LIGHT UNFLAVORED MESONS (S = C = B = 0)
|
|
- Κύμα Ιωάννου
- 8 χρόνια πριν
- Προβολές:
Transcript
1 LIGHT UNFLAVORED MESONS (S = C = B = 0) For I = 1 (π, b, ρ, a): ud, (uu dd)/ 2, du; for I = 0 (η, η, h, h, ω, φ, f, f ): c 1 (uu + d d) + c 2 (s s) π ± I G (J P ) = 1 (0 ) Mass m = ± MeV (S = 1.2) Mean life τ = ( ± ) 10 8 s (S = 1.2) cτ = m π ± l ± νγ form factors [a] F V = ± F A = ± F V slope parameter a = 0.10 ± 0.06 R = π modes are charge conjugates of the modes below. For decay limits to particles which are not established, see the section on Searches for Axions and Other Very Light Bosons. p π + DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) µ + ν µ [b] ( ± ) % 30 µ + ν µ γ [c] ( 2.00 ±0.25 ) e + ν e [b] ( ±0.004 ) e + ν e γ [c] ( 7.39 ±0.05 ) e + ν e π 0 ( ±0.006 ) e + ν e e + e ( 3.2 ±0.5 ) e + ν e νν < % 70 Lepton Family number (LF) or Lepton number (L) violating modes µ + ν e L [d] < % 30 µ + ν e LF [d] < % 30 µ e + e + ν LF < % 30 Page 1 Created: 7/12/ :49
2 π 0 I G (J PC ) = 1 (0 + ) Mass m = ± MeV (S = 1.1) m π ± m π 0 = ± MeV Mean life τ = (8.52 ± 0.18) s (S = 1.2) cτ = 25.5 nm For decay limits to particles which are not established, see the appropriate Search sections (A 0 (axion) and Other Light Boson (X 0 ) Searches, etc.). Scale factor/ p π 0 DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) 2γ (98.823±0.034) % S= e + e γ ( 1.174±0.035) % S= γpositronium ( 1.82 ±0.29 ) e + e + e e ( 3.34 ±0.16 ) e + e ( 6.46 ±0.33 ) γ < CL=90% 67 νν [e] < CL=90% 67 ν e ν e < CL=90% 67 ν µ ν µ < CL=90% 67 ν τ ν τ < CL=90% 67 γνν < CL=90% 67 Charge conjugation (C) or Lepton Family number (LF) violating modes 3γ C < CL=90% 67 µ + e LF < CL=90% 26 µ e + LF < CL=90% 26 µ + e + µ e + LF < CL=90% 26 η I G (J PC ) = 0 + (0 + ) Mass m = ± MeV Full width Γ = 1.31 ± 0.05 kev C-nonconserving decay parameters π + π π 0 left-right asymmetry = ( ) 10 2 π + π π 0 sextant asymmetry = ( ) 10 2 π + π π 0 quadrant asymmetry = ( 0.09 ± 0.09) 10 2 π + π γ left-right asymmetry = (0.9 ± 0.4) 10 2 π + π γ β (D-wave) = 0.02 ± 0.07 (S = 1.3) CP-nonconserving decay parameters π + π e + e decay-plane asymmetry A φ = ( 0.6 ± 3.1) Page 2 Created: 7/12/ :49
3 Dalitz plot parameter π 0 π 0 π 0 α = ± Scale factor/ p η DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) Neutral modes neutral modes (72.12±0.34) % S=1.2 2γ (39.41±0.20) % S= π 0 (32.68±0.23) % S= π 0 2γ ( 2.7 ±0.5 ) 10 4 S= π 0 2γ < CL=90% 238 4γ < CL=90% 274 invisible < CL=90% Charged modes charged modes (28.10±0.34) % S=1.2 π + π π 0 (22.92±0.28) % S= π + π γ ( 4.22±0.08) % S= e + e γ ( 6.9 ±0.4 ) 10 3 S= µ + µ γ ( 3.1 ±0.4 ) e + e < CL=90% 274 µ + µ ( 5.8 ±0.8 ) e + 2e ( 2.40±0.22) π + π e + e (γ) ( 2.68±0.11) e + e µ + µ < CL=90% 253 2µ + 2µ < CL=90% 161 µ + µ π + π < CL=90% 113 π + e ν e + c.c. < CL=90% 256 π + π 2γ < π + π π 0 γ < CL=90% 174 π 0 µ + µ γ < CL=90% 210 Charge conjugation (C), Parity (P), Charge conjugation Parity (CP), or Lepton Family number (LF) violating modes π 0 γ C < CL=90% 257 π + π P,CP < CL=90% 236 2π 0 P,CP < CL=90% 238 2π 0 γ C < CL=90% 238 3π 0 γ C < CL=90% 179 3γ C < CL=90% Page 3 Created: 7/12/ :49
4 4π 0 P,CP < CL=90% 40 π 0 e + e C [f ] < CL=90% 257 π 0 µ + µ C [f ] < CL=90% 210 µ + e + µ e + LF < CL=90% 264 f 0 (500) or σ [g] was f 0 (600) I G (J PC ) = 0 + (0 + + ) Mass m = ( ) MeV Full width Γ = ( ) MeV f 0 (500) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) π π dominant γγ seen ρ(770) [h] I G (J PC ) = 1 + (1 ) Mass m = ± 0.25 MeV Full width Γ = ± 0.8 MeV Γ ee = 7.04 ± 0.06 kev Scale factor/ p ρ(770) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) ππ 100 % 363 ρ(770) ± decays π ± γ ( 4.5 ±0.5 ) 10 4 S= π ± η < CL=84% 152 π ± π + π π 0 < CL=84% 254 ρ(770) 0 decays π + π γ ( 9.9 ±1.6 ) π 0 γ ( 6.0 ±0.8 ) ηγ ( 3.00±0.20 ) π 0 π 0 γ ( 4.5 ±0.8 ) µ + µ [i] ( 4.55±0.28 ) e + e [i] ( 4.72±0.05 ) π + π π 0 ( π + π π + π ( 1.8 ±0.9 ) π + π π 0 π 0 ( 1.6 ±0.8 ) π 0 e + e < CL=90% Page 4 Created: 7/12/ :49
5 ω(782) ω(782) I G (J PC ) = 0 (1 ) Mass m = ± 0.12 MeV (S = 1.9) Full width Γ = 8.49 ± 0.08 MeV Γ ee = 0.60 ± 0.02 kev Scale factor/ p ω(782) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) π + π π 0 (89.2 ±0.7 ) % 327 π 0 γ ( 8.28±0.28) % S= π + π ( ) % S= neutrals (excludingπ 0 γ) ( ) 10 3 S=1.1 ηγ ( 4.6 ±0.4 ) 10 4 S= π 0 e + e ( 7.7 ±0.6 ) π 0 µ + µ ( 1.3 ±0.4 ) 10 4 S= e + e ( 7.28±0.14) 10 5 S= π + π π 0 π 0 < CL=90% 262 π + π γ < CL=95% 366 π + π π + π < CL=90% 256 π 0 π 0 γ ( 6.6 ±1.1 ) ηπ 0 γ < CL=90% 162 µ + µ ( 9.0 ±3.1 ) γ < CL=95% 391 Charge conjugation (C) violating modes ηπ 0 C < CL=90% 162 2π 0 C < CL=90% 367 3π 0 C < CL=90% Page 5 Created: 7/12/ :49
6 η (958) I G (J PC ) = 0 + (0 + ) Mass m = ± 0.06 MeV Full width Γ = ± MeV p η (958) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) π + π η (42.9 ±0.7 ) % 232 ρ 0 γ(including non-resonant (29.1 ±0.5 ) % 165 π + π γ) π 0 π 0 η (22.2 ±0.8 ) % 239 ωγ ( 2.75±0.23) % 159 γγ ( 2.20±0.08) % 479 3π 0 ( 2.14±0.20) µ + µ γ ( 1.08±0.27) π + π µ + µ < % 401 π + π π 0 ( 3.8 ±0.4 ) π 0 ρ 0 < 4 % 90% 111 2(π + π ) < % 372 π + π 2π 0 < % 376 2(π + π ) neutrals < 1 % 95% 2(π + π )π 0 < % 298 2(π + π )2π 0 < 1 % 95% 197 3(π + π ) < % 189 π + π e + e ( π + e ν e + c.c. < % 469 γe + e < % 479 π 0 γγ < % 469 4π 0 < % 380 e + e < % 479 invisible < % Charge conjugation (C), Parity (P), Lepton family number (LF) violating modes π + π P,CP < % 458 π 0 π 0 P,CP < % 459 π 0 e + e C [f ] < % 469 ηe + e C [f ] < % 322 3γ C < % 479 µ + µ π 0 C [f ] < % 445 µ + µ η C [f ] < % 273 e µ LF < % Page 6 Created: 7/12/ :49
7 f 0 (980) [j] I G (J PC ) = 0 + (0 + + ) Mass m = 990 ± 20 MeV Full width Γ = 40 to 100 MeV f 0 (980) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) π π dominant 476 K K seen 36 γγ seen 495 a 0 (980) [j] I G (J PC ) = 1 (0 + + ) Mass m = 980 ± 20 MeV Full width Γ = 50 to 100 MeV a 0 (980) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) η π dominant 319 K K seen γγ seen 490 φ(1020) φ(1020) I G (J PC ) = 0 (1 ) Mass m = ± MeV (S = 1.1) Full width Γ = 4.26 ± 0.04 MeV (S = 1.4) Scale factor/ p φ(1020) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) K + K (48.9 ±0.5 ) % S= K 0 L K0 S (34.2 ±0.4 ) % S= ρπ + π + π π 0 (15.32 ±0.32 ) % S=1.1 η γ ( 1.309±0.024) % S= π 0 γ ( 1.27 ±0.06 ) l + l 510 e + e ( 2.954±0.030) 10 4 S= µ + µ ( 2.87 ±0.19 ) ηe + e ( 1.15 ±0.10 ) π + π ( 7.4 ±1.3 ) ωπ 0 ( 4.7 ±0.5 ) ω γ < 5 % CL=84% 209 ργ < CL=90% 215 π + π γ ( 4.1 ±1.3 ) Page 7 Created: 7/12/ :49
8 f 0 (980)γ ( 3.22 ±0.19 ) 10 4 S= π 0 π 0 γ ( 1.13 ±0.06 ) π + π π + π ( ) π + π + π π π 0 < CL=90% 342 π 0 e + e ( 1.12 ±0.28 ) π 0 ηγ ( 7.27 ±0.30 ) 10 5 S= a 0 (980)γ ( 7.6 ±0.6 ) K 0 K 0 γ < CL=90% 110 η (958)γ ( 6.25 ±0.21 ) ηπ 0 π 0 γ < CL=90% 293 µ + µ γ ( 1.4 ±0.5 ) ργγ < CL=90% 215 ηπ + π < CL=90% 288 ηµ + µ < CL=90% 321 Lepton Faminly number (LF) violating modes e ± µ LF < CL=90% 504 h 1 (1170) I G (J PC ) = 0 (1 + ) Mass m = 1170 ± 20 MeV Full width Γ = 360 ± 40 MeV h 1 (1170) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ρπ seen 308 b 1 (1235) I G (J PC ) = 1 + (1 + ) Mass m = ± 3.2 MeV (S = 1.6) Full width Γ = 142 ± 9 MeV (S = 1.2) p b 1 (1235) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) ω π dominant [D/S amplitude ratio = ± 0.027] 348 π ± γ ( 1.6±0.4) ηρ seen π + π + π π 0 < 50 % 84% 535 K (892) ± K seen (KK) ± π 0 < 8 % 90% 248 K 0 S K0 L π± < 6 % 90% 235 K 0 S K0 S π± < 2 % 90% 235 φ π < 1.5 % 84% Page 8 Created: 7/12/ :49
9 a 1 (1260) [k] I G (J PC ) = 1 (1 + + ) Mass m = 1230 ± 40 MeV [l] Full width Γ = 250 to 600 MeV a 1 (1260) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) (ρπ) S wave seen 353 (ρπ) D wave seen 353 (ρ(1450)π) S wave seen (ρ(1450)π) D wave seen σπ seen f 0 (980)π not seen 179 f 0 (1370)π seen f 2 (1270)π seen K K (892)+ c.c. seen πγ seen 608 f 2 (1270) I G (J PC ) = 0 + (2 + + ) Mass m = ± 1.2 MeV (S = 1.1) Full width Γ = MeV (S = 1.5) Scale factor/ p f 2 (1270) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) ππ ( ) % S= π + π 2π 0 ( ) % S= K K ( 4.6 ±0.4 ) % S= π + 2π ( 2.8 ±0.4 ) % S= ηη ( 4.0 ±0.8 ) 10 3 S= π 0 ( 3.0 ±1.0 ) γγ ( 1.64±0.19) 10 5 S= ηππ < CL=95% 477 K 0 K π + + c.c. < CL=95% 293 e + e < CL=90% Page 9 Created: 7/12/ :49
10 f 1 (1285) I G (J PC ) = 0 + (1 + + ) Mass m = ± 0.5 MeV (S = 1.8) Full width Γ = 24.2 ± 1.1 MeV (S = 1.3) Scale factor/ p f 1 (1285) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) 4π ( ) % S= π 0 π 0 π + π ( ) % S= π + 2π ( ) % S= ρ 0 π + π ( ) % S= ρ 0 ρ 0 seen 4π 0 < CL=90% 568 ηπ + π (35 ±15 ) % 479 ηππ ( ) % S= a 0 (980)π [ignoring a 0 (980) (36 ± 7 ) % 238 K K] ηππ [excluding a 0 (980)π] (16 ± 7 ) % 482 K K π ( 9.0± 0.4) % S= K K (892) not seen π + π π 0 ( 3.0± 0.9) ρ ± π < CL=95% 390 γρ 0 ( 5.5± 1.3) % S= φγ ( 7.4± 2.6) η(1295) η(1295) I G (J PC ) = 0 + (0 + ) Mass m = 1294 ± 4 MeV (S = 1.6) Full width Γ = 55 ± 5 MeV η(1295) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ηπ + π seen 487 a 0 (980)π seen 248 ηπ 0 π 0 seen 490 η(ππ) S-wave seen Page 10 Created: 7/12/ :49
11 π(1300) π(1300) I G (J PC ) = 1 (0 + ) Mass m = 1300 ± 100 MeV [l] Full width Γ = 200 to 600 MeV π(1300) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ρπ seen 404 π(ππ) S-wave seen a 2 (1320) I G (J PC ) = 1 (2 + + ) Mass m = MeV (S = 1.2) Full width Γ = 107 ± 5 MeV [l] Scale factor/ p a 2 (1320) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) 3π (70.1 ±2.7 ) % S= ηπ (14.5 ±1.2 ) % 535 ωππ (10.6 ±3.2 ) % S= K K ( 4.9 ±0.8 ) % 437 η (958)π ( 5.3 ±0.9 ) π ± γ ( 2.68±0.31) γγ ( 9.4 ±0.7 ) e + e < CL=90% 659 f 0 (1370) [j] I G (J PC ) = 0 + (0 + + ) Mass m = 1200 to 1500 MeV Full width Γ = 200 to 500 MeV f 0 (1370) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ππ seen 672 4π seen 617 4π 0 seen 617 2π + 2π seen 612 π + π 2π 0 seen 615 ρ ρ dominant 2(ππ) S-wave seen π(1300)π seen a 1 (1260)π seen 35 Page 11 Created: 7/12/ :49
12 ηη seen 411 K K seen 475 K K nπ not seen 6π not seen 508 ωω not seen γγ seen 685 e + e not seen 685 π 1 (1400) [n] I G (J PC ) = 1 (1 + ) Mass m = 1354 ± 25 MeV (S = 1.8) Full width Γ = 330 ± 35 MeV π 1 (1400) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ηπ 0 seen 557 ηπ seen 556 η(1405) [o] I G (J PC ) = 0 + (0 + ) Mass m = ± 1.8 MeV [l] (S = 2.1) Full width Γ = 51.0 ± 2.9 MeV [l] (S = 1.8) p η(1405) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) K K π seen 424 ηππ seen 562 a 0 (980)π seen 345 η(ππ) S-wave seen f 0 (980)η seen 4π seen 639 ρρ <58 % 99.85% ρ 0 γ seen 491 K (892)K seen Page 12 Created: 7/12/ :49
13 f 1 (1420) [p] I G (J PC ) = 0 + (1 + + ) Mass m = ± 0.9 MeV (S = 1.1) Full width Γ = 54.9 ± 2.6 MeV f 1 (1420) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) K K π dominant 438 K K (892)+ c.c. dominant 163 η π π possibly seen 573 φγ seen 349 ω(1420) [q] I G (J PC ) = 0 (1 ) Mass m ( ) MeV Full width Γ ( ) MeV ω(1420) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ρ π dominant 486 ωππ seen 444 b 1 (1235)π seen 125 e + e seen 710 a 0 (1450) [j] I G (J PC ) = 1 (0 + + ) Mass m = 1474 ± 19 MeV Full width Γ = 265 ± 13 MeV a 0 (1450) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) πη seen 627 πη (958) seen 410 K K seen 547 ωππ seen 484 a 0 (980)ππ seen 342 γγ seen Page 13 Created: 7/12/ :49
14 ρ(1450) [r] I G (J PC ) = 1 + (1 ) Mass m = 1465 ± 25 MeV [l] Full width Γ = 400 ± 60 MeV [l] ρ(1450) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ππ seen 720 4π seen 669 e + e seen 732 η ρ possibly seen 311 a 2 (1320)π not seen 54 K K not seen 541 K K (892)+ c.c. possibly seen 229 η γ possibly seen 630 f 0 (500)γ not seen f 0 (980)γ not seen 398 f 0 (1370)γ not seen 92 f 2 (1270)γ not seen 178 η(1475) [o] I G (J PC ) = 0 + (0 + ) Mass m = 1476 ± 4 MeV (S = 1.3) Full width Γ = 85 ± 9 MeV (S = 1.5) η(1475) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) K K π dominant 477 K K (892)+ c.c. seen 245 a 0 (980)π seen 396 γγ seen Page 14 Created: 7/12/ :49
15 f 0 (1500) [n] I G (J PC ) = 0 + (0 + + ) Mass m = 1505 ± 6 MeV (S = 1.3) Full width Γ = 109 ± 7 MeV p f 0 (1500) DECAY MODES Fraction (Γ i /Γ) Scale factor (MeV/c) π π (34.9±2.3) % π + π seen 740 2π 0 seen 741 4π (49.5±3.3) % π 0 seen 691 2π + 2π seen 687 2(ππ) S-wave seen ρρ seen π(1300)π seen 144 a 1 (1260)π seen 218 ηη ( 5.1±0.9) % ηη (958) ( 1.9±0.8) % 1.7 K K ( 8.6±1.0) % γ γ not seen 753 f 2 (1525) IG (J PC ) = 0 + (2 + + ) Mass m = 1525 ± 5 MeV [l] Full width Γ = MeV [l] f 2 (1525) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) K K (88.7 ±2.2 ) % 581 ηη (10.4 ±2.2 ) % 530 ππ ( 8.2 ±1.5 ) γγ ( 1.11±0.14) Page 15 Created: 7/12/ :49
16 π 1 (1600) [n] I G (J PC ) = 1 (1 + ) Mass m = MeV Full width Γ = 241 ± 40 MeV (S = 1.4) π 1 (1600) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) πππ not seen 803 ρ 0 π not seen 641 f 2 (1270)π not seen 318 b 1 (1235)π seen 357 η (958)π seen 543 f 1 (1285)π seen 314 η 2 (1645) I G (J PC ) = 0 + (2 + ) Mass m = 1617 ± 5 MeV Full width Γ = 181 ± 11 MeV η 2 (1645) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) a 2 (1320)π seen 242 K K π seen 580 K K seen 404 ηπ + π seen 685 a 0 (980)π seen 499 f 2 (1270)η not seen ω(1650) [s] I G (J PC ) = 0 (1 ) Mass m = 1670 ± 30 MeV Full width Γ = 315 ± 35 MeV ω(1650) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ρπ seen 647 ωππ seen 617 ωη seen 500 e + e seen Page 16 Created: 7/12/ :49
17 ω 3 (1670) I G (J PC ) = 0 (3 ) Mass m = 1667 ± 4 MeV Full width Γ = 168 ± 10 MeV [l] ω 3 (1670) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ρπ seen 645 ωππ seen 615 b 1 (1235)π possibly seen 361 π 2 (1670) I G (J PC ) = 1 (2 + ) Mass m = ± 3.0 MeV [l] (S = 1.4) Full width Γ = 260 ± 9 MeV [l] (S = 1.2) p π 2 (1670) DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) 3π (95.8±1.4) % 809 f 2 (1270)π (56.3±3.2) % 329 ρπ (31 ±4 ) % 648 σπ (10.9±3.4) % (ππ) S-wave ( 8.7±3.4) % K K (892)+ c.c. ( 4.2±1.4) % 455 ωρ ( 2.7±1.1) % 304 γγ < % 836 ρ(1450)π < % 147 b 1 (1235)π < % 365 f 1 (1285)π possibly seen 323 a 2 (1320)π not seen 292 φ(1680) φ(1680) I G (J PC ) = 0 (1 ) Mass m = 1680 ± 20 MeV [l] Full width Γ = 150 ± 50 MeV [l] φ(1680) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) K K (892)+ c.c. dominant 462 K 0 S K π seen 621 K K seen 680 e + e seen 840 ωππ not seen 623 K + K π + π seen Page 17 Created: 7/12/ :49
18 ρ 3 (1690) I G (J PC ) = 1 + (3 ) Mass m = ± 2.1 MeV [l] Full width Γ = 161 ± 10 MeV [l] (S = 1.5) p ρ 3 (1690) DECAY MODES Fraction (Γ i /Γ) Scale factor (MeV/c) 4π (71.1 ± 1.9 ) % 790 π ± π + π π 0 (67 ±22 ) % 787 ωπ (16 ± 6 ) % 655 ππ (23.6 ± 1.3 ) % 834 K K π ( 3.8 ± 1.2 ) % 629 K K ( 1.58± 0.26) % ηπ + π seen 727 ρ(770)η seen 520 ππρ seen 633 Excluding 2ρ and a 2 (1320)π. a 2 (1320)π seen 307 ρρ seen 335 ρ(1700) [r] I G (J PC ) = 1 + (1 ) Mass m = 1720 ± 20 MeV [l] (ηρ 0 and π + π modes) Full width Γ = 250 ± 100 MeV [l] (ηρ 0 and π + π modes) ρ(1700) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) 2(π + π ) large 803 ρππ dominant 653 ρ 0 π + π large 651 ρ ± π π 0 large 652 a 1 (1260)π seen 404 h 1 (1170)π seen 447 π(1300)π seen 349 ρρ seen 372 π + π seen 849 ππ seen 849 K K (892)+ c.c. seen 496 ηρ seen 545 a 2 (1320)π not seen 334 K K seen 704 e + e seen 860 π 0 ω seen Page 18 Created: 7/12/ :49
19 f 0 (1710) [t] I G (J PC ) = 0 + (0 + + ) Mass m = 1720 ± 6 MeV (S = 1.6) Full width Γ = 135 ± 8 MeV (S = 1.1) f 0 (1710) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) K K seen 704 ηη seen 663 ππ seen 849 ωω seen 357 π(1800) π(1800) I G (J PC ) = 1 (0 + ) Mass m = 1812 ± 12 MeV (S = 2.3) Full width Γ = 208 ± 12 MeV π(1800) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) π + π π seen 879 f 0 (500)π seen f 0 (980)π seen 625 f 0 (1370)π seen 368 f 0 (1500)π not seen 250 ρπ not seen 732 ηηπ seen 661 a 0 (980)η seen 473 a 2 (1320)η not seen f 2 (1270)π not seen 442 f 0 (1370)π not seen 368 f 0 (1500)π seen 250 ηη (958)π seen 375 K 0 (1430)K seen K (892)K not seen Page 19 Created: 7/12/ :49
20 φ 3 (1850) I G (J PC ) = 0 (3 ) Mass m = 1854 ± 7 MeV Full width Γ = MeV (S = 1.2) φ 3 (1850) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) K K seen 785 K K (892)+ c.c. seen 602 π 2 (1880) I G (J PC ) = 1 (2 + ) Mass m = 1895 ± 16 MeV Full width Γ = 235 ± 34 MeV f 2 (1950) I G (J PC ) = 0 + (2 + + ) Mass m = 1944 ± 12 MeV (S = 1.5) Full width Γ = 472 ± 18 MeV f 2 (1950) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) K (892)K (892) seen 387 π + π seen 962 π 0 π 0 seen 963 4π seen 925 ηη seen 803 K K seen 837 γγ seen 972 pp seen 254 f 2 (2010) I G (J PC ) = 0 + (2 + + ) Mass m = MeV Full width Γ = 202 ± 60 MeV f 2 (2010) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) φφ seen K K seen Page 20 Created: 7/12/ :49
21 a 4 (2040) I G (J PC ) = 1 (4 + + ) Mass m = MeV (S = 1.1) Full width Γ = MeV (S = 1.3) a 4 (2040) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) K K seen 868 π + π π 0 seen 974 ρπ seen 841 f 2 (1270)π seen 580 ωπ π 0 seen 819 ωρ seen 624 ηπ 0 seen 918 η (958)π seen 761 f 4 (2050) I G (J PC ) = 0 + (4 + + ) Mass m = 2018 ± 11 MeV (S = 2.1) Full width Γ = 237 ± 18 MeV (S = 1.9) f 4 (2050) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) ωω seen 637 π π (17.0±1.5) % 1000 K K ( ηη ( 2.1±0.8) π 0 < 1.2 % 964 a 2 (1320)π seen Page 21 Created: 7/12/ :49
22 φ(2170) φ(2170) I G (J PC ) = 0 (1 ) Mass m = 2175 ± 15 MeV (S = 1.6) Full width Γ = 61 ± 18 MeV φ(2170) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) e + e seen 1087 φf 0 (980) seen 416 K + K f 0 (980) seen K + K π + π K + K f 0 (980) K + K π 0 π 0 seen K 0 K ± π not seen 770 K (892) 0 K (892) 0 not seen 622 f 2 (2300) I G (J PC ) = 0 + (2 + + ) Mass m = 2297 ± 28 MeV Full width Γ = 149 ± 40 MeV f 2 (2300) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) φφ seen 529 K K seen 1037 γγ seen 1149 f 2 (2340) I G (J PC ) = 0 + (2 + + ) Mass m = 2339 ± 60 MeV Full width Γ = MeV f 2 (2340) DECAY MODES Fraction (Γ i /Γ) p (MeV/c) φφ seen 573 ηη seen Page 22 Created: 7/12/ :49
23 NOTES [a] See the Note on π ± l ± νγ and K ± l ± νγ Form Factors in the π ± Particle Listings for definitions and details. [b] Measurements of Γ(e + ν e )/Γ(µ + ν µ ) always include decays with γ s, and measurements of Γ(e + ν e γ) and Γ(µ + ν µ γ) never include low-energy γ s. Therefore, since no clean separation is possible, we consider the modes with γ s to be subreactions of the modes without them, and let [Γ(e + ν e ) + Γ(µ + ν µ )]/Γ total = 100%. [c] See the π ± Particle Listings for the energy limits used in this measurement; low-energy γ s are not included. [d] Derived from an analysis of neutrino-oscillation experiments. [e] Astrophysical and cosmological arguments give limits of order ; see the π 0 Particle Listings. [f ] C parity forbids this to occur as a single-photon process. [g] See the Note on scalar mesons in the f 0 (500) Particle Listings. The interpretation of this entry as a particle is controversial. [h] See the Note on ρ(770) in the ρ(770) Particle Listings. [i] The ωρ interference is then due to ωρ mixing only, and is expected to be small. If e µ universality holds, Γ(ρ 0 µ + µ ) = Γ(ρ 0 e + e ) [j] See the Note on scalar mesons in the f 0 (500) Particle Listings. [k] See the Note on a 1 (1260) in the a 1 (1260) Particle Listings in PDG 06, Journal of Physics, G 33 1 (2006). [l] This is only an educated guess; the error given is larger than the error on the average of the published values. See the Particle Listings for details. [n] See the Note on non-qq mesons in the Particle Listings in PDG 06, Journal of Physics, G 33 1 (2006). [o] See the Note on the η(1405) in the η(1405) Particle Listings. [p] See the Note on the f 1 (1420) in the η(1405) Particle Listings. [q] See also the ω(1650) Particle Listings. [r] See the Note on the ρ(1450) and the ρ(1700) in the ρ(1700) Particle Listings. [s] See also the ω(1420) Particle Listings. [t] See the Note on f 0 (1710) in the f 0 (1710) Particle Listings in 2004 edition of Review of Particle Physics. Page 23 Created: 7/12/ :49
LEPTONS. Mass m = ( ± ) 10 6 u Mass m = ± MeV me + m e
LEPTONS e J = 1 2 Mass m = (548.5799110 ± 0.0000012) 10 6 u Mass m = 0.510998902 ± 0.000000021 MeV me + m e /m < 8 10 9, CL = 90% qe + + q / e e < 4 10 8 Magnetic moment µ =1.001159652187 ± 0.000000000004
Διαβάστε περισσότεραHadronic Tau Decays at BaBar
Hadronic Tau Decays at BaBar Swagato Banerjee Joint Meeting of Pacific Region Particle Physics Communities (DPF006+JPS006 Honolulu, Hawaii 9 October - 3 November 006 (Page: 1 Hadronic τ decays Only lepton
Διαβάστε περισσότεραST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
Διαβάστε περισσότεραThree coupled amplitudes for the πη, K K and πη channels without data
Three coupled amplitudes for the πη, K K and πη channels without data Robert Kamiński IFJ PAN, Kraków and Łukasz Bibrzycki Pedagogical University, Kraków HaSpect meeting, Kraków, V/VI 216 Present status
Διαβάστε περισσότεραPARTIAL NOTES for 6.1 Trigonometric Identities
PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot
Διαβάστε περισσότεραEE512: Error Control Coding
EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3
Διαβάστε περισσότεραHOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
Διαβάστε περισσότερα6.1. Dirac Equation. Hamiltonian. Dirac Eq.
6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2
Διαβάστε περισσότεραExample Sheet 3 Solutions
Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note
Διαβάστε περισσότεραFinite Field Problems: Solutions
Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The
Διαβάστε περισσότεραCHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS
CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =
Διαβάστε περισσότεραOther Test Constructions: Likelihood Ratio & Bayes Tests
Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :
Διαβάστε περισσότεραMath 6 SL Probability Distributions Practice Test Mark Scheme
Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry
Διαβάστε περισσότεραk A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +
Chapter 3. Fuzzy Arithmetic 3- Fuzzy arithmetic: ~Addition(+) and subtraction (-): Let A = [a and B = [b, b in R If x [a and y [b, b than x+y [a +b +b Symbolically,we write A(+)B = [a (+)[b, b = [a +b
Διαβάστε περισσότεραΜηχανική Μάθηση Hypothesis Testing
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Μηχανική Μάθηση Hypothesis Testing Γιώργος Μπορμπουδάκης Τμήμα Επιστήμης Υπολογιστών Procedure 1. Form the null (H 0 ) and alternative (H 1 ) hypothesis 2. Consider
Διαβάστε περισσότεραStatistical Inference I Locally most powerful tests
Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided
Διαβάστε περισσότεραDynamic types, Lambda calculus machines Section and Practice Problems Apr 21 22, 2016
Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Dynamic types, Lambda calculus machines Apr 21 22, 2016 1 Dynamic types and contracts (a) To make sure you understand the
Διαβάστε περισσότεραC.S. 430 Assignment 6, Sample Solutions
C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order
Διαβάστε περισσότεραEPS On Behalf of Belle Collaboration. Takayoshi Ohshima Nagoya University, Japan
1 τ-decays at Belle On Behalf of Belle Collaboration Takayoshi Ohshima Nagoya University, Japan KEKB/ Belle PEP-II/ BaBar 1. τ K s π ν τ study Branching ratio Mass spectrum (vector & scalar FF; mass &
Διαβάστε περισσότεραAreas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
Διαβάστε περισσότεραEcon 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1
Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test
Διαβάστε περισσότεραInverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------
Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin
Διαβάστε περισσότεραApproximation of distance between locations on earth given by latitude and longitude
Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth
Διαβάστε περισσότερα( ) 2 and compare to M.
Problems and Solutions for Section 4.2 4.9 through 4.33) 4.9 Calculate the square root of the matrix 3!0 M!0 8 Hint: Let M / 2 a!b ; calculate M / 2!b c ) 2 and compare to M. Solution: Given: 3!0 M!0 8
Διαβάστε περισσότεραPotential Dividers. 46 minutes. 46 marks. Page 1 of 11
Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and
Διαβάστε περισσότεραHomework 3 Solutions
Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For
Διαβάστε περισσότεραOrdinal Arithmetic: Addition, Multiplication, Exponentiation and Limit
Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal
Διαβάστε περισσότεραω ω ω ω ω ω+2 ω ω+2 + ω ω ω ω+2 + ω ω+1 ω ω+2 2 ω ω ω ω ω ω ω ω+1 ω ω2 ω ω2 + ω ω ω2 + ω ω ω ω2 + ω ω+1 ω ω2 + ω ω+1 + ω ω ω ω2 + ω
0 1 2 3 4 5 6 ω ω + 1 ω + 2 ω + 3 ω + 4 ω2 ω2 + 1 ω2 + 2 ω2 + 3 ω3 ω3 + 1 ω3 + 2 ω4 ω4 + 1 ω5 ω 2 ω 2 + 1 ω 2 + 2 ω 2 + ω ω 2 + ω + 1 ω 2 + ω2 ω 2 2 ω 2 2 + 1 ω 2 2 + ω ω 2 3 ω 3 ω 3 + 1 ω 3 + ω ω 3 +
Διαβάστε περισσότερα1 String with massive end-points
1 String with massive end-points Πρόβλημα 5.11:Θεωρείστε μια χορδή μήκους, τάσης T, με δύο σημειακά σωματίδια στα άκρα της, το ένα μάζας m, και το άλλο μάζας m. α) Μελετώντας την κίνηση των άκρων βρείτε
Διαβάστε περισσότεραWhat happens when two or more waves overlap in a certain region of space at the same time?
Wave Superposition What happens when two or more waves overlap in a certain region of space at the same time? To find the resulting wave according to the principle of superposition we should sum the fields
Διαβάστε περισσότεραLight Hadrons and New Enhancements in J/ψ Decays at BESII
Light Hadrons and New Enhancements in J/ψ Decays at BESII Guofa XU Representing BES Collaboration Institute of High Energy Physics Chinese Academy of Sciences Beijing, China xugf@ihep.ac.cn Outline Introduction
Διαβάστε περισσότεραSolution Series 9. i=1 x i and i=1 x i.
Lecturer: Prof. Dr. Mete SONER Coordinator: Yilin WANG Solution Series 9 Q1. Let α, β >, the p.d.f. of a beta distribution with parameters α and β is { Γ(α+β) Γ(α)Γ(β) f(x α, β) xα 1 (1 x) β 1 for < x
Διαβάστε περισσότεραStrain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
Διαβάστε περισσότεραMatrices and Determinants
Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z
Διαβάστε περισσότεραSection 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
Διαβάστε περισσότεραLecture 26: Circular domains
Introductory lecture notes on Partial Differential Equations - c Anthony Peirce. Not to be copied, used, or revised without eplicit written permission from the copyright owner. 1 Lecture 6: Circular domains
Διαβάστε περισσότεραΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται
Διαβάστε περισσότεραDerivation of Optical-Bloch Equations
Appendix C Derivation of Optical-Bloch Equations In this appendix the optical-bloch equations that give the populations and coherences for an idealized three-level Λ system, Fig. 3. on page 47, will be
Διαβάστε περισσότεραJesse Maassen and Mark Lundstrom Purdue University November 25, 2013
Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering
Διαβάστε περισσότεραProblem 7.19 Ignoring reflection at the air soil boundary, if the amplitude of a 3-GHz incident wave is 10 V/m at the surface of a wet soil medium, at what depth will it be down to 1 mv/m? Wet soil is
Διαβάστε περισσότεραAreas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
Διαβάστε περισσότερα4.6 Autoregressive Moving Average Model ARMA(1,1)
84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this
Διαβάστε περισσότεραMATH423 String Theory Solutions 4. = 0 τ = f(s). (1) dτ ds = dxµ dτ f (s) (2) dτ 2 [f (s)] 2 + dxµ. dτ f (s) (3)
1. MATH43 String Theory Solutions 4 x = 0 τ = fs). 1) = = f s) ) x = x [f s)] + f s) 3) equation of motion is x = 0 if an only if f s) = 0 i.e. fs) = As + B with A, B constants. i.e. allowe reparametrisations
Διαβάστε περισσότεραSpace-Time Symmetries
Chapter Space-Time Symmetries In classical fiel theory any continuous symmetry of the action generates a conserve current by Noether's proceure. If the Lagrangian is not invariant but only shifts by a
Διαβάστε περισσότεραCRASH COURSE IN PRECALCULUS
CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter
Διαβάστε περισσότεραBayesian statistics. DS GA 1002 Probability and Statistics for Data Science.
Bayesian statistics DS GA 1002 Probability and Statistics for Data Science http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall17 Carlos Fernandez-Granda Frequentist vs Bayesian statistics In frequentist
Διαβάστε περισσότεραThe Simply Typed Lambda Calculus
Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and
Διαβάστε περισσότεραSecond Order Partial Differential Equations
Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y
Διαβάστε περισσότεραMathCity.org Merging man and maths
MathCity.org Merging man and maths Exercise 10. (s) Page Textbook of Algebra and Trigonometry for Class XI Available online @, Version:.0 Question # 1 Find the values of sin, and tan when: 1 π (i) (ii)
Διαβάστε περισσότεραTrigonometry 1.TRIGONOMETRIC RATIOS
Trigonometry.TRIGONOMETRIC RATIOS. If a ray OP makes an angle with the positive direction of X-axis then y x i) Sin ii) cos r r iii) tan x y (x 0) iv) cot y x (y 0) y P v) sec x r (x 0) vi) cosec y r (y
Διαβάστε περισσότεραTridiagonal matrices. Gérard MEURANT. October, 2008
Tridiagonal matrices Gérard MEURANT October, 2008 1 Similarity 2 Cholesy factorizations 3 Eigenvalues 4 Inverse Similarity Let α 1 ω 1 β 1 α 2 ω 2 T =......... β 2 α 1 ω 1 β 1 α and β i ω i, i = 1,...,
Διαβάστε περισσότερα상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님
상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님 Motivation Bremsstrahlung is a major rocess losing energies while jet articles get through the medium. BUT it should be quite different from low energy
Διαβάστε περισσότεραPhys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Διαβάστε περισσότεραAnswers - Worksheet A ALGEBRA PMT. 1 a = 7 b = 11 c = 1 3. e = 0.1 f = 0.3 g = 2 h = 10 i = 3 j = d = k = 3 1. = 1 or 0.5 l =
C ALGEBRA Answers - Worksheet A a 7 b c d e 0. f 0. g h 0 i j k 6 8 or 0. l or 8 a 7 b 0 c 7 d 6 e f g 6 h 8 8 i 6 j k 6 l a 9 b c d 9 7 e 00 0 f 8 9 a b 7 7 c 6 d 9 e 6 6 f 6 8 g 9 h 0 0 i j 6 7 7 k 9
Διαβάστε περισσότερα2 Composition. Invertible Mappings
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,
Διαβάστε περισσότεραLecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3
Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 1 State vector space and the dual space Space of wavefunctions The space of wavefunctions is the set of all
Διαβάστε περισσότεραHW 3 Solutions 1. a) I use the auto.arima R function to search over models using AIC and decide on an ARMA(3,1)
HW 3 Solutions a) I use the autoarima R function to search over models using AIC and decide on an ARMA3,) b) I compare the ARMA3,) to ARMA,0) ARMA3,) does better in all three criteria c) The plot of the
Διαβάστε περισσότερα6.3 Forecasting ARMA processes
122 CHAPTER 6. ARMA MODELS 6.3 Forecasting ARMA processes The purpose of forecasting is to predict future values of a TS based on the data collected to the present. In this section we will discuss a linear
Διαβάστε περισσότεραis like multiplying by the conversion factor of. Dividing by 2π gives you the
Chapter Graphs of Trigonometric Functions Answer Ke. Radian Measure Answers. π. π. π. π. 7π. π 7. 70 8. 9. 0 0. 0. 00. 80. Multipling b π π is like multipling b the conversion factor of. Dividing b 0 gives
Διαβάστε περισσότεραNuclear Physics 5. Name: Date: 8 (1)
Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly
Διαβάστε περισσότεραΑΝΙΧΝΕΥΣΗ ΓΕΓΟΝΟΤΩΝ ΒΗΜΑΤΙΣΜΟΥ ΜΕ ΧΡΗΣΗ ΕΠΙΤΑΧΥΝΣΙΟΜΕΤΡΩΝ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΕΠΙΚΟΙΝΩΝΙΩΝ ΗΛΕΚΤΡΟΝΙΚΗΣ ΚΑΙ ΣΥΣΤΗΜΑΤΩΝ ΠΛΗΡΟΦΟΡΙΚΗΣ ΑΝΙΧΝΕΥΣΗ ΓΕΓΟΝΟΤΩΝ ΒΗΜΑΤΙΣΜΟΥ ΜΕ ΧΡΗΣΗ ΕΠΙΤΑΧΥΝΣΙΟΜΕΤΡΩΝ
Διαβάστε περισσότερα2. Μηχανικό Μαύρο Κουτί: κύλινδρος με μια μπάλα μέσα σε αυτόν.
Experiental Copetition: 14 July 011 Proble Page 1 of. Μηχανικό Μαύρο Κουτί: κύλινδρος με μια μπάλα μέσα σε αυτόν. Ένα μικρό σωματίδιο μάζας (μπάλα) βρίσκεται σε σταθερή απόσταση z από το πάνω μέρος ενός
Διαβάστε περισσότερα2. THEORY OF EQUATIONS. PREVIOUS EAMCET Bits.
EAMCET-. THEORY OF EQUATIONS PREVIOUS EAMCET Bits. Each of the roots of the equation x 6x + 6x 5= are increased by k so that the new transformed equation does not contain term. Then k =... - 4. - Sol.
Διαβάστε περισσότεραΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ
Διαβάστε περισσότεραHigher Derivative Gravity Theories
Higher Derivative Gravity Theories Black Holes in AdS space-times James Mashiyane Supervisor: Prof Kevin Goldstein University of the Witwatersrand Second Mandelstam, 20 January 2018 James Mashiyane WITS)
Διαβάστε περισσότεραMINIMAL CLOSED SETS AND MAXIMAL CLOSED SETS
MINIMAL CLOSED SETS AND MAXIMAL CLOSED SETS FUMIE NAKAOKA AND NOBUYUKI ODA Received 20 December 2005; Revised 28 May 2006; Accepted 6 August 2006 Some properties of minimal closed sets and maximal closed
Διαβάστε περισσότεραDESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.
DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec
Διαβάστε περισσότεραArtiste Picasso 9.1. Total Lumen Output: lm. Peak: cd 6862 K CRI: Lumen/Watt. Date: 4/27/2018
Color Temperature: 62 K Total Lumen Output: 21194 lm Light Quality: CRI:.7 Light Efficiency: 27 Lumen/Watt Peak: 1128539 cd Power: 793 W x: 0.308 y: 0.320 Test: Narrow Date: 4/27/2018 0 Beam Angle 165
Διαβάστε περισσότεραAn Inventory of Continuous Distributions
Appendi A An Inventory of Continuous Distributions A.1 Introduction The incomplete gamma function is given by Also, define Γ(α; ) = 1 with = G(α; ) = Z 0 Z 0 Z t α 1 e t dt, α > 0, >0 t α 1 e t dt, α >
Διαβάστε περισσότεραSecond Order RLC Filters
ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor
Διαβάστε περισσότεραPractice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1
Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the
Διαβάστε περισσότεραΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3:
4 Πρόλογος Η παρούσα διπλωµατική εργασία µε τίτλο «ιερεύνηση χωρικής κατανοµής µετεωρολογικών µεταβλητών. Εφαρµογή στον ελληνικό χώρο», ανατέθηκε από το ιεπιστηµονικό ιατµηµατικό Πρόγραµµα Μεταπτυχιακών
Διαβάστε περισσότεραEvery set of first-order formulas is equivalent to an independent set
Every set of first-order formulas is equivalent to an independent set May 6, 2008 Abstract A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent
Διαβάστε περισσότεραthe total number of electrons passing through the lamp.
1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy
Διαβάστε περισσότεραD Alembert s Solution to the Wave Equation
D Alembert s Solution to the Wave Equation MATH 467 Partial Differential Equations J. Robert Buchanan Department of Mathematics Fall 2018 Objectives In this lesson we will learn: a change of variable technique
Διαβάστε περισσότεραˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ Ä ³ Éμ. Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê ƒμ Ê É Ò Ê É É Ê, Ê, μ Ö
ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ 2018.. 49.. 4.. 1291Ä1301 Š œ Š ˆŒ CMS LHC ˆ Š ˆ ˆŠˆ ŒŠ Œˆ Œ ˆ.. ³ Éμ Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê ƒμ Ê É Ò Ê É É Ê, Ê, μ Ö μ É Ö ± ɱ μ μ ʲÓÉ Éμ Ô± ³ É CMS μ²óïμ³ μ μ³ ±μ²² μ μ ±Ê Ë ± ³± ³
Διαβάστε περισσότεραSUPERPOSITION, MEASUREMENT, NORMALIZATION, EXPECTATION VALUES. Reading: QM course packet Ch 5 up to 5.6
SUPERPOSITION, MEASUREMENT, NORMALIZATION, EXPECTATION VALUES Readig: QM course packet Ch 5 up to 5. 1 ϕ (x) = E = π m( a) =1,,3,4,5 for xa (x) = πx si L L * = πx L si L.5 ϕ' -.5 z 1 (x) = L si
Διαβάστε περισσότεραderivation of the Laplacian from rectangular to spherical coordinates
derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used
Διαβάστε περισσότεραLecture 2. Soundness and completeness of propositional logic
Lecture 2 Soundness and completeness of propositional logic February 9, 2004 1 Overview Review of natural deduction. Soundness and completeness. Semantics of propositional formulas. Soundness proof. Completeness
Διαβάστε περισσότεραThe challenges of non-stable predicates
The challenges of non-stable predicates Consider a non-stable predicate Φ encoding, say, a safety property. We want to determine whether Φ holds for our program. The challenges of non-stable predicates
Διαβάστε περισσότερα5.4 The Poisson Distribution.
The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable
Διαβάστε περισσότεραSurface Mount Multilayer Chip Capacitors for Commodity Solutions
Surface Mount Multilayer Chip Capacitors for Commodity Solutions Below tables are test procedures and requirements unless specified in detail datasheet. 1) Visual and mechanical 2) Capacitance 3) Q/DF
Διαβάστε περισσότεραMean-Variance Analysis
Mean-Variance Analysis Jan Schneider McCombs School of Business University of Texas at Austin Jan Schneider Mean-Variance Analysis Beta Representation of the Risk Premium risk premium E t [Rt t+τ ] R1
Διαβάστε περισσότερα(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)
Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)
Διαβάστε περισσότεραMean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O
Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.
Διαβάστε περισσότεραConcrete Mathematics Exercises from 30 September 2016
Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)
Διαβάστε περισσότεραDong Liu State Key Laboratory of Particle Detection and Electronics University of Science and Technology of China
Dong Liu State Key Laboratory of Particle Detection and Electronics University of Science and Technology of China ISSP, Erice, 7 Outline Introduction of BESIII experiment Motivation of the study Data sample
Διαβάστε περισσότεραw o = R 1 p. (1) R = p =. = 1
Πανεπιστήµιο Κρήτης - Τµήµα Επιστήµης Υπολογιστών ΗΥ-570: Στατιστική Επεξεργασία Σήµατος 205 ιδάσκων : Α. Μουχτάρης Τριτη Σειρά Ασκήσεων Λύσεις Ασκηση 3. 5.2 (a) From the Wiener-Hopf equation we have:
Διαβάστε περισσότεραProblem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ.
Chemistry 362 Dr Jean M Standard Problem Set 9 Solutions The ˆ L 2 operator is defined as Verify that the angular wavefunction Y θ,φ) Also verify that the eigenvalue is given by 2! 2 & L ˆ 2! 2 2 θ 2 +
Διαβάστε περισσότεραwave energy Superposition of linear plane progressive waves Marine Hydrodynamics Lecture Oblique Plane Waves:
3.0 Marine Hydrodynamics, Fall 004 Lecture 0 Copyriht c 004 MIT - Department of Ocean Enineerin, All rihts reserved. 3.0 - Marine Hydrodynamics Lecture 0 Free-surface waves: wave enery linear superposition,
Διαβάστε περισσότεραSection 7.6 Double and Half Angle Formulas
09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)
Διαβάστε περισσότεραΕ Κ Θ Ε Σ Η Δ Ο Κ Ι Μ Ω Ν
Αριθμός έκθεζης δοκιμών / Test report number Σειριακός αριθμός οργάνοσ / Instrument serial No T Πελάηης / Customer TOTAL Q Επγαζηήπια Διακπιβώζεων A.E. Κοπγιαλενίος 20, Τ.Κ. 11526 Αθήνα 20 Korgialeniou
Διαβάστε περισσότεραNotes on the Open Economy
Notes on the Open Econom Ben J. Heijdra Universit of Groningen April 24 Introduction In this note we stud the two-countr model of Table.4 in more detail. restated here for convenience. The model is Table.4.
Διαβάστε περισσότεραΑναζητώντας παράξενα σωµατίδια στο ALICE
Αναζητώντας παράξενα σωµατίδια στο ALICE K 0 s π+ π - Λ π - p Ξ - π - Λ π - p π - 7.7.018 Δέσποινα Χατζηφωτιάδου 1 παράξενα σωµατίδια µεσόνιο βαριόνιο s K 0 s ds, ds Λ uds αδρόνια που περιέχουν τουλάχιστον
Διαβάστε περισσότεραBounding Nonsplitting Enumeration Degrees
Bounding Nonsplitting Enumeration Degrees Thomas F. Kent Andrea Sorbi Università degli Studi di Siena Italia July 18, 2007 Goal: Introduce a form of Σ 0 2-permitting for the enumeration degrees. Till now,
Διαβάστε περισσότεραΠτυχιακή Εργασι α «Εκτι μήσή τής ποιο τήτας εικο νων με τήν χρή σή τεχνήτων νευρωνικων δικτυ ων»
Ανώτατο Τεχνολογικό Εκπαιδευτικό Ίδρυμα Ανατολικής Μακεδονίας και Θράκης Σχολή Τεχνολογικών Εφαρμογών Τμήμα Μηχανικών Πληροφορικής Πτυχιακή Εργασι α «Εκτι μήσή τής ποιο τήτας εικο νων με τήν χρή σή τεχνήτων
Διαβάστε περισσότεραSolutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz
Solutions to the Schrodinger equation atomic orbitals Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz ybridization Valence Bond Approach to bonding sp 3 (Ψ 2 s + Ψ 2 px + Ψ 2 py + Ψ 2 pz) sp 2 (Ψ 2 s + Ψ 2 px + Ψ 2 py)
Διαβάστε περισσότεραSrednicki Chapter 55
Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third
Διαβάστε περισσότερα1) Formulation of the Problem as a Linear Programming Model
1) Formulation of the Problem as a Linear Programming Model Let xi = the amount of money invested in each of the potential investments in, where (i=1,2, ) x1 = the amount of money invested in Savings Account
Διαβάστε περισσότεραΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Όλοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα μικρότεροι του 10000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Αν κάπου κάνετε κάποιες υποθέσεις
Διαβάστε περισσότερα