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## Mannque Rho CEA Saclay

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**Nuclear tensor forces and a signal for**scale-chiral symmetry in nuclei What I would propose to work out at RAON Mannque Rho CEA Saclay 2nd APCTP-ECT* Workshop 2015**Monday’s talk:**• Start with scale-invariant hidden local symmetry • with dilaton s and pions p coupled to matter fields • r and w subject to explicit symmetry breaking away from • the IR fixed point and current quark masses. • The degrees of freedom are the nucleons (N), the hidden • gauge mesons r & w and a multiplet of pNG s and p‘s. • The effective Lagrangian is matched via correlators to QCD • at the matching scale LM from which the EFT picks up • IDD (intrinsic density dependence) from QCD condensates. • Nuclear dynamics is described by “double decimation” RG • flows from LM, the first decimation leading to Vlowk endowed • with IDD and the second to what corresponds to Fermi-liquid • fixed point approach to many body problem. • d) Monday’s talk was focused on dense matter, n > n0 .**This talk**I will focus on processes near nuclear matter, in particular connected to nuclear tensor forces. I will then propose how to “see” the manifestation – i.e., a signal – of scale-chiral symmetry of QCD in nuclear medium. Perhaps in RAON-type physics!(?) Debate between Gerry Brown and Steven Weinberg in early 1990’s.**To go from soft-pion scale up to higher scale**• At E ≈ 0 , Soft pion/current algebra applies: Write • Notice An Invariance: This is a “redundancy” , exploit it to gauge the symmetry to “hidden local symmetry (HLS)” à la Harada and Yamawaki. Provides potentially powerful tool to go toward the vector meson scale.**Brown-Weinberg debate**On EFT in nuclear physics Brown (espousing HLS): “the r meson is essential in nuclear physics”. Weinberg (espousing standard pChPT): “the r is not needed, its effect can be incorporated in counter terms involving pions only” Weinberg’s “mended symmetry” acknowledges Brown’s thesis**Something deep about**HLS is involved in the debate Approaching QCD with effective fields involves Infinite towers of vector mesons as hidden gauge fields Georgi et al. 1999 Moose construction by • One vector meson:**Two vector mesons …**• Many (K=) vector mesons in “open moose”: where**And take continuum limit with K = , e→0 : → 5D YM**• Chiral symmetry in 4D is elevated to a local gauge symmetry in 5D. It also comes from string theory, e.g., Sakai and Sugimoto 2003. So at some mass scale, vector mesons must appear. But the question is: Is any of them essential in nuclear physics? The answer is most likely YES.**Tensor forces:**An old problem with a new twist**What scale-chiral symmetry predicts for nuclear**tensor forces p, r N N IDD (intrinsic density dependence), representing matching of EFT and QCD, in the “bare” parameters of the EFT Lagrangian reflects the vacuum change in nuclear matter.**Crucial ingredient: chiral**symmetry locked to scale symmetry Crewther and Tunstall 2013 • At aIR, in the chiral limit , mDm =qmm= mAm = 0. • s (“dialon”) and p (pseudo) NG bosons • fp <c> = fs • Dilaton condensate provides IDD’s to EFT Lagrangian**2-phase baryon structure via topology**n= density**Consequence on the nucleon mass**• “Emergent” parity-doublet symmetry for nucleons: m* = m0 + D (S*) Y.L. Ma et al 2013 m0 (0.6 – 0.8) mN n1/2**IDDs drastically modify tensor forces**• For density n < n1/2: IDD • For density n n1/2: n1/2 n=0 n=n0 p+r n=2n0 Net tensor decreases Net tensor increases The pion tensor is protected by chiral symmetry, so only the r tensor is affected by density.**Impact on EoS**For matter with excess of neutrons (i.e., neutron star) the “symmetry energy” Esym plays a dominant role.**Esymby closure approximation**G.E. Brown and R. Machleidt n=n0 n=0 n > n1/2 Increasing tensor Decreasing tensor Esym is dominated by tensor forces cusp n1/2**Esymfrom half-skyrmion matter**H.K. Lee, B.Y. Park, R. 2010 The Esymcalculated with theIDDs extracted from the topology change matches the Esym given by the order 1/Nc (rotational quantized) skyrmion energy. This supports the robustness of using the topology change for the IDDs.**Esymin Vlowk**Paeng, Kuo, Lee, R n1/2**Surprising things happen in**Finite nuclei and nuclear matter**Use “Double decimation”**Bogner, Kuo et al, arXiv:nucl-th/0305035 • There are roughly two RG decimations in • nuclear many-body EFT • Decimate from Lcto ~ (2-3) fm-1or ~ 400 MeV • up to which accurate NN scattering data are available, • say, Elab ≤ 350 MeV. Call it Ldata. Yields VlowK • Decimate from Ldata to Fermi surface scale LFS using • VlowK operative up to Elab. This derives Fermi liquid • fixed point theory valid for nuclear matter. • Fluctuate around Fermi surface; Many body technique**Vlowk- RG approach**Kuo, Brown, Holt, Schwenk et al**Observation but no proof**Tensor forces are not renormalized !!**Non-renormalization of the tensor force**In deuteron Tom Kuo 2013**In second decimation**Ring diagram summation À la Kuo et al.**Tensor forces in shell evolution**In exotic nuclei T. Otsuka 05 Monopole matrix element Evolution of single-particle energy**Conclusion**In light as well as complex nuclei at low density involving no IDD, i.e., . I take one step further and assume that the b remains zero independently of the IDD. This means that tensor forces with IDD’s for varying densities are non-renormalized.**How to “see” IDD**• Tensor forces are “scale-independent” at • any density, i.e., fixed-point quantity. • If one can dial the density, then tensor forces will • offer a pristine signal for IDD free of renormalization. • Zero-in on processes probing tensor forces.**An “evidence”: C14 dating**probes scaling J.W. Holt et al, PRL 100, 062501 (08) n=0 n=n0**Caveat? Many-body forces**The long lifetime of C14 has also been explained by 3-body forces without IDD (Holt and Weise 2010, Maris et al 2011…). Way out: The contact 3-body force (c) is of the same mass-scale as IDD. In medium with HLS, it is encoded in the IDD. With p + r exchange, the contact term should be negligible. (a) (b) (c)**What are the observables in RIB physics that**can zero-in -- like in the C14 case – on tensor forces acting in varying density regimes? If feasible, it will give a pristine signal if one can reach a density regime n1/2 ~ 2n0.