Detecting Leading Protons in Central Diffractive Process at the LHC

Detecting Leading Protons in Central Diffractive Process at the LHC;(1) Low * (=0.5m) optics

J. Kalliopuska, A. Kiiskinen, Jerry Lämsä1, T. Mäki, Risto Orava, K. Österberg, M. Ottela, N. van Remortel and S. Tapprogge

High Energy Physics Division, Department of Physical Sciences, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FIN-00014 University of Helsinki, Finland

15. October 2004

Abstract

By detecting leading protons produced in the exclusive central diffractive process, pp  p + X + p, one can measure the missing mass and scan for possible new particle states such as the Higgs boson. This approach augments – in a model independent way – the standard methods for new particle searches at the LHC and will allow detailed analyses of the produced central system, such as the spin-parity properties of the Higgs boson. The exclusive central diffractive process makes possible precision studies of gluons at the LHC and complements the physics scenarios foreseen at the next e+e- linear collider. In this paper, we present the conclusions of the first systematic analysis of the expected precision measurement of the leading proton momentum and the accuracy of the reconstructed missing mass. For our analysis, we track the scattered protons along the LHC beam line using the nominal * = 0.5m machine optics and account for the uncertainties expected in beam transport and detection of the scattered protons. On the basis of our analysis we strongly recommend that an additional leading proton measurement station be added to both sides of the CMS experiment at 420m from the interaction point IP5. 1 Introduction

It has been recently suggested that the Higgs boson mass could be measured to an accuracy of order 1 GeV in the exclusive central diffractive process 1:

p1p2  p’1 + H + p’2 (1)

In contrast to this, the direct measurement of the Higgs boson mass, based on the pair of b-bbar jets in H  bbbar, is estimated to yield a precision of order 10 GeV 2. The range of predictions for the production cross section of the Standard Model Higgs boson through the exclusive process (1) at the LHC energies is constrained by the measurements at the Tevatron 3, and yield 1 – 10fb for the SM Higgs of mass around 120 GeV 4. A recent thorough analysis of the process based on perturbative QCD calculations including uncertainties in background and estimates of rapidity gap survival probability gives a cross section prediction of 3fb for the SM Higgs boson with the mass of 120 GeV 5. The missing mass MM, i.e. the mass of the Higgs boson in (1), can be reconstructed from the four-momenta of the incoming (p1,2) and scattered (p’1,2) proton four-momenta as 6:

2 2 MM = (p1 + p2 – p’1 – p’2) . (2)

The two scattered protons are expected to have small transverse momenta, therefore the missing mass can be approximated as:

2 MM  12s, (3)

Where 1,2 = 1 - p’1,2/p1,2 denote the momentum loss fractions of the two scattered protons. In the following, we present the conclusions of our recent investigation of acceptances and accuracies expected in detecting the pair of leading protons and in reconstructing the central missing mass in process (1).

2 Inputs to the analysis

Our analysis is based on a chain of simulation programs which includes the event generation (PHOJET) and simulation package for the Higgs boson decays (PYTHIA) 7, smearing routines of the interaction point (IP), LHC beam transport code 8, detector simulation package and proton reconstruction programs 9. The following beam related uncertainties are used as inputs to the simulation programs 10: 1 -width of the pp interaction region : x,y = 11m,z = 5cm

- beam divergence: x,y = 30rad - beam energy spread: 1.110-4

1 2x,y of the beam spread (16m) The beam momentum is expected to vary by (4-5)  10-4 over a year and by (1-2)  10-4 over 24 hours. These variations are mostly driven by changes in the circumference of the machine and can be controlled to better than 510-5 11. The IP smearing can be independently measured to an accuracy of x,y = 10m, z=15m 12. Variations of the IP in the longitudinal (beam) direction have a negligible effect on the proton fractional momentum resolution. Before tracking the leading protons along the machine, we recalculated their four-momenta by using the MAD beam transport code. Concerning the detector response, we only consider the horinzontal scattering plane and assume the following input parameters:

- Active detector area is at the distance  from the beam axis:  = kx(z) + , where integer k, k=10, describes the number of standard deviations

required as a safety margin with respect to the rms beam width, x(z), in each detector location. The physical edge of the detector is at a distance of  = 100m from the active area of the detector.2 - For the protons within the fiducial area of a detector, we obtain the position uncertainty by smearing the predicted hit coordinates according to det a Gaussian distribution with the rms width of  x= 10m. - The uncertainty due to the beam position smearing at each detector location is accounted for by smearing the hit coordinates by a correlated beam Gaussian distribution with the rms width of  x= 5m. - Uncertainty of the absolute beam position is introduced as an offset of 10m. - Possible mis-alignment between the two detector planes in each measurement station is accounted for as an offset of 10m.

3. Leading proton transport calculation

The trajectory of a proton in the transverse plane at a given position z along the beam line can be expressed in terms of the initial conditions (x*,y*) and (*x,

*y) at the interaction point as:

eff x(z) = vx(z) x* + L x(z) *x +  D(z) (4)

eff y(z) = vy(z) y* + L y(z) *y, (5)

eff where L x,y(z) is the effective length, vx,y(z) the magnification along the beam line, and D(z) the dispersion. We track the protons were traced by using the Methodical Accelerator Design (MAD) package with the LHC optics version 6.2 (*=0.5m) 8. Although the analysis was carried out for the CMS (IP5), the results should be equally valid for the ATLAS (IP4). At each accelerator element, we registered each proton that remained within the beam pipe.

2 The LHC collimators extend to 6  rms beam width. The safety margin could be anywhere between 9- 15  the rms beam width. It is feasible to assume that the active detector edge is as close as 10m from the physical detector edge 13. 4. Proton momentum reconstruction

The observed proton x-coordinate, at any given location along the beam line, depends on three degrees of freedom: the fractional momentum loss, , the initial scattering angle, *x, and the initial vertex position, x*, at the IP (see Eq. 4). A single measurement of the proton x-coordinate does not completely constrain the proton location; In the following we consider the influence of transverse vertex location as an independent source of uncertainty.

Detector Locations

For extending the acceptance in proton fractional momentum loss, several detector locations are required. In addition, to cross-calibrate the detectors, an overlap between different measurement stations is desired. Based on the LHC beam optics and the criteria above, we have chosen the following three detector positions, each consisting of a doublet of proton detector stations:

(1) 215 and 225 meters, (2) 308 and 338 meters, and (3) 420 and 430 meters from the IP5.

The layout of the detectors in these regions is determined by the planned LHC machine elements. Locations (2) and (3) are in the cryogenic section of the machine and require special design consideration. In location (2) the available space is minimal since there are two dipole magnets in between the two detector stations.

Observables and Coordinate Transformation

The three detector doublets (i=1,2,3) each yield two observables: the average horizontal proton coordinate with respect to the beam axis, xi = (x1,i + x2,i)/2, and the difference xi = x2,i - x1,i = ix zi between the two detectors in a doublet.

The measured values of xi and xi are related to the proton fractional momentum loss, , and the scattering angle *x at the IP. This is demonstrated in

Figs. 3, where the proton  values, plotted as a function of xi and xi , are seen to decrease from =0.015 to 0.002 in steps of 5 10-4 (each step is indicated by a change of colour) (Fig. 3a). In Fig. 3b, the regions of constant *x are shown in the same coordinate system with each step corresponding to *x=28rad. In the following, we define a coordinate transformation which allows us to relate the measured horizontal values of xi and xi to proton  and *x.

To obtain  and *x from the measured values of xi and xi in each detector doublet, an unfolding procedure is required. To simplify this, we first make a coordinate transformation that allows us to spread the data more uniformly (see Fig. 4 where the same data as in Fig. 3 is presented in the transformed coordinates (x',y')).

Proton Momentum Reconstruction

To efficiently reconstruct proton fractional momentum loss, we parametrize the dependence of  on the transformed coordinates (x',y') by fitting a function f(x',y') to the observed average  in a given region of (x',y'). In locations (2) and (3), we were able to define a simple paramterization f(x',y') that connects the measured variables to proton . In region (1), however, no simple solution for f(x',y') was found, and we use instead a two-dimensional interpolation between the elements of a matrix containing 200x200 (x',y') bins with the corresponding average -values.

The relative error, (-calc/) of the resulting proton fractional momentum loss values is depicted in Fig. 5 as a function of the true value of  for the protons moving clockwise along the LHC ring, and in Fig. 6 for the ones moving counterclockwise. The relative spread for all the three detector locations (1-3) on both sides of the IP is of order 0.002, and the central value (bias) less than 0.002. The accuracy of the unfolding procedure is reasonably good and allows us to use the method in the resolution studies presented here. Further improvement could be achieved by increasing the granularity of interpolation in unfolding the data at detector location (1) and/or by further optimization of the parametrization f(x',y') of in regions (2) and (3).

5 Proton acceptances and resolutions

Acceptances

The  acceptances of protons moving in the clockwise and counter-clockwise directions along the LHC beam lines are shown in Figs. 7 for the three detector locations and in Table 3. for the efficiencies   50%.

Table 3. Leading proton  acceptances for   50% in detector locations (1)-(3).

Detector location Clockwise protons Counterclockwise protons (1) 215&225m 0.022-0.200 0.020-0.200 (2) 308&338m 0.003-0.025 0.003-0.022 (3) 420&430m 0.002-0.016 0.002-0.013

Resolution

The  resolutions / = (-calc)/ are summarized in Fig. x where the uncertainties in (1) the transverse location of the interaction spot, (2) detector resolution, (3) beam energy resolution, (4) beam-beam crossing angle at the IP, and (5) the beam position resolution are plotted as functions of  for the protons circulating in the clockwise and counterclockwise directions along the LHC beam line. At all detector locations, it is the uncertainty of the transverse location of the interaction spot that dominates. The interaction region is defined to 11 m by the transverse spread of the two LHC beams. In Table x, we list the studied five sources of uncertainty for the three detector locations. In addition to the transverse IP position, detector resolution and beam energy uncertainty contribute significantly to the over- all  resolution. In general, the two protons are highly correlated; the correlations will be discussed in the next chapter. Table x. Summary of resolution effects at different detector locations

Resolution effects Location (1) Location (2) Location (3) IP location 1.6%-0.5% 4%-2% 7%-1% Detector resolution 1.0%-1.5% 1.2% 5%-0.1% Beam energy < 1% 1.7% 3.5%-0.1% Crossing angle <1% <1% <1% Beam position <1% <1% <1%

Systematic Effects

Alignment errors of the detectors and the uncertainty about the absolute beam position introduce systematic shifts in the measured proton -values. Detector mis- alignment (rms average assumed to be 10m) dominates together with the uncertainty in absolute beam position (rms average assumed to be 10m). The effects of systematic shifts are listed in Table y. for the three detector locations.

Table y. Effects of systematic shifts in proton  resolution.

Systematic shift Location (1) Location (2) Location (3) Detector alignment 0.6%-0.8% 0.1%-0.3% 4%-0.2% Beam position 0.2%-0.1% 0.6%-0.8% 0.7%-0.003%

Correlations

The resolution effects of the two scattered protons are, in general, highly correlated. The protons are created in a single point of interaction, which is determined by the rms spreads of the LHC beams at the IP. Assuming 16m beam spread, the transverse interaction point is determined to x = 2  16m  11m. The interaction vertex is independently measured by the experiment surrounding the IP; with the assumed precision of x = 10m, we obtain: x = (1/2) (11)2 + (10)2 m  7.5 m.

Parametrization of the Resolution Effects

We account for the interdependences between the two scattered protons to obtain the correlated  resolutions from the independent distributions (Fig. ) and parametrize the five different proton resolution effects as functions of  (Table xx). These parametrizations are used to evaluate the mass acceptances and resolutions of the central system produced in pp  p + X + p. Table xy. Parametrizations of the proton  resolution effects at different detector locations - clockwise protons.

Resolution effect Location (1) Location (2) Location (3) IP location 0,0358exp(-23,81) 0,0009^(-0,713) 0,000009^(-1,5388)

Detector resolution 0,0144exp(-4,2693) -1471,4^3 + 0,000002^(-1,7886) 93,223^2 - 1,5665 + 0,0138 Beam energy -0,0071 + 0,0022 0,0001^(-0,9408) 0,00001^(-1,3763) Crossing angle (included above) -0,0471 + 0,0032 -0,3846 + 0,0108 Beam position (included above) (included above) (included above)

Table xz. Parametrizations of the proton resolution effects at different detector locations - counterclockwise protons.

Resolution effect Location (1) Location (2) Location (3) IP location 0,0349exp(-22,314) 0,0013^(-0,669) 0,1883exp(-312,67)

Detector resolution 0,0114exp(-2,5995) 0,1017^(+0,5375) 0,2355exp(-443,27) Beam energy -0,0143 + 0,0024 0,0001^(-0,9859) 0,0962exp(-314,18) Crossing angle (included above) 0,005 -1,3077 + 0,0226 Beam position (included above) (included above) (included above)

Central Mass Acceptances

The mass acceptances in Figures xx are calculated for by using combinations

of the  acceptances of the two leading protons in each event. The combinations 12 are given by the initial state gluon density functions and the central mass by Eq. 3, i.e. 2 MM =12 s. We include three possible scenarios between the two proton measurements: 1) full positive correlation, 2) no correlation, and 3) full negative correlation. The differences between these three possible cases are marginal, and we will adopt the scenario where the pair of final state protons is considered uncorrelated. Mass resolution 420-430m (%)

% 4,5 ( 4 n o

i 3,5 t

o 2,5 s

e 2 r 1,5 s

m 1 r 0,5 0 0 50 100 150 200 250 Mass (GeV)

Figure xx. Rms mass resolution of the Higgs boson produced in exclusive central diffraction: pp -> p + H + p for three alternative scenarios: 1) full positive correlations (stars), 2) no correlations (squares), and 3) full negative correlations (triangles)., 420- 430m location.

Mass resolution 308-338m (%)

% 4,5 (

i 3,5 t

o 2,5 s

e 2 r 1,5 s

m 1 r 0,5 0 0 50 100 150 200 250 Mass (GeV)

Figure xx. Rms mass resolution of the Higgs boson produced in exclusive central diffraction: pp -> p + H + p for three alternative scenarios: 1) full positive correlations (stars), 2) no correlations (squares), and 3) full negative correlations (triangles)., 308- 338m location. 3

) 3,00 % ( 2,50 n o

i Series1 t 2,00 u l Series2 o

s 1,50

e Series3 r

s 1,00 m r 0,50 0,00 0 50 100 150 200 250 Mass (GeV)

Figure xx. The combined rms mass resolution of the Higgs boson produced in exclusive central diffraction: pp -> p + H + p for the detector locations at 308-430m for three alternative scenarios: 1) full positive correlations (stars), 2) no correlations (squares), and 3) full negative correlations (triangles).