Results for Charged-Current Deep-Inelastic Scattering at three - PowerPoint PPT Presentation

Results for Charged-Current Deep-Inelastic Scattering at three loops Mikhail Rogal Mikhail.Rogal@desy.de DESY, Zeuthen, Germany ————————————————————————————————————– – RADCOR 2007, Florence, Italy, October 1-5, 2007 – Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.1

Content Introduction to the Deep-Inelastic Scattering � Charged-current deep-inelastic scattering at three loops. S. Moch and M. R. Nucl. Phys. B 782 , 51 (2007) � Differences between CC coefficient functions S. Moch, M. R. and A. Vogt. arXiv:0708.3731v1 [hep-ph]; Nucl. Phys., in press. Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.2

Content Introduction to the Deep-Inelastic Scattering Related experiments � Charged-current deep-inelastic scattering at three loops. S. Moch and M. R. Nucl. Phys. B 782 , 51 (2007) � Differences between CC coefficient functions S. Moch, M. R. and A. Vogt. arXiv:0708.3731v1 [hep-ph]; Nucl. Phys., in press. Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.2

Content Introduction to the Deep-Inelastic Scattering Related experiments Perturbative QCD corrections at three loops in QCD � Charged-current deep-inelastic scattering at three loops. S. Moch and M. R. Nucl. Phys. B 782 , 51 (2007) � Differences between CC coefficient functions S. Moch, M. R. and A. Vogt. arXiv:0708.3731v1 [hep-ph]; Nucl. Phys., in press. Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.2

Content Introduction to the Deep-Inelastic Scattering Related experiments Perturbative QCD corrections at three loops in QCD Results: its analysis and applications � Charged-current deep-inelastic scattering at three loops. S. Moch and M. R. Nucl. Phys. B 782 , 51 (2007) � Differences between CC coefficient functions S. Moch, M. R. and A. Vogt. arXiv:0708.3731v1 [hep-ph]; Nucl. Phys., in press. Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.2

Introduction Deep-inelastic lepton-hadron scattering ( e ± p, e ± n, νp, ¯ νp, ... - collisions) Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.3

Introduction Deep-inelastic lepton-hadron scattering ( e ± p, e ± n, νp, ¯ νp, ... - collisions) k’ lepton’ k lepton q Gauge boson P hadron X Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.3

Introduction Deep-inelastic lepton-hadron scattering ( e ± p, e ± n, νp, ¯ νp, ... - collisions) k’ k’ lepton’ lepton’ k k lepton lepton q q Gauge boson Gauge boson = ⇒ p’ P P p hadron X hadron Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.3

Introduction Deep-inelastic lepton-hadron scattering ( e ± p, e ± n, νp, ¯ νp, ... - collisions) k’ k’ lepton’ lepton’ k k lepton lepton q q Gauge boson Gauge boson = ⇒ p’ P P p hadron X hadron Kinematic variables Gauge boson : momentum transfer Q 2 = − q 2 > 0 γ, Z 0 - NC Bjorken variable x = Q 2 / (2 P · q ) W ± - CC Inelasticity y = ( P · q ) / ( P · k ) Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.3

DIS experiments EW unification at HERA: neutral vs . charged current Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.4

DIS experiments EW unification at HERA: neutral vs . charged current Charged and neutral deep in- elastic scattering cross sections become comparable when Q 2 reaches the electroweak scale ⇐ = Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.4

Polarized charged current DIS at HERA CC cross section modified by polarization: P e = N R − N L σ e ± p CC ( P e ) = (1 ± P e ) · σ e ± p CC ( P e = 0) N R + N L Cross section is linearly proportional to polarization P e Standard model prediction: vanishing cross section for P e = +1( − 1) in e − (+) scattering Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.5

Calculation V V � V V � � � Leading order diagrams at parton level q q Vector and axial-vector interaction aγ µ + bγ µ γ 5 q q p + q p � q � � � � � � � � 0 0 quark quark p p p p quark quark quark quark Mellin moments with definite symmetry properties process dependent distinction even/odd N (from OPE) � 1 F i ( N, Q 2 ) dx x N − 2 F i ( x, Q 2 ) , = i = 2 , L 0 � 1 F 3 ( N, Q 2 ) dx x N − 1 F 3 ( x, Q 2 ) = 0 Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.6

Known → F eP NC (exchange via γ gauge boson) − 2 CC (exchange via W ± gauge boson) − → F νp +¯ , F νp +¯ νp νp 2 3 even N for F 2 , odd N for F 3 NLO Bardeen, Buras, Duke, Muta ‘78 N 2 LO Zijlstra, van Neerven ‘92 N 3 LO Moch, Vermaseren, Vogt ‘05/‘06 Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.7

Known → F eP NC (exchange via γ gauge boson) − 2 CC (exchange via W ± gauge boson) − → F νp +¯ , F νp +¯ νp νp 2 3 even N for F 2 , odd N for F 3 NLO Bardeen, Buras, Duke, Muta ‘78 N 2 LO Zijlstra, van Neerven ‘92 N 3 LO Moch, Vermaseren, Vogt ‘05/‘06 New NC γ − Z interference at N 3 LO still missing CC (exchange via W ± gauge boson) − → F νp − ¯ νp , F νp − ¯ νp 2 3 odd N for F 2 , even N for F 3 order N 3 LO already known Moch, M. R. ’07 best use: difference “even-odd” Moch, M. R. and Vogt. ‘07 Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.7

In practice The calculation Big number of diagrams ⇒ need of automatization e.g. DIS structure functions F νp ± ¯ - 1076 diagrams, F νp ± ¯ νp νp - 1314 2 ,L 3 diagrams up to 3 loops Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.8

In practice The calculation Big number of diagrams ⇒ need of automatization e.g. DIS structure functions F νp ± ¯ - 1076 diagrams, F νp ± ¯ νp νp - 1314 2 ,L 3 diagrams up to 3 loops latest version of FORM and TFORM (multi-threaded version) Vermaseren, FORM version 3.2 (Apr 16 2007); Tentyukov, Vermaseren ’07 TFORM up to 5 times faster with 8 threads! Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.8

In practice The calculation Big number of diagrams ⇒ need of automatization e.g. DIS structure functions F νp ± ¯ - 1076 diagrams, F νp ± ¯ νp νp - 1314 2 ,L 3 diagrams up to 3 loops latest version of FORM and TFORM (multi-threaded version) Vermaseren, FORM version 3.2 (Apr 16 2007); Tentyukov, Vermaseren ’07 TFORM up to 5 times faster with 8 threads! QGRAF �→ generation of diagrams for DIS structure functions Nogueira ’93 Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.8

In practice The calculation Big number of diagrams ⇒ need of automatization e.g. DIS structure functions F νp ± ¯ - 1076 diagrams, F νp ± ¯ νp νp - 1314 2 ,L 3 diagrams up to 3 loops latest version of FORM and TFORM (multi-threaded version) Vermaseren, FORM version 3.2 (Apr 16 2007); Tentyukov, Vermaseren ’07 TFORM up to 5 times faster with 8 threads! QGRAF �→ generation of diagrams for DIS structure functions Nogueira ’93 Calculation of diagrams �→ MINCER in FORM Larin, Tkachev, Vermaseren ’91 What does MINCER do? Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.8

MINCER minces integrals Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.9

Results Nucl. Phys. B 782, 51 (2007) „ 597399446375524589 1953379 „ − 537659500957277 « C ns 138600 + a 2 + a 2 2 = 1 + a s C F s C F n s C F 3 , 10 f 15975002736000 14760902528064000 + 7202 « „ 5832602058122267 − 99886 « + a 2 105 ζ 3 s C A C F 1155 ζ 3 29045459520000 „ 51339756673194617191 + 48220 « + a 3 2 s C F n 18711 ζ 3 f 996360920644320000 „ − 125483817946055121351353 − 59829376 3274425 ζ 3 + 24110 « + a 3 2 n s C F 693 ζ 4 f 209235793335307200000 „ − 744474223606695878525401307 + 28630985464358 + a 3 3 s C F ζ 3 7088908678200207936000000 24960941775 + 151796299 8004150 ζ 4 − 53708 « ζ 5 99 „ − 185221350045507487753 + 8071097 39690 ζ 3 − 24110 « + a 3 s C A C F n 693 ζ 4 f 226445663782800000 „ 19770078729338607732075449 − 619383700181 + a 3 2 s C A C F 5546875950 ζ 3 8369431733412288000000 − 151796299 5336100 ζ 4 − 37322 « ζ 5 99 „ 93798719639056648125143 − 43202630363 + a 3 2 C F s C A ζ 3 36231306205248000000 20582100 + 151796299 16008300 ζ 4 + 195422 « ζ 5 . 231 Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.10

Checks Known Mellin moments for F νP +¯ νP (even) and F νP +¯ νP (odd) 3 2 ,L recalculated Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.11

Checks Known Mellin moments for F νP +¯ νP (even) and F νP +¯ νP (odd) 3 2 ,L recalculated All calculations with gauge parameter ξ for gluon propagator (Up to 10’th MM) i − g µν + (1 − ξ ) q µ q ν q 2 Results for Charged-CurrentDeep-Inelastic Scattering at three loops – p.11