Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions arXiv:1106.3509 Motivation Scalar Bremsstrahlung in Gravity-Mediated Introduction General setup Ultrarelativistic Collisions The radiation amplitude The emitted Energy - Spectral and Angular Distribution Yiannis Constantinou Summary of Results Future work Physics Department University of Crete December 9, 2011 Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 1 / 29
Outline Scalar Bremsstrahlung in 1 Motivation Gravity-Mediated Ultrarelativistic Collisions Introduction 2 arXiv:1106.3509 General setup 3 Motivation The action Introduction Equations of motion General setup Iterative solution The radiation amplitude Φ radiation The emitted Energy - Spectral and Angular Distribution 4 The radiation amplitude Summary of Results The local amplitude Future work The non-local amplitude The part j n z ( k ) of the radiation amplitude and destructive interference The part j n z ′ ( k ) of the amplitude Summary The emitted Energy - Spectral and Angular Distribution 5 Summary of Results 6 7 Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 2 / 29
Motivation Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions arXiv:1106.3509 Motivation Introduction General setup The radiation amplitude The emitted Energy - Spectral and Angular Distribution Summary of Results Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 3 / 29
Motivation Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions arXiv:1106.3509 Motivation Introduction In the context of large extra dimensions, it is possible to have TeV General setup scale gravity [ADD]. The radiation amplitude The emitted Energy - Spectral and Angular Distribution Summary of Results Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 3 / 29
Motivation Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions arXiv:1106.3509 Motivation Introduction In the context of large extra dimensions, it is possible to have TeV General setup scale gravity [ADD]. The radiation amplitude Black holes can be formed in colliders for M > M ∗ and b ≤ R s The emitted Energy - Spectral and Angular [Argyres et. al. 1998]. Distribution Summary of Results Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 3 / 29
Motivation Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions arXiv:1106.3509 Motivation Introduction In the context of large extra dimensions, it is possible to have TeV General setup scale gravity [ADD]. The radiation amplitude Black holes can be formed in colliders for M > M ∗ and b ≤ R s The emitted Energy - Spectral and Angular [Argyres et. al. 1998]. Distribution Various models have been proposed to compute the Summary of Results Future work gravitational bremstrahlung[ D’Eath and Payne, Eardley and Giddings] (Colliding waves model, ACV model). Alternative methods are desirable. Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 3 / 29
Introduction Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions arXiv:1106.3509 Based on work with Dmitry Gal’tsov, Pavel Spirin and Theodore Motivation Introduction Tomaras General setup Gravitational bremstrahlung two massive particles → The radiation amplitude complicated. The emitted Energy - Spectral and Angular Emission of scalar radiation of gravitationally interacting particles Distribution → intermediate step. Summary of Results Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 4 / 29
Introduction Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions arXiv:1106.3509 Based on work with Dmitry Gal’tsov, Pavel Spirin and Theodore Motivation Introduction Tomaras General setup Gravitational bremstrahlung two massive particles → The radiation amplitude complicated. The emitted Energy - Spectral and Angular Emission of scalar radiation of gravitationally interacting particles Distribution → intermediate step. Summary of Results Future work Two massive particles, one of which is coupled to a scalar field. The interaction is purely gravitational. Non-linear problem, because of the graviton - graviton - scalar interaction Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 4 / 29
The action Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions We assume the ADD scenario and a space-time M 4 × T d arXiv:1106.3509 Motivation Introduction General setup The action Equations of motion Iterative solution Φ radiation The radiation amplitude The emitted Energy - Spectral and Angular Distribution Summary of Results Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 5 / 29
The action Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions We assume the ADD scenario and a space-time M 4 × T d arXiv:1106.3509 Two classical massive particles with mass m and m ′ that interact Motivation only gravitationally. Introduction General setup The action Equations of motion Iterative solution Φ radiation The radiation amplitude The emitted Energy - Spectral and Angular Distribution Summary of Results Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 5 / 29
The action Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions We assume the ADD scenario and a space-time M 4 × T d arXiv:1106.3509 Two classical massive particles with mass m and m ′ that interact Motivation only gravitationally. Introduction A massless scalar field Φ that interacts with m but not m ′ . General setup The action Equations of motion Iterative solution Φ radiation The radiation amplitude The emitted Energy - Spectral and Angular Distribution Summary of Results Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 5 / 29
The action Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions We assume the ADD scenario and a space-time M 4 × T d arXiv:1106.3509 Two classical massive particles with mass m and m ′ that interact Motivation only gravitationally. Introduction A massless scalar field Φ that interacts with m but not m ′ . General setup The action The action will be: Equations of motion Iterative solution Φ radiation S = S g + S Φ + S m + S m ′ The radiation amplitude The emitted Energy - Spectral and Angular Distribution Summary of Results � � � − R + 1 d D x � 2 g MN ∂ M Φ ∂ N Φ S = | g | Future work κ 2 D z N + ( m + f Φ) 2 z ′ N + m ′ 2 � � � � � � − 1 d τ − 1 z M ˙ z ′ M ˙ e ′ g MN ˙ d τ ′ e g MN ˙ e ′ 2 e 2 Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 5 / 29
Equations of motion Scalar Bremsstrahlung in Gravity-Mediated The equations of motion for the two particles are produced by Ultrarelativistic Collisions arXiv:1106.3509 varying the action: Motivation = e ′ d = e d Introduction � eg ′ z N � 2 g ′ z L ˙ z R , � e ′ g MN ˙ z ′ N � z ′ L ˙ z ′ R , MN ˙ LR , M ˙ 2 g LR , M ˙ d τ d τ General setup The action Equations of motion Iterative solution Φ radiation The radiation amplitude The emitted Energy - Spectral and Angular Distribution Summary of Results Future work Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 6 / 29
Equations of motion Scalar Bremsstrahlung in Gravity-Mediated The equations of motion for the two particles are produced by Ultrarelativistic Collisions arXiv:1106.3509 varying the action: Motivation = e ′ d = e d Introduction � eg ′ z N � 2 g ′ z L ˙ z R , � e ′ g MN ˙ z ′ N � z ′ L ˙ z ′ R , MN ˙ LR , M ˙ 2 g LR , M ˙ d τ d τ General setup The action Equations of motion Iterative solution Φ radiation while variation with respect to the einbeins gives The radiation amplitude z M ˙ z ′ M ˙ g ′ MN ˙ z N e ′− 2 = g MN ˙ z ′ N The emitted Energy - e − 2 = Spectral and Angular Distribution ( m + f Φ) 2 m ′ 2 Summary of Results Plugging these back into the action and varying with respect to Future work Φ , we obtain the scalar field EOM: � D Φ = − κ D � z M ˙ MN Φ , MN + f z N ) 1 / 2 δ D ( x − z ( τ )) d τ, 2 h ′ � D Φ+ κ D h ′ ( g ′ MN ˙ Scalar Bremsstrahlung in Gravity-Mediated Ultrarelativistic Collisions : arXiv:1106.3509 (Physics Department, UoC) 6 / 29
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