Patterns of high energy massive string scatterings in the Regge regime

We calculate high energy massive string scattering amplitudes of open bosonic string in the Regge regime (RR). We found that the number of high energy amplitudes for each fixed mass level in the RR is much more numerous than that of Gross regime (GR) calculated previously. Moreover, we discover that the leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. In particular, based on a summation algorithm for Stirling number identities developed recently, we discover that the ratios calculated previously among scattering amplitudes in the GR can be extracted from this Kummer function in the RR. We conjecture and give evidences that the existence of these GR ratios in the RR persists to subleading orders in the Regge expansion of all string scattering amplitudes. Finally, we demonstrate the universal power-law behavior for all massive string scattering amplitudes in the RR.

[1]  Manuel Kauers,et al.  Summation algorithms for Stirling number identities , 2007, J. Symb. Comput..

[2]  Yi Yang,et al.  Linear relations and their breakdown in high energy massive string scatterings in compact spaces , 2007, 0705.1872.

[3]  Yi Yang,et al.  Linear relations of high energy absorption/emission amplitudes of D-brane , 2006, hep-th/0612059.

[4]  R. Brower,et al.  Preprint typeset in JHEP style- HYPER VERSION BROWN-HET-1462 The Pomeron and Gauge/String Duality , 2006 .

[5]  Yi Yang,et al.  Notes on High Energy Bosonic Closed String Scattering Amplitudes , 2006 .

[6]  Yi Yang,et al.  Notes on high-energy limit of bosonic closed string scattering amplitudes , 2006, hep-th/0604122.

[7]  L. Lipatov,et al.  BFKL pomeron in string models , 2006, hep-ph/0603073.

[8]  Yi Yang,et al.  High energy scattering amplitudes of superstring theory , 2005, hep-th/0510247.

[9]  Yi Yang,et al.  Comments on the high energy limit of bosonic open string theory , 2005, hep-th/0509009.

[10]  Yi Yang,et al.  High-energy zero-norm states and symmetries of string theory. , 2005, Physical review letters.

[11]  P. West,et al.  Arbitrary four string scattering at high energy and fixed angle , 2005, hep-th/0507152.

[12]  Yi Yang,et al.  Solving all 4-point correlation functions for bosonic open string theory in the high-energy limit , 2005, hep-th/0504138.

[13]  Yi Yang,et al.  Anatomy of zero-norm states in string theory , 2005, hep-th/0501020.

[14]  Jen-Chi Lee,et al.  Ward identities and high-energy scattering amplitudes in string theory , 2004, hep-th/0410194.

[15]  Jen-Chi Lee,et al.  Stringy symmetries and their high-energy limits , 2003, hep-th/0312226.

[16]  O. Andreev.  Remarks on the high-energy behavior of string scattering amplitudes in warped spacetimes , 2004, hep-th/0402017.

[17]  Jen-Chi Lee,et al.  Zero-norm states and high-energy symmetries of string theory , 2004, hep-th/0401133.

[18]  Jen-Chi Lee,et al.  Decoupling of degenerate positive-norm states in Witten's string field theory , 2002, hep-th/0212196.

[19]  M. Kachelriess,et al.  Remarks on the high-energy behaviour of cross-sections in weak-scale string theories , 2001, hep-ph/0109184.

[20]  E. Lee,et al.  Generalized On-Shell Ward Identities in String Theory , 2000 .

[21]  Jen-Chi Lee.  SO(2,C) invariant discrete gauge states in liouville gravity coupled to minimal conformal matter , 1998, hep-th/0501075.

[22]  Jen-Chi Lee,et al.  Superfield form of discrete gauge states in ĉ = 1 2d supergravity , 1995, hep-th/9505107.

[23]  P. West.  PHYSICAL STATES AND STRING SYMMETRIES , 1995 .

[24]  Jen-Chi Lee,et al.  Discrete gauge states and w, charges in c = 1 2D gravity , 1994, hep-th/9412095.

[25]  G. Moore.  Symmetries of the Bosonic String S-Matrix , 1993, hep-th/9310026.

[26]  G. Moore.  Finite in All Directions , 1993, hep-th/9305139.

[27]  B. Ovrut,et al.  Zero-norm states and enlarged gauge symmetries of the closed bosonic string with massive background fields , 1990 .

[28]  Jen-Chi Lee.  New symmetries of higher spin states in string theory , 1990 .

[29]  Lee.  Decoupling of degenerate positive-norm states in string theory. , 1990, Physical review letters.

[30]  D. Gross.  Strings at superplanckian energies: in search of the string symmetry , 1989, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[31]  D. Gross,et al.  The High-energy Behavior of Open String Scattering , 1989 .

[32]  D. Amati,et al.  Can spacetime be probed below the string size , 1989 .

[33]  D. Gross,et al.  String Theory Beyond the Planck Scale , 1988 .

[34]  D. Gross,et al.  High-energy symmetries of string theory. , 1988, Physical review letters.

[35]  Soldate,et al.  High-energy unitarity of gravitation and strings. , 1988, Physical review. D, Particles and fields.

[36]  D. Amati,et al.  CLASSICAL AND QUANTUM GRAVITY EFFECTS FROM PLANCKIAN ENERGY SUPERSTRING COLLISIONS , 1988 .

[37]  D. Amati,et al.  Superstring collisions at planckian energies , 1987 .

[38]  D. Gross,et al.  The High-Energy Behavior of String Scattering Amplitudes , 1987 .

[39]  M. Soldate.  Partial-wave unitarity and closed-string amplitudes , 1987 .