F(q 2 ) = 1 Q Q = d 3 re i q r ρ(r) d 3 rρ(r),
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- Geraldine O’Neal’
- 5 years ago
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1 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ Ó Ø ÔÓÒ Ò ÖÐ ÕÙÖ ÑÓÐ ÏÓ ÖÓÒÓÛ ÂÒ ÃÓÒÓÛ ÍÒÚÖ ØÝ ÃÐ ÁÒ ØØÙØ Ó ÆÙÐÖ ÈÝ ÈÆ ÖÓÛ ÛØ º ÊÙÞ ÖÖÓÐ Ò º º ÓÖÓÓÚ ÅÒ¹ÏÓÖ ÓÔ Ð ¾¼½½ ÍÒÖ ØÒÒ ÀÖÓÒ ËÔØÖ Ð ËÐÓÚÒµ ¹½¼ ÂÙÐÝ ¾¼½½ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
2 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ØÐ Ò ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ Ó Ø ÔÓÒ Ò ÖÐ ÕÙÖ ÑÓÐ Ï ÐÜÒÖ º ÓÖÓÓÚ ÒÖÕÙ ÊÙÞ ÖÖÓÐ ÈÊ ¾ ¾¼½¼µ ¼¼¼½ ÖÚ½¼¼º¼ Ô¹Ô Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
3 ÇÙØÐÒ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ½ ¾ ÁÒØÖÓÙØÓÒ ÒØÓÒ ÅÓØÚØÓÒ ÜÐÙ Ú ÔÖÓ ÖÐ ÕÙÖ ÑÓÐ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ Ê ÙÐØ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
4 ØÖÙØÓÒ Ó Ö ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÒØÓÒ ÜÐÙ Ú ÔÖÓ Ρr r Q = d 3 rρ(r), F(q 2 ) = 1 Q d 3 re i q r ρ(r) Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
5 ØÖÙØÓÒ Ó Ö ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÒØÓÒ ÜÐÙ Ú ÔÖÓ Ρr r = 1 Q Q = d 3 rρ(r), F(q 2 ) = 1 d 3 re i q r ρ(r) Q d 3 rρ(r)[1 i q r 1 2 ( q r)2 +...] = 1 q2 d 3 rr 2 ρ(r)+... 6Q r 2 = 6 d dq 2F(q2 ) Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
6 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÒØÓÒ ÜÐÙ Ú ÔÖÓ ÒØÓÒ Ó ØÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÖÐØ ØÓ Ø ØÖÒ ÚÖ ØÝ ÒÖÐÞ ÈÖØÓÒ ØÖÙØÓÒ ÑÜÑÙѹÐØÝ È ÖÐØ ØÓ ÔÒ ØÖÙØÓÒ µ π + (p ) O µνµ 1 µ n 1 T n 1 π + (p) =AS p µ ν i=0 ÚÒ µ1 µi p µ i+1 p µ n 1 Bπ,u Tni (t) m π p = 1 2 (p +p) = p p t = 2 AS ÝÑÑØÖÞØÓÒ Ò ν,...,µ n 1 ÓÐÐÓÛ Ý ÒØ ÝÑÑØÖÞØÓÒ Ò µ,ν ØÖ Ò ÐÐ ÒÜ ÔÖ Ö ÙØÖغ O µνµ 1 µ n 1 T = AS u(0)iσ µν id µ 1...iD µ n 1 u(0) Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
7 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÒØÓÒ ÜÐÙ Ú ÔÖÓ ÒØÓÒ Ó ØÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÖÐØ ØÓ Ø ØÖÒ ÚÖ ØÝ ÒÖÐÞ ÈÖØÓÒ ØÖÙØÓÒ ÑÜÑÙѹÐØÝ È ÖÐØ ØÓ ÔÒ ØÖÙØÓÒ µ π + (p ) O µνµ 1 µ n 1 T n 1 π + (p) =AS p µ ν i=0 ÚÒ µ1 µi p µ i+1 p µ n 1 Bπ,u Tni (t) m π p = 1 2 (p +p) = p p t = 2 AS ÝÑÑØÖÞØÓÒ Ò ν,...,µ n 1 ÓÐÐÓÛ Ý ÒØ ÝÑÑØÖÞØÓÒ Ò µ,ν ØÖ Ò ÐÐ ÒÜ ÔÖ Ö ÙØÖغ O µνµ 1 µ n 1 T = AS u(0)iσ µν id µ 1...iD µ n 1 u(0) π + (p ) u(0)σ µν u(0) π + (p) = AS p µ ν B π,u T10 (t) m π AS π + (p ) u(0)σ µν D µ 1 u(0) π + (p) = AS p µ ν p µ 1 Bπ,u T20 (t) m π Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
8 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÜÐÙ Ú ÔÖÓ Ò É ÒØÓÒ ÜÐÙ Ú ÔÖÓ P 2 N k 2 R q - (a) q R k + 2 RP + 2 N P 2 N k 2 q R - q 0 (b) R k + 2 RP + 2 N ÔÐÝ ÎÖØÙÐ ÓÑÔØÓÒ ËØØÖÒ non-zero momentum transfer to the target, at least one photon virtual L P 2 N R q k 2 T H ` p M p M + ` R k + 2 M RP + 2 N ÀÖ Å ÓÒ ÈÖÓÙØÓÒ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
9 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ØÓÒÖÝ Ó ÑØÖÜ ÐÑÒØ ÒØÓÒ ÜÐÙ Ú ÔÖÓ ÒÖÐ ØÖÙØÙÖ Ó Ø ÓØ ÑØÖÜ ÐÑÒØ A O B ÓÒ¹ÔÖØÐ ØØ ÈÖØÓÒ ØÖÙØÓÒ Ó ÒÐÙ Ú Á˵ ÓÒ¹ÔÖØÐ ØØ ÚÙÙÑ ØÖÙØÓÒ ÑÔÐØÙ µ Ó ÖÓÒ ÓÖÑ ØÓÖ ÀÅȵ ÓÒ¹ÔÖØÐ ØØ Ó ÖÒØ ÑÓÑÒØÙÑ È ÜÐÙ Ú ÁË ÎË ÀÅȵ ÑÒݹÔÖØÐ ØØ ÚÙÙÑ ØÖÒ ØÓÒ ÓÖÑ ØÓÖ µ ÖÒØ ÖÓÒ ØØ µ ÌÖÒ ØÓÒ ØÖÙØÓÒ ÑÔÐØÙ h h γγ ÈÖ ² ËÞÝÑÒÓÛ ¾¼¼µ ººº Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
10 ÄØØ Ö ÙÐØ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÒØÓÒ ÜÐÙ Ú ÔÖÓ ÅÒÝ Ö ÙÐØ Û ÓÑ ÖÓÑ ÐØØ ÔÐÐÝ ÓÖ Ø ÔÓÒ ÛÐÐ ÒÓØ Ð Ò ÔÝ Ð ÜÔÖÑÒØ º Ï ÛÒØ ØÓ ÓÑÔÙØ ØÑ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
11 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÅÓØÚØÓÒ ÉË Ø ÒØÓÒ ÜÐÙ Ú ÔÖÓ Ø ÖÓÑ º ÖÓÑÑÐ Ø Ðº É˵ ÈÊÄ ½¼½ ¾¼¼µ ½¾¾¼¼½ Π,u B n0t n 1 monopole n tgev 2 ÅÓÒÓÔÓÐ Ø m 1 = 760±50 ÅÎ ρµ m 2 = 1120±250 ÅÎ f 2 µ Ñ ÓÒ ÓÑÒÒµ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
12 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ Ó ÖÐ ÕÙÖ ÑÓÐ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ F? C 9! A 8 O µνµ1 µn 1 T π(p) π(p ) ÖÓ one-quark-loop, large N c covariant Lagrangian calculation soft regime chiral symmetry breaking NJL, local and nonlocal, instanton-motivated few parameters (traded for f π, m π,... ) numerous processes with pions, γ,... no confinement - careful not to open the qq threshold quark model scale low - need for QCD evolution to higher scales Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
13 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÈÓÒ ÚÐÓÔ ØÖÙØÙÖ Ú Ø ÕÙÖ ÐÓÓÔ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
14 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÈÓÒ ÚÐÓÔ ØÖÙØÙÖ Ú Ø ÕÙÖ ÐÓÓÔ ÔÔÖÓ ÑÓÐ É ÚÓÐÙØÓÒ ÚÓÐÙØÓÒ ÒÖØ ÐÙÓÒ Ò Ø ÕÙÖ Ø Ð ÒÖ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
15 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÈÓÒ ÚÐÓÔ ØÖÙØÙÖ Ú Ø ÕÙÖ ÐÓÓÔ ÔÔÖÓ ÑÓÐ É ÚÓÐÙØÓÒ ÚÓÐÙØÓÒ ÒÖØ ÐÙÓÒ Ò Ø ÕÙÖ Ø Ð ÒÖ ÐÐ ØÙÖ Ø ÙÔÔÓÖØ ÔÓÐÝÒÓÑÐØÝ ÔÓ ØÚØÝ Ö Ò ÑÓÑÒØÙÑ ÙÑ ÖÙÐ ÐÐÒ¹ÖÓ F 2 = 2xF 1 µ º º º µ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
16 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÈÓÒ ÚÐÓÔ ØÖÙØÙÖ Ú Ø ÕÙÖ ÐÓÓÔ ÔÔÖÓ ÑÓÐ É ÚÓÐÙØÓÒ ÚÓÐÙØÓÒ ÒÖØ ÐÙÓÒ Ò Ø ÕÙÖ Ø Ð ÒÖ ÐÐ ØÙÖ Ø ÙÔÔÓÖØ ÔÓÐÝÒÓÑÐØÝ ÔÓ ØÚØÝ Ö Ò ÑÓÑÒØÙÑ ÙÑ ÖÙÐ ÐÐÒ¹ÖÓ F 2 = 2xF 1 µ º º º µ ÆÜØ ÐÓ ÖÝ Ó ÓÙÖ ÓÐ Ö ÙÐØ ÓÛÒ ØØ Ø ÔÔÖÓ Ö ÓÒÐ ÓÖ ÓÑÔÙØÒ ÓØ ÑØÖÜ ÐÑÒØ ÔÔÖÒ Ò ¹ÒÖÝ ÜÔÖÑÒØ Ò ÐØØ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
17 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÈÖØÓÒ ØÖÙØÓÒ ÙÒØÓÒ Ó Ø ÔÓÒ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ NJL gives the constant valence PDF [Davidson, Arriola, 1995]: q(x) = 1 Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
18 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÈÖØÓÒ ØÖÙØÓÒ ÙÒØÓÒ Ó Ø ÔÓÒ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ x qx NJL gives the constant valence PDF [Davidson, Arriola, 1995]: q(x) = 1 LO DGLAP QCD evolution (good at intermediate x) to higher scales Q 0.313, 0.350, 0.4, 1 GeV x constant PDF of the also pion follows from AdS/CFT models [Brodsky, Teramond 2008] BaBar pion-photon transition form factor The question of renormalization scale: momentum sum-rule µ MeV at 2 GeV valence quarks carry 47% of the momentum (Durham), α(µ 0 )/π = 0.68 Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
19 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÎÐÒ È ÖÓÑ ÆÂÄ Ú ½ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ x qx points: Drell-Yan from E615 dashed: reanalysis of the data [Wijesooriya et al., 2005] x band: valence PDF from NJL evolved from the QM scale µ 0 = MeV to µ = 2 GeV of the experiment Ð Ø ÝÖ³ ÒÐÝ Ó Ö ËÖ Ò ÎÓÐ Ò ÒÐÙÒ Ø ÓØ ÐÙÓÒ Ö ÙÑÑØÓÒ ÑÓÚ Ø ØÖÒØ ØÓ ÐÓÛÖ xµ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
20 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÎÐÒ È ÖÓÑ ÆÂÄ Ú º ØÖÒ ÚÖ ÐØØ ØÖÒ ÚÖ ÐØØ ÙÖÖØ ÐÐÝ ÎÒ ËÒ x qx ÔÓÒØ ØÖÒ ÚÖ ÐØØ ÐÐÝ ÎÒ ËÒ ¾¼¼ ÝÐÐÓÛ ÆÂÄ ÚÓÐÚ ØÓ µ = 0.35 Î ÔÒ ÆÂÄ ÚÓÐÚ ØÓ µ = 0.5 Î ÊË ÔÖÑØÖÞØÓÒ Ø µ = 0.5 Î 0.0 x Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
21 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ È ÖÓÑ ÆÂÄ Ú º ½ Ò ÐØØ Ø Φx x points: E791 data from di-jet production in π +A band: NJL evolved to µ = 2 GeV dashed line: asymptotic form (µ ) Φx x points: transverse lattice data [Dalley, Van de Sande, 2003] band: NJL evolved to µ = 0.5 GeV Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
22 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÖÚØØÓÒÐ ÓÖÑ ØÓÖ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ A 10 A tgev 2 tgev ÈÓÒ Ö Ðص Ò Ø ÕÙÖ ÔÖØ Ó Ø ÔÒ¹¾ ÖÚØØÓÒÐ Öص Ò ËÉÅ ÓÐ ÐÒµ Ò ÆÂÄ ÐÒµ Ï Ê ¾¼¼ ÓÑÔÖ ØÓ Ø Ø ÖÑÑÐ Ø Ðº ¾¼¼¹ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
23 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÖÚØØÓÒÐ ÓÖÑ ØÓÖ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ A A tgev tgev 2 ÈÓÒ Ö Ðص Ò Ø ÕÙÖ ÔÖØ Ó Ø ÔÒ¹¾ ÖÚØØÓÒÐ Öص Ò ËÉÅ ÓÐ ÐÒµ Ò ÆÂÄ ÐÒµ Ï Ê ¾¼¼ ÓÑÔÖ ØÓ Ø Ø ÖÑÑÐ Ø Ðº ¾¼¼¹ ÉÙÖ¹ÑÓÐ ÖÐØÓÒ r 2 Θ = 1 2 r2 V ÅØØÖ ÑÓÖ ÓÒÒØÖØ ØÒ Ö ÐØÖ Ð Ó ÓÙÒ Ò ÓعÛÐÐ Ë»Ì Ý ÖÓ Ý Ò ÌÖÑÓÒµ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
24 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÓÖÛÖ ξ = 0µ È Ò ØÖÒ ÚÖ ÐØØ Ï Ò Ê ÁÑÔØ ÔÖÑØÖ ÔÒÒ Ó Ø ÒÖÐÞ ÔÖØÓÒ ØÖÙØÓÒ Ó Ø ÔÓÒ Ò ÖÐ ÕÙÖ ÑÓÐ ÈÄ ¾¼¼ µ Ø ÖÓÑ Ëº ÐÐÝ Èļ ¾¼¼ µ ½½ > O >! B > N b ÓÒÙØ ØÓ ÑÓÑÒØÙÑ ÐÐÒ Ó ÐØØ ÔÐÕÙØØ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
25 N N ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÓÖÛÖ È Ó Ø ÔÓÒ Ò ÆÂÄ Ú ÐØØ ÑÓÐ ÐØØ Ø 5 3 >! B =!! A 8 = " A 8 8 > N & $ " & $ " " $ & = # A 8 " $ & & $ " & $ " " $ & = / A 8 " $ & Ö ÖÑÒØ ÓÖ Ð µ 400 ÅÎ 8 > N & $ " J H = I L A H I A = J J E? A 3 # A 8 5, = A O E > N E > > O > >! B = " $ & Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
26 ÌÅ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÌÅ k T ¹ÙÒÒØÖØ È ÃÛÒ ¾¼¼¾ ÛÖÓÒ ÃÛÒ Ï ¾¼¼ Ê Ï ¾¼¼ ÓÐ ÚÐÒ ÓØØ ÐÙÓÒ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
27 F F ÈÓÒ ÛÚ ÙÒØÓÒ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÈÓÒ ÛÚ ÙÒØÓÒ ÖÓÑ ÐØØ É Ú º ÖÐ ÕÙÖ ÑÓÐ Ï Ëº ÈÖÐÓÚ Äº ËÒØÐ º ÊÙÞ ÖÖÓÐ ÈÄ ¾¼½¼µ ½ ÖÚ¼½½º¼ = > E C # J = G G Ψ PrΨP0 N H J E C # J = / = G G N J F B E N / = P Ψ TrΨT0 Ψ ArΨA A rfm T rfm rfm Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
28 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ º º º ØÓ ØÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
29 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÚÓÐÙØÓÒ Ó ØÖÒ ÚÖ ØÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ Ï Ê ÈÊ ¾¼¼µ ¼¼½ ÄÇ ÄȹÊÄ ÚÓÐÙØÓÒ Ó γ T n = 2C F (3 4 n 1 ) ( ) γ T 1 α(µ) n /(2β 0 ), L n = k α(µ 0) B T10(t;µ) = L 1B T10(t;µ 0) B T20(t;µ) = L 2B T20(t;µ 0) B T30(t;µ) = L 3B T30(t;µ 0) B T32(t;µ) = 1 (L1 L3)BT30(t;µ0)+L3BT32(t;µ0) 5... ÅÙÐØÔÐØÚ ÚÓÐÙØÓÒ ÓÖ B Tn0 ÓÐÙØ ÔÖØÓÒ ÓÖ Ø Ø ÓÖÒ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
30 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÚÓÐÙØÓÒ Ó ØÖÒ ÚÖ ØÝ ÐÓ ÖÝ Ó ÕÙÖ¹ÑÓÐ Ö ÙÐØ ÁÒ ØÒعÓÖÑ ÔÓÒ ÛÚ ÙÒØÓÒ É ÚÓÐÙØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ Ï Ê ÈÊ ¾¼¼µ ¼¼½ ÄÇ ÄȹÊÄ ÚÓÐÙØÓÒ Ó γ T n = 2C F (3 4 n 1 ) ( ) γ T 1 α(µ) n /(2β 0 ), L n = k α(µ 0) B T10(t;µ) = L 1B T10(t;µ 0) B T20(t;µ) = L 2B T20(t;µ 0) B T30(t;µ) = L 3B T30(t;µ 0) B T32(t;µ) = 1 (L1 L3)BT30(t;µ0)+L3BT32(t;µ0) 5... ÅÙÐØÔÐØÚ ÚÓÐÙØÓÒ ÓÖ B Tn0 ÓÐÙØ ÔÖØÓÒ ÓÖ Ø Ø ÓÖÒ γ1 T = 8 3, γt 2 = 8 B T10(t;2 GeV) = 0.75B T10(t;313 MeV) B T20(t;2 GeV) = 0.43B T20(t;313 MeV) Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
31 B T10 Ò B T20 Ò ÆÂÄ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ n 1 m Π 600MeV Π,u B n0t n tgev 2 ÆÂÄ M = 250 ÅÎ m π = 600 ÅÎ ÚÓÐÚ ØÓ Ø ÐØØ Ð Ó ¾ Î Ø ÖÓÑ ÖÓÑÑÐ Ø Ðº ÓÖÖØ ÐÐ¹Ó Ò ÒØÖÐ ÚÐÙ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
32 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ ÌÖÒ ÚÖ ØÝ Ò ÒÓÒÐÓÐ ÑÓÐ Π,u B n0t n 1 m Π 600MeV 0.4 n tgev 2 Ò ØÒØÓÒ¹ ÑÓÐ F = M(k+ 2 )M(k2 ( ) ÓÐ ÀÓÐÓѹÌÖÒÒ¹ÎÖ ÀÌε F = 1 2 M(k 2 + )+M(k ) ) 2 ÈÄ ¾ ½¼µ ½¾ ÀÌÎ Ò ØØÖ ÖÑÒØ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
33 ÀÌÎ Ú ÆÂÄ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ n 1 m Π 600MeV Π,u B n0t n tgev 2 ÓÐ ÐÓÐ ÆÂÄ ÀÌÎ ÀÌÎ ÚÖÝ ÐÓ ØÓ ÐÓÐ ÆÂÄ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
34 ÀÖ ÓÖÑ ØÓÖ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ µ = 313 ÅÎ µ = 2 Î Bni tgev tgev Bni tgev tgev ÓÐ B π,u T10 Bπ,u T20 ÓØØ Bπ,u T30 Óع Bπ,u T32 Ò Ñ ÙÖ ÓÒ Ø ÐØØ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
35 ÌÖÒ ÚÖ ØÝ È ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ ÙÐÐ È È ÒÒØ ÓÐÐØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ 1 1 n 1 dx X n 1 ET π (x,ξ,t) = (2ξ) i BTni π (t) i=0, even Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
36 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ ÚÓÐÙØÓÒ Ó ØÖÒ ÚÖ ØÝ È ξ = 1/3 t = 0 E T S X N E T A X N X ÐÓÐ ÆÂÄ t = 0 ξ = 1/3 µ = 313 ÅÎ 2 Î 1 ÌÎ X Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
37 ËÑ ÓÖ ξ = 0 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ ÐÓÐ ÆÂÄ ÒÓÒÐÓÐ Ò ØÒØÓÒ ÚÖØÜ XET X N X XET X N X ÐÓÐ ÆÂÄ Ú ÒÓÒÐÓÐ Ò ØÒØÓÒ t = 0 ξ = 0 µ = 313 ÅÎ 2 Î 1 ÌÎ ÖÒØ Ò¹ÔÓÒØ ÚÓÖ ÖÐØ ØÓ Ø ÒÓÒ¹ÐÓÐØÝ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
38 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ Å ÓÒ ÓÑÒÒ Ó ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ Ö ÔÓÒ m ρ ÖÚØØÓÒÐ ÔÓÒ m f2 (1270) ÔÒ ¾µ m σ ÔÒ ¼µ B π T10 m ρ B π T20 m f 2 (1270) ÅÓÒÓÔÓÐ Ø ØÓ Ø ÐØØ Ø M 1 = 760(50) ÅÎ BT10 π (t = 0) = 0.97(6) M 2 = 1120(250) ÅÎ BT20 π (t = 0) = 0.20(3) ÎÐÙ Ø Ø ÓÖÒ Ö ÑÓÐ ÔÖØÓÒ É ÚÓÐÙØÓÒ Ò ÖÝ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
39 ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ Å ÓÒ ÓÑÒÒ Ñ ØÓ ÛÓÖÒ ÚÖÝ ÛÐÐ Ò ÐÐ ÒÒÐ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
40 σ(600) ÓÑÔÐØÓÒ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ÓÖÑ ØÓÖ ÌÖÒ ÚÖ ØÝ È Å ÓÒ ÓÑÒÒ Particle Data Group Roy equations spectrum, Regge Fit I spectrum, Regge Fit II Π gff, ReggeQCDSF data Π gff, monopoleqcdsf data Ê Ï ÈÊ ½ ¾¼½¼µ ¼¼¼ Ö ÙÐØ ÓÒ ØÒØ ÛØ Ø ÖÒ Ò ÅÖ ÒÐÝ ÊÓÝ ÕÙØÓÒ µ N gff, monopolelhcp data slope of N gff, monopoleqcdsf data m Σ MeV Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
41 ËÙÑÑÖÝ ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÅÓÐ ÚÓÐÙØÓÒ È Ò ÚÖÓÙ ÒÒÐ Ö ÓÐÐØÓÒ Ó ÒÖÐÞ ÓÖÑ ØÓÖ ÓÑÔÙØ ÓÒ Ø ÐØØ ÖÐ ÕÙÖ ÑÓÐ ÓÑÔÖ ÒÐÝ ØÓ ÐØØ Ö ÙÐØ ÐÒ ØÛÒ Ø ¹ Ò ÐÓÛ¹ÒÖÝ ÒÐÝ Ì É ÚÓÐÙØÓÒ Ò ÖÝ Ø ÕÙÖ¹ÑÓÐ Ð µ 0 ÐÓÛ 320 ÅÎ ÒÓ ÐÙÓÒ µ B Tn0 ÚÓÐÚ ÑÙÐØÔÐØÚÐÝ ÓÐÙØ ÔÖØÓÒ ÆÂÄ ÛÓÖ ÖÐ ÝÑÑØÖÝ ÖÒ Ø Ý ÝÒÑÐ ØÓÖ ÓÖ ÓØ ÔÝ ÄØØ ÓÖÑ ØÓÖ Ú Ø Ñ ÓÒ Ñ ÔÖØØÝ ÙÖØÐÝ Å ÓÒ ÓÑÒÒ ÛÓÖ ÖÑÖÐÝ ÛÐÐ ÓÖ Ø ÚØÓÖ ¾ ÖÚØØÓÒÐ Ò ¾ ØÖÒ ÚÖ ØÝ Ø Ð Ó ÛÓÖ Ò Ø ÒÙÐÓÒ ÒÒе ÓÒ ØØÙÒØ ÕÙÖ ÖÓÒ ÙÐØÝ ÐÐ ÛÓÖ Ï ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ
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