Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 1 Excitation function of elastic pp scattering from a unitary extension of Bialas-Bzdak model T. Csörgő 1,2, F. Nemes 1,3 and M. Csanád 4 1 Wigner Research Center for Physics, Budapest, Hungary 1 Wigner Research Center for Physics, Budapest, Hungary 2 KRF, Gyöngyös, Hungary 3 CERN, Geneve, Switzerland 4 ELTE, Budapest, Hungary ISR 7 TeV LHC ISR 7 TeV LHC Real extension of Bialas-Bzdak New: focusing ReBB on low t d  /dt New: excitation functions arXiv: arXiv: arXiv: arXiv:submit/ [hep-ph] 30 Nov 2014

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 2 S-matrix Unitarity, Optical Theorem S-matrix Unitarity, Optical Theorem Note: diffraction also measures |Fourier-transform| 2 images of sources of elastic scattering -ideal for femtoscopic studies -several similarities e.g. non- Gaussian sources etc Black (grey) disc limit (important) →  (b) ~  (R-b)

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 3 Diffraction in quark-diquark models Diffraction in quark-diquark models Structure of protons = ? → Diffractive p+p at ISR (23.5 – 62.5 GeV) and LHC (7 TeV). Bialas and Bzdak, Acta Phys. Polon. B 38 (2007) 159 p= (q, d) or p = (q, (q, q))  (b) = b dependent prob. of interaction → connection to scattering centers

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 4 Diffraction a la Bialas and Bzdak Diffraction a la Bialas and Bzdak The quark-diquark model of Bialas and Bzdak has been analytically integrated in a Gaussian approximation, assuming that the real part of forward scattering is negligible. Two different pictures: p = (q, d) or p = (q, (q,q)) Note: p= (q,q,q) model fails, quarks are correlated W. Czyz and L. C. Maximon, Annals. Phys. 52 (1969) 59

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 5 Diffractive p+p scattering Diffractive p+p scattering p = (q, d) p = (q, (q,q))

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 6 Real extended BB model for the dip Real extended BB model for the dip Real extension of an imaginary t el New parameter Im added Bialas-Bzdak obtained if Re (t el )  = 0

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 7 reBB model for the dip (2) reBB model for the dip (2) Bialas-Bzdak model is „realized”: p = (q,d) p= (q, (q,q))

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 8 reBB model: two choices reBB model: two choices Similar to a constant  but not favored by data For small values of  we recover our first attempt, the BB model This choice is also favoured by data T. Cs., F. Nemes, arxiv:

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 9 reBB model, final fit range studies reBB model, final fit range studies fit: 0 ≤ –t ≤ 2.5 GeV 2, ~ OKfit: 0.36≤ –t ≤ 2.5 GeV 2, OK remarkable stability of extrapolation to the unfitted region

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 10 reBB model, combined data sets reBB model, combined data sets fit: 0 ≤ –t ≤ 2.5 GeV 2, ~not OK Shadow profile function

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 11 reBB shadow profile functions reBB shadow profile functions Indication of saturation at 7 TeV: A(b) ~ 1 at low b. ~ max probability of interaction at low b

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 12 Imaging on the sub-femtometer scale at 23 GeV ISR and 7 TeV LHC energy at 23 GeV ISR and 7 TeV LHC energy But what about future LHC energies?

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 13 Black disc limit? Scaling but not in the black disc limit: T. Cs. and F. Nemes arXiv: Int. J. Mod. Phys. A (2014) C(data) ~ 50 mb GeV 2 ≠ C(black) ~ 36 mb GeV 2

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 14 Black disc limit? Scaling but not in the black disc limit: T. Cs. and F. Nemes arXiv: Int. J. Mod. Phys. A (2014) C(data) ~ 50 mb GeV 2 ≠ C(black) ~ 36 mb GeV 2

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 15 Black disc limit? Scaling but not a black disc limit: T. Cs. and F. Nemes arXiv: IJMPA (2014) G(z) = (|t dip z|/ tot ) d/dt plotted vs z = t/t dip

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 16 Excitation function: geometric scaling Geometric scaling: {R q, R d, R qd, a} = p 0 + p 1 ln (s/s 0 )

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 17 Excitation function: geometric scaling Geometric scaling: {R q, R d, R qd, a} = p 0 + p 1 ln (s/s 0 )

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 18 Excitation function: d  /dt Geometric scaling: modest change from 7 TeV to 28 TeV Dips to lower –t by ~10%  tot increases by ~10%, with √s from 7 to 15 TeV but t dip  tot ~ const (2 %) Similar to: K.A. Kohara, T. Kodama, E. Ferreira, arXiv:

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 19 Predictions for the shadow profile Blacker and Larger, but not Edgier: BnEL effect at LHC energies Similar to: K.A. Kohara, T. Kodama, E. Ferreira, arXiv: But they claim BEL effect asymtotically

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 20 Blacker and Larger, but not Edgier: BnEL effect at LHC energies Predictions for the shadow profile

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 21 Black disc limit? Scaling but not a black disc limit: T. Cs. and F. Nemes arXiv: IJMPA (2014) G(z) = (|t dip z|/ tot ) d/dt plotted vs z = t/t dip

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 22 TOTEM preliminary 8 TeV data: in 8 TeV TOTEM preliminary data exponential shape excluded at 7 Theoretical support, from ISR to LHC energies, unitarity L. Jenkovszky and A. Lengyel, arXiv:

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 23 Non-exponential behaviour in ReBB Similar non-exponential feature seen at 7 TeV as in 8 TeV TOTEM preliminary data

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 24 What have we learned? saturation is not yet reached but approaching BnEL: Blacker, Edgier, Larger for details, see arXiv:submit/ [hep-ph] reBB and gGV models: non-trivial structure at low-t similar to non-Gaussian HBT correlations in femtoscopy Bialas-Bzdak

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 25 Backup slides – Questions? Backup slides – Questions?

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 26 reBB model, first fit range studies reBB model, first fit range studies fit: 0 ≤ –t ≤ 2.5 GeV 2, ~not OK fit: 0.36≤ –t ≤ 2.5 GeV 2, OK

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 27 Focusing reBB on the low-t region Focusing reBB on the low-t region Saturation is apparent if fit range is limited to |t| < 0.36 GeV 2

Zimányi School, Budapest, Hungary, 2014/12/01 Csörgő, T. 28 Focusing reBB on even lower -t region Focusing reBB on even lower -t region Saturation still apparent, fit range |t| < 0.18 GeV 2 Connection to TOTEM