into pieces above certain critical separation R$_{br}$ because of the light quark-antiquark pair creation. The pair cre- ation leads to the collapse of the string, and, as a con- sequence, to formation of mesonic heavy-light bounds states, Indeed, at large separations it is more favorable to create the light pair because of the energy-related considera- tions: the energy of unbroken state [given by the total mass 2 m$_{Q}$ of the two heavy (or, test) quark sources Q and ¯ Q and the energy of the string (3)] is larger com- pared to the energy of the broken string state (given by the mass 2 m$_{Q}$$_{¯}$ q of the created light-heavy mesons Q ¯ q and ¯ Qq ). The critical string-breaking distance R$_{br}$ is thus de- termined by the energy balance: (here we neglect a weak Coulomb interaction between the quarks in the unbroken state and we also disregard exponentially suppressed van der Waals interaction be- tween the heavy-light mesons in the broken state). If R > R$_{br}$ , then the string breaks and light-heavy mesons are formed, Fig. 1 (we consider here a simplest case ignor- ing a multiple pair production via string fragmentation). The string breaking was observed in lattice simulations of QCD with two flavors of equal-mass quarks [16]. An extrapolation of the lattice results to the real QCD gives the following string breaking distance [16]: where statistical and systematical errors are of the order of 0 . 1 fm each. A sufficiently strong background magnetic field should In QCD the influence of the magnetic field should be- come significant when the magnetic length (10) becomes comparable with a typical QCD length scale Λ$_{QCD}$ ∼ 1 fm − 1 ∼ 200 MeV, The transverse dynamics (i.e., the motion of the quark in the plane orthogonal to the magnetic field) is restricted to a region of a typical size of the order of the magnetic length (10), Thus, at the LLL the motion of quarks becomes es- sentially (1+1) dimensional. The quark moves along the axis of the magnetic field and the longitudinal dynamics of a free quark is governed by one-dimensional relativistic dispersion relation: is the magnetic length of the quark q . FIG. 1. The conventional string breaking: the QCD string spanned between the static quark Q and the static antiquark ¯ Q breaks due to light q ¯ q pair creation. In a strong magnetic field the lowest Landau level (LLL) with n = 0 and s$_{z}$ = 1 / 2 plays a dominant role in the quark’s motion because the excited states are too heavy. Indeed, for the soft (low-momentum) fermions the spin flips, s$_{z}$ → − s$_{z}$ and jumps to the higher states with n ⩾ 1 are energetically suppressed by the typical gap where m$_{q}$ and e$_{q}$ are, respectively, the mass and the elec- tric charge of the fermion, p$_{‖}$ ≡ p$_{z}$ is the momentum of the fermion along the direction of the magnetic field, and s$_{‖}$ = ± 1 / 2 is the projection of the fermion’s spin onto the axis of the magnetic field. The integer num- ber n = 0 , 1 , 2 , . . . labels the Landau levels. The signs “ ± ” in front of the square root in Eq. (7) refer to, re- spectively, particle and antiparticle branches of the en- ergy spectrum. The electric charges of the light u and d quarks are, respectively: modify the dynamics of the quarks, affecting not only the chiral features, but also influencing the confining proper- ties of the system. An anisotropic effect of the magnetic field on the confining scales of QCD was first pointed out by Miransky and Shovkovy in Ref. [12]. The energy spectrum of a free relativistic quark in a uniform magnetic field B follows a typical Landau pat- tern [17]: 2 QCD string breaking at nonzero magnetic field. δE$_{q}$ ∼ √$_{2}$$_{/l}$$_{q}$$_{,}$ (9) l$_{q}$ ( B ) = 1 / √ | e$_{q}$B | , q = u, d (10) ω$_{LLL}$ ( p$_{‖}$ ) = ± √ p 2 ‖ + m 2 $_{q}$. | δr | q ≲ l$_{q}$ ( B ) . (11) l$_{q}$ ( B ) ≃ Λ − 1 QCD ≃ R$_{br}$ . (12) R$_{br}$ ≈ 1 . 13 fm , (6) q$_{u}$ = + 2 e 3 , q$_{d}$ = − e 3 . (8) 2 m$_{Q}$ + σR$_{br}$ = 2 m$_{Q}$$_{¯}$ q (5) ω$_{n,s}$$_{‖}$ ( p$_{‖}$ ) = ± √ p 2 ‖ + m 2 q + (2 n + 1 − 2 s$_{z}$ ) | e$_{q}$ | B , (7) Q ¯ Q → Q ¯ Q + q ¯ q → Q ¯ q + q ¯ Q . (4) where