The Nucleon Structure and the EOS of Nuclear Matter Jacek Rozynek INS Warsaw Nuclear Physics Workshop KAZIMIERZ DOLNY 2006

Summary EMC effect Relativistic Mean Field Problems Hadron with quark primodial distributions Pion contributions Nuclear Bjorken Limit - M N (x) Higher densities & EOS Conclusions

PARTONS INDISPARTONS INDIS

EMC effect (J.R.) by the direct change of the partonic primodial distribution. S.Kin, R.Close Sea quarks from pion cloud. G.Wilk+J.R.,…. Historically ratio R(x) = F 2 A (x)/ F 2 N (x) Three approaches to its description: x Pion excess

Three approaches to EMC effect  in term of nucleon degrees of freedom through the nuclear spectral function. (nonrelativistic off shell effects) G.A.Miller&J. Smith, O. Benhar, I. Sick, Pandaripande,E Oset  in terms of quark meson coupling model modification of quark propagation by direct coupling of quarks to nuclear envirovment A.Thomas+Adelaide/Japan group, Mineo, Bentz, Ishii, Thomas, Yazaki (2004) by the direct change of the partonic primodial distribution. S.Kinm, R.Close Sea quarks from pion cloud. G.Wilk+J.R., (J.R.) by the direct change of the partonic primodial distribution. S.Kin, R.Close Sea quarks from pion cloud. G.Wilk+J.R.,….

Hit quark has momentum j + = x p + Experimentaly x =  and is iterpreted as fraction of longitudinal nucleon momentum carried by parton(quark) for 2  Q  2  On light cone Bjorken x is defined as x = j + /p + where p + =p 0 + p z e p r(emnant) Q 2, Q 2 / 2M D I S j

Light cone coordinates

Relativistic Mean Field Problems In standard RMF electrons will be scattered on nucleons in average scalar and vector potential:  p +  M+U S ) - ( e -U V  where U S =-g S /m S  S  U V =-g V /m V  U S = 300MeV    U V = 300MeV  

Relativistic Mean Field Problems In standard RMF electrons will be scattered on nucleons in average scalar and vector potential:  p +  M+U S ) - ( e -U V  where U S =-g S /m S  S  U V =-g V /m V  U S = -400MeV    U V = 300MeV   Gives the nuclear distribution f(y) of longitudinal nucleon momenta p + =y A M A S N () - spectral fun.  - nucleon chemical pot.

Relativistic Mean Field Problems connected with Helmholz-van Hove theorem - e(p F )=M-  In standard RMF electrons will be scattered on nucleons in average scalar and vector potential:  p +  M+U S ) - ( e -U V  where U S =-g S /m S  S  U V =-g V /m V  U S = -400MeV    U V = 300MeV   Gives the nuclear distribution f(y) of longitudinal nucleon momenta p + =y A M A S N () - spectral fun.  - nucleon chemical pot. Strong vector-scalar cancelation

Hadrons with quark primodial distributions based on Heinserberg uncertainty relation Gaussian distribution of quark (u and d ) momenta j

Hadrons with quark primodial distributions based on Heinserberg uncertainty relation Gaussian distribution of quark momenta j Monte Carlo simulations Proton Width -.18GeV 0 < (j+q) < W 0 < r < W ’ W - invariant mass

Hadrons with quark primodial distributions based on Heinserberg uncertainty relation Gaussian distribution of quark momenta j Monte Carlo simulations Proton Width -.18GeV Pion width -.18MeV 0 < (j+q) < W 0 < r < W ' W - invariant mass

Hadron with quark primodial distributions Good description - Edin, Ingelman Phys. Let. B432 (1999) Gaussian distribution of quark momenta j Monte Carlo simulations Proton Width -.18GeV Pion Component width =52MeV N =7.7 % 0 < (j+q) < W 0 < r < W ’ W - invariant mass Sea parton distribution is given by the pionic (fock) component of the nucleon

Change of nucleon primodial distribution inside medium Gaussian distribution of quark momenta j Monte Carlo simulations in medium pion cloud (mass) renormalization momentum sum rule Proton Width -.18GeV Pion width - 52MeV N =7.7 % IN MEDIUM Proton Width -.165GeV Pion width =52MeV N =7.7 % 0 < (j+q) < W m 0 < r < W’ m W - invariant mass

Primodial Distributios and Monte –Carlo Simulations for NM Calculations for the realistic nuclear distributions The Change of the primodial disribution in medium

Results

with G. Wilk Phys.Lett. B473, (2000), 167

Today - Convolution model Today - Convolution model for x <0.15 We will show that in deep inelastic scattering the magnitude of the nuclear Fermi motion is sensitive to residual interaction between partons influencing both the Nucleon Structure FunctionWe will show that in deep inelastic scattering the magnitude of the nuclear Fermi motion is sensitive to residual interaction between partons influencing both the Nucleon Structure Function and nucleon mass in th NMand nucleon mass in th NM M B (x) M B (x) Relativistic Mean Field problems Primodial parton distributions Bjorken x scaling in nuclear medium F 2 N (x) N O S H A D O W I N G

Nuclear Deep Inelastic limit

To much pions

RMF failure & Where the nuclear pions are M Birse PLB 299(1985), JR IJMP(2000), G Miller J Smith PR (2001) GE Brown, M Buballa, Li, Wambach, Bertsch, Frankfurt, Strikman

z=9fm TTwo resolutions scales in deep inelastic scattering 1 1/ Q 2  connected with virtuality of  probe. (A-P evolution equation - well known) 1/Mx = z  distance how far can propagate the quark in the medium. (Final state quark interaction - not known) For x=0.05 z=4fm

Nuclear final state interaction z(x) Effective nucleon Mass M(x)=M( z(x), r C,r N ) J.R. Nucl.Phys.A in print r N - av. NN distance r C - nucleon radius if z(x) > r N M(x) = M N if z(x) < r C M(x) = M B

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

M(x) & in RMF solution 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 Because of Momentum Sum Rule in DIS The pions play role rather on large distances?

Results Fermi Smearing

Results Fermi Smearing Constant effective nucleon mass

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

Drell Yan Calculations Good description due to the x dependence of nucleon mass (no nuclear pions in Sum Rules)

The QCD vacuum is the vaccum state of quark & gluon system. It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon & quark condensates. These condensates characterize the normal phase or the confined phase of quark matter. Unsolved problems in physics: QCD in the non- perturbative regime: confinement The equations of QCD remain unsolved at energy scale relevant for describing atomic nuclei. How does QCD give rise to the physics of nuclei and nuclear constituents ?

In vacuum In nuclear medium Phys.Rev.C

Derivative Coupling for scalars RMF Models ZM A. Delfino, CT Coelho and M. Malheiro, Phys. Rev. C51, 2188 (1995). {Tensor coupling vector (Bender, Rufa)} Review J. R. Stone, P.-G. Reinhard nucl-th/ (2006). M. Baldo, Nuclear Methods and the Nuclear Equation of State (World Scientific, 1999)

Effective Mass in RMF W - Nucleon bare mass in the Walecka mean field approach ZM - constructed by changing of covariant derivative in W model. Langrangian describes the motion of baryons with effective mass and the density dependent scalar (vector) coupling constant. ZM - Zimanyi Moszkowski

Relativistic Mean Field & EOS quark condensate m in the medium 0 Delfino, Coelho, Malheiro  for  models) m

Condensate Ratios in RMF

SF - Evolution in Density “no” free parameters Saturation density

SF - Evolution in Density “no” free parameters Saturation density Walecka ( density- 6 fm -3) Stiff EOS

SF - Evolution in Density “no” free parameters Saturation density Soft EOS ( density-.6 fm -3 ) pions take 5% of nuclear longitudinal momenta Chiral instability Walecka ( density- 6 fm -3) Stiff EOS

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

For such pionic cutoff Λ fluctuation of pion field pola shift the ground state out of magic circle to =0. In our model : Λ>700MeV for ρ=5ρ 0 (chiral symmetry restoration) For NJL Chiral Restoration occures when Λ >0.8 Λ q.. where Λ q cutoff for quark momenta In our model : Λ >0.8 Λ q for ρ=(4-5)ρ 0. Estimate of Chiral Stability H.Kleinert, B. Vanden Bossche Phys. Lett. B474 (2000)

Conclusions Good fit to data for Bjorken x>0.1 by modfying the nucleon mass in the medium (~24 MeV depletion) will correct the EOS for NM. Although such subtle changes of nucleons mass is difficult to measure inside nuclear medium due to final state interaction this reduction of nucleon mass is compatible with recent observation of similar reduction in Delta invariant mass in the decay spectrum to (N+Pion) T.Matulewicz Eur. Phys. J A9 (2000) (~ 1% only) of nuclear momentum is carried by sea quarks nuclear pions) due to x dependent effective nucleon mass supported by Drell-Yan nuclear experiments for higher densities increase for soft EOS towards chiral phase transition. Increase of the „additional nuclear pion mass” 5% means that nuclear density is about 2 times smaller than critical. x – dependent correction to the distribution for higher density SF strongly depend from EOS correction to effective NN interaction for high density?

x dependent nucleon effective mass it is possible to show that in DIS M 2 In the x>0.6 limit (no NN interaction) Nuclear = Nukleon Bartelski Acta Phys.Pol.B9 (1978)

Dependence from initial in p-A collision X-N Wang Phys. Rev.C (2000)

Chiral solitons in nuclei Miller, Smith, Phys. Rev. Lett Chiral Quark Soliton Model Petrov- Diakonov So far effect to strong

Nuclear Vector Potential in DIS Free Nucleon

Quark inside nucleus QMC model

Deep inelastic scattering