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Title: Perturbative corrections to heavy quark-diquark symmetry predictions for doubly heavy baryon hyperfine splittings

Journal Article · · Physical Review. D.

Doubly heavy baryons ($$\textit{QQq}$$) and singly heavy antimesons ($$\bar{Q}q$$) are related by the heavy quark-diquark (HQDQ) symmetry because in the $$m_Q → ∞$$ limit, the light degrees of freedom (d.o.f.) in both the hadrons are expected to be in identical configurations. Hyperfine splittings of the ground states in both systems are nonvanishing at $$O(1/m_Q)$$ in the heavy quark mass expansion, and HQDQ symmetry relates the hyperfine splittings in the two sectors. In this paper, working within the framework of nonrelativistic QCD (NRQCD), we point out the existence of an operator that couples four heavy quark fields to the chromomagnetic field with a coefficient that is enhanced by a factor from Coulomb exchange. This operator gives a correction to doubly heavy baryon hyperfine splittings that scales as $$1/m^2_Q × α_S/r$$, where $$\textit{r}$$ is the separation between the heavy quarks in the diquark. This correction can be calculated analytically in the extreme heavy quark limit in which the potential between the quarks in the diquark is Coulombic. In this limit, the correction is $$O(α^2_s/m_Q)$$ and comes with a small coefficient. For values of $$α_s$$ relevant to doubly charm and doubly bottom systems, the correction to the hyperfine splittings in doubly heavy baryons is only a few percent or smaller. We also argue that nonperturbative corrections to the prediction for the hyperfine splittings are suppressed by $$Λ^2_{\text{QCD}}/m^2_Q$$ rather than $$Λ_{\text{QCD}}/m_Q$$. Corrections should be ≈10% in the charm sector and smaller in heavier systems.

Research Organization:
Duke Univ., Durham, NC (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
FG02-05ER41368
OSTI ID:
1570865
Alternate ID(s):
OSTI ID: 1800273
Journal Information:
Physical Review. D., Vol. 100, Issue 7; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 10 works
Citation information provided by
Web of Science

References (48)

Charmed and bottom baryons from lattice nonrelativistic QCD journal July 2002
Confirmation of the doubly charmed baryon Ξcc+(3520) via its decay to pD+K− journal November 2005
The direct coupling of light quarks to heavy di-quarks journal January 2019
Baryon spectrum with N f = 2 + 1 + 1 twisted mass fermions journal October 2014
Doubly heavy baryons at the LHC journal December 2018
Lifetimes of doubly charmed baryons journal December 2018
First Observation of the Doubly Charmed Baryon Ξ c c + journal August 2002
Erratum: Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium [Phys. Rev. D 51 , 1125 (1995)] journal May 1997
Lattice QCD study of doubly charmed strange baryons text January 2019
Heavy meson form factors from QCD journal October 1990
Lattice QCD with $N_f = 2+1+1 $ domain-wall quarks text January 2017
Baryons with two heavy quarks text January 2001
Baryons with two heavy quarks: Masses, production, decays, and detection text January 2014
Spectroscopy of doubly-charmed baryons in lattice QCD journal July 2003
Baryons with two heavy quarks journal May 2002
Charmed bottom baryon spectroscopy from lattice QCD journal November 2014
Doubly heavy baryons, heavy quark-diquark symmetry, and nonrelativistic QCD journal February 2006
Search for doubly charmed baryons Ξ c c + and Ξ c c ++ in BABAR journal July 2006
Spectrum of baryons with two heavy quarks journal September 1990
Lattice QCD with N f = 2 + 1 + 1 domain-wall quarks journal April 2017
The Direct Coupling of Light Quarks to Heavy Di-quarks text January 2018
Spectroscopy of doubly-charmed baryons from lattice QCD text January 2015
Search for doubly charmed baryons and study of charmed strange baryons at Belle text January 2013
Lifetimes of doubly heavy baryons B b b and B b c journal April 2019
An effective field theory for the calculation of matrix elements involving heavy quarks journal January 1990
Low-lying baryon masses using N f = 2 twisted mass clover-improved fermions directly at the physical pion mass journal August 2017
Search for doubly charmed baryons and study of charmed strange baryons at Belle journal March 2014
Charmed baryons at the physical point in 2 + 1 flavor lattice QCD journal May 2013
Implications of heavy quark-diquark symmetry for excited doubly heavy baryons and tetraquarks journal November 2017
An estimate of the inclusive branching ratio to B ¯ c in Ξ decay journal June 2019
New results on c-baryons and a search for cc-baryons in FOCUS journal February 2003
Renormalization group scaling in nonrelativistic QCD journal March 2000
Baryon Masses in Lattice QCD with Exact Chiral Symmetry journal June 2005
Baryons with two heavy quarks: Masses, production, decays, and detection journal November 2014
Superflavor symmetry for heavy particles journal June 1990
Potential NRQCD: an effective theory for heavy quarkonium journal January 2000
Effective field theory Lagrangians for baryons with two and three heavy quarks journal August 2005
Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium journal February 1995
Charmed baryons in lattice QCD journal October 2001
Spectroscopy of doubly charmed baryons from lattice QCD journal May 2015
Charmed-baryon spectroscopy from lattice QCD with N f = 2 + 1 + 1 flavors journal November 2012
Observation of the Doubly Charmed Baryon Ξ c c + + journal September 2017
Study of uptake of zinc into blood from a Nigerian diet using INAA journal January 2003
Observation of New States Decaying into Λ c + K − π + and Λ c + K S 0 π − journal October 2006
Baryons with two heavy quarks [Bariony s dvumya tyazhelymi kvarkami] journal January 2002
Chiral Lagrangian with heavy quark-diquark symmetry journal March 2006
Charmed baryon spectroscopy and light flavor symmetry from lattice QCD journal August 2015
First Observation of the Doubly Charmed Baryon Decay Ξ c c + + → Ξ c + π + journal October 2018

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