Charmed hypernuclei, nuclear-bound heavy-flavor hadrons · 2018-07-10 · Charmed hypernuclei,...
Transcript of Charmed hypernuclei, nuclear-bound heavy-flavor hadrons · 2018-07-10 · Charmed hypernuclei,...
Charmed hypernuclei, nuclear-bound heavy-flavor hadrons
Gastão KreinInstituto de Física Teórica, São Paulo
Motivation for charm in nuclei— Overwhelming evidence QCD is the fundamental theory
of the strong interaction
— Yet, we are very far of understanding how it actually works
— Lattice QCD has had remarkable progress with masses of ground-state quark-antiquark and three valence quark hadrons
— Yet beyond that, our ignorance is profound
Prominent nonperturbative QCD phenomenaVital role of gluons: Color confinement, mass generation— origin proton mass: probed with quarkonium-nucleon— chiral symmetry restoration: D-mesin nuclei, charm hypernuclei— X,Y,Z: what are they?
This talk, concentrate on:
— charmed hypernuclei
— heavy quarkonia in nuclei
Not covered:— D-mesic nuclei— phi-meson in nuclei
P. Gubler, talk at this conference
Recent reviews:— Nuclear-bound quarkonia and heavy-flavor hadrons
GK, A.W. Thomas & K. Tsushima Prog. Part. Nucl. Phys. 100, 161 (2018)
— Heavy hadrons in nuclear matter A. Hosaka, T. Hyodo, K. Sudoh, Y. Yamaguchi & S. Yasui Prog. Part. Nucl. Phys. 96, 88 (2017)
— Right after discovery of charm, suggestion (Tyapkin) possible existence of charm hypernuclei
— Binding energies calculated, using meson-exchange models, SU(4) flavor symmetry for couplings (Dover & Kahanna, Iwao, Gibson et al.)
— One (inconclusive) experimental evidence
Charmed hypernuclei
⇤(uds) ! ⇤+c (udc)
A primary vertex
B vertex decay of a supernucleus
C decay of D0 — signal of pair productioncc̄
Fermilab — Emulsion experiment (1976)
Interesting because
— opportunity to learn about medium effects on diquark correlations, as the masses of u and d quarks are affected by the medium
— few-nucleon charmed states have the potential of having a rich spectroscopy similar to the X,Y,Z hadrons
— opportunity to learn about the interactions of charmed baryons with nucleons
Production at FAIR, J-PARC(future Super-B, EIC)
Antiproton beam, production of charmed hadrons in the Hadron Hall at J-PARC
@ FAIRB⇤+
cZ
<latexit sha1_base64="rInl+i/OxR7+Z8LtUbuQAus0tjs=">AAACJnicbVDLSsNAFJ34Nr6qLt2kFkEUSuJGQQSpGxcuKthabGq4mdzWwckkzkyEEvI1bvwVNy4qIu78FKe1C18HBg7nnDsz94QpZ0q77rs1MTk1PTM7N28vLC4tr5RW15oqySTFBk14IlshKORMYEMzzbGVSoQ45HgZ3p4M/ct7lIol4kL3U+zE0BOsyyhoIwWlIz/EHhM53gmQEvo7hR3k/pm5IILr3C/vFgEtDDmsFX75yvZRRN+yQaniVt0RnL/EG5MKGaMelAZ+lNAsRqEpB6XanpvqTg5SM8qxsP1MYQr0FnrYNlRAjKqTj9YsnC2jRE43keYI7YzU7xM5xEr149AkY9A36rc3FP/z2pnuHnRyJtJMo6BfD3Uz7ujEGXbmREwi1bxvCFDJzF8degMSqDbN2qYE7/fKf0lzr+q5Ve98r3JcG9cxRzbIJtkmHtknx+SU1EmDUPJAnsiAvFiP1rP1ar19RSes8cw6+QHr4xOiraXX</latexit><latexit sha1_base64="rInl+i/OxR7+Z8LtUbuQAus0tjs=">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</latexit><latexit sha1_base64="rInl+i/OxR7+Z8LtUbuQAus0tjs=">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</latexit><latexit sha1_base64="rInl+i/OxR7+Z8LtUbuQAus0tjs=">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</latexit>
BZ<latexit sha1_base64="WNPGK50CCqC2Gdetgf1SdGvl4Lc=">AAACFHicbVBNS8NAEN3Urxq/oh69RIsgCiXpRcFLqRePFewHNrVsttN26WYTdzdCCfkRXvwrXjwo4tWDN/+N2zaH2vpg4PHeDDPz/IhRqRznx8gtLa+sruXXzY3Nre0da3evLsNYEKiRkIWi6WMJjHKoKaoYNCMBOPAZNPzh1dhvPIKQNOS3ahRBO8B9TnuUYKWljnXm+dCnPIEHjoXAo9PUvE+8y0rqHd6ZHvDujNOxCk7RmcBeJG5GCihDtWN9e92QxAFwRRiWsuU6kWonWChKGKSmF0uIMBniPrQ05TgA2U4mT6X2sVa6di8UuriyJ+rsRIIDKUeBrzsDrAZy3huL/3mtWPUu2gnlUayAk+miXsxsFdrjhOwuFUAUG2mCiaD6VpsMsMBE6RxNHYI7//IiqZeKrlN0b0qFciWLI48O0BE6QS46R2V0jaqohgh6Qi/oDb0bz8ar8WF8TltzRjazj/7A+PoFec6ebw==</latexit><latexit sha1_base64="WNPGK50CCqC2Gdetgf1SdGvl4Lc=">AAACFHicbVBNS8NAEN3Urxq/oh69RIsgCiXpRcFLqRePFewHNrVsttN26WYTdzdCCfkRXvwrXjwo4tWDN/+N2zaH2vpg4PHeDDPz/IhRqRznx8gtLa+sruXXzY3Nre0da3evLsNYEKiRkIWi6WMJjHKoKaoYNCMBOPAZNPzh1dhvPIKQNOS3ahRBO8B9TnuUYKWljnXm+dCnPIEHjoXAo9PUvE+8y0rqHd6ZHvDujNOxCk7RmcBeJG5GCihDtWN9e92QxAFwRRiWsuU6kWonWChKGKSmF0uIMBniPrQ05TgA2U4mT6X2sVa6di8UuriyJ+rsRIIDKUeBrzsDrAZy3huL/3mtWPUu2gnlUayAk+miXsxsFdrjhOwuFUAUG2mCiaD6VpsMsMBE6RxNHYI7//IiqZeKrlN0b0qFciWLI48O0BE6QS46R2V0jaqohgh6Qi/oDb0bz8ar8WF8TltzRjazj/7A+PoFec6ebw==</latexit><latexit sha1_base64="WNPGK50CCqC2Gdetgf1SdGvl4Lc=">AAACFHicbVBNS8NAEN3Urxq/oh69RIsgCiXpRcFLqRePFewHNrVsttN26WYTdzdCCfkRXvwrXjwo4tWDN/+N2zaH2vpg4PHeDDPz/IhRqRznx8gtLa+sruXXzY3Nre0da3evLsNYEKiRkIWi6WMJjHKoKaoYNCMBOPAZNPzh1dhvPIKQNOS3ahRBO8B9TnuUYKWljnXm+dCnPIEHjoXAo9PUvE+8y0rqHd6ZHvDujNOxCk7RmcBeJG5GCihDtWN9e92QxAFwRRiWsuU6kWonWChKGKSmF0uIMBniPrQ05TgA2U4mT6X2sVa6di8UuriyJ+rsRIIDKUeBrzsDrAZy3huL/3mtWPUu2gnlUayAk+miXsxsFdrjhOwuFUAUG2mCiaD6VpsMsMBE6RxNHYI7//IiqZeKrlN0b0qFciWLI48O0BE6QS46R2V0jaqohgh6Qi/oDb0bz8ar8WF8TltzRjazj/7A+PoFec6ebw==</latexit><latexit sha1_base64="WNPGK50CCqC2Gdetgf1SdGvl4Lc=">AAACFHicbVBNS8NAEN3Urxq/oh69RIsgCiXpRcFLqRePFewHNrVsttN26WYTdzdCCfkRXvwrXjwo4tWDN/+N2zaH2vpg4PHeDDPz/IhRqRznx8gtLa+sruXXzY3Nre0da3evLsNYEKiRkIWi6WMJjHKoKaoYNCMBOPAZNPzh1dhvPIKQNOS3ahRBO8B9TnuUYKWljnXm+dCnPIEHjoXAo9PUvE+8y0rqHd6ZHvDujNOxCk7RmcBeJG5GCihDtWN9e92QxAFwRRiWsuU6kWonWChKGKSmF0uIMBniPrQ05TgA2U4mT6X2sVa6di8UuriyJ+rsRIIDKUeBrzsDrAZy3huL/3mtWPUu2gnlUayAk+miXsxsFdrjhOwuFUAUG2mCiaD6VpsMsMBE6RxNHYI7//IiqZeKrlN0b0qFciWLI48O0BE6QS46R2V0jaqohgh6Qi/oDb0bz8ar8WF8TltzRjazj/7A+PoFec6ebw==</latexit>
p̄<latexit sha1_base64="dxj4XIA3/LBEaRuTOT2/k8Oszmg=">AAACEnicbVC7TgMxEPTxDOEVoKSxiJCAIrpLA2UEDWWQyENKomjPt5dY8fkO24cUnfINNPwKDQUI0VLR8Tc4jyIkjGR5NLO79o6fCK6N6/44K6tr6xubua389s7u3n7h4LCu41QxrLFYxKrpg0bBJdYMNwKbiUKIfIENf3Az9huPqDSP5b0ZJtiJoCd5yBkYK3UL520fe1xm+CBBKRhejPJtH1SW2BtlMKd3C0W35E5Al4k3I0UyQ7Vb+G4HMUsjlIYJ0LrluYnpZKAMZwLt/FRjAmwAPWxZKiFC3ckmK43oqVUCGsbKHmnoRJ3vyCDSehj5tjIC09eL3lj8z2ulJrzqZFwmqUHJpg+FqaAmpuN8aMAVMiOGlgBT3P6Vsj4oYMammLcheIsrL5N6ueS5Je+uXKxcz+LIkWNyQs6IRy5JhdySKqkRRp7IC3kj786z8+p8OJ/T0hVn1nNE/sD5+gUIIJ5O</latexit><latexit sha1_base64="dxj4XIA3/LBEaRuTOT2/k8Oszmg=">AAACEnicbVC7TgMxEPTxDOEVoKSxiJCAIrpLA2UEDWWQyENKomjPt5dY8fkO24cUnfINNPwKDQUI0VLR8Tc4jyIkjGR5NLO79o6fCK6N6/44K6tr6xubua389s7u3n7h4LCu41QxrLFYxKrpg0bBJdYMNwKbiUKIfIENf3Az9huPqDSP5b0ZJtiJoCd5yBkYK3UL520fe1xm+CBBKRhejPJtH1SW2BtlMKd3C0W35E5Al4k3I0UyQ7Vb+G4HMUsjlIYJ0LrluYnpZKAMZwLt/FRjAmwAPWxZKiFC3ckmK43oqVUCGsbKHmnoRJ3vyCDSehj5tjIC09eL3lj8z2ulJrzqZFwmqUHJpg+FqaAmpuN8aMAVMiOGlgBT3P6Vsj4oYMammLcheIsrL5N6ueS5Je+uXKxcz+LIkWNyQs6IRy5JhdySKqkRRp7IC3kj786z8+p8OJ/T0hVn1nNE/sD5+gUIIJ5O</latexit><latexit sha1_base64="dxj4XIA3/LBEaRuTOT2/k8Oszmg=">AAACEnicbVC7TgMxEPTxDOEVoKSxiJCAIrpLA2UEDWWQyENKomjPt5dY8fkO24cUnfINNPwKDQUI0VLR8Tc4jyIkjGR5NLO79o6fCK6N6/44K6tr6xubua389s7u3n7h4LCu41QxrLFYxKrpg0bBJdYMNwKbiUKIfIENf3Az9huPqDSP5b0ZJtiJoCd5yBkYK3UL520fe1xm+CBBKRhejPJtH1SW2BtlMKd3C0W35E5Al4k3I0UyQ7Vb+G4HMUsjlIYJ0LrluYnpZKAMZwLt/FRjAmwAPWxZKiFC3ckmK43oqVUCGsbKHmnoRJ3vyCDSehj5tjIC09eL3lj8z2ulJrzqZFwmqUHJpg+FqaAmpuN8aMAVMiOGlgBT3P6Vsj4oYMammLcheIsrL5N6ueS5Je+uXKxcz+LIkWNyQs6IRy5JhdySKqkRRp7IC3kj786z8+p8OJ/T0hVn1nNE/sD5+gUIIJ5O</latexit><latexit sha1_base64="dxj4XIA3/LBEaRuTOT2/k8Oszmg=">AAACEnicbVC7TgMxEPTxDOEVoKSxiJCAIrpLA2UEDWWQyENKomjPt5dY8fkO24cUnfINNPwKDQUI0VLR8Tc4jyIkjGR5NLO79o6fCK6N6/44K6tr6xubua389s7u3n7h4LCu41QxrLFYxKrpg0bBJdYMNwKbiUKIfIENf3Az9huPqDSP5b0ZJtiJoCd5yBkYK3UL520fe1xm+CBBKRhejPJtH1SW2BtlMKd3C0W35E5Al4k3I0UyQ7Vb+G4HMUsjlIYJ0LrluYnpZKAMZwLt/FRjAmwAPWxZKiFC3ckmK43oqVUCGsbKHmnoRJ3vyCDSehj5tjIC09eL3lj8z2ulJrzqZFwmqUHJpg+FqaAmpuN8aMAVMiOGlgBT3P6Vsj4oYMammLcheIsrL5N6ueS5Je+uXKxcz+LIkWNyQs6IRy5JhdySKqkRRp7IC3kj786z8+p8OJ/T0hVn1nNE/sD5+gUIIJ5O</latexit>
p<latexit sha1_base64="fTBv2t+q32zM4cVtTXb0OO+6WHE=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxE9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gX12JuJ</latexit><latexit sha1_base64="fTBv2t+q32zM4cVtTXb0OO+6WHE=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxE9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gX12JuJ</latexit><latexit sha1_base64="fTBv2t+q32zM4cVtTXb0OO+6WHE=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxE9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gX12JuJ</latexit><latexit sha1_base64="fTBv2t+q32zM4cVtTXb0OO+6WHE=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxE9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gX12JuJ</latexit>
⇤+c
<latexit sha1_base64="TL1trh0NlqeLEywtx3wQmaQZuzU=">AAACFnicbVC7SgNBFJ2Nrxhfq5Y2i0EQxbCbRsugjYVFBPOAJIa7szfJkNnZdWZWCEu+wsZfsbFQxFbs/BsnjyImHhg4nHMPd+7xY86Udt0fK7O0vLK6ll3PbWxube/Yu3tVFSWSYoVGPJJ1HxRyJrCimeZYjyVC6HOs+f2rkV97RKlYJO70IMZWCF3BOoyCNlLbPmv62GUixQcBUsLgZJhr3ph4APenbZproghmvLaddwvuGM4i8aYkT6Yot+3vZhDRJEShKQelGp4b61YKUjPK0exKFMZA+9DFhqECQlStdHzW0DkySuB0Imme0M5YnU2kECo1CH0zGYLuqXlvJP7nNRLduWilTMSJRkEnizoJd3TkjDpyAiaRaj4wBKhk5q8O7YEEqk2TOVOCN3/yIqkWC55b8G6L+dLltI4sOSCH5Jh45JyUyDUpkwqh5Im8kDfybj1br9aH9TkZzVjTzD75A+vrFz4Kn2U=</latexit><latexit sha1_base64="TL1trh0NlqeLEywtx3wQmaQZuzU=">AAACFnicbVC7SgNBFJ2Nrxhfq5Y2i0EQxbCbRsugjYVFBPOAJIa7szfJkNnZdWZWCEu+wsZfsbFQxFbs/BsnjyImHhg4nHMPd+7xY86Udt0fK7O0vLK6ll3PbWxube/Yu3tVFSWSYoVGPJJ1HxRyJrCimeZYjyVC6HOs+f2rkV97RKlYJO70IMZWCF3BOoyCNlLbPmv62GUixQcBUsLgZJhr3ph4APenbZproghmvLaddwvuGM4i8aYkT6Yot+3vZhDRJEShKQelGp4b61YKUjPK0exKFMZA+9DFhqECQlStdHzW0DkySuB0Imme0M5YnU2kECo1CH0zGYLuqXlvJP7nNRLduWilTMSJRkEnizoJd3TkjDpyAiaRaj4wBKhk5q8O7YEEqk2TOVOCN3/yIqkWC55b8G6L+dLltI4sOSCH5Jh45JyUyDUpkwqh5Im8kDfybj1br9aH9TkZzVjTzD75A+vrFz4Kn2U=</latexit><latexit sha1_base64="TL1trh0NlqeLEywtx3wQmaQZuzU=">AAACFnicbVC7SgNBFJ2Nrxhfq5Y2i0EQxbCbRsugjYVFBPOAJIa7szfJkNnZdWZWCEu+wsZfsbFQxFbs/BsnjyImHhg4nHMPd+7xY86Udt0fK7O0vLK6ll3PbWxube/Yu3tVFSWSYoVGPJJ1HxRyJrCimeZYjyVC6HOs+f2rkV97RKlYJO70IMZWCF3BOoyCNlLbPmv62GUixQcBUsLgZJhr3ph4APenbZproghmvLaddwvuGM4i8aYkT6Yot+3vZhDRJEShKQelGp4b61YKUjPK0exKFMZA+9DFhqECQlStdHzW0DkySuB0Imme0M5YnU2kECo1CH0zGYLuqXlvJP7nNRLduWilTMSJRkEnizoJd3TkjDpyAiaRaj4wBKhk5q8O7YEEqk2TOVOCN3/yIqkWC55b8G6L+dLltI4sOSCH5Jh45JyUyDUpkwqh5Im8kDfybj1br9aH9TkZzVjTzD75A+vrFz4Kn2U=</latexit><latexit sha1_base64="TL1trh0NlqeLEywtx3wQmaQZuzU=">AAACFnicbVC7SgNBFJ2Nrxhfq5Y2i0EQxbCbRsugjYVFBPOAJIa7szfJkNnZdWZWCEu+wsZfsbFQxFbs/BsnjyImHhg4nHMPd+7xY86Udt0fK7O0vLK6ll3PbWxube/Yu3tVFSWSYoVGPJJ1HxRyJrCimeZYjyVC6HOs+f2rkV97RKlYJO70IMZWCF3BOoyCNlLbPmv62GUixQcBUsLgZJhr3ph4APenbZproghmvLaddwvuGM4i8aYkT6Yot+3vZhDRJEShKQelGp4b61YKUjPK0exKFMZA+9DFhqECQlStdHzW0DkySuB0Imme0M5YnU2kECo1CH0zGYLuqXlvJP7nNRLduWilTMSJRkEnizoJd3TkjDpyAiaRaj4wBKhk5q8O7YEEqk2TOVOCN3/yIqkWC55b8G6L+dLltI4sOSCH5Jh45JyUyDUpkwqh5Im8kDfybj1br9aH9TkZzVjTzD75A+vrFz4Kn2U=</latexit>
⇤̄�c
<latexit sha1_base64="OICGDHYgKSxD1R5pOb86fAIliQY=">AAACHHicbVC7SgNBFJ2NrxhfUUubxSCIYNiNhZZBGwuLCOYB2Rjuzt4kQ2Zn15lZISz5EBt/xcZCERsLwb9x8ihi4oWBwznn3jv3+DFnSjvOj5VZWl5ZXcuu5zY2t7Z38rt7NRUlkmKVRjySDR8Uciawqpnm2IglQuhzrPv9q5Fef0SpWCTu9CDGVghdwTqMgjZUO3/m+dhlIsUHAVLC4GSY83yQqXdjZgQwvD9t05yHIphxtPMFp+iMy14E7hQUyLQq7fyXF0Q0CVFoykGppuvEupWC1IxyNBsThTHQPnSxaaCAEFUrHR83tI8ME9idSJontD1mZztSCJUahL5xhqB7al4bkf9pzUR3LlopE3GiUdDJok7CbR3Zo6TsgEmkmg8MACqZ+atNeyCBapNnzoTgzp+8CGqlousU3dtSoXw5jSNLDsghOSYuOSdlck0qpEooeSIv5I28W8/Wq/VhfU6sGWvas0/+lPX9C2yAoiw=</latexit><latexit sha1_base64="OICGDHYgKSxD1R5pOb86fAIliQY=">AAACHHicbVC7SgNBFJ2NrxhfUUubxSCIYNiNhZZBGwuLCOYB2Rjuzt4kQ2Zn15lZISz5EBt/xcZCERsLwb9x8ihi4oWBwznn3jv3+DFnSjvOj5VZWl5ZXcuu5zY2t7Z38rt7NRUlkmKVRjySDR8Uciawqpnm2IglQuhzrPv9q5Fef0SpWCTu9CDGVghdwTqMgjZUO3/m+dhlIsUHAVLC4GSY83yQqXdjZgQwvD9t05yHIphxtPMFp+iMy14E7hQUyLQq7fyXF0Q0CVFoykGppuvEupWC1IxyNBsThTHQPnSxaaCAEFUrHR83tI8ME9idSJontD1mZztSCJUahL5xhqB7al4bkf9pzUR3LlopE3GiUdDJok7CbR3Zo6TsgEmkmg8MACqZ+atNeyCBapNnzoTgzp+8CGqlousU3dtSoXw5jSNLDsghOSYuOSdlck0qpEooeSIv5I28W8/Wq/VhfU6sGWvas0/+lPX9C2yAoiw=</latexit><latexit sha1_base64="OICGDHYgKSxD1R5pOb86fAIliQY=">AAACHHicbVC7SgNBFJ2NrxhfUUubxSCIYNiNhZZBGwuLCOYB2Rjuzt4kQ2Zn15lZISz5EBt/xcZCERsLwb9x8ihi4oWBwznn3jv3+DFnSjvOj5VZWl5ZXcuu5zY2t7Z38rt7NRUlkmKVRjySDR8Uciawqpnm2IglQuhzrPv9q5Fef0SpWCTu9CDGVghdwTqMgjZUO3/m+dhlIsUHAVLC4GSY83yQqXdjZgQwvD9t05yHIphxtPMFp+iMy14E7hQUyLQq7fyXF0Q0CVFoykGppuvEupWC1IxyNBsThTHQPnSxaaCAEFUrHR83tI8ME9idSJontD1mZztSCJUahL5xhqB7al4bkf9pzUR3LlopE3GiUdDJok7CbR3Zo6TsgEmkmg8MACqZ+atNeyCBapNnzoTgzp+8CGqlousU3dtSoXw5jSNLDsghOSYuOSdlck0qpEooeSIv5I28W8/Wq/VhfU6sGWvas0/+lPX9C2yAoiw=</latexit><latexit sha1_base64="OICGDHYgKSxD1R5pOb86fAIliQY=">AAACHHicbVC7SgNBFJ2NrxhfUUubxSCIYNiNhZZBGwuLCOYB2Rjuzt4kQ2Zn15lZISz5EBt/xcZCERsLwb9x8ihi4oWBwznn3jv3+DFnSjvOj5VZWl5ZXcuu5zY2t7Z38rt7NRUlkmKVRjySDR8Uciawqpnm2IglQuhzrPv9q5Fef0SpWCTu9CDGVghdwTqMgjZUO3/m+dhlIsUHAVLC4GSY83yQqXdjZgQwvD9t05yHIphxtPMFp+iMy14E7hQUyLQq7fyXF0Q0CVFoykGppuvEupWC1IxyNBsThTHQPnSxaaCAEFUrHR83tI8ME9idSJontD1mZztSCJUahL5xhqB7al4bkf9pzUR3LlopE3GiUdDJok7CbR3Zo6TsgEmkmg8MACqZ+atNeyCBapNnzoTgzp+8CGqlousU3dtSoXw5jSNLDsghOSYuOSdlck0qpEooeSIv5I28W8/Wq/VhfU6sGWvas0/+lPX9C2yAoiw=</latexit>
Chances of a charmed hadron meeting one or two nucleons not much smaller than of two antinucleons and one antiyperon meeting to form an antihypernucleus
Coalescence at the LHC— heavy-ion collisions
Most recent theory (spectrum)— QMC model
— No SU(4) uncertainties; mean meson fields couple directly to the light quarks in the nucleons and hyperons
— No free parameters, all fixed by normal nuclear matter and normal nuclei
Nonmesonic weak decay (NMWD)
C. Conti, C.E. Fontoura, A.P. Galeao, GK, F. KrmpoticJ Phys G 45, 01501 (2018)
L: weak vertex+
R: strong vertex
In nuclear medium
⇤+c
<latexit sha1_base64="TL1trh0NlqeLEywtx3wQmaQZuzU=">AAACFnicbVC7SgNBFJ2Nrxhfq5Y2i0EQxbCbRsugjYVFBPOAJIa7szfJkNnZdWZWCEu+wsZfsbFQxFbs/BsnjyImHhg4nHMPd+7xY86Udt0fK7O0vLK6ll3PbWxube/Yu3tVFSWSYoVGPJJ1HxRyJrCimeZYjyVC6HOs+f2rkV97RKlYJO70IMZWCF3BOoyCNlLbPmv62GUixQcBUsLgZJhr3ph4APenbZproghmvLaddwvuGM4i8aYkT6Yot+3vZhDRJEShKQelGp4b61YKUjPK0exKFMZA+9DFhqECQlStdHzW0DkySuB0Imme0M5YnU2kECo1CH0zGYLuqXlvJP7nNRLduWilTMSJRkEnizoJd3TkjDpyAiaRaj4wBKhk5q8O7YEEqk2TOVOCN3/yIqkWC55b8G6L+dLltI4sOSCH5Jh45JyUyDUpkwqh5Im8kDfybj1br9aH9TkZzVjTzD75A+vrFz4Kn2U=</latexit><latexit sha1_base64="TL1trh0NlqeLEywtx3wQmaQZuzU=">AAACFnicbVC7SgNBFJ2Nrxhfq5Y2i0EQxbCbRsugjYVFBPOAJIa7szfJkNnZdWZWCEu+wsZfsbFQxFbs/BsnjyImHhg4nHMPd+7xY86Udt0fK7O0vLK6ll3PbWxube/Yu3tVFSWSYoVGPJJ1HxRyJrCimeZYjyVC6HOs+f2rkV97RKlYJO70IMZWCF3BOoyCNlLbPmv62GUixQcBUsLgZJhr3ph4APenbZproghmvLaddwvuGM4i8aYkT6Yot+3vZhDRJEShKQelGp4b61YKUjPK0exKFMZA+9DFhqECQlStdHzW0DkySuB0Imme0M5YnU2kECo1CH0zGYLuqXlvJP7nNRLduWilTMSJRkEnizoJd3TkjDpyAiaRaj4wBKhk5q8O7YEEqk2TOVOCN3/yIqkWC55b8G6L+dLltI4sOSCH5Jh45JyUyDUpkwqh5Im8kDfybj1br9aH9TkZzVjTzD75A+vrFz4Kn2U=</latexit><latexit sha1_base64="TL1trh0NlqeLEywtx3wQmaQZuzU=">AAACFnicbVC7SgNBFJ2Nrxhfq5Y2i0EQxbCbRsugjYVFBPOAJIa7szfJkNnZdWZWCEu+wsZfsbFQxFbs/BsnjyImHhg4nHMPd+7xY86Udt0fK7O0vLK6ll3PbWxube/Yu3tVFSWSYoVGPJJ1HxRyJrCimeZYjyVC6HOs+f2rkV97RKlYJO70IMZWCF3BOoyCNlLbPmv62GUixQcBUsLgZJhr3ph4APenbZproghmvLaddwvuGM4i8aYkT6Yot+3vZhDRJEShKQelGp4b61YKUjPK0exKFMZA+9DFhqECQlStdHzW0DkySuB0Imme0M5YnU2kECo1CH0zGYLuqXlvJP7nNRLduWilTMSJRkEnizoJd3TkjDpyAiaRaj4wBKhk5q8O7YEEqk2TOVOCN3/yIqkWC55b8G6L+dLltI4sOSCH5Jh45JyUyDUpkwqh5Im8kDfybj1br9aH9TkZzVjTzD75A+vrFz4Kn2U=</latexit><latexit sha1_base64="TL1trh0NlqeLEywtx3wQmaQZuzU=">AAACFnicbVC7SgNBFJ2Nrxhfq5Y2i0EQxbCbRsugjYVFBPOAJIa7szfJkNnZdWZWCEu+wsZfsbFQxFbs/BsnjyImHhg4nHMPd+7xY86Udt0fK7O0vLK6ll3PbWxube/Yu3tVFSWSYoVGPJJ1HxRyJrCimeZYjyVC6HOs+f2rkV97RKlYJO70IMZWCF3BOoyCNlLbPmv62GUixQcBUsLgZJhr3ph4APenbZproghmvLaddwvuGM4i8aYkT6Yot+3vZhDRJEShKQelGp4b61YKUjPK0exKFMZA+9DFhqECQlStdHzW0DkySuB0Imme0M5YnU2kECo1CH0zGYLuqXlvJP7nNRLduWilTMSJRkEnizoJd3TkjDpyAiaRaj4wBKhk5q8O7YEEqk2TOVOCN3/yIqkWC55b8G6L+dLltI4sOSCH5Jh45JyUyDUpkwqh5Im8kDfybj1br9aH9TkZzVjTzD75A+vrFz4Kn2U=</latexit>
⇤<latexit sha1_base64="xfiO1RyK2ArKnW5H1aGyHprmZQg=">AAACEnicbVC7SgNBFJ2Nr7i+opY2i0FQi7CbRsugjYVFBPOAJIS7szfJkNnZdWZWCEu+wcZfsbFQxNbKzr9xkmwREw8MHM65hzv3+DFnSrvuj5VbWV1b38hv2lvbO7t7hf2DuooSSbFGIx7Jpg8KORNY00xzbMYSIfQ5Nvzh9cRvPKJULBL3ehRjJ4S+YD1GQRupWzhr+9hnIsUHAVLC6Hxst29NPAC7jSKY07uFoltyp3CWiZeRIslQ7Ra+20FEkxCFphyUanlurDspSM0oR7MnURgDHUIfW4YKCFF10ulJY+fEKIHTi6R5QjtTdT6RQqjUKPTNZAh6oBa9ifif10p077KTMhEnGgWdLeol3NGRM+nHCZhEqvnIEKCSmb86dAASqDYt2qYEb/HkZVIvlzy35N2Vi5WrrI48OSLH5JR45IJUyA2pkhqh5Im8kDfybj1br9aH9TkbzVlZ5pD8gfX1C3YmnfI=</latexit><latexit sha1_base64="xfiO1RyK2ArKnW5H1aGyHprmZQg=">AAACEnicbVC7SgNBFJ2Nr7i+opY2i0FQi7CbRsugjYVFBPOAJIS7szfJkNnZdWZWCEu+wcZfsbFQxNbKzr9xkmwREw8MHM65hzv3+DFnSrvuj5VbWV1b38hv2lvbO7t7hf2DuooSSbFGIx7Jpg8KORNY00xzbMYSIfQ5Nvzh9cRvPKJULBL3ehRjJ4S+YD1GQRupWzhr+9hnIsUHAVLC6Hxst29NPAC7jSKY07uFoltyp3CWiZeRIslQ7Ra+20FEkxCFphyUanlurDspSM0oR7MnURgDHUIfW4YKCFF10ulJY+fEKIHTi6R5QjtTdT6RQqjUKPTNZAh6oBa9ifif10p077KTMhEnGgWdLeol3NGRM+nHCZhEqvnIEKCSmb86dAASqDYt2qYEb/HkZVIvlzy35N2Vi5WrrI48OSLH5JR45IJUyA2pkhqh5Im8kDfybj1br9aH9TkbzVlZ5pD8gfX1C3YmnfI=</latexit><latexit sha1_base64="xfiO1RyK2ArKnW5H1aGyHprmZQg=">AAACEnicbVC7SgNBFJ2Nr7i+opY2i0FQi7CbRsugjYVFBPOAJIS7szfJkNnZdWZWCEu+wcZfsbFQxNbKzr9xkmwREw8MHM65hzv3+DFnSrvuj5VbWV1b38hv2lvbO7t7hf2DuooSSbFGIx7Jpg8KORNY00xzbMYSIfQ5Nvzh9cRvPKJULBL3ehRjJ4S+YD1GQRupWzhr+9hnIsUHAVLC6Hxst29NPAC7jSKY07uFoltyp3CWiZeRIslQ7Ra+20FEkxCFphyUanlurDspSM0oR7MnURgDHUIfW4YKCFF10ulJY+fEKIHTi6R5QjtTdT6RQqjUKPTNZAh6oBa9ifif10p077KTMhEnGgWdLeol3NGRM+nHCZhEqvnIEKCSmb86dAASqDYt2qYEb/HkZVIvlzy35N2Vi5WrrI48OSLH5JR45IJUyA2pkhqh5Im8kDfybj1br9aH9TkbzVlZ5pD8gfX1C3YmnfI=</latexit><latexit sha1_base64="xfiO1RyK2ArKnW5H1aGyHprmZQg=">AAACEnicbVC7SgNBFJ2Nr7i+opY2i0FQi7CbRsugjYVFBPOAJIS7szfJkNnZdWZWCEu+wcZfsbFQxNbKzr9xkmwREw8MHM65hzv3+DFnSrvuj5VbWV1b38hv2lvbO7t7hf2DuooSSbFGIx7Jpg8KORNY00xzbMYSIfQ5Nvzh9cRvPKJULBL3ehRjJ4S+YD1GQRupWzhr+9hnIsUHAVLC6Hxst29NPAC7jSKY07uFoltyp3CWiZeRIslQ7Ra+20FEkxCFphyUanlurDspSM0oR7MnURgDHUIfW4YKCFF10ulJY+fEKIHTi6R5QjtTdT6RQqjUKPTNZAh6oBa9ifif10p077KTMhEnGgWdLeol3NGRM+nHCZhEqvnIEKCSmb86dAASqDYt2qYEb/HkZVIvlzy35N2Vi5WrrI48OSLH5JR45IJUyA2pkhqh5Im8kDfybj1br9aH9TkbzVlZ5pD8gfX1C3YmnfI=</latexit>
⇤+c + n ! ⇤+ p
<latexit sha1_base64="enotRV3+kKoBEcunjFtDugMmF0A=">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</latexit><latexit sha1_base64="enotRV3+kKoBEcunjFtDugMmF0A=">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</latexit><latexit sha1_base64="enotRV3+kKoBEcunjFtDugMmF0A=">AAACXHicbVFNT+MwEHXCVylfZVfaCxeLCgkBqhIEBW7V7oUDB5AoIDWhmjjT1MJxgu2wqqL+yb31sn8F3NIivkay9PTe+I3nOcoF18bzRo47N7+wuFRZrq6srq1v1DZ/3OisUAzbLBOZuotAo+AS24YbgXe5QkgjgbfRw5+xfvuESvNMXptBjmEKieQ9zsBYqlvTQYQJlyU+SlAKBnvDahlMbDsqicLSa3jHzeZZ88Br+N7piX904De8SQ2DCzsmhvv9LqP7VNJA8aRvrEv2l041y+d0WA1Qxu8mdGv1mS2d2dKZ7Ruok2lddmv/gjhjRYrSMAFad3wvN2EJynAm0PoXGnNgD5Bgx0IJKeqwnGwxpDuWiWkvU/ZIQyfs+xslpFoP0sh2pmD6+rM2Jr/TOoXpnYYll3lhULLXQb1CUJPRcdI05gqZEQMLgClu30pZHxQwY/+jakP4svJXcHNo82n4V4f11u9pHBWyRbbJLvHJCWmRc3JJ2oSREXl2Ks6y89+dd1fctddW15ne+Uk+lPvrBXMnsRk=</latexit><latexit sha1_base64="enotRV3+kKoBEcunjFtDugMmF0A=">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</latexit>
Model
Nuclear structure — Independent particle shell model*— relativistic mean fields (NL3, Ring et al)
Decay — Pion and Kaon exchange
Recoil of nucleus— Fully relativistic
*Ramos et al, Parreño et al
Decay rates Free-space decay rate
~1/2 free-space decay rate
C. Conti, C.E. Fontoura, A.P. Galeao, GK, F. KrmpoticJ Phys G 45, 01501 (2018)
100 200 300 400 500
TΛ [MeV]
0.000
0.002
0.004
0.006
0.008
0.010
0.012
S(T Λ
) x
1011
no recoil
nonrel. recoil
rel. recoil
Effect of nuclear recoilSpectrum of emitted strange hyperon
C. Conti, C.E. Fontoura, A.P. Galeao, GK, F. KrmpoticJ Phys G 45, 01501 (2018)
few-nucleon bound states⇤+c
<latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit>
Several model calculations— potential model— meson-exchange model— constituent quark model
- Bando & Bando PLB 109, 1604 (1982)- Gibson, Bhamathi, Dover & Lehman PRC 27, 2085 (1983)- Liu & Oka PRD 85, 014015 (2012)- Huang, Ping & Wang PRC 87, 034002 (2013)- Gal, Garcilazo, Valcarce & Caramès PRD 90, 014019 (2014)- Garcilazo, Valcarce & Caramès PRC 92, 024006 (2015)- Maeda, Oka, Yokota, Hiyama & Liu, PTEP 2016, 023D2 (2016)- Ohtani, Araki & Oka, PRC 96, 055208 (2017)
few-nucleon bound states⇤+c
<latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">AAACPnicbVA9SwNBEN3zM8avqKXNYRBEJeylMWXQxsIiglEhd4a5vUlc3Ns7d/eEcOSX2fgb7CxtLBSxtXQTI8Tog4XHm5k3sy9MBdeG0idnanpmdm6+sFBcXFpeWS2trZ/rJFMMmywRiboMQaPgEpuGG4GXqUKIQ4EX4c3RoH5xh0rzRJ6ZXopBDF3JO5yBsVK71PRD7HKZ460EpaC32y/m/tC2pbphkNNKjVrs0wqlv0jfP7FbIrjaa7N+0UcZjXm0S+WfPvcv8UakTEZotEuPfpSwLEZpmACtWx5NTZCDMpwJtP6ZxhTYDXSxZamEGHWQD+/su9tWidxOouyTxh2q4xM5xFr34tB2xmCu9WRtIP5Xa2WmUwtyLtPMoGTfizqZcE3iDrJ0I66QGdGzBJji9laXXYMCZmziRRuCN/nlv+S8WvFoxTutluuHozgKZJNskR3ikQNSJ8ekQZqEkXvyTF7Jm/PgvDjvzsd365Qzmtkgv+B8fgEF6av9</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit>
Several model calculations— potential model— meson-exchange model— constituent quark model
- Bando & Bando PLB 109, 1604 (1982)- Gibson, Bhamathi, Dover & Lehman PRC 27, 2085 (1983)- Liu & Oka PRD 85, 014015 (2012)- Huang, Ping & Wang PRC 87, 034002 (2013)- Gal, Garcilazo, Valcarce & Caramès PRD 90, 014019 (2014)- Garcilazo, Valcarce & Caramès PRC 92, 024006 (2015)- Maeda, Oka, Yokota, Hiyama & Liu, PTEP 2016, 023D2 (2016)- Ohtani, Araki & Oka, PRC 96, 055208 (2017)
⇤+c
<latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit>
-nucleon interactionCrucial input:
-nucleon from lattice QCD⇤+c
<latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit>
HAL collab. NPA 971, 113 (2018)
J. Haidenbauer and G.K, arXiv:1711.06470
Extrapolation to physical pion masses
Chiral EFT
— one-pion exchange
— contact terms
— Lippmann-Schwinger eq, coupled channels⇤cN
⇡�! ⌃cN<latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit>
J. Haidenbauer and G.K, arXiv:1711.06470
Red bands, extrapolation to m⇡ = 138 MeV<latexit sha1_base64="o3pto93eTrdFtOJyTiddAR5ShJA=">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</latexit><latexit sha1_base64="o3pto93eTrdFtOJyTiddAR5ShJA=">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</latexit><latexit sha1_base64="o3pto93eTrdFtOJyTiddAR5ShJA=">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</latexit><latexit sha1_base64="o3pto93eTrdFtOJyTiddAR5ShJA=">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</latexit>
⇤cN⇡�! ⌃cN
<latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit>
very small effect
Charmed hypernuclei — physical pion masses
— No bound state
— , perhaps bound
— certainly bound to large nuclei
N⇤+c
<latexit sha1_base64="Nl6HzJEMm5AeCbhhAddd+R5WS2g=">AAACGHicbVBNS8NAEN3U7/gV9ehlsQiiUJNe9Fj04kFEwarQ1DLZTNulm03c3Qgl9Gd48a948aCIV2/+G7e1B60+GHi8N7M786JMcG18/9MpTU3PzM7NL7iLS8srq97a+pVOc8WwzlKRqpsINAousW64EXiTKYQkEngd9Y6H/vU9Ks1TeWn6GTYT6Eje5gyMlVrefhhhh8sC7yQoBf3dgXtGw1P7QAy3ey3mhijjH27LK/sVfwT6lwRjUiZjnLe8jzBOWZ6gNEyA1o3Az0yzAGU4Ezhww1xjBqwHHWxYKiFB3SxGhw3otlVi2k6VLWnoSP05UUCidT+JbGcCpqsnvaH4n9fITfuwWXCZ5QYl+/6onQtqUjpMicZcITOibwkwxe2ulHVBATM2S9eGEEye/JdcVSuBXwkuquXa0TiOebJJtsgOCcgBqZETck7qhJEH8kReyKvz6Dw7b877d2vJGc9skF9wPr4ASVGf5w==</latexit><latexit sha1_base64="Nl6HzJEMm5AeCbhhAddd+R5WS2g=">AAACGHicbVBNS8NAEN3U7/gV9ehlsQiiUJNe9Fj04kFEwarQ1DLZTNulm03c3Qgl9Gd48a948aCIV2/+G7e1B60+GHi8N7M786JMcG18/9MpTU3PzM7NL7iLS8srq97a+pVOc8WwzlKRqpsINAousW64EXiTKYQkEngd9Y6H/vU9Ks1TeWn6GTYT6Eje5gyMlVrefhhhh8sC7yQoBf3dgXtGw1P7QAy3ey3mhijjH27LK/sVfwT6lwRjUiZjnLe8jzBOWZ6gNEyA1o3Az0yzAGU4Ezhww1xjBqwHHWxYKiFB3SxGhw3otlVi2k6VLWnoSP05UUCidT+JbGcCpqsnvaH4n9fITfuwWXCZ5QYl+/6onQtqUjpMicZcITOibwkwxe2ulHVBATM2S9eGEEye/JdcVSuBXwkuquXa0TiOebJJtsgOCcgBqZETck7qhJEH8kReyKvz6Dw7b877d2vJGc9skF9wPr4ASVGf5w==</latexit><latexit sha1_base64="Nl6HzJEMm5AeCbhhAddd+R5WS2g=">AAACGHicbVBNS8NAEN3U7/gV9ehlsQiiUJNe9Fj04kFEwarQ1DLZTNulm03c3Qgl9Gd48a948aCIV2/+G7e1B60+GHi8N7M786JMcG18/9MpTU3PzM7NL7iLS8srq97a+pVOc8WwzlKRqpsINAousW64EXiTKYQkEngd9Y6H/vU9Ks1TeWn6GTYT6Eje5gyMlVrefhhhh8sC7yQoBf3dgXtGw1P7QAy3ey3mhijjH27LK/sVfwT6lwRjUiZjnLe8jzBOWZ6gNEyA1o3Az0yzAGU4Ezhww1xjBqwHHWxYKiFB3SxGhw3otlVi2k6VLWnoSP05UUCidT+JbGcCpqsnvaH4n9fITfuwWXCZ5QYl+/6onQtqUjpMicZcITOibwkwxe2ulHVBATM2S9eGEEye/JdcVSuBXwkuquXa0TiOebJJtsgOCcgBqZETck7qhJEH8kReyKvz6Dw7b877d2vJGc9skF9wPr4ASVGf5w==</latexit><latexit sha1_base64="Nl6HzJEMm5AeCbhhAddd+R5WS2g=">AAACGHicbVBNS8NAEN3U7/gV9ehlsQiiUJNe9Fj04kFEwarQ1DLZTNulm03c3Qgl9Gd48a948aCIV2/+G7e1B60+GHi8N7M786JMcG18/9MpTU3PzM7NL7iLS8srq97a+pVOc8WwzlKRqpsINAousW64EXiTKYQkEngd9Y6H/vU9Ks1TeWn6GTYT6Eje5gyMlVrefhhhh8sC7yQoBf3dgXtGw1P7QAy3ey3mhijjH27LK/sVfwT6lwRjUiZjnLe8jzBOWZ6gNEyA1o3Az0yzAGU4Ezhww1xjBqwHHWxYKiFB3SxGhw3otlVi2k6VLWnoSP05UUCidT+JbGcCpqsnvaH4n9fITfuwWXCZ5QYl+/6onQtqUjpMicZcITOibwkwxe2ulHVBATM2S9eGEEye/JdcVSuBXwkuquXa0TiOebJJtsgOCcgBqZETck7qhJEH8kReyKvz6Dw7b877d2vJGc9skF9wPr4ASVGf5w==</latexit>
NN⇤+c
<latexit sha1_base64="QaLQmRLqW6xpIdJ+eQYzIWksgsQ=">AAACGHicbVBNS8NAEN34WeNX1aOXYBFEoSa96LHoxYMUBWsLTS2TzaQubjZxdyOU0J/hxb/ixYMiXr35b9zWHGr1wcDjvZndmReknCntul/WzOzc/MJiacleXlldWy9vbF6rJJMUmzThiWwHoJAzgU3NNMd2KhHigGMruDsd+a0HlIol4koPUuzG0BcsYhS0kXrlQz/APhM53guQEgb7Q7vR8M/NAyHcHPSo7aMIJ9xeueJW3TGcv8QrSIUUuOiVP/0woVmMQlMOSnU8N9XdHKRmlOPQ9jOFKdA76GPHUAExqm4+Pmzo7BoldKJEmhLaGauTEznESg3iwHTGoG/VtDcS//M6mY6OuzkTaaZR0J+Poow7OnFGKTkhk0g1HxgCVDKzq0NvQQLVJkvbhOBNn/yXXNeqnlv1LmuV+kkRR4lskx2yRzxyROrkjFyQJqHkkTyTV/JmPVkv1rv18dM6YxUzW+QXrM9vk+OgFQ==</latexit><latexit sha1_base64="QaLQmRLqW6xpIdJ+eQYzIWksgsQ=">AAACGHicbVBNS8NAEN34WeNX1aOXYBFEoSa96LHoxYMUBWsLTS2TzaQubjZxdyOU0J/hxb/ixYMiXr35b9zWHGr1wcDjvZndmReknCntul/WzOzc/MJiacleXlldWy9vbF6rJJMUmzThiWwHoJAzgU3NNMd2KhHigGMruDsd+a0HlIol4koPUuzG0BcsYhS0kXrlQz/APhM53guQEgb7Q7vR8M/NAyHcHPSo7aMIJ9xeueJW3TGcv8QrSIUUuOiVP/0woVmMQlMOSnU8N9XdHKRmlOPQ9jOFKdA76GPHUAExqm4+Pmzo7BoldKJEmhLaGauTEznESg3iwHTGoG/VtDcS//M6mY6OuzkTaaZR0J+Poow7OnFGKTkhk0g1HxgCVDKzq0NvQQLVJkvbhOBNn/yXXNeqnlv1LmuV+kkRR4lskx2yRzxyROrkjFyQJqHkkTyTV/JmPVkv1rv18dM6YxUzW+QXrM9vk+OgFQ==</latexit><latexit sha1_base64="QaLQmRLqW6xpIdJ+eQYzIWksgsQ=">AAACGHicbVBNS8NAEN34WeNX1aOXYBFEoSa96LHoxYMUBWsLTS2TzaQubjZxdyOU0J/hxb/ixYMiXr35b9zWHGr1wcDjvZndmReknCntul/WzOzc/MJiacleXlldWy9vbF6rJJMUmzThiWwHoJAzgU3NNMd2KhHigGMruDsd+a0HlIol4koPUuzG0BcsYhS0kXrlQz/APhM53guQEgb7Q7vR8M/NAyHcHPSo7aMIJ9xeueJW3TGcv8QrSIUUuOiVP/0woVmMQlMOSnU8N9XdHKRmlOPQ9jOFKdA76GPHUAExqm4+Pmzo7BoldKJEmhLaGauTEznESg3iwHTGoG/VtDcS//M6mY6OuzkTaaZR0J+Poow7OnFGKTkhk0g1HxgCVDKzq0NvQQLVJkvbhOBNn/yXXNeqnlv1LmuV+kkRR4lskx2yRzxyROrkjFyQJqHkkTyTV/JmPVkv1rv18dM6YxUzW+QXrM9vk+OgFQ==</latexit><latexit sha1_base64="QaLQmRLqW6xpIdJ+eQYzIWksgsQ=">AAACGHicbVBNS8NAEN34WeNX1aOXYBFEoSa96LHoxYMUBWsLTS2TzaQubjZxdyOU0J/hxb/ixYMiXr35b9zWHGr1wcDjvZndmReknCntul/WzOzc/MJiacleXlldWy9vbF6rJJMUmzThiWwHoJAzgU3NNMd2KhHigGMruDsd+a0HlIol4koPUuzG0BcsYhS0kXrlQz/APhM53guQEgb7Q7vR8M/NAyHcHPSo7aMIJ9xeueJW3TGcv8QrSIUUuOiVP/0woVmMQlMOSnU8N9XdHKRmlOPQ9jOFKdA76GPHUAExqm4+Pmzo7BoldKJEmhLaGauTEznESg3iwHTGoG/VtDcS//M6mY6OuzkTaaZR0J+Poow7OnFGKTkhk0g1HxgCVDKzq0NvQQLVJkvbhOBNn/yXXNeqnlv1LmuV+kkRR4lskx2yRzxyROrkjFyQJqHkkTyTV/JmPVkv1rv18dM6YxUzW+QXrM9vk+OgFQ==</latexit>
While experimental data not available, lattice QCD only hope to make real progress
Quantum theory
— this is the trace anomaly— no scale invariance— trace of is nonzeroTµ⌫
The entire mass
comes from gluons
ATHENNA* collaboration JLab @ 12 GeV
*A J/Ψ THreshold Electroproduction on the Nucleon and Nuclei Analysis
Hall A — E12-12-006K. Hafidi, Z.-E. Meziani, N. Sparveris, Z. W. Zhao
Hall C — E-12-16-007 (Pentaquarks)Z.-E. Meziani, S. Joosten, et al.
— Chances of a quarkonium meeting one or two nucleons
not much smaller than of two antinucleons and one
antihyperon meeting to form an antihypernucleus
Coalescence at the LHC— heavy-ion collisions
Antiproton annihilation on deuteron, re-scattering on spectator nucleon
@ FAIR
⇡0<latexit sha1_base64="Y3I/Y/k6UZe1iT8KZ30XGtoQNkQ=">AAACEHicbVC7TsNAEDyHVzAvAyWNRYRAFJGdBsoIGsogkYcUm+h8XiennM/m7oxkWfkEGn6FhgKEaCnp+BsujyIkjLTSaGZXuztByqhUjvNjlFZW19Y3ypvm1vbO7p61f9CSSSYINEnCEtEJsARGOTQVVQw6qQAcBwzawfB67LcfQUia8DuVp+DHuM9pRAlWWupZp14AfcoLeOBYCJyfj0wvpfeO6QEP59SeVXGqzgT2MnFnpIJmaPSsby9MSBYDV4RhKbuukyq/wEJRwkBvySSkmAxxH7qachyD9IvJQyP7RCuhHSVCF1f2RJ2fKHAsZR4HujPGaiAXvbH4n9fNVHTpF5SnmQJOpouijNkqscfp2CEVQBTLNcFEUH2rTQZYYKJ0hqYOwV18eZm0alXXqbq3tUr9ahZHGR2hY3SGXHSB6ugGNVATEfSEXtAbejeejVfjw/ictpaM2cwh+gPj6xfB2Z0E</latexit><latexit sha1_base64="Y3I/Y/k6UZe1iT8KZ30XGtoQNkQ=">AAACEHicbVC7TsNAEDyHVzAvAyWNRYRAFJGdBsoIGsogkYcUm+h8XiennM/m7oxkWfkEGn6FhgKEaCnp+BsujyIkjLTSaGZXuztByqhUjvNjlFZW19Y3ypvm1vbO7p61f9CSSSYINEnCEtEJsARGOTQVVQw6qQAcBwzawfB67LcfQUia8DuVp+DHuM9pRAlWWupZp14AfcoLeOBYCJyfj0wvpfeO6QEP59SeVXGqzgT2MnFnpIJmaPSsby9MSBYDV4RhKbuukyq/wEJRwkBvySSkmAxxH7qachyD9IvJQyP7RCuhHSVCF1f2RJ2fKHAsZR4HujPGaiAXvbH4n9fNVHTpF5SnmQJOpouijNkqscfp2CEVQBTLNcFEUH2rTQZYYKJ0hqYOwV18eZm0alXXqbq3tUr9ahZHGR2hY3SGXHSB6ugGNVATEfSEXtAbejeejVfjw/ictpaM2cwh+gPj6xfB2Z0E</latexit><latexit sha1_base64="Y3I/Y/k6UZe1iT8KZ30XGtoQNkQ=">AAACEHicbVC7TsNAEDyHVzAvAyWNRYRAFJGdBsoIGsogkYcUm+h8XiennM/m7oxkWfkEGn6FhgKEaCnp+BsujyIkjLTSaGZXuztByqhUjvNjlFZW19Y3ypvm1vbO7p61f9CSSSYINEnCEtEJsARGOTQVVQw6qQAcBwzawfB67LcfQUia8DuVp+DHuM9pRAlWWupZp14AfcoLeOBYCJyfj0wvpfeO6QEP59SeVXGqzgT2MnFnpIJmaPSsby9MSBYDV4RhKbuukyq/wEJRwkBvySSkmAxxH7qachyD9IvJQyP7RCuhHSVCF1f2RJ2fKHAsZR4HujPGaiAXvbH4n9fNVHTpF5SnmQJOpouijNkqscfp2CEVQBTLNcFEUH2rTQZYYKJ0hqYOwV18eZm0alXXqbq3tUr9ahZHGR2hY3SGXHSB6ugGNVATEfSEXtAbejeejVfjw/ictpaM2cwh+gPj6xfB2Z0E</latexit><latexit sha1_base64="Y3I/Y/k6UZe1iT8KZ30XGtoQNkQ=">AAACEHicbVC7TsNAEDyHVzAvAyWNRYRAFJGdBsoIGsogkYcUm+h8XiennM/m7oxkWfkEGn6FhgKEaCnp+BsujyIkjLTSaGZXuztByqhUjvNjlFZW19Y3ypvm1vbO7p61f9CSSSYINEnCEtEJsARGOTQVVQw6qQAcBwzawfB67LcfQUia8DuVp+DHuM9pRAlWWupZp14AfcoLeOBYCJyfj0wvpfeO6QEP59SeVXGqzgT2MnFnpIJmaPSsby9MSBYDV4RhKbuukyq/wEJRwkBvySSkmAxxH7qachyD9IvJQyP7RCuhHSVCF1f2RJ2fKHAsZR4HujPGaiAXvbH4n9fNVHTpF5SnmQJOpouijNkqscfp2CEVQBTLNcFEUH2rTQZYYKJ0hqYOwV18eZm0alXXqbq3tUr9ahZHGR2hY3SGXHSB6ugGNVATEfSEXtAbejeejVfjw/ictpaM2cwh+gPj6xfB2Z0E</latexit>
p̄<latexit sha1_base64="EenaU/2ZSAmSPlRHB069CbSZVP4=">AAACEXicbVA9SwNBEN3zM55fUUubxSAEi3CXRsugjWUE8wFJCHN7k2TJ3t65uyeEI3/Bxr9iY6GIrZ2d/8bNRxETHww83pthZl6QCK6N5/04a+sbm1vbuR13d2//4DB/dFzXcaoY1lgsYtUMQKPgEmuGG4HNRCFEgcBGMLyZ+I1HVJrH8t6MEuxE0Je8xxkYK3XzxXaAfS4zfJCgFIwuxm47AEUTt40yXJC7+YJX8qagq8SfkwKZo9rNf7fDmKURSsMEaN3yvcR0MlCGM4F2TaoxATaEPrYslRCh7mTTj8b03Coh7cXKljR0qi5OZBBpPYoC2xmBGehlbyL+57VS07vqZFwmqUHJZot6qaAmppN4aMgVMiNGlgBT3N5K2QAUMGNDdG0I/vLLq6ReLvleyb8rFyrX8zhy5JSckSLxySWpkFtSJTXCyBN5IW/k3Xl2Xp0P53PWuubMZ07IHzhfv4QKnWw=</latexit><latexit sha1_base64="EenaU/2ZSAmSPlRHB069CbSZVP4=">AAACEXicbVA9SwNBEN3zM55fUUubxSAEi3CXRsugjWUE8wFJCHN7k2TJ3t65uyeEI3/Bxr9iY6GIrZ2d/8bNRxETHww83pthZl6QCK6N5/04a+sbm1vbuR13d2//4DB/dFzXcaoY1lgsYtUMQKPgEmuGG4HNRCFEgcBGMLyZ+I1HVJrH8t6MEuxE0Je8xxkYK3XzxXaAfS4zfJCgFIwuxm47AEUTt40yXJC7+YJX8qagq8SfkwKZo9rNf7fDmKURSsMEaN3yvcR0MlCGM4F2TaoxATaEPrYslRCh7mTTj8b03Coh7cXKljR0qi5OZBBpPYoC2xmBGehlbyL+57VS07vqZFwmqUHJZot6qaAmppN4aMgVMiNGlgBT3N5K2QAUMGNDdG0I/vLLq6ReLvleyb8rFyrX8zhy5JSckSLxySWpkFtSJTXCyBN5IW/k3Xl2Xp0P53PWuubMZ07IHzhfv4QKnWw=</latexit><latexit sha1_base64="EenaU/2ZSAmSPlRHB069CbSZVP4=">AAACEXicbVA9SwNBEN3zM55fUUubxSAEi3CXRsugjWUE8wFJCHN7k2TJ3t65uyeEI3/Bxr9iY6GIrZ2d/8bNRxETHww83pthZl6QCK6N5/04a+sbm1vbuR13d2//4DB/dFzXcaoY1lgsYtUMQKPgEmuGG4HNRCFEgcBGMLyZ+I1HVJrH8t6MEuxE0Je8xxkYK3XzxXaAfS4zfJCgFIwuxm47AEUTt40yXJC7+YJX8qagq8SfkwKZo9rNf7fDmKURSsMEaN3yvcR0MlCGM4F2TaoxATaEPrYslRCh7mTTj8b03Coh7cXKljR0qi5OZBBpPYoC2xmBGehlbyL+57VS07vqZFwmqUHJZot6qaAmppN4aMgVMiNGlgBT3N5K2QAUMGNDdG0I/vLLq6ReLvleyb8rFyrX8zhy5JSckSLxySWpkFtSJTXCyBN5IW/k3Xl2Xp0P53PWuubMZ07IHzhfv4QKnWw=</latexit><latexit sha1_base64="EenaU/2ZSAmSPlRHB069CbSZVP4=">AAACEXicbVA9SwNBEN3zM55fUUubxSAEi3CXRsugjWUE8wFJCHN7k2TJ3t65uyeEI3/Bxr9iY6GIrZ2d/8bNRxETHww83pthZl6QCK6N5/04a+sbm1vbuR13d2//4DB/dFzXcaoY1lgsYtUMQKPgEmuGG4HNRCFEgcBGMLyZ+I1HVJrH8t6MEuxE0Je8xxkYK3XzxXaAfS4zfJCgFIwuxm47AEUTt40yXJC7+YJX8qagq8SfkwKZo9rNf7fDmKURSsMEaN3yvcR0MlCGM4F2TaoxATaEPrYslRCh7mTTj8b03Coh7cXKljR0qi5OZBBpPYoC2xmBGehlbyL+57VS07vqZFwmqUHJZot6qaAmppN4aMgVMiNGlgBT3N5K2QAUMGNDdG0I/vLLq6ReLvleyb8rFyrX8zhy5JSckSLxySWpkFtSJTXCyBN5IW/k3Xl2Xp0P53PWuubMZ07IHzhfv4QKnWw=</latexit>
d<latexit sha1_base64="eMkyl0Xc7Q4szr458xd07Lq6ZN0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxQ9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gXi6Jt9</latexit><latexit sha1_base64="eMkyl0Xc7Q4szr458xd07Lq6ZN0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxQ9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gXi6Jt9</latexit><latexit sha1_base64="eMkyl0Xc7Q4szr458xd07Lq6ZN0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxQ9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gXi6Jt9</latexit><latexit sha1_base64="eMkyl0Xc7Q4szr458xd07Lq6ZN0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxQ9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gXi6Jt9</latexit>
n<latexit sha1_base64="xAuQZsQKtuX5P8wGJ9zJk8lMua0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxhe2BCBcUk3Jqzgx4lbgFqaICzX7l2wtjmkYgNOVEqZ7rJNrPidSMcpjYXqogIXRMhtAzVJAIlJ/PjpngM6OEeBBL84TGM3VxIieRUlkUmGRE9Egte1PxP6+X6sGVnzORpBoEnS8apBzrGE+bwSGTQDXPDCFUMvNXTEdEEqpNf7YpwV0+eZW06zXXqbl39WrjuqijjE7QKTpHLrpEDXSLmqiFKHpCL+gNvVvP1qv1YX3OoyWrmDlGf2B9/QLysJuH</latexit><latexit sha1_base64="xAuQZsQKtuX5P8wGJ9zJk8lMua0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxhe2BCBcUk3Jqzgx4lbgFqaICzX7l2wtjmkYgNOVEqZ7rJNrPidSMcpjYXqogIXRMhtAzVJAIlJ/PjpngM6OEeBBL84TGM3VxIieRUlkUmGRE9Egte1PxP6+X6sGVnzORpBoEnS8apBzrGE+bwSGTQDXPDCFUMvNXTEdEEqpNf7YpwV0+eZW06zXXqbl39WrjuqijjE7QKTpHLrpEDXSLmqiFKHpCL+gNvVvP1qv1YX3OoyWrmDlGf2B9/QLysJuH</latexit><latexit sha1_base64="xAuQZsQKtuX5P8wGJ9zJk8lMua0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxhe2BCBcUk3Jqzgx4lbgFqaICzX7l2wtjmkYgNOVEqZ7rJNrPidSMcpjYXqogIXRMhtAzVJAIlJ/PjpngM6OEeBBL84TGM3VxIieRUlkUmGRE9Egte1PxP6+X6sGVnzORpBoEnS8apBzrGE+bwSGTQDXPDCFUMvNXTEdEEqpNf7YpwV0+eZW06zXXqbl39WrjuqijjE7QKTpHLrpEDXSLmqiFKHpCL+gNvVvP1qv1YX3OoyWrmDlGf2B9/QLysJuH</latexit><latexit sha1_base64="xAuQZsQKtuX5P8wGJ9zJk8lMua0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxhe2BCBcUk3Jqzgx4lbgFqaICzX7l2wtjmkYgNOVEqZ7rJNrPidSMcpjYXqogIXRMhtAzVJAIlJ/PjpngM6OEeBBL84TGM3VxIieRUlkUmGRE9Egte1PxP6+X6sGVnzORpBoEnS8apBzrGE+bwSGTQDXPDCFUMvNXTEdEEqpNf7YpwV0+eZW06zXXqbl39WrjuqijjE7QKTpHLrpEDXSLmqiFKHpCL+gNvVvP1qv1YX3OoyWrmDlGf2B9/QLysJuH</latexit>
n<latexit sha1_base64="xAuQZsQKtuX5P8wGJ9zJk8lMua0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxhe2BCBcUk3Jqzgx4lbgFqaICzX7l2wtjmkYgNOVEqZ7rJNrPidSMcpjYXqogIXRMhtAzVJAIlJ/PjpngM6OEeBBL84TGM3VxIieRUlkUmGRE9Egte1PxP6+X6sGVnzORpBoEnS8apBzrGE+bwSGTQDXPDCFUMvNXTEdEEqpNf7YpwV0+eZW06zXXqbl39WrjuqijjE7QKTpHLrpEDXSLmqiFKHpCL+gNvVvP1qv1YX3OoyWrmDlGf2B9/QLysJuH</latexit><latexit sha1_base64="xAuQZsQKtuX5P8wGJ9zJk8lMua0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxhe2BCBcUk3Jqzgx4lbgFqaICzX7l2wtjmkYgNOVEqZ7rJNrPidSMcpjYXqogIXRMhtAzVJAIlJ/PjpngM6OEeBBL84TGM3VxIieRUlkUmGRE9Egte1PxP6+X6sGVnzORpBoEnS8apBzrGE+bwSGTQDXPDCFUMvNXTEdEEqpNf7YpwV0+eZW06zXXqbl39WrjuqijjE7QKTpHLrpEDXSLmqiFKHpCL+gNvVvP1qv1YX3OoyWrmDlGf2B9/QLysJuH</latexit><latexit sha1_base64="xAuQZsQKtuX5P8wGJ9zJk8lMua0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxhe2BCBcUk3Jqzgx4lbgFqaICzX7l2wtjmkYgNOVEqZ7rJNrPidSMcpjYXqogIXRMhtAzVJAIlJ/PjpngM6OEeBBL84TGM3VxIieRUlkUmGRE9Egte1PxP6+X6sGVnzORpBoEnS8apBzrGE+bwSGTQDXPDCFUMvNXTEdEEqpNf7YpwV0+eZW06zXXqbl39WrjuqijjE7QKTpHLrpEDXSLmqiFKHpCL+gNvVvP1qv1YX3OoyWrmDlGf2B9/QLysJuH</latexit><latexit sha1_base64="xAuQZsQKtuX5P8wGJ9zJk8lMua0=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxhe2BCBcUk3Jqzgx4lbgFqaICzX7l2wtjmkYgNOVEqZ7rJNrPidSMcpjYXqogIXRMhtAzVJAIlJ/PjpngM6OEeBBL84TGM3VxIieRUlkUmGRE9Egte1PxP6+X6sGVnzORpBoEnS8apBzrGE+bwSGTQDXPDCFUMvNXTEdEEqpNf7YpwV0+eZW06zXXqbl39WrjuqijjE7QKTpHLrpEDXSLmqiFKHpCL+gNvVvP1qv1YX3OoyWrmDlGf2B9/QLysJuH</latexit>
p<latexit sha1_base64="fTBv2t+q32zM4cVtTXb0OO+6WHE=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxE9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gX12JuJ</latexit><latexit sha1_base64="fTBv2t+q32zM4cVtTXb0OO+6WHE=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxE9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gX12JuJ</latexit><latexit sha1_base64="fTBv2t+q32zM4cVtTXb0OO+6WHE=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxE9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gX12JuJ</latexit><latexit sha1_base64="fTBv2t+q32zM4cVtTXb0OO+6WHE=">AAACDHicbVC7TsMwFHXKq4RXgZHFokJCDFXSBcYKFsYi0YfURJXj3LZWHSfYDlIU9QNY+BUWBhBi5QPY+BvcNkNpOZKlo3PO1fU9QcKZ0o7zY5XW1jc2t8rb9s7u3v5B5fCoreJUUmjRmMeyGxAFnAloaaY5dBMJJAo4dILxzdTvPIJULBb3OkvAj8hQsAGjRBupX6l6AQyZyOFBEClJdjGxE9sDES4oJuXUnBnwKnELUkUFmv3KtxfGNI1AaMqJUj3XSbSfE6kZ5TCxvVRBQuiYDKFnqCARKD+fHTPBZ0YJ8SCW5gmNZ+riRE4ipbIoMMmI6JFa9qbif14v1YMrP2ciSTUIOl80SDnWMZ42g0MmgWqeGUKoZOavmI6IJFSb/mxTgrt88ipp12uuU3Pv6tXGdVFHGZ2gU3SOXHSJGugWNVELUfSEXtAbereerVfrw/qcR0tWMXOM/sD6+gX12JuJ</latexit>
J/ <latexit sha1_base64="gYrGH65T0e/aE/OYf8IXisLfvBA=">AAACEXicbVBNS8NAEN3Urxq/oh69BItQPNSkFz0WvYinCvYDmlA2m2m7dLOJuxshhP4FL/4VLx4U8erNm//GbZuDtj4YeLw3w8y8IGFUKsf5Nkorq2vrG+VNc2t7Z3fP2j9oyzgVBFokZrHoBlgCoxxaiioG3UQAjgIGnWB8NfU7DyAkjfmdyhLwIzzkdEAJVlrqW1UvgCHlOdxzLATOTifmzZnXlNT0gIe/5L5VcWrODPYycQtSQQWafevLC2OSRsAVYVjKnuskys+xUJQwmJheKiHBZIyH0NOU4wikn88+mtgnWgntQSx0cWXP1N8TOY6kzKJAd0ZYjeSiNxX/83qpGlz4OeVJqoCT+aJBymwV29N47JAKIIplmmAiqL7VJiMsMFE6RFOH4C6+vEza9Zrr1NzbeqVxWcRRRkfoGFWRi85RA12jJmohgh7RM3pFb8aT8WK8Gx/z1pJRzByiPzA+fwBQZJ1M</latexit><latexit sha1_base64="gYrGH65T0e/aE/OYf8IXisLfvBA=">AAACEXicbVBNS8NAEN3Urxq/oh69BItQPNSkFz0WvYinCvYDmlA2m2m7dLOJuxshhP4FL/4VLx4U8erNm//GbZuDtj4YeLw3w8y8IGFUKsf5Nkorq2vrG+VNc2t7Z3fP2j9oyzgVBFokZrHoBlgCoxxaiioG3UQAjgIGnWB8NfU7DyAkjfmdyhLwIzzkdEAJVlrqW1UvgCHlOdxzLATOTifmzZnXlNT0gIe/5L5VcWrODPYycQtSQQWafevLC2OSRsAVYVjKnuskys+xUJQwmJheKiHBZIyH0NOU4wikn88+mtgnWgntQSx0cWXP1N8TOY6kzKJAd0ZYjeSiNxX/83qpGlz4OeVJqoCT+aJBymwV29N47JAKIIplmmAiqL7VJiMsMFE6RFOH4C6+vEza9Zrr1NzbeqVxWcRRRkfoGFWRi85RA12jJmohgh7RM3pFb8aT8WK8Gx/z1pJRzByiPzA+fwBQZJ1M</latexit><latexit sha1_base64="gYrGH65T0e/aE/OYf8IXisLfvBA=">AAACEXicbVBNS8NAEN3Urxq/oh69BItQPNSkFz0WvYinCvYDmlA2m2m7dLOJuxshhP4FL/4VLx4U8erNm//GbZuDtj4YeLw3w8y8IGFUKsf5Nkorq2vrG+VNc2t7Z3fP2j9oyzgVBFokZrHoBlgCoxxaiioG3UQAjgIGnWB8NfU7DyAkjfmdyhLwIzzkdEAJVlrqW1UvgCHlOdxzLATOTifmzZnXlNT0gIe/5L5VcWrODPYycQtSQQWafevLC2OSRsAVYVjKnuskys+xUJQwmJheKiHBZIyH0NOU4wikn88+mtgnWgntQSx0cWXP1N8TOY6kzKJAd0ZYjeSiNxX/83qpGlz4OeVJqoCT+aJBymwV29N47JAKIIplmmAiqL7VJiMsMFE6RFOH4C6+vEza9Zrr1NzbeqVxWcRRRkfoGFWRi85RA12jJmohgh7RM3pFb8aT8WK8Gx/z1pJRzByiPzA+fwBQZJ1M</latexit><latexit sha1_base64="gYrGH65T0e/aE/OYf8IXisLfvBA=">AAACEXicbVBNS8NAEN3Urxq/oh69BItQPNSkFz0WvYinCvYDmlA2m2m7dLOJuxshhP4FL/4VLx4U8erNm//GbZuDtj4YeLw3w8y8IGFUKsf5Nkorq2vrG+VNc2t7Z3fP2j9oyzgVBFokZrHoBlgCoxxaiioG3UQAjgIGnWB8NfU7DyAkjfmdyhLwIzzkdEAJVlrqW1UvgCHlOdxzLATOTifmzZnXlNT0gIe/5L5VcWrODPYycQtSQQWafevLC2OSRsAVYVjKnuskys+xUJQwmJheKiHBZIyH0NOU4wikn88+mtgnWgntQSx0cWXP1N8TOY6kzKJAd0ZYjeSiNxX/83qpGlz4OeVJqoCT+aJBymwV29N47JAKIIplmmAiqL7VJiMsMFE6RFOH4C6+vEza9Zrr1NzbeqVxWcRRRkfoGFWRi85RA12jJmohgh7RM3pFb8aT8WK8Gx/z1pJRzByiPzA+fwBQZJ1M</latexit>
J/ <latexit sha1_base64="gYrGH65T0e/aE/OYf8IXisLfvBA=">AAACEXicbVBNS8NAEN3Urxq/oh69BItQPNSkFz0WvYinCvYDmlA2m2m7dLOJuxshhP4FL/4VLx4U8erNm//GbZuDtj4YeLw3w8y8IGFUKsf5Nkorq2vrG+VNc2t7Z3fP2j9oyzgVBFokZrHoBlgCoxxaiioG3UQAjgIGnWB8NfU7DyAkjfmdyhLwIzzkdEAJVlrqW1UvgCHlOdxzLATOTifmzZnXlNT0gIe/5L5VcWrODPYycQtSQQWafevLC2OSRsAVYVjKnuskys+xUJQwmJheKiHBZIyH0NOU4wikn88+mtgnWgntQSx0cWXP1N8TOY6kzKJAd0ZYjeSiNxX/83qpGlz4OeVJqoCT+aJBymwV29N47JAKIIplmmAiqL7VJiMsMFE6RFOH4C6+vEza9Zrr1NzbeqVxWcRRRkfoGFWRi85RA12jJmohgh7RM3pFb8aT8WK8Gx/z1pJRzByiPzA+fwBQZJ1M</latexit><latexit sha1_base64="gYrGH65T0e/aE/OYf8IXisLfvBA=">AAACEXicbVBNS8NAEN3Urxq/oh69BItQPNSkFz0WvYinCvYDmlA2m2m7dLOJuxshhP4FL/4VLx4U8erNm//GbZuDtj4YeLw3w8y8IGFUKsf5Nkorq2vrG+VNc2t7Z3fP2j9oyzgVBFokZrHoBlgCoxxaiioG3UQAjgIGnWB8NfU7DyAkjfmdyhLwIzzkdEAJVlrqW1UvgCHlOdxzLATOTifmzZnXlNT0gIe/5L5VcWrODPYycQtSQQWafevLC2OSRsAVYVjKnuskys+xUJQwmJheKiHBZIyH0NOU4wikn88+mtgnWgntQSx0cWXP1N8TOY6kzKJAd0ZYjeSiNxX/83qpGlz4OeVJqoCT+aJBymwV29N47JAKIIplmmAiqL7VJiMsMFE6RFOH4C6+vEza9Zrr1NzbeqVxWcRRRkfoGFWRi85RA12jJmohgh7RM3pFb8aT8WK8Gx/z1pJRzByiPzA+fwBQZJ1M</latexit><latexit sha1_base64="gYrGH65T0e/aE/OYf8IXisLfvBA=">AAACEXicbVBNS8NAEN3Urxq/oh69BItQPNSkFz0WvYinCvYDmlA2m2m7dLOJuxshhP4FL/4VLx4U8erNm//GbZuDtj4YeLw3w8y8IGFUKsf5Nkorq2vrG+VNc2t7Z3fP2j9oyzgVBFokZrHoBlgCoxxaiioG3UQAjgIGnWB8NfU7DyAkjfmdyhLwIzzkdEAJVlrqW1UvgCHlOdxzLATOTifmzZnXlNT0gIe/5L5VcWrODPYycQtSQQWafevLC2OSRsAVYVjKnuskys+xUJQwmJheKiHBZIyH0NOU4wikn88+mtgnWgntQSx0cWXP1N8TOY6kzKJAd0ZYjeSiNxX/83qpGlz4OeVJqoCT+aJBymwV29N47JAKIIplmmAiqL7VJiMsMFE6RFOH4C6+vEza9Zrr1NzbeqVxWcRRRkfoGFWRi85RA12jJmohgh7RM3pFb8aT8WK8Gx/z1pJRzByiPzA+fwBQZJ1M</latexit><latexit sha1_base64="gYrGH65T0e/aE/OYf8IXisLfvBA=">AAACEXicbVBNS8NAEN3Urxq/oh69BItQPNSkFz0WvYinCvYDmlA2m2m7dLOJuxshhP4FL/4VLx4U8erNm//GbZuDtj4YeLw3w8y8IGFUKsf5Nkorq2vrG+VNc2t7Z3fP2j9oyzgVBFokZrHoBlgCoxxaiioG3UQAjgIGnWB8NfU7DyAkjfmdyhLwIzzkdEAJVlrqW1UvgCHlOdxzLATOTifmzZnXlNT0gIe/5L5VcWrODPYycQtSQQWafevLC2OSRsAVYVjKnuskys+xUJQwmJheKiHBZIyH0NOU4wikn88+mtgnWgntQSx0cWXP1N8TOY6kzKJAd0ZYjeSiNxX/83qpGlz4OeVJqoCT+aJBymwV29N47JAKIIplmmAiqL7VJiMsMFE6RFOH4C6+vEza9Zrr1NzbeqVxWcRRRkfoGFWRi85RA12jJmohgh7RM3pFb8aT8WK8Gx/z1pJRzByiPzA+fwBQZJ1M</latexit>
Quarkonium in nuclei:
— scattering amplitude is enhanced
— formation of a new exotic nuclear state
— adds a new flavor axis in the nuclear e.o.s.
Low-momentum quarkonium in a nucleus
— Quarkonium interacts with light quarks in nucleons by exchanging gluons with wavelengths
� ⇠ rN
— Size of quarkonium
� � 2 rJ/
rJ/ ⇠ 0.35 fm
Quarkonium behaves as a small color dipole
immersed in a uniform gluon field
hTNi ⇠3
5
k2F2mN
⇠ 20MeV ⌧ ⇤QCD
rN ⇠qhr2chi ' 0.88 fm ⇠ ⇤�1
QCD
Embbeding quakonium-nucleon into aNonrelativistic nuclear many-body problem
quarkonium-nucleon
G.K., A.W. Thomas & K. Tsushima,PPNP 100, 161 (2018)
Hartree-Fock equation— for quarkonium in a nucleus
quarkonium-nucleus potential
nuclear density functional
Neglecting back reaction of quarkonium on nucleons, take density from a model or experiment
Degrees of freedom & Scales & Power counting
DOF: nucleons, quarkonia, pions
terms of the effective Lagrangian organized in powers of
EN , E� ⇠ m⇡ ⌧ ⇤� ⇠ 1GeVScales:
Power counting:(~ Weinberg for NN)
m⇡
⇤�
Loops: dimensional regularization
Low-energy quarkonium-nucleon dynamics
Quarkonium-nucleon dynamics, e.g bound to nucleus occurs at energies
E�N ⇠k2�N2µ�N
<m2
⇡
⇤�⌧ m⇡
Integrate out the pion
Matching
Renormalization of couplings + van der Waals
C0 = c0 + 4m2⇡dm +
9g2Am2⇡c0
64⇡2F 2
✓log
m2⇡
⌫2+
2
3
◆+
3g2Am3⇡
64⇡F 2(5cdi � 3cm)
D1 = d1 +g2Am⇡
256⇡F 2(23cdi � 5cm)
Dj = dj for j = 2, 3 and 4
Long-distance part of QN potential— vdW force
No free parameters here:— trace anomaly— chiral physics
First, model-independent derivation of a quarkonium-nucleon van der Waals force
For :
V (r) =3g2Am
4⇡ (cdi + cm)
128⇡2F 2
e�2m⇡r
r2
r � 1
2m⇡
To extrapolate lattice data to physical quark masses, need:
mN = m̂N � 4c1m2⇡ � 3g2Am
3⇡
32⇡F 2
m� = m̂� � F 2cmm2⇡
Unknown contact couplings— get them from lattice QCD
Lattice: [27] Yokokawa et al PRD 74, 034504 (2006) [28] Liu et al PoS (LATTICE) 2008, 112 (2008) [29] Kanaway & Sasaki PoS (LATTICE) 2010, 156 (2010)
↵J/ <latexit sha1_base64="0V3f1b4rJzq6sVrOYsfr/d1Z8+4=">AAACGnicbVC7TsMwFHXKq5RXgZElokJCDCXpAmMFC2IqEn1IbRTduLetVccJtoMURf0OFn6FhQGE2BALf4P7GErLkSwdn3Pvte8JYs6UdpwfK7eyura+kd8sbG3v7O4V9w8aKkokxTqNeCRbASjkTGBdM82xFUuEMODYDIbXY7/5iFKxSNzrNEYvhL5gPUZBG8kvup0A+0xk+CBASkjPRoUO8HgAfnZ73qkpZu4ounO+Xyw5ZWcCe5m4M1IiM9T84lenG9EkRKEpB6XarhNrLwOpGeVo5icKY6BD6GPbUAEhKi+brDayT4zStXuRNEdoe6LOd2QQKpWGgakMQQ/UojcW//Paie5dehkTcaJR0OlDvYTbOrLHOdldJpFqnhoCVDLzV5sOQALVJs2CCcFdXHmZNCpl1ym7d5VS9WoWR54ckWNySlxyQarkhtRInVDyRF7IG3m3nq1X68P6nJbmrFnPIfkD6/sX4vahXw==</latexit><latexit sha1_base64="0V3f1b4rJzq6sVrOYsfr/d1Z8+4=">AAACGnicbVC7TsMwFHXKq5RXgZElokJCDCXpAmMFC2IqEn1IbRTduLetVccJtoMURf0OFn6FhQGE2BALf4P7GErLkSwdn3Pvte8JYs6UdpwfK7eyura+kd8sbG3v7O4V9w8aKkokxTqNeCRbASjkTGBdM82xFUuEMODYDIbXY7/5iFKxSNzrNEYvhL5gPUZBG8kvup0A+0xk+CBASkjPRoUO8HgAfnZ73qkpZu4ounO+Xyw5ZWcCe5m4M1IiM9T84lenG9EkRKEpB6XarhNrLwOpGeVo5icKY6BD6GPbUAEhKi+brDayT4zStXuRNEdoe6LOd2QQKpWGgakMQQ/UojcW//Paie5dehkTcaJR0OlDvYTbOrLHOdldJpFqnhoCVDLzV5sOQALVJs2CCcFdXHmZNCpl1ym7d5VS9WoWR54ckWNySlxyQarkhtRInVDyRF7IG3m3nq1X68P6nJbmrFnPIfkD6/sX4vahXw==</latexit><latexit sha1_base64="0V3f1b4rJzq6sVrOYsfr/d1Z8+4=">AAACGnicbVC7TsMwFHXKq5RXgZElokJCDCXpAmMFC2IqEn1IbRTduLetVccJtoMURf0OFn6FhQGE2BALf4P7GErLkSwdn3Pvte8JYs6UdpwfK7eyura+kd8sbG3v7O4V9w8aKkokxTqNeCRbASjkTGBdM82xFUuEMODYDIbXY7/5iFKxSNzrNEYvhL5gPUZBG8kvup0A+0xk+CBASkjPRoUO8HgAfnZ73qkpZu4ounO+Xyw5ZWcCe5m4M1IiM9T84lenG9EkRKEpB6XarhNrLwOpGeVo5icKY6BD6GPbUAEhKi+brDayT4zStXuRNEdoe6LOd2QQKpWGgakMQQ/UojcW//Paie5dehkTcaJR0OlDvYTbOrLHOdldJpFqnhoCVDLzV5sOQALVJs2CCcFdXHmZNCpl1ym7d5VS9WoWR54ckWNySlxyQarkhtRInVDyRF7IG3m3nq1X68P6nJbmrFnPIfkD6/sX4vahXw==</latexit><latexit sha1_base64="0V3f1b4rJzq6sVrOYsfr/d1Z8+4=">AAACGnicbVC7TsMwFHXKq5RXgZElokJCDCXpAmMFC2IqEn1IbRTduLetVccJtoMURf0OFn6FhQGE2BALf4P7GErLkSwdn3Pvte8JYs6UdpwfK7eyura+kd8sbG3v7O4V9w8aKkokxTqNeCRbASjkTGBdM82xFUuEMODYDIbXY7/5iFKxSNzrNEYvhL5gPUZBG8kvup0A+0xk+CBASkjPRoUO8HgAfnZ73qkpZu4ounO+Xyw5ZWcCe5m4M1IiM9T84lenG9EkRKEpB6XarhNrLwOpGeVo5icKY6BD6GPbUAEhKi+brDayT4zStXuRNEdoe6LOd2QQKpWGgakMQQ/UojcW//Paie5dehkTcaJR0OlDvYTbOrLHOdldJpFqnhoCVDLzV5sOQALVJs2CCcFdXHmZNCpl1ym7d5VS9WoWR54ckWNySlxyQarkhtRInVDyRF7IG3m3nq1X68P6nJbmrFnPIfkD6/sX4vahXw==</latexit>
Are there quarkonium-nucleonbound states at this order in pQNEFT?
Scattering amplitude (s-wave)
a0 =
µ�N
2⇡
c0 + 4dmm2
⇡ +
9g2Am2⇡c0
64⇡2F 2
✓log
m2⇡
⌫2+
2
3
◆+
3g2A64⇡F 2
m3⇡ (5cdi � 3cm)
�
A =
2⇡
µ�N
1
p cot � � ip=
2⇡
µ�N
1
� 1a0
+
12r0p
2+ . . .
r0 =8⇡
µ�Nc20
(d1 + d2) +
g2A256⇡F 2
m⇡ (23cdi � 5cm)
�
No quarkonium-nucleon bound states within the applicability of the present calculation:
|p�N | m⇡
YES, for sufficiently large nuclei
Are there quarkonium-nucleusbound states at this order in pQNEFT?
Perspectives
Charmed hypernuclei— experiments: LHC (existing data), future FAIR, J-PARC, … — theory: lattice crucial for progress
Quarkonium-nucleon— experiments: JLab data (2018?) LHC (existing data), PANDA (2025)— theory: EFT, lattice