H1 FPS + ZEUS LPS 1

Regge fit, H1 FPS HERA II data

• Parameterization of xIP and t dependences for IP and IR

),(),(),(),(),,,( 22

22

2)4(2 QFtxfnQFtxftxQF IR

IPIRIRIP

IPIPIPD

tt IPIPIP ')0()( 2 ' ln(1/ )IP IP IPB B x

• Fixed parameters for IR (from H1 DPDF Fits): α´IR=0.3 GeV-2, BIR=1.6 GeV-2, F2

IR(β,Q2) – π structure function (Owens), small FLD contribution is

not corrected yet (→ H1 2006 DPDF fit B)

• Free parameters: αIP(0), α´IP, BIP, nIR, αIR(0) and IP normalization F2IP(β,Q2)

in every (β,Q2) bin

→ 322 σrD(4) data points, 288 degrees of freedom (DESY 10-095)

→ total errors (statistical and systematic errors added in quadrature)

• Assume proton vertex factorization for IP and IR

H1 FPS + ZEUS LPS 2

Regge fit, ZEUS LPS data

),(),(),(),(1),,,(1 22

max

min

22

max

min

max

min

2)4(2 QFdttxftnQFdttxftdttxQFt IR

t

t

IPIRIRIP

t

t

IPIP

t

t

IPD

• Fixed parameters for IR (as in ZEUS Regge Fit): α´IR=0.9 GeV-2, BIR=2.0 GeV-2, F2

IR(β,Q2) – π structure function (Owens instead of GRV), selection of data points with y<0.5, where FL

D contribution is neglected

• Free parameters: αIP(0), α´IP, BIP, nIR, αIR(0) and IP normalization F2IP(β,Q2)

in every (β,Q2) bin

→ 178 σrD(4) data points, 153 degrees of freedom (DESY 08-175)

→ total errors (statistical and systematic errors added in quadrature)

• Integrate over Δt bins for IP and IR

H1 FPS + ZEUS LPS 3

Results of H1+ZEUS Regge fits

tt IPIPIP ')0()(

2 ' ln(1/ )IP IP IPB B x

αIP(0) = 1.075 ± 0.010

α´IP = -0.008 ± 0.03 GeV-2

BIP = 6.3 ± 0.3 GeV-2

αIR(0) = 0.44 ± 0.013

nIR ≃ 2.0 , χ2 = 514 / 450 (~1.14)ZEUS LPS Regge fit, y<0.5 (cross check)

αIP(0) = 1.175 ± 0.015

α´IP = 0.28 ± 0.03 GeV-2

BIP = 3.0 ± 0.3 GeV-2

αIR(0) = 0.65 ± 0.06

nIR ≃ 2.2 , χ2 = 470 / 450 (~1.05)

H1+ZEUS Regge fit, IR(H1) H1+ZEUS Regge fit, IR(ZEUS)

αIP(0) = 1.09 ± 0.02

α´IP = -0.006 ± 0.06 GeV-2

BIP = 7.2 ± 0.65 GeV-2

αIR(0) = 0.66 ± 0.10

nIR ≃ 1.8 , χ2 = 146 / 153 (~0.95)

IR(H1) αIP (soft) ~ 1.08 α'IP ≃ 0 → no “shrinkage”

IR(ZEUS) αIP ~ 1.18 α'IP (soft)~ 0.28 GeV-2

H1 FPS + ZEUS LPS 4

xIPσrD(4)(β,Q2,xIP,t)

DESY 10-095

H1 FPS HERA II

σrD(4) as a function of

β,Q2,xIP,t (322 points)

─ H1+ZEUS Regge fit IR(H1)

Χ2 = 253 / 288 (~0.88)

--- H1+ZEUS Regge fit IR(ZEUS)

Χ2 = 242 / 288 (~0.84)

H1 FPS + ZEUS LPS 5

t-slope: H1 FPS HERA II

DESY 10-095

H1 FPS HERA II

t-slope as a function of β,Q2,xIP (108 data points)

─ H1+ZEUS Regge fit IR(H1)

--- H1+ZEUS Regge fit IR(ZEUS)

)(),,()()),,(1(),,( 222IPIRIPIRIPIPIPIRIP xBQxWxBQxWQxB

H1 FPS + ZEUS LPS 6

xIPσrD(4)(β,Q2,xIP,t)

DESY 08-175

ZEUS LPS

σrD(4) as a function of

β,Q2,xIP,t (182 points, no y<0.5 cut)

─ H1+ZEUS Regge fit IR(H1)

Χ2 = 262 / 157 (~1.67)

--- H1+ZEUS Regge fit IR(ZEUS)

Χ2 = 229 / 157 (~1.46)

H1 FPS + ZEUS LPS 7

Average t-slope as a function of xIP

)()()())(1()( IPIRIPIRIPIPIPIRIP xBxWxBxWxB

─ WIR from ZEUS (β,Q2,xIP) points

-- WIR from ZEUS (β,Q2,xIP) points

─ H1 FPS HERA II Regge fit

H1+ZEUS Regge fits with IR(H1) and IR(ZEUS) give different average

t-slope behavior with xIP

average t-slope depends on WIR

H1 FPS + ZEUS LPS 8

Average t-slope as a function of xIP

--- Regge fit uncertainty band

• H1 FPS HERA II DESY 10-095

• H1 FPS HERA I DESY 06-048

• ZEUS LPS 2 DESY 08-175

─ H1 FPS HERA II Regge fit

H1 FPS + ZEUS LPS 9

Backup: published H1 and ZEUS Regge fits

tt IPIPIP ')0()(

2 ' ln(1/ )IP IP IPB B x

0.19 -20.06' 0.06 GeVIP

H1 FPS HERA-1 parameterization:

2,0 -20.75.5 GeVIPB

αIP(0) = 1.10 ± 0.02 (exp.) ± 0.03 (model)

α´IP = 0.04 ±0.02 (exp.) ±0.08 (model) GeV-2

BIP = 5.73 ±0.25 (exp.) ±0.80 (model) GeV-2

ZEUS LPS Regge fit:

)model((exp.)022.0114.1)0( 040.0020.0IP model)(02.0)syst.((stat.)02.011.1)0( 01.0

02.0 IP

-204.008.0 GeV (model)04.0)syst.((stat.)06.001.0 IP'

-24.17.0 GeV )syst.((stat.)7.01.7 IPB

Compare with published HERA results:

αIP (0) ≃ αIP (soft)~1.08 α'IP ≃ 0 → no “shrinkage” (α'IP (soft)~0.25 GeV-2 ) BIP consistent with hard process

H1 FPS HERA-2 DESY 10-095:

0.90

0.06

H1 FPS + ZEUS LPS 10

ZEUS LPS DESY 08-175