Gravitino Phenomenology with Supernovae Timon Emken Institute of - - PowerPoint PPT Presentation
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks Gravitino Phenomenology with Supernovae Timon Emken Institute of Theoretical Physics, G ottingen 17.09.2013 1 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Timon Emken
Institute of Theoretical Physics, G¨
17.09.2013
1 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1
Supersymmetry and Supergravity
2
Gravitino Phenomenology
3
Supernovae Constraints on superlight Gravitinos
4
Concluding Remarks
3 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1
Supersymmetry and Supergravity
2
Gravitino Phenomenology
3
Supernovae Constraints on superlight Gravitinos
4
Concluding Remarks
3 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1
Supersymmetry and Supergravity
2
Gravitino Phenomenology
3
Supernovae Constraints on superlight Gravitinos
4
Concluding Remarks
3 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1
Supersymmetry and Supergravity
2
Gravitino Phenomenology
3
Supernovae Constraints on superlight Gravitinos
4
Concluding Remarks
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Supersymmetry is an hypothetical extension of the spacetime symmetries. Its generators satisfy the super algebra
β
α ˙ βPµ
These generators relate bosonic states with fermionic ones and vice versa, Q|boson ∼ |fermion , Q|fermion ∼ |boson
5 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Supersymmetry is an hypothetical extension of the spacetime symmetries. Its generators satisfy the super algebra
β
α ˙ βPµ
These generators relate bosonic states with fermionic ones and vice versa, Q|boson ∼ |fermion , Q|fermion ∼ |boson
5 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Supersymmetry is an hypothetical extension of the spacetime symmetries. Its generators satisfy the super algebra
β
α ˙ βPµ
These generators relate bosonic states with fermionic ones and vice versa, Q|boson ∼ |fermion , Q|fermion ∼ |boson
5 / 33
Gauge Coupling Unification In the MSSM the gauge couplings unify at high energies. Hierarchy Problem The quantum corrections to the Higgs mass of bosons and fermions can cancel in a supersymmetric theory. Dark Matter SUSY leads to the introduction of new particles which could act as DM. Theoretical Appeal The SUSY algebra is the most general Lie algebra of a symmetry of the S-matrix (Haag- Lopusza´ nski-Sohnius-Theorem).
Gauge Coupling Unification In the MSSM the gauge couplings unify at high energies. Hierarchy Problem The quantum corrections to the Higgs mass of bosons and fermions can cancel in a supersymmetric theory. Dark Matter SUSY leads to the introduction of new particles which could act as DM. Theoretical Appeal The SUSY algebra is the most general Lie algebra of a symmetry of the S-matrix (Haag- Lopusza´ nski-Sohnius-Theorem).
Gauge Coupling Unification In the MSSM the gauge couplings unify at high energies. Hierarchy Problem The quantum corrections to the Higgs mass of bosons and fermions can cancel in a supersymmetric theory. Dark Matter SUSY leads to the introduction of new particles which could act as DM. Theoretical Appeal The SUSY algebra is the most general Lie algebra of a symmetry of the S-matrix (Haag- Lopusza´ nski-Sohnius-Theorem).
Gauge Coupling Unification In the MSSM the gauge couplings unify at high energies. Hierarchy Problem The quantum corrections to the Higgs mass of bosons and fermions can cancel in a supersymmetric theory. Dark Matter SUSY leads to the introduction of new particles which could act as DM. Theoretical Appeal The SUSY algebra is the most general Lie algebra of a symmetry of the S-matrix (Haag- Lopusza´ nski-Sohnius-Theorem).
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
In a supersymmetric theory the particles form supermultiplets (φ, χ, F), whose bosonic and fermionic fields should be degenerate in mass. If this would be the case in nature, where is the selectron? If SUSY is a symmetry of nature, it must be a broken one. This can be achieved if one of the fields acquire a vacuum expectation value (VEV) F. After SUSY breaking a massless Goldstone fermion, the goldstino, appears in the spectrum. It has scalar superpartners, the sgoldstinos.
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
In a supersymmetric theory the particles form supermultiplets (φ, χ, F), whose bosonic and fermionic fields should be degenerate in mass. If this would be the case in nature, where is the selectron? If SUSY is a symmetry of nature, it must be a broken one. This can be achieved if one of the fields acquire a vacuum expectation value (VEV) F. After SUSY breaking a massless Goldstone fermion, the goldstino, appears in the spectrum. It has scalar superpartners, the sgoldstinos.
7 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
In a supersymmetric theory the particles form supermultiplets (φ, χ, F), whose bosonic and fermionic fields should be degenerate in mass. If this would be the case in nature, where is the selectron? If SUSY is a symmetry of nature, it must be a broken one. This can be achieved if one of the fields acquire a vacuum expectation value (VEV) F. After SUSY breaking a massless Goldstone fermion, the goldstino, appears in the spectrum. It has scalar superpartners, the sgoldstinos.
7 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
In a supersymmetric theory the particles form supermultiplets (φ, χ, F), whose bosonic and fermionic fields should be degenerate in mass. If this would be the case in nature, where is the selectron? If SUSY is a symmetry of nature, it must be a broken one. This can be achieved if one of the fields acquire a vacuum expectation value (VEV) F. After SUSY breaking a massless Goldstone fermion, the goldstino, appears in the spectrum. It has scalar superpartners, the sgoldstinos.
7 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Up until now we considered global Supersymmetry. What happens if we promote SUSY to a local symmetry? The SUSY generators are connected to the generators of the Poincar´ e group:
β
α ˙ βPµ
= ⇒ You cannot have a locally supersymmetric model without gravity. Local Supersymmetry is Supergravity.
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Up until now we considered global Supersymmetry. What happens if we promote SUSY to a local symmetry? The SUSY generators are connected to the generators of the Poincar´ e group:
β
α ˙ βPµ
= ⇒ You cannot have a locally supersymmetric model without gravity. Local Supersymmetry is Supergravity.
8 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The action of the gravity sector is given by S =
2κ2 R − 1 2ǫκλµνψκγ5γλ∂µψν
The spectrum consists of a massless spin-2 graviton and its spin- 3
2 superpartner, the gravitino.
Before SUSY breaking the gravitino has to be massless (m3/2 = 0).
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The action of the gravity sector is given by S =
2κ2 R − 1 2ǫκλµνψκγ5γλ∂µψν
The spectrum consists of a massless spin-2 graviton and its spin- 3
2 superpartner, the gravitino.
Before SUSY breaking the gravitino has to be massless (m3/2 = 0).
9 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The action of the gravity sector is given by S =
2κ2 R − 1 2ǫκλµνψκγ5γλ∂µψν
The spectrum consists of a massless spin-2 graviton and its spin- 3
2 superpartner, the gravitino.
Before SUSY breaking the gravitino has to be massless (m3/2 = 0).
9 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The action of the gravity sector is given by S =
2κ2 R − 1 2ǫκλµνψκγ5γλ∂µψν
The spectrum consists of a massless spin-2 graviton and its spin- 3
2 superpartner, the gravitino.
Before SUSY breaking the gravitino has to be massless (m3/2 = 0).
9 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
A non-zero gravitino mass is a clear indicator of SUSY breaking. The mass m3/2 is connected to the SUSY breaking scale ΛSUSY, m3/2 ∼ κΛ2
SUSY ,
where κ =
In scenarios with Planck-mediated SUSY breaking the gravitino is very heavy. But in general the value of m3/2 depends on the chosen scheme of SUSY breaking.
10 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
A non-zero gravitino mass is a clear indicator of SUSY breaking. The mass m3/2 is connected to the SUSY breaking scale ΛSUSY, m3/2 ∼ κΛ2
SUSY ,
where κ =
In scenarios with Planck-mediated SUSY breaking the gravitino is very heavy. But in general the value of m3/2 depends on the chosen scheme of SUSY breaking.
10 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
After SUSY breaking the goldstino becomes the ± 1
2 helicity
states of the gravitino. The gravitino becomes massive and the goldstino disappears. This is similar to the massive gauge bosons in the electroweak theory. Super-Higgs Mechanism
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
After SUSY breaking the goldstino becomes the ± 1
2 helicity
states of the gravitino. The gravitino becomes massive and the goldstino disappears. This is similar to the massive gauge bosons in the electroweak theory. Super-Higgs Mechanism
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
As a spin 3
2 field its dynamics are governed by the
Rarita-Schwinger equation, ǫµνκλγ5γν∂κψλ + 1 2m3/2 [γµ, γν] ψν = 0 . Its solution can be written as ψµ ∼ e−ipx ˜ ψµ ˜ ψµ( p, λ) =
1 2, s
3 2, λ
p, s)ǫµ( p, m) .
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
As a spin 3
2 field its dynamics are governed by the
Rarita-Schwinger equation, ǫµνκλγ5γν∂κψλ + 1 2m3/2 [γµ, γν] ψν = 0 . Its solution can be written as ψµ ∼ e−ipx ˜ ψµ ˜ ψµ( p, λ) =
1 2, s
3 2, λ
p, s)ǫµ( p, m) .
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
We will also need the spin polarization tensor, Π(±)
µν (p) =
ψs
µ(k) ¯
ψs
ν(k) = −(/
p ± m3/2) ×
m2
3/2
3
m2
3/2
m2
3/2
3 kµkν m2
3/2
/ k ± 1 3 4kµkν − kµ/ kγν − kνγµ/ k m3/2 + O(m0
3/2) .
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
In 1977 the French physicist Pierre Fayet came to the conclusion ” [...]that the super-Higgs mechanism gives to the gravitino, and to gravitation effects in particle physics, their chance to be detected, since weak interactions can be generated from gravitational ones.” An example: Example The gravitino-gaugino-gauge boson coupling is proportional to κ m ˜
V
m3/2 .
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
In 1977 the French physicist Pierre Fayet came to the conclusion ” [...]that the super-Higgs mechanism gives to the gravitino, and to gravitation effects in particle physics, their chance to be detected, since weak interactions can be generated from gravitational ones.” An example: Example The gravitino-gaugino-gauge boson coupling is proportional to κ m ˜
V
m3/2 .
15 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
If m3/2 is very small, its couplings to matter will be enhanced. The interactions will be dominated by its 1
2 helicity states.
It behaves like the goldstino and we can write ψµ ∼ i
3 1 m3/2 ∂µχ . This is the statement of the equivalence theorem.
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
If m3/2 is very small, its couplings to matter will be enhanced. The interactions will be dominated by its 1
2 helicity states.
It behaves like the goldstino and we can write ψµ ∼ i
3 1 m3/2 ∂µχ . This is the statement of the equivalence theorem.
16 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
If m3/2 is very small, its couplings to matter will be enhanced. The interactions will be dominated by its 1
2 helicity states.
It behaves like the goldstino and we can write ψµ ∼ i
3 1 m3/2 ∂µχ . This is the statement of the equivalence theorem.
16 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
If m3/2 is very small, its couplings to matter will be enhanced. The interactions will be dominated by its 1
2 helicity states.
It behaves like the goldstino and we can write ψµ ∼ i
3 1 m3/2 ∂µχ . This is the statement of the equivalence theorem.
16 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
If m3/2 is very small, its couplings to matter will be enhanced. The interactions will be dominated by its 1
2 helicity states.
It behaves like the goldstino and we can write ψµ ∼ i
3 1 m3/2 ∂µχ . This is the statement of the equivalence theorem.
16 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
We will also need the spin polarization tensor, Π(±)
µν (p) =
ψs
µ(k) ¯
ψs
ν(k) = −(/
p ± m3/2) ×
m2
3/2
3
m2
3/2
m2
3/2
3 kµkν m2
3/2
/ k ± 1 3 4kµkν − kµ/ kγν − kνγµ/ k m3/2 + O(m0
3/2) .
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L = − 1 2κ2 R − 1 2ǫκλµνψκγ5γλ∂µψν − 1 4 m3/2ψα
ψβ − 1 4FµνF µν + 1 2λ
(a) [γµ∂µ − mγ] λ(a) − i
8κ
γµλ(a)
αβ
− κ 2 hµν 1 2ηµν ηαβ∂λAα∂λAβ − ∂βAα∂αAβ + ηαβ∂νAα∂µAβ + δν
αδµ β∂λAα∂λAβ − δν α∂βAα∂µAβ − δµ β∂νAα∂αAβ
4 m3/2hαβ
ψµψν − i κ 4 ∂λhαβǫψµγ5
ψν + κ 4
4 cFµνF µνS + i κ 2 m3/2dψµσµνψνS + κ 8 cǫµνρσFµνFρσP + i κ 4 dǫµνρσψµγνψρ∂σP .
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Low mass WIMPs are able to contribute to the energy loss of stars and supernovae. During a Supernova, the binding energy of E ∼ GNM2 R ∼ 3 × 1053erg get released. Most of this energy (> 99%) is released in the form of neutrinos. These neutrinos have been observed in the SN1987A by Kamiokande and IMB. → They found Eν ≥ 2 × 1053erg. Every anomalous energy loss mechanism is bounded by LX < 1052 erg
s .
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Low mass WIMPs are able to contribute to the energy loss of stars and supernovae. During a Supernova, the binding energy of E ∼ GNM2 R ∼ 3 × 1053erg get released. Most of this energy (> 99%) is released in the form of neutrinos. These neutrinos have been observed in the SN1987A by Kamiokande and IMB. → They found Eν ≥ 2 × 1053erg. Every anomalous energy loss mechanism is bounded by LX < 1052 erg
s .
20 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Low mass WIMPs are able to contribute to the energy loss of stars and supernovae. During a Supernova, the binding energy of E ∼ GNM2 R ∼ 3 × 1053erg get released. Most of this energy (> 99%) is released in the form of neutrinos. These neutrinos have been observed in the SN1987A by Kamiokande and IMB. → They found Eν ≥ 2 × 1053erg. Every anomalous energy loss mechanism is bounded by LX < 1052 erg
s .
20 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Low mass WIMPs are able to contribute to the energy loss of stars and supernovae. During a Supernova, the binding energy of E ∼ GNM2 R ∼ 3 × 1053erg get released. Most of this energy (> 99%) is released in the form of neutrinos. These neutrinos have been observed in the SN1987A by Kamiokande and IMB. → They found Eν ≥ 2 × 1053erg. Every anomalous energy loss mechanism is bounded by LX < 1052 erg
s .
20 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Low mass WIMPs are able to contribute to the energy loss of stars and supernovae. During a Supernova, the binding energy of E ∼ GNM2 R ∼ 3 × 1053erg get released. Most of this energy (> 99%) is released in the form of neutrinos. These neutrinos have been observed in the SN1987A by Kamiokande and IMB. → They found Eν ≥ 2 × 1053erg. Every anomalous energy loss mechanism is bounded by LX < 1052 erg
s .
20 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Low mass WIMPs are able to contribute to the energy loss of stars and supernovae. During a Supernova, the binding energy of E ∼ GNM2 R ∼ 3 × 1053erg get released. Most of this energy (> 99%) is released in the form of neutrinos. These neutrinos have been observed in the SN1987A by Kamiokande and IMB. → They found Eν ≥ 2 × 1053erg. Every anomalous energy loss mechanism is bounded by LX < 1052 erg
s .
20 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Low mass WIMPs are able to contribute to the energy loss of stars and supernovae. During a Supernova, the binding energy of E ∼ GNM2 R ∼ 3 × 1053erg get released. Most of this energy (> 99%) is released in the form of neutrinos. These neutrinos have been observed in the SN1987A by Kamiokande and IMB. → They found Eν ≥ 2 × 1053erg. Every anomalous energy loss mechanism is bounded by LX < 1052 erg
s .
20 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1 Find the dominating channels of gravitino production in a
supernova.
2 Calculate the cross-section. 3 Use known properties of supernovae to calculate the
luminosity of the gravitinos produced in a supernova.
4 The luminosity is bounded by L < 1052 erg
s . This constraint
comes from
Stellar Models, Neutrino detection of SN1987A.
5 This can be translated into constraints on m3/2. 21 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1 Find the dominating channels of gravitino production in a
supernova.
2 Calculate the cross-section. 3 Use known properties of supernovae to calculate the
luminosity of the gravitinos produced in a supernova.
4 The luminosity is bounded by L < 1052 erg
s . This constraint
comes from
Stellar Models, Neutrino detection of SN1987A.
5 This can be translated into constraints on m3/2. 21 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1 Find the dominating channels of gravitino production in a
supernova.
2 Calculate the cross-section. 3 Use known properties of supernovae to calculate the
luminosity of the gravitinos produced in a supernova.
4 The luminosity is bounded by L < 1052 erg
s . This constraint
comes from
Stellar Models, Neutrino detection of SN1987A.
5 This can be translated into constraints on m3/2. 21 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1 Find the dominating channels of gravitino production in a
supernova.
2 Calculate the cross-section. 3 Use known properties of supernovae to calculate the
luminosity of the gravitinos produced in a supernova.
4 The luminosity is bounded by L < 1052 erg
s . This constraint
comes from
Stellar Models, Neutrino detection of SN1987A.
5 This can be translated into constraints on m3/2. 21 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1 Find the dominating channels of gravitino production in a
supernova.
2 Calculate the cross-section. 3 Use known properties of supernovae to calculate the
luminosity of the gravitinos produced in a supernova.
4 The luminosity is bounded by L < 1052 erg
s . This constraint
comes from
Stellar Models, Neutrino detection of SN1987A.
5 This can be translated into constraints on m3/2. 21 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1 Find the dominating channels of gravitino production in a
supernova.
2 Calculate the cross-section. 3 Use known properties of supernovae to calculate the
luminosity of the gravitinos produced in a supernova.
4 The luminosity is bounded by L < 1052 erg
s . This constraint
comes from
Stellar Models, Neutrino detection of SN1987A.
5 This can be translated into constraints on m3/2. 21 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
1 Find the dominating channels of gravitino production in a
supernova.
2 Calculate the cross-section. 3 Use known properties of supernovae to calculate the
luminosity of the gravitinos produced in a supernova.
4 The luminosity is bounded by L < 1052 erg
s . This constraint
comes from
Stellar Models, Neutrino detection of SN1987A.
5 This can be translated into constraints on m3/2. 21 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
In supernovae gravitinos could be produced via
1 photon-photon collision γγ −
→ ˜ G ˜ G,
2 nucleon-nucleon Bremsstrahlung NN −
→ NN ˜ G ˜ G,
3 electron-electron Bremsstrahlung e−e− −
→ e−e− ˜ G ˜ G,
4 and electron-positron annihilation e−e+ −
→ ˜ G ˜ G. Especially since nγ ≫ np = ne, nN the first channel is the dominant
22 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
In supernovae gravitinos could be produced via
1 photon-photon collision γγ −
→ ˜ G ˜ G,
2 nucleon-nucleon Bremsstrahlung NN −
→ NN ˜ G ˜ G,
3 electron-electron Bremsstrahlung e−e− −
→ e−e− ˜ G ˜ G,
4 and electron-positron annihilation e−e+ −
→ ˜ G ˜ G. Especially since nγ ≫ np = ne, nN the first channel is the dominant
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
iM = p1 − k2 ǫβ
2
ǫα
1
v ν
1
uµ
2
+ p2 − k2 ǫβ
2
ǫα
1
v ν
1
uµ
2
+ ǫβ
2
ǫα
1
v ν
1
uµ
2
+ ǫβ
2
ǫα
1
v ν
1
uµ
2
+ ǫβ
2
ǫα
1
v ν
1
uµ
2
.
23 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
iM = iMPhotino + iMGraviton + iMScalar + iMPseudoscalar , where iMPhotino = iκ2 4 ǫα
1 ǫβ 2 pκ 1 pλ 2
uµ
2 σακγµ
/ q1 − mγ q2
1 − m2 γ
γνσβλvν
1
+ iκ2 4 ǫα
2 ǫβ 1 pκ 2 pλ 1
uµ
2 σακγµ
/ q2 − mγ q2
2 − m2 γ
γνσβλvν
1 ,
iMGraviton = κ2 2(p1 + p2)2
1 pρ 2 +
1 2
+ (p1 · p2)ǫλ
1 ǫρ 2 − (p2 · ǫ1)ǫρ 2 pλ 1 − (p1 · ǫ2)pλ 2 ǫρ 1 + (ρ ↔ λ)
2
i 2 ǫµσν(λγ5 γσ, σρ)τ
1 ,
iMScalar = iκ2mγ (p1 + p2)2 ǫα
1 ǫβ 2
1 pα 2
2 vν 1 ,
iMPseudoScalar = − iκ2mγ 2m3/2 1 (p1 + p2)2 ǫα
1 ǫβ 2 pκ 1 pλ 2 ǫκλαβ (p1 + p2)ζ ǫµδνζ uµ 2 γδvν 1 .
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
After squaring the amplitude we obtain terms like |MPseudoScalar|2 = 1 m2
3/2
Tr
i MPseudoScalar
1 m3/2 Tr
2,µν
25 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The result for the cross-section is given by σ(γγ → ˜ G ˜ G) = κ4m4
˜ γs
1728πm4
3/2
1 + x
x − 24 x2
1 x + 2 48 x3 + 24 x2 − 6 x
where x ≡
s m2
˜ γ . For this calculation we used the Mathematica
package FeynCalc. In the limit m˜
γ ≫ √s this yields
σ(γγ → ˜ G ˜ G) = κ4s2m2
˜ γ
576πm4
3/2
+ O(x0) .
26 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The result for the cross-section is given by σ(γγ → ˜ G ˜ G) = κ4m4
˜ γs
1728πm4
3/2
1 + x
x − 24 x2
1 x + 2 48 x3 + 24 x2 − 6 x
where x ≡
s m2
˜ γ . For this calculation we used the Mathematica
package FeynCalc. In the limit m˜
γ ≫ √s this yields
σ(γγ → ˜ G ˜ G) = κ4s2m2
˜ γ
576πm4
3/2
+ O(x0) .
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Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The gravitino luminosity is given by
L = V
(2π)3 2p0
1
2nγ(p0
1)
(2π)3 2p0
2
2nγ(p0
2)
(2π)3 2k0
1
(2π)3 2k0
2
(2π)4δ(4)(p1 + p2 − k1 − k2)(k0
1 + k0 2)
G ˜ G)
,
leading to
L > 8V (2π)6
1+p0 2)/T(p0
1 + p0 2) (1 − cos α) σ(γγ −
→ ˜ G ˜ G) = 160 π5
m3/2 4 m2
˜ γVT 11 SN. 27 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Now we are able to translate this relation into a constraint on m3/2 using the observational bound from SN1987A. m3/2 > 1.8 × 10−5eV . But this bound is valid only as long as the gravitinos are not trapped inside the SN core like the neutrinos.
28 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Now we are able to translate this relation into a constraint on m3/2 using the observational bound from SN1987A. m3/2 > 1.8 × 10−5eV . But this bound is valid only as long as the gravitinos are not trapped inside the SN core like the neutrinos.
28 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The mean-free-path of a gravitino in the SN core is given by λMFP ∼
G − → γ ˜ G) −1 = 8π3 9ζ(3)m4
3/2κ−4m−2 ˜ γ
T −7 . The bound is only valid if λMFP > RSN. We obtain λMFP ∼ 2.1 × 106
1.8 × 10−5eV 4 km ≫ 10 RSN 10km
29 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The mean-free-path of a gravitino in the SN core is given by λMFP ∼
G − → γ ˜ G) −1 = 8π3 9ζ(3)m4
3/2κ−4m−2 ˜ γ
T −7 . The bound is only valid if λMFP > RSN. We obtain λMFP ∼ 2.1 × 106
1.8 × 10−5eV 4 km ≫ 10 RSN 10km
29 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The whole argument breaks down, if the gravitino is so light such that λMFP ≪ RSN. This gives us an upper bound on the gravitino mass. Main Result We can exclude the range 6.2 × 10−8eV < m3/2 < 1.8 × 10−5eV for the gravitino mass based on the observation of SN1987A.
30 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
The whole argument breaks down, if the gravitino is so light such that λMFP ≪ RSN. This gives us an upper bound on the gravitino mass. Main Result We can exclude the range 6.2 × 10−8eV < m3/2 < 1.8 × 10−5eV for the gravitino mass based on the observation of SN1987A.
30 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
This result was verified during the first months of my Master’s thesis. This is work in progress. Right now we are working on including bilinear R parity violations. In scenarios with bilinear RPV, we typically obtain a non-vanishing sneutrino VEV and neutralino-neutrino mixing. This gives rise to an effective gravitino-photon-neutrino vertex. Therefore single gravitino production becomes possible and we are looking for the dominating channels.
31 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
This result was verified during the first months of my Master’s thesis. This is work in progress. Right now we are working on including bilinear R parity violations. In scenarios with bilinear RPV, we typically obtain a non-vanishing sneutrino VEV and neutralino-neutrino mixing. This gives rise to an effective gravitino-photon-neutrino vertex. Therefore single gravitino production becomes possible and we are looking for the dominating channels.
31 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
This result was verified during the first months of my Master’s thesis. This is work in progress. Right now we are working on including bilinear R parity violations. In scenarios with bilinear RPV, we typically obtain a non-vanishing sneutrino VEV and neutralino-neutrino mixing. This gives rise to an effective gravitino-photon-neutrino vertex. Therefore single gravitino production becomes possible and we are looking for the dominating channels.
31 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
This result was verified during the first months of my Master’s thesis. This is work in progress. Right now we are working on including bilinear R parity violations. In scenarios with bilinear RPV, we typically obtain a non-vanishing sneutrino VEV and neutralino-neutrino mixing. This gives rise to an effective gravitino-photon-neutrino vertex. Therefore single gravitino production becomes possible and we are looking for the dominating channels.
31 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
This result was verified during the first months of my Master’s thesis. This is work in progress. Right now we are working on including bilinear R parity violations. In scenarios with bilinear RPV, we typically obtain a non-vanishing sneutrino VEV and neutralino-neutrino mixing. This gives rise to an effective gravitino-photon-neutrino vertex. Therefore single gravitino production becomes possible and we are looking for the dominating channels.
31 / 33
Supersymmetry and Supergravity Gravitino Phenomenology Supernovae Constraints on superlight Gravitinos Concluding Remarks
Supersymmetry and its local version, Supergravity are very appealing extensions of the SM. In some Supergravity models there are superlight gravitinos. A significant and observable amount of these could be produced in Supernovae. This would extend the known energy loss mechanisms of SN. The observation of SN1987A allows us to exclude the mass range 6.2 × 10−8eV < m3/2 < 1.8 × 10−5eV. In the future we hope to find new results for models with R parity violations.
32 / 33