Electroweak Processes in Few-Nucleon Systems
|
|
|
- Alexandrina Underwood
- 9 years ago
- Views:
Transcription
1 Electroweak Processes in Few-Nucleon Systems M. Viviani INFN, Sezione di Pisa & Department of Physics, University of Pisa Pisa (Italy) Electron Nucleon Scattering XI, June 25-29, 212, Marciana Marina, Isola d Elba M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
2 Outline 1 EFT approach 2 EM Processes 3 Compton scattering 4 Weak interactions 5 Outlook Collaborators F. Spadoni Graduate student, Pisa R. Schiavilla Jefferson Lab. & ODU, Norfolk (VA, USA) S. Pastore ANL (USA) L. Girlanda University of Salento & INFN-Lecce, Lecce (Italy) A. Kievsky & L.E. Marcucci - INFN-Pisa & Pisa University, Pisa (Italy) M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
3 Chiral symmetry - QCD with u and d quarks only u q = d «q R/L = (1 ± «γ5 ) ur/l q = 2 d R/L q R = Rq R = exp i θ R τ/2 q R q L = Lq L = exp i θ L τ/2 q L θ R = θ L = θ V : isospin transformation θ R = θ L = θ A : axial transformation L QCD (almost) invariant under the L, R transformations since m u, m d small also for locals transformations introducing external currents L = L QCD + q L γµ`l µ(x) v(s) µ(x) q L + q R γ µ`r µ(x) v(s) µ(x) q R q R (x)`s(x) + ip(x) q L (x) q L (x)`s(x) ip(x) q R (x) r µ(x) r µ (x) = R(x)rµ(x)R (x) + ir(x) µr (x), etc The external current are related to A µ(x) and W µ ± (x) to reproduce the EM and weak interactions of the quarks Example r µ(x) = l µ(x) = e τz Aµ(x) v(s) µ (x) = e 2 2 Aµ(x) 2 L em = ea µ 3 uγµ u 1 «3 dγµ d M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
4 Chiral Symmetry - Hadrons Non-linear realization of the chiral symmetry for hadrons [Weinberg, 1968, 199],[CCWZ, 1969],[Gasser & Leutwyler, 1984],... Compensator field h u = exp(i π τ/2f π) u = Luh = hur h h(l, R, π) N = hn Nucleons However ( µn) does not transform covariantly u µ = i[u ( µ ir µ)u u( µ il µ)u ] D µ = µ [u ( µ ir µ)u + u( µ il µ)u ] iv (s) µ Transformations: u µ = hu µh (D µn) = hd µn Lagrangian L πn = N `iγ µ D µ m N + g A 2 γ µ γ 5 u µ N + + CS NNNN + it contains an infinite number of LECs Contributions organized as an expansion over (Q/Λ χ) ν [Λ χ 1 GeV] M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
![] D µ = µ + 1 2 [u ( µ ir µ)u + u( µ il µ)u ] iv (s) µ Transformations: u µ = hu µh (D µn) = hd µn Lagrangian L πn = N `iγ µ D µ m N + g A 2 γ µ γ 5 u µ N + + CS](/docs-images/48/19237894/images/page_4.jpg "NNNN + it contains an infinite number of LECs Contributions organized as an expansion over (Q/Λ χ) ν [Λ χ 1 GeV] M.")
5 NN, 3N,..., potentials from the EFT NN Potential V Two methods: S-matrix: for a given process NN NN define V so that (on-shell) NN T EFT NN NN T V NN Unitary transformation: find U in order to decouple NN Hilbert space from NNπ, etc. Realization thanks to the chiral counting: all terms can be organized as powers of Q/Λ χ, Q small momenta or the pion mass Alternatively: Lattice χeft [Lee et al., 21] Example T EFT = T V V + VG V + G = (E H + iǫ) 1 T EFT T () EFT + T (1) EFT + T (2) EFT... V V() + V (1) + V (2)... T (n) EFT, V(n) Q n p 1 p 2 V(n ) G V (n) p 1 p 2 = X p 1 p 2 p 1 p 2 V(n ) p 1 p 2 Then V () = T () EFT V (1) = T (1) EFT V() G V (), etc p 1 p 2 V(n) p 1 p 2 Q n+n +1 E p1 + E p2 E p 1 E p 2 + iǫ M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
6 NN, 3N,..., potentials from the EFT NN Potential V Two methods: S-matrix: for a given process NN NN define V so that (on-shell) NN T EFT NN NN T V NN Unitary transformation: find U in order to decouple NN Hilbert space from NNπ, etc. Realization thanks to the chiral counting: all terms can be organized as powers of Q/Λ χ, Q small momenta or the pion mass Alternatively: Lattice χeft [Lee et al., 21] Example T EFT = T V V + VG V + G = (E H + iǫ) 1 T EFT T () EFT + T (1) EFT + T (2) EFT... V V() + V (1) + V (2)... T (n) EFT, V(n) Q n p 1 p 2 V(n ) G V (n) p 1 p 2 = X p 1 p 2 p 1 p 2 V(n ) p 1 p 2 Then V () = T () EFT V (1) = T (1) EFT V() G V (), etc p 1 p 2 V(n) p 1 p 2 Q n+n +1 E p1 + E p2 E p 1 E p 2 + iǫ M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
7 NN & 3N interaction For more information see for example [Epelbaum et al., NPA 714, 535 (23)] NN interaction J-N3LO [Epelbaum and Coll, ] I-N3LO [Entem & Machleidt, 23] Part of the LEC s fitted to the NN database or πn database 3N interaction J-N2LO [Epelbaum et al, 22] N-N2LO [Navratil, 27] 3N force at N3LO [see Kreb s talk] At N2LO there are two LECS c D and c E : fitted to some 3N data (see later) At N3LO no new parameters At N4LO 1 new LECs [Girlanda et al., 211] M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
![database or πn database 3N interaction J-N2LO [Epelbaum et al, 22] N-N2LO [Navratil, 27] 3N force at N3LO [see Kreb s talk] At N2LO there](/docs-images/48/19237894/images/page_7.jpg "are two LECS c D and c E : fitted to some 3N data (see later) At N3LO no new parameters At N4LO 1 new LECs [Girlanda et al., 211] M.")
8 EM current Basic problem: transition α + γ β β H e.m. α; qλ = Ψ β K 1 Ψ α K 1 = e Z 2ωΩ dx e iq x bǫ qλ Ĵ(x) K 1 acts only on the nucleons d.o.f. α, β initial & final nuclear states, Ψ α, Ψ β corresponding w.f. q, ω, ˆǫ qλ = momentum, energy, polarization of the emitted photon for virtual photons, one needs also the m.e. of ˆq bj and ρ Z J µ (q) = dx e iq x b J µ (x) µ =, 1, 2, 3 M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
9 Meson exchange currents bj(x) = P i b j i (x) + 2B + 3B +... Current conservation Ĵ(x) = i[h, ρ(x)] Strict interplay between H, b J and bρ bρ(x) = AX i=1 1 + τ z(i) δ(r i x) 2 [Buchmann et al, 1985] [Riska, 1989], [Schiavilla et al, 199] EFT approach: H and J µ derived from the same Lagrangian. M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
![i=1 1 + τ z(i) δ(r i x) 2 [Buchmann et al, 1985] [Riska, 1989], [Schiavilla et al, 199] EFT](/docs-images/48/19237894/images/page_9.jpg "approach: H and J µ derived from the same Lagrangian. M.")
10 Current at N3LO [Park et al, 1993], [Kolling et al, 29], [Pastore et al, 29] N3LO (Q 1 ) terms LO (Q 2 ) NLO (Q 1 ) NNLO (Q ) black square= (Q/M N ) 2 relativistic correction to the NNγ vertex Note: NNγ vertex = (e N /2M N )(p+p )+i(e N +κ N )µ N (σ q) it takes into account the Pauli term + pion loop corrections 2 new LECs black dot= three (Q/Λ χ) 2 vertices 3 new LECs Most of the LECs enter also the NN potential. There are 5 uncostrained LECs ( µ d, µ 3 H, µ3 He, etc.) M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
11 Wave functions HH variational method: A. Kievsky, S. Rosati, MV, L.E. Marcucci, and L. Girlanda J. Phys. G, 35, 6311 (28) A benchmark for A = 4 AGS: Deltuva & Fonseca, PRL (27) FY: Lazauskas & Carbonell, PRC 7, 442 (24) n 3 H & p 3 He elastic scattering E c.m. B 3 B MeV NN interaction models: AV18 [Wiringa, Stoks & Schiavilla (1995)] I-N3LO [Entem & Machleidt (23)] V low q [Bogner, Kuo & Schwenk, (23)] (derived from the CD-Bonn potential [Machleidt (21)]) Results reported in [MV et al., 211] M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
12 n 3 H scattering (I-N3LO pot.) dσ/dω [mb/sr] MeV AGS 2 MeV 3.5 MeV 6 MeV 18,4 A y,2,2 18 A y,1 -,1 18 M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
13 n 3 H scattering (I-N3LO pot.) dσ/dω [mb/sr] MeV AGS HH 2 MeV 3.5 MeV 6 MeV 18,4 A y,2,2 18 A y,1 -,1 18 M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
14 n 3 H scattering (I-N3LO pot.) dσ/dω [mb/sr] MeV AGS HH FY 2 MeV 3.5 MeV 6 MeV 18,4 A y,2,2 18 A y,1 -,1 18 M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
15 p 3 He scattering (I-N3LO pot.) dσ/dω [mb/sr] MeV Famularo 1954 Fisher MeV Mcdonald 1964 Fisher MeV Mcdonald A y,4,2 Fisher 26 George 21 Fisher 26 Alley 1993 A y,2,1 Daniels 21 Daniels Alley 1993 Daniels M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
16 Predictions by different potentials dσ/dω [mb/sr] MeV Famularo 1954 Fisher 26 I-N3LO AV18 low-k 4.5 MeV Mcdonald 1964 Fisher MeV Mcdonald ,4 Fisher 26 George 21 Fisher 26 Alley 1993 A y,2 A y,2,1 Daniels 21 Daniels Alley 1993 Daniels M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
17 ,4 2.25MeV 4.5MeV 5.54 MeV,2 Daniels 21 Daniels 21 Daniels 21 Alley 1993 A yy -,2 -,4 -, ,2 Daniels 21 Daniels 21 Alley 1993 A xx,1 -, ,4,3,2,1 -,1 -,2 A xz Alley MeV A zx 5.54 MeV Alley 1993 A zz Alley θ [c.m.] θ [c.m.] θ [c.m.] M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
18 Results for A = 3, 4 (1) 4 p-d E c.m. = 2. MeV 4 p- 3 He E c.m. =4.15 MeV 3 AV18 AV18/UIX I-N3LO I-N3LO/N-N2LO 3 I-N3LO AV18 AV18/UIX I-N3LO/N-N2LO dσ/dω [mb/sr] 2 dσ/dω [mb/sr] M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
19 Results for A = 3, 4 (2),6 A y p-d E c.m. =2 MeV A y p- 3 He E c.m. =4.15 MeV,5,4,5,4 Alley 1993a Alley 1993b AV18 I-N3LO I-N3LO/N-N2LO A y,3,3,2,1 AV18 AV18/UIX I-N3LO I-N3LO/N-N2LO,2, Study of the 3N force in A = 4 scattering in progress M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
20 Fit of the LECS Fit of the LECs Current at N3LO (O(Q)) NN potential at NLO (O(Q 2 )) q bj(q) = [H, ρ(q)] We have constructed a NN potential at NLO and fitted the corresponding LECs to the NN database: [Pastore et al., 29] In J there are 5 additional LECs: fitted to the A = 2, 3 magnetic moments & n p capture cross section at thermal energies using the I-N3LO NN potential The model depends on a cutoff Λ (Λ = 5 6 MeV) the dependence on Λ is used to test the convergence [Girlanda et al., 21] n.m..9 µ d exp LO NLO N 2 LO N 3 LO(S-L) σ γ np mb n.m. n.m. µ S ( 3 He/ 3 H) µ V ( 3 He/ 3 H) Λ (MeV) Λ(MeV) M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
![, 29] In J there are 5 additional LECs: fitted to the A = 2, 3 magnetic moments & n p capture cross section at thermal energies using the I-N3LO NN potential The model depends on](/docs-images/48/19237894/images/page_20.jpg "a cutoff Λ (Λ = 5 6 MeV) the dependence on Λ is used to test the convergence [Girlanda et al., 21] n.m..9 µ d exp LO NLO N 2 LO N 3 LO(S-L) σ γ np 36 34 32 mb.85 3.45-2. n.m. n.m. µ S ( 3 He/ 3 H) µ V ( 3 He/ 3 H).")
21 Deuteron-photodisintegration Wave functions calculated using I-N3LO for Λ = 5 & 6 MeV Observable dominated by the E1 transitions.28 Deuteron photo-disintegration total cross section (mb).24.2 EXP I-N3LO5 JEFT1(FULL) I-N3LO5 JEFT1(E1) σ dis (fm 2 ) H(γ,n) 1 H E Lab (MeV) M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
22 n d & n 3 He radiative captures at thermal energies n d capture from the 2 S 1/2 & 4 S 3/2 waves n 3 He capture from the 3 S 1 wave Scattering lenghts Case I-N3LO/N-N2LO Expt. a nd doublet (1) a nd quartet (2) a n 3 He doublet (53) n d & n 3 He capture cross sections Order σ n d [mb] σ n 3 He [µb] LO NLO N2LO N3LO (loops) N3LO (LECs) Expt.58(15) 52(4) mb σ γ nd R c Λ (MeV) σ γ n 3 He Λ (MeV) exp LO NLO N 2 LO N 3 LO(S-L) N 3 LO(LECs) SNPA SNPA* µb M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
23 Compton scattering (1) Nucleon Polarizabilities Induced dipoles by an EM field: d = αe µ = βb» H eff = 2π αe 2 + βb 2 + γ E1E1 σ E E «+ t Experimental status [Griesshammer et al., 212] proton: from γp γp experiments (MAMI [de Lèon et al., 21],...) α p = (1.7 ±.3(stat) ±.2(Baldin) ±.8(theory)) 1 4 fm 3 β p = (3.1 ±.3(stat) ±.2(Baldin) ±.8(theory)) 1 4 fm 3 neutron: from γd γd experiments or with other methods Data sparse and not accurate [Illinois (1994), SAL (2), Lund (23)] α n = (11.1 ± 1.8(stat) ±.4(Baldin) ±.8(theory)) 1 4 fm 3 β n = ( (stat) ±.4(Baldin) ±.8(theory)) 1 4 fm 3 Theory input needed to separate: 1) structure effects 2) MEC effects New experiments on d, 3 He, 6 Li planned/in progress at TUNL/HγGS, MaxLab (Lund), S-DALINAC (Darmstaad) M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
24 Compton scattering (2) Status of the calculations First applications to γn: [Bernard et al, 1992] Recent applications to γd: [Beane et al, 24]: NNLO, no rescattering [Griesshammer & Shukla, 29]: NLO, rescattering calculated with AV18 Review: [Griesshammer et al., 212] Only a few applications to γ 3 He Aims of the new calculation NNγ NN transition operators derived from the EFT at N3LO [Pastore et al., 29] NN interaction derived from the same EFT (at present we have used the I-N3LO potential by Entem & Machleidt) Future: applications to 3 He and 6 Li M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
25 General framework K 1 K1 K 1 K1 + V V K K1 K 1 K1 K 1 } {{ } termini dispersivi d f γ f T d i γ i = Ψ d f K 2 + K 1 GK 1 + K 1 GK 1 Ψd i {z } Dispersive part The Green function G = (E H + iǫ) 1 describes the rescattering of the NN pair between the two EM vertices NN interaction from [Entem & Machleidt, 23] The irriducible kernel K 2 derived from the EFT at NLO ( Q 2 ) (PRELIMNARY) In literature K 2 is derived up to NNLO [Griesshammer et al, 212] inclusion of d.o.f. [Hildebrandt Ph.D. Thesis, München, 25] M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
26 Diagrams (1) Diagrams (a): contribution to K 2 seagull (SG) & spin-orbit (SO) P =q q K (SG) 2 = X j e j 2M ǫ i ǫ f ei(q q ) r j, e j = 1 + τ j z 2 P= (b2) (b1) (a) (b3) (b4) (b5) Note: the SG can be derived from H NR = (1/2M)(p ea) 2 SG: order Q 3, SO=corrections to the SG Q 2 Diagrams (b): contribution to K 2 from the polarization of the nucleon They can be used to estimate α and β [Bernard et al, 1992] We ll consider α and β as free parameters (α j = α p(1 + τz)/2 j + α n(1 τz)/2) j K (αβ) = X h 2πα 2 j ǫ i ǫ f qq j 2πβ j (q ǫ i ) (q ǫ f ) ie i(q q ) r j M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
27 Diagrams (2) Diagrams (c-f): Contributions taken into account by the dispersive part Φ f d K 1 GK 1 + K 1 GK 1 Φi d (d1) (c2) (c1) V (e1) (e2) (f1) V V V (f2) (g1) (g2) (c1), (f1) Q 3, (e1), (f2) Q 4 Exact resummation [Ishikawa et al., 1998] Ψ 1 = GK 1 Φ i d Ψ 2 = GK 1 Φi d (E H + iǫ) Ψ 1 = K 1 Φ i d (E = q B d > ) (E H + iǫ) Ψ 2 = K 1 Φi d (E = q B d < ) Diagrams (g): contribution taken into account by the fact that Φ d are solution of the Schroedinger equation Diagrams (h): Contribution to K 2 (h1) (h2) (h3) (h4) M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
28 Test Photodisintegration I[ Φ f d K 1 GK 1 Φ i d σ γ+d n+p In our calculation [ Φ f d K 1 GK 1 Φ i d = Φf d K 1 Ψ 1 At E γ = 2 MeV σ γ+d n+p = 54.7 µb: we find µb (I-N3LO + JEFT Λ = 5 MeV) Thomson limit For E γ, the calculation should reproduce the Thomson limit Compton amplitude M (TL) = e 2 /M d (note: M (SG) = e 2 /M 2M (TL) ) True if V, K 1, and K 2 are consistent (current conservation) I-N3LO6 JEFT2 SG SG+Dh SG+Dh+DS(NLO) SG+Dh+DS(N3LO) limite di Thomson dσ/dω[nb/sr] θ M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
29 Results (1) 4 49 MeV -- I-N3LO + JEFT (Λ=5 MeV) 35 dσ/dω [nb/sr] Illinois Data SG +SO +DS +Dh +αβ 1 5 (α p +α n )/2=11.5 (β p +β n )/2= θ M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
30 Results (2) 4 66 MeV -- I-N3LO + JEFT (Λ=5 MeV) 35 dσ/dω [nb/sr] Lundin (2) SG +SO +DS (N3LO) +Dh +Pol. (standard) θ M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
31 Sensitivity to α n & β n 4 49 MeV -- I-N3LO + JEFT (Λ=5 MeV) 35 3 Illinois Data α n =2, β n =2 dσ/dω [nb/sr] (α p +α n )/2=11.5 (β p +β n )/2= θ M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
32 β-decay and the 3N force e [Gardestig & Phillips, 26], [Gazit et al., 29] c D c E d R d R = Mn Λ χg A c D M N(c 3 + 2c 4 ) New fit of c D and c E using 3 H binding energy and tritium β-decay lifetime New versions of the 3N at N2LO: first application for µ-capture on d and 3 He [Marcucci et al., 212] M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
33 pp capture at astrophysical energies Aim: new calculation of the astrophysical factor S 11 of the p + p 2 H + e + ν e reaction S 11 (E) = S 11 + S 11 E S 11 E2 + Preliminary Results units 1 25 MeV b I-N3LO NN interaction + weak transition operator derived from EFT S 11 S 11 /S 11 [MeV 1 ] S [MeV 2 ] LO Λ = LO Λ = Full Λ = Full Λ = M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
34 Outlook Motivations of this work consistent calculations for a variety of processes using potential/current/wave functions derived from the same EFT Applications Main interest: test of 3N interaction in A = 3, 4 systems, study of reactions of astrophysical interest p d & d d captures, form factors of light nuclei, ldots) Compton scattering on 3 He & 6 Li (in the near future new data at HIγS & Lund) weak transitions (pp capture, µ-capture, parity-violation in nuclei,...) M. Viviani (INFN-Pisa) Electroweak Processes Elba, June 28, / 31
Basic Concepts in Nuclear Physics
Basic Concepts in Nuclear Physics Paolo Finelli Corso di Teoria delle Forze Nucleari 2011 Literature/Bibliography Some useful texts are available at the Library: Wong, Nuclear Physics Krane, Introductory
Theoretical nuclear physics
Theoretical nuclear physics Laura Elisa Marcucci (Univ. Pisa & INFN-Pisa) The Pisa Group Ignazio Bombaci (Univ. Pisa & INFN-Pisa) Angela Bonaccorso (INFN-Pisa) Alejandro Kievsky (INFN-Pisa) Laura Elisa
arxiv:hep-lat/0408024v1 16 Aug 2004
BU-HEPP-04-02 Electric Polarizability of Neutral Hadrons from Lattice QCD Joe Christensen Physics Department, McMurry University, Abilene, TX, 79697 Walter Wilcox Department of Physics, Baylor University,
Masses in Atomic Units
Nuclear Composition - the forces binding protons and neutrons in the nucleus are much stronger (binding energy of MeV) than the forces binding electrons to the atom (binding energy of ev) - the constituents
Basic Concepts in Nuclear Physics. Paolo Finelli
Basic Concepts in Nuclear Physics Paolo Finelli Literature/Bibliography Some useful texts are available at the Library: Wong, Nuclear Physics Krane, Introductory Nuclear Physics Basdevant, Rich and Spiro,
α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =
Nuclear Physics. Nuclear Physics comprises the study of:
Nuclear Physics Nuclear Physics comprises the study of: The general properties of nuclei The particles contained in the nucleus The interaction between these particles Radioactivity and nuclear reactions
Spontaneous symmetry breaking in particle physics: a case of cross fertilization
Spontaneous symmetry breaking in particle physics: a case of cross fertilization Yoichiro Nambu lecture presented by Giovanni Jona-Lasinio Nobel Lecture December 8, 2008 1 / 25 History repeats itself 1960
Recent developments in Electromagnetic Hadron Form Factors
Recent developments in Electromagnetic Hadron Form Factors (JOH7RPDVL*XVWDIVVRQ '$31,$63K16DFOD\ :KDW are Form Factors? :K\ to measure? +RZ to measure? :KDWLVQHZ" Consequences, Conclusions 6SRNHSHUVR QV
Solutions to Problems in Goldstein, Classical Mechanics, Second Edition. Chapter 7
Solutions to Problems in Goldstein, Classical Mechanics, Second Edition Homer Reid April 21, 2002 Chapter 7 Problem 7.2 Obtain the Lorentz transformation in which the velocity is at an infinitesimal angle
High Energy Physics. Lecture 4 More kinematics and a picture show of particle collisions
High Energy Physics Lecture 4 More kinematics and a picture show of particle collisions 1 Recall from the previous lecture: the momentum of the scattered Particle in an elastic collision is given by p
Basic Nuclear Concepts
Section 7: In this section, we present a basic description of atomic nuclei, the stored energy contained within them, their occurrence and stability Basic Nuclear Concepts EARLY DISCOVERIES [see also Section
PION SCALAR FORM FACTORS FROM
MENU 27 th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon September-4, 27 IKP, Forschungzentrum Jülich, Germany PION SCALAR FORM FACTORS FROM J/ψ DECAYS Timo A. Lähde
University of Maryland Fraternity & Sorority Life Spring 2015 Academic Report
University of Maryland Fraternity & Sorority Life Academic Report Academic and Population Statistics Population: # of Students: # of New Members: Avg. Size: Avg. GPA: % of the Undergraduate Population
PHY4604 Introduction to Quantum Mechanics Fall 2004 Practice Test 3 November 22, 2004
PHY464 Introduction to Quantum Mechanics Fall 4 Practice Test 3 November, 4 These problems are similar but not identical to the actual test. One or two parts will actually show up.. Short answer. (a) Recall
Electric Dipole moments as probes of physics beyond the Standard Model
Electric Dipole moments as probes of physics beyond the Standard Model K. V. P. Latha Non-Accelerator Particle Physics Group Indian Institute of Astrophysics Plan of the Talk Parity (P) and Time-reversal
Concepts in Theoretical Physics
Concepts in Theoretical Physics Lecture 6: Particle Physics David Tong e 2 The Structure of Things 4πc 1 137 e d ν u Four fundamental particles Repeated twice! va, 9608085, 9902033 Four fundamental forces
Perfect Fluids: From Nano to Tera
Perfect Fluids: From Nano to Tera Thomas Schaefer North Carolina State University 1 2 Perfect Fluids sqgp (T=180 MeV) Neutron Matter (T=1 MeV) Trapped Atoms (T=0.1 nev) 3 Hydrodynamics Long-wavelength,
Feynman diagrams. 1 Aim of the game 2
Feynman diagrams Contents 1 Aim of the game 2 2 Rules 2 2.1 Vertices................................ 3 2.2 Anti-particles............................. 3 2.3 Distinct diagrams...........................
Particle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 7 : Symmetries and the Quark Model. Introduction/Aims
Particle Physics Michaelmas Term 2011 Prof Mark Thomson Handout 7 : Symmetries and the Quark Model Prof. M.A. Thomson Michaelmas 2011 206 Introduction/Aims Symmetries play a central role in particle physics;
UN PICCOLO BIG BANG IN LABORATORIO: L'ESPERIMENTO ALICE AD LHC
UN PICCOLO BIG BANG IN LABORATORIO: L'ESPERIMENTO ALICE AD LHC Parte 1: Carlos A. Salgado Universidade de Santiago de Compostela [email protected] http://cern.ch/csalgado LHC physics program Fundamental
0.33 d down 1 1. 0.33 c charm + 2 3. 0 0 1.5 s strange 1 3. 0 0 0.5 t top + 2 3. 0 0 172 b bottom 1 3
Chapter 16 Constituent Quark Model Quarks are fundamental spin- 1 particles from which all hadrons are made up. Baryons consist of three quarks, whereas mesons consist of a quark and an anti-quark. There
KE A = PE MAX 1/2M v 2 = k q1 q2 /R
CHAPTER 13 NUCLEAR STRUCTURE NUCLEAR FORCE The nucleus is help firmly together by the nuclear or strong force, We can estimate the nuclear force by observing that protons residing about 1fm = 10-15m apart
Standard Model of Particle Physics
Standard Model of Particle Physics Chris Sachrajda School of Physics and Astronomy University of Southampton Southampton SO17 1BJ UK SUSSP61, St Andrews August 8th 3rd 006 Contents 1. Spontaneous Symmetry
Bounding the Higgs width at the LHC
Bounding the Higgs width at the LHC Higgs XSWG workshop, June 2014 John Campbell, Fermilab with K. Ellis, C. Williams 1107.5569, 1311.3589, 1312.1628 Reminder of the method This is the essence of the original
Perfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Hydrodynamics Long-wavelength, low-frequency dynamics of conserved or spontaneoulsy broken symmetry variables τ
Nuclear Physics and Radioactivity
Nuclear Physics and Radioactivity 1. The number of electrons in an atom of atomic number Z and mass number A is 1) A 2) Z 3) A+Z 4) A-Z 2. The repulsive force between the positively charged protons does
PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS
PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS 1. Photons 2. Photoelectric Effect 3. Experimental Set-up to study Photoelectric Effect 4. Effect of Intensity, Frequency, Potential on P.E.
Directed by: Prof. Yuanning Gao, IHEP, Tsinghua University Prof. Aurelio Bay, LPHE, EPFL
Masters Thesis in High Energy Physics Directed by: Prof. Yuanning Gao, IHEP, Tsinghua University Prof. Aurelio Bay, LPHE, EPFL 1 Study for CP-violation in the ψ π + π J/ψ transition Vincent Fave July 18,
Quark Model. Quark Model
Quark odel Outline Hadrons Isosin Strangeness Quark odel Flavours u d s esons Pseudoscalar and vector mesons Baryons Deculet octet Hadron asses Sin-sin couling Heavy Quarks Charm bottom Heavy quark esons
Part II: Heavy Quark Expansion
Part II: Heavy Quark Expansion Thomas Mannel CERN-PH-TH and Theoretische Physik I, Siegen University KITPC, June 24th, 2008 Contents 1 Introduction to HQE Set-up: OPE Spectra of Inclusive Decays 2 Theory
Cross section, Flux, Luminosity, Scattering Rates
Cross section, Flux, Luminosity, Scattering Rates Table of Contents Paul Avery (Andrey Korytov) Sep. 9, 013 1 Introduction... 1 Cross section, flux and scattering... 1 3 Scattering length λ and λ ρ...
Lecture 5 Motion of a charged particle in a magnetic field
Lecture 5 Motion of a charged particle in a magnetic field Charged particle in a magnetic field: Outline 1 Canonical quantization: lessons from classical dynamics 2 Quantum mechanics of a particle in a
ffmssmsc a C++ library for spectrum calculation and renormalization group analysis of the MSSM
ffmssmsc a C++ library for spectrum calculation and renormalization group analysis of the MSSM Alexei Sheplyakov Joint Institute for Nuclear Research, Dubna, Russia SUSY 07 Karlsruhe, July 31, 2007 version
Topic 3. Evidence for the Big Bang
Topic 3 Primordial nucleosynthesis Evidence for the Big Bang! Back in the 1920s it was generally thought that the Universe was infinite! However a number of experimental observations started to question
Weak Interactions: towards the Standard Model of Physics
Weak Interactions: towards the Standard Model of Physics Weak interactions From β-decay to Neutral currents Weak interactions: are very different world CP-violation: power of logics and audacity Some experimental
2, 8, 20, 28, 50, 82, 126.
Chapter 5 Nuclear Shell Model 5.1 Magic Numbers The binding energies predicted by the Liquid Drop Model underestimate the actual binding energies of magic nuclei for which either the number of neutrons
Radiative corrections to anti-neutrino proton scattering
Radiative corrections to anti-neutrino proton scattering Udit Raha, a b and Kuniharu Kubodera b a Indian Institute of Technology Guwahati, 78 039 Assam, India b Dept. Physics and Astronomy, University
EQUATION OF STATE. e (E µ)/kt ± 1 h 3 dp,
EQUATION OF STATE Consider elementary cell in a phase space with a volume x y z p x p y p z = h 3, (st.1) where h = 6.63 1 7 erg s is the Planck constant, x y z is volume in ordinary space measured in
Monday 11 June 2012 Afternoon
Monday 11 June 2012 Afternoon A2 GCE PHYSICS B (ADVANCING PHYSICS) G495 Field and Particle Pictures *G412090612* Candidates answer on the Question Paper. OCR supplied materials: Data, Formulae and Relationships
Basic Equations, Boundary Conditions and Dimensionless Parameters
Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were
Free Electron Fermi Gas (Kittel Ch. 6)
Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals -- they are the glue that hold the nuclei together Types of binding (see next slide)
Brief remarks. m 2hyp,i + p2π,i + 2π + p 2π,i = m 2 hyp,i + p2 π,i + E π,i (2) m K + m A =
1 Brief remarks In FINUDA the strangeness-exchange reaction is used to produce Λ- hypernuclei with stopped K s: K stop + Z A Z Λ A + π (1) Thanks to the energy conservation, we can write for each bound
Ω I (JP ) = 0( 3 2 + ) Status:
Ω I (JP ) = 0( 3 2 + ) Status: The unambiguous discovery in both production and decay was by BARNES 64. The quantum numbers follow from the assignment of the particle to the baryon decuplet. DEUTSCHMANN
UNIVERSITETET I OSLO
UNIVERSITETET I OSLO Det matematisk-naturvitenskapelige fakultet Exam in: FYS 310 Classical Mechanics and Electrodynamics Day of exam: Tuesday June 4, 013 Exam hours: 4 hours, beginning at 14:30 This examination
Gauge theories and the standard model of elementary particle physics
Gauge theories and the standard model of elementary particle physics Mark Hamilton 21st July 2014 1 / 35 Table of contents 1 The standard model 2 3 2 / 35 The standard model The standard model is the most
ASCII CODES WITH GREEK CHARACTERS
ASCII CODES WITH GREEK CHARACTERS Dec Hex Char Description 0 0 NUL (Null) 1 1 SOH (Start of Header) 2 2 STX (Start of Text) 3 3 ETX (End of Text) 4 4 EOT (End of Transmission) 5 5 ENQ (Enquiry) 6 6 ACK
Chapter NP-5. Nuclear Physics. Nuclear Reactions TABLE OF CONTENTS INTRODUCTION OBJECTIVES 1.0 NUCLEAR REACTIONS 2.0 NEUTRON INTERACTIONS
Chapter NP-5 Nuclear Physics Nuclear Reactions TABLE OF CONTENTS INTRODUCTION OBJECTIVES 1.0 2.0 NEUTRON INTERACTIONS 2.1 ELASTIC SCATTERING 2.2 INELASTIC SCATTERING 2.3 RADIATIVE CAPTURE 2.4 PARTICLE
PoS(Baldin ISHEPP XXII)026
On the modified Yamaguchi-type functions for the Bethe-Salpeter equation Joint Institute for Nuclear Research, Dubna, Russia E-mail: [email protected] V. V. Burov Joint Institute for Nuclear Research,
Suggested solutions, FYS 500 Classical Mechanics and Field Theory 2014 fall
UNIVERSITETET I STAVANGER Institutt for matematikk og naturvitenskap Suggested solutions, FYS 500 Classical Mecanics and Field Teory 014 fall Set 11 for 17/18. November 014 Problem 59: Te Lagrangian for
Atomic and Nuclear Physics Laboratory (Physics 4780)
Gamma Ray Spectroscopy Week of September 27, 2010 Atomic and Nuclear Physics Laboratory (Physics 4780) The University of Toledo Instructor: Randy Ellingson Gamma Ray Production: Co 60 60 60 27Co28Ni *
The Standard Model of Particle Physics - II
The Standard Model of Particle Physics II Lecture 4 Gauge Theory and Symmetries Quantum Chromodynamics Neutrinos Eram Rizvi Royal Institution London 6 th March 2012 Outline A Century of Particle Scattering
Three-nucleon interaction dynamics studied via the deuteron-proton breakup. Elżbieta Stephan Institute of Physics, University of Silesia
Three-nucleon interaction dynamics studied via the deuteron-proton breakup Elżbieta Stephan Institute of Physics, University of Silesia Studies of the 1 H(d,pp)n Breakup at 130 MeV University of Silesia,
arxiv:nucl-th/0609031v2 16 Oct 2006
A realistic model of superfluidity in the neutron star inner crust. M. Baldo 1, E.E. Saperstein 2 and S.V. Tolokonnikov 2 1 INFN, Sezione di Catania, 64 Via S.-Sofia, I-95123 Catania, Italy 2 Kurchatov
Basic Geometry Review For Trigonometry Students. 16 June 2010 Ventura College Mathematics Department 1
Basic Geometry Review For Trigonometry Students 16 June 2010 Ventura College Mathematics Department 1 Undefined Geometric Terms Point A Line AB Plane ABC 16 June 2010 Ventura College Mathematics Department
Group Theory and Chemistry
Group Theory and Chemistry Outline: Raman and infra-red spectroscopy Symmetry operations Point Groups and Schoenflies symbols Function space and matrix representation Reducible and irreducible representation
arxiv:1008.4792v2 [hep-ph] 20 Jun 2013
![arxiv:1008.4792v2 [hep-ph] 20 Jun 2013](/thumbs/40/21085474.jpg "arxiv:1008.4792v2 [hep-ph] 20 Jun 2013")
A Note on the IR Finiteness of Fermion Loop Diagrams Ambresh Shivaji Harish-Chandra Research Initute, Chhatnag Road, Junsi, Allahabad-09, India arxiv:008.479v hep-ph] 0 Jun 03 Abract We show that the mo
Physics 1104 Midterm 2 Review: Solutions
Physics 114 Midterm 2 Review: Solutions These review sheets cover only selected topics from the chemical and nuclear energy chapters and are not meant to be a comprehensive review. Topics covered in these
Special Theory of Relativity
Special Theory of Relativity In ~1895, used simple Galilean Transformations x = x - vt t = t But observed that the speed of light, c, is always measured to travel at the same speed even if seen from different,
Lepton Flavour Violation @ LHC?
m ν (charged) lepton flavour change happens, and the LHC exists...so look for Lepton Flavour Violation @ LHC? Sacha Davidson, P Gambino, G Grenier, S Lacroix, ML Mangano, S Perries, V Sordini, P Verdier
Meson spectroscopy and pion cloud effect on baryon masses
Meson spectroscopy and pion cloud effect on baryon masses Stanislav Kubrak, Christian Fischer, Helios Sanchis-Alepuz, Richard Williams Justus-Liebig-University, Giessen 13.06.2014 SK, C. Fischer, H. Sanchis-Alepuz,
Statistical Physics, Part 2 by E. M. Lifshitz and L. P. Pitaevskii (volume 9 of Landau and Lifshitz, Course of Theoretical Physics).
Fermi liquids The electric properties of most metals can be well understood from treating the electrons as non-interacting. This free electron model describes the electrons in the outermost shell of the
Introduction to SME and Scattering Theory. Don Colladay. New College of Florida Sarasota, FL, 34243, U.S.A.
June 2012 Introduction to SME and Scattering Theory Don Colladay New College of Florida Sarasota, FL, 34243, U.S.A. This lecture was given at the IUCSS summer school during June of 2012. It contains a
Study of the B D* ℓ ν with the Partial Reconstruction Technique
Study of the B D* ℓ ν with the Partial Reconstruction Technique + University of Ferrara / INFN Ferrara Dottorato di Ricerca in Fisica Ciclo XVII Mirco Andreotti 4 March 25 Measurement of B(B D*ℓν) from
Radioactivity III: Measurement of Half Life.
PHY 192 Half Life 1 Radioactivity III: Measurement of Half Life. Introduction This experiment will once again use the apparatus of the first experiment, this time to measure radiation intensity as a function
Search for solar axions with the CCD detector at CAST (CERN Axion Solar Telescope)
Search for solar axions with the CCD detector at CAST (CERN Axion Solar Telescope) Donghwa Kang FAKULTÄT FÜR MATHEMATIK UND PHYSIK ALBERT-LUDWIGS-UNIVERSITÄT FREIBURG Search for solar axions with the
Høgskolen i Narvik Sivilingeniørutdanningen
Høgskolen i Narvik Sivilingeniørutdanningen Eksamen i Faget STE66 ELASTISITETSTEORI Klasse: 4.ID Dato: 7.0.009 Tid: Kl. 09.00 1.00 Tillatte hjelpemidler under eksamen: Kalkulator Kopi av Boken Mechanics
arxiv:hep-ph/0410120v2 2 Nov 2004
Photon deflection by a Coulomb field in noncommutative QED C. A. de S. Pires Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-970, João Pessoa - PB, Brazil. Abstract arxiv:hep-ph/0410120v2
Lecture 8. Generating a non-uniform probability distribution
Discrete outcomes Lecture 8 Generating a non-uniform probability distribution Last week we discussed generating a non-uniform probability distribution for the case of finite discrete outcomes. An algorithm
Big Bang Cosmology. Big Bang vs. Steady State
Big Bang vs. Steady State Big Bang Cosmology Perfect cosmological principle: universe is unchanging in space and time => Steady-State universe - Bondi, Hoyle, Gold. True? No! Hubble s Law => expansion
Lecture 3: Optical Properties of Bulk and Nano. 5 nm
Lecture 3: Optical Properties of Bulk and Nano 5 nm The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model) 0 e - n( ) n' n '' n ' = 1 + Nucleus
Gravity and running coupling constants
Gravity and running coupling constants 1) Motivation and history 2) Brief review of running couplings 3) Gravity as an effective field theory 4) Running couplings in effective field theory 5) Summary 6)