4 The critical fields (19) belong to the confinement region below the T = 0 crossover scale, Eq. (2), as anticipated. At the background magnetic field 0 < B < B ( u ) cr the string breaking in the B -transverse plane may proceed via the creation of both u and d quarks. In the field window B ( u ) cr < B < B ( d ) cr the creation of the u ¯ u pairs be- comes energetically unfavorable, while the string break- ing via the d ¯ pair creation can still occur. At B > B ( d ) cr the QCD string cannot be broken neither by u ¯ u - or by d ¯ -pair creation. The difference in the critical values (19) can be un- derstood as follows. According to Eqs. (8) and (10), the magnetic length l$_{d}$ of the d -quark is √$_{2 times longer then}$ the magnetic length l$_{u}$ of the u -quark. Consequently, the gain in the energy due to the d ¯ -pair creation is larger compared to the energy gain achieved due to emergence of the u -quark pair. Thus, one needs a stronger magnetic field to suppress the d ¯ -pair creation compared to a field needed to suppress the creation of a u ¯ u -pair, B ( u ) cr < B ( d ) cr . Proposal for numerical simulations. The effect of “freezing” of the QCD string breaking can be tested in the lattice simulations of QCD with dynamical fermions. The magnetic fields of the order of (19) and higher were already achieved in the (quenched) lattice simulations [7, 8, 10, 11]. There are no principal obstacles to extend these simulations to QCD with dynamical fermions and check the prediction (19). Possible experimental consequences. The freez- ing of the QCD string breaking in the magnetic field may also have experimental consequences. Firstly, according to the estimation (1) of Ref. [1], the fields of the order of the critical value (19) may emerge in noncentral heavy- ion collisions at the LHC. However, our considerations do not apply to the first moments of the created quark- gluon fireball because the system stays in the deconfine- ment phase due to hot environment of the collision. As the plasma expands and cools down, it hadronizes in the presence of the decaying magnetic fields. The hadroniza- tion process in the magnetic field background involves string breaking events which are more favorable for the u quarks compared to the d quarks. Thus, the flavor- dependent freezing of the string breaking in the external magnetic field leads to the u -quark-rich content of the hadrons created in noncentral heavy-ion collisions com- pared to the central ones. Secondly, the background magnetic field stabilizes highly excited mesons by (i) freezing the quarks at the end-points of QCD string and (ii) suppressing the pro- cess of the light pair creation in the B -transverse plane. Since in the noncentral collisions the magnetic field axis is perpendicular to the reaction plane, we expect that the magnetic field reveals itself via abundance of radially excited mesons in the noncentral collisions compared to the central ones. The excited mesons should dominantly be polarized in the reaction plane, as the QCD string in such mesons should tend to be perpendicular to the magnetic field axis. In each noncentral collision the ori- entation of the reaction plane can easily be determined from the elliptic flow of the emitted particles. Thus, we are coming to a qualitative prediction that can in principle be checked experimentally in the heavy- ion collision experiments. The long QCD strings should break into pieces by multiple q ¯ q pair creation leading to formation of generally unstable hadrons. These primary hadrons later decay into more stable hadrons, leptons and photons, eventually forming jets [18]. Since the particles in the jets come out essentially aligned along the original string axis, we expect that the flavor-dependent freezing effect of the magnetic field on the QCD string breaking leads to an excess of the u -quark rich jets parallel to the reaction plane of the noncentral heavy-ion collisions. ∗ On leave of absence from ITEP, Moscow, Russia. [1] V. Skokov, A. Illarionov and V. Toneev, arXiv:0907.1396. [2] D.E. Kharzeev, L.D. McLerran, and H.J. Warringa, Nucl. Phys. A 803 , 227 (2008) [arXiv:0711.0950]; K. Fukushima, D.E. Kharzeev, and H.J. Warringa, Phys. Rev. D 78 , 074033 (2008) [arXiv:0808.3382]. [3] V.P. Gusynin, V.A. Miransky, I.A. Shovkovy, Phys. Rev. Lett. 73 , 3499 (1994); Phys. Rev. D 52 , 4747 (1995); Nucl. Phys. B 462 , 249 (1996); ibid. B 563 , 361 (1999). [4] I. A. Shushpanov and A. V. Smilga, Phys. Lett. B 402 , 351 (1997); T. D. Cohen, D. A. McGady and E. S. Wer- bos, Phys. Rev. C 76 , 055201 (2007). [5] E. S. Fraga and A. J. Mizher, Phys. Rev. D 78 , 025016 (2008) [arXiv:0804.1452]; Nucl. Phys. A 820 , 103C (2009) [arXiv:0810.3693]. [6] B. I. Abelev et al. [STAR Collaboration], Phys. Rev. Lett. 103 , 251601 (2009) [arXiv:0909.1739]; arXiv:0909.1717; see also a Viewpoint of B. M¨ uller, Physics 2 , 104 (2009). [7] P. V. Buividovich et al, Phys. Rev. D 80 , 054503 (2009) [arXiv:0907.0494 [hep-lat]]; M. Abramczyk, T. Blum, G. Petropoulos and R. Zhou, arXiv:0911.1348 [hep-lat]. [8] P. V. Buividovich et al, Phys. Lett. B 682 , 484 (2010) [arXiv:0812.1740 [hep-lat]]. [9] B. L. Ioffe, A. V. Smilga, Nucl. Phys. B 232 , 109 (1984). [10] P. V. Buividovich et al, Nucl. Phys. B 826 , 313 (2010) [arXiv:0906.0488 [hep-lat]]. [11] P. V. Buividovich et al, arXiv:0909.2350 [hep-ph]. [12] V. A. Miransky and I. A. Shovkovy, Phys. Rev. D 66 , 045006 (2002) [arXiv:hep-ph/0205348]. [13] N. O. Agasian and S. M. Fedorov, Phys. Lett. B 663 , 445 (2008) [arXiv:0803.3156 [hep-ph]]. [14] D. N. Kabat, K. M. Lee and E. J. Weinberg, Phys. Rev. D 66 , 014004 (2002) [arXiv:hep-ph/0204120]. [15] D. T. Son and M. A. Stephanov, Phys. Rev. D 77 , 014021 (2008) [arXiv:0710.1084 [hep-ph]]. [16] B. Bolder et al. , Phys. Rev. D 63 , 074504 (2001); G. S. Bali et al. , ibid. D 71 , 114513 (2005). [17] M.H.Johnson, B.A.Lippmann, Phys. Rev. 77 , 702 (1950). [18] B. Andersson, G. Gustafson, G. Ingelman and T. Sjos- trand, Phys. Rept. 97 , 31 (1983).