the heavy baryon masses and spin-isospin dependence
DESCRIPTION
The Heavy baryon masses and Spin-Isospin Dependence. Z. Ghalenovi, A.A. Rajabi, A. Tavakolinezhad. Shahrood University of Technology, Shahrood , Iran. Outline 1- The Models 2- The Heavy Baryons Masses 3- The Heavy Baryons Magnetic Moments. The First Model. - PowerPoint PPT PresentationTRANSCRIPT
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The Heavy baryon masses and Spin-Isospin Dependence
Z. Ghalenovi ,A.A. Rajabi ,
A. Tavakolinezhad
Shahrood University of Technology, Shahrood, Iran
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Outline
1- The Models
2- The Heavy Baryons Masses
3- The Heavy Baryons Magnetic Moments
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The First Model
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4
To describe the baryon containing three quarks , we use the Jacobi coordinates and as
(1)
Such that
(2)
the hyperradius and the hyperangle , defined by
(3)
),2(6
1),(
2
132121 rrrrr
)(2
)(3;
2
321
213
21
21
mmm
mmmm
mm
mmm
x
,22
x )(tan 1
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Therefore
)4()(2
),(22
222
xVm
pV
m
p
m
pH
The remaining hyperradial part of the wave function is determined by
)5(
)()(2)()4(5
22
2
xxVEmxxdx
d
xdx
d
Where
) 6 (
and
)7(
)2(
mm
mmm
2
ll 2
5
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Then the Schrodinger equation will be
)9(0)()]
8
15)([2
)(22
2
xx
xVEdx
xd
)()( 2
5
xxx
We use the transformation
)8(
Where
)10(xcbxaxxV /)( 2
6
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We use a new variable , then the equation (9) becomes
)11(
xx
0)()]8
15)([2)(
2
xx
xVEx
We introduce a simple variational ansatz for
)12(
)(x
222/5322)( xpexpx
7
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And the energy
)13(
)(min0 pEEp
Where
)14(pcpb
appHpE .2
.4
3..
2.
16
15.
2
33)( 122
8
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The Second Model
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)()(2)()4(5
22
2
xxVEmxxdx
d
xdx
d
By using the hyperspherical coordinates , The hypercentral Schrodinger equation will be
) 15(
)()( 2
5
xxx
)()(]4
)52)(32([)(
21
12
1 xxxx
cxbxax
xcbxaxxV /)( 2
Where)16(
10
reduces Eq. (15) to the form
)18(
The transformation
)17 (
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mccmbbmaamE 2,2,2,2 111
let us assume for the wave function
)20 ()](exp[()()( xgxfx
Now for the function f(x) and g(x) we make use of the ansatz
)21 (
1
0),(
01
)(
ii ifax
if
xf
xxxxg ln2
1)( 2
and
11
Where
)19(
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and
)22(
,1a ,2 1
1
a
b,21 c
2)21(, 2
5
2/1)2
(m
aThe frequence of oscillating is , Therefore
)23(
,2 mma .)52(
2
mcb
.)2
5(
mb
c
12
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.)52(
2
2)62(
2
2
0
mcE
))52(
2
2exp( 2
002
5
00 xmc
xm
xNxN
The energy eigenvalue and the normalized eigenfunction of the system are obtained as
)24(
and
)25(
13
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The Heavy Baryons Masses
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The ground state heavy baryon masses are obtained by
)26( int0321 HEmmmM baryon
)()()()(int xHxHxHxH SIIS
where
and
)27(
).)(/exp()1
( 21223 ssxAH S
s
SS
).)(/exp()1
( 21223 ttxAH I
I
II
).)(.)(/exp()1
( 2121223 ttssxAH SI
SI
SISI
15
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The Heavy Baryons Magnetic Moments
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The effective quark mass is defined as
)28()1( int
i i
ieffi
m
HEmm
Such that the mass of the baryon is
)29(. i
effiB mM
The magnetic moment of baryon is as
)30( sfiii
sfB ||
where
effi
ii m
e
2
17
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um
dm
sm
cm
2.37
quark massvalue
320MeV
325MeV
440MeV
1310MeV
4690MeV
S fm
sA
2fm
SI fm
SIA2fm
I fm
IA
2fm
3fm
2fm
54.7
2.15
90
1.12
85
0.23
parametersvalue
0.52
Table 1 The fitted values of the parameters of potentials,obtained with a global fit to the experimental masses.
bm
0.61
a
b
c
18
The first model
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um
dm
sm
cm
2.87
quark massvalue
350MeV
350MeV
400MeV
1500MeV
4980MeV
S fm
sA
2fm
SI fm
SIA2fm
I fm
IA
2fm
1fm
67.4
2.31
-106.2
3.45
51.7
o.832
parametersvalue
0.62
Table2 The fitted values of the parameters of potentials,fited to the experimental masses.
bm
c
19
The second model
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c
c
0c
0c
c
c
Table 3 Single charm baryon masses (masses are in GeV)
baryonOur model (1)Our model (2)Exp[9][11][12]
2.4502.4572.4512.4482.4602.461
2.5372.5862.5182.5052.5252.526
2.4552.461--2.4772.471
2.5422.591--2.5442.536
2.4682.4662.4672.4962.5302.485
2.5562.5962.6462.6332.6032.672
2.4732.4712.471-2.5482.494
2.5612.6012.646-2.6232.680
2.5882.4762.6992.7012.6202.696
2.6762.606-2.7592.7042.757
0c
0 c
0c
0c20
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b
b
b
b
Table 5 Single beauty baryon masses (masses are in GeV)
baryonOur model (1)Our model (2)Exp[9][10][12]
5.8035.8075.807--5.801
5.9125.9365.829--5.823
5.8135.8185.815--5.821
5.9225.9465.836--5.834
5.8485.8215.7925.8795.9705.872
5.9365.956-5.9675.9805.936
5.968--6.0376.0816.005
6.0565.961-6.0906.1026.065
0b
0b
b
b
21
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2/3pJ
N
c
0c
c
0c
0c
Table 6 Magnetic moments of single charm baryons with
in terms of nuclear magneton
.
baryonOur model (1)[4][8][11][12]
1.0971.1701.1301.1581.252
-1.115-1.230-1.146-1.101-0.848
1.3901.4301.2641.2421.513
-0.960-1.000-0.986-1.002-0.688
-0.770-0.770-0.833-0.904-0.865
22
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2/3pJ
NTable 7 Magnetic moments of single beauty baryons with
in terms of nuclear magneton
b
b
0b
b
baryonOur model (1)[8][12]
3.4603.0823.234
-1.790-1.634-1.655
-1.423-1.477-1.095
-1.368-1.292-1.199
23
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REFS:
1. H. HASSANABADI, A.A.RAJABI AND S. ZARRINKAMAR: SPECTRUM OF BARYONS AND SPIN-ISOSPIN DEPENDENCE. 2. S. BOFFI, C. CIOFI DEGLE ATTI AND M. M. GIANNINI (WORLD SCIENTIFIC, 19980, P. 363). 3. M. NARODETSKII, M. A. TRUSOV: THE HEAVY BARYONS IN THE NONPERTURBATIVE STRING APPROACH. ARXIV; HEP-PH/0104019V2 (2001) 72, 4, 679-688 (2009) 4. R. DHIR, R.C. VERMA: MAGNETIC MOMENTS OF () HEAVY BARYONS USING EFFECTIVE MASS AND SCREENED CHARGED SCHEME. EUR. PHYS. J. A 42, 243-249 (2009) 5. B. PATEL, A. MAJETHIYA AND P.C. VINODKUMAR: MASSES AND MAGNETIC MOMENTS OF TRIPLE HEAVY FLAVOUR 6. M.M GIANNINI, E.SANTOPINTO A. VASSALO: AN OVERVIEW OF THE HYPERCENTRAL CONSTITUENT QUARK MODEL. PROG. PART. NUCL. PHYS. 50, 263-272 (2003)7. D. EBERT, R.N. FAUSTOV, V.O. GALKIN, PHYS. REV. D 72 034026 (2005)8. A. MAJETHIYA, B. PATEL, P.C. VINODKUMAR: SINGLE HEAVY FLAVOUR BARYONS USING COULOMB PLUS A POWER LAW INTERQUARK POTENTIAL. EUR. PHYS. J. A 38, 307-315 (2008)9. H. GARCILAZO, J. VIJANDE, A. VALCARCE, J. PHYS. G: NUCL. PART. PHYS. 34, 961-76 (2007) 10. W. ROBERTS, MUSLEMA PERVIN: HEAVY BARYONS IN A QUARK MODEL. ARXIV:0711.2492V2 [NUCL-TH] (2008)11. B. PATEL, A. KUMAR RAI, P. C. VINODKUMAR: MASSES AND MAGNETIC MOMENTS OF CHARMED BARYONS USING HYPER CENTRAL MODEL. ARXIV: 0803.0221V1 [HEP-PH] (2008) BARYONS IN HYPERCENTRAL MODEL. PRAMANA J. PHYS. 12. B. PATEL, A. KUMAR RAI, P.C. VINODKUMAR: MASSES AND MAGNETIC MOMENTS OF HEAVY BARYONS IN THE HYPER CENTRAL MODEL. J. PHYS. G: NUCL. PART. PHYS. 35, 065001 (2008).13. K. NAKAMURA ET AL (PDG), JPG 37, 075021 (2010)
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