Włodek Guryn

Brookhaven National Laboratory, Upton, NY 11973, USA

**Outline of the Talk**

1.  PP2PP experiment with ***p*** and ***p*^↑^**.

2.  Program with transversely polarized beams

3.  Summary

**Total and Differential Cross Sections, and Polarization**

**Effects in pp Elastic Scattering at RHIC**

**B. Chrien, R. Gill, W. Guryn\*, D. Lynn, A. Rusek, M. Sakitt, S.
Tepikian**

*Brookhaven National Laboratory, USA*

**J. Bourotte, M. Haguenauer**

*Ecole Polytechnique/IN2P3-CNRS, Palaiseau, France*

**M. Conte**

*Universita di Genova and Sezione INFN, Italy*

**M. Buenerd**

*Institut des Sciences Nucleaires, Grenoble, France*

**N. Akchurin, C. Newsom, Y. Onel**

*University of Iowa, Iowa City, USA*

**A. A. Bogdanov, V. A. Kaplin, A. Karakash, S.B. Nurushev, M.F Runtzo,
M. N. Strikhanov**

*Moscow Engineering Physics Institute (MEPHI), Moscow, Russia*

**M*.* Pusterla**

*Universita di Padova, Italy*

A.  **Ufimtsev**

*IHEP Serpukhov, Russia*

**M*.* Rijssenbeek, C. Tang**

*SUNY Stony Brook, USA*

**K. De, A. Vartapetian**

*University of Texas at Arlington, USA*

**G.N.Dudkin, I.V.Glavanakov, Yu.F.Krechetov, G.A.Naumenko,
A.P.Potylitsin, G.M.Radutsky**

*Tomsk Nuclear Physics Institute, Tomsk, Russia*

**R. Giacomich, A. Penzo, P. Schiavon**

*Universita di Trieste and Sezione INFN, Italy*

\* Spokesperson

1\. Coulomb Region
$\frac{d\sigma}{\text{dt}}\text{\textasciitilde}\frac{1}{t^{2}}$ **--**
Normalization (ℒ)

2\. Coulomb -- Nuclear Interference -- "ρ" Value

3\. Diffraction
$$$\frac{d\sigma}{\text{dt}}\text{\textasciitilde}e^{\text{Bt}}$ --
σ**~tot~**

4\. Structure Region -- Peaks & Bumps

5\. Large \|*t*\| **≳** 5 GeV^2^ -- Pert. QCD Large *t*

**PP2PP PHYSICS PROGRAM**

Studying total and elastic cross sections played a crucial role in
particle and nuclear physics, in particular *pp* and
![](media/image1.wmf){width="0.3333333333333333in"
height="0.3055555555555556in"} experiments extend to the highest ***s.*
Elastic** **scattering has been measured at every accelerator**, for
every ***s*** energy available.

**The main goal of the experiment is to map in great detail the spin
dependence of the proton-proton interaction over a wide range of *s* and
\|*t*\|, 50≤√*s*≤500 GeV, 4x10^-4^≤\|*t*\|≤1.5 GeV^2^. In order to
understand the features of the exchange mechanism (Pomeron), in terms of
QCD concepts.**

**Polarization observables *A*~N~, *A*~NN~, (*A*~LL~,) will give access
to spin degrees of freedom**, which distinguish between **different
nucleon structure models**; e.g. the three-quark model of the proton
versus the quark-diquark model of the proton.

By measuring **spin asymmetries *A*~N,~ *A*~NN~, *A*~LL~**, we will be
able to determine the **helicity amplitudes φ~I,~** which describe the
dynamics of nucleon-nucleon elastic scattering, and which are poorly
known at best:

**φ~1~ \~ \< ++\| *M* \|++ \> φ~2~ \~ \<−−\| *M* \|++\> φ~3~ \~ \<+−\|
*M* \|+−\>**

**φ~4~ \~ \<+−\| *M* \|−+\> φ~5~ \~ \<++\| *M* \|+−\>**

**Their measurement will shed light on the exchange mechanism (Pomeron)
including its spin dependence.**

1.  **Proton constituent quark structure through A~N~, being sensitive
    to hadronic spin flip in CNI region, is sensitive quark -- diquark
    proton structure:**

2.  **The spin dependance of nucleon-nucleon interactions and determine
    features of the Pomeron in terms of QCD concepts and its spin
    dependence.**

3.  **Large-\|*t*\| region, for tests of pQCD:**

Other topics done with the same experimental setup:

-   **Diffractive *pp* scattering** can be done, with four momenta
    transfer \|*t*\|\<1.5 GeV^2^, where one studies the dynamics of
    long-range strong interactions.

-   **Elastic scattering of *p*d, *p*^↑^d, dd, *p*^↑4^He** can be
    measured with the **same experimental setup**.

These measurements challenge strong interaction theory, since they
involve the application of QCD in a kinematical region where
non-perturbative effects are important.

# Polarized beams

With transversely polarized protons and measuring of **∆σ~tot~, A~N~,
A~NN~** we will determine helicity amplitudes **φ~i~(s,t)~iii~ :**

**φ~1~ \~ \< ++\| M \|++ \> φ~2~ \~ \<−−\| M \|++\> φ~3~ \~ \<+−\| M
\|+−\>**

**φ~4~ \~ \<+−\| M \|−+\> φ~5~ \~ \<++\| M \|+−\>.**

1.  **THE ODDERON AND SPIN DEPENDENCE OF HIGH-ENERGY PROTON-PROTON
    SCATTERING. E. Leader, T.L. Trueman. Phys.Rev.D61:077504,2000**

2.  **THE SPIN DEPENDENCE OF HIGH-ENERGY PROTON SCATTERING.**

> **N.H. Buttimore, B.Z. Kopeliovich, E. Leader, J. Soffer, T.L. Trueman
> Phys.Rev.D59:14010,1999**

• the difference of **σtot** as function of pure initial transverse
spin:

$${\Delta\sigma}_{\text{tot}} = \sigma_{\text{tot}}( \uparrow \downarrow ) - \sigma_{\text{tot}}( \uparrow \uparrow )$$

• the analyzing power, **AN**:

$$A_{N} = \frac{1}{P\text{cos}f}\frac{N_{­} - N_{¯}}{N_{­} + N_{¯}}$$

• and the double-spin correlation parameter, **ANN**:

$$A_{\text{NN}} = \frac{1}{P_{1}P_{2}\text{cos}^{2}f}\frac{N_{\text{­­}} + N_{\text{¯¯}} - N_{\text{­¯}} - N_{\text{¯­}}}{N_{\text{­­}} + N_{\text{¯¯}} + N_{\text{­¯}} + N_{\text{¯­}}}$$

(*Pi* is beam polarization, φ is scattering azimuth

# 

We shall study systematically ***pp*** elastic scattering with polarized
and unpolarized beams p~lab~ \< 250 GeV/c and in both colliding beam
mode and fixed target mode, using a polarized gas jet target.

The four-momentum transferred ***-t*** is sub-divided in two kinematic
ranges:

1.  Medium ***t*** region, **day one pp running**, no special conditions
    required:

> **[0.006 \< -t \< 1.5 (GeV/c)2]{.mark}**

• evolution of dip structure observed at the ISR in **dσel/dt**;

***• s*** and **t** dependence of the nuclear slope, ***b***.

2\. Coulomb Nuclear Interference ( **CNI** ) region:

**[0.0004 \< -t \< 0.12 (GeV/c)2]{.mark}**

***•** s* dependence of σtot and dσel/dt;

• ratio of real to imaginary part of the forward scattering amplitude,
**ρ**;

• nuclear slope parameter of the ***pp*** elastic scattering,

**PHYSICS PROGRAM**

1.  By measuring **spin asymmetries A~N,~ A~NN~, A~LL~**, we will be
    able to determine the **helicity amplitudes φ~I~,** which describe
    elastic scattering. They are not well known now.

**φ~1~ \~ \< ++\| M \|++ \> φ~2~ \~ \<−−\| M \|++\> φ~3~ \~ \<+−\| M
\|+−\>**

**φ~4~ \~ \<+−\| M \|−+\> φ~5~ \~ \<++\| M \|+−\>.**

2.  **Polarization observables will give access to spin degrees of
    freedom**, which distinguish between different nucleon structure
    models, like quark diquark model of the proton and its appropriate
    wave function of the proton.

3.  **In the medium *t* region**, with four momenta transfer
    \|t\|\<1.5GeV^2^, we will study the dynamics of long range strong
    interactions, the non-perturbative regime of QCD. Hence, the
    experiment will address one of the main, unsolved problems in
    particle and nuclear physics: **long range QCD** and confinement.

4.  By appropriate design of the veto system and an additional trigger
    condition, the experiment will also measure **single diffraction
    dissociation.**

5.  **In the small momentum transferred \|t\| region,** one tests in a
    model independent way, general analytical properties of scattering
    amplitudes: analyticity, unitarity crossing symmetry.

6.  Using the same detectors and an additional magnet in the IR for
    momentum reconstruction will allow measurement of elastic scattering
    **in large *t* region**, hence tests of **pQCD** calculations.

For small scattering angles the protons follow the accelerator lattice,
hence one can use the transport matrix to relate the position at the
detection point to the scattering angle at the collision point:

[]{.mark}$$y_{\text{det}} = \sqrt{\beta/\beta^{}}\left( \text{cos}\Phi + \alpha^{}\text{sin}\Phi \right)y^{} + \sqrt{\text{ββ}^{}}\left( \text{sin}\Phi \right)\Theta_{\text{SC}}$$

or:

y~det~ = a~11~ y\* + Leff Θsc.

The optimum condition, called parallel to point focusing, is when a~11~=
0 and L~eff~ is large. So that for small Θsc one gets large displacement
at the detection point, with no sensitivity to y\*.

The smallest **t** expressed in terms of beam parameters is:

tmin ∝

This implies the need for **large β\* and small ε**.

(In order to reach Coulomb region special tune, **β\* = 195 m** and low
emmitance **ε** = **5π**, are required.)

Roman pot location is determined by parallel to point focusing.

![](media/image2.wmf){width="5.995138888888889in"
height="2.651388888888889in"}

More than one p*beam* at RHIC, 100 GeV/c and 250 GeV/c proton beams,
will allow us to take data at two √s points.

At luminosity 4x10**^30^** cm**^-2^**sec**^-1^**, 200 hrs data on tape
to acquire 1000 evts/0.02 GeV**^2^**/c**^2^** bin will be needed.

Silicon strip detectors are our choice. They will provide:

-   uniformity of efficiency \~ 0.1% not to dominate errors on σtot and
    ρ;

-   small dead area between the sensitive part of the detector and the
    beam 0.5mm

-   many detector layers with high efficiency;

-   small cell size to limit occupancy per readout channel;

-   in the CNI region good detector resolution is needed:

$$dt\text{<<}\text{10}^{- 4}\text{GeV}^{2}(\text{bins}) \Rightarrow dy»0\text{.}1\text{mm}$$

-   in the dip region detector resolution set by momentum reconstruction
    (δp/p \~ 1%) and vertex size (y\* \~ 1mm):

![](media/image5.wmf)

## 

## Status and Plans

## Our goal is to be ready for running in spring of 2001.

## Experiment has scientific approval and has received funding for equipment. 

## Since the approval time we have:

## optimized the experiment, involving RHIC accelerator group to find placement for detectors (parallel to point focusing;)

## designed of parts that are critical: Roman pots, detectors;

## designed the veto system;

1.  2000 finish design and prototyping of the Roman pots, Si strip
    detectors and of the inelastic detector system.

2.  2001 construction and commissioning of detectors, Roman pots,

**Engineering run in Spring of 2001**

3.  2002 physics run.

#######