Advances in High Energy Physics
Volume 2018 (2018), Article ID 1326438, 11 pages
https://doi.org/10.1155/2018/1326438

Research Article

A New Model for Calculating the Ground and Excited States Masses Spectra of Doubly Heavy Baryons

Neda Mohajery,¹ Nasrin Salehi,¹ and Hassan Hassanabadi²

¹Department of Basic Sciences, Shahrood Branch, Islamic Azad University, Shahrood, Iran
²Faculty of Physics, Shahrood University of Technology, Shahrood, Iran

Correspondence should be addressed to Nasrin Salehi; salehi@shahroodut.ac.ir

Received 9 March 2018; Revised 31 May 2018; Accepted 11 June 2018; Published 26 July 2018

Academic Editor: Chun-Sheng Jia

Copyright © 2018 Neda Mohajery et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³.

Abstract.

Since the doubly heavy baryons masses are experimentally unknown (except and ), we present the ground state masses and the positive and negative parity excited state masses of doubly heavy baryons. For this purpose, we have solved the six-dimensional hyperradial Schrödinger equation analytically for three particles under the hypercentral potential by using the ansatz approach. In this paper, the hypercentral potential is regarded as a combination of the color Coulomb plus linear confining term and the six-dimensional harmonic oscillator potential. We also added the first-order correction and the spin-dependent part contains three types of interaction terms (the spin-spin term, spin-orbit term, and tensor term) to the hypercentral potential. Our obtained masses for the radial excited states and orbital excited states of , , , , , and systems are compared with other theoretical reports, which could be a beneficial tool for the interpretation of experimentally unknown doubly heavy baryons spectrum.

1. Introduction

The doubly heavy baryons have two heavy quarks (c and b) with a light quark (d or u or s). The doubly heavy baryons family have up or down quarks but family has a light strange quark and their masses spectra have been predicted in the quark model [1]. The SELEX collaboration announced only the experimental mass for the ground state of baryon and LHCb has determined the ground state of baryon mass while no triply heavy baryons have been observed yet [2]. Recently experiments and theoretical outcomes have been used in studying the heavy baryons. A lot of new experimental results have been reported by various experimental facilities like CLEO, Belle, BaBar, LHCb, and so forth [3, 4] on ground states and many new excited states of heavy flavor baryons. Bottom baryons are investigated at LHC and Lattice QCD whereas charm baryons are announced at the B-factories [5, 6]. On the other hand, the theoretical works are providing new results for doubly heavy baryons like the Hamiltonian model [7], relativistic quark model [8], the chiral unitary model [9], QCD sum rule [10, 11], and many more. Single- and double- heavy baryons in the constituent quark model were studied by Yoshida et al. They used a model in which there were two exceptions, a color Coulomb term depending on quark masses and an antisymmetric L.S force. They studied the low-lying negative parity states and structures within the framework of a constituent quark model [7]. In [12], the authors calculated the masses of baryons with the quadratic mass relations for ground and orbitally excited states. Wei et al. estimated the masses of singly, doubly, and triply bottom baryons in [13]. Then they studied the linear mass relations and quadratic mass relations.

The light flavor dependence of the singly and doubly charmed states is investigated by Rubio et al. They focused on searching the masses of charmed baryons with positive and negative parity [5]. In [14], the authors used lattice QCD for baryons containing one, two, or three heavy quarks. They applied nonrelativistic QCD for the bottom quarks and relativistic heavy-quark action for the charm quarks. Padmanath et al. determined the ground and excited state spectra of doubly charmed baryons from lattice QCD with dynamical quark fields [15]. The mass of the heavy baryons with two heavy b or c quarks for spin in the framework of QCD sum rules is estimated by Aliev et al. They use the most general form of the interpolating current in its symmetric and antisymmetric forms with respect to the exchange of heavy quarks, to calculate the two point correlation functions describing the baryons under consideration [16]. The authors calculated the masses and residues of the spin doubly heavy baryons within the QCD sum rules method. In [17], Eakins et al. ignored all spin-dependent interactions and assume a flavor independent potential, working in the limit where the two heavy quarks are massive enough that their motion can be treated as essentially nonrelativistic, and QCD interactions can be well described by an adiabatic potential [18]. The three-quark problem was solved by Valcarce et al. by means of the Faddeev method in momentum space [19].

The masses of the ground and excited states of the doubly heavy baryons were calculated by Ebert et al. baryons on the basis of the quark-diquark approximation in the framework of the relativistic quark model [20]. In [21], the authors, in the model with the quark-diquark factorization of wave functions, estimated the spectroscopic characteristics of baryons containing two heavy quarks. Albertus et al. used five different quark-quark potentials that include a confining term plus Coulomb and hyperfine terms coming from one–gluon exchange. They solved the three-body problem by means of a variational ansatz made possible by heavy-quark spin symmetry constraints [22].

In this study, we have used the hypercentral constituent quark model (hCQM) with Coulombic-like term plus a linear confining term and the harmonic oscillator potential [23]. We also added the first-order correction and the spin-dependent part to the potential and calculation has been performed by solving six-dimensional hyperradial Schrödinger equations by using the ansatz method. We have obtained the mass spectra of radial excited states up to 5S and orbital excited states for 1P-5P, 1D-4D, and 1F-2F states.

This paper is organized as follows: we briefly present the hypercentral constituent quark model and introduce the interaction potentials between three quarks in doubly heavy baryons in Section 2. In Section 3, we present the exact analytical solution of the hyperradial Schrödinger equation for our proposed potential. In Section 4, our masses spectra results for ground, radial, and orbital excited states of baryon family with six members are given and compared with other predictions. We present the conclusions in Section 5.

2. Theoretical Framework: The HCQM Model and Hypercentral Potential

The hypercentral model has been applied to solve bound states and scattering problems in many various fields of physics. In this model, we consider baryons as three-body systems of constituent quarks. In the center of mass frame, the internal quark motion is described by the Jacobi coordinates ( and ) [37] and the respective reduced masses are given by

Here , , and are the current quark masses. In order to describe three-quark dynamics, we define hyperradius and hyperangle [38]. In present work, the confining three-body potential is regarded as a combination of three hypercentral interacting potentials. First, the six-dimensional hyper-Coulomb potential , which is attractive for small separations [39–41], while at large separations a hyper-linear term, , gives rise to quark confinement [42], where corresponds to the string tension of the confinement [43]. Third, the six-dimension harmonic oscillator potential , which has a two-body character and turns out to be exactly hypercentral [44], where is constant. The solution of the hypercentral Schrödinger equation with Coulombic-like term plus a linear confining term potential cannot be obtained analytically [45]; therefore, Giannini et al. used the dynamic symmetry O(7) of the hyper-Coulomb problem to obtain the hyper-Coulomb Hamiltonian and eigenfunctions analytically and they regarded the linear term as a perturbation. Combination of the color Coulomb plus linear confining term and the six-dimensional harmonic oscillator potential has interesting properties since it can be solved analytically, with a good correspondence to physical results. The first-order correction can be written as [44–47]

The parameters and are the Casimir charges of the fundamental and adjoint representation. The hyper-Coulomb strength , is the color factor for the baryon. is the strong running coupling constant, which is written as

The spin-dependent part is given as

The spin-dependent potential, , contains three types of the interaction terms [48], such as the spin-spin term , the spin-orbit term , and tensor term described as [35]. Here , where and are the spin vectors associated with the and variables, respectively. The coefficient of these spin-dependent terms of the above equation can be written in terms of the vector, , and scalar, parts of the static potential as [38]

In our model, the hypercentral interaction potential is assumed as follows [48]:

where is given by

The baryons masses are determined by the sum of the model quark masses plus kinetic energy, potential energy, and the spin-dependent interaction as [49]. First, we have solved the hyperradial Schrödinger equation exactly and find eigenvalue under the proposed potential by using the ansatz approach.

3. The Exact Analytical Solution of the Hyperradial Schrödinger Equation under the Hypercentral Potential

The Hamiltonian of three bodies’ baryonic system in the hypercentral constituent quark model is expressed as [50]

and the hyperradial wave function is determined by the hypercentral Schrödinger equation. The hyperradial Schrödinger equation corresponding to the above Hamiltonian can be written as [51]

where is the grand angular quantum number and given by , and are the angular momenta associated with the   and variable and denotes the number of nodes of the space three-quark wave function [36]. In (11), is the reduced mass which is defined as [32]. By regarding [20, 35], (11) reduces to the following form:

The hyperradial wave function is a solution of the reduced Schrödinger equation for each of the three identical particles with the mass m and interacting potential (8), where

We suppose the form for the wave function. Now we make use of the ansatz for and [33, 34]:

where , , , and are positive. From (14), we obtain

Comparing (12) and (15), it can be found that

By substituting (14) into (16), we obtained the following equation:

By equating the corresponding powers of on both sides of (17), we can obtain

Since , we have , , . The energy eigenvalues for the mode and grand angular momentum from (13) and (18) are given as follows:

At last for the best doubly heavy baryons masses (, , , , , ) predictions, the values of , , , , , , and (which are listed in Table 1) are selected using genetic algorithm. The cost function of a genetic algorithm is the minimum difference between our calculated baryon mass and the reported baryons mass of other works.

Table 1: The quark mass (in GeV) and the fitted values of the parameters used in our calculations.

4.750
1.348
0.35
0.34
0.340

3
0.02
0.11 fm⁻¹

4. Results and Discussions: Mass Spectrum

The ground and excited states of doubly heavy baryons are unclear to us experimentally (except and ). Hence, we have obtained the ground and excited state masses of , , , , , and (see Tables 2, 3, 4, 5, and 6, respectively). These mass spectra are estimated by using the hypercentral potential equation (8) in the hypercentral constituent quark model. We begin with the ground state 1S; the masses are computed for both parities and . Our predicted ground state masses of doubly heavy baryons are compared with other predictions in Table 2.

Table 2: The outcomes ground state masses of are listed with other theoretical predictions (in GeV). Standard devotion of the result is 0.350.

Baryon
/
/
/

Our Calc
3.522 / 3.515
3.696 / 3.689
9.716 / 9.711
9.894 / 9.889
6.628 / 6.622
6.688 / 6.682

Ref.[1]
3.520 / 3.511
3.695 / 3.687
10.317 / 10.312
10.340 / 10.335
6.920 / 6.914
6.986 / 6.980

Ref.[24]
3.519

Ref.[7]
3.685
3.754
10.314

Ref.[12, 13]
3.520
3.695
10.199
10.316

Ref.[5]
3.610
3.694

Ref.[14]
3.610
3.692
10.143
10.178
6.943
6.985

Ref.[25]
3.561
3.642

Ref.[17]
3.720

9.960

6.720

Ref.[18]
3.687
3.752
10.322
10.352
7.014
7.064

Ref.[26]
3.676
3.753
10.340
10.367
7.011
7.074

Ref.[27]
3.547
3.719
10.185
10.216
6.904
6.936

Ref.[19]
3.579
3.656
10.189
10.218

Ref.[20]
3.620
3.727
10.202
10.237
6.933
6.980

Ref.[21]
3.478
3.610
10.093
10.133
6.820
6.900

Ref.[28]
3.627
3.690
10.162
10.184
6.914

Ref.[29]
3.519
3.620
9.800
9.980
6.650
6.690

Ref.[22]
3.612
3.706
10.197
10.136
6.919
6.986

Ref.[30]
3.510
3.548
10.130
10.144
6.792
6.827

Ref.[31]
3.570
3.610
10.170
10.220

Table 3: The masses of radial excited states for doubly heavy baryons (in GeV). Standard devotions of the result are 0.435 and 0.434.

Baryon
State

Our Calc
Our Calc
[1]
[1]
[7]
[26]
[27]
[19]
[20]
[18]

and

2S

3.905
3.901
3.925
3.920
4.079
4.029
4.183
3.976
3.910
4.030

3S
4.185
4.118
4.233
4.159
4.206

4.640

4.154

4S
4.430
4.429
4.502
4.501

5S
4.653
4.653
4.748
4.748

2S

3.962
3.958
3.988
3.983
4.114
4.042
4.282
4.025
4.027
4.078

3S
4.213
4.211
4.264
4.261
4.131

4.719

4S
4.446
4.445
4.520
4.519

5S
4.663
4.663
4.759
4.759

and

2S

9.984
9.981
10.612
10.609
10.571
10.576
10.751
10.482
10.441
10.551

3S
10.211
10.211
10.862
10.862
10.612

11.170

10.630

4S
10.417
10.418
11.088
11.090

10.812

5S
10.606
10.610
11.297
11.301

2S

9.990
9.988
10.619
10.617
10.592
10.578
10.770
10.501
10.482
10.574

3S
10.205
10.233
10.855
10.866
10.593

11.184

10.673

4S
10.418
10.420
11.090
11.092

10.856

5S
10.607
10.611
11.298
11.302

and

2S

6.922
6.919
7.244
7.240

7.478

7.321

3S
7.163
7.161
7.509
7.507

7.904

4S
7.379
7.377
7.746
7.744

5S
7.576
7.581
7.963
7.964

2S

6.943
6.939
7.267
7.263

7.495

7.353

3S
7.174
7.171
7.521
7.518

7.917

4S
7.384
7.384
7.752
7.752

5S
7.580
7.581
7.968
7.969

Table 4: The masses of orbital excited states for baryon (in GeV). Standard devotions of the result are 0.072 and 0.068.

(a)

State
Our cal  

Our Cal  

[1]   

[1]   

[7]
[26]
[19]
[20]
[12]
[21]
[18]
[5]

3.851
3.847
3.865
3.861
3.947
3.910
3.880
3.838

4.073
3.892

3.834
3.830
3.847
3.842
3.949
3.921

3.959
3.786
3.834
4.079
3.989

3.860
3.856
3.875
3.871

3.842
3.838
3.856
3.851

3.873
3.872
3.890
3.888
4.163
4.092

4.155
3.949
4.047
4.089

4.120
4.101
4.161
4.140
4.135
4.074
4.018
4.085

4.104
4.101
4.144
4.140
4.137
4.078
4.197

4.127
4.125
4.169
4.167

4.111
4.109
4.152
4.149

4.140
4.138
4.183
4.181
4.488

4.361
4.345
4.426
4.409
4.149

4.347
4.345
4.411
4.409
4.159

4.367
4.366
4.433
4.432

4.354
4.352
4.419
4.417

4.336
4.333
4.399
4.396
4.534

4.583
4.583
4.671
4.671

4.571
4.571
4.658
4.657

4.590
4.590
4.678
4.678

4.577
4.577
4.664
4.664

4.561
4.561
4.646
4.646

4.792
4.793
4.901
4.902

4.781
4.781
4.889
4.889

4.799
4.800
4.908
4.909

4.705
4.788
4.895
4.896

4.771
4.772
4.878
4.879

)
4.043
4.038
4.077
4.071

4.018
4.013
4.049
4.044

4.026
4.022
4.058
4.053

3.995
3.991
4.024
4.019
4.043
4.115
4.047

4.391
4.034
4.050
4.388

4.003
4.000
4.033
4.029
4.027
4.052

4.187
4.089
4.393

3.975
3.972
4.002
3.998
4.097

)
4.287
4.284
4.345
4.342

4.265
4.262
4.321
4.318

4.272
4.270
4.329
4.326

4.245
4.243
4.299
4.297
4.164
4.091

4.252
4.251
4.307
4.305

4.228
4.226
4.280
4.278
4.394

(b)

State
Our Cal  

Our Cal  

[1]  

[1]  

[7]
[32]
[33]
[34]
[35]
[33]
[36]
[5]

)
4.511
4.511
4.592
4.592
4.511
4.511
4.592
4.592
4.511
4.511
4.592
4.592

4.492
4.491
4.571
4.570
4.492
4.491
4.571
4.570
4.492
4.491
4.571
4.570

4.499
4.499
4.578
4.578

4.475
4.474
4.552
4.551
4.348

4.481
4.481
4.559
4.558

4.460
4.459
4.535
4.534

)
4.723
4.724
4.825
4.826

4.706
4.706
4.806
4.806

4.711
4.712
4.812
4.813

4.690
4.690
4.788
4.788

4.696
4.696
4.795
4.795

4.675
4.675
4.772
4.772

4.198
4.193
4.247
4.242

4.169
4.164
4.215
4.210

4.142
4.172
4.186
4.219

4.150
4.147
4.194
4.191

4.178
4.139
4.225
4.182

4.267

4.118
4.115
4.159
4.156

4.413

4.422
4.425
4.494
4.497

4.399
4.399
4.468
4.468

4.405
4.406
4.475
4.476

4.378
4.382
4.445
4.450

4.384
4.376
4.452
4.443

4.359
4.355
4.424
4.420

Table 5: The masses of orbital excited states for baryon (in GeV).

State
Our cal  

Our Cal  

[1]  

[1]  

[7]
[26]
[19]
[20]
[12]
[18]
Others

9.895
9.892
10.514
10.511
10.476
10.493
10.406
10.368

10.691

9.890
9.887
10.509
10.506
10.476
10.495

10.408
10.474
10.692
10.390 [31]

9.897
9.895
10.517
10.514

9.893
9.890
10.512
10.509

10.430 [17]

9.901
9.898
10.521
10.518
10.759

10.588
10.695

10.127
10.127
10.77
10.77
10.703
10.710
10612
10.563

10.124
10.120
10.766
10.762
10.704
10.713

10.607

10.129
10.129
10.772
10.772

10.126
10.125
10.768
10.767

10.121
10.133
10.763
10.776
10.973
10.713

10.337
10.338
11.001
11.002
10.740

10.744

10.334
10.335
10.997
10.998
10.742

10.788

10.339
10.340
11.003
11.004

10.336
10.337
10.999
11.000

10.331
10.343
10.994
11.007
11.004

10.531
10.534
11.214
11.217

10.900

10.527
10.530
11.21
11.213

10.533
10.536
11.216
11.219

10.529
10.532
11.212
11.215

10.526
10.538
11.208
11.222

10.712
10.716
11.413
11.418

10.709
10.714
11.41
11.415

10.714
10.718
11.415
11.420

10.711
10.716
11.412
11.417

10.706
10.721
11.407
11.423

10.043
10.041
10.677
10.675

10.037
10.035
10.670
10.668

10.038
10.037
10.672
10.670

11.011

10.030
10.028
10.663
10.661
10.592
10.676

10.742
11.002

10.033
10.031
10.666
10.664

10.026
10.024
10.658
10.656

10.608

10.853
11.011

10.257
10.257
10.913
10.913

10.252
10.252
10.907
10.907

10.254
10.254
10.909
10.909

10.247
10.247
10.901
10.901

10.712

10.248
10.248
10.903
10.903
10.613

10.242
10.242
10.896
10.896

11.057

10.455
10.457
11.13
11.133

4.592
4.592

10.450
10.452
11.125
11.127

4.571
4.570

10.451
10.454
11.126
11.129

10.446
10.447
11.120
11.122

10.447
10.449
11.122
11.124
10.809

10.442
10.444
11.116
11.118

10.639
10.643
11.333
11.337

10.635
10.638
11.328
11.332

10.636
10.640
11.330
11.334

10.631
10.635
11.324
11.328

10.632
10.636
11.325
11.33

10.627
10.631
11.320
11.324

10.173
10.172
10.82
10.819

10.166
10.165
10.812
10.811

10.158
10.167
10.804
10.813

10.167
10.160
10.814
10.806

10.160
10.157
10.806
10.803

11.004

10.152
10.152
10.797
10.797

11.112

10.357
10.376
11.022
11.043

10.368
10.369
11.035
11.036

10.369
10.371
11.036
11.038

10.362
10.365
11.028
11.031

10.364
10.363
11.030
11.029

10.357
10.357
11.022
11.023

Table 6: The masses of orbital excited states for baryon (in GeV).

State
Our cal
Our Cal
[1]
[1]
[18]

6.846
6.842
7.16
7.156
7.390

6.836
6.831
7.149
7.144
7.394

6.851
6.847
7.166
7.161
7.399

6.841
6.837
7.155
7.15

6.859
6.856
7.175
7.171

7.087
7.084
7.425
7.422

7.078
7.075
7.415
7.412

7.091
7.088
7.43
7.426

7.082
7.079
7.42
7.417

7.071
7.095
7.408
7.434

7.304
7.302
7.664
7.662

7.296
7.295
7.655
7.654

7.308
7.306
7.668
7.666

7.299
7.299
7.659
7.658

7.289
7.312
7.648
7.673

7.504
7.623
7.884
8.015

7.497
7.498
7.876
7.877

7.508
7.508
7.888
7.888

7.500
7.500
7.88
7.88

7.491
7.514
7.87
7.895

7.692
7.693
8.091
8.092

7.686
7.687
8.084
8.085

7.695
7.697
8.094
8.096

7.689
7.689
8.087
8.088

7.680
7.681
8.078
8.079

7.006
7.004
7.336
7.334

6.992
6.989
7.321
7.318

6.997
6.980
7.326
7.308
7.324

6.980
6.977
7.308
7.304

6.985
6.969
7.313
7.295
7.309

6.969
6.953
7.296
7.278
7.292

7.087
7.227
7.425
7.579
7.579

7.216
7.214
7.567
7.565

7.219
7.219
7.571
7.57

7.205
7.203
7.555
7.553
7.538

7.209
7.208
7.559
7.558

7.196
7.195
7.545
7.544

7.431
7.431
7.804
7.804

7.420
7.420
7.792
7.792

7.411
7.424
7.782
7.796

7.415
7.410
7.786
7.781

7.402
7.414
7.772
7.785

7.402
7.402
7.772
7.772

7.429
7.504
7.801
7.884
7.797

7.611
7.613
8.002
8.004

7.615
7.617
8.006
8.008

7.603
7.604
7.993
7.994

7.606
7.608
7.996
7.998

7.596
7.597
7.985
7.986

7.143
7.141
7.487
7.485

7.127
7.125
7.469
7.467

7.131
7.129
7.474
7.472

7.117
7.114
7.458
7.455

7.112
7.109
7.453
7.45

7.099
7.097
7.439
7.436

7.350
7.350
7.715
7.715

7.337
7.336
7.7
7.699

7.340
7.339
7.704
7.703

7.328
7.327
7.69
7.689

7.324
7.323
7.686
7.685

7.313
7.311
7.674
7.672

We can observe that, in the case of baryon, for 2S states and , our predictions are close to [34] and [1], respectively. Our outcomes for 3S state of baryon show 21 MeV (with [7]) and shows 51 MeV (with [1]) difference. Analyzing the 2S and 3S states masses for and baryons (with both parities) shows that our masses have a difference in the range of 0.5 GeV with [1, 7, 20, 32–34, 36].

To calculate the orbital excited state masses (1P–5P, 1D– 4D, 1F–2F), we have considered all possible isospin splitting and all combinations of total spin and total angular momentum . Our outcomes and the comparison of masses with other approaches are also tabulated in Tables 4, 5, and 6.

Our obtained orbital excited masses for , 1P state show a difference of 14 MeV (with [1]), 29 MeV (with [33]), 13 MeV (with [34]), and 41 MeV (with [5]), while 1P state shows 14 MeV (with [1]), 48 MeV (with [35]), and 0 MeV (with [33]). Our 2P state shows a difference of 15 MeV (with [7]), 35 MeV (with [34]), and 41 MeV (with [1]), while 2P state shows 26 MeV (with [32]), 33 MeV (with [7]), and 40 MeV (with [1]). Results for 3P states and show a difference in the range of 60 MeV with [1]. We can easily observe that our calculated masses for 4P-5P, 1D-3D, and 1F-2F are matched with [1]. Our outcome for 3D state is quite equal to the predictions of [7, 32, 33, 35]. For the ground and excited states of doubly heavy baryons (), the minimum and maximum percentage of relative error values are 0% and 3.53% between our calculations and the masses reported by Shah et al. [1].

For and baryons, the mass difference from our calculations and other references is large.

Comparing our findings with the masses reported by Shah et al. [1], the minimum and maximum percentage of relative error values are 1.2% (0.8%) and 10.317% (6.92%) for the ground and excited states of doubly heavy baryons and , respectively.

5. Conclusion

In this study, we have computed the mass spectra of ground and excited states for doubly heavy baryons by using a hypercentral constituent quark model. For this goal, we have analytically solved the hyperradial Schrödinger equation for three identical interacting particles under the effective hypercentral potential by using the ansatz method. Our proposed potential is regarded as a combination of the Coulombic-like term plus a linear confining term and the harmonic oscillator potential. We also added the first-order correction and the spin-dependent part to the potential. In our calculations, the and quarks have 10 MeV difference mass, so there is a very small mass difference between and , and , and . Our model has succeeded to assign the values to the exited states of doubly heavy baryons (, , , , , and ). Comparison of the results with other predictions revealed that they are in agreement and our proposed model can be useful to investigate the doubly heavy baryons states masses. For example, for the ground, radial, and orbital excited states masses of doubly heavy baryons the minimum and the maximum percentage of relative error values are 0% and 6% between our calculations and the masses reported by Shah et al. [1].

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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