GeVL2 2

-1

2 Br

Log10 @Λ2 D

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So explanation of PAMELA in MSSM requires:

• m3/2 ≈ 400 GeV • m`˜ ≈ 500 TeV

(or more) (or more)

• mq˜ ≈ O(TeV) if λ0 small (or bigger if λ0 large)


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Fit now both PAMELA and FERMI (m3/2 > ∼ few TeV) • m3/2 = 3.3 TeV • τ3/2 = 5 × 1025 sec (Γ3/2 = 1.4 × 10−50 GeV) • mν = 0.03 eV • m2è/λ ' 1010 TeV2

(best fit)

-1

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(e )]

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GeV ]

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This fit is valid for different values of (m2è)LR and λ providing we are in the white region below (for example): m32 =3 TeV, Hm slepton 2 LLR =H2.5 TeVL2 2.0

Log10 @Λ2 D

1.5

1.0

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4.6

4.8

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5.2

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Log10 @mslepton TeVD


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So explanation of PAMELA and FERMI in MSSM requires:

• m3/2 ≈ 3 TeV • m`˜ ≈ 105 TeV

(or a bit more) (or a bit more)

• mq˜ ≈ O(TeV) if λ0 small (or bigger if λ0 large)


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Tests/consequences of gravitino DM • no sleptons at LHC if only PAMELA is described: m`˜ > ∼ few hundreds TeV • nothing except the Higgs if also Fermi/LAT is explained msuperpartners > mLSP = m3/2 = few TeV • in this last case excess of antiprotons will have to be seen with a 1 order of magnitude improvement in precision

Γ2 = Γ3 /10 saturated here MPI Heidelberg, 2010

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• in this same case (PAMELA + Fermi/LAT) gravitino mass large and close to upper limit. Due to perturbativity requirements hierarchical neutrino pattern preferred. 2 2 m 3 m 2 λ Γ3 0.1eV 3/2 3/2 1+ .2 3 TeV 3 TeV 4π 10−49 GeV mν For m3/2 = 3.3 TeV, λ2 = 4π, Γ3 = 10−49 GeV =⇒ mν . 0.08 eV


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6 5 4 m32 HTeVL 3 2 1 0

0

2

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Λ2

H 4 Π LH 10 MPI Heidelberg, 2010

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G3 -49

LH GeV

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0.1 eV mΝ

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L

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• Flavor lepton violation small and should not be see in the near future 4 4 λ MW B(µ → 3e) ' g mè µ → eγ, µ → e conversion, etc even smaller, further loop suppression


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Conclusion • It is natural to try with the MSSM when something cannot be explained in the SM • From nonzero neutrino mass only gravitino with R couplings remains a DM candidate • Here an analysis of both neutrino masses and Fermi/LAT and/or PAMELA data done. • It is possible to descibe PAMELA (and Fermi/LAT ) providing sleptons are much too heavy to be seen at LHC • No restrictions on squarks, neutralino, chargino masses, but for heavy gravitino (from Fermi/LAT ) they seem also out of reach • Some tests possible, in spite of massive sleptons and/or other superpartners. MPI Heidelberg, 2010

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