^{1}

^{,*}

^{2}

^{,†}

^{3}.

We present the energy spectra of the low-lying doubly charmed baryons using lattice quantum chromodynamics. We precisely predict the ground state mass of the charmed-strange

The recent discovery of a doubly charmed baryon,

The charm quark being heavy, lattice calculations of charmed hadrons, particularly with multiple charm quarks, are plagued by the ultraviolet cutoff effects (lattice spacing). Thanks to recent developments in algorithms and accessibility of petaflops computing, gauge ensembles at multiple fine lattice spacings and adequate lattice volumes are available providing opportunities to perform detailed investigations of charmed hadrons on the lattice

We perform this calculation on three dynamical

For valence quark propagators, we employ the overlap fermion action

The effect of discretization is the dominant systematic error in the lattice study of heavy hadrons and crucially depends on the tuning of heavy quark masses. We follow the Fermilab prescription of heavy quarks

We use the conventional baryon interpolators given by

In this work, results for spin-

To reduce the systematics associated with cutoff effects, instead of calculating the hadron masses, we extract the mass differences. This method was found to be very effective previously

To show the robustness of the ground state mass extraction, in Fig.

(Top) Effective mass plot of the ground state of

In Fig.

Ground state mass of

Note that the HQET interpolator estimates a mass of 3735(11)(12) MeV which is 23 MeV higher than that we obtain from the relativistic interpolator. We believe this difference is due to the nonheaviness of the charm quark (see Supplemental Material

In Fig.

Hyperfine splitting between

Comparison of hyperfine splitting between the ground states of

We also calculate the ground state masses of the negative parity baryons. In Fig.

Ground state mass of (top)

In Table

Energy spectra of the low-lying

Low-lying

The use of wall sources helps to obtain long and stable fit ranges in the correlation functions, as demonstrated in Fig.

With long and stable plateau we find uncertainty due to different fitting windows for the

The use of overlap action ensures no

An alternate determination of the lattice spacing was performed

The charm quark mass is tuned following the Fermilab prescription

Again, as in the charm quark mass tuning we use multiple strange quark masses and Eqs.

Studies of the same observables on ensembles with similar lattice size indicated finite size effects to be within an MeV

For these baryons, no chiral extrapolation is involved. Errors due to mixed action effects are found to be small within this lattice set up

Error budget in the calculation of

In this article, using various state-of-the-art lattice techniques, we present a precise prediction of the ground state mass of

To date, only one doubly charmed baryon, the spin

We thank our colleagues within the ILGTI Collaboration. We are thankful to the MILC Collaboration and, in particular, to S. Gottlieb for providing us with the HISQ lattices. We are thankful to an unknown referee for pointing us toward the absence of cubic terms in the continuum extrapolations with chiral fermions. Computations are carried out on the Cray-XC30 of ILGTI, TIFR, and on the Gaggle/Pride clusters of the Department of Theoretical Physics, TIFR. N. M. would like to thank Stefan Sint for his valuable comments on continuum extrapolation. N. M. would like to thank P. Junnarkar for discussions and Ajay Salve, Kapil Gadhiali and P. M. Kulkarni for computational support. M. P. acknowledges support from the EU under Grant No. MSCA-IF-EF-ST-744659 (XQCDBaryons) and the Deutsche Forschungsgemeinschaft under Grant No. SFB/TRR 55.