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Using petawatt laser pulses of picosecond duration for detailed diagnostics of creation and decay processes of B-mesons in the LHC

Published online by Cambridge University Press:  04 September 2008

Heinrich Hora  and
Dieter H.H. Hoffmann
Heinrich Hora*
Affiliation:
University of New South Wales, Kensington, Australia
Dieter H.H. Hoffmann
Affiliation:
Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany
*
Address correspondence and reprint requests to: Heinrich Hora, University of New South Wales, Kensington, Australia. E-mail: h.hora@unsw.edu.au
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Abstract

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Type
Short Communication
Information
Laser and Particle Beams , Volume 26 , Issue 3 , September 2008 , pp. 503 - 505
Copyright
Copyright © Cambridge University Press 2008

The co-incidence of the lifetime of B-mesons in the range of ps with the technology of laser pulses of about picoseconds (ps) or shorter duration with up to petawatt (PW) power will provide diagnostic techniques revealing very fine details about the timing of the generation of B-mesons within the collision area of the large hadron collider LHC. The fine structure of the time dependence as well as the degree of dependence of the polarization directions of the decay products as e.g. protons, antiprotons, π-mesons and others may be detected by taking into account the acceleration processes by the nonlinear (ponderomotive) forces in the laser focus and the colliding area where the high laser powers are essential.

Generation of very large numbers of B-mesons in the large hadron collider (LHC) was considered as a very first field of gaining new insights into high energy physics (Gershon, Reference Gershon2008) using the LHCb detector before the other detectors may be successful with measurements about Higgs particles and others. A combination of the experiments with the interaction of the petawatt-picosecond laser pulses is evident as it was proposed with laser pulses with the then lower powers (Hora, Reference Hora1992) for interaction within the collider region. Initially, the combination of laser interaction with the collider region of an electron accelerator was following the results of an experiment (Boreham et al., Reference Boreham and Hora1979). For historical details, see Hora (Reference Hora1991, p. 305)

For the laser interaction with the much heavier charged B-mesons or other heavy charged particles, only the presently available PW laser pulses may be considered. These lasers using the CPA (chirped pulse amplification) technique (Mourou et al., Reference Mourou, Tajima, Tanaka, Meyerhofer and Meyer-ter-Vehn2002) are either neodymium glass lasers or titanium-sapphir lasers or those using the Schäfer technique for excimer lasers (Szatmari et al., Reference Szatmari and Schäfer1988, Sauerbrey, Reference Sauerbrey1996). This work was essential for discovering an anomaly of laser-plasma interaction for application to inertial fusion energy (Hora et al., Reference Hora, Badziak, Read, Li, Liang, Ang, Liu, Sheng, Zhang, Osmanm, Miley, Zhang, He, Peng, Glowacz, Jablonski, Wolowski, Skladanovski, Jungwirth, Rohlena and Ullschmied2007; Ghoranneviss et al., Reference Ghoranneviss, Malekynia, Hora, Miley and He2008, Hora et al., Reference Hora, Malekynia, Ghoranneviss, Miley and He2008). Today, tabletop lasers with pulses up to 100 TW power and a pulse sequence of seconds or shorter are available for synchronizing with the colliding events in the LHC.

The experiment by Boreham et al. (Reference Boreham and Hora1979) was aiming to prove the action of the nonlinear (ponderomotive) forces at laser interaction in plasmas (Hora, Reference Hora1969). After the characteristic property of producing a density minimum (caviton) by the nonlinear force was confirmed by several experiments (Hora, Reference Hora1991, see Chapter 10.4), it was of interest whether the free electrons in a laser focus will receive a radial acceleration by the negative gradient of high-frequency electric laser field E, given by −∇E2, as it was known as ponderomotive force in electrostatics. The general expression of the nonlinear force density in plasma (after eliminating gas dynamic, thermokinetic forces is given by

(1)
\eqalign{{\bf f}_{\rm NL} &= \nabla \bullet \lsqb {\bf EE}+{\bf HH} - 0.5\lpar {\bf E}^{2} + {\bf H}^{2}\rpar {\bf 1} \cr &\quad + \lpar 1 + \lpar \partial/\partial t\rpar /{\rm \omega}\rpar \lpar {\bf n}^{2} - 1\rpar {\bf EE}\rsqb /\lpar 4{\rm \pi}\rpar \cr &\quad -\lpar \partial/\partial t\rpar {\bf E} \times {\bf H}/\lpar 4{\rm \pi c}\rpar \cr}

where H is the laser field vector, 1 is the unity tensor, ω the laser radian frequency, c the vacuum speed of light, and n is the (complex) refractive index. The prove of the correctness of equation (1) was given from the fact that these and only these terms of the forces were derived from momentum conservation for the non-transient case (Hora, Reference Hora1969) and by symmetry reasons for the transient case (Hora, Reference Hora1985). A further proof was given from Lorentz- and gauge-invariance (Rowlands, Reference Rowlands2006). For simplified geometry, the force (1) can be reduced to

(2)
{\bf f}_{\rm NL} = - \lpar \partial/\partial {\rm x}\rpar \lpar {\bf E}^{2} + {\bf H}^{2}\rpar /\lpar 8{\rm \pi}\rpar = \lpar {\bf n}^{2} - 1\rpar \nabla {\bf E}^{2}/\lpar 8{\rm \pi} \rpar . \eqno \lpar 2\rpar

When plasma effects can be neglected for sufficiently large Debye lengths (Boreham et al., Reference Boreham and Hora1979), single electron motion can be considered. It should be mentioned that the evaluation of the single particle motion enforced the use of the Maxwellian exact description of the laser beam with the then necessary tiny longitudinal field components (Hora, Reference Hora1981, section 12.3; Cicchitelli et al., Reference Cicchitelli, Hora and Postle1990) indicating that neglection of tiny quantities in linear physics can lead to completely wrong results compared with the correct theory in precise nonlinear physics (Hora, Reference Hora2000).

The result of the force is given by acceleration of the electron through the gradient of the laser field where the kinetic energy of the quiver motion of the electron in the laser field with its energy ɛoc is converted into translative energy ɛtrans = ɛoc/2

(3)
\varepsilon_{\rm trans} = \hbox{E}^{2}\hbox{e}^{2}/\lpar 4{\rm \omega}^{2}\hbox{m}\rpar \eqno \lpar 3\rpar

where E is the amplitude of the laser field and e is the charge and m the mass of the electron. The general quiver energy of the electron in a laser field of intensity I is

(4)
\varepsilon_{\rm os} = \hbox{mc}^{2}\lsqb \lpar 1 + 3{\rm I}/{\rm I_{rel}}\rpar ^{1/2} - 1\rsqb \eqno \lpar 4\rpar

The relativistic threshold intensity, where the quiver energy is mc2 (Hora, Reference Hora1981, Reference Hora1991) is

(5)
\hbox{I}_{\rm rel} = 3\hbox{m}^{2} {\rm \omega}^{2}\hbox{c}^{3}/\lpar 8{\rm \pi} \hbox{e}^{2}\rpar \eqno \lpar 5\rpar

The experiment (Boreham et al., Reference Boreham and Hora1979) measured the emission of electrons form the cylindrical focus of a neodymium glass laser beam (wavelength λ = 1.053 µm, relativistic threshold intensity 3.68 × 1018W/cm2) with axial maximum intensity I = 1016W/cm2 in low density helium from where the electrons after ionisation received an energy of 1 keV in radial direction of the laser beam. The theoretical value, Eq. (3), is 1.039 keV. The photon energy which goes into the kinetic energy of the quiver motion of the electron has a momentum ɛtrans/c resulting in a forward component of the electron velocity parallel to the axis of the laser beam. This was calculated (Hora et al., Reference Hora, Viera, Hora and Miley1984) and measured in full agreement (Meyerhofer et al., Reference Meyerhofer, Knauer, Mcnaught and Moore1996).

What was interesting in these experiments is that there was a definite limit for the maximum emission energy of the electrons (Boreham et al., Reference Boreham and Hora1979) and the maximum relativistic forward shift (Meyerhofer et al., Reference Meyerhofer, Knauer, Mcnaught and Moore1996). Beyond these values, nothing should be measured theoretically. But there was a whole spectrum of electron energies and shift angels due to the fact that electrons were emitted from parts of the laser beam and at times where the laser intensity I is lower than the maximum value. This was also evaluated by Meyerhofer et al. (Reference Meyerhofer, Knauer, Mcnaught and Moore1996). These spectra describe the whole spatial and temporal property of the laser pulse by functional-analytical folding of the distribution functions of the involved integral equations. For the experiment of laser interaction with the electrons in the LEP (Large Electron Positron Collider) (Hora, Reference Hora1992), these properties were first of all of interest only about the electron distributions and again about the laser pulse properties. An effect on the generation of charged Z-particles was discussed.

For an application of the PW-ps laser pulses interacting with the colliding protons and the generated charged B-mesons and their subsequent longer living charged decay products, one has to take into account the comparably large masses of these particles requiring then the now available very high laser powers and intensities. First one has to confirm that the relativistic threshold intensity Irel for these heavy particle is much higher than the quiver energy such that the subrelativistic branch of Eq. (5) is valid. Further it is interesting what maximum energy gain Δɛ the particle can reach by the laser field in order to check whether this change can be measured in the particle detectors for comparison with and without laser interaction.

For a modest tabletop laser to be added to the LHCb diagnostics one may consider a 100 TW laser pulse of 1 ps duration focused to 20 µm diameter. This pulse has a length of 0.3 mm and the temporal and/or radial intensity profile can be varied by the usual techniques such that a wide range of functional-analytical variations is possible for the evaluation of measured spectra of added energies or bending directions against the cases without laser interaction. For these interaction the following values result for neodymium glass lasers:

  1. (1) charged B-mesons:

    \hbox{I}_{\rm rel} = 3.9 \times 10^{26}\, \hbox{W/cm}^{2} \quad \Delta \varepsilon = 424\, \hbox{eV}

  2. (2) protons (from LHC or protons or antiprotons form the B-decay):

    \hbox{I}_{\rm rel} = 1.2 \times 10^{25}\, \hbox{W/cm}^{2}\quad \Delta \varepsilon = 2.41\, \hbox{keV}

  3. (3) charged π-mesons from decay of B-mesons:

    \hbox{I}_{\rm rel} = 2.73 \times 10^{23}\, \hbox{W/cm}^{2} \quad \Delta \varepsilon = 31.5\, \hbox{keV}

If these energy gains Δɛ from the laser interaction are too small, an increase by the use of more than 10 times higher laser power or by smaller focus diameter may lead to 100 to 1000 times higher values. However, the installation of the lasers near the LHC colliding volume may be a question of available space.

References

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