Heavy quarkonia at finite temperature: The EFT approach

Transcription

1 Heavy quarkonia at finite temperature: he EF approach Jacopo Ghiglieri - echnische Universität München 5th Vienna Central European Seminar on QF 28 November 2008

2 Outline Motivation Introduction to Effective Field heories at =0 he EF approach for quarkonia at finite temperature [( )( )] } Conclusions alk based on N. Brambilla, J. Ghiglieri, A. Vairo, and P. Petreczky, Phys. Rev. D78, (2008)

3 Motivations Effective Field heories of QCD have been successful in the last decades on a variety of physical problems Examples: ChP for the study of low-energy hadronic physics Non-Relativistic QCD / potential NRQCD for heavy quarkonium physics

4 EFs prove to be a valuable computational tool for physical problems characterized by various sufficiently separated energy scales An EF is constructed by integrating out modes of energy and momentum larger than the cut-off μ L EF = n Wilson coefficient c n (E Λ /µ) O n(µ) E Λ Low-energy operator/ cutoff he Wilson coefficient are obtained by matching appropriate Green functions in the two theories

5 Goal Our goal is then to extend the wellestablished =0 EF formalism for heavy quarkonia to the finite temperature situation

6 Physical picture Hypothesis of quarkonium ( QQ) dissociation in a thermal medium (QGP) due to color screening (Matsui, Satz, 1986) Can thus quarkonium dissociation be a signature of QGP formation? 1.00! S(J/ ) In!In, SPS Pb!Pb, SPS Au!Au, RHIC, y < 0.35 Au!Au, RHIC, y =[1.2,2.2] " (GeV/fm 3)

7 Physical picture Past studies based mainly on phenomenological potential models or lattice computations of the free energy F 1 (r,)/! 1/ r! 1/2 / c =0.75 / c =0.82 / c =0.91 / c =0.97 / c =1.01 / c =1.03 / c =1.07 / c =1.12 / c =1.16 / c =

8 =0 NR EFs: a Short Primer Non-relativistic QQ bound states are characterized by the hierarchy of the mass, energy and momentum scales m

9 =0 NR EFs: a Short Primer Non-relativistic QQ bound states are characterized by the hierarchy of the mass, energy and momentum scales One can then expand observables in terms of the ratio of the scales and construct a hierarchy of EFs that are equivalent to QCD order-by-order in the expansion parameter m

10 m =0 Scales

11 m =0 Scales Integration of the mass scale: NRQCD

12 m =0 Scales Integration of the soft (momentum transfer) scale: pnrqcd

13 m =0 Scales Integration of the soft (momentum transfer) scale: Λ QCD pnrqcd

14 m =0 Scales Integration of the soft (momentum transfer) scale: pnrqcd Λ QCD

15 Weakly coupled pnrqcd Degrees of freedom: QQ and momentum p mv Singlet and octet color states states with energy E Λ QCD, mv 2 Gluons with energy/momentum mv Gluon fields are multipole-expanded in the centre of mass coordinate R A(R, r, t) =A(R, t)+r A(R, t)+... Expansion in α s (m), 1 and r m Potential as a Wilson coefficient, receives contributions from all higher scales

16 hermodynamical scales he thermal medium introduces new scales in the physical problem he temperature he electric screening scale (Debye mass) he magnetic screening scale (magnetic mass) In the weak coupling assumption these scales develop a hierarchy

17 hermodynamical scales he thermal medium introduces new scales in the physical problem he temperature he electric screening scale (Debye mass) he magnetic screening scale (magnetic mass) In the weak coupling assumption these scales develop a hierarchy g m D g 2 m m

18 Scales of the problem m

19 Scales of the problem m Λ QCD

20 Scales of the problem m g m D g 2 m m Λ QCD

21 Scales of the problem m? g m D g 2 m m Λ QCD

22 Scales of the problem In our work various possibilities have been studied, from E to m 1/r m D Here we illustrate the intermediate case m 1/r m D E A good showcase of the EF approach with the interplay of different scales We don t consider the (suppressed) magnetic mass effects

23 m Mass scale QCD NRQCD g m D We only consider the leading ) term 0, corresponding to ( 1 m treating heavy quarks/antiquarks as static sources So far everything goes exactly as in the =0 case Λ QCD

24 m Mass scale g m D... Λ QCD

25 m Soft scale NRQCD pnrqcd Integrating out the soft modes causes the singlet and octet g m D potentials to appear Λ QCD

26 m Soft scale g m D Λ QCD 1 E p 2 /m V (r)

27 m he static potential g m D α Vs (1/r) V s (r, µ) = C F r { α s (1/r) = C F 1+ α s(1/r) a 1 + r 4π } + ( ) 2 αs (1/r) a 2 4π Λ QCD

28 m he temperature g m D First thermal corrections to the potential Corrections appear as loops in the effective theory Real and imaginary parts, contributing to energy and decay width observables Λ QCD

29 m V Re δv s (r) = π 9 N cc F α 2 s r 2 g 2 r 2 3 V g m D Im δv s (r) = N 2 c C F 6 V V α 3 s g 2 r 2 3 he imaginary part correspond to singlet-to-octet thermal breakup ( V ) 2 Λ QCD

30 m g m D Re δv s (r) = 3 2 ζ(3) C F α s π r2 m 2 D ζ(3) N cc F α 2 s r 2 3 g 2 r 2 3 Im δv s (r) =+ C ( F 1 6 α s r 2 m 2 D ɛ + γ E + ln π ln 2 µ ) 3 4 ln 2 (2) 2ζ ζ(2) + 4π 9 ln 2 N cc F α 2 s r 2 3 ( md ) 2 Λ QCD g 2 r 2 3 ( md ) 2

31 m g m D Re δv s (r) = 3 2 ζ(3) C F α s π r2 m 2 D ζ(3) N cc F α 2 s r 2 3 g 2 r 2 3 Im δv s (r) =+ C ( F 1 6 α s r 2 m 2 D ɛ + γ E + ln π ln 2 µ ) 3 4 ln 2 (2) 2ζ ζ(2) + 4π 9 ln 2 N cc F α 2 s r 2 3 ( md ) 2 Λ QCD g 2 r 2 3 ( md ) 2

32 m he Debye Mass After having integrated out the temperature Hard hermal Loop contributions have to be resummed, giving the longitudinal gluon propagator a mass and and imaginary part g m D Λ QCD his contribution cancels the divergence in the previous expression

33 m HL Propagator Re δv s (r) g 2 r 2 3 ( md ) 3 Im δv s (r) = C F 6 α s r 2 m 2 D ( 1 ɛ γ E + ln π + ln µ2 m 2 D ) g m D he real part is suppressed but the imaginary part indeed cancels the divergence Λ QCD

34 m HL Propagator Re δv s (r) g 2 r 2 3 ( md ) 3 Im δv s (r) = C F 6 α s r 2 m 2 D ( 1 ɛ γ E + ln π + ln µ2 m 2 D ) g m D he real part is suppressed but the imaginary part indeed cancels the divergence Λ QCD

35 Summing up Re V s Im V s = C F α VS r 3 2 ζ(3) C F = N 2 c C F 6 + π 9 N cc F α 2 s r 2 α s π r2 m 2 D ζ(3) N cc F α 2 s r 2 3 αs 3 4π 9 ln 2 N cc F αs 2 r 2 3 (2γ E ln 2 C F 6 α s r 2 m 2 D m 2 D 1 4 ln 2 2 ζ (2) ζ(2) ) he imaginary part of the static potential gives the decay width, which has two origins: singlet-tooctet breakup and Landau damping. he former is suppressed by ( E m D ) 2 vs the latter

36 Summing up Re V s Im V s = C F α VS r 3 2 ζ(3) C F = N 2 c C F 6 + π 9 N cc F α 2 s r 2 α s π r2 m 2 D ζ(3) N cc F α 2 s r 2 3 αs 3 4π 9 ln 2 N cc F αs 2 r 2 3 (2γ E ln 2 C F 6 α s r 2 m 2 D m 2 D 1 4 ln 2 2 ζ (2) ζ(2) ) he imaginary part of the static potential gives the decay width, which has two origins: singlet-tooctet breakup and Landau damping. he former is suppressed by ( E m D ) 2 vs the latter

37 Conclusions We have shown how to employ the EF approach to deal with a problem characterized by various separated energy scales We have obtained new result in the intermediate regime which could be relevant for LHC phenomenology m 1/r m D E We have introduced a new mechanism of thermal decay