arXiv:1002.2471v2 [hep-ph] 28 Apr 2010
Analysis of the
+heavy and doubly heavy baryon states with QCD
Department of Physics, North China Electric Power University, Baoding 071003, P. R.
In this article, we study the
make reasonable predictions for their masses.
+heavy and doubly heavy baryon states Ξ∗
bby subtracting the contributions from the cor-
−heavy and doubly heavy baryon states with the QCD sum rules, and
PACS number: 14.20.Lq, 14.20.Mr
Key words: Heavy baryon states, QCD sum rules
In 2006, the Babar collaboration reported the first observation of the3
c→ Ωcγ . By now, the
c), and the
In 2008, the D0 collaboration reported the first observation of the doubly strange
baryon state Ω−
. The experimental value MΩ−
than the most theoretical calculations [4, 5, 6, 7, 8, 9, 10, 11, 12, 14]. However, the
CDF collaboration did not confirm the measured mass , i.e. they observed the mass
of the Ω−
bis about (6.0544 ± 0.0068 ± 0.0009)GeV, which is consistent with the most
theoretical calculations. On the other hand, the theoretical prediction MΩ0
[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] is consistent with the experimental data MΩ0
(2.6975 ± 0.0026)GeV . The S-wave bottom baryon states are far from complete, only
the Λb, Σb, Σ∗
In 2002, the SELEX collaboration reported the first observation of a signal for the
doubly charm baryon state Ξ+
confirmed later by the same collaboration in the decay mode Ξ+
mass MΞ= (3518.9±0.9)MeV . However, the Babar and Belle collaborations have not
observed any evidence for the doubly charm baryon states in e+e−annihilations [19, 20].
No experimental evidences for the3
have been several approaches to deal with the doubly heavy baryon masses, such as the
relativistic quark model [21, 22], the non-relativistic quark model [14, 23, 24, 25], the
three-body Faddeev method , the potential approach combined with the QCD sum
rules , the quark model with AdS/QCD inspired potential , the MIT bag model
, the full QCD sum rules [29, 30], the Feynman-Hellmann theorem and semiempirical
mass formulas , and the effective field theories , etc.
cin the radiative decay Ω∗
+antitriplet states (Λ+
+sextet states (Ωc,Σc,Ξ′c) and (Ω∗
c) have been well
bin the decay channel Ω−
b→ J/ψ Ω−in p¯ p collisions at√s = 1.96 TeV
b= (6.165 ± 0.010 ± 0.013) GeV is about 0.1GeV larger
b, Ξb, Ωbhave been observed .
ccin the charged decay mode Ξ+
cc→ pD+K−with measured
+doubly heavy baryon states are observed . There
The charm and bottom baryon states which contain one (two) heavy quark(s) are
particularly interesting for studying dynamics of the light quarks in the presence of the
heavy quark(s), and serve as an excellent ground for testing predictions of the quark
models and heavy quark symmetry. On the other hand, the QCD sum rules is a powerful
theoretical tool in studying the ground state heavy baryon states [33, 34, 35].
In the QCD sum rules, the operator product expansion is used to expand the time-
ordered currents into a series of quark and gluon condensates which parameterize the
long distance properties of the QCD vacuum. Based on the quark-hadron duality, we can
obtain copious information about the hadronic parameters at the phenomenological side
[33, 34, 35]. There have been several works on the masses of the heavy baryon states with
the full QCD sum rules and the QCD sum rules in the heavy quark effective theory (one
can consult Ref. for more literatures).
In Ref., Jido et al introduce a novel approach based on the QCD sum rules to
separate the contributions of the negative-parity light flavor baryons from the positive-
parity light flavor baryons, as the interpolating currents may have non-vanishing couplings
to both the negative- and positive-parity baryons . Before the work of Jido et al, Bagan
et al take the infinite mass limit for the heavy quarks to separate the contributions of the
positive and negative parity heavy baryon states unambiguously .
In Refs.[40, 41, 42], we study the heavy baryon states ΩQ, Ξ′
with the full QCD sum rules, and observe that the pole residues of the3
from the sum rules with different tensor structures are consistent with each other, while the
pole residues of the1
differ from each other greatly. In Refs.[36, 43], we follow Ref. and study the masses and
pole residues of the1
contributions of the negative parity heavy baryon states to overcome the embarrassment.
Those pole residues are important parameters in studying the radiative decays Ω∗
Q→ ΣQγ [42, 44], etc. In Ref., we extend our previous works to
In this article, we study the3
bby subtracting the contributions from the corresponding
The article is arranged as follows: we derive the QCD sum rules for the masses and
the pole residues of the heavy and doubly heavy baryon states Ξ∗
bin Sect.2; in Sect.3, we present the numerical results and discussions;
and Sect.4 is reserved for our conclusions.
Q, ΣQ, Ω∗
+heavy baryons from the sum rules with different tensor structures
+heavy baryon states ΩQ, Ξ′
Q, ΣQ, ΛQand ΞQby subtracting the
Qγ and Σ∗
+doubly heavy baryon states ΞQQand ΩQQwith the full QCD sum rules.
+heavy and doubly heavy baryon states Ξ∗
−heavy and doubly heavy baryon states with the QCD sum rules.
2 QCD sum rules for the baryon states Ω∗
+heavy and doubly heavy baryon states Ω∗
µ (x), J
µ (x) and J
Qcan be inter-
µ (x) respec-polated by the following currents J
where the Q represents the heavy quarks c and b, the i, j and k are color indexes, and
the C is the charge conjunction matrix. In the heavy quark limit, the heavy and doubly
heavy baryon states can be described by the diquark-quark model .
the currents J−
, where the J+
µdenotes the currents J
The correlation functions Π±
µν(p) are defined by
The currents J±
−heavy and doubly heavy baryon states can be interpolated by
µbecause multiplying iγ5to the J+
µchanges the parity of the J+
µ (x), J
µ (x) and J
±baryon states B∗
µ(x) couple to both the3
±baryon states B±
the λ±and λ∗are the pole residues and M∗are the masses, and the spinor U(p,s) satisfies
the usual Dirac equation (?p − M∗)U(p) = 0.
µν(p) have the following relation
We insert a complete set of intermediate baryon states with the same quantum numbers
as the current operators J±
representation [33, 34]. After isolating the pole terms of the lowest states of the heavy
and doubly heavy baryons, we obtain the following result :
µ(x) into the correlation functions Π+
µν(p) to obtain the hadronic
−Π+(p)gµν+ ··· ,
?p + M+
+− p2gµν− λ2
?p − M−
−− p2gµν+ ··· ,
 B. Aubert et al, Phys. Rev. Lett. 97 (2006) 232001.
 C. Amsler et al, Phys. Lett. B667 (2008) 1.
 V. Abazov et al, Phys. Rev. Lett. 101 (2008) 232002.
 R. Roncaglia, D. B. Lichtenberg, and E. Predazzi, Phys. Rev. D52, 1722 (1995).
 A. Valcarce, H. Garcilazo and J. Vijande, Eur. Phys. J. A37 (2008) 217.
 E. Jenkins, Phys. Rev. D54, 4515 (1996).
 K. C. Bowler et al., Phys. Rev. D54, 3619 (1996).
 N. Mathur, R. Lewis, and R. M. Woloshyn, Phys. Rev. D66, 014502 (2002).
 D. Ebert, R. N. Faustov, and V. O. Galkin, Phys. Rev. D72, 034026 (2005).
 D. Ebert, R. N. Faustov, and V. O. Galkin, Phys. Lett. B659, 612 (2008).
 M. Karliner, B. Keren-Zura, H. J. Lipkin, and J. L.Rosner, arXiv:0706.2163;
 X. Liu, H. X. Chen, Y. R. Liu, A. Hosaka, and S. L. Zhu, Phys. Rev. D77, 014031
 J. R. Zhang and M. Q. Huang, Phys. Rev. D78 (2008) 094015.
 W. Roberts and M. Pervin, Int. J. Mod. Phys. A23 (2008) 2817.
 L. Liu, H. W. Lin, K. Orginos and A. Walker-Loud, arXiv:0909.3294.
 T. Aaltonen et al, Phys. Rev. D80 (2009) 072003.
 M. Mattson et al, Phys. Rev. Lett. 89, 112001 (2002).
 A. Ocherashvili et al, Phys. Lett. B628, 18 (2005).
 B. Aubert et al, Phys. Rev. D74, 011103 (2006).
 R. Chistov et al, Phys. Rev. Lett. 97, 162001 (2006).
 D. Ebert, R. N. Faustov, V. O. Galkin and A. P. Martynenko, Phys. Rev. D66 (2002)
 A. P. Martynenko, Phys. Lett. B663 (2008) 317.
 C. Albertus, E. Hernandez, J. Nieves and J. M. Verde-Velasco, Eur. Phys. J. A32
 J. Vijande, H. Garcilazo, A. Valcarce and F. Fernandez, Phys. Rev. D70, 054022
 S. S. Gershtein, V. V. Kiselev, A. K. Likhoded and A. I. Onishchenko, Phys. Rev.
D62, 054021 (2000).
 V. V. Kiselev and A. K. Likhoded, Phys. Usp. 45 (2002) 455.
 F. Giannuzzi, Phys. Rev. D79 (2009) 094002.
 D. H. He, K. Qian, Y. B. Ding, X. Q. Li and P. N. Shen, Phys. Rev. D70 (2004)
 E. Bagan, M. Chabab and S. Narison, Phys. Lett. B306 (1992) 350.
 J. R. Zhang and M. Q. Huang, Phys. Rev. D78 (2008) 094007.
 D. B. Lichtenberg, R. Roncaglia, and E. Predazzi, Phys. Rev. D53, 6678 (1996).
 N. Brambilla, T. Roesch and A. Vairo, Phys. Rev. D72 (2005) 034021.
 M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147 (1979) 385,
 L. J. Reinders, H. Rubinstein and S. Yazaki, Phys. Rept. 127 (1985) 1.
 S. Narison, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 17 (2002) 1.
 Z. G. Wang, Phys. Lett. B685 (2010) 59.
 D. Jido, N. Kodama and M. Oka, Phys. Rev. D54 (1996) 4532.
 Y. Chung, H. G. Dosch, M. Kremer and D. Schall, Nucl. Phys. B197 (1982) 55.
 E. Bagan, M. Chabab, H. G. Dosch and S. Narison, Phys. Lett. B301, 243 (1993).
 Z. G. Wang, Eur. Phys. J. C54 (2008) 231.
 Z. G. Wang, Eur. Phys. J. C61 (2009) 321.
 Z. G. Wang, Eur. Phys. J. A44 (2010) 105.
 Z. G. Wang, arXiv:1001.1652.
 Z. G. Wang, Phys. Rev. D81 (2010) 036002.
 Z. G. Wang, arXiv:1001.4693.
 B. L. Ioffe, Prog. Part. Nucl. Phys. 56 (2006) 232.
 P. Colangelo and A. Khodjamirian, hep-ph/0010175.
 A. Khodjamirian and R. Ruckl, Adv. Ser. Direct. High Energy Phys. 15 (1998) 345.
 A. A. Ovchinnikov, A. A. Pivovarov and L. R. Surguladze, Int. J. Mod. Phys. A6
 W. Lucha, D. Melikhov and S. Simula, Phys. Rev. D76 (2007) 036002.
 D. M. Asner et al, arXiv:0809.1869.
 M. F. M. Lutz et al, arXiv:0903.3905.
 G. Kane and A. Pierce, ”Perspectives On LHC Physics”, World Scientific Publishing