1. December 14, 2007K.Mawatari (KIAS) @ KEKPH07121/24 Azimuthal angle correlation in vector-boson fusion processes at hadron colliders arXiv:0712.XXXX Kentarou Mawatari with K.Hagiwara (KEK) and Q.Li (Karlsruhe)

2. December 14, 2007K.Mawatari (KIAS) @ KEKPH07122/24 Contents  Motivation I. the Higgs properties II. massive gravitons III. production correlation vs. decay correlation  Helicity formalism for the VBF process  Kinematics  Helicity amplitudes  Azimuthal angle correlations  Summary

3. December 14, 2007K.Mawatari (KIAS) @ KEKPH07123/24 Motivation I: the Higgs properties  After observation of a Higgs boson at LHC, determination of its properties, i.e., all the quantum numbers and couplings, is the next goal to unravel the underlying theory. the gauge, Yukawa, and self-couplings the charge, color, spin, CP quantum numbers  For the CP property at LHC Higgs decay, e.g. H->ZZ->(ll)(ll) Higgs+2jet production, pp->Hjj Dell ’ Aquila,Nelson(1986) S.Y.Choi et al.(2003) Buszello et al.(2004) T.Plehn et al.(2002)

4. December 14, 2007K.Mawatari (KIAS) @ KEKPH07124/24 Higgs production at LHC A.Djouadi hep-ph/0503172 WBF

5. December 14, 2007K.Mawatari (KIAS) @ KEKPH07125/24 WBF (weak-boson fusion)  The distinctive kinematics of WBF Far forward and backward jets. The Higgs boson is produced centrally. the t-channel weak-boson propagator D.Rainwater hep-ph/0702124

6. December 14, 2007K.Mawatari (KIAS) @ KEKPH07126/24 Azimuthal angle correlations in WBF  The anomalous HWW coupling  The azimuthal correlations reflects the tensor structure of the Higgs couplings.  Why is SM flat ? Why is CP-even (odd) suppressed at phi=90 (0 and 180) ? T.Plehn, D.Rainwater, D.Zeppenfeld PRL88(2002)051801

7. December 14, 2007K.Mawatari (KIAS) @ KEKPH07127/24 WBF vs. GF  Higgs + 2 jet events are produced also via gluon fusion (GF); qq->qqH, qg->qgH, gg->ggH V. Del Duca et al. NPB616(2001)367 hep-ph/0312184 We consider both of them VBF as VBF systematically.

8. December 14, 2007K.Mawatari (KIAS) @ KEKPH07128/24 Motivation II: massive gravitons  As another interest to study the azimuthal correlations at LHC, we attempt to apply it to massive-graviton productions.  We consider the simplest Randall-Sundrum (RS) model, where only gravitons can propagate in extra dimension.  So far, several phenomenological studies have been made on the s-channel graviton resonances and their decays for the discovery and the determination of the spin-2 nature. Davoudiasl et al. (2000,2001) Allanach et al. (2000,2002), Traczyk, Wrochna (2002) Abazov et al. [D0 collaboration] (2005)  We study the massive-graviton production via the VBF process, which may have a potential to determine its properties as in the Higgs case.

9. December 14, 2007K.Mawatari (KIAS) @ KEKPH07129/24 Motivation III: production v. decay correlation  X + 2 jet production via VBF  X decay to 4 jets via a vector-boson pair Both have identical topology.  It may be useful to compare the production correlations with the decay correlations.

10. December 14, 2007K.Mawatari (KIAS) @ KEKPH071210/24 X + 2 jet production  The subprocesses qq ’ ->qq ’ X (V=W,Z,g)  H: only one t-channel VBF diagram  G: 28 diagrams qg->qgX (V=g)  H: 8 diagrams  G: 21 diagrams gg->ggX (V=g)  H: 26 diagrams  G: 26 diagrams (in the Higgs effective field theory)  We consider only one VBF diagram for a while. by MG/ME

11. December 14, 2007K.Mawatari (KIAS) @ KEKPH071211/24 Helicity formalism  For the VBF process the completeness relation for space-like vector-boson the conserved current

12. December 14, 2007K.Mawatari (KIAS) @ KEKPH071212/24 Kinematics

13. December 14, 2007K.Mawatari (KIAS) @ KEKPH071213/24 Current amplitudes  For the production quark: gluon:  For the decay quark: gluon:

14. December 14, 2007K.Mawatari (KIAS) @ KEKPH071214/24 Quark current amplitudes

15. December 14, 2007K.Mawatari (KIAS) @ KEKPH071215/24 Gluon current amplitudes

16. December 14, 2007K.Mawatari (KIAS) @ KEKPH071216/24 Relation to splitting amplitudes  For the production z: the energy fraction of the initial parton that is carried off by the space-like vector-boson  For the decay z: the energy fraction of the time-like vector- boson that is carried off by the final parton the collinear limit

17. December 14, 2007K.Mawatari (KIAS) @ KEKPH071217/24 Quark splitting amplitudes

18. December 14, 2007K.Mawatari (KIAS) @ KEKPH071218/24 Gluon splitting amplitudes

19. December 14, 2007K.Mawatari (KIAS) @ KEKPH071219/24 VBF vertex   The XVV vertex The polarization tensor and the GXX vertex

20. December 14, 2007K.Mawatari (KIAS) @ KEKPH071220/24 VBF amplitudes for

21. December 14, 2007K.Mawatari (KIAS) @ KEKPH071221/24 Azimuthal angle correlations The WBF cuts can select the VBF diagram effectively.

22. December 14, 2007K.Mawatari (KIAS) @ KEKPH071222/24 Quantum interference between the different helicity states  The full helicity amplitude for the Higgs boson  For, e.g., H(WBF): H: A:

23. December 14, 2007K.Mawatari (KIAS) @ KEKPH071223/24 Quantum interference between the different helicity states  The full helicity amplitude for the massive- graviton The caes is dominant. There is no interference term.  No azimuthal dependence.

24. December 14, 2007K.Mawatari (KIAS) @ KEKPH071224/24 Summary  We studied Higgs boson and massive-graviton productions in association with two jets via VBF (=WBF+GF) and their decays at hadron colliders.  We presented the helicity amplitudes for the subprocesses explicitly, and showed that quantum interference between different helicity states leads to a non-trivial azimuthal angle correlation of the jets in the production and in the decay.  These correlations reflect the spin and CP nature of the Higgs bosons and the massive-gravitons.