Gluo-dissociation and quasi-free dissociation in the EFT framework Miguel A. Escobedo Physik-Department T30f. Technische Universit¨ at M¨ unchen 6th of october Nora Brambilla, MAE, Jacopo Ghiglieri, Antonio Vairo. [arxiv:1109.5826] QWG workshop 2011, Optober 6, GSI Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 1 / 38
Outline Motivation 1 Gluo-dissociation 2 Quasi-free dissociation 3 Conclusions 4 Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 2 / 38
Motivation Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 3 / 38
What has been found until now using EFTs in Quarkonia? EFT provide a systematic way to extract information from the fact that m Q ≫ 1 r ≫ E in Quarkonia. Computations are easier and it is more difficult to neglect a needed resummation. For T ≫ 1 r ∼ m D we recover the perturbative potential with an imaginary part found by Laine, Philipsen, Romatschke and Tassler (2007). For T � 1 r we were able to compute thermal corrections to the binding energies and the decay width. For the decay width we found two different mechanism. Gluo-dissociation and Landau damping (or quasi-free dissociation). Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 4 / 38
Other approach to quarkonia decay width Use a cross-section computed at T = 0, σ ( k ). Convolute with the thermal distribution d 3 k � Γ = (2 π ) 3 f ( k ) σ ( k ) These cross-sections are computed in perturbation theory and later they are ”adapted” to strong coupling by using α s as a free parameter, introducing thermal masses... This information is used as an input to predict the observed suppression in nowadays experiments. See for example Zhao and Rapp (2010). Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 5 / 38
Perturbative computations of cross-section for quarkonia in the literature Gluo-dissociation Bhanot and Peskin (1979) Quasi-free dissociation Combridge (1978), Park, Kim, Song, Lee and Wong (2007) Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 6 / 38
Motivation Translate the EFT results that have been found to cross-sections convoluted with distribution function ”language”. Analyze the assumptions made by previous perturbative computations and check if they agree or disagree with the EFT framework. Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 7 / 38
Gluo-dissociation Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 8 / 38
Gluo-dissociation in Bhanot and Peskin They use OPE. The interaction between the singlet, the octet and the gluon is a color dipole interaction. Similar to what is done in pNRQCD. They use the large N c limit approximation. In this limit V o = 0 and computations are simplified. We are going to see that the large N c limit is a good approximation for T ≫ E but not for T ∼ E . Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 9 / 38
Gluo-dissociation in pNRQCD Computed for T ≫ E in HQ. Brambilla, MAE, Ghiglieri, Soto and Vairo (2010) δ Γ n = 1 s T − 16 3 mC F α s TE n + 4 2 3 N 2 C C F α 3 3 N C C F α 2 s T mn 2 a 0 where E n is the binding energy and a 0 the Bohr radius. Computed for T ∼ E in the hydrogen atom. MAE and Soto (2008). | E n − h o | 3 δ Γ n = 4 3 α s C F T � n | r i e β | E n − h o | − 1 r i | n � Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 10 / 38
Cutting rules at finite temperature Similar to what is found at T = 0. Multiply by n B ( k ) ( n F ( k )) for in-coming bosons (fermions). Multiply by 1 + n B ( k ) (1 − n F ( k )) for out-going bosons (fermions). Kobes and Semenoff (1986) Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 11 / 38
Cutting rules at finite temperature Similar to what is found at T = 0. Multiply by n B ( k ) ( n F ( k )) for in-coming bosons (fermions). Multiply by 1 + n B ( k ) (1 − n F ( k )) for out-going bosons (fermions). In this case we get a structure d 3 k � δ Γ n = (2 π ) 3 n B ( k ) � n | h σ ( r , p , k ) | n � Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 12 / 38
A choice d 3 k � (2 π ) 3 n B ( k ) � n | h σ ( r , p , k ) | n � δ Γ n = If we integrate out k first we recover the pNRQCD result If we choose for example n = 1 S and compute the matrix element. d 3 k � δ Γ 1 S = (2 π ) 3 n B ( k ) σ gd ( k ) Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 13 / 38
pNRQCD gluo-dissociation σ gd for 1 S If we do the same approximations as Bhanot and Peskin (large N c limit) we recover their result. Without doing this approximation we get σ gd ( k ) = 8 π 2 C F α s ma 2 0 k |� 1 S | r i | ma 2 0 ( k + E 1 ) � o | 2 Θ( k + E 1 ) 3 | ǫ � o are the octet wave function taking into account the octet potential. � ∞ d ǫ � ǫ | ǫ � o = 1 0 Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 14 / 38
pNRQCD gluo-dissociation σ gd for 1 S The Coulomb wave-function with a repulsive potential (as the one of the octet) were taken from Abramowitz and Stegun (1972) �� 2 � �� 2 � � � 32 π C F α s ma 3 1 1 0 k C 1 f 8 √ τ √ τ σ gd ( k ) = Θ( τ ) 3 τ 7 / 2 where τ = ma 2 0 ( k + E 1 ) √ � 1+ x 2 2 π x C 1 ( x ) = 3 e 2 π x − 1 x 4 arccot ( x ) f ( x ) = 51 xe 2 ( x +1) 3 Agrees with Brezinski and Wolschin (2011) Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 15 / 38
Comparison between Bhanot and Peskin and pNRQCD gluo-dissociation σ gd ( k ) = σ R g ( x ) with σ R = 32 π C F α s a 2 k 0 and x = 3 | E 1 | g 3.0 2.5 2.0 1.5 1.0 0.5 x 2 4 6 8 10 Bhanot and Peskin large N c limit pNRQCD Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 16 / 38
Comparison between Bhanot and Peskin and pNRQCD gluo-dissociation Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 17 / 38
Comparison between Bhanot and Peskin and pNRQCD gluo-dissociation Bhanot and Peskin, pNRQCD Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 18 / 38
Comparison between Bhanot and Peskin and pNRQCD gluo-dissociation At asymptotically high values of T the ratio tends to the constant 289 256 . Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 19 / 38
Quasi-free dissociation bo (Or Landau damping) Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 20 / 38
Quasi-free in Combridge He computed the process qc → qc for a charm quark, no information of the bound state is included. Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 21 / 38
Quasi-free in Combridge He computed the process qc → qc for a charm quark, no information of the bound state is included. Note that in NRQCD (valid for m Q ≫ T ) and using the Coulomb gauge the crossed diagrams are subleading. Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 22 / 38
HQ potential for T ≫ 1 r ∼ m D Laine, Philipsen, Romatschke and Tassler pNRQCD + + = Miguel A. Escobedo (Physik-Department T30f. Technische Universit¨ Gluo-dissociation and quasi-free dissociation in the EFT framework at M¨ unchen) 6th of october 23 / 38
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