2nd Hadron Spanish Network Days. Universidad Complutense de Madrid (Spain) September 8-9, Rubén Oncala. In collaboration with Prof.

Transcription

1 2nd Hadron Spanish Network Days Universidad Complutense de Madrid (Spain) September 8-9, Rubén Oncala In collaboration with Prof. Joan Soto

2 Heavy Quarkonium is a heavy quark-antiquark pair in a colour singlet sate. Heavy Hybrid is a heavy quark-antiquark pair in an colour octet state and a gluon excitation that leave the system in a physical state. We study charm and bottom systems.

3 Understanding some of the XYZ mesons discovered in the last decades as heavy hybrids.

4 The effective potentials of heavy quarkonium and heavy hybrid have been calculated in the lattice: Heavy quarkonium Heavy Hybrids Heavy Tetraquarks, Pentaquarks... (adding light quarks operators) Molecular states...

5 The large ratio of the time scale for the motion of the heavy quarks and the evolution of the gluon field (which is a consequence of mq>> ) let us to apply a non-relativistic approximation. It is possible to solve the Schrödinger equation and get the spectrum of heavy quarkonium and heavy hybrids with the inputs: o Lattice potentials o o Heavy quarkonium spectrum (additive Energy constant) The potentials for H are obtained from fitting the plots of (Juge, Kuti, Morningstar (2002)), and imposing: o Weak coupling pnrqcd constraints at short distances o QCD string constraints at long distances

6 Using lattice potentials is possible to solve the Schrödinger equation and get the spectrum of heavy quarkonium and heavy hybrid: Some of the hybrid states can be identified as XYZ mesons States with the compatible quantum number may mix. The mixing contribution could be important for states with similar energy.

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8 Space The Lagrangian that describes the quarkonium and hybrid system is: Annihilate a quark Creates an antiquark We can study the mixing contributions using the Wilson loop matching between both states: Quarkonium Hybrid Time

9 Computing the Wilson loops of both operators, we can take the mixing potentials for the spin and angular momentum term: But... How can we get the Wilson loops without lattice calculations? To take a first idea we can approximate the long and short distance and interpolate.

10 The short distance limit can be studied using the pnrqcd Lagrangian in the weak coupling regime: In this Lagrangian, the hybrid state is represented as: Mixing terms in 1/m expansion. In the short distance limit the operators in the Wilson loop do not depend on r, we can approximate the fields in the spin and angular momentum term as constant on the order of

11 The long distance behaviour of the Wilson loops is a little more complicated. We use the. QCD string. A two dimensional QFT that implements confinement and the symmetries of the system. For the spin term, we have: And for the angular momentum term:

12 Using the long and short distance information, we can interpolate the effective potentials for spin and angular momentum term: Spin: Angular momentum: Using this information we can solve the mixing problem. is the string tension, The long distance parameter can be extracted from available lattice results of the long distance potentials. Short distance constants are unknown, no lattice data. The energy solutions depend strongly of this parameter.

13 To estimate the decay width of the transition from hybrids to quarkonium we use the self-energy diagram and the optical theorem:

14 Hybrids with L=J do not decay to Heavy Quarkonium Restrictions: Lowest heavy quarkonium: Weak coupling pnrqcd:

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16 The lower lying states of the Heavy Hybrid Spectrum have been calculated at LO in the 1/mQ expansion of the potentials. Some XYZ mesons have been identified as hybrids, for one of these identifications we can compute a lower bound of the decay width. Using approximations for the Wilson loop matching, we can obtain the long and short distance behaviour of the mixing potentials. The decay width to lower lying Heavy Quarkonium states has been estimated using weak coupling pnrqcd.

17 Thanks for your attention.