Disintegration of quarkonia in QGP due to time dependent potential

Transcription

1 Disintegration of quarkonia in QGP due to time dependent potential Partha Bagchi Institute Of Physics December 9, 2014 XXI DAE-BRNS High Energy Physics Symposium 2014, 8-12 December 2014, IIT Guwahati, India

2 Outline of talk

3 Outline of talk Review of Conventional Mechanism of quarkonia suppression

4 Outline of talk Review of Conventional Mechanism of quarkonia suppression New Mechanisms of Quarkonia Suppression Quarkonia Suppression Due to Rapid Thermalisation With Ajit M. Srivastava Quarkonia Suppression Due to Scattering With Z(3) interfaces With Abhishek Atreya and Ajit M. Srivastava

5 Outline of talk Review of Conventional Mechanism of quarkonia suppression New Mechanisms of Quarkonia Suppression Quarkonia Suppression Due to Rapid Thermalisation With Ajit M. Srivastava Quarkonia Suppression Due to Scattering With Z(3) interfaces With Abhishek Atreya and Ajit M. Srivastava Conclusion

6 Conventional mechanism for quarkonia suppression Quantum chromodynamics predicts that at extreme high conditions of baryon density and /or temperature there should be a deconfinement of quarks and gluons, and hadrons should undergo a phase transition to quark-gluon plasma (QGP). We cannot prob QGP directly. Observing quarkonia suppression is one of several indirect method to prob QGP.

7 Conventional mechanism for quarkonia suppression Continued... Matsui and Satz 1 proposed J/ψ suppression as a signal for QGP due to Debye screening of the potential between q q If at a temperature T D, the Debye screening length of the medium becomes less than the radius of quarkonia, then q q may not form bound states In the above picture, suppression of quarkonia occurs when the temperature of QGP achieves a value higher than T D 1 T. Matsui and H. Satz, PRL B178,416 (1986)

8 Important points about the conventional mechanism for quarkonia suppression If the QGP temperature remains below T D, no quarkonia suppression is expected in the conventional mechanism. This type of picture is consistent with the adiabatic evolution of a quantum state under changing potential. As the q q potential changes from zero temperature (V(T=0)) to the finite temperature one (V(T)), initial quarkonium state evolves to the state corresponding to V(T) which is also a bound state for T < T D, hence no quarkonium suppression for T < T D. We question this assumption of adiabatic evolution for ultra-relativistic heavy-ion collisions, such as at RHIC, and especially at LHC.

9 Important points...continued... At such energies, thermalization is achieved in time scale less than 1 fm (from elliptic flow measurements) and may be as short as 0.25 fm for RHIC and about 0.1 fm for LHC 2 For J/ψ and even for Υ, typical time scale of q q dynamics will be at least 1-2 fm from the size of the bound state (as can be seen from the extent of the wave function) and the fact that q, q have non-relativistic velocities Also, E between J/ψ and its next excited state (χ) is about 300 MeV (400 MeV for Υ states), leading to transition time scale 0.7 fm (0.5 fm for Υ). Thus, the time scale of change in potential from V (T = 0) to V (T ) is at most the same as the time scale of the dynamics of q q in quarkonium, or the transition time scale between relevant states. 2 D.M. Elliott and D.H. Rischke, Nucl. Phys. A 671, 583 (2000)

10 Quarkonia wave functions J/ψ ϒ ψ(z) z(fm) Figure : Wave function for J/ψ and Υ at T= 0.

11 Time dependent potential for studying quarkonia wave function evolution The evolution of the wave function, thus, cannot be taken to be adiabatic and it should be treated in terms of a time dependent perturbation theory Survival probability of quarkonia should be calculated under this perturbation Adiabatic assumption has been questioned earlier by Dutta and Borghini 3, but only for the cooling part, they discuss only the case when T 0 > T D. Whereas, we discuss violation of adiabaticity for heating part, and especially consider the case when T 0 < T D. 3 Nirupam Dutta, Nicolas Borghini arxiv:

12 Time dependent potential for studying quarkonia wave function evolution Continued... It is clear that even if the final temperature remains less than T D (above which Debye screening can melt quarkonia), if the change in potential is fast enough invalidating the adiabatic assumption then transition of initial quarkonium state to other excited states, or unbound state, will occur These excited states will have larger profile and will easily melt in medium. Thus: Quarkonia melting can occur even when QGP temperature remains below T D.

13 Quarkonia Suppression Due to Rapid Thermalisation of QGP As Thermalisation may happen in very short time, about 0.25 fm for RHIC and 0.1 fm for LHC, it seems reasonable to use the sudden perturbation approximation instead of adiabatic approximation. The initial wave function of the quarkonium cannot change under this sudden perturbation. Thus, as soon as thermalization is achieved the initial quarkonium wave function is no longer an energy eigen state of the new Hamiltonian with the q q potential corresponding to temperature T 0 of QGP.

14 Results we calculate wave functions for J/ψ and Υ at different temperatures V (r) = α s r exp( ω Dr) + σ ω D r(1 exp( ω D r)) ω D = T 6πα s, α s = π 12 σ = 0.16GeV 2 ψ(z) J/ψ(T = 0 MeV) J/ψ(T = 200 MeV) ψ(z) ϒ(T = 0 MeV) ϒ(T = 200 MeV) ϒ(T = 400 MeV) ϒ(T = 500 MeV) z(fm) z(fm) Figure : Wave functions for J/ψ and Υ at different temperatures.

15 Results: Continued... As a result, one can find overlap with the new eigen states, giving us the survival probability of the quarkonium as well as the probability of its transition to other excited states. p 1 J/ψ 0.9 ϒ T (GeV) Figure : Survival Probability p of J/ψ and Υ vs. temperature of medium. Plots are given upto the temperature T D for J/ψ and Υ.

16 Summery for this part It does not seems reasonable to use the adiabatic approximation for quarkonia wave function evolution in medium in the case of rapid thermalization We have used sudden perturbation approximation instead of adiabatic approximation. Quarkonia melting can occur even when QGP temperature remains below T D. More detailed calculations can be done by modeling initial thermalization in terms of time dependent temperature and using time dependent perturbation theory.

17 Quarkonia suppression due to scattering with Z(3) wall

18 Quarkonia suppression due to scattering with Z(3) wall There are Z(3) interfaces in the QGP phase arising from spontaneous breaking of the center symmetry of QCD. Scattering of quarkonia with these interfaces can lead to disintegration of quarkonia Again, quarkonia disintegration can occur even if temperature of QGP remains less than T D

19 Order Parameter for QCD Phase Transition Z(3) interfaces arises due to spontaneous breaking of Z(3) symmetry in QGP during Confinement-deconfinement (C-D) phase transition Order parameter for C-D phase transition is Polyakov loop, which is defined as, L(x) = 1 ( β )] [Pexp N Tr ig A 0 ( x, τ)dτ 0

20 Effective Potential for l(x) Effective Potential 4 ( V (L) = b 2 2 L 2 b 3 (L 3 + (L ) 3) + 1 ) 6 4 ( L 2 ) 2 b 4 T 4 For T > T c, second term leads to the three degenerate vacua corresponding to the three L(x) values. Z(3) interfaces correspond to interpolating L(x) profile between these vacua. 4 R.D. Pisarski, PRD 62, (2000) 5 Dimitru and Pisarski, Phys, Lett. B 504, (2001); PRD 66, (2000); Nucl. Phys. A 698 (2002)

21 Effective Potential for l(x) Effective Potential 4 ( V (L) = b 2 2 L 2 b 3 (L 3 + (L ) 3) + 1 ) 6 4 ( L 2 ) 2 b 4 T 4 For T > T c, second term leads to the three degenerate vacua corresponding to the three L(x) values. Z(3) interfaces correspond to interpolating L(x) profile between these vacua. Parameters fixed from lattice results. 5 b 3 = 2.0 and b 4 = /16 b 2 = (1 1.11/x) ( /x) 2 ( /x) ; where x = T /T c with T c 182 MeV 4 R.D. Pisarski, PRD 62, (2000) 5 Dimitru and Pisarski, Phys, Lett. B 504, (2001); PRD 66, (2000); Nucl. Phys. A 698 (2002)

22 Plot of effective potential V(L) Figure : Surface plot of potential in the complex L(x) plane for T=400 MeV.

23 Profile for L(x) for a Z(3) interface Profile for L(x) by energy minimization. 6 l(z) MeV MeV z(fm) 6 Layek, Mishra, Srivastava, PRD 71, (2005)

24 Quarkonia scattering from Z(3) wall 7 B. Layek, A. P. Mishra, A. M. Srivastava, and V. K. Tiwari, Phys. Rev. D73, (2006), hep-ph/

25 Quarkonia scattering from Z(3) wall As L(x) is order parameter for C-D transition, effective quark mass may depend on L(x) (constituent quark mass) We propose 7 m(x) = m q + m 0 (l 0 l(x) ) m 0 = 300 MeV characterizes the constituent mass contribution for the quark. m q is the current quark mass of the quark as appropriate for the QGP phase with l(x) = l 0 x dependent mass acts as nontrivial potential in Dirac equation for quark propagation A quarkonia propagating through the wall can get excited to higher states, due to the interaction, which easily melts in QGP (or directly to unbound states) 7 B. Layek, A. P. Mishra, A. M. Srivastava, and V. K. Tiwari, Phys. Rev. D73, (2006), hep-ph/

26 Results we have calculated transition probability to several excited states for prompt charmonium. For Thermal charmonium (T = 200) MeV, other states are not bound due to Debye screening. we have also calculated transition probability to several excited states for prompt bottomonium and only to n = 2, l = 0 for tharmal bottomonium. For Thermal bottomonium (T = 200) MeV, other states are not bound due to Debye screening.

27 Results (Continuation..) p Total To (n=2, l=0) To (n=1, l=2) To (n=3, l=0) To (n=2, l=2) v Figure : Above figure shows probability of transition from J/ψ to other excited states.

28 Results (Continuation...) p Total To (n=2, l=0) To (n=1, l=2) To (n=3, l=0) p Prompt Thermal v v Figure : Above figure shows probability of transition from Υ to other excited states. Left one for transi to different excited states for prompt Υ. And right one to compare transition to n = 2, l = 0 for prompt bottomonium and thermal bottomonium at T = 200 MeV.

29 Quarkonia scattering due Z(3) wall Scattering due to A 0 profile (2012) 8 A. Atreya, A. M. Srivastava, and A. Sarkar Phys. Rev. D 85,

30 Quarkonia scattering due Z(3) wall Scattering due to A 0 profile From the definition of L(x) we note that presence of nontrivial profile of l(x) may lead to a nontrivial profile of A 0 8 L(x) = 1 ( β )] [Pexp N Tr ig A 0 ( x, τ)dτ 0 This leads to nontrivial color electric field which interacts with q and q differently leading to spontaneous CP violation This leads to excitation of quarkonia to excited states which easily melt in QGP, it can also lead to direct transition to unbound states. (2012) 8 A. Atreya, A. M. Srivastava, and A. Sarkar Phys. Rev. D 85,

31 Results p v Figure : Probability p of transition of J/ψ to color octet χ states vs. its velocity v. Note that the probability rapidly rises with v.

32 Summery and Conclusion We have proposed several mechanisms due to which quarkonia can dissociate in QGP even when its temperature T remains less than T D so that conventional mechanism of quarkonia melting is not effective. These new mechanisms are: Time dependent change in potential due to initial rapid thermalization of QGP leading to dissociation of initial quarkonia Nontrivial scattering with Z(3) wall leading to dissociation of quarkonia This dissociation will happen either by direct transition to unbound states, or by transition to excited states which easily melt in QGP due to Debye screening.

33 Thank You!