Bled Workshops in Physics Vol. 16, No. 1 p. 4
A
Proceedings of the Mini-Workshop
Exploring Hadron Resonances
Bled, Slovenia, July 5 - 11, 2015

In-medium properties of the nucleon within a n-p-^ model*
Ju-Hyun Junga, Ulugbek Yakhshievb, Hyun-Chul Kimb
aTheoretical Physics, Institute of Physics, University of Graz, Universitatsplatz 5, A-8010 Graz, Austria
b Department of Physics, Inha University, Incheon 402-751, Republic of Korea
Abstract. In this talk, we report on a recent investigation of the transverse charge and energy-momentum densities of the nucleon in the nuclear medium, based on an in-medium modified n-p-w soliton model. The results allow us to establish general features of medium modifications of the structure of nucleons bound in a nuclear medium. We briefly discuss the results of the transverse charge and energy-momentum densities.
1	Introduction
The generalized parton distributions (GPDs) provide a new aspect of the structure of the nucleon, since they contain essential information on how the constituents of the nucleon behave inside a nucleon. The energy-momentum tensor (EMT) form factors (FFs) are given by Mellin moments of certain GPDs and characterize how mass, spin, and internal forces are distributed inside a nucleon. The EMT FFs are essential quantities in understanding the internal structure of the nucleon [1-3]. Furthermore the transverse charge which is defined by a Fourier transform in the transverse plane provides a tomographic picture of how the charge densities of quarks are distributed transversely [4,5].
2	Lagrangian of the model
We start from the in-medium modified effective chiral Lagrangian with the n, p, and w meson degrees of freedom, where the nucleon arises as a topological soliton. Using the asteriks to indicate medium modified quantities, the Lagrangian has the form
— + LV + Lkin +
(1)
* Talk delivered by Ju-Hyun Jung
In-medium properties of the nucleon within a n-p-w model where the corresponding terms are expressed as
f 2 f 2 f 2 m2 = Tr (3oU3oU^ - ^ ^ Tr (3^3^) + as^
f2 2 LV = f Tr [D,^ • ^ + • ^ ,
Tr (U - 1) , (2)
(3)
r> * _
Lkin —
2gV Zv
Tr (F
2 ] J
lWz H	^T Tr {(Ut3vU) (Ut3aU) (Ut3pU)} .

(4)
(5)
Here, the SU(2) chiral field is written as U = £,[ £,R in unitary gauge, and the field-strength tensor and the covariant derivative are defined, respectively, as
= 02Vv - SvV, - i[V2,Vv]
D2 £l(R) = d2 ^L(R) - Î V2 ^L(R) .
(6) (7)
We assume the following ansatze for the pseudoscalar and vector mesons
U = exp ^ — F(r)
V, = g (t • p, + œ,),
Po = 0, Pi" = g^ G(r), œ, = œ(r)5,0
(8)
with the Pauli matrices t in isospin space. One can minimize the static mass functional related to the Lagrangian in Eq. (1) and find the solitonic solutions corresponding to a unit baryon number (B = 1 ). The integrand of the static mass functional corresponds to T00 component of the energy momentum tensor presented below. The details of the minimization procedure can be found in Ref. [6].
Using the Lagrangian in Eq. (1), one can calculate each component of the EMT as follows:
T00* (r) = ap f| ( 2 ^ + F A + af^m* (1 - cos F)
2
r2
(1 - cos F + G)2 - Zg2f>2
+{2r2G '2 +G2 (g+2)2}- r
2g2Zr2 '3

1
T0i* (r, s) =
gilmrlgm
(s x r)
2n2r2
T PJ (r) ,
œsin2 FF',
Tij* (r) = s (r) ( ^ - ^ ) + p (r) 5ij ,
r2
3
(9) (10) (11)
5
6	Ju-Hyun Jung, Ulugbek Yakhshiev, Hyun-Chul Kim
where
f2 1 n
PÍ M = 3f
3A
+
3g2r2ZA
is the angular momentum density and
sin2 F + 8 sin4 2 - 4 sin2 2^,1 1 [(2 - 2£,! - £,2) G2] +	sin2 FF'
(12)
1
p* (r)=-6apfn F'2 + 2 r2
sin2 f'
asfnm7t (1 - cos F)
2
3T2
fn (1 - cos F + G)2 + f^gW
+^g^Wi 2r2 G '2 + G2 (G + 2)2} + " '
6g2 Zr2
s* (r)= f F'2 -	- f (1 - cos F + G)2
r
r2
(13)
+
g2r2Z
[r2G'2 - G2 (G + 2)2}
w
2
(14)
are the pressure and the shear force distributions inside the nucleon. The moment of inertia of the rotating soliton including 1/Nc corrections is given by the expression
A* = 4n
dr
f (sin2 F + 8 sin4 2 - 4 sin2 2^
+
2
gVZ,
{(2 - 2^ - ^2) G2} + ® sin2 FF'
3g2r2Z
4n2
(15)
As we mentioned above, the integral of Too gives the soliton mass at zero momentum transfer t = 0. Therefore, the M2 (t) form factor is normalized by the nucleon mass as
M2 (0) =
1
mn
d3r Too (r) = 1
(16)
to leading order in MN, which is equals to the soliton mass [7]. For details, we refer to Refs. [8,9]
The EMT FFs of the nucleon parametrize the nucleon matrix elements of the symmetric EMT operator as follows [2,3]:
<p'lV(0)|p> = ü(p', s')
M2(q2)	+ J(q2)	+ Pv^.p)qP (17)
Mn
2
+d!(q2) q.qv -
2Mn
5Mn
ü(p, s) ,
(18)
where P = (p + p ')/2.
In-medium properties of the nucleón within a n-p-œ model
7
One can be related GPDs. In the specific case, £ = 0, one has
r i
A20 (t) = M2 (t) =
-1
dxxH (x,0,t) ,
B20 (t) = 2J (t) - M2 (t) =
dxxE (x, 0, t) .
(19)
(20)
In the isospin symmetric approximation the proton and neutron EMT FFs are similar. Therefore we introduce the nucleon transverse EMT densities instead of considering the proton and neutron EMT densities separately. In this approximation an unpolarized nucleon transverse EMT density takes the form
p02) (b)=r (bQ) A2° (q2) •
For a polarized nucleon one has the following transverse EMT density
pT2)(b) = p°2) (b)- sin - fo)
(21)
Q2dQ .
4nMN
ji (bQ) B20 (Q2) .
(22)
x
3 Results
Now let us discuss the energy-momentum form factors of the nucleons. First of all, it is necessary to notice that in the case of exact isospin symmetry the energy-momentum form factors of the protons and neutrons cannot be distinguished in free space. The same result holds for the nucleons embedded in isospin symmetric nuclear matter. The situation changes if one introduces isospin breaking effects in the mesonic sector. In the case of in-medium nucleons the isospin asymmetric nuclear environment can generate differences in EMT form factors of the nucleons even if one has isospin symmetry in the mesonic sector in free space. For simplicity we concentrate in this work on the isopin symmetric case for both, free space as well as in medium nucleons, considering an isospin symmetric nuclear environment.
The energy-momentum form factors of the nucleons as functions of t are presented in Fig. 1 for free space nucleons and in-medium nucleons at normal nuclear matter density p°.
Finally, in Fig. 2 we present the transverse energy-momentum densities inside an unpolarized and polarized nucleon for the fixed value of bx = 0.
Our complete results will appear in some detail elsewhere [10].
Acknowledgments
This work is supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Korean government (Ministry of Education, Science and Technology), Grant No. 2011-0023478 (J.H.Jung and U.Yakhshiev) and Grant No. 2012004024 (H.Ch.Kim). J.-H.Jung. acknowledges also partial support by the "Fonds zur Forderung der wissenschaftlichen Forschung in Österreich via FWF DK W1203-N16."
8	Ju-Hyun Jung, Ulugbek Yakhshiev, Hyun-Chul Kim
Fig. 1. The EMT form factors of the nucleon, A20 and B20, as functions of t. The solid curve depicts the form factors in free space. The dotted and dotted-dashed ones represent, respectively, those from Model I and Model II in nuclear medium at the normal nuclear matter density p0.
Fig. 2. Transverse energy-momentum densities inside an unpolarized and polarized nucleon with bx = 0 fixed. The solid curve depicts the form factors in free space. The dotted and dotted-dashed ones represent, respectively, those from model I and model II in nuclear matter.
References
1.	X. D. Ji, Phys. Rev. D 55, 7114 (1997).
2.	X. D. Ji, Phys. Rev. Lett. 78, 610 (1997).
3.	M. V. Polyakov, Phys. Lett. B 555, 57 (2003).
4.	U. Yakhshiev and H. -Ch. Kim, Phys. Lett. B 726, 375 (2013).
5.	K. Goeke, M. V. Polyakov and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 47 401 (2001).
6.	J. -H. Jung, U. T. Yakhshiev and H. -Ch. Kim, Phys. Lett. B 723, 442 (2013).
7.	H. -Ch. Kim, P. Schweitzer and U. T. Yakhshiev, Phys. Lett. B 718, 625 (2012).
8.	J. -H. Jung, U. Yakhshiev and H. -Ch. Kim, J. Phys. G 41, 055107 (2014).
9.	J. -H. Jung, U. Yakhshiev, H. -Ch. Kim and P. Schweitzer Phys. Rev. D 89,114021 (2014).
10.	J. -H. Jung, U. T. Yakhshiev and H. -Ch. Kim, in preparation.
11.	T. Ericson and W. Weise, Pions and Nuclei (Clarendon, Oxford, 1988).
Povzetki v slovenščini
Resonance in njihova razvejitvena razmerja iz perspektive časovnega razvoj
Ido Gilary
Shulich Faculty of Chemistry, Technion, Haifa, 3200003, Israel
Časovni razvojmetastabilnih stanjkaže znacinosti vezanih stanjin sipanih stanj. Dinamiko teh stanjlahko opisemo s kompleksno energijo, ki ponazarja lego in sirino resonance. Opisani in pojasneni so razni pristopi k temu problemu.
Lastnosti nukleona v snovi, v modelu z mezoni n, p in tu
Ju-Hyun Junga, Ulugbek Yakhshievb in Hyun-Chul Kimb
a Theoretical Physics, Institute of Physics, University of Graz, Universitaetsplatz 5, A-8010 Graz, Austria
b Department of Physics, Inha University, Incheon 402-751, Republic of Korea
Poročamo o svezih raziskavah transverzalne gostote naboja in energije/gibalne količine pri nukleonu v jedrski snovi, osnovanih na solitonskem modelu n— p—w, prilagojenem za sistem v snovi. Rezultati nam pomagajo ugotoviti splosne las-tosti taksne prilagoditve zgradbe nukleonov, vezanih v jedrsko snov. Na kratko predstavimo rezultate za transverzalno gostoto naboja in energije/gibalne kolici-ne.
nMAID-2015: posodobitev z novimi podatki in novimi resonancami
V.L. Kashevarov, L. Tiator, M. Ostrick
Institut fuer Kernphysik, Johannes Gutenberg-Universitaet D-55099 Mainz, Germany
Predstavimo sveze podatke o fotoprodukciji n in n' na protonih, ki jih je izmerila Kolaboracija A2 na pospesevalniku MAMI. Celotni presek za fotoprodukcijo n kaze ost pri energiji praga za n'. Analizirali smo nove podatke in stare podatke (od kolaboracijGRAAL, CBELSA/TAPS in ČLAS) z razvojem po pridruzenih Legendreovih polinomih. Za reproduciranje novih podatkov smo uporabili izo-barni model nMAID, posodobljen s kanalom n' in novimi resonancami. Nova verzija, n MAID-2015, razmeroma dobro opise podatke, pridobljene s fotonskimi zarki z energijami do 3.7 GeV.