Elastic pp scattering and TOTEM experiment Jan Kas par TOTEM - PowerPoint PPT Presentation

Elastic pp scattering and TOTEM experiment Jan Kas ˇpar

TOTEM experiment (Total Cross Section, Elastic Scattering and Diffraction Dissociation at the LHC) The smallest, but independent experiment at the LHC at CERN. Its physical program [1] 1) Total cross section – precise measurement (error ≈ 1 mb ), lu- minosity independent method 16 π d N el / d t | t =0 GeV 2 ̺ ( s ) = ℜ T ( s, 0) σ tot ( s ) = 1 + ̺ 2 N el + N inel ℑ T ( s, 0) 2) Elastic scattering ... 3) Diffraction and the Pomeron – inelastic processes ”not too dif- ferent” from elastic, various X ∼ various physics p + p → p + X p + p → p + p + X

There is no satisfactory theory of diffraction so far. On the other hand there is a variety of phenomenological models and the TOTEM experiment will provide a tool to sort out the models that are based on true physical nature.

TOTEM detectors It will share location with CMS. The forward inelastic detectors will be assembled in CMS. Elastic detectors will be placed far from IP in Roman pots

Roman pots

TOTEM/CMS acceptance Angle corresponding to pseudorapidity η = 10 is ϑ ≈ 2 e − η ≈ 9 · 10 − 5 .

TOTEM elastic scattering aims During one run, d σ/ d t can be measured in a relatively narrow t region. Finally, these pieces of data will have to be fitted together.

What can one find in this thesis? 1) Elastic pp scattering analysis a) Islam’s model b) Impact parameter point of view c) Coulomb interference 2) Calibration of detector alignment – my summer project in CERN

The model • Interesting is small t region, where coupling constant is too large to use perturbative approach within QCD ⇒ phenomeno- logical models are employed. • Model of Islam et al. ([2], [3], [4]) was used. It is based on idea of proton structure. They start from SU (3) L × SU (3) R gauged nonlinear sigma model.

They distinguish 3 mechanisms (diffraction, core scattering and quark scattering) d σ π sp 2 | T ( s, t ) | 2 T ( s, t ) = T D ( s, t ) + T C ( s, t ) + T Q ( s, t ) d t = Diffraction is a consequence of interaction of the outer clouds. The corresponding amplitude is parametrised ∞ √ � � � 1 1 T D ( s, t ) ∼ b d b J 0 ( b − t ) + − 1 b − R − b − R 1 + e 1 + e a a 0 Scattering one core off the other gives birth to the core scattering . It should be go via ω exchange, therefore T C ( s, t ) ∼ s F 2 ( t ) m 2 ω − t

Quark amplitude reflects transition to perturbative regime of QCD. They take into account ”distribution functions”, elastic qq amplitude. The latter is obtained with BFKL theory. The former leads to appearance of form factor F ( q ⊥ ) . The quark amplitude reads T Q ( s, t ) ∼ s F ( q ⊥ ) | t | + r − 2 0

Alltogether, there are 17 (13) energy–independent parameters. Authors determined these parameters by fitting data on σ tot ( s ) , pp at energies √ s = 541 GeV , 630 GeV and ρ ( s ) and d σ/ d t for ¯ 1 . 8 TeV .

Impact parameter representation • Basic idea is to replace T ( s, t ) by A ( s, b ) , where b is impact parameter. • It naturally follows from eikonal approximation in QM. • There is precise formulation based on Fourier–Bessel transform [5] ∞ ∞ � A ( b ) = 1 � U ( q ) = c b d b J 0 ( bq ) A ( b ) q d q J 0 ( bq ) U ( q ) c 0 0 • However, it requires both A ( b ) and U ( q ) to be defined on (0 , ∞ ) . We want to identify U ( q ) with amplitude T ( s, t = − q 2 ) , but it is constrained to t min < t < 0 ⇒ we introduce arbitrary function ˜ T � T ( s, t = − q 2 ) for t min < t < 0 U ( q ) = ˜ T ( s, t = − q 2 ) for t < t min

˜ • T represents ambiguity in i.p. amplitude ⇒ it is necessary to introduce a physical requirement for ˜ T , that would remove the ambiguity. • A ( s, b ) = a ( s, b ) + ˜ a ( s, b ) ∞ ∞ � � b d b b 2 n ˜ a ∗ ( s, b ) a ( s, b ) = 0 a ( s, b ) = 0 b d b ˜ 0 0 ∞ ∞ � � d 2 b | a ( s, b ) | 2 ⇒ d 2 b ℑ A ( s, b ) , • σ tot ( s ) = 4 π σ el ( s ) = 4 π 0 0 seems natural to interpret 4 π ℑ A ( s, b ) resp. 4 π | a ( s, b ) | 2 as total resp. elastic collisions density ̺ el, tot ( s, b ) . To do so, ℑ A ( s, b ) a (or ˜ must be non–negative ⇒ physical constraint on ˜ T ).

• If we adopt the density interpretation we can define mean value of b 2 (independent on ˜ T choice) � − 1 � �� d 2 b b 2 ̺ el, tot ( s, b ) � b 2 ( s ) � el, tot = d 2 b ̺ el, tot ( s, b ) Islam model is central, with weak t dependence of amplitude phase ⇒ � b � tot > � b � el . It is in contradiction with diffraction, which is described by peripheral models.

Coulomb–Hadron interference • Two fundamental forces are essential for pp scattering. Namely, electromagnetic and strong. We know scattering amplitudes for each interaction separately. The problem, how to determine amplitude for both interactions acting simultaneously. • One problem, two (approximate) solutions: a) eikonal additivity way b) summing some relevant Feynman diagrams Eikonal approximation in QM gives following prescription ∞ A ( s, b ) = e 2 δ ( s,b ) − 1 δ ( s, b ) = − 1 � b 2 + z 2 ) � d z V ( 2 i 2 p 0

Potential is additive ⇒ eikonal δ is additive. For V = V 1 + V 2 , the total amplitude A ( s, b ) = A 1 ( s, b ) + A 2 ( s, b ) + 2 iA 1 ( s, b ) A 2 ( s, b ) Jump to the final result [6], [7]  0 d F 2 ( t ′ ) d t ′ ( ln t ′ T ( s, t ) = ∓ αs � t F 2 ( t ) + T H ( s, t )  1 ± iα − t d t t min � � T H ( s, t ′ ) � I ( t, t ′ ) − T H ( s, t ) − 1  2 π √ d ϕF 2 ( t ′′ ) I ( t, t ′ ) = 1 � t ′′ = t + t ′ + 2 tt ′ cos ϕ t ′′ 2 π 0 – Two ways of possible use: T ⇒ T H and T ⇐ T H – One formula for whole t region.

Feynman diagrams technique (West–Yennie formula) [8], [9] – Uses scalar field for protons. – Needs to know off shell hadron amplitude. – A ”model independent contribution” is introduced. It de- pends on amplitude on the mass shell only and does not suffer from IR divergence. – Final formula is equivalent with simplified formula derived within the previous approach. Conventional analysis – simplified WY formula assumes – Purely exponential decay of amplitude in whole t region. – Constant phase in whole t region. Relative importance of interference f ( s, t ) = | T ( s, t ) | 2 − | T H ( s, t ) | 2 − | T C ( s, t ) | 2 | T H ( s, t ) | 2

For pp at energy √ s = 53 GeV Prediction for LHC has the same character, with 2 quantitative differences. The blue and the red line are closer (diff. cross section is higher) and the peak in f ( t ) is at t ≈ 5 · 10 − 1 GeV 2 (position of diffraction dip).

My summer project in CERN calibration of detector alignment • In every roman pot, there will be a bunch of 10 planar strip detectors (with strip pitch 66 µm ). One half having the strips perpendicular to the other half. • The detectors will be adapted for TOTEM special needs, they will be edgeless . • This new technology need to be tested. For this pourpose it is crucial to know precise position of every detector. • Estimated maximum error of mechanical placement is 20 µ m . This induces maximum possible slant 10 − 3 .

Test detector geometry

The method • We know distribution of tracks from beam source. σ a = 3 · 10 − 3 , � a � = 0 , � b � = 0 mm , σ b ≈ 12 mm • Difference in x positions measured in i -th and j -th detector D ij = x ′ i − x ′ j = a x ( z i − z j ) − (∆ x i − ∆ x j ) − a y ( z i s i − z j s j ) − − b y ( s i − s j ) + (∆ y i s i − ∆ y j s j )

Shifts • Event-averaged value of D ij N D ij = 1 ¯ � D n ij = − (∆ x i − ∆ x j ) + ¯ a x ( z i − z j ) − N n =0 a y ( z i s i − z j s j ) − ¯ − ¯ b y ( s i − s j ) • Deviation of arithmetic mean a x = σ a x σ ¯ √ N D ij ≈ − (∆ x i − ∆ x j ) with error 0 . 7 µ m for 5 · 10 4 events. ¯ •

Slants • Linear regression applied on data D n ij versus b n y T ij = − ( s i − s j ) + F √ • It can be shown � F � = 0 m − 1 and σ F ∼ 1 / N • T ij ≈ − ( s i − s j ) with error 2 . 2 · 10 − 4 for 5 · 10 4 events.

Real situation g ( b ) f ( a ) h ( a, b ) = b max a max ( b ) � g ( b ) � f ( a ) b min a min ( b )

That’s all, thank you for attention :-)

References [1] TOTEM-Technical Design Report-001, CERN-LHC-2004-002 [2] M.M.Islam, V.Innocente, T.Fearnley, G.Sanguietti, Europhysics Letters 4, 189–196 (1987) [3] M.M.Islam, R.J.Luddy, A.V.Prokudin, Modern Physics Letters A 18, 743– 752 (2003) [4] Islam, M. M. and Luddy, R. J. and Prokudin, A. V., Phys. Lett. B605, 115–122 (2005) [5] T.Adachi, T.Kotani, Progr. Theor. Phys. Suppl. Commemoration issue, 316–331 (1965) [6] Cahn, R., Zeit. Phys. C15, 253 (1982) [7] Kundrat, V. and Lokajicek, M., Z. Phys. C63, 619–630 (1994) [8] West, Geoffrey B. and Yennie, D. R., Phys. Rev. 172, 1413-1422 (1968) [9] J. Rix, R. M. Thaler, Phys. Rev. 152, 1357–1363 (1966)