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Modification of scalar field inside dense nuclear matter

Modification of scalar field inside dense nuclear matter. D I S. j. e. Q 2 , n. p. r emnant. Hit quark has momentum j + = x p + Experimentaly x = Q 2 /2 M n and is iterpreted as fraction of longitudinal nucleon momentum carried by parton(quark)

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Modification of scalar field inside dense nuclear matter

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  1. Modification of scalar field inside dense nuclear matter

  2. D I S j e Q2, n p remnant Hit quark has momentum j + = x p + Experimentalyx =Q2/2Mn and is iterpreted as fraction of longitudinal nucleon momentum carried by parton(quark) for n2 >Q2 -> oo (Bjorken lim) On light cone Bjorken x is defined as x = j+ /p+ where p+ =p0 + pz In Nuclear Matter due to final state NN interaction, nucleon mass M(x) depends on x , and consequently fromenergye and density r. for large x (no NN int.) the nucleon mass has limit Due to renomalization of the nucleon mass in medium we have enhancement of the pion cloud from momentum sum rule ds~lmn WmnWmn(W1 , W2) Bjorken Scaling F2(x)=lim[(n/M)W2(q2,n)]Bjo Rescaling inside nucleus F2A(x)= F2[xM/M(x)] + F2p(x)

  3. Relativistic Mean Field Problemsconnected with Helmholz-van Hove theorem - e(pF)=M-e In standard RMF electrons will be scattered on nucleons in average scalar and vector potential: [ap+ b(M+US) - (e -UV)]y=0 where US=-gS /mSrSUV =-gV /mVr US = -400MeVr/r0 UV = 300MeVr/r0 Gives the nuclear distribution f(y) of longitudinal nucleon momenta p+=yAMA SN() - spectral fun. m - nucleon chemical pot. Strong vector-scalar cancelation

  4. Relativistic MF rN - av. NN distance rC - nucleon radius if z(x) > rN M(x) = MN if z(x) < rC M(x) = MB Nuclear Final State Interaction in the Deep Inelastic Scatt. z(x)  1/Mx = z distance how far can propagate the quark in the medium. (Final state quark interaction - not known) Effective nucleon Mass M(x)=M( z(x) , rC ,rN ) renomalization of the nucleon mass in medium with the enhancement of the pion cloud Kazimierz 2009

  5. Because of Momentum Sum Rule in DIS M(x) & in RMF the nuclear pions almost disappear Nuclear sea is slightly enhanced in nuclear medium - pions have bigger mass according to chiral restoration scenario BUT also change sea quark contribution to nucleon SF rather then additional (nuclear) pions appears The pions play role rather on large distances?

  6. SF - Evolution in Density R(x) = F2NM(x)/ F2N(x) “no” free parameters Correction to Equation Of State for Nuclear Matter - ap. in Astrophysics Soft EOS (density - 4r) Non Linear RMF Models Pions take 5% of longitudinal momenta Good compressibility Chiral instability (phase transition) correction to effective NNs interaction for high density? Feeq. densityr=0.12fm-3 with G. Wilk Phys.Rev. C71 (2005) Stiff EOS (density - 4r)Walecka RMF Model No enhancement of pion cloud Bad compressibilty K>300MeV J Rozynek Int. Journal of Mod. Phys. In print

  7. Results“no” free paramerers Fermi Smearing Constant effective nucleon mass x dependent effective nucleon mass with G. Wilk Phys.Rev. C71 (2005)

  8. Nuclear deep inelastic limit revisitedx dependent nucleon „rest” mass in NM • Momentum Sum Rule violation f(x) - probability that struck quark originated from correlated nucleon

  9. But in the medium we have correction to the Hugenholtz-vanHove theorem: On the other hand we have nuclear energy the energy of quarks (plus gluons) as the integral over the structure function F2(x) and is given by EF. Therefore in this model we have to scale Bjorken x=-q/2Mn the ratio of old and new nucleon mass. EF/M > (E/A)/M

  10. Now the new nucleon nass will dependent on the nucleon energy in pressure but will remain constant below saturation point. Mm=M/(1+(dE/dr)(r/E)) and we have new equation for the relativistic (Walecka type) effective mass which now include the pressure correction. Nuclear energy per nucleon for Walecka abd nonlinear models The density dependent energy carried by meson field

  11. Results Density correction started from ρ=.16fm-3 Flow Constrain P.Danielewicz Science(2002) Pressure(MeV/fm3) Walecka Density correction started from ρ=.19fm-3 Dash curve include the reduction of the  field in medium.

  12. Maxwell construction

  13. Spinodal phase transition

  14. EOS in NJL EMC effect • pion mass in the medium in chiral symmetry restoration • Nucleon mass in the medium ? Bernard,Meissner,Zahed PRC (1987)

  15. Condensates and quark masses

  16. The pressure at critcal temperature

  17. CEP and Statistics

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