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Test of the X(3872) structure in antiproton-nucleus collisions

This study investigates the possible structures of the exotic X(3872) state through D(D*)-stripping reactions in collisions with nuclei. The cross section for D*(D) production is calculated using the generalized eikonal approximation. The results provide insights into the molecular structure of X(3872).

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Test of the X(3872) structure in antiproton-nucleus collisions

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  1. Test of the X(3872) structurein antiproton-nucleus collisions Alexei Larionov1,2, Mark Strikman 3,Markus Bleicher 1,4 1)Frankfurt Institute for Advanced Studies (FIAS), D-60438 Frankfurt am Main, Germany 2) National Research Centre “Kurchatov Institute”, RU-123182 Moscow, Russia 3) Pennsylvania State University, University Park, PA 16802, USA 4) Institut für Theoretische Physik, J.W. Goethe-Universität , D-60438 Frankfurt am Main, Germany HADRON 2015, Newport News, Virginia, 15.09.2015

  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. 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 JPC=1++ are determined at LHCb R. Aaij et al., PRL 2013 - Structure is largely unknown • Mass is very close to the two-meson thresholds • for and

  4. Exotic possibilities for the X(3872) structure : Figure from S. Godfrey and S.L. Olsen, Annu. Rev. Nucl. Part. Sci., 2008.

  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 affectedby 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 - elastic scattering amplitude - Moeller flux factor In the c.m. frame of X: • wave function • of X impulse approximation (IA) from screening correction from antiscreening correction from

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

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

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

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

  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: - arbitrary set of outgoing particles 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

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

  15. - in-medium width of w/r to production of X • longitudinal momentum of the struck proton • satisfying - proton phase space occupation number • Wigner function of the ith proton • occupied state 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

  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) To exclude possible D*D-resonance decay we require that only one particle (D* or D) is emitted near α≈1. Then the sharp peaks at α≈1 at small kt would clearly signal the DD* molecule structure of X(3872).

  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 • Major uncertatainty is due to unknown binding energy of the D0D*0 • molecule. The most recent measurement of the mass by CLEO gives A. Tomaradze et al., PRD 2015 • pD and pD* cross sections influence only weakly. • Background cross section is broadly distributed in α.

  20. Similar analysis of molecular structures can be also performed for other noncharmonium mesons containing a pair: *) accoding toT. 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 2015 - beam momentum for the on-shell X(Y) production

  21. 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. AL, M. Strikman, M. Bleicher, work in progress

  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=1031 cm-2 s-1 the rate of D*0(+c.c.) production is ~2 events per hour.

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

  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

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