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QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar Sector

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(1)QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar Sector P. Bialas, A. Morel, B. Petersson, K. Petrov, T. Reisz. To cite this version: P. Bialas, A. Morel, B. Petersson, K. Petrov, T. Reisz. QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar Sector. Nuclear Physics B, Elsevier, 2001, 603, pp.369-388. �hal-00166267�. HAL Id: hal-00166267 https://hal.archives-ouvertes.fr/hal-00166267 Submitted on 2 Aug 2007. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(27) . f–`‡\ rÅh4v kj \P^†^ ƒŒh r `%Z_` q—krƒ„ˆyƒHk4ƒ ŠŸe ‹[k, \ v kSk˜qlj \ ƒ„q—k4x \ rÅk Ÿk!ƒ„q Z v k  \ `l` B } « ¬ ~=jlh  >‡*h*krq Ž  'h ^ ˆ \PŠ h4v ^ h h‚ ` ƒ„h j—jlk ^]\ q Z h r ` « ¬ eN\ rxµƒ„h*‚ \ j—k4x Z q,qlhyqlHk B v \4^†Ž k ` h   q \4Z rHk!x   ˆ0h Ž j[°q ` qlh ¸ mlc m Y © kðÆrx*ql \ qOB } «  ¬ Z_`Z rxkk4xVrHk \ j ^ ˆ*ƒŒh r ` q \ rq eHZ rV~ \ ƒŒq `%^ h4‹ ^ ˆyx:k!ƒ„jlk \`oZ r q—h4‹ \ j x `$\ v \4^†Ž k0ƒ„h*‚ \ q Z† E^ k$‹ Z ql B e x Ž kqlh `  \P^ž^ kj \ rx ` q—kk‚kj ƒŒh rqlj Zž HŽ q Z h r ` qlh@« ¬ h4~q—HkOHk \ v Z kjĂ \ j—q Z ƒ ^ k ,Y f ƒ„h rqlj \ j Z h e ‹Äk Z r:v \P^žZ x \ qlkyqlHk Z rqlkj—‚Hjlkq \ q Z h rµh4~Sq—Hk ^]\ j k ` q@ƒ„h j—jlk ^]\ q Z h r ^ kr ql Z r ¸‡¹ c ¹Ê\ `0  k Z r » q Z *k `S` Eh jlq—kj*q— \ r qlHk Ì # k   ˆ k ` ƒ„j—kkr Z r ·^ kr qlÍ e qlEk Z rv kj ` k h4~ \  \`l` B \ `—` hƒ Z]\ qlk!x ‹ Z q— Ìlk ^ k4ƒ„qlj Z ƒÍ ^žŽ h r ` hP~ÃqlHk Z r Z q Z]\P^ «• ³, ¬ # 8hx:k ^ «=qlHk ` ƒ \P^]\ j ` h4~q—HkÅj—k4x Ž ƒŒk4x*hx:k ^ ¬ Y [ Z]`X` ƒ„kr \ j Z h ‹ \ `@\ xv hƒ \ q—k4x   ˆ #43Ð" h Š kj Z r6 Z]` Y \ q Zž µqlk8‚>kj \ q Ž jlk Ï •Y  ~ `%Ž ƒª‹ \` q—Hk@ƒ \` k e qlHk ‚kj—q Ž j  \ q Z v k ` q Ž xˆªhP~ s hr: \ ˜ Z_` ƒ„h j—jlk ^]\ q Z h r `¸¹ c ¹º` Hh ŽH^ x@j \ q—Hkj ^ h h Š@^†ZžŠ k ¹   ³  «— ¬ ¸ ¹ c ¹ «•» B   ¬ U  U  U  B  a m B «  !  ¬  a m.   . . . . .   +. . .-  1.  4 1

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(55) +Ä«T/ ¬ +[«² ¬

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(71) 1e−03 1e−04 1e−05 1e−06 1e−07 1e−08. β3=29 A2,2. 1e−09. A2,4 A4,4. 1e−10. A3,3 A3,5. 1e−11 1e−12. A5,5 0. 10. 5. 15. r. ‘TZ† Ž jlk® 4 [Hk*h r \ ˜ ]Z ` ƒ„hjlj—k ^_\ q Z hr `¸‡¹ c  «  ¬ \ q,K s ¼  ’Yµ[Hk*kv krµƒ \ ` k ` Ï»TÂCB ‡¼  : •Â :Âl  \ rx ÑEÂl) P\ ^ž^  \ v k@q—Hk `l\ *k `  \ ‚>k e$\ rÆxqlHkyhxHx6ƒ \ ` k `  ‰  ‰ •Â ‰  \ rx  :  eE\P \4Z r `oZ  Z†^_\ j‹ Z lq yk \ ƒ*hqlHkj Z r `  \ ‚ k e\ jlk ` q—kk‚kjY. . .

(72) β3=29 ~ X2 X2 1.1. 1.05. 1 0. 10. 5. 15. r. #. ‘TZ† Ž jlk@ 4 zk `oZ x Ž kV~ \ „ƒ qlhj Z†{!\ q Z h r 4 x \ q \ ~=hjqlHk  Ž\ r:q Z q%ˆ m e& Y«— ‰ ¬ \ q,K s ¼  ’Y  q \ ‚H‚Hj—h \ ƒbHk ` h rHk \ q ]^ \ j k  YÅ[Ek  Ž\ r:q Z q%ˆ m ƒŒh jlj—k ` ‚hrx ` qlh®h Ž j Z rqlkj—‚Hjlkq \ q Z h r «% k4ƒ„q Z hr* eš& Y«² ¬—¬ h4 ~ q—Hk,x:kv Z_\ q Z hr*~=jlh Çh rHkOhP~ m \ q ` Hh j—qlkj–x Z_` q \  r ƒ„k ` Y. #. . ’. #.

(73) β3=29 ~ X3 X3. 1.3. 1.2. 1.1. 1. 0.9. 0. 2. 4. 8. 6. 10. 12. r. #. ‘TZ† Ž jlk ‰ 4 zk `oZ x Ž kV~ \ „ƒ qlhj Z†{!\ q Z h r 4 x \ q \ ~=hjqlHk  Ž\ r:q Z q%ˆ s e& Y«— ‰ ¬ \ q,K s ¼  ’Y  q \ ‚H‚Hj—h \ ƒbHk ` h rHk \ q ]^ \ j k  YÅ[Ek  Ž\ r:q Z q%ˆ s ƒŒh jlj—k ` ‚hrx ` qlh®h Ž j Z rqlkj—‚Hjlkq \ q Z h r «% k4ƒ„q Z hr* eš& Y«² ’ ¬—¬ h4 ~ q—Hk,x:kv Z_\ q Z hr*~=jlh Çh rHkOhP~ s \ q ` Hh j—qlkj–x Z_` q \  r ƒ„k ` Y. #.  . #.

(74) β3=84 ~ X2 X2 1.1. 1.05. 1 0. 10. 5 r ‘'Z† Ž jlkO. 4 \ *k \`Z r ‘'Z† Y \ q K s ¼ 4 iY. :. 15.

(75) β3=84 ~ X3 X3. 1.3. 1.2. 1.1. 1. 0. 2. 4. 6. 8. r ‘'Z† Ž jlk,. 4 \ *k \`Z r ‘'Z† Y ‰ \ q K s ¼ 4 iY.  . 10. 12.

(76) 1.1. 1.05. 1. 0.95. 0.9. 0. 10. 5. 15. r ‘'Zž Ž j—k,. 4  ^ h qh4~ ¸ m•| Ë4 ¸ m ¸ m%m \ qOK s ¼  ’ e ‹ Z ƒb Z]` h rHk Z ~ & Y«²P ¬ Hh ^ x ` Y.  ‰.

(77)

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