K meson in dense matter L. Tols 1 , R. Molina 2 , E. Oset 2 and A. - PowerPoint PPT Presentation

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results K ∗ meson in dense matter ¯ L. Tolós 1 , R. Molina 2 , E. Oset 2 and A. Ramos 3 1 Theory Group. KVI. University of Groningen, Zernikelaan 25, 9747 AA Groningen, The Netherlands 2 Instituto de Física Corpuscular (centro mixto CSIC-UV) Institutos de Investigación de Paterna, Aptdo. 22085, 46071, Valencia, Spain 3 Estructura i Constituents de la Materia. Facultat de Física. Universitat de Barcelona, Avda. Diagonal 647, 08028 Barcelona, Spain

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results Outline Introduction 1 K ∗ self-energy from the s-wave ¯ ¯ K ∗ N interaction 2 K ∗ → ¯ ¯ K π in dense matter 3 Results 4 Nuclear transparency in the γ A → K + K ∗− A ′ reaction 5 Conclusions 6

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results Previous results on the interaction of vector mesons with nuclear matter Within the Nambu Jona Lasinio model there is no shift of the vector masses while the σ -mass decreases sharply with the density. V. Bernard and U. G. Meissner, Nucl. Phys. A 489 , 647 (1988). Recent calculations show no shift of the ρ meson and a broadening of the vector meson in nuclear matter. Rapp, 97; Urban, 99; D. Cabrera, E. Oset and M. J. Vicente Vacas, Nucl. Phys. A 705 , 90 (2002): △ M ( ρ 0 ) ∼ 30 MeV, Γ( ρ 0 ) ∼ 200 MeV. In the case of the φ meson, theoretical calculations also show no shift of the mass and a broadening of the meson. D. Cabrera and M. J. Vicente Vacas, Phys. Rev. C 67 , 045203 (2003): △ M ( ρ 0 ) ∼ 8 MeV, Γ( ρ 0 ) ∼ 30 MeV. The case of the ω meson had been more controvelsial [1,2,3,4,5]. M. Post, S. Leupold and U. Mosel, Nucl. Phys. A 741 , 81 (2004) 1. M. Kaskulov, H. Nagahiro, S. Hirenzaki and E. Oset, Phys. Rev. C 75 , 064616 (2007) 2. D. Trnka et al. [CBELSA/TAPS Collaboration], Phys. Rev. Lett. 94 , 192303 (2005) 3. 4. Mariana Nanova, Talk given at the XIII International Conference on Hadron Spectroscopy, December 2009, Florida State University. M. Kotulla et al. [CBELSA/TAPS Collaboration], Phys. Rev. Lett. 100 , 192302 (2008) 5.

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results Previous results on the interaction of vector mesons with nuclear matter In M. Kaskulov, E. Hernandez and E. Oset, Eur. Phys. J. A 31 , 245 (2007) the authors predict no shift and a width of Γ( ρ 0 ) ∼ 90 MeV at normal nuclear density. Experiments done by the CLASS Collaboration confirms this null shift for the ρ mass and a broadening of the ρ, ω, φ mesons at normal nuclear density. M. H. Wood et al. [CLAS Collaboration], Phys. Rev. C 78 , 015201 (2008). C. Djalali et al. , Nucl. Part. Phys. 35 , 104035 (2008). These theoretical predictions and the results of CLASS are in contradiction with the parametrization derived by Hatsuda and Lee: m = m 0 ( 1 − 0 . 16 ρ ) ρ 0 and with the 20 % decrease in the ρ meson mass predicted by Brown and Rho. While the KEK team had earlier reported an attractive mass shift of the ρ . Conclusions could depend on the way the background is subtracted. R. Muto et al. [KEK-PS-E325 Collaboration], Phys. Rev. Lett. 98 , 042501 (2007)

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results The VB → VB interaction L III = − 1 L ( 3 V ) 4 � V µν V µν � = ig � ( ∂ µ V ν − ∂ ν V µ ) V µ V ν � III III = g 2 L ( c ) 2 � V µ V ν V µ V ν − V ν V µ V µ V ν � V µν , g V µ ρ 0 V µν = ∂ µ V ν − ∂ ν V µ − ig [ V µ , V ν ]   ω ρ + K ∗ + 2 + √ √ 2  − ρ 0  g = MV K ∗ 0   ω ρ − 2 + 2 f  √ √  2   K ∗ 0 K ∗− ¯ φ µ L BBV = g 2 ( � ¯ B γ µ [ V µ , B ] � + � ¯ B γ µ B �� V µ � ) 1. Klingl,97; Palomar,02; M. Bando, T. Kugo, S. Uehara, K. Yamawaki, 1985, 88, 03 2. E. Oset and A. Ramos, arXiv:0905.0973 (2009, Eur. Phys. J. A)

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results The VB → VB interaction I=0, S=-1 I=1, S=-1 Figure: | T | 2 for 5 200 * N * N K K different channels 100 for I = 0 , 1 and 0 0 -2 ] 20 3 strangeness 2 [MeV ωΛ ρΛ 2 S = − 1 . Channel 10 100x|T| 1 thresholds are 0 0 20 3 indicated by ρΣ ρΣ 2 vertical dotted 10 lines. 3 Λ and 2 Σ 1 appear: Λ( 1783 ) , 0 0 20 0.5 φΛ ωΣ Λ( 1900 ) , Λ( 2158 ) 10 and Σ( 1830 ) , 0 0 100 3 Σ( 1987 ) . PDG: Λ( 1800 ) , * Ξ * Ξ K K 2 50 Λ( 2000 ) , Σ( 1750 ) , Σ( 1940 ) , 1 Σ( 2000 ) . 0 0 1800 2000 2200 0.5 E cm [MeV] φΣ 0 1800 2000 2200 E cm [MeV]

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results K ∗ self-energy from the s-wave ¯ K ∗ N interaction ¯ Meson-baryon function loop in nuclear matter: G 0 ( √ s ) + lim Λ →∞ δ G ρ G ρ ( P ) Λ ( P ) , = Λ ( √ s ) Λ ( P ) − G 0 δ G ρ G ρ Λ ( P ) ≡ d 4 q � M ( q ) − D 0 B ( P − q ) D 0 i2 M D ρ B ( P − q ) D ρ M ( q ) � � = ( 2 π ) 4 Λ In-medium propagators: 2 M N � 1 − n ( � p ) n ( � p ) � v r ( − � p )¯ v r ( − � p ) D ρ N ( p ) u r ( � p )¯ u r ( � p ) + = { + } p 0 − E N ( � p 0 − E N ( � p 0 + E N ( � 2 E N ( � p ) p ) + i ε p ) − i ε p ) − i ε p 0 − E N ( � � � p ) δ D 0 N ( p ) + 2 π i n ( � p ) = 2 E N ( � p ) � S ¯ � ∞ q ) S K ∗ ( ω,� q ) � − 1 = K ∗ ( ω,� ( q 0 ) 2 − ω ( � q ) 2 − Π ¯ � � D ρ K ∗ ( q ) K ∗ ( q ) d ω = − ¯ q 0 − ω + i ε q 0 + ω − i ε 0

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results K ∗ self-energy from the s-wave ¯ K ∗ N interaction ¯ d 3 q M N � − n ( � p ) K ∗ N ( √ s ) + K ∗ N ( P ) = G 0 � G ρ ¯ + ¯ ( 2 π ) 3 ( P 0 − E N ( � p )) 2 − ω ( � q ) 2 + i ε E N ( � p ) − 1 / ( 2 ω ( � � q )) � ∞ S ¯ q ) ��� K ∗ ( ω,� � ( 1 − n ( � p )) d ω + � P 0 − E N ( � P 0 − E N ( � p ) − ω ( � q ) + i ε p ) − ω + i ε � 0 � p = � P − q � � 1 V I ( √ s ) T ρ ( I ) ( P ) = 1 − V I ( √ s ) G ρ ( I ) ( P ) K ∗ self-energy is then obtained by integrating T ρ ¯ The in-medium ¯ K ∗ N over the nucleon Fermi sea, d 3 p T ρ ( I = 0 ) P ) + 3 T ρ ( I = 1 ) K ∗ ( q 0 ,� � K ∗ N ( P 0 ,� K ∗ N ( P 0 ,� � q ) ( 2 π ) 3 n ( � p ) P ) = � Π ¯ ¯ ¯

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results K ∗ selfenergy coming from its decay into ¯ ¯ K π ¯ K ¯ K K ∗ ¯ K ∗ ¯ K ∗ ¯ K ∗ ¯ = ⇒ π π Figure: The ¯ K propagator in the free space (l), and in the medium (r). In the free space, we have: d 4 q i i � − i Π = − 6 g 2 µ q µ ǫ ν q ν K + i ǫǫ ′ ( 2 π ) 4 q 2 − m 2 ( P − q ) 2 − m 2 π ν q ν − ǫ ′ · � ǫ 1 q 2 δ ij m K ∗− ∼ 0 , ǫ µ q µ ǫ ′ P � For low momenta, → � 3 � → Im Π = g 2 ǫ ′ q 3 1 → Γ = 42 MeV Cutkosky rules − 4 π � ǫ · � P 0 −

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results K ∗ selfenergy coming from its decay into ¯ ¯ K π In the medium, we have: 1 1 → q 2 − m 2 q 2 − m 2 π − Π π ( q 0 ,� q ) π 1 1 → ( P − q ) 2 − m 2 ( P − q ) 2 − m 2 K − Π K ( P 0 − q 0 ,� P − � q ) K We use their Lehmann representations, this is: � ∞ d 4 q Im D π ( ω,� d ω q ) � K ∗ ( P 0 ,� 2 g 2 � q 2 π ( − 2 ω ) − i Π ¯ P ) ǫ ′ = ǫ · � ( 2 π ) 4 � ( q 0 ) 2 − ω 2 + i ǫ 0 � ∞ π ( − ) { Im D ¯ P 0 − q 0 − ω ′ + i η − Im D K ( ω ′ ,� d ω ′ K ( ω ′ ,� P − � q ) P − � q ) × P 0 − q 0 + ω ′ − i η } 0

K ∗ self-energy from the s-wave ¯ K ∗ → ¯ ¯ K ∗ N interaction ¯ K π in dense matter Nuclear transparency in the γ A Introduction Results K ∗ selfenergy coming from its decay into ¯ ¯ K π K ∗ selfenergy is subtracted to get its The real part of the free ¯ physical mass at ρ = 0 The last term is ∝ Im D K is small and as approximation can be cancelled with the term in the free space Therefore, K ∗ ( P 0 ,� P ) = Π ¯ � ∞ � ∞ d 3 q q 2 1 d ω ′ Im D ¯ K ( ω ′ ,� P − � q ) � 2 g 2 ǫ · ǫ ′ { d ω Im D π ( ω,� q ) ( 2 π ) 3 � π 2 P 0 − ω − ω ′ + i η 0 0 d 3 q q 2 1 1 � � − Re P 0 − ω π ( q ) − ω K ( P − q ) + i ǫ } ( 2 π ) 3 2 ω π ( q ) 2 ω K ( P − q )