Particle Production from a HERA perspective Daniel Traynor, - PowerPoint PPT Presentation

NON-PERTURBATIVE Particle Production from a HERA perspective Daniel Traynor, Birmingham seminar 15/10/09 1

Overview The Trouble With QCD. HERA and the H1 experiment. Fragmentation functions. Strangeness production. Bonus : More strangeness, Instantons, Pentaquarks, Glueballs 2

The Trouble With QCD QED TO CUT A LONG STORY SHORT. THE FIELD STRENGTH TENSOR INVARIANCE OF THE QED LAGRANGIAN UNDER LOCAL GAUGE TRANSFORMATIONS REQUIRES F µ ν = δ µ A ν − δ ν A µ THE EXISTENCE OF A GAUGE FIELD. THIS IS THE ELECTROMAGNETIC FIELD AND MEDIATES THE FORCE BETWEEN CHARGED PARTICLES THE QUANTA OF THIS FIELD ARE THE SYMBOLICALLY THE QED MASSLESS PHOTONS LAGRANGIAN HAS THESE TERMS U(1) SYMMETRY ABELIAN PROPAGATION OF CHARGED PARTICLES INTERACTION OF PHOTONS AND VECTOR FIELD A μ (GAUGE PROPAGATION CHARGED PARTICLES OF PHOTONS FIELD) WHICH COUPLES TO CHARGE. IT IS A NUMBER 3

The Trouble With QCD QCD TO CUT A LONG STORY SHORT. THE FIELD STRENGTH TENSOR INVARIANCE OF THE QCD LAGRANGIAN UNDER LOCAL GAUGE TRANSFORMATIONS F µ ν = δ µ A ν − δ ν A µ − ig [ A µ A ν − A ν A µ ] REQUIRES THE EXISTENCE OF A GAUGE FIELD. THIS IS THE COLOUR FIELD AND MEDIATES THE FORCE BETWEEN COLOURED SELF INTERACTION TERM PARTICLES. THE QUANTA OF THIS FIELD ARE THE MASSLESS GLUONS SYMBOLICALLY THE QCD LAGRANGIAN HAS THESE TERMS SU(3) SYMMETRY NON-ABELIAN VECTOR FIELD A μ (GAUGE FIELD) WHICH COUPLES TO COLOUR. IT IS A MATRIX THREE AND FOUR GLUON VERTICES 4

The Trouble With QCD ELECTRIC CHARGE 0 R, 1/Q SCREENING OF ELECTRIC CHARGE IN QED HIGHER ORDER PROCESSES ARE LESS IMPORTANT DUE TO THE SMALLNESS OF α em (1/137) . 5

The Trouble With QCD R ~1/ Λ ~10 -15 M PERTURBATION THEORY FAILS ELECTRIC CHARGE COLOUR CHARGE 2 π α s ( Q ) ∼ 7 ln ( Q/ Λ ) 0 R, 1/Q 0 R, 1/Q SCREENING OF ELECTRIC CHARGE ANTI SCREENING OF COLOUR CHARGE IN QED HIGHER ORDER PROCESSES ARE AT LARGE DISTANCES α s BECOMES LARGE LESS IMPORTANT DUE TO THE (~1) AND HIGHER ORDER PROCESSES SMALLNESS OF α em (1/137) . BECOME MORE IMPORTANT ASYMPTOTIC FREEDOM AT SMALL DISTANCES 5

THE PERTURBATIVE EXPANSION QED α em α 2em α 3em 6

THE PERTURBATIVE EXPANSION QED e + e + Q 2 � * α em α 2em α 3em q x QCD q x i+1 , k � i+1 x i , k � i x 0 , k � 0 p α 2s α ns α s 6

α 2s NLO time-like splitting functions (diagonal singlet) � P ( 1 ) ns , + ( x ) ≡ P ( 1 ) T ns , + ( x ) − P ( 1 ) S ns , + ( x ) = 2 � H 0 ( 6 ( 1 − x ) − 1 − 5 − x )+ H 0 , 0 ( − 8 ( 1 − x ) − 1 + 6 + 6 x )+( H 1 , 0 + H 2 )( − 8 ( 1 − x ) − 1 q → q(g) 4 C F � + 4 + 4 x ) . g → qqg � P ( 1 ) ps ( x ) ≡ P ( 1 ) T ( x ) − P ( 1 ) S ( x ) = ps ps � � − 20 / 9 x − 1 − 3 − x + 56 / 9 x 2 − ( 3 + 7 x + 8 / 3 x 2 ) H 0 + 2 ( 1 + x ) H 0 , 0 8 C F n f . g → g(g) � P ( 1 ) gg ( x ) ≡ P ( 1 ) T ( x ) − P ( 1 ) S ( x ) = gg gg � � � 8 C 2 +[ 6 ( 1 − x ) − 22 / 3 ( x − 1 − x 2 )] H 0 ... p gg ( x ) 11 / 3H 0 − 4 ( H 0 , 0 + H 1 , 0 + H 2 ) A � � 20 / 9 x − 1 + 3 + x − 56 / 9 x 2 − 8 ( 1 + x ) H 0 , 0 − 16 / 3 C A n f p gg ( x ) H 0 + 8 C F n f +[ 4 + 6 x + 4 / 3 ( x − 1 + x 2 )] H 0 + 2 ( 1 + x ) H 0 , 0 � . 7