1 Alexei Larionov 1,2, Mark Strikman 3, Markus Bleicher 1,4 2) National Research Centre “Kurchatov Institute”, RU Moscow, Russia Test of the X(3872) structure in antiproton-nucleus collisions 1) Frankfurt Institute for Advanced Studies (FIAS), D Frankfurt am Main, Germany 4) Institut für Theoretische Physik, J.W. Goethe-Universität, D Frankfurt am Main, Germany 3) Pennsylvania State University, University Park, PA 16802, USA HADRON 2015, Newport News, Virginia,

2 Outline Exotic X(3872) state and its possible structures; D(D*)-stripping reaction as a tool to test the molecular structure of X(3872) Calculation of D*(D) production cross section in collisions within the generalized eikonal approximation Conclusions and outlook AL, M. Strikman, M. Bleicher, PLB 749, 35 (2015)

3 - Mass is very close to the two-meson thresholds for and The containing noncharmonium state X(3872) -Discovered by BELLE S.K. Choi et al., PRL 2003 as a peak in invariant mass spectrum from decays - Quantum numbers J PC =1 ++ are determined at LHCb R. Aaij et al., PRL Structure is largely unknown

4 Figure from S. Godfrey and S.L. Olsen, Annu. Rev. Nucl. Part. Sci., Exotic possibilities for the X(3872) structure :

5 Size of the molecule : r.m.s. distance between and Comparable with distance between n and p in the deuteron The radiative decays are not sensitive to the X(3872) structure at large distances. The decay is more affected by wave function at large separations. However, still many uncertainties (couplings, FSI effects). F.-K. Guo et al., Hyperfine Interact, 2015.

6 The nucleus may be used to test the possible molecular structure of X(3872) (similar do the studies of the deuteron structure by stripping reactions):

7 D-stripping cross section - arbitrary set of outgoing particles impulse approximation (IA) from screening correction from antiscreening correction from - Moeller flux factor - elastic scattering amplitude In the c.m. frame of X: -wave function of X

8 - asymptotic solution of Schroedinger equation at large distances - range parameter, - reduced mass * ) percent contribution according to the local hidden gauge calculations F. Aceti, R. Molina, E. Oset, PRD 2012 Molecule wave function:

9 Estimations within the color dipole model: Educated guess: - in agreement with effective field theory calculations L. Tolos, J.M. Torres-Rincon, PRD For simplicity assume PDG: K.A. OIlive et al., 2014 c.f. AL, M. Bleicher, A. Gillitzer, M. Strikman, PRC 2013 and refs therein (both D* and D are S-wave mesons) Elementary cross sections:

10 I. Ambats et al., PRL 1972 Slopes of q t – dependence are weakly sensitive to the meson radius: Assumption :

11 D* 0 production cross section in X-proton interactions Sharp peak at α=2m D* /m R ≈1.04 for k t =0 is not influenced by screening and antiscreening. Influence of screening and antiscreening increases with k t. -light cone momentum fraction of produced D*

12 D* ± production cross section in X-proton interactions Similar trends as in the case of D* 0 production. However, the α-distributions are broader due to broader D + D* − +c.c. wave function in momentum space.

13 Feynman diagram representation of a multiple scattering amplitude on the nucleus: Generalized eikonal approximation (GEA) L. Frankfurt, M. Sargsian, M. Strikman, PRC 56, 1124 (1997); M. Sargsian, Int. J. Mod. Phys. E 10, 405 (2001). ― neglect energy transfer in rescatterings (soft rescatterings on nonrelativistic nucleons) ― eikonal form of propagators (nonrelativistic initial and final nucleons) ― keep only transverse momentum transfer dependence in elementary amplitudes (soft scatterings at high energies) Leading order contribution to the cross section is given by products of amplitudes with the same hard nucleon scatterers (1,2) but nonoverlapping sets of soft nucleon scatterers - arbitrary set of outgoing particles

14 Glauber-type expression: - in-medium width of w/r to production of X with transverse momentum - antiproton velocity - light cone momentum fraction of D* - invariant cross section of D* production (or D-stripping)

15 -longitudinal momentum of the struck proton satisfying -Wigner function of the i th proton occupied state - proton phase space occupation number Local density approximation with short-range np correlations L. Frankfurt, M. Strikman, Phys. Rep. 1981: - proton Fermi momentum - proton fraction above Fermi surface - deuteron wave function - in-medium width of w/r to production of X

16 Molecule production matrix element: E. Braaten, PRD 2008 Comparable to Molecule-proton cross section: -Glauber screening correction (cross section defect) similar to deuteron-proton cross section V. Franco, R.J. Glauber, PR 1966

17 Differential cross sections of D* and D production off nucleus in the two-step process - light cone momentum fraction of D*(D) Then the sharp peaks at α≈1 at small k t would clearly signal the DD* molecule structure of X(3872). To exclude possible D*D-resonance decay we require that only one particle (D* or D) is emitted near α≈1.

18 Background due to the direct production process: - c.m. energy of D and D*, - c.m. momenta of incoming and outgoing particles S-wave cross section taken from E. Braaten, PRD 2008

19 Uncertainty and background pD and pD* cross sections influence only weakly. Background cross section is broadly distributed in α. The most recent measurement of the mass by CLEO gives A. Tomaradze et al., PRD 2015 Major uncertatainty is due to unknown binding energy of the D 0 D* 0 molecule.

20 Similar analysis of molecular structures can be also performed for other noncharmonium mesons containing a pair: * ) accoding to T. Branz, T. Gutsche, V.E. Lyubovitskij, PRD 2009; Y. Dong, A. Faessler, T. Gutsche, V.E. Lyubovitskij, PRD 2014; M. Cleven, F.-K. Guo, C. Hanhart, Q. Wang, Q. Zhao, PRD beam momentum for the on-shell X(Y) production

21 AL, M. Strikman, M. Bleicher, work in progress For higher than X(3872) X and Y exotic states the α-distributions are broader since their momentum space wave functions are broader due to larger binding energy.

22 Conclusions - Possible DD* molecular structure of X(3872) manifests itself in the sharp peaks of exclusive D* or D production at α≈1 for small transverse momenta. The peaks are well visible on the smooth background due to direct production. - Other possible structures of X(3872), e.g. tetraquark or -gluon hybrid, should produce more flat α-distributions of D* and D due to more violent production mechanisms in X(3872) N collisions (likely to be phase space distributions in the X(3872) N c.m. frame). -The target mass dependence of the D* 0 (+c.c.) production cross section by stripping from intermediate X(3872) can be well approximated by formula With the expected PANDA luminocity L=10 31 cm -2 s -1 the rate of D* 0 (+c.c.) production is ~2 events per hour.

23 Thank you for your attention ! Other possibilities for studies of possible molecular states by stripping reactions:

24 Backup

25 R-proton total cross section (calculation in the R c.m. frame): - Moeller flux factor - molecule wave function in the R c.m. frame