Hadrons in the Nuclear Medium

Mesons in Nuclei

Steffen Strauch University of South Carolina

26th Annual Hampton University Graduate Studies Program Jefferson Lab, Newport News, Virginia May 31 - June 17, 2011 108 Meson Masses From A Nambu- Jona-Lasinio Model

In the spontaneously broken phase, the quarks acquire a dynamical mass which is different from their current (bare) mass mu. ˆ M = M − mu )

dynamical quark bare quark V mass mass e G (

• JP = 0±: The scalar σ-meson follows the ) ρ behavior of the dynamical quark mass and ( decreases sharply with density. In the M restored phase, the pion and the σ-meson have the same mass, which increases with density.

• JP = 1±: The ρ and the ω are fairly independent of density, whereas the A1, mass decreases with density and joins the ρ.

V. Bernard and U.G. Meissner, Nucl. Phys. A489, 647 (1988). 109 Scaling Laws

• Since hadron masses are closely connected with the chiral condensate, one expects that they scale with density accordingly. • By using effective chiral Lagrangians Brown and Rho ﬁnd an universal, approximate, in-medium scaling law: in-medium f * (ρ) m* (ρ) m* (ρ) M * (ρ) 〈qq〉* Φ(ρ) = π ≈ σ ≈ V ≈ ≈ fπ mσ mV M 〈qq〉 free Φ(ρ = ρ0 ) ≈ 0.78

• Hatsuda and Lee found for V = ρ, ω:

* mV (ρ) ⎛ ρ ⎞ ≈ 1− 0.18⎜ ⎟ mV ⎝ ρ0 ⎠

G.E. Brown, Mannque Rho, Phys. Rev. Lett. 66, 2720 (1991) and Phys. Rep. 363, 85 (2002); T. Hatsuda and Su Houng Lee, Phys. Rev. C. 46, 34R (1992); W. Weise, Nucl. Phys. A 553, 59c (1993) 110 In-Medium ρ Spectral Functions

• In-medium properties of mesons (π,η,ρ) and baryon resonances in cold nuclear matter within a coupled-channel analysis • Constituents of the model: π, η, and ρ meson and the nucleon and baryonic resonances.

in vacuum in medium

π π N(1520) ρ ρ ρ ρ ρ ρ ⇒ Δ(1232) + + ... π N-1 N-1

M. Post, S. Leupold, U. Mosel, Nucl. Phys. A 741, 81 (2004);K. Nakamura et al. (Particle Data Group), JP G 37, 075021 (2010) 111 In-Medium ρ Spectral Functions (II)

• Signiﬁcant shift of spectral strength down to smaller invariant masses generated by −1 its coupling to the D13(1520)N state • At smaller momenta, the coupling to this state leads to a pronounced double-peak structure in the spectral function.

M. Post, S. Leupold, U. Mosel, Nucl. Phys. A 741, 81 (2004). 112 Chiral Condensate as a Function of ρB and T

• Study the medium modiﬁcation of vector mesons • The predicted medium modiﬁcations are large, even at normal nuclear density Vacuu m

Elementary Reactions • cold & dense ρB ≤ ρ0; T = 0 • γA, πA, ... → V + x • Example: CLAS g7 experiment at JLab

Heavy Ion Reactions: • hot & dense ρB >> ρ0; T > 0 Restoration of chiral symmetry? • AA → V + x • Example: CERES experiment at the SPS NJL Model: S. Klimt et al., Phys. Lett. B 249, 386 (1990). 113 Properties of Vector Mesons

Amsler et al., (The Particle Data Group), Phys. Lett. B 667, 1 (2008)

Mass Γ cτ Main Γe+e-/Γtot Γμ+μ-/Γtot (MeV/c2) (MeV/c2) (fm) decay (⨉ 10-5) (⨉ 10-5)

ρ0 775.49 ± 0.34 149.4 ± 1.0 1.3 π+π- 4.7 4.6

ω 782.65 ± 0.12 8.49 ± 0.08 23.2 π+π-π0 7. 2 9.0

ϕ 1019.455 ± 0.020 4.26 ± 0.04 46.2 K+K- 29.7 28.6

• Due to short life time, ρ0 mesons have larger probability to decay in Di-lepton ﬁnal-state interactions medium. invariant mass • Di-leptons (no FSI) carry “clean e+ information” of the system at the large e- time of production (either a nucleus 2 ρ 2 µ µ π or a ﬁre ball in HI collisions). m = p + + p − ρ small ee ( e e ) • Small di-lepton decay branching ratio π

C. Djalali, 2009 Ecole Internationale Joliot Curie 114 Processes Producing Di-Leptons

• Many processes can produce di-leptons

Direct decays: ρ → e+e−, ω → e+e−, ϕ → e+e−, + − + − J/ψ → e e , ψ’ → e e Dalitz decays: Δ → Ne+e−, η → e+e−γ, π0 → e+e−γ, ω → π0e+e−, ϕ → ηe+e− Heavy ﬂavor: cc → Xe+e−, bb → Xe+e− Drell-Yan: qq̄ → e+e− Pair production: γ → e+e−

• Combinatorial background • Sophisticated Monte-Carlo and transport calculations are needed to compare the measured (and background-subtracted) di-lepton invariant mass spectra to background from known processes.

115 Combinatorial Background

• Di-leptons from a given di-lepton decay are correlated and have always (+,-) or (-,+) charge. • Di-lepton pairs from two uncorrelated reactions may consist of (+,+), (-,-), (+,-), and (-,+) charge pairs. e+ ‣ Probability p+ for a positive lepton γ ρ * ‣ Probability p- for a negative lepton

e- pCB = p+ p− + p− p+ = 2 p+ p−

a ρπ0 0 / - N * e p = p p = ++ a + + + N e+

N−− p = p p = e- − − − N 0 * a π/0 e+ assuming same detector a acceptance and efﬁciency for NCB = 2 N++ N−− positively and negatively charged leptons 116 CERES Experiment at the SPS

×103 -1

) + − 2 1000 • e e pair production in unlike-sign pairs 208 197 combinatorial background central Pb– Au 800 collisions at 158 AGeV/c /dm(1 GeV/c ee

dN 600

400

200 S/B = 1/22 for • Unlike-sign pair yield 2 mee > 0.2 GeV/c (histogram) and combinatorial background 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 2 (dashed curve) mee (GeV/c )

Adamova et al., Phys. Lett. B 666, 524 (2008); http://alice.web.cern.ch/Alice/html/challenge/ 117 CERES Experiment at the SPS (Cocktail)

-4 -1

) 10 2 CERES/NA45 Pb-Au 158 A GeV • “Hadronic Cocktail”. The m /m 5 7 % trig tot yield from hadronic p >200 MeV/c t decays in A–A collisions -5 >35 mrad 10 Oee >(100 MeV/c 2.1/

ee (a) composition inside the 10-6 /dm

ee ﬁreball is ﬁxed) d A

ee 2 10 0.2 < mee < 1.1 GeV/c , A t 0 A /

ee ee ee / 0 A A the data are enhanced t q ee A d  l over the cocktail by a A -8 ee 10 a factor ≃ 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 2 mee (GeV/c )

Adamova et al., Phys. Lett. B 666, 524 (2008). 118 CERES Experiment at the SPS (Results)

-6 -1 10 ) × 2 1.8 In order to exhibit the shape of cocktail l • 1.6 dropping l mass the in-medium contribution, the in-medium hadronic hadronic cocktail (excluding the 1.4 >(100 MeV/c

ch (a) ρ meson) is subtracted from the 1.2

0.6 The e+e− data favor present models 0.4 including a strong broadening of 0.2 the ρ-spectral function in a hot and dense hadronic medium over a 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 2 density dependent ρ mass shift. mee (GeV/c )

Adamova et al., Phys. Lett. B 666, 524 (2008). 119 CLAS g7a Experiment

e+ ρ: cτ ≈ 1.3 fm e- ρ decay inside nucleus

γ e+

ω, φ decay outside nucleus

12000 Pb e- 10000 8000 γ A → ρA → e+e− A 6000

Counts Fe Ti

4000 C C C C 2H 2 2000 • Targets: H, C, Ti, Fe, (Pb)

0 -25 -20 -15 -10 -5 0 5 ρ z (cm) • Momentum of between 0.8 and 2 GeV

CLAS Experiment E01-112 (g7a) Spokespersons: C. Djalali, M. Kossov, D. Weygand; M. Wood et al., Phys. Rev. C 78, 015201 (2008); R. Nasseripour et al., Phys Rev. Lett. 99, 262302 (2007) 120 CLAS g7a Experiment (Event Selection)

(a) 2 2 µ µ m = p + + p − ee ( e e )

+ − e e invariant mass spectrum summed over all targets (b) same (a) before applying any cuts to sector pair candidates (b) after vertex position and

timing cuts, and (c) after the vertex position, ω (c) timing, lepton momenta, and different-sector cuts ρ ϕ M. Wood et al., Phys. Rev. C 78, 015201 (2008) 121 CLAS g7a Experiment (Combinatorial Background)

2 calculations from transport distributions cocktail H C S/B = 2-3

and the data ﬁt to C removal of combinatorial background Fe/Ti Fe/Ti ω ρ ϕ

M. Wood et al., Phys. Rev. C 78, 015201 (2008) 122 The ρ-Mass Spectra

C Fe Extraction of ρ-mass spectra after subtraction of ω and φ contributions and combinatorial background.

e+e- Invariant Mass (GeV)

Mass (MeV/c2) Width (MeV/c2) Mass (MeV/c2) Width (MeV/c2) Target CLAS data CLAS data Giessen BUU Giessen BUU 12C 762.5 ± 3.7 176.4 ± 9.5 773.8 ± 0.9 177.6 ± 2.1 48Ti-56Fe 779.0 ± 5.7 217.7 ± 14.5 773.8 ± 5.4 202.5 ± 11.6

• The vacuum properties of the ρ meson are: m = 770 MeV/c2 and Γ = 150 MeV. • No mass shift; broadening of the ρ width is consistent with many-body effects.

R. Nasseripour et al., Phys. Rev. Lett. 99, 262302 (2007); M.H. Wood et al., Phys. Rev. C 78, 015201 (2008). 123 Hadronic Model

140 (a) (b) full calculation 100 full calculation l = 0.3 l 120 12 0 56 l = 0.4 l0 C 80 Fe 100 80 60 60 40 40 20 20

Yield [arb. units] Yield [arb. units] 0 0 -20 -20 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 e+e- inv. mass [GeV] e+e- inv. mass [GeV]

• Good description found in an effective hadronic model combing in a consistent way an elementary production amplitude (γp→e+e-p) with an in-medium ρ propagator. • To increase the sensitivity to medium effects: ‣ provide absolute normalization ‣ increase of the mass number to A ≃ 200 ‣ cut on small outgoing lepton pair momenta F. Riek et al., Phys. Rev. Lett. C 82, 015202 (2010). 124 Deeply-Bound Pionic Atom Spectroscopy

• The 1s wave function of π- bound to π- a heavy nucleus overlaps appreciably with the nuclear density distribution, and hence the in-medium 1s modiﬁcation of the pion properties may have detectable effects on the binding energy and/or width. • Experiment idea: ‣ Implant a π- in a nuclear medium of density ρ (deeply bound 1s wave) 〈qq〉ρ σ ≈ 1− N ρ 2 2 ‣ Determine the 1s binding energies 〈qq〉0 mπ fπ and widths precisely 2 b1 f *π (ρ) ‣ Deduce the in-medium value of the ≈ 2 ≈ 1− αρ b *1 (ρ) fπ isovector πN scattering length b1

Ryugo S. Hayano and Tetsuo Hatsuda, Rev. Mod. Phys. 82, 2949 (2010) 125 GSI S236—Sn(d,3He) Experiment

124 3 p(d,3He)/0 Sn(d, He) 30 (1s) - 123Sn Recoil-less / • 3 20 Sn(d, He) kinematics 10 ensures that the

B [MeV] nucleus is in the 012345 0 120 3 ground state. Sn(d, He) 3 0 30 p(d, He)/ 119 (1s)/- Sn b/sr/MeV] µ 20

dE [

1 10 d /

m B [MeV] 2 012345 d 0 • Observed binding energies (B1s) and 116Sn(d,3He) - 30 p(d,3He)/0 widths (Γ1s) of the 1s π states in 115,119,123Sn isotopes. (1s) - 115Sn 20 / • Fitting of B1s and Γ1s of the three Sn 10 isotopes together with those of

B [MeV] symmetric light nuclei, leaving b0, b1, 012345 0 360 365 370 ReB0, and ImB0 as free parameters 3He Kinetic Energy [MeV] K. Suzuki, et al., Phys. Rev. Lett. 92, 072302 (2004). 126 GSI S236—Sn(d,3He) Results

Chiral perturbation theory prediction • Enhancement of the b1 _l 0 0.5 0.4 0.3 0.2 0.1 0.0 parameter relative to the free b1 / b1 0.7 0.8 0.9 1.0 free value, 205Pb b1/b1(ρ) = 0.78 ± 0.05 123,119,115Sn, 28Si,20Ne,16O free value • Suzuki et al.: “We have 0.050 4m thus found clear evidence ]

-4 3m for the partial restoration / 0.048 2m

[m 1m of chiral symmetry, probed 0

B by well-deﬁned pionic 0.046 Im states in a well-deﬁned

0.044 nuclear density.” -0.13 -0.12 -0.11 -0.10 -0.09 -1 b1 [m/ ]

b1 and Im B0 are s-wave potential parameters 〈qq〉ρ ρ ≈ 1− 0.37 〈qq〉0 ρ0

K. Suzuki, et al., Phys. Rev. Lett. 92, 072302 (2004). 127 Summary Part IV

• The chiral condensate < 0| qq̄ |0 > is a measure of the breaking of chiral symmetry and its study is as important as the search for the Higgs to understand the origin of the mass of hadrons. • Evidences for partial restoration of Chiral Symmetry ? ‣ Excess of dileptons in RHIR in the region of vector mesons can be explained by a widening of the ρ. ‣ Several “elementary reactions” report medium modiﬁcations for the ρ, mainly broadening. ‣ Strongest evidence for partial restoration of Chiral Symmetry is reported in deeply bound pionic states • Substantial theoretical and experimental efforts are being carried out in this very active ﬁeld.

C. Djalali, 2009 Ecole Internationale Joliot Curie 128 Some Topical Review Articles

• D.F. Geesaman, K. Saito, A.W. Thomas, “The Nuclear EMC Effect”, Annu. Rev. Nucl. Part. Sci. 45, 337 (1995) • P.R. Norton, “The EMC Effect”, Rep. Prog. Phys. 66, 1253 (2003) • Benhar, Day, and Sick, “Inclusive quasielastic electron-nucleus scattering”, Rev. Mod. Phys. 80, 189 (2008) • C.F. Perdrisat, V. Punjabi, M. Vanderhaeghen, “Nucleon electromagnetic form factors”, Progress in Particle and Nuclear Physics 59, 694 (2007) • K. Saito, K. Tsushima, A.W. Thomas, “Nucleon and hadron structure changes in the nuclear medium and the impact on observables”, Progress in Particle and Nuclear Physics 58, 1–167 (2007) • Ryugo S. Hayano and Tetsuo Hatsuda, “Hadron properties in the nuclear medium”, Rev. Mod. Phys. 82, 2949 (2010)

This is a brief selection, there are many more ... 129