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Alexei Larionov 1,2, Mark Strikman 3, Markus Bleicher 1,4

2) National Research Centre “Kurchatov Institute”, RU-123182 Moscow, Russia

Test of the X(3872) structurein antiproton-nucleus collisions

1) Frankfurt Institute for Advanced Studies (FIAS), D-60438 Frankfurt am Main, Germany

4) Institut für Theoretische Physik, J.W. Goethe-Universität , D-60438 Frankfurt am Main, Germany

3) Pennsylvania State University, University Park, PA 16802, USA

HADRON 2015, Newport News, Virginia, 15.09.2015

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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)

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- 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 JPC=1++ are determined at LHCb R. Aaij et al., PRL 2013

- Structure is largely unknown

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Figure from S. Godfrey and S.L. Olsen, Annu. Rev. Nucl. Part. Sci., 2008.

Exotic possibilities for the X(3872) structure :

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Size of the molecule :

r.m.s. distancebetween and

Comparable with distance between n and p in the deuteron

The radiative decays are not sensitiveto the X(3872) structure at large distances.

The decay is more affected by wave functionat large separations. However, still many uncertainties (couplings, FSI effects). F.-K. Guo et al., Hyperfine Interact, 2015.

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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):

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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

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- 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:

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Estimations within the color dipole model:

Educated guess:

- in agreement with effective field theory calculations L. Tolos, J.M. Torres-Rincon, PRD 2013.

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:

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I. Ambats et al., PRL 1972

Slopes of qt – dependence are weakly sensitive to the meson radius:

Assumption :

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D*0 production crosssection in X-proton interactions

Sharp peak at α=2mD*/mR≈1.04 for kt=0 is not influenced by screening and antiscreening.

Influence of screening and antiscreeningincreases with kt .

-light cone momentum fraction of produced D*

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D*± production crosssection in X-proton interactions

Similar trends as in the case of D*0 production. However, the α-distributions are broader due tobroader D+D*−+c.c. wave function in momentum space.

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Feynman diagram representation of a multiple scattering amplitudeon 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

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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)

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-longitudinal momentum of the struck proton satisfying

-Wigner function of the ith proton occupied state

- proton phase space occupation number

Local density approximation with short-range np correlationsL. 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

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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

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Differential cross sections of D* and D production off nucleusin the two-step process

- light cone momentum fraction of D*(D)

Then the sharp peaks at α≈1 at small kt would clearly signal the DD* molecule structure of X(3872).

To exclude possible D*D-resonance decaywe require that only one particle (D* or D) is emitted near α≈1.

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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

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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 D0D*0

molecule.

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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 2015

- beam momentum for the on-shell X(Y) production

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

For higher than X(3872) X and Y exotic states the α-distributions are broadersince their momentum space wave functions are broader due tolarger binding energy.

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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 ofD*0(+c.c.) production is ~2 events per hour.

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Thank you for your attention !

Other possibilities for studies of possible molecular states by stripping reactions:

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Backup

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R-proton total cross section (calculation in the R c.m. frame):

- Moeller flux factor

- molecule wave function

in the R c.m. frame