Bjorken Scaling & modification of nucleon mass inside dense nuclear matter Jacek Rozynek INS Warsaw Nuclear Physics Workshop HCBM 2010

1. Nuclear structure function in Deep Inelastic Scattering (DIS) - review. 2. Finite pressure corrections. 3. Implication to the EOS for Nuclear matter. 4. Conclusion. Plan EMC effect Relativistic Mean Field Problems Hadron with quark primodial distributions Pion contributions Nuclear Bjorken Limit - M N (x)

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)/ AF 2 N (x) 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.,….

The graphical representation of the convolution model for the deep inelastic electron nucleus scattering with: (a) the active nucleon N (with hit quark q) including exchange final state interaction with nucleon spectators and (b) virtual pion

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

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

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

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?

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 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

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

Hit quark has momentum j + = x p + Experimentaly x = Experimentaly x = Q 2 /2M and is iterpreted as fraction of longitudinal nucleon momentum carried by parton(quark)  jorken lim) for 2  Q  2  jorken lim) D I S remnant e p Q 2, j On light cone Bjorken x is defined as x = j + /p + where p + =p 0 + p z d  ~  l  W  W   W 1, W 2 ) Bjorken Scaling F 2 (x)=lim[(  W 2 (q 2,  Bjo In Nuclear Matter due to final state NN interaction, nucleon mass M(x) depends on x, and consequently from energy  and density . 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 F 2 A (x)= F 2 [xM/M(x)] + F 2  (x) Rescaling inside nucleus

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)

Conclusions part1 Good fit to data for Bjorken x>0.1 by modfying the nucleon mass in the medium (~24 MeV depletion) in x dependent way with Unchanged nucleon M for medium and small x. 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 comp atible 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% compatible with chiral restoration. x – dependent correction to the distribution

In vacuum In nuclear medium Phys.Rev.C

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 ?

pion mass in the medium in chiral symmetry restoration Nucleon mass in the medium ? EOS in NJL Bernard,Meissner,Zahed PRC (1987) EMC effect R. Rapp and J.Wambach, Adv. Nucl. Phys. 25, 1 (2000) Brown- Rho scaling

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

Positive Pressure in NM A OURMODELOURMODEL

But in the medium we have correction to the Hugenholtz-van Hove theorem: On the other hand we have momentum sum rule of quarks (plus gluons) as the integral over the structure function F N 2 (x) shold compensate factor E F /(E/A). Therefore in this model we have to scale Bjorken x=q/2M. E F /M > (E/A)/M

Nuclear energy per nucleon for Walecka abd nonlinear models The density dependent energy carried by meson field Now the new nucleon nass will dependent on the nucleon energy in pressure but will remain constant below saturation point. M mod =M/ ( 1+(  d(E/A)/d   and we have new equation for the relativistic (Walecka type) effective mass which now include the pressure correction.

Basic Equations o

Masses - solution of modified RMF equation with pressure corrections compare to ZM Partially published in IJMP & Acta Phys Pol

EOS results P.Danielewicz et al Science(2002)

David Blaschke

Physically CONCLUSIONS Presented model correspond to the scenario where the part of nuclear momentum carried by meson field and coming from the strongly correlation region, reduce the nucleon mass by corrections proportional to the pressure. In the same time in the low density limit the spin-orbit splitting of single particle levels remains in agreement with experiments, like in the classical Walecka Relativistic Mean Field Approach, but the equation of state for nuclear matter is softer from the classical scalar- vector Walecka model and now the compressibility K -1 =9(r 2 d 2 /dr 2 )E/A = 230MeV, closed to experimental estimate. Pressure dependent meson contributions when added to EOS and to the nuclear structure function improve the EOS and give well satisfied Momentum Sum Rule for the parton constituents. New EOS is enough soft to be is in agreement with estimates from compact stars for higher densities. Finally we conclude that we found the corrections to Relativistic Mean Field Approach from parton structure measured in DIS, which improve the mean field description of nuclear matter from saturation density    to 3  .

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

Spinodal phase transition

Deep inelastic scattering

Quark inside nucleus QMC model

Condensates and quark masses

Maxwell construction

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

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)