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Holographic 3-jet events
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Nuclear and Particle Physics Proceedings 276–278 (2016) 115–116 www.elsevier.com/locate/nppp
Holographic 3-jet events Jorge Casalderrey-Solanaa , Andrej Ficnarb a Departament
d’Estructura i Constituents de la Mat`eria and Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona, Mart´ı i Franqu`es 1, 08028 Barcelona, Spain b Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
Abstract We numerically simulate classical falling string configurations in AdS with non-trivial transverse dynamics. These strings develop kink-like structures which, in the dual theory, can be interpreted as the propagation of hard gluons produced in association with a quark-antiquark pair in a strongly coupled plasma. We observe the appearance of two physically distinct regimes of the in-plasma dynamics depending on whether the medium is able to resolve the transverse structure of the string prior to its total quench. From these regimes we extract the transverse resolution angle of the strongly coupled SYM plasma and confront it with perturbative results. Keywords: Holography, quark-gluon plasma, jet quenching 8
1. Introduction
http://dx.doi.org/10.1016/j.nuclphysbps.2016.05.022 2405-6014/© 2016 Published by Elsevier B.V.
6
Τ y0,Σ
Light quarks in holography can be modeled with classical strings that have one endpoint attached to a D7brane in the bulk of AdS . A light qq¯ pair that has undergone a hard scattering is then typically modeled by an initially pointlike open string created close to the boundary with endpoints that are free to fly apart and fall towards the black hole, the so-called falling strings [1]. We will use this model to simulate a production of a hard gluon in a strongly coupled plasma, associated with this qq¯ pair. A simple way to achieve this is to add extra transverse structure to this configuration, by including an additional initial velocity profile in the transverse y−direction, such that the endpoint (σ = 0) gets a “kick” in one direction, while some other part of the string gets a “kick” in the other direction (Fig. 1). A generic consequence of this is that, at late times, the string can develop a well defined kink where the string doubles back on itself (Fig. 2). There is a part of the string between the endpoint and the kink that reaches the horizon first, causing the endpoint and the kink to be causally separated. We interpret this as the medium resolving the “quark” (endpoint) from the emitted “gluon” (doubled part of the string).
4 2 0 2 4 0.0
0.5
1.0
1.5
Σ Figure 1: Initial velocity profile in the transverse y−direction as a function of the string parameter σ.
2. Resolved and unresolved cases As we can see in Fig. 2, the endpoint and the kink define an angle, θqg , which, at high energies, is related to the ratio of the momenta in the y− and x− directions. Keeping this angle and the initial radial depth at which the string is produced fixed, while increasing the energy, more and more of the string gets pushed further out in the x−direction, eventually saturating the maximum stopping distance limit (Fig. 3).
J. Casalderrey-Solana, A. Ficnar / Nuclear and Particle Physics Proceedings 276–278 (2016) 115–116
116 5
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Θqg 1o Θqg 3.2o Θqg 10o
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100
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Energy of the right half of the string 1.0
Figure 4: Ratio of the endpoint’s stopping distance and the minimal stopping distance as a function of energy, for several fixed angles (different colors) and for a variety of initial conditions in the longitudinal direction (different families are connected by lines). Figure 2: A 3D plot of typical falling string profiles with the extra transverse structure from Fig. 1, at several fixed times (corresponding to different colors). 6
y zH
4 2 0 2 4 6 0
5
10
15
20
x zH
Figure 3: Plot of the string profiles at different fixed times in the x − y plane, for the unresolved case. The dashed line indicates the maximum stopping distance, as given by the corresponding null geodesic.
We see that, for a fixed angle θqg , there is a minimal energy, below which this ratio is roughly unity, indicating that we cannot resolve the quark and the gluon. Extracting this minimal resolution energy from Fig. 4 and repeating the analysis for several functionally different set of initial conditions in the transverse direction, our numerical simulations indicate that they are all consistent with the following scaling θqg ∼ E −0.64 . This can be directly compared to the perturbative result, where, relating the typical energy dependence of stopping distance in pQCD [2] and the angle dependence of the transverse coherence length [3], one gets θqg,pQCD ∼ E −3/4 . 4. Acknowledgements
In this case, the causal separation is lost, the quark and the gluon are not well defined, and this is what we call the unresolved case. 3. Finding the minimal resolution energy As we just saw, for some sets of initial conditions, corresponding to very low or very high energies, the medium will not be able to resolve the transverse structure. We will be, therefore, looking for an intermediate energy scale, where, for a fixed angle, the medium is be able to resolve the quark and the gluon as separate objects. For this purpose, we can vary the initial conditions, while keeping the angle θqg fixed, and repeat this for several angles. As we saw before, a simple resolution criterion is to look at the ratio of the endpoint’s stopping distance and the minimal stopping distance (Fig. 4).
AF was supported by the European Research Council under the European Union’s Seventh Framework Programme (ERC Grant agreement 307955). JCS was supported by a Ram´on y Cajal fellowship and by grants FP7-PEOPLE-2012-GIG-333786, FPA201346570 and FPA2013-40360-ERC, MDM-2014-0369 and 2014-SGR-104. References [1] P. M. Chesler, K. Jensen, A. Karch, Jets in strongly-coupled N = 4 super Yang-Mills theory, Phys. Rev. D79 (2009) 025021. arXiv:0804.3110, doi:10.1103/PhysRevD.79.025021. [2] R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne, D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark - gluon plasma, Nucl. Phys. B483 (1997) 291–320. arXiv:hep-ph/9607355, doi:10.1016/S0550-3213(96)00553-6. [3] J. Casalderrey-Solana, E. Iancu, Interference effects in mediuminduced gluon radiation, JHEP 08 (2011) 015. arXiv:1105.1760, doi:10.1007/JHEP08(2011)015.
Nuclear and Particle Physics Proceedings 276–278 (2016) 115–116 www.elsevier.com/locate/nppp
Holographic 3-jet events Jorge Casalderrey-Solanaa , Andrej Ficnarb a Departament
d’Estructura i Constituents de la Mat`eria and Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona, Mart´ı i Franqu`es 1, 08028 Barcelona, Spain b Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
Abstract We numerically simulate classical falling string configurations in AdS with non-trivial transverse dynamics. These strings develop kink-like structures which, in the dual theory, can be interpreted as the propagation of hard gluons produced in association with a quark-antiquark pair in a strongly coupled plasma. We observe the appearance of two physically distinct regimes of the in-plasma dynamics depending on whether the medium is able to resolve the transverse structure of the string prior to its total quench. From these regimes we extract the transverse resolution angle of the strongly coupled SYM plasma and confront it with perturbative results. Keywords: Holography, quark-gluon plasma, jet quenching 8
1. Introduction
http://dx.doi.org/10.1016/j.nuclphysbps.2016.05.022 2405-6014/© 2016 Published by Elsevier B.V.
6
Τ y0,Σ
Light quarks in holography can be modeled with classical strings that have one endpoint attached to a D7brane in the bulk of AdS . A light qq¯ pair that has undergone a hard scattering is then typically modeled by an initially pointlike open string created close to the boundary with endpoints that are free to fly apart and fall towards the black hole, the so-called falling strings [1]. We will use this model to simulate a production of a hard gluon in a strongly coupled plasma, associated with this qq¯ pair. A simple way to achieve this is to add extra transverse structure to this configuration, by including an additional initial velocity profile in the transverse y−direction, such that the endpoint (σ = 0) gets a “kick” in one direction, while some other part of the string gets a “kick” in the other direction (Fig. 1). A generic consequence of this is that, at late times, the string can develop a well defined kink where the string doubles back on itself (Fig. 2). There is a part of the string between the endpoint and the kink that reaches the horizon first, causing the endpoint and the kink to be causally separated. We interpret this as the medium resolving the “quark” (endpoint) from the emitted “gluon” (doubled part of the string).
4 2 0 2 4 0.0
0.5
1.0
1.5
Σ Figure 1: Initial velocity profile in the transverse y−direction as a function of the string parameter σ.
2. Resolved and unresolved cases As we can see in Fig. 2, the endpoint and the kink define an angle, θqg , which, at high energies, is related to the ratio of the momenta in the y− and x− directions. Keeping this angle and the initial radial depth at which the string is produced fixed, while increasing the energy, more and more of the string gets pushed further out in the x−direction, eventually saturating the maximum stopping distance limit (Fig. 3).
J. Casalderrey-Solana, A. Ficnar / Nuclear and Particle Physics Proceedings 276–278 (2016) 115–116
116 5
20 10
0
2.2
0
5
10 20
y
x
2.0
rendpoint rmin
0.0
z
Θqg 1o Θqg 3.2o Θqg 10o
1.8 1.6 1.4
0.5
1.2 1.0
10
100
1000
104
105
106
107
Energy of the right half of the string 1.0
Figure 4: Ratio of the endpoint’s stopping distance and the minimal stopping distance as a function of energy, for several fixed angles (different colors) and for a variety of initial conditions in the longitudinal direction (different families are connected by lines). Figure 2: A 3D plot of typical falling string profiles with the extra transverse structure from Fig. 1, at several fixed times (corresponding to different colors). 6
y zH
4 2 0 2 4 6 0
5
10
15
20
x zH
Figure 3: Plot of the string profiles at different fixed times in the x − y plane, for the unresolved case. The dashed line indicates the maximum stopping distance, as given by the corresponding null geodesic.
We see that, for a fixed angle θqg , there is a minimal energy, below which this ratio is roughly unity, indicating that we cannot resolve the quark and the gluon. Extracting this minimal resolution energy from Fig. 4 and repeating the analysis for several functionally different set of initial conditions in the transverse direction, our numerical simulations indicate that they are all consistent with the following scaling θqg ∼ E −0.64 . This can be directly compared to the perturbative result, where, relating the typical energy dependence of stopping distance in pQCD [2] and the angle dependence of the transverse coherence length [3], one gets θqg,pQCD ∼ E −3/4 . 4. Acknowledgements
In this case, the causal separation is lost, the quark and the gluon are not well defined, and this is what we call the unresolved case. 3. Finding the minimal resolution energy As we just saw, for some sets of initial conditions, corresponding to very low or very high energies, the medium will not be able to resolve the transverse structure. We will be, therefore, looking for an intermediate energy scale, where, for a fixed angle, the medium is be able to resolve the quark and the gluon as separate objects. For this purpose, we can vary the initial conditions, while keeping the angle θqg fixed, and repeat this for several angles. As we saw before, a simple resolution criterion is to look at the ratio of the endpoint’s stopping distance and the minimal stopping distance (Fig. 4).
AF was supported by the European Research Council under the European Union’s Seventh Framework Programme (ERC Grant agreement 307955). JCS was supported by a Ram´on y Cajal fellowship and by grants FP7-PEOPLE-2012-GIG-333786, FPA201346570 and FPA2013-40360-ERC, MDM-2014-0369 and 2014-SGR-104. References [1] P. M. Chesler, K. Jensen, A. Karch, Jets in strongly-coupled N = 4 super Yang-Mills theory, Phys. Rev. D79 (2009) 025021. arXiv:0804.3110, doi:10.1103/PhysRevD.79.025021. [2] R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne, D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark - gluon plasma, Nucl. Phys. B483 (1997) 291–320. arXiv:hep-ph/9607355, doi:10.1016/S0550-3213(96)00553-6. [3] J. Casalderrey-Solana, E. Iancu, Interference effects in mediuminduced gluon radiation, JHEP 08 (2011) 015. arXiv:1105.1760, doi:10.1007/JHEP08(2011)015.