HEAVY QUARK JET PRODUCTION AT TEVATRON IN THE REGGE LIMIT OF QCD - PowerPoint PPT Presentation

Bogolyubov Readings - 2010, Dubna 1 HEAVY QUARK JET PRODUCTION AT TEVATRON IN THE REGGE LIMIT OF QCD V.A. Saleev Samara State University, Samara, Russia and Samara Aerospace State University, Samara, Russia In collaboration with B. A. Kniehl and A. V. Shipilova V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 2 Outlook 1. Introduction 2. Particle production in the Regge kinematics 3. Effective vertices in the MRK and QMRK, and high-energy factorization 4. Inclusive jet and prompt photon production at Tevatron 5. Inclusive b and b + ¯ b production at Tevatron 6. Associated b + γ, c + γ production at Tevatron 7. Conclusions V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 3 Particle production in the Regge kinematics P ′ P A A 1 t 1 P C 1 t 2 − P B P ′ B S AB = ( P A + P B ) 2 , S A ′ C = ( P A ′ + P C ) 2 , S B ′ C = ( P B ′ + P C ) 2 S A ′ C , S B ′ C , P 2 C , P 2 T C ≪ S AB , ( P A · P A ′ ) ≪ ( P A · P C ) ≪ ( P A · P B ′ ) y A ′ ≫ y C ≫ y B ′ V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 4 Electron Reggeization in QED: M. Gell-Mann, M. L. Goldberger, F. E. Low, E. Marx, and F. Zachariasen, 1964 . Quark Reggeization in QCD: V. S. Fadin and V. E. Sherman, 1976 Qluon Reggeization in QCD: E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, 1975 I. I. Balitsky and L. N. Lipatov, 1978 V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 5 b ¯ b − jet production in the multi-Regge kinematics y 1 R y b Q y ¯ b R y 2 y 1 ≫ y b ≫ y ¯ b ≫ y 2 � ω R ( t 1 ) � ω R ( t 2 ) � s 1 � s 2 � s � ω Q ( t ) A MRK ∼ Γ R ¯ × Γ b b × Γ R P P × RQ × × Γ QR × P P t 1 t t 2 V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 6 b ¯ b − jet production in the quasi-multi-Regge kinematics y 1 R y b y ¯ b R y 2 y 1 ≫ y b ≃ y ¯ b ≫ y 2 � ω R ( t 1 ) � ω R ( t 2 ) � s 1 � s 2 A QMRK ∼ Γ R × Γ b ¯ b × Γ R P P × RR × P P t 1 t 2 σ ( PP → b ¯ σ ( RR → b ¯ bX ) = Φ R ⊗ ˆ b ) ⊗ Φ R V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 7 b − jet production in the multi-Regge kinematics y 1 ≃ y b y 1 Q R y ¯ b y b R Q y 2 y 2 ≃ y ¯ b y 1 ≃ y b ≫ y ¯ b ≫ y 2 y 1 ≫ y b ≫ y ¯ b ≃ y 2 � ω R ( t 1 ) � ω Q ( t 2 ) � s 1 � s 2 A QMRK ∼ Γ Q × Γ b × Γ R P P × QR × P P t 1 t 2 σ ( PP → bX ) = Φ Q ⊗ ˆ σ ( Q b R → b ) ⊗ Φ R V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 8 P 1 = E 1 (1 , 0 , 0 , 1) , P 2 = E 2 (1 , 0 , 0 , − 1) , S = 4 E 1 E 2 ( n + ) µ = P µ ( n − ) µ = P µ k ± = k · n ± = k µ n ± 2 /E 2 , 1 /E 1 , µ t 1 = − q 2 1 = − q 2 t 2 = − q 2 2 = − q 2 q 1 = x 1 P 1 + q 1 T , q 2 = x 2 P 2 + q 2 T , 1 T , 2 T V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 9 Vertex functions: q n ± γ ± g ( k ) + Q ( q ) → q ( k + q ) : µ ( q, k ) = γ µ + ˆ k ± , q 2 n + q 1 n − ( q 1 , q 2 ) = γ µ − ˆ − ˆ Q ( q 1 ) + ¯ µ µ γ + − Q ( q 2 ) → g ( q 1 + q 2 ) : µ q + q − 2 1 V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 10 Effective vertices in the QMRK approach The QMRK approach is based on effective quantum field theory implemented with the non-Abelian gauge-invariant action: Reggeized gluons (R), L. N. Lipatov, 1995 , Reggeized quarks (Q), L. N. Lipatov and M. I. Vyazovsky, 2001 Feynman rules for the effective theory: E. N. Antonov, L. N. Lipatov, E. A. Kuraev, and I. O. Cherednikov, 2005 L. N. Lipatov and M. I. Vyazovsky, 2001 V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 11 RR → g RR ( q 1 , q 2 ) = − g s f abc q + 1 q − ( q 1 − q 2 ) µ + ( n + ) µ − ( n − ) µ � �� C g,µ 2 q 2 2 + q + 1 q − q 2 1 + q + 1 q − � � � 2 √ t 1 t 2 2 2 q + q − 1 2 Q ¯ Q → γ ( n − ) µ ( n + ) µ � � γ µ − ˆ C γ,µ Q ( q 1 , q 2 ) = − iee q q 1 − ˆ q 2 Q ¯ q + 1 + q + q − 1 + q − 2 2 RQ → q ( q 1 , q 2 )Π (+) µ C RQ → q ( q 1 , q 2 ) = − ig s T a γ ( − ) ( q 2 ) µ T ( q 2 ) = q µ ( q 2 ) = − x 2 E 2 ( n + ) µ Π (+) µ Π (+) µ 2 T q 2 T | , . T T | � | � q 2 T | V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 12 RQ → γq q 1 − ˆ ˆ k 2 � ( q 1 , q 2 , k 1 , k 2 ) = − ee q g s T b Π (+) ν ( q 1 − k 2 ) 2 γ ( − ) C RQ → γq ( q 2 ) γ ν ( − k 2 , q 1 )+ µ µ T k 1 + ˆ ˆ n − µ n − k 2 � ν ( k 1 + k 2 ) 2 γ ( − ) γ µ ( q 2 , q 1 ) − ˆ q 1 ν q − 2 k − 2 V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 13 |M ( RR → g ) | 2 = 3 2 πα s � k 2 T . |M ( Q b R → b ) | 2 = 2 3 πα s � k 2 T . Q → γ ) | 2 = 4 |M ( Q ¯ q 2 q 2 3 παe q ( � 1 T + � 2 T ) . We have � k 2 q 2 q 2 T = � 1 T + � 2 T + 2 | � q 1 T || � q 2 T | cos φ 12 , where � q 1 T and � q 2 T are the transverse momenta of the Reggeized quark and gluon, respectively, and φ 12 is the azimuthal angle enclosed between them. V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 14 � 1 � N c b ) | 2 = 256 π 2 α 2 |M ( R + R → b + ¯ M A + c − 1) M NA , s 2( N 2 2 N c where � 2 t 1 t 2 � 1 + α 1 β 2 S + α 2 β 1 S M A = u − , ˜ ˜ u ˜ t ˜ t � α 1 β 2 S 2 � � α 2 β 1 S 2 2 + S 2 + ∆ + S 2 − ∆ � M NA = ˜ S 2 u ˜ s ˆ s ˆ t �� 1 � � − t 1 t 2 t − 1 ( α 1 β 2 − α 2 β 1 ) + x 1 x 2 ˆ s − 2 , ˜ ˜ x 1 x 2 ˆ s u ˜ S t ˜ u � � S β 1 − β 2 α 1 − α 2 u − ˜ ∆ = ˜ t + 2 S ( α 1 β 2 − α 2 β 1 ) + t 1 − t 2 , 2 β 1 + β 2 α 1 + α 2 t = ˆ ˜ t − m 2 , ˜ u − m 2 , t 1 = − q 2 1 , t 2 = − q 2 u = ˆ 2 , α 1 = 2( k 1 · P 2 ) /S , α 2 = 2( k 2 · P 2 ) /S , β 1 = 2( k 1 · P 1 ) /S , and β 2 = 2( k 2 · P 1 ) /S . Here, the Mandelstam variables are defined as s = ( q 1 + q 2 ) 2 , ˆ t = ( q 1 − k 1 ) 2 , ˆ u = ( q 2 − k 1 ) 2 , S = ( P 1 + P 2 ) 2 . ˆ V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 15 − 16 x 1 S � w 0 + w 1 S + w 2 S 2 � 3 π 2 αα s e 2 | M ( QR → qγ ) | 2 = , q b 2 ˆ s ˆ ut 2 w 0 = b 2 u ) − b 1 b 2 ( t 2 ˆ u + ˆ u ) − b 2 t 1 t 2 + t 2 (ˆ u ˆ � � 1 t 2 ( t 1 − ˆ t + 2 t 2 ˆ t ˆ t + ˆ u ) + t 1 ˆ u + ˆ t , 2 � � 2 a 1 b 2 ( t 1 + ˆ t ) + a 1 b 1 ( t 2 + ˆ w 1 = − b 2 x 2 t ) + a 2 b 1 ( t 2 + ˆ u ) , 1 + ˆ s � � � � w 2 = a 1 b 2 x 2 a 1 b 2 − a 2 b 1 , 2 u ˆ V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 16 − 128 x 1 x 2 � w 0 + w 1 S + w 2 S 2 + w 3 S 3 � | M ( Q ¯ 9 S π 2 αα s e 2 Q → gγ ) | 2 = , q a 1 a 2 b 1 b 2 ˆ t ˆ u − t 1 t 2 ( t 1 + t 2 ) + ˆ u (ˆ w 0 = t ˆ t + ˆ u ) , x 2 t 1 ( a 1 ˆ u ) + x 1 t 2 ( b 2 ˆ u ) + t 1 t 2 ( a 1 − a 2 )( b 1 − b 2 ) + ˆ w 1 = t + a 2 ˆ t + b 1 ˆ t ˆ u (2 a 1 b 2 + x 1 b 1 + x 2 a 2 ) x 2 2 a 1 a 2 t 1 + x 2 1 b 1 b 2 t 2 + a 1 b 2 ˆ w 2 = t ( x 2 a 1 + a 2 b 2 ) + a 2 b 1 ˆ u ( x 1 b 1 + a 2 b 2 ) , � a 1 b 2 ˆ t + a 2 b 1 ˆ u � w 3 = a 1 a 2 b 1 b 2 . ˆ u ˆ t V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD

Bogolyubov Readings - 2010, Dubna 17 q f ) | 2 = − 64 π 2 α 2 |M ( Q r ¯ s w 0 + w 1 S + w 2 S 2 � � Q r → q f ¯ , s 2 9 x 1 x 2 ˆ � ˜ � w 0 = x 1 x 2 ˆ s t + ˜ u , − 2 x 2 2 α 1 α 2 t 2 − 2 x 2 s − 2 m 2 ) + w 1 = 1 β 1 β 2 t 1 + x 1 x 2 { ( α 1 β 2 + α 2 β 1 )(ˆ s + t 1 + t 2 ) + x 1 x 2 (ˆ u ) + β 2 ( t 1 + ˜ t )] + x 2 [ α 1 ( t 2 + ˜ + x 1 [ β 1 ( t 1 + ˜ t ) + α 2 ( t 2 + ˜ u )] } , − 2 x 1 x 2 ( α 1 β 2 − α 2 β 1 ) 2 . w 2 = V.A. Saleev ,Heavy quark jet production at Tevatron in the Regge limit of QCD